851
eng
reportzib
0
2005-03-14
2005-03-14
--
ZIBgridfree - Adaptive Conformation Analysis with qualified Support of Transition States and Thermodynamic Weights
This paper introduces a new algorithm of conformational analysis based on mesh-free methods as described in [M. Weber. Mehless methods in Conformation Dynamics.(2005)]. The adaptive decomposition of the conformational space by softly limiting functions avoids trapping effects and allows adaptive refinement strategies. These properties of the algorithm makes ZIBgridfree particularly suitable for the complete exploration of high-dimensional conformational space. The adaptive control of the algorithm benefits from the tight integration of molecular simulation and conformational analysis. An emphasized part of the analysis is the Robust Perron Cluster Analysis (PCCA+) based on the work of Peter Deuflhard and Marcus Weber. PCCA+ supports an almost-characteristic cluster definition with an outstanding mapping of transition states. The outcome is expressed by the metastable sets of conformations, their thermodynamic weights and flexibility.
05-17
851
urn:nbn:de:0297-zib-8514
Marcus Weber
Holger Meyer
ZIB-Report
05-17
eng
uncontrolled
Molecular Dynamics
eng
uncontrolled
Meshfree Methods
eng
uncontrolled
Conformation Analysis
eng
uncontrolled
Quality Functions
Informatik, Informationswissenschaft, allgemeine Werke
Dynamical systems in statistical mechanics [See also 82Cxx]
Computational methods in Markov chains [See also 65C40]
Classification and discrimination; cluster analysis [See also 68T10]
ZIB Allgemein
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/851/ZR-05-17.pdf
https://opus4.kobv.de/opus4-zib/files/851/ZR-05-17.ps
679
eng
reportzib
0
2002-03-15
2002-03-15
--
Characterization of Transition States in Conformational Dynamics using Fuzzy Sets
Recently, a novel approach for the analysis of molecular dynamics on the basis of a transfer operator has been introduced. Therein conformations are considered to be disjoint metastable clusters within position space of a molecule. These clusters are defined by almost invariant characteristic functions that can be computed via {\em Perron Cluster} analysis. The present paper suggests to replace crisp clusters with {\em fuzzy} clusters, i.e. to replace characteristic functions with membership functions. This allows a more sufficient characterization of transiton states between different confor conformations and therefore leads to a better understanding of molecular dynamics. Fur thermore, an indicator for the uniqueness of metastable fuzzy clusters and a fast algorithm for the computation of these clusters are described. Numerical examples are included.
02-12
680
urn:nbn:de:0297-zib-6791
Marcus Weber
Tobias Galliat
ZIB-Report
02-12
eng
uncontrolled
biochemical conformations
eng
uncontrolled
conformational dynamics
eng
uncontrolled
molecular dynamics
eng
uncontrolled
cluster analysis
eng
uncontrolled
transition states
eng
uncontrolled
fuzzy sets
Informatik, Informationswissenschaft, allgemeine Werke
Fuzzy set theory
Classification and discrimination; cluster analysis [See also 68T10]
Computational methods
ZIB Allgemein
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/679/ZR-02-12.ps
https://opus4.kobv.de/opus4-zib/files/679/ZR-02-12.pdf
707
eng
reportzib
0
2002-11-15
2002-11-15
--
Metastable Conformations via successive Perron-Cluster Cluster Analysis of dihedrals
Decomposition of the high dimensional conformational space of bio-molecules into metastable subsets is used for data reduction of long molecular trajectories in order to facilitate chemical analysis and to improve convergence of simulations within these subsets. The metastability is identified by the Perron-cluster cluster analysis of a Markov process that generates the thermodynamic distribution. A necessary prerequisite of this analysis is the discretization of the conformational space. A combinatorial approach via discretization of each degree of freedom will end in the so called ''curse of dimension''. In the following paper we analyze Hybrid Monte Carlo simulations of small, drug-like biomolecules and focus on the dihedral degrees of freedom as indicators of conformational changes. To avoid the ''curse of dimension'', the projection of the underlying Markov operator on each dihedral is analyzed according to its metastability. In each decomposition step of a recursive procedure, those significant dihedrals, which indicate high metastability, are used for further decomposition. The procedure is introduced as part of a hierarchical protocol of simulations at different temperatures. The convergence of simulations within metastable subsets is used as an ''a posteriori'' criterion for a successful identification of metastability. All results are presented with the visualization program AmiraMol.
02-40
708
urn:nbn:de:0297-zib-7074
Frank Cordes
Marcus Weber
Johannes Schmidt-Ehrenberg
ZIB-Report
02-40
eng
uncontrolled
metastability
eng
uncontrolled
Perron-Cluster Cluster Analysis
eng
uncontrolled
curse of dimension
eng
uncontrolled
Hybrid Monte Carlo
eng
uncontrolled
significant dihedrals
Informatik, Informationswissenschaft, allgemeine Werke
Classification and discrimination; cluster analysis [See also 68T10]
ZIB Allgemein
Weber, Marcus
MOLVIS
https://opus4.kobv.de/opus4-zib/files/707/ZR-02-40.ps
https://opus4.kobv.de/opus4-zib/files/707/ZR-02-40.pdf
876
eng
reportzib
0
2005-09-28
2005-09-28
--
Conformation Kinetics as a Reduced Model for Transition Pathways
The complexity of molecular kinetics can be reduced significantly by a restriction to metastable conformations which are almost invariant sets of molecular dynamical systems. With the Robust Perron Cl uster Analysis PCCA+, developed by Weber and Deuflhard, we have a tool available which can be used to identify these conformations from a transition probability matrix. This method can also be applied to the corresponding transition rate matrix which provides important information concerning transition pathways of single molecules. In the present paper, we explain the relationship between these tw o concepts and the extraction of conformation kinetics from transition rates. Moreover, we show how transition rates can be approximated and conclude with numerical examples.
05-43
876
urn:nbn:de:0297-zib-8763
Susanna Kube
Marcus Weber
ZIB-Report
05-43
eng
uncontrolled
conformation kinetics
eng
uncontrolled
transition rates
eng
uncontrolled
Robust Perron Cluster Analysis
Informatik, Informationswissenschaft, allgemeine Werke
Jump processes
Classification and discrimination; cluster analysis [See also 68T10]
ZIB Allgemein
Röblitz, Susanna
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/876/ZR-05-43.pdf
814
eng
reportzib
0
2004-09-29
2004-09-29
--
Perron Cluster Analysis and Its Connection to Graph Partitioning for Noisy Data
The problem of clustering data can be formulated as a graph partitioning problem. Spectral methods for obtaining optimal solutions have reveceived a lot of attention recently. We describe Perron Cluster Cluster Analysis (PCCA) and, for the first time, establish a connection to spectral graph partitioning. We show that in our approach a clustering can be efficiently computed using a simple linear map of the eigenvector data. To deal with the prevalent problem of noisy and possibly overlapping data we introduce the min Chi indicator which helps in selecting the number of clusters and confirming the existence of a partition of the data. This gives a non-probabilistic alternative to statistical mixture-models. We close with showing favorable results on the analysis of gene expressi on data for two different cancer types.
04-39
815
urn:nbn:de:0297-zib-8140
Marcus Weber
Wasinee Rungsarityotin
Alexander Schliep
ZIB-Report
04-39
eng
uncontrolled
Perron cluster analysis
eng
uncontrolled
spectral graph theory
eng
uncontrolled
clustering
eng
uncontrolled
gene expression
Informatik, Informationswissenschaft, allgemeine Werke
Classification and discrimination; cluster analysis [See also 68T10]
Eigenvalues, eigenvectors
Computational methods
ZIB Allgemein
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/814/ZR-04-39.ps
https://opus4.kobv.de/opus4-zib/files/814/ZR-04-39.pdf
726
eng
reportzib
0
2003-03-06
2003-03-06
--
Improved Perron Cluster Analysis
The problem of clustering data can often be transformed into the problem of finding a hidden block diagonal structure in a stochastic matrix. Deuflhard et al. have proposed an algorithm that state s the number $k$ of clusters and uses the sign structure of $k$ eigenvectors of the stochastic matrix to solve the cluster problem. Recently Weber and Galliat discovered that this system of eigenvectors can easily be transformed into a system of $k$ membership functions or soft characteristic functions describing the clusters. In this article we explain the corresponding cluster algorithm and point out the underlying theory. By means of numerical examples we explain how the grade of membership can be interpreted.
03-04
727
urn:nbn:de:0297-zib-7260
Marcus Weber
ZIB-Report
03-04
eng
uncontrolled
cluster analysis
eng
uncontrolled
stochastic matrices
eng
uncontrolled
almost invariant sets
Informatik, Informationswissenschaft, allgemeine Werke
Classification and discrimination; cluster analysis [See also 68T10]
ZIB Allgemein
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/726/ZR-03-04.ps
https://opus4.kobv.de/opus4-zib/files/726/ZR-03-04.pdf
741
eng
reportzib
0
2003-07-01
2003-07-01
--
Robust Perron Cluster Analysis in Conformation Dynamics
The key to molecular conformation dynamics is the direct identification of metastable conformations, which are almost invariant sets of molecular dynamical systems. Once some reversible Markov operator has been discretized, a generalized symmetric stochastic matrix arises. This matrix can be treated by Perron cluster analysis, a rather recent method involving a Perron cluster eigenproblem. The paper presents an improved Perron cluster analysis algorithm, which is more robust than earlier suggestions. Numerical examples are included.
03-19
742
urn:nbn:de:0297-zib-7415
Appeared in : Linear Algebra and Its Applications, Special Issue on Matrices and Mathematical Biology, Vol. 398c, 161-184 (2005)
Peter Deuflhard
Marcus Weber
ZIB-Report
03-19
eng
uncontrolled
Markov chains
eng
uncontrolled
cluster algorithms
eng
uncontrolled
Perron cluster analysis
eng
uncontrolled
conformation dynamics
Informatik, Informationswissenschaft, allgemeine Werke
Classification and discrimination; cluster analysis [See also 68T10]
Eigenvalues, eigenvectors
Clustering [See also 62D05]
ZIB Allgemein
Deuflhard, Peter
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/741/ZR_03_19_erratum.pdf
https://opus4.kobv.de/opus4-zib/files/741/ZR-03-19.ps
https://opus4.kobv.de/opus4-zib/files/741/ZR-03-19.pdf
778
eng
reportzib
0
2003-12-19
2003-12-19
--
Clustering by using a simplex structure
In this paper we interpret clustering as a mapping of data into a simplex. If the data itself has simplicial struture this mapping becomes linear. Spectral analysis is an often used tool for clustering data. We will show that corresponding singular vectors or eigenvectors comprise simplicial structure. Therefore they lead to a cluster algorithm, which consists of a simple linear mapping. An example for this kind of algorithms is the Perron cluster analysis (PCCA). We have applied it in practice to identify metastable sets of molecular dynamical systems. In contrast to other algorithms, this kind of approach provides an a priori criterion to determine the number of clusters. In this paper we extend the ideas to more general problems like clustering of bipartite graphs.
04-03
779
urn:nbn:de:0297-zib-7782
Marcus Weber
ZIB-Report
04-03
eng
uncontrolled
cluster algorithms
eng
uncontrolled
Perron cluster analysis
eng
uncontrolled
stochastic matrices
eng
uncontrolled
bipartite graphs
Informatik, Informationswissenschaft, allgemeine Werke
Classification and discrimination; cluster analysis [See also 68T10]
Eigenvalues, eigenvectors
ZIB Allgemein
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/778/ZR-04-03.ps
https://opus4.kobv.de/opus4-zib/files/778/ZR-04-03.pdf
1143
eng
reportzib
0
2009-09-07
2009-09-07
--
A Subspace Approach to Molecular Markov State Models via an Infinitesimal Generator
Supercomputers can simulate complex molecular systems. However, there is a very large gap between the fastest oscillations of covalent bonds of a molecule and the time-scale of the dominant processes. In order to extract the dominant time-scales and to identify the dominant processes, a clustering of information is needed. This thesis shows that only the subspace-based Robust Perron Cluster Analysis (PCCA+) can solve this problem correctly by the construction of a Markov State Model. PCCA+ allows for time-extrapolation in molecular kinetics. This thesis shows the difference between molecular dynamics and molecular kinetics. Only in the molecular kinetics framework a definition of transition rates is possible. In this context, the existence of an infinitesimal generator of the dynamical processes is discussed. If the existence is assumed, the Theorem of Gauß can be applied in order to compute transition rates efficiently. Molecular dynamics, however, is not able to provide a suitable statistical basis for the determination of the transition pattern.
09-27
1438-0064
1192
urn:nbn:de:0297-zib-11432
Marcus Weber
unknown unknown
ZIB-Report
09-27
deu
uncontrolled
Robuste Perron Cluster Analyse
deu
uncontrolled
Molekülkinetik
deu
uncontrolled
Übergangsraten
eng
uncontrolled
Robust Perron cluster analysis
eng
uncontrolled
molecular kinetics
eng
uncontrolled
transition rates
Mathematik
Continuous-time Markov processes on general state spaces
Classification and discrimination; cluster analysis [See also 68T10]
Statistical thermodynamics [See also 80-XX]
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/1143/ZR_09_27_rev.pdf
https://opus4.kobv.de/opus4-zib/files/1143/ZR_09_27.pdf
1087
eng
reportzib
0
2008-08-25
2008-08-25
--
An efficient analysis of rare events in canonical ensemble dynamics
For an analysis of a molecular system from a computational statistical thermodynamics point of view, extensive molecular dynamics simulations are very inefficient. During this procedure, at lot of redundant data is generated. Whereas the algorithms spend most of the computing time for a sampling of configurations within the basins of the potential energy landscape of the molecular system, the important information about the long-time behaviour of the molecules is given by transition regions and barriers between the basins, which are sampled rarely only. Thinking of molecular dynamics trajectories, researchers try to figure out which kind of dynamical model is suitable for an efficient simulation. This article suggests to change the point of view from extensive simulation of molecular dynamics trajectories to more efficient sampling strategies of the conformation dynamics approach.
08-36
1438-0064
1123
urn:nbn:de:0297-zib-10871
Marcus Weber
unknown unknown
ZIB-Report
08-36
deu
uncontrolled
Moleküldynamik
deu
uncontrolled
Kanonische Gesamtheit
deu
uncontrolled
Metastabilität
eng
uncontrolled
molecular dynamics
eng
uncontrolled
canonical ensemble
eng
uncontrolled
metastability
Naturwissenschaften und Mathematik
Spectral methods
Numerical Mathematics
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/1087/ZR_08_36.pdf
925
eng
reportzib
0
2006-06-15
2006-06-15
--
ConFlow? A new space-based Application for complete Conformational Analysis of Molecules
Biochemical interactions are determined by the 3D-structure of the involved components - thus the identification of conformations is a key for many applications in rational drug design. {\sf ConFlow} is a new multilevel approach to conformational analysis with main focus on completeness in investigation of conformational space. In contrast to known conformational analysis, the starting point for design is a space-based description of conformational areas. A tight integration of sampling and analysis leads to an identification of conformational areas simultaneously during sampling. An incremental decomposition of high-dimensional conformational space is used to guide the analysis. A new concept for the description of conformations and their path connected components based on convex hulls and {\em Hypercubes}is developed. The first results of the {\sf ConFlow} application constitute a 'proof of concept' and are further more highly encouraging. In comparison to conventional industrial applications, {\sf ConFlow} achieves higher accuracy and a specified degree of completeness with comparable effort.
06-31
925
urn:nbn:de:0297-zib-9258
Holger Meyer
Sebastian Moll
Frank Cordes
Marcus Weber
ZIB-Report
06-31
eng
uncontrolled
conformational-analysis in-silico-screening drug-design
Informatik, Informationswissenschaft, allgemeine Werke
Computational methods
Biochemistry, molecular biology
ZIB Allgemein
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/925/ZR-06-31.pdf
https://opus4.kobv.de/opus4-zib/files/925/ZR-06-31.ps
929
eng
reportzib
0
2006-06-27
2006-06-27
--
Coarse Grained Molecular Kinetics
The dynamic behavior of molecules can often be described by Markov processes. From computational molecular simulations one can derive transition rates or transition probabilities between subsets of the discretized conformational space. On the basis of this dynamic information, the spatial subsets are combined into a small number of so-called metastable molecular conformations. This is done by clustering methods like the Robust Perron Cluster Analysis (PCCA+). Up to now it is an open question how this coarse graining in space can be transformed to a coarse graining of the Markov chain while preserving the essential dynamic information. In the following article we aim at a consistent coarse graining of transition probabilities or rates on the basis of metastable conformations such that important physical and mathematical relations are preserved. This approach is new because PCCA+ computes molecular conformations as linear combinations of the dominant eigenvectors of the transition matrix which does not hold for other clustering methods.
06-35
929
urn:nbn:de:0297-zib-9299
Appeared as : "A coarse grained method for the identification of transition rates between molecular conformations" in Journal of Chemical Physics, 126(2) 2007
Susanna Kube
Marcus Weber
ZIB-Report
06-35
Informatik, Informationswissenschaft, allgemeine Werke
Computational Markov chains
Eigenvalues, eigenvectors
None of the above, but in this section
Chemical kinetics [See also 76V05, 92C45, 92E20]
ZIB Allgemein
Röblitz, Susanna
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/929/ZR-06-35.pdf
960
eng
reportzib
0
2007-07-23
2007-07-23
--
Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics
Wigner transformation provides a one-to-one correspondence between functions on position space (wave functions) and functions on phase space (Wigner functions). Weighted integrals of Wigner functions yield quadratic quantities of wave functions like position and momentum densities or expectation values. For molecular quantum systems, suitably modified classical transport of Wigner functions provides an asymptotic approximation of the dynamics in the high energy regime. The article addresses the computation of Wigner functions by Monte Carlo quadrature. An ad aption of the Metropolis algorithm for the approximation of signed measures with disconnected support is systematically tested in combination with a surface hopping algorithm for non-adiabatic quantum dynamics. The numerical experiments give expectation values and level populations with an error of two to three percent, which agrees with the theoretically expected accuracy.
07-17
960
urn:nbn:de:0297-zib-9604
A rev. vers. appeared in: Journal of Computational Physics 228 (2009) pp. 1947-1962. doi:10.1016/j.jcp.2008.11.016
Susanna Kube
Caroline Lasser
Marcus Weber
ZIB-Report
07-17
eng
uncontrolled
Metropolis Monte Carlo
eng
uncontrolled
approximation
eng
uncontrolled
quadrature
eng
uncontrolled
oscillating functions
Informatik, Informationswissenschaft, allgemeine Werke
Sampling theory, sample surveys
Numerical integration
Numerical Mathematics
ZIB Allgemein
Computational Molecular Design
Computational Systems Biology
Röblitz, Susanna
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/960/ZR_07_17.pdf
933
eng
reportzib
0
2006-07-06
2006-07-06
--
Stable computation of probability densities for metastable dynamical systems
Whenever the invariant stationary density of metastable dynamical systems decomposes into almost invariant partial densities, its computation as eigenvector of some transition probability matrix is an ill-conditioned problem. In order to avoid this computational difficulty, we suggest to apply an aggregation/disaggregation method which only addresses wellconditioned sub-problems and thus results in a stable algorithm. In contrast to existing methods, the aggregation step is done via a sampling algorithm which covers only small patches of the sampling space. Finally, the theoretical analysis is illustrated by two biomolecular examples.
06-39
933
urn:nbn:de:0297-zib-9331
Appeared in: SIAM J. Multisc. Mod. Sim. 2007, 6(2), pp. 396-416
Marcus Weber
Lionel Walter
Susanna Kube
Peter Deuflhard
ZIB-Report
06-39
eng
uncontrolled
dynamical systems
eng
uncontrolled
metastability
eng
uncontrolled
molecular conformations
eng
uncontrolled
cluster analysis
eng
uncontrolled
sampling
eng
uncontrolled
aggregation/disaggregation
eng
uncontrolled
domain decomposition
Informatik, Informationswissenschaft, allgemeine Werke
Classification and discrimination; cluster analysis [See also 68T10]
Eigenvalues, eigenvectors
Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]
ZIB Allgemein
Deuflhard, Peter
Röblitz, Susanna
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/933/ZR-06-39.pdf
895
eng
reportzib
0
2005-12-29
2005-12-29
--
Identification of Metastabilities in Monomolecular Conformation Kinetics
The identification of metastable conformations of molecules plays an important role in computational drug design. One main difficulty is the fact that the underlying dynamic processes take place in high dimensional spaces. Although the restriction of degrees of freedom to a few dihedral angles significantly reduces the complexity of the problem, the existing algorithms are time-consuming. They are based on the approximation of transition probabilities by an extensive sampling of states according to the Boltzmann distribution. We present a method which can identify metastable conformations without sampling the complete distribution. Our algorithm is based on local transition rates and uses only pointwise information about the potential energy surface. In order to apply the cluster algorithm PCCA+, we compute a few eigenvectors of the rate matrix by the Jacobi-Davidson method. Interpolation techniques are applied to approximate the thermodynamical weights of the clusters. The concluding example illustrates our approach for epigallocatechine, a molecule which can be described by seven dihedral angles.
06-01
895
urn:nbn:de:0297-zib-8956
Susanna Kube
Marcus Weber
ZIB-Report
06-01
eng
uncontrolled
metastable conformations
eng
uncontrolled
potential energy surface
eng
uncontrolled
transition rates
eng
uncontrolled
eigenvectors
eng
uncontrolled
clustering
Informatik, Informationswissenschaft, allgemeine Werke
Eigenvalues, eigenvectors
Chemical kinetics [See also 76V05, 92C45, 92E20]
Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]
Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
ZIB Allgemein
Röblitz, Susanna
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/895/ZR-06-01.pdf
946
eng
reportzib
0
2006-12-19
2006-12-19
--
Efficient Sampling of the Stationary Distribution of Metastable Dynamical Systems
In this article we aim at an efficient sampling of the stationary distribution of dynamical systems in the presence of metastabilities. In the past decade many sophisticated algorithms have been inven ted in this field. We do not want to simply add a further one. We address the problem that one has applied a sampling algorithm for a dynamical system many times. This leads to different samplings which more or less represent the stationary distribution partially very well, but which are still far away from ergodicity or from the global stationary distribution. We will show how these samplings can be joined together in order to get one global sampling of the stationary distribution.
07-03
946
urn:nbn:de:0297-zib-9467
Marcus Weber
Susanna Kube
Alexander Riemer
Alexander Bujotzek
ZIB-Report
07-03
eng
uncontrolled
dynamical systems
eng
uncontrolled
stationary distribution
eng
uncontrolled
rare events
eng
uncontrolled
metastability
eng
uncontrolled
cluster analysis
Informatik, Informationswissenschaft, allgemeine Werke
Computational Markov chains
Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]
ZIB Allgemein
Röblitz, Susanna
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/946/ZR-07-03.pdf
920
eng
reportzib
0
2006-05-09
2006-05-09
--
ConfJump : a fast biomolecular sampling method which drills tunnels through high mountains
In order to compute the thermodynamic weights of the different metastable conformations of a molecule, we want to approximate the molecule's Boltzmann distribution in a reasonable time. This is an essential issue in computational drug design. The energy landscape of active biomolecules is generally very rough with a lot of high barriers and low regions. Many of the algorithms that perform such samplings (e.g. the hybrid Monte Carlo method) have difficulties with such landscapes. They are trapped in low-energy regions for a very long time and cannot overcome high barriers. Moving from one low-energy region to another is a very rare event. For these reasons, the distribution of the generated sampling points converges very slowly against the thermodynamically correct distribution of the molecule. The idea of ConfJump is to use $a~priori$ knowledge of the localization of low-energy regions to enhance the sampling with artificial jumps between these low-energy regions. The artificial jumps are combined with the hybrid Monte Carlo method. This allows the computation of some dynamical properties of the molecule. In ConfJump, the detailed balance condition is satisfied and the mathematically correct molecular distribution is sampled.
06-26
920
urn:nbn:de:0297-zib-9204
Lionel Walter
Marcus Weber
ZIB-Report
06-26
eng
uncontrolled
Monte Carlo simulation
eng
uncontrolled
rare events
eng
uncontrolled
rough potential energy function
eng
uncontrolled
molecular dynamics
Informatik, Informationswissenschaft, allgemeine Werke
Dynamical systems in statistical mechanics [See also 82Cxx]
Computational methods in Markov chains [See also 65C40]
Monte Carlo methods
Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
ZIB Allgemein
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/920/ZR-06-26.pdf
https://opus4.kobv.de/opus4-zib/files/920/ZR-06-26.ps
1023
eng
doctoralthesis
0
2006-12-31
2006-12-31
--
Meshless Methods in Confirmation Dynamics
1049
urn:nbn:de:0297-zib-10232
Marcus Weber
unknown unknown
Peter Deuflhard
M. Dellnitz
Mathematik
Dissertationen
Numerical Mathematics
Weber, Marcus
Freie Universität Berlin
https://opus4.kobv.de/opus4-zib/files/1023/promotionweber.pdf
1030
eng
reportzib
Zuse-Institut Berlin
0
2007-11-07
2007-11-07
--
Classical hybrid Monte-Carlo simulations of the interconversion of hexabromocyclododecane
In this paper, we investigate the interconversion processes of the major flame retardant -- 1,2,5,6,9,10-hexabromocyclododecane (HBCD) -- by the means of statistical thermodynamics based on classical force-fields. Three ideas will be presented. First, the application of classical hybrid Monte-Carlo simulations for quantum mechanical processes will be justified. Second, the problem of insufficient convergence properties of hybrid Monte-Carlo methods for the generation of low temperature canonical ensembles will be solved by an interpolation approach. Furthermore, it will be shown how free energy differences can be used for a rate matrix computation. The results of our numerical simulations will be compared to experimental results.
07-31
1438-0064
1059
urn:nbn:de:0297-zib-10308
A substantially revised version appeared under the title "Classical hybrid Monte-Carlo simulation of the interconversion of hexabromocyclododecane stereoisomers" in: Journal of Molecular Simulation, 34(7):727 - 736, June 2008
Marcus Weber
unknown unknown
Roland Becker
Robert Köppen
Vedat Durmaz
ZIB-Report
07-31
eng
uncontrolled
Markov process
eng
uncontrolled
molecular dynamics
eng
uncontrolled
rate matrix
Mathematik
Thermodynamics of continua [See also 74A15]
Computational methods
Numerical Mathematics
Durmaz, Vedat
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/1030/ZR_07_31.pdf
961
eng
reportzib
0
2007-07-23
2007-07-23
--
Conformation-based transition state theory
For the treatment of equilibrated molecular systems in a heat bath we propose a transition state theory that is based on conformation dynamics. In general, a set-based discretization of a Markov operator ${\cal P}^\tau$ does not preserve the Markov property. In this article, we propose a discretization method which is based on a Galerkin approach. This discretization method preserves the Markov property of the operator and can be interpreted as a decomposition of the state space into (fuzzy) sets. The conformation-based transition state theory presented here can be seen as a first step in conformation dynamics towards the computation of essential dynamical properties of molecular systems without time-consuming molecular dynamics simulations.
07-18
961
urn:nbn:de:0297-zib-9612
Marcus Weber
ZIB-Report
07-18
eng
uncontrolled
dynamical systems
eng
uncontrolled
transition state theory
eng
uncontrolled
rare events
Informatik, Informationswissenschaft, allgemeine Werke
Classification and discrimination; cluster analysis [See also 68T10]
Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]
Numerical Mathematics
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/961/ZR_07_18.pdf
1476
eng
reportzib
0
2012-03-02
2012-03-02
--
The funnel trap paradox
In this article, an illustrative example is given for the coarse-graining of a
Markov process which leads to a shift in the statistical weights of a two-states-system.
The example is based on a 2D-funnel trap. The funnel trap is constructed in such a
way, that the area inside and outside of the trap is identical. However, observing the
flight of the insect as a Markov process, the probability for being “in the trap” is higher.
This example can be transferred to several kinds of processes (like receptor-ligandbinding
processes in chemistry) and describes the influence of “re-entering events”.
1438-0064
12-12
urn:nbn:de:0297-zib-14765
Marcus Weber
Marcus Weber
ZIB-Report
12-12
eng
uncontrolled
Markov process
eng
uncontrolled
Robust Perron Cluster Analysis
eng
uncontrolled
Conformation Dynamics
Continuous-time Markov processes on general state spaces
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
Matheon-A19
SFB765-C2
https://opus4.kobv.de/opus4-zib/files/1476/ZR-12-12.pdf
1913
2011
2011
eng
article
0
--
--
--
DNA-controlled bivalent presentation of ligands for the estrogen receptor
Angew. Chem. Int. Ed.
yes
Frank Abendroth
Alexander Bujotzek
Min Shan
Rainer Haag
Marcus Weber
Oliver Seitz
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
1402
eng
habilitation
0
2011-09-15
2011-09-15
2011-07-13
A Subspace Approach to Molecular Markov State Models via a New Infinitesimal Generator
Supercomputers can simulate complex molecular systems. However, there is a very large gap between the fastest oscillations of covalent bonds of a molecule and the time-scale of the dominant processes. In order to extract the dominant time-scales and to identify the dominant processes, a clustering of information is needed. This thesis shows that only the subspace-based Robust Perron Cluster Analysis (PCCA+) can solve this problem correctly by the construction of a Markov State Model. PCCA+ allows for time-extrapolation in molecular kinetics. This thesis shows the difference between molecular dynamics and molecular kinetics. Only in the molecular kinetics framework a definition of transition rates is possible. In this context, the existence of an infinitesimal generator of the dynamical processes is discussed. If the existence is assumed, the Theorem of Gauß can be applied in order to compute transition rates efficiently. Molecular dynamics, however, is not able to provide a suitable statistical basis for the determination of the transition pattern.
urn:nbn:de:0297-zib-14025
Marcus Weber
Marcus Weber
eng
uncontrolled
Conformation Dynamics
eng
uncontrolled
Molecular Kinetics
eng
uncontrolled
Transition Rates
eng
uncontrolled
Markov State Models
Continuous-time Markov processes on general state spaces
Classification and discrimination; cluster analysis [See also 68T10]
Statistical thermodynamics [See also 80-XX]
Numerical Mathematics
Habilitationen
Computational Molecular Design
Weber, Marcus
Zuse Institute Berlin (ZIB)
Freie Universität Berlin
https://opus4.kobv.de/opus4-zib/files/1402/WeberHabil.pdf
https://opus4.kobv.de/opus4-zib/files/1402/WeberHabil-Titel.pdf
https://opus4.kobv.de/opus4-zib/files/1402/Acknowledgement.pdf
1990
2011
2011
eng
253
262
25(3)
article
0
--
--
--
Towards a rational spacer design for bivalent inhibition of estrogen receptor
J. Comput.-Aided Mol. Des.
yes
Alexander Bujotzek
Min Shan
Rainer Haag
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
2016
2005
2005
eng
161
184
398
bookpart
Elsevier Journals
Germany
0
--
--
--
Robust Perron Cluster Analysis in Conformation Dynamics
Lin. Alg. Appl. – Special Issue on Matrices and Mathematical Biology
urn:nbn:de:0297-zib-7415
Peter Deuflhard
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Deuflhard, Peter
Weber, Marcus
2207
2010
2010
eng
1585
1588
1
1281
article
AIP
0
--
--
--
Adaptive Spectral Clustering for Conformation Analysis
AIP Conference Proceedings
10.1063/1.3498116
http://link.aip.org/link/?APC/1281/1585/1
yes
Fiete Haack
Susanna Röblitz
Olga Scharkoi
Burkhard Schmidt
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Röblitz, Susanna
Weber, Marcus
2261
2008
2008
eng
339
342
1048
conferenceobject
AIP Conference Proceedings
0
--
--
--
Computation of equilibrium densities in metastable dynamical systems by domain decomposition
Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics 2008
Susanna Kube
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Röblitz, Susanna
Weber, Marcus
2262
2007
2007
eng
2
126
article
0
--
--
--
A Coarse Graining Method for the Identification of Transition rates between Molecular Conformations
Journal of Chemical Physics
10.1063/1.2404953
Susanna Kube
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Röblitz, Susanna
Weber, Marcus
2289
2010
2010
eng
031114
3
82
article
American Physical Society
0
--
--
--
Observation uncertainty in reversible Markov chains
Phys. Rev. E
10.1103/PhysRevE.82.031114
yes
Ph. Metzner
Marcus Weber
Christof Schütte
Numerical Mathematics
Computational Molecular Design
Schütte, Christof
Weber, Marcus
2192
2007
2007
eng
article
0
--
--
--
Selection and flexible optimization of binding modes from conformation ensembles
Biosystems
A. Gürler
Sebastian Moll
Marcus Weber
Holger Meyer
Frank Cordes
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
2194
2008
2008
eng
42
48
1
92
article
0
--
--
--
Selection and flexible optimization of binding modes from conformation ensembles
Biosystems
DOI: 10.1016/j.biosystems.2007.11.004
http://www.sciencedirect.com/science/article/pii/S0303264707001670
A. Guerler
Sebastian Moll
Marcus Weber
Holger Meyer
Frank Cordes
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
2247
2005
2005
eng
57
66
conferenceobject
0
--
--
--
Robust Perron Cluster Analysis for Various Applications in Computational Life Science
Computational Life Sciences
Marcus Weber
Susanna Kube
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Röblitz, Susanna
Weber, Marcus
2255
2011
2011
eng
333
346
65(2)
article
0
--
--
--
Direct Reweighting Strategies in Conformation Dynamics
MATCH Commun. Math. Comp. Chem.
yes
Martina Klimm
Alexander Bujotzek
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
Salsa-Klimm
2645
2012
2012
eng
2399
2408
18
article
0
--
--
--
How to Simulate Affinities for Host-Guest Systems Lacking Binding Mode Information: application to the liquid chromatographic separation of hexabromocyclododecane stereoisomers
Journal of Molecular Modeling
10.1007/s00894-011-1239-5
yes
Vedat Durmaz
Marcus Weber
Roland Becker
Numerical Mathematics
Computational Molecular Design
Durmaz, Vedat
Weber, Marcus
BAM-Becker
BAM-glycosidases
BB3R
TransRisk
2646
2012
2012
eng
054111
5
137
article
0
--
--
--
Quantifying the rebinding effect in multivalent chemical ligand-receptor systems
J. Chem. Phys.
yes
Marcus Weber
Alexander Bujotzek
Rainer Haag
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
EyeTracking
Matheon-A19
SFB765-C2
2649
2012
2012
eng
10472
10498
42
51
article
0
--
--
--
Multivalency as a Chemical Organization and Action Principle
Angew. Chem. Int. Ed.
yes
Carlo Fasting
Christoph A. Schalley
Marcus Weber
Oliver Seitz
Stefan Hecht
Beate Koksch
Jens Dernedde
Christina Graf
Ernst-Walter Knapp
Rainer Haag
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
SFB765-C2
2644
2012
2012
eng
11733
11740
60
article
0
--
--
--
Photochemical trans-/cis-isomerization and quantification of zearalenone in edible oils
J. Agric. Food Chem.
10.1021/jf3037775
yes
Robert Köppen
Juliane Riedel
Matthias Proske
Sarah Drzymala
Tatjana Rasenko
Vedat Durmaz
Marcus Weber
Matthias Koch
Numerical Mathematics
Computational Molecular Design
Durmaz, Vedat
Weber, Marcus
BAM-ZEN
2619
2008
2008
eng
1947
1962
6
228
article
0
--
--
--
Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics
Journal of Computational Physics
10.1016/j.jcp.2008.11.016
urn:nbn:de:0297-zib-9604
Susanna Kube
Caroline Lasser
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Röblitz, Susanna
Weber, Marcus
2627
2007
2007
eng
2
other
DFG-Forschungszentrum Matheon
0
--
--
--
Vom Dietrich zum Sicherheitsschlüssel – Mathematiker des Matheon simulieren neuen Wirkstoff für die Diabetes-Behandlung
R. Kellermann
Marcus Weber
Alexander Bujotzek
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
2628
2009
2009
eng
910
913
70
article
0
--
--
--
HBCD stereoisimers: Thermal interconversion and enantiospecific trace analysis in biota
Organohalogen Compounds
yes
Robert Köppen
Roland Becker
Marcus Weber
Vedat Durmaz
Irene Nehls
Numerical Mathematics
Computational Molecular Design
Durmaz, Vedat
Weber, Marcus
2629
2009
2009
eng
811
831
7(5)
article
0
--
--
--
Efficient Simulation of Ligand-Receptor Binding Processes Using the Conformation Dynamics Approach
Journal of Bioinformatics and Computational Biology
yes
Alexander Bujotzek
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
2630
2009
2009
eng
bookpart
0
--
--
--
Spurenstoffe im Trinkwasser - Risikoqualifizierung im Rechner?
Schriftenreihe des Vereins für Wasser-, Boden- und Lufthygiene
no
Marcus Weber
L. Dunemann
O. Schmoll
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
2631
2009
2009
eng
247
252
71
article
0
--
--
--
Predictive Identification of Pentabromocyclododecane (PBCD) Isomers with high Binding Affinity to hTTR
Organohalogen Compounds
yes
Marcus Weber
Vedat Durmaz
Roland Becker
Susanne Esslinger
Numerical Mathematics
Computational Molecular Design
Durmaz, Vedat
Weber, Marcus
5141
2015
eng
69
78
1
113
article
0
--
--
--
Markov State Models and Molecular Alchemy
In recent years Markov State Models (MSMs) have attracted a consid-
erable amount of attention with regard to modelling conformation changes and associated function of biomolecular systems. They have been used successfully, e.g., for peptides including time-resolved spectroscopic experiments, protein function and protein folding , DNA and RNA, and ligand-receptor interaction in drug design and more complicated multivalent scenarios. In this article a novel reweighting scheme is introduced that allows to construct an MSM for certain molecular system out of an MSM for a similar system. This permits studying how molecular properties on long timescales differ between similar molecular systems without performing full molecular dynamics simulations for each system under con-
sideration. The performance of the reweighting scheme is illustrated for simple test cases including one where the main wells of the respective energy landscapes are located differently and an alchemical transformation of butane to pentane where the dimension of the state space is changed.
Molecular Physics
10.1080/00268976.2014.944597
yes
urn:nbn:de:0297-zib-46718
Christof Schütte
Erlinda Körnig
Adam Nielsen
Marcus Weber
eng
uncontrolled
MSM
deu
uncontrolled
Reweighting
deu
uncontrolled
Girsanov
Numerical Mathematics
Computational Molecular Design
Schütte, Christof
Weber, Marcus
BMS-Nielsen
EyeTracking
NonequiMSM
SFB1114-A5
TransRisk
5164
2013
eng
other
0
--
--
--
Fentanyl derivatives as pH-dependent opioid receptor agonists
European Patent Application, Bulletin 2013/08
https://data.epo.org/publication-server/rest/v1.0/publication-dates/20130220/patents/EP2559685NWA1/document.pdf
no
Christoph Stein
Olga Scharkoi
Marcus Weber
Christian Zöllner
Olga Scharkoi
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
NAMPAR
Salsa-Klimm
5165
2013
eng
other
0
--
--
--
Method and system for identifying compounds that bind and preferably activate a target opioid receptor in a pH-dependent manner
European Patent Application, Bulletin 2013/28
no
http://worldwide.espacenet.com/publicationDetails/originalDocument?CC=EP&NR=2613277A1&KC=A1&locale=en_EP&date=&FT=D
Christoph Stein
Olga Scharkoi
Marcus Weber
Olga Scharkoi
Peter Deuflhard
Numerical Mathematics
Computational Molecular Design
Deuflhard, Peter
Weber, Marcus
NAMPAR
Salsa-Klimm
4671
eng
reportzib
0
--
2014-03-05
--
Markov State Models and Molecular Alchemy
In recent years Markov State Models (MSMs) have attracted a consid-
erable amount of attention with regard to modelling conformation changes
and associated function of biomolecular systems. They have been used
successfully, e.g., for peptides including time-resolved spectroscopic ex-
periments, protein function and protein folding , DNA and RNA, and
ligand-receptor interaction in drug design and more complicated multi-
valent scenarios. In this article a novel reweighting scheme is introduced
that allows to construct an MSM for certain molecular system out of an
MSM for a similar system. This permits studying how molecular proper-
ties on long timescales differ between similar molecular systems without
performing full molecular dynamics simulations for each system under con-
sideration. The performance of the reweighting scheme is illustrated for
simple test cases including one where the main wells of the respective en-
ergy landscapes are located differently and an alchemical transformation
of butane to pentane where the dimension of the state space is changed.
1438-0064
urn:nbn:de:0297-zib-46718
10.1080/00268976.2014.944597
appeared in: Mol. Phys. 2014 (epub ahead of print)
Christof Schütte
Adam Nielsen
Adam Nielsen
Marcus Weber
ZIB-Report
14-05
deu
uncontrolled
Girsanov Theorem
deu
uncontrolled
Stochastic Differential Equation
deu
uncontrolled
Importance Sampling
Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]
Numerical Mathematics
Computational Molecular Design
Schütte, Christof
Weber, Marcus
TransRisk
https://opus4.kobv.de/opus4-zib/files/4671/article_zib.pdf
4650
2013
eng
707
715
4
8
article
0
--
--
--
Nonsteroidal Bivalent Estrogen Ligands - An Application of the Bivalent Concept to the Estrogen Receptor
ACS Chem. Biol.
yes
http://pubs.acs.org/doi/abs/10.1021/cb3006243
Min Shan
Adam Nielsen
Kathryn E. Carlson
Alexander Bujotzek
Anja Wellner
Ronald Gust
Marcus Weber
John A. Katzenellenbogen
Rainer Haag
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
4652
2013
deu
147
157
article
0
--
--
--
Adaptive Spectral Clustering in Molecular Simulation. In: Studies in Classification, Data Analysis, and Knowledge Organization
XIV: Classification and Data Mining, A. Giusti, G. Ritter, M. Vichi (Eds.), Springer Series
yes
Marcus Weber
Adam Nielsen
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
BMS-Nielsen
Matheon-A19
NAMPAR
4655
2011
eng
2587
2598
article
0
--
--
--
Conformational Analysis of Bivalent Estrogen Receptor-Ligands: From Intramolecular to Intermolecular Binding
ChemBioChem, 12(17)
10.1002/cbic.201100529
yes
Min Shan
Adam Nielsen
Alexander Bujotzek
Frank Abendroth
Oliver Seitz
Marcus Weber
Rainer Haag
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
4639
2014
eng
article
0
2014-03-25
--
--
Predicting sites of cytochrome P450-mediated hydroxylation applied to CYP3A4 and hexabromocyclododecane
Molecular Simulation
10.1080/08927022.2014.898845
yes
Adam Nielsen
Olga Scharkoi
Susanne Esslinger
Roland Becker
Marcus Weber
Irene Nehls
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
BAM-Becker
BAM-glycosidases
BB3R
TransRisk
4647
2011
deu
730
733
73
article
0
--
--
--
Phase I oxidation of alpha- and gamma-hexabromocyclododecane by cytochrome P450 enzymes: simulation of the stereoisomerism of hydroxylated metabolites
Organohalogen Compounds
yes
http://www.dioxin20xx.org/pdfs/2011/1810.pdf
O. Scharkoi
Adam Nielsen
Susanne Esslinger
Roland Becker
Marcus Weber
Irene Nehls
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
4648
2013
eng
2681
2688
10
53
article
0
--
--
--
A hands-off linear interaction energy approach to binding mode and affinity estimation of estrogens
Journal of Chemical Information and Modeling
yes
http://pubs.acs.org/doi/abs/10.1021/ci400392p
Vedat Durmaz
Adam Nielsen
Sebastian Schmidt
Peggy Sabri
Christian Piechotta
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Durmaz, Vedat
Weber, Marcus
BAM-Becker
BAM-glycosidases
BB3R
TransRisk
4649
2013
deu
12307
12317
23
117
article
0
--
--
--
Investigations of Host-Guest Interactions with Shape-persistent Nonionic Dendritic Micelles
J. Phys. Chem. C
yes
Rahul Tyagi
Adam Nielsen
Shashwat Malhotra
Andreas F. Thünemann
Amir Sedighi
Marcus Weber
Andreas Schäfer
Rainer Haag
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
SFB765-C2
5428
2014
eng
234
5
5
article
0
--
--
--
Free Energy Simulations of Drug loading for Core-Multishell Nanotransporters
J Nanomed Nanotechnol
10.4172/2157-7439.1000234
yes
Marcus Weber
Marcus Weber
Christian Zoschke
Amir Sedighi
Emanuel Fleige
Rainer Haag
Monika Schäfer-Korting
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
BB3R
5794
2016
eng
1319
1340
4
14
article
0
--
--
--
Finding dominant structures of nonreversible Markov processes
Multiscale Modeling and Simulation
10.1137/15M1032272
yes
urn:nbn:de:0297-zib-55739
Natasa Djurdjevac Conrad
Regine Kossick
Marcus Weber
Christof Schütte
Numerical Mathematics
Computational Molecular Design
Schütte, Christof
Weber, Marcus
BMS-Nielsen
EyeTracking
MODAL-MedLab
NonequiMSM
TransRisk
Conrad, Natasa
MODAL-Gesamt
6034
2015
eng
conferenceobject
0
--
--
--
Identifying Multivalent Binding Kinetics of Precision Glycomacromolecules: A Kinetic Study Using kinITC
Multivalent sugar/protein interactions are well-known to proceed through different binding modes 1-5 which in turn can be described by their binding kinetics 3-5. This study provides additional insight into the association and dissociation reaction rates of complex multivalent sugar/protein interactions. Binding kinetics of recently introduced multivalent precision glycomacromolecules 6-8 to Concanavalin A (Con A) were studied by " kinetic Isothermal Titration Calorimetry " (kinITC) 9-11. The effect of multivalency is evaluated by comparing rate constants of glycomacromolecules obtaining the same and different valency of mannose ligands and by variation of the overall backbone properties, such as hydrophilic/ hydrophoboc. In addition, binding kinetics were studied using different conformations of Con A (homodimer vs.-tetramer) and thus a different protein valency. Our results show that precision glycomacromolecule/Con A binding proceeds non-cooperatively. Further, association and dissociation rates are mainly described by intermolecular complex formation. Together with the so-called functional valency, we can discriminate between " bound " and " unbound " states for macroscopic on-and off-rates, even for such complex glycooligomer/protein systems. By comparing e.g. a mono-to a divalent glycomacromolecule for their binding to dimeric Con A, we see a lower dissociation rate for the latter. As both bind monovalently to Con A, this is a strong indication for a statistical rebinding event. Further, there is a strong dependence of multivalent binding kinetics on the ligand density of glycomacromolecules as well as the Con A conformation and thus the overall on-and off-rates.
Münster Symposium on Cooperative Effects 2015 - SFB 858, at Westfälische Wilhelms-Universität Münster, 2015
no
Sinaida Igde
Regine Kossick
Hendrik Wölk
Susanna Röblitz
Marco Reidelbach
Marcus Weber
Laura Hartmann
Numerical Mathematics
Computational Molecular Design
Röblitz, Susanna
Weber, Marcus
SFB765-C2
6053
2016
eng
197
297
19/4
article
0
--
--
--
IR-MALDI ion mobility spectrometry: physical source characterization and application as HPLC detector
International Journal for Ion Mobility Spectrometry
10.1007/s12127-016-0208-1
yes
José Villatoro
Regine Kossick
Martin Zühlke
Daniel Riebe
Toralf Beitz
Marcus Weber
Jens Riedel
Hans-Gerd Löhmannsröben
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
SALSA-IR-MALDI
4985
2014
eng
49
65
1
incollection
European Mathematical Society
0
--
--
--
Design of functional molecules
MATHEON-Mathematics for Key Technologies
Series in Industrial and Applied Mathematics
no
Christof Schütte
Peter Deuflhard
Erlinda Körnig
Peter Deuflhard
Martin Grötschel
Frank Noé
Dietmar Hömberg
Marcus Weber
Ulrich Horst
Jürg Kramer
Volker Mehrmann
Konrad Polthier
Frank Schmidt
Christof Schütte
Martin Skutella
Jürgen Sprekels
Numerical Mathematics
Computational Molecular Design
Schütte, Christof
Weber, Marcus
BMS-Nielsen
Matheon-A19
6646
2017
eng
1700198
12
17
article
0
--
--
--
Linear Precision Glycomacromolecules with Varying Interligand Spacing and Linker Functionalities Binding to Concanavalin A and the Bacterial Lectin FimH
Marcomolecular Bioscience
10.1002/mabi.201700198
yes
Sinaida Igde
Marcus Weber
Susanna Röblitz
Anne Müller
Katharina Kolbe
Sophia Boden
Claudia Fessele
Thisbe Lindhorst
Marcus Weber
Laura Hartmann
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Röblitz, Susanna
Weber, Marcus
SFB765-C2
6710
2018
eng
20
1
6
article
0
--
--
--
Implications of PCCA+ in Molecular Simulation
Upon ligand binding or during chemical reactions the state of a molecular system changes in time. Usually we consider a finite set of (macro-) states of the system (e.g., ’bound’ vs. ’unbound’), although the process itself takes place in a continuous space. In this context, the formula chi=XA connects the micro-dynamics of the molecular system to its macro-dynamics. Chi can be understood as a clustering of micro-states of a molecular system into a few macro-states. X is a basis of an invariant subspace of a transfer operator describing the micro-dynamics of the system. The formula claims that there is an unknown linear relation A between these two objects. With the aid of this formula we can understand rebinding effects, the electron flux in pericyclic reactions, and systematic changes of binding rates in kinetic ITC experiments. We can also analyze sequential spectroscopy experiments and rare event systems more easily. This article provides an explanation of the formula and an overview of some of its consequences.
Computation
10.3390/computation6010020
yes
Creative Commons - CC BY - Namensnennung 4.0 International
Marcus Weber
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
SFB1114-A5
6713
2017
eng
researchdata
0
--
--
--
Supplementary simulation data for Science Manuscript ai8636
The simulation data has been produced by Vedat Durmaz, Peggy Sabri and Marco Reidelbach inside the "Computational Molecular Design" Group headed by Marcus Weber at Zuse-Institut Berlin, Takustr. 7, D-14195 Berlin, Germany.
The file contains classical simulation data for different fentanyl derivates in the MOR binding pocket at different pHs. It also includes instruction files for quantum-chemical pKa-value estimations and a description of how we derived the pKa-values from the Gaussian09 log-files.
10.12752/5.MWB.1.0
GROMACS trajectories and GAUSSIAN files of MOR and fentanyl derivates
yes
Dataset
Berlin
2016
2017
https://doi.org/10.1126/science.aai8636
http://www.zib.de/ext-data/selective-opioids/data_4manuscript.tar
Creative Commons - CC BY - Namensnennung 4.0 International
Marcus Weber
Marcus Weber
Vedat Durmaz
Peggy Sabri
Marco Reidelbach
Computational Molecular Design
Durmaz, Vedat
Weber, Marcus
NAMPAR
6663
2018
eng
e0191423
e0191423
30
1
13
article
0
--
--
--
An AKAP-Lbc-RhoA interaction inhibitor promotes the translocation of aquaporin-2 to the plasma membrane of renal collecting duct principal cells
Stimulation of renal collecting duct principal cells with antidiuretic hormone (arginine-vasopressin, AVP) results in inhibition of the small GTPase RhoA and the enrichment of the water channel aquaporin-2 (AQP2) in the plasma membrane. The membrane insertion facilitates water reabsorption from primary urine and fine-tuning of body water homeostasis. Rho guanine nucleotide exchange factors (GEFs) interact with RhoA, catalyze the exchange of GDP for GTP and thereby activate the GTPase. However, GEFs involved in the control of AQP2 in renal principal cells are unknown. The A-kinase anchoring protein, AKAP-Lbc, possesses GEF activity, specifically activates RhoA, and is expressed in primary renal inner medullary collecting duct principal (IMCD) cells. Through screening of 18,431 small molecules and synthesis of a focused library around one of the hits, we identified an inhibitor of the interaction of AKAP-Lbc and RhoA. This molecule, Scaff10-8, bound to RhoA, inhibited the AKAP-Lbc-mediated RhoA activation but did not interfere with RhoA activation through other GEFs or activities of other members of the Rho family of small GTPases, Rac1 and Cdc42. Scaff10-8 promoted the redistribution of AQP2 from intracellular vesicles to the periphery of IMCD cells. Thus, our data demonstrate an involvement of AKAP-Lbc-mediated RhoA activation in the control of AQP2 trafficking.
PLOS ONE
10.1371/journal.pone.0191423
yes
Katharina Schrade
Marcus Weber
Jessica Tröger
Adeep Eldashan
Kerstin Zühlke
Kamal R. Abdul Azees
Jonathan M. Elkins
Martin Neuenschwander
Andreas Oder
Mohamed Elkewedi
Sarah Jaksch
Karsten Andrae
Jinliang Li
Jaoa Fernandes
Paul Markus Müller
Stephan Grunwald
Stephen F. Marino
Tanja Vukicevic
Jenny Eichhorst
Burkhard Wiesner
Marcus Weber
Michael Kapiloff
Oliver Rocks
Oliver Daumke
Thomas Wieland
Stefan Knapp
Jens Peter von Kries
Enno Klussmann
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
NAMPAR
6714
2018
eng
researchdata
0
--
--
--
Supplementary: Implications of PCCA+ in Molecular Simulation
Matlab-software and data sets to recapitulate the presented results in M. Weber: Implications of PCCA+ in Molecular Simulation. Computation, 6(1):20, 2018.
This data set includes one folder per published figure. The folders contain all needed resources to recapitulate the presented results.
yes
Software
Berlin
2017
2018
MATLAB-files
https://doi.org/10.3390/computation6010020
http://www.mdpi.com/2079-3197/6/1/20/s1
Creative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International
Marcus Weber
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
SFB1114-A5
6214
2017
eng
966
969
6328
355
article
0
--
--
--
A nontoxic pain killer designed by modeling of pathological receptor conformations
Science
10.1126/science.aai8636
yes
Viola Spahn
Marcus Weber
Giovanna Del Vecchio
Dominika Labuz
Antonio Rodriguez-Gaztelumendi
N. Massaly
Julia Temp
Vedat Durmaz
P. Sabri
Marco Reidelbach
Halina Machelska
Marcus Weber
Christoph Stein
Numerical Mathematics
Computational Molecular Design
Durmaz, Vedat
Weber, Marcus
NAMPAR
TransRisk
6219
eng
reportzib
0
--
2017-03-09
--
Eigenvalues of non-reversible Markov chains – A case study
Finite reversible Markov chains are characterized by a transition matrix P that has real eigenvalues and pi-orthogonal eigenvectors, where pi is the stationary distribution of P. This means, that a transition matrix with complex eigenvalues corresponds to a non-reversible Markov chain. This observation leads to the question, whether the imaginary part of that eigendecomposition corresponds to or indicates the “pattern” of the nonreversibility. This article shows that the direct relation between imaginary parts of eigendecompositions and the non-reversibility of a transition matrix is not given. It is proposed to apply the Schur decomposition of P instead of the eigendecomposition in order to characterize its nonreversibility.
1438-0064
urn:nbn:de:0297-zib-62191
Marcus Weber
Regine Kossick
ZIB-Report
17-13
eng
uncontrolled
non-reversible
eng
uncontrolled
transition matrix
eng
uncontrolled
detailed balance
Markov chains (discrete-time Markov processes on discrete state spaces)
Eigenvalues, eigenvectors
Irreversible thermodynamics, including Onsager-Machlup theory
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
SFB1114-A5
https://opus4.kobv.de/opus4-zib/files/6219/ZR-17-13.pdf
2407
2010
2010
eng
2206
15
1217(15)
article
0
--
--
--
Dynamic covalent hydrazine chemistry as a specific extraction and cleanup technique for the quantification of the Fusarium mycotoxin zearalenone in edible oils
Journal of Chromatography A
yes
D. Siegel
Karsten Andrae
Matthias Proske
C. Kochan
Matthias Koch
Marcus Weber
Irene Nehls
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
2397
2011
2011
eng
770
775
2
article
0
--
--
--
DNA-programmed spatial screening of carbohydrate-lectin interactions
Chem. Sci.
yes
Ch. Scheibe
Alexander Bujotzek
Jens Dernedde
Marcus Weber
O. Seitz
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
2443
2006
2006
eng
103
110
bookpart
Springer Berlin Heidelberg
0
--
--
--
An Indicator for the Number of Clusters
From Data and Information Analysis to Knowledge Engineering
http://dx.doi.org/10.1007/3-540-31314-1_11
Studies in Classification, Data Analysis, and Knowledge Organization
Marcus Weber
Myra Spiliopoulou
Wasinee Rungsarityotin
Rudolf Kruse
Alexander Schliep
Christian Borgelt
Andreas Nürnberger
Wolfgang Gaul
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
2447
2010
2010
eng
319
332
63(2)
article
0
--
--
--
A simple method for the estimation of entropy differences
MATCH Commun. Math. Comp. Chem. 2010
yes
Marcus Weber
Karsten Andrae
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
2448
2008
2008
eng
727
736
7
34
article
0
--
--
--
Classical hybrid Monte-Carlo simulations of the interconversion of hexabromocyclododecane
Journal of Molecular Simulation
urn:nbn:de:0297-zib-10308
Marcus Weber
Roland Becker
Robert Köppen
Vedat Durmaz
Numerical Mathematics
Computational Molecular Design
Durmaz, Vedat
Weber, Marcus
2450
2011
2011
eng
article
0
--
--
--
Computational entropy estimation of linear polyether modified surfaces and correlation with protein resistant properties of such surfaces
J. Mol. Sim.
yes
Marcus Weber
Alexander Bujotzek
Karsten Andrae
M. Weinhart
Rainer Haag
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
2451
2007
2007
eng
415
418
2
362
article
0
--
--
--
Visualization of the tRNA(Ser) acceptor step binding site in the seryl-tRNA synthetase
BBRC
C. Förster
Arnd B. E. Brauer
J. Fürste
C. Betzel
Marcus Weber
Frank Cordes
V. Erdmann
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
2452
2008
2008
eng
593
596
1048
conferenceobject
0
--
--
--
Preserving the Markov Property of Reduced Reversible Markov Chains
Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics 2008
Susanna Kube
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Röblitz, Susanna
Weber, Marcus
2439
2006
2006
eng
doctoralthesis
Freie Universität Berlin, department of mathematics
0
--
--
--
Meshless Methods in Conformation Dynamics
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
2455
2007
2007
eng
396
416
2
6
article
0
--
--
--
Stable Computation of Probability Densities of Metastable Dynamical Systems
SIAM J. Multiscale Model. Simul.
Marcus Weber
Susanna Kube
Lionel Walter
Peter Deuflhard
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Deuflhard, Peter
Röblitz, Susanna
Weber, Marcus
5879
2015
eng
poster
0
--
--
--
Topological analysis and visualization of scalar functions characterizing conformational transitions of molecules on multiple time-scales
Molecular processes such as protein folding or ligand-receptor-binding can be understood by analyzing the free energy landscape. Those processes are often metastable, i.e. the molecular systems remain in basins around local minima of the free energy landscape, and in rare cases undergo gauche transitions between metastable states by passing saddle-points of this landscape. By discretizing the configuration space, this can be modeled as a discrete Markov process. One way to compute the transition rates between conformations of a molecular system is by utilizing Transition Path Theory and the concept of committor functions. A fundamental problem from the computational point of view is that many time-scales are involved, ranging from 10^(-14) sec for the fastest motion to 10^(-6) sec or more for conformation changes that cause biological effects.
The goal of our work is to provide a better understanding of such transitions in configuration space on various time-scales by analyzing characteristic scalar functions topologically and geometrically. We are developing suitable visualization and interaction techniques to support our analysis. For example, we are analyzing a transition rate indicator function by computing and visualizing its Reeb graph together with the sets of molecular states corresponding to maxima of the transition rate indicator function. A particular challenge is the high dimensionality of the domain which does not allow for a straightforward visualization of the function.
The computational topology approach to the analysis of the transition rate indicator functions for a molecular system allows to explore different time scales of the system by utilizing coarser or finer topological partitioning of the function. A specific goal is the development of tools for analyzing the hierarchy of these partitionings. This approach tackles the analysis of a complex and sparse dataset from a different angle than the well-known spectral analysis of Markov State Models.
Shape Up 2015 - Exercises in Materials Geometry and Topology, 14-18 Sept. 2015, Berlin, Germany
no
Stefan Bojarovski
Hans-Christian Hege
Hans-Christian Hege
Han Cheng Lie
Marcus Weber
Numerical Mathematics
Visual Data Analysis
Computational Molecular Design
Visual Data Analysis in Science and Engineering
Hege, Hans-Christian
TopoMol
Visual and Data-centric Computing
5882
2016
eng
15475
15484
43
22
article
0
--
--
--
Allosteric and Chelate Cooperativity in Divalent Crown Ether–Ammonium Complexes with Strong Binding Enhancements
Chem. Eur. J.
10.1002/chem.201603098
Has been announced under the title: Cooperativity in Multivalent Binding: A Detailed Experimental and Theoretical Thermochemical Study of Divalent Crown Ether-Ammonium Complexes
yes
Larissa K. S. Krebek, von
Regine Kossick
Andreas J. Achazi
Marthe Solleder
Marcus Weber
Beate Paulus
Christoph A. Schalley
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
Matheon-A19
Salsa-Klimm
SFB765-C2
5573
eng
reportzib
0
--
2015-08-19
--
Finding dominant structures of nonreversible Markov processes
Finding metastable sets as dominant structures of Markov processes has been shown to be especially useful in modeling interesting slow dynamics of various real world complex processes. Furthermore, coarse graining of such processes based on their dominant structures leads to better understanding and dimension reduction of observed systems. However, in many cases, e.g. for nonreversible Markov processes, dominant structures are often not formed by metastable sets but by important cycles or mixture of both. This paper aims at understanding and identifying these different types of dominant structures for reversible as well as nonreversible ergodic Markov processes. Our algorithmic approach generalizes spectral based methods for reversible process by using Schur decomposition techniques which can tackle also nonreversible cases. We illustrate the mathematical construction of our new approach by numerical experiments.
1438-0064
urn:nbn:de:0297-zib-55739
10.1137/15M1032272
Appeared in: Multiscale Modeling and Simulation 14(4): 1319-1340
Natasa Djurdjevac Conrad
Erlinda Koernig
Marcus Weber
Christof Schütte
ZIB-Report
15-40
eng
uncontrolled
nonreversible Markov processes
eng
uncontrolled
metastable sets
eng
uncontrolled
cycle decomposition
eng
uncontrolled
Schur decomposition
Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]
Computational Markov chains
Dynamic and nonequilibrium phase transitions (general)
Numerical Mathematics
Schütte, Christof
Weber, Marcus
BMS-Nielsen
EyeTracking
NonequiMSM
Conrad, Natasa
https://opus4.kobv.de/opus4-zib/files/5573/ZIB-Report_15-40.pdf
5592
2015
eng
2157
2166
10
2015
article
0
--
--
--
High affinity flourescence labelled ligands for the estrogen receptor
Eur. J. Org. Chem.
yes
Frank Abendroth
Marcus Weber
Marthe Solleder
Pia Welker
Kai Licha
Marcus Weber
Oliver Seitz
Dorothea Mangoldt
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
Matheon-A19
Salsa-Klimm
SFB765-C2
5593
2015
eng
837
847
11
article
0
--
--
--
Peptide polymer ligands for a tandem WW-domain, a soft multivalent protein-protein interaction: lessons on the thermodynamic fitness of flexible ligands
Beilstein J. Org. Chem.
yes
Koschek
Marcus Weber
Vedat Durmaz
Krylova
Wieczorek
Pooja Gupta
Richter
Alexander Bujotzek
Fischer
Rainer Haag
Freund
Marcus Weber
Rademann
Numerical Mathematics
Computational Molecular Design
Durmaz, Vedat
Weber, Marcus
Matheon-A19
Salsa-Klimm
SFB765-C2
5594
2015
deu
264
267
3/15
article
0
--
--
--
Computergestützte Simulationen zur Abschätzung gesundheitlicher Risiken durch anthropogene Spurenstoffe der Wassermatrix
KA Korrespondenz Abwasser, Abfall
yes
Vedat Durmaz
Marcus Weber
Marcus Weber
Meyer
Mückter
Numerical Mathematics
Computational Molecular Design
Durmaz, Vedat
Weber, Marcus
BB3R
TransRisk
4583
2013
eng
147
179
2
7
article
0
--
--
--
Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification
Advances in Data Analysis and Classification
10.1007/s11634-013-0134-6
yes
Susanna Röblitz
Stötzel
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Röblitz, Susanna
Weber, Marcus
BMS-Nielsen
EyeTracking
Matheon-A19
5329
2014
eng
reportzib
0
--
2014-12-10
--
Computing the nearest reversible Markov chain
Reversible Markov chains are the basis of many applications. However, computing transition probabilities by a finite sampling of a Markov chain can lead to truncation errors. Even if the original Markov chain is reversible, the approximated Markov chain might be non-reversible and will lose important properties, like the real valued spectrum. In this paper, we show how to find the closest reversible Markov chain to a given transition matrix. It turns out that this matrix can be computed by solving a convex minimization problem.
1438-0064
urn:nbn:de:0297-zib-53292
Adam Nielsen
Adam Nielsen
Marcus Weber
ZIB-Report
14-48
eng
uncontrolled
Reversible Markov Chain
eng
uncontrolled
Convex Optimization
eng
uncontrolled
MSM
LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY
COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
BMS-Nielsen
https://opus4.kobv.de/opus4-zib/files/5329/ZR-14-48.pdf
5330
2015
eng
483
499
3
22
article
0
--
--
--
Computing the nearest reversible Markov chain
Reversible Markov chains are the basis of many applications. However, computing transition probabilities by a finite sampling of a Markov chain can lead to truncation errors. Even if the original Markov chain is reversible, the approximated Markov chain might be non-reversible and will lose important properties, like the real valued spectrum. In this paper, we show how to find the closest reversible Markov chain to a given transition matrix. It turns out that this matrix can be computed by solving a convex minimization problem.
Numerical Linear Algebra with Applications
10.1002/nla.1967
yes
urn:nbn:de:0297-zib-53292
Adam Nielsen
Adam Nielsen
Marcus Weber
eng
uncontrolled
Reversible Markov Chain
deu
uncontrolled
Convex Optimization
deu
uncontrolled
MSM
LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY
COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
BMS-Nielsen
EyeTracking
NonequiMSM
SFB1114-A5
5233
2014
eng
26
28
1
incollection
European Mathematical Society
0
--
--
--
Mathematics without pain
MATHEON-Mathematics for Key Technologies
10.4171/137
Series in Industrial and Applied Mathematics
no
Peter Deuflhard
Peter Deuflhard
Erlinda Körnig
Marcus Weber
Martin Grötschel
Dietmar Hömberg
Ulrich Horst
Jürg Kramer
Volker Mehrmann
Konrad Polthier
Frank Schmidt
Martin Skutella
Jürgen Sprekels
Numerical Mathematics
Computational Molecular Design
Deuflhard, Peter
Weber, Marcus
Matheon-A19
NAMPAR
Salsa-Klimm
4614
2009
eng
73
79
WIAS Report No. 26
article
0
--
--
--
Fuzzy Spectral Clustering by PCCA+
Classification and Clustering: Models, Software and Applications
http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Report&year=2009&number=26
no
Susanna Röblitz
Stötzel
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Röblitz, Susanna
Weber, Marcus
7563
2019
eng
46
3
7
article
0
--
--
--
Modeling of Multivalent Ligand-Receptor Binding Measured by kinITC
In addition to the conventional Isothermal Titration Calorimetry (ITC), kinetic ITC (kinITC) not only gains thermodynamic information, but also kinetic data from a biochemical binding process. Moreover, kinITC gives insights into reactions consisting of two separate kinetic steps, such as protein folding or sequential binding processes. The ITC method alone cannot deliver kinetic parameters, especially not for multivalent bindings. This paper describes how to solve the problem using kinITC and an invariant subspace projection. The algorithm is tested for multivalent systems with different valencies.
Computation
10.3390/computation7030046
yes
2019-08-16
Franziska Erlekam
Marcus Weber
Sinaida Igde
Susanna Röblitz
Laura Hartmann
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Röblitz, Susanna
Weber, Marcus
SFB765-C2
7564
2019
deu
551
557
7
article
0
--
--
--
Transformationsprodukte im Klärwerk: Mathematische Ansätze der Bewertung
KA Korrespondenz Abwasser, Abfall
yes
Marcus Weber
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
BB3R
7565
2019
eng
1900501
13
6
article
0
--
--
--
Mussel-glue inspired adhesives: A study on the relevance of L-Dopa and the function of the sequence at nanomaterial-peptide interfaces
Mussel glue‐proteins undergo structural transitions at material interfaces to optimize adhesive surface contacts. Those intriguing structure responses are mimicked by a mussel‐glue mimetic peptide (HSY*SGWSPY*RSG (Y* = l‐Dopa)) that was previously selected by phage‐display to adhere to Al2O3 after enzymatic activation. Molecular level insights into the full‐length adhesion domain at Al2O3 surfaces are provided by a divergent‐convergent analysis, combining nuclear Overhauser enhancement based 2D NOESY and saturation transfer difference NMR analysis of submotifs along with molecular dynamics simulations of the full‐length peptide. The peptide is divided into two submotifs, each containing one Dopa “anchor” (Motif‐1 and 2). The analysis proves Motif‐1 to constitute a dynamic Al2O3 binder and adopting an “M”‐structure with multiple surface contacts. Motif‐2 binds stronger by two surface contacts, forming a compact “C”‐structure. Taking these datasets as constraints enables to predict the structure and propose a binding process model of the full‐length peptide adhering to Al2O3.
Advanced Materials Interfaces
10.1002/admi.201900501
yes
Narendra Lagumaddepalli Venkatareddy
Marcus Weber
Patrick Wilke
Natalia Ernst
Justus Horch
Marcus Weber
Andre Dallmann
Hans G. Börner
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
SFB765-C2
Ernst, Natalia
7571
2019
eng
19344
9
article
0
--
--
--
pKa of opioid ligands as a discriminating factor for side effects
The non-selective activation of central and peripheral opioid receptors is a major shortcoming of currently available opioids. Targeting peripheral opioid receptors is a promising strategy to preclude side effects. Recently, we showed that fentanyl-derived μ-opioid receptor (MOR) agonists with reduced acid dissociation constants (pKa) due to introducing single fluorine atoms produced injury-restricted antinociception in rat models of inflammatory, postoperative and neuropathic pain. Here, we report that a new double-fluorinated compound (FF6) and fentanyl show similar pKa, MOR affinity and [35S]-GTPγS binding at low and physiological pH values. In vivo, FF6 produced antinociception in injured and non-injured tissue, and induced sedation and constipation. The comparison of several fentanyl derivatives revealed a correlation between pKa values and pH-dependent MOR activation, antinociception and side effects. An opioid ligand's pKa value may be used as discriminating factor to design safer analgesics.
Scientific Reports
10.1038/s41598-019-55886-1
yes
Giovanna Del Vecchio
Marcus Weber
Dominika Labuz
Julia Temp
Viola Seitz
Michael Kloner
Roger Negrete
Antonio Rodriguez-Gaztelumendi
Marcus Weber
Halina Machelska
Christoph Stein
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
NAMPAR
7959
2020
eng
5247
5260
412
article
0
--
--
--
Sub-ambient pressure IR-MALDI ion mobility spectrometer for the determination of low and high field mobilities
A new ion mobility (IM) spectrometer, enabling mobility measurements in the pressure range between 5 and 500 mbar and in the reduced field strength range E/N of 5–90 Td, was developed and characterized. Reduced mobility (K0) values were studied under low E/N (constant value) as well as high E/N (deviation from low field K0) for a series of molecular ions in nitrogen. Infrared matrix-assisted laser desorption ionization (IR-MALDI) was used in two configurations: a source working at atmospheric pressure (AP) and, for the first time, an IR-MALDI source working with a liquid (aqueous) matrix at sub-ambient/reduced pressure (RP). The influence of RP on IR-MALDI was examined and new insights into the dispersion process were gained. This enabled the optimization of the IM spectrometer for best analytical performance. While ion desolvation is less efficient at RP, the transport of ions is more efficient, leading to intensity enhancement and an increased number of oligomer ions. When deciding between AP and RP IR-MALDI, a trade-off between intensity and resolving power has to be considered. Here, the low field mobility of peptide ions was first measured and compared with reference values from ESI-IM spectrometry (at AP) as well as collision cross sections obtained from molecular dynamics simulations. The second application was the determination of the reduced mobility of various substituted ammonium ions as a function of E/N in nitrogen. The mobility is constant up to a threshold at high E/N. Beyond this threshold, mobility increases were observed. This behavior can be explained by the loss of hydrated water molecules.
Analytical and Bioanalytical Chemistry
10.1007/s00216-020-02735-0
yes
José Villatoro
Marcus Weber
Martin Zühlke
Daniel Riebe
Toralf Beitz
Marcus Weber
Hans-Gerd Löhmannsröben
Numerical Mathematics
Weber, Marcus
SALSA-IR-MALDI
Modeling and Simulation of Complex Processes
8013
2021
eng
4
4
article
Wiley-VCH
0
2021-03-09
--
--
The Augmented Jump Chain
Modern methods of simulating molecular systems are based on the mathematical theory of Markov operators with a focus on autonomous equilibrated systems. However, non-autonomous physical systems or non-autonomous simulation processes are becoming more and more important. A representation of non-autonomous Markov jump processes is presented as autonomous Markov chains on space-time. Augmenting the spatial information of the embedded Markov chain by the temporal information of the associated jump times, the so-called augmented jump chain is derived. The augmented jump chain inherits the sparseness of the infinitesimal generator of the original process and therefore provides a useful tool for studying time-dependent dynamics even in high dimensions. Furthermore, possible generalizations and applications to the computation of committor functions and coherent sets in the non-autonomous setting are discussed. After deriving the theoretical foundations, the concepts with a proof-of-concept Galerkin discretization of the transfer operator of the augmented jump chain applied to simple examples are illustrated.
Advanced Theory and Simulations
2008.04624
10.1002/adts.202000274
yes
2021-01-05
Alexander Sikorski
Alexander Sikorski
Marcus Weber
Christof Schütte
Numerical Mathematics
Schütte, Christof
Weber, Marcus
SFB1114-A5
Sikorski, Alexander
Modeling and Simulation of Complex Processes
7163
2018
eng
e0207718
e0207718
23
12
13
article
0
--
--
--
Prediction of perturbed proton transfer networks
The transfer of protons through proton translocating channels is a complex process, for which direct samplings of different protonation states and side chain conformations in a transition network calculation provide an efficient, bias-free description. In principle, a new transition network calculation is required for every unsampled change in the system of interest, e.g. an unsampled protonation state change, which is associated with significant computational costs. Transition networks void of or including an unsampled change are termed unperturbed or perturbed, respectively. Here, we present a prediction method, which is based on an extensive coarse-graining of the underlying transition networks to speed up the calculations. It uses the minimum spanning tree and a corresponding sensitivity analysis of an unperturbed transition network as initial guess and refinement parameter for the determination of an unknown, perturbed transition network. Thereby, the minimum spanning tree defines a sub-network connecting all nodes without cycles and minimal edge weight sum, while the sensitivity analysis analyzes the stability of the minimum spanning tree towards individual edge weight reductions. Using the prediction method, we are able to reduce the calculation costs in a model system by up to 80%, while important network properties are maintained in most predictions.
PLoS ONE
https://doi.org/10.1371/journal.pone.0207718
yes
Marco Reidelbach
Marcus Weber
Marcus Weber
Petra Imhof
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
SFB765-C2
7164
2019
eng
108
117
436
article
0
--
--
--
Structural characterization of synthetic peptides using electronspray ion mobility spectrometry and molecular dynamics simulations
Electrospray ionization-ion mobility spectrometry was employed for the determination of collision cross sections (CCS) of 25 synthetically produced peptides in the mass range between 540–3310 Da. The experimental measurement of the CCS is complemented by their calculation applying two different methods. One prediction method is the intrinsic size parameter (ISP) method developed by the Clemmer group. The second new method is based on the evaluation of molecular dynamics (MD) simulation trajectories as a whole, resulting in a single, averaged collision cross-section value for a given peptide in the gas phase. A high temperature MD simulation is run in order to scan through the whole conformational space. The lower temperature conformational distribution is obtained through thermodynamic reweighting. In the first part, various correlations, e.g. CCS vs. mass and inverse mobility vs. m/z correlations, are presented. Differences in CCS between peptides are also discussed in terms of their respective mass and m/z differences, as well as their respective structures. In the second part, measured and calculated CCS are compared. The agreement between the prediction results and the experimental values is in the same range for both calculation methods. While the calculation effort of the ISP method is much lower, the MD method comprises several tools providing deeper insights into the conformations of peptides. Advantages and limitations of both methods are discussed. Based on the separation of two pairs of linear and cyclic peptides of virtually the same mass, the influence of the structure on the cross sections is discussed. The shift in cross section differences and peak shape after transition from the linear to the cyclic peptide can be well understood by applying different MD tools, e.g. the root-mean-square deviation (RMSD) and the root mean square fluctuation (RMSF).
International Journal of Mass Spectrometry
10.1016/j.ijms.2018.10.036
yes
2018/10/27
José Villatoro
Marcus Weber
Marcus Weber
Martin Zühlke
Andreas Lehmann
Karl Zechiowski
Daniel Riebe
Toralf Beitz
Hans-Gerd Löhmannsröben
Oliver Kreuzer
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
SALSA-IR-MALDI
7176
2019
eng
47
60
152
article
0
--
--
--
What you extract is what you see: Optimising the preparation of water and wastewater samples for in vitro bioassays
The assessment of water quality is crucial for safeguarding drinking water resources and ecosystem integrity. To this end, sample preparation and extraction is critically important, especially when investigating emerging contaminants and the toxicity of water samples. As extraction methods are rarely optimised for bioassays but rather adopted from chemical analysis, this may result in a misrepresentation of the actual toxicity.
In this study, surface water, groundwater, hospital and municipal wastewater were used to characterise the impacts of common sample preparation techniques (acidification, filtration and solid phase extraction (SPE)) on the outcomes of eleven in vitro bioassays. The latter covered endocrine activity (reporter gene assays for estrogen, androgen, aryl-hydrocarbon, retinoic acid, retinoid X, vitamin D, thyroid receptor), mutagenicity (Ames fluctuation test), genotoxicity (umu test) and cytotoxicity. Water samples extracted using different SPE sorbents (Oasis HLB, Supelco ENVI-Carb+, Telos C18/ENV) at acidic and neutral pH were compared for their performance in recovering biological effects.
Acidification, commonly used for stabilisation, significantly altered the endocrine activity and toxicity of most (waste)water samples. Sample filtration did not affect the majority of endpoints but in certain cases affected the (anti-)estrogenic and dioxin-like activities. SPE extracts (10.4 × final concentration), including WWTP effluents, induced significant endocrine effects that were not detected in aqueous samples (0.63 × final concentration), such as estrogenic, (anti-)androgenic and dioxin-like activities. When ranking the SPE methods using multivariate Pareto optimisation an extraction with Telos C18/ENV at pH 7 was most effective in recovering toxicity. At the same time, these extracts were highly cytotoxic masking the endpoint under investigation. Compared to that, extraction at pH 2.5 enriched less cytotoxicity.
In summary, our study demonstrates that sample preparation and extraction critically affect the outcome of bioassays when assessing the toxicity of water samples. Depending on the water matrix and the bioassay, these methods need to be optimised to accurately assess water quality.
Water Research
10.1016/j.watres.2018.12.049
yes
Aennes Abbas
Marcus Weber
Ilona Schneider
Anna Bollmann
Jan Funke
Jörg Oehlmann
Carsten Prasse
Ulrike Schulte-Oehlmann
Wolfram Seitz
Thomas Ternes
Marcus Weber
Henning Wesely
Martin Wagner
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
TransRisk
6897
2018
eng
6963
6975
23
34
article
0
2018-10-03
2018-10-03
--
Role of Counterions in Molecularly Imprinted Polymers for Anionic Species
Small-molecule oxoanions are often imprinted noncovalently as carboxylates into molecularly imprinted polymers (MIPs), requiring the use of an organic counterion. Popular species are either pentamethylpiperidine (PMP) as a protonatable cation or tetraalkylammonium (TXA) ions as permanent cations. The present work explores the influence of the TXA as a function of their alkyl chain length, from methyl to octyl, using UV/vis absorption, fluorescence titrations, and HPLC as well as MD simulations. Protected phenylalanines (Z-L/D-Phe) served as templates/analytes. While the influence of the counterion on the complex stability constants and anion-induced spectral changes shows a monotonous trend with increasing alkyl chain length at the prepolymerization stage, the cross-imprinting/rebinding studies showed a unique pattern that suggested the presence of adaptive cavities in the MIP matrix, related to the concept of induced fit of enzyme–substrate interaction. Larger cavities formed in the presence of larger counterions can take up pairs of Z-x-Phe and smaller TXA, eventually escaping spectroscopic detection. Correlation of the experimental data with the MD simulations revealed that counterion mobility, the relative distances between the three partners, and the hydrogen bond lifetimes are more decisive for the response features observed than actual distances between interacting atoms in a complex or the orientation of binding moieties. TBA has been found to yield the highest imprinting factor, also showing a unique dual behavior regarding the interaction with template and fluorescent monomer. Finally, interesting differences between both enantiomers have been observed in both theory and experiment, suggesting true control of enantioselectivity. The contribution concludes with suggestions for translating the findings into actual MIP development.
Langmuir
10.1021/acs.langmuir.8b00500
yes
2018-05-23
Sabine Wagner
Marcus Weber
Carlos Zapata
Wei Wan
Kornelia Gawlitza
Marcus Weber
Knut Rurack
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
MIP_FORMATION
6898
2018
eng
8965
8
article
Springer Nature
0
--
2018-06-12
--
Opioid receptor signaling, analgesic and side effects induced by a computationally designed pH-dependent agonist
Novel pain killers without adverse effects are urgently needed.
Scientific Reports
yes
2018-06-01
Creative Commons - CC BY - Namensnennung 4.0 International
Viola Spahn
Marcus Weber
Giovanna Del Vecchio
Antonio Rodriguez-Gaztelumendi
Julia Temp
Dominika Labuz
Michael Kloner
Marco Reidelbach
Halina Machelska
Marcus Weber
Christoph Stein
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
NAMPAR
6899
2018
deu
article
0
--
--
--
Transformationsprodukte im Klärwerk: Mathematische Ansätze der Bewertung
KA Korrespondenz Abwasser, Abfall
yes
accepted for publication
2018-06-04
Marcus Weber
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
TransRisk
8802
2022
2022
eng
297
9
15
article
0
2022-08-15
2022-08-15
--
SepFree NMF: A Toolbox for Analyzing the Kinetics of Sequential Spectroscopic Data
This work addresses the problem of determining the number of components from sequential spectroscopic data analyzed by non-negative matrix factorization without separability assumption (SepFree NMF). These data are stored in a matrix M of dimension “measured times” versus “measured wavenumbers” and can be decomposed to obtain the spectral fingerprints of the states and their evolution over time. SepFree NMF assumes a memoryless (Markovian) process to underline the dynamics and decomposes M so that M=WH, with W representing the components’ fingerprints and H their kinetics. However, the rank of this decomposition (i.e., the number of physical states in the process) has to be guessed from pre-existing knowledge on the observed process. We propose a measure for determining the number of components with the computation of the minimal memory effect resulting from the decomposition; by quantifying how much the obtained factorization is deviating from the Markovian property, we are able to score factorizations of a different number of components. In this way, we estimate the number of different entities which contribute to the observed system, and we can extract kinetic information without knowing the characteristic spectra of the single components. This manuscript provides the mathematical background as well as an analysis of computer generated and experimental sequentially measured Raman spectra.
Algorithms
10.3390/a15090297
yes
2022-08-15
publish
Renata Sechi
Renata Sechi
Konstantin Fackeldey
Surahit Chewle
Marcus Weber
Fackeldey, Konstantin
Weber, Marcus
MathPlusAA1-1
Modeling and Simulation of Complex Processes
Chewle, Surahit
MathPlusAA1-15
8516
2021
eng
2456
12
13
article
0
--
--
--
Plasma Proteome Fingerprints Reveal Distinctiveness and Clinical Outcome of SARS-CoV-2 Infection
We evaluated how plasma proteomic signatures in patients with suspected COVID-19 can unravel the pathophysiology, and determine kinetics and clinical outcome of the infection. We identified distinct plasma proteins linked to the presence and course of COVID-19. These plasma proteomic findings may translate to a protein fingerprint, helping to assist clinical management decisions.
Viruses
10.3390/v13122456
yes
publish
Wolfgang Bauer
Marcus Weber
Marcus Weber
Eva Diehl-Wiesenecker
Noa Galtung
Monika Prpic
Rajan Somasundaram
Rudolf Tauber
Jochen Schwenk
Patrick Micke
Kai Kappert
Computational Molecular Design
Weber, Marcus
MathPlusAA1-1
Mathematics for Life and Materials Science
Modeling and Simulation of Complex Processes
7960
2020
deu
article
0
--
--
--
DIN SPEC 2343: Übertragung von sprachbasierten Daten zwischen Künstlichen Intelligenzen - Festlegung von Parametern und Formaten
Dieses Dokument legt Parameter und Formate für die Übertragung sprachbasierter Daten zwischen verschiedenen KI-Ökosystemen fest.
Beuth Verlag
yes
Marcus Weber
Marcus Weber
Christine Reichardt
Weitere Autoren
Numerical Mathematics
Weber, Marcus
MathPlusAA1-1
Modeling and Simulation of Complex Processes
8871
2022
eng
poster
0
--
--
--
MaRDI - The mathematical Research Data Initiative
Aktionstag Forschungsdaten
10.5281/zenodo.7397588
no
publish
Marco Reidelbach
Marco Reidelbach
Marcus Weber
Weber, Marcus
Modeling and Simulation of Complex Processes
Reidelbach, Marco
MaRDI-TA4
6207
eng
reportzib
0
--
2017-01-03
--
An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates
In this article we propose an adaptive importance sampling scheme for dynamical quantities of high dimensional complex systems which are metastable. The main idea of this article is to combine a method coming from Molecular Dynamics Simulation, Metadynamics, with a theorem from stochastic analysis, Girsanov's theorem. The proposed algorithm has two advantages compared to a standard estimator of dynamic quantities: firstly, it is possible to produce estimators with a lower variance and, secondly, we can speed up the sampling. One of the main problems for building importance sampling schemes for metastable systems is to find the metastable region in order to manipulate the potential accordingly. Our method circumvents this problem by using an assimilated version of the Metadynamics algorithm and thus creates a non-equilibrium dynamics which is used to sample the equilibrium quantities.
1438-0064
urn:nbn:de:0297-zib-62075
Jannes Quer
Jannes Quer
Luca Donati
Bettina Keller
Marcus Weber
ZIB-Report
17-09
eng
uncontrolled
Adaptive Importance Sampling
eng
uncontrolled
Molecular Dynamics
eng
uncontrolled
Metastability
eng
uncontrolled
Variance Reduction
eng
uncontrolled
Non Equilibrium Sampling
eng
uncontrolled
Metadynamics
eng
uncontrolled
Girsanov
Computer Applications
DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)
NUMERICAL ANALYSIS
COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)
Numerical Mathematics
Weber, Marcus
SFB1114-A5
Quer, jannes
https://opus4.kobv.de/opus4-zib/files/6207/AISZIB.pdf
5662
eng
reportzib
0
--
2015-11-26
--
Estimating exit rates in rare event dynamical systems via extrapolation
In this article we present a new idea for approximating exit rates for diffusion processes living in a craggy landscape. We are especially interested in the exit rates of a process living in a metastable regions. Due to the fact that Monte Carlo simulations perform quite poor and are very computational expensive in this setting we create several similar situations with a smoothed potential. For this we introduce a new parameter $\lambda \in [0,1]$ ($\lambda = 1$ very smoothed potential, $\lambda=0$ original potential) into the potential which controls the influence the smoothing. We then sample the exit rate for different parameters $\lambda$ the exit rate from a given region. Due to the fact that $\lambda$ is connected to the exit rate we can use this dependency to approximate the real exit rate. The method can be seen as something between hyperdynamics and temperature accelerated MC.
1438-0064
urn:nbn:de:0297-zib-56622
Marcus Weber
Jannes Quer
Jannes Quer
ZIB-Report
15-54
eng
uncontrolled
rare event sampling, smoothing, membership functions, perturbed potential
PROBABILITY AND STATISTICS
Electronic structure of atoms and molecules: theory
PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)
STATISTICAL MECHANICS, STRUCTURE OF MATTER
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
SFB1114-A5
SFB765-C2
Quer, jannes
https://opus4.kobv.de/opus4-zib/files/5662/Homotopy.pdf
https://opus4.kobv.de/opus4-zib/files/5662/ConExitTimes-2.pdf
1603
eng
reportzib
0
2012-10-12
2012-10-12
--
Free Energy Calculation Using Mayer Cluster Expansion and Fluctuation Free Integration
This work aims to develop a new algorithm to calculate the free energy of water molecules by using a deterministic way.
For this purpose, we assume a closed system confined to a physical volume, having water molecules in gas phase.
To calculate the free energy of this sytem we utilized Mayer cluster expansion and the fluctuation free integration
method.
1438-0064
urn:nbn:de:0297-zib-16031
Burcu Tunga
Burcu Tunga
Marcus Weber
ZIB-Report
12-35
Mathematics of Computing
PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES
STATISTICAL MECHANICS, STRUCTURE OF MATTER
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
Matheon-A19
https://opus4.kobv.de/opus4-zib/files/1603/freeenergycalc.pdf
8837
2022
eng
123306-1
123306-21
21
12
63
article
AIP Publishing
0
2022-12-14
2022-12-14
--
A review of Girsanov Reweighting and of Square Root Approximation for building molecular Markov State Models
Dynamical reweighting methods permit to estimate kinetic observables of a stochastic process governed by a target potential U(x) from trajectories that have been generated at a different potential V(x). In this article, we present Girsanov reweighting and Square Root Approximation (SqRA): the first method reweights path probabilities exploiting the Girsanov theorem and can be applied to Markov State Models (MSMs) to reweight transition probabilities; the second method was originally developed to discretize the Fokker-Planck operator into a transition rate matrix, but here we implement it into a reweighting scheme for transition rates. We begin by reviewing the theoretical background of the methods, then present two applications relevant to Molecular Dynamics (MD), highlighting their strengths and weaknesses.
Journal of Mathematical Physics
10.1063/5.0127227
yes
2022-11-26
publish
Luca Donati
Luca Donati
Marcus Weber
Bettina G. Keller
Weber, Marcus
Modeling and Simulation of Complex Processes
MathPlusAA1-15
Donati, Luca
SFB1444
8956
2022
eng
e202208647
48
61
article
0
--
--
--
Cyanine Dye Coupling Mediates Self-assembly of a pH Sensitive Peptide into Novel 3D Architectures
A conjugated Cy5 dye-peptide system reveals the formation of two novel and structurally distinct supramolecular assemblies with photo-physical characteristics of H-type dimers or tetramers, respectively. The molecular ultrastructures are triggered by the complementary interplay of mutual chromophore coupling and pH induced changes in the peptide charge pattern.
Angewandte Chemie
yes
publish
Rita Fernandes
Weber
Suvrat Chaowdhary
Noureldin Saleh
Natalia Mikula
Katerina Kanevche
Hans Berlepsch
Naoki Hosogi
Joachim Heberle
Marcus Weber
Christoph Böttcher
Beate Koksch
Weber, Marcus
MathPlusAA1-1
Modeling and Simulation of Complex Processes
8545
2022
eng
article
0
--
--
--
Consistency and order 1 convergence of cell-centered finite volume discretizations of degenerate elliptic problems in any space dimension
We study consistency of cell-centered finite difference methods for elliptic equations with degenerate coefficients in any space dimension $d \geq 2$. This results in order of convergence estimates in the natural weighted energy norm and in the weighted discrete $L^2$-norm on admissible meshes. The cells of meshes under consideration may be very irregular in size. We particularly allow the size of certain cells to remain bounded from below even in the asymptotic limit. For uniform meshes we show that the order of convergence is at least 1 in the energy semi-norm, provided the discrete and continuous solutions exist and the continuous solution has $H^2$ regularity.
SIAM Journal on Numerical Analysis
10.20347/WIAS.PREPRINT.2913
under review
publish
yes
Martin Heida
Marcus Weber
Alexander Sikorski
Marcus Weber
Computational Molecular Design
Weber, Marcus
SFB1114-A5
Sikorski, Alexander
Modeling and Simulation of Complex Processes
8105
2020
eng
1107
12
10
article
0
--
--
--
Effect of choice of solvent on crystallization pathway of Paracetamol: An experimental and theoretical case study
The choice of solvents influences crystalline solid formed during the crystallization of active pharmaceutical ingredients (API). The underlying effects are not always well understood because of the complexity of the systems. Theoretical models are often insufficient to describe this phenomenon. In this study, the crystallization behavior of the model drug paracetamol in different solvents was studied based on experimental and molecular dynamics data. The crystallization process was followed in situ using time-resolved Raman spectroscopy. Molecular dynamics with simulated annealing algorithm was used for an atomistic understanding of the underlying processes. The experimental and theoretical data indicate that paracetamol molecules adopt a particular geometry in a given solvent predefining the crystallization of certain polymorphs.
Crystals
10.3390/cryst10121107
2020-12-02
yes
Surahit Chewle
Marcus Weber
Franziska Emmerling
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
SALSA-IR-MALDI
Mathematics for Life and Materials Science
Modeling and Simulation of Complex Processes
Chewle, Surahit
7065
2018
eng
425201
425201
42
30
article
0
--
--
--
Estimation of the infinitesimal generator by square-root approximation
In recent years, for the analysis of molecular processes, the estimation of time-scales and transition rates has become fundamental. Estimating the transition rates between molecular conformations is—from a mathematical point of view—an invariant subspace projection problem. We present a method to project the infinitesimal generator acting on function space to a low-dimensional rate matrix. This projection can be performed in two steps. First, we discretize the conformational space in a Voronoi tessellation, then the transition rates between adjacent cells is approximated by the geometric average of the Boltzmann weights of the Voronoi cells. This method demonstrates that there is a direct relation between the potential energy surface of molecular structures and the transition rates of conformational changes. We will show also that this approximation is correct and converges to the generator of the Smoluchowski equation in the limit of infinitely small Voronoi cells. We present results for a two dimensional diffusion process and alanine dipeptide as a high-dimensional system.
J. Phys.: Condens. Matter
10.1088/1361-648X/aadfc8
yes
2018-09-07
Luca Donati
Marcus Weber
Martin Heida
Bettina G. Keller
Marcus Weber
Numerical Mathematics
Weber, Marcus
SFB1114-A5
Donati, Luca
9069
2021
eng
115902
11
33
article
0
--
--
--
Markov models from the square root approximation of the Fokker–Planck equation: calculating the grid-dependent flux
Molecular dynamics (MD) are extremely complex, yet understanding the slow components of their dynamics is essential to understanding their macroscopic properties. To achieve this, one models the MD as a stochastic process and analyses the dominant eigenfunctions of the associated Fokker–Planck operator, or of closely related transfer operators. So far, the calculation of the discretized operators requires extensive MD simulations. The square-root approximation of the Fokker–Planck equation is a method to calculate transition rates as a ratio of the Boltzmann densities of neighboring grid cells times a flux, and can in principle be calculated without a simulation. In a previous work we still used MD simulations to determine the flux. Here, we propose several methods to calculate the exact or approximate flux for various grid types, and thus estimate the rate matrix without a simulation. Using model potentials we test computational efficiency of the methods, and the accuracy with which they reproduce the dominant eigenfunctions and eigenvalues. For these model potentials, rate matrices with up to $\mathcal{O}\left(1{0}^{6}\right)$ states can be obtained within seconds on a single high-performance compute server if regular grids are used.
Journal of Physics: Condensed Matter
10.1088/1361-648X/abd5f7
yes
2020-12-22
publish
Luca Donati
Luca Donati
Marcus Weber
Bettina G. Keller
Weber, Marcus
SFB1114-A5
Modeling and Simulation of Complex Processes
Donati, Luca
8823
2022
eng
224103-1
224103-14
14
22
157
article
AIP Publishing
0
2022-12-08
2022-12-08
--
Assessing transition rates as functions of environmental variables
We present a method to estimate the transition rates of molecular systems under different environmental conditions which cause the formation or the breaking of bonds and require the sampling of the Grand Canonical Ensemble. For this purpose, we model the molecular system in terms of probable "scenarios", governed by different potential energy functions, which are separately sampled by classical MD simulations. Reweighting the canonical distribution of each scenario according to specific environmental variables, we estimate the grand canonical distribution, then we use the Square Root Approximation (SqRA) method to discretize the Fokker-Planck operator into a rate matrix and the robust Perron Cluster Cluster Analysis (PCCA+) method to coarse-grain the kinetic model. This permits to efficiently estimate the transition rates of conformational states as functions of environmental variables, for example, the local pH at a cell membrane. In this work we formalize the theoretical framework of the procedure and we present a numerical experiment comparing the results with those provided by a constant-pH method based on non-equilibrium Molecular Dynamics Monte Carlo simulations. The method is relevant for the development of new drug design strategies which take into account how the cellular environment influences biochemical processes.
The Journal of Chemical Physics
10.1063/5.0109555
yes
2022-11-21
publish
Luca Donati
Luca Donati
Marcus Weber
Weber, Marcus
Modeling and Simulation of Complex Processes
MathPlusAA1-15
Donati, Luca
8925
2023
deu
T1/2023
incollection
DWA
0
--
--
--
Handlungsempfehlung zur integrativen Bewertung der weitergehenden Abwasserbehandlung von kommunalen Kläranlagen
Der DWA-Themenband beschreibt ein Konzept zur weitergehenden Abwasserbehandlung für die Bewertung von Aufbereitungsverfahren, sowohl in einer Pilotphase zur Auswahl von Verfahrensoptionen als auch für die Bewertung großtechnischer Anlagen. Emissionsseitig basiert das Konzept auf bereits regulatorisch definierten Parametern wie anorganischen Stickstoff-Verbindungen oder Phosphat sowie auf neuen noch nicht in der Abwasserverordnung regulierten Parametern. Die immissionsseitige Betrachtung erfolgt auf Basis der rechtlich durch die Europäische Wasserrahmenrichtlinie und andere Anforderungen bindenden Instrumente. Hierfür werden spezifische Vorgehensweisen vorgeschlagen. Anhand zweier ausgewählter Praxisbeispiele wird deutlich, dass es zur Bewertung der Verfahrensoptionen an einem Standort dienlich ist, ausgewählte Reduktionen bzw. Entfernungen von Stoffen, Organismen und Effekten zu bestimmen.
DWA-Themen
yes
publish
Thomas Ternes
Marcus Weber
Karl-Heinz Bauer
Frank Brauer
Jürgen Drewes
Kevin Jewell
Adriano Joss
Jörg Oehlmann
Michael Radtke
Ulrike Schulte-Oehlmann
Thomas Schwartz
Peter Seel
Jeanette Völker
Lilo Weber
Marcus Weber
Computational Molecular Design
Weber, Marcus
BB3R
Modeling and Simulation of Complex Processes
6035
eng
reportzib
0
--
2016-05-09
--
Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes
In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst.
1438-0064
urn:nbn:de:0297-zib-60353
10.1137/16M1091162
Jakob Witzig
Jakob Witzig
Isabel Beckenbach
Leon Eifler
Konstantin Fackeldey
Ambros Gleixner
Andreas Grever
Marcus Weber
ZIB-Report
16-39
eng
uncontrolled
Non-reversible Markov Processes
eng
uncontrolled
NESS
eng
uncontrolled
Mixed-Integer Programming
eng
uncontrolled
Markov State Models
PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)
STATISTICS
STATISTICAL MECHANICS, STRUCTURE OF MATTER
OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
Numerical Mathematics
Mathematical Optimization
Computational Molecular Design
Mathematical Optimization Methods
Fackeldey, Konstantin
Gleixner, Ambros
Weber, Marcus
Beckenbach, Isabel
MIP-ZIBOPT
MODAL-SynLab
Eifler, Leon
SparseApproxiTN
MODAL-Gesamt
https://opus4.kobv.de/opus4-zib/files/6035/ZR-16-39-revised2.pdf
6029
2018
eng
248
265
1
16
article
0
2018-02-15
--
--
Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes
In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst.
Multiscale Modeling and Simulation
1438-0064
10.1137/16M1091162
yes
urn:nbn:de:0297-zib-60353
Multiscale Modeling and Simulation
2017-10-18
Jakob Witzig
Jakob Witzig
Isabel Beckenbach
Leon Eifler
Konstantin Fackeldey
Ambros Gleixner
Andreas Grever
Marcus Weber
eng
uncontrolled
Markov State Models
eng
uncontrolled
NESS
eng
uncontrolled
Non-reversible Markov Processes
eng
uncontrolled
Mixed-Integer Programming
PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)
STATISTICAL MECHANICS, STRUCTURE OF MATTER
OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
Numerical Mathematics
Mathematical Optimization
Computational Molecular Design
Mathematical Optimization Methods
Fackeldey, Konstantin
Gleixner, Ambros
Weber, Marcus
Beckenbach, Isabel
MIP-ZIBOPT
MODAL-RailLab
MODAL-SynLab
Eifler, Leon
SparseApproxiTN
MODAL-Gesamt
8928
2024
eng
article
0
2022-12-30
2024-01-12
--
Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN
The dominant eigenfunctions of the Koopman operator characterize the metastabilities and slow-timescale dynamics of stochastic diffusion processes. In the context of molecular dynamics and Markov state modeling, they allow for a description of the location and frequencies of rare transitions, which are hard to obtain by direct simulation alone. In this article, we reformulate the eigenproblem in terms of the ISOKANN framework, an iterative algorithm that learns the eigenfunctions by alternating between short burst simulations and a mixture of machine learning and classical numerics, which naturally leads to a proof of convergence. We furthermore show how the intermediate iterates can be used to reduce the sampling variance by importance sampling and optimal control (enhanced sampling), as well as to select locations for further training (adaptive sampling). We demonstrate the usage of our proposed method in experiments, increasing the approximation accuracy by several orders of magnitude.
Journal of Mathematical Physics
2301.00065
https://doi.org/10.1063/5.0140764
publish
yes
Alexander Sikorski
Alexander Sikorski
Enric Ribera Borrell
Marcus Weber
Weber, Marcus
SFB1114-A5
Sikorski, Alexander
Ribera Borrell, Enric
Modeling and Simulation of Complex Processes
6595
2018
eng
A653
A670
18
2
40
article
0
2018-03-01
2018-02-01
--
An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates
In this article we propose an adaptive importance sampling scheme for dynamical quantities of high dimensional complex systems which are metastable. The main idea of this article is to combine a method coming from Molecular Dynamics Simulation, Metadynamics, with a theorem from stochastic analysis, Girsanov's theorem. The proposed algorithm has two advantages compared to a standard estimator of dynamic quantities: firstly, it is possible to produce estimators with a lower variance and, secondly, we can speed up the sampling. One of the main problems for building importance sampling schemes for metastable systems is to find the metastable region in order to manipulate the potential accordingly. Our method circumvents this problem by using an assimilated version of the Metadynamics algorithm and thus creates a non-equilibrium dynamics which is used to sample the equilibrium quantities.
SIAM Journal on Scientific Computing
10.1137/17m1124772
yes
urn:nbn:de:0297-zib-62075
2017-11-17
Jannes Quer
Julia Boltze
Luca Donati
Bettina Keller
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
SFB1114-A5
Quer, jannes
Donati, Luca
7898
2021
eng
460
477
18
1
19
article
0
--
--
--
Computing the minimal rebinding effect for non-reversible processes
The aim of this paper is to investigate the rebinding effect, a phenomenon describing a "short-time memory" which can occur when projecting a Markov process onto a smaller state space. For guaranteeing a correct mapping by the Markov State Model, we assume a fuzzy clustering in terms of membership functions, assigning degrees of membership to each state. The macro states are represented by the membership functions and may be overlapping. The magnitude of this overlap is a measure for the strength of the rebinding effect, caused by the projection and stabilizing the system. A minimal bound for the rebinding effect included in a given system is computed as the solution of an optimization problem. Based on membership functions chosen as a linear combination of Schur vectors, this generalized approach includes reversible as well as non-reversible processes.
Multiscale Modeling and Simulation
2007.08403
https://doi.org/10.1137/20M1334966
yes
2020-11-30
Susanne Röhl
Marcus Weber
Marcus Weber
Konstantin Fackeldey
Numerical Mathematics
Fackeldey, Konstantin
Weber, Marcus
MathPlusAA1-1
Modeling and Simulation of Complex Processes
5550
2015
eng
reportzib
0
--
--
--
G-PCCA: Spectral Clustering for Non-reversible Markov Chains
Spectral clustering methods are based on solving eigenvalue problems for the identification of clusters, e.g., the identification of metastable subsets of a Markov chain. Usually, real-valued eigenvectors are mandatory for this type of algorithms. The Perron Cluster Analysis (PCCA+) is a well-known spectral clustering method of Markov chains. It is applicable for reversible Markov chains, because reversibility implies a real-valued spectrum. We extend this spectral clustering method also to non-reversible Markov chains and give some illustrative examples. The main idea is to replace the eigenvalue problem by a real-valued Schur decomposition. By this extension, non-reversible Markov chains can be analyzed. Furthermore, the chains need not have a positive stationary distribution. And additionally to metastabilities, dominant cycles and sinks can be identified, too.
urn:nbn:de:0297-zib-55505
Marcus Weber
Konstantin Fackeldey
Konstantin Fackeldey
ZIB-Report
15-35
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
EyeTracking
Salsa-Klimm
SFB765-C2
https://opus4.kobv.de/opus4-zib/files/5550/ZR-15-35.pdf
7314
2019
eng
174103
150
17
article
0
--
--
--
Generalized Markov modeling of nonreversible molecular kinetics
Markov state models are to date the gold standard for modeling molecular kinetics since they enable the identification and analysis of metastable states and related kinetics in a very instructive manner. The state-of-the-art Markov state modeling methods and tools are very well developed for the modeling of reversible processes in closed equilibrium systems. On the contrary, they are largely not well suited to deal with nonreversible or even nonautonomous processes of nonequilibrium systems. Thus, we generalized the common Robust Perron Cluster Cluster Analysis (PCCA+) method to enable straightforward modeling of nonequilibrium systems as well. The resulting Generalized PCCA (G-PCCA) method readily handles equilibrium as well as nonequilibrium data by utilizing real Schur vectors instead of eigenvectors. This is implemented in the G-PCCA algorithm that enables the semiautomatic coarse graining of molecular kinetics. G-PCCA is not limited to the detection of metastable states but also enables the identification and modeling of cyclic processes. This is demonstrated by three typical examples of nonreversible systems.
The Journal of Chemical Physics
10.1063/1.5064530
yes
Bernhard Reuter
Konstantin Fackeldey
Konstantin Fackeldey
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
SFB765-C2
2647
2012
eng
141
154
89
conferenceobject
Springer
0
--
--
--
A meshless discretization method for Markov state models applied to explicit water peptide folding simulations
Meshfree Methods for Partial Differential Equations VI
Lecture Notes in Computational Science and Engineering
yes
Konstantin Fackeldey
Alexander Bujotzek
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
Matheon-A19
SFB765-C2
4257
eng
reportzib
0
2013-09-27
2013-09-27
--
Efficient Conformational Analysis by Partition-of-Unity Coupling
Obtaining a sufficient sampling of conformational space is a common problem in molecular simulation. We present the implementation of an umbrella-like adaptive sampling approach based on function-based meshless discretization of conformational space that is compatible with state of the art molecular dynamics code and that integrates an eigenvector-based clustering approach for conformational analysis and the computation of inter-conformational transition rates. The approach is applied to three example systems, namely n-pentane, alanine dipeptide, and a small synthetic host-guest system, the latter two including explicitly modeled solvent.
Math Chem
1438-0064
urn:nbn:de:0297-zib-42570
Alexander Bujotzek
Konstantin Fackeldey
Ole Schütt
Adam Nielsen
Konstantin Fackeldey
Marcus Weber
ZIB-Report
13-58
eng
uncontrolled
Markov State Models
eng
uncontrolled
Meshfree
eng
uncontrolled
Molecular Simulation
eng
uncontrolled
Partition of Unity
MATHEMATICAL SOFTWARE
Markov processes (NEW)
General theory and mathematical aspects
Markov processes
Computational methods
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
BMS-Nielsen
Matheon-A19
MIP_FORMATION
NAMPAR
Salsa-Klimm
SFB1114-A5
SFB765-C2
https://opus4.kobv.de/opus4-zib/files/4257/MolPyPUM.pdf
7021
eng
reportzib
0
--
2018-08-24
--
Spectral Clustering for Non-reversible Markov Chains
Spectral clustering methods are based on solving eigenvalue problems for the identification of clusters, e.g. the identification of metastable subsets of a Markov chain. Usually, real-valued eigenvectors are mandatory for this type of algorithms. The Perron Cluster Analysis (PCCA+) is a well-known spectral clustering method of Markov chains. It is applicable for reversible Markov chains, because reversibility implies a real-valued spectrum. We also extend this spectral clustering method to non-reversible Markov chains and give some illustrative examples. The main idea is to replace the eigenvalue problem by a real-valued Schur decomposition. By this extension non-reversible Markov chains can be analyzed. Furthermore, the chains do not need to have a positive stationary distribution. In addition to metastabilities, dominant cycles and sinks can also be identified. This novel method is called GenPCCA (i.e.
Generalized PCCA), since it includes the case of non reversible processes.
We also apply the method to real world eye tracking data.
1438-0064
urn:nbn:de:0297-zib-70218
01.07.2018
Comp. Appl. Math., pp 1-16, https://doi.org/10.1007/s40314-018-0697-0
Konstantin Fackeldey
Konstantin Fackeldey
Alexander Sikorski
Marcus Weber
ZIB-Report
18-48
eng
uncontrolled
spectral clustering
eng
uncontrolled
Markov chain
eng
uncontrolled
Schur decomposition
eng
uncontrolled
non-reversible
Numerical Linear Algebra
Statistical physics, thermodynamics, and nonlinear dynamical systems (see also 02.50.-r Probability theory, stochastic processes, and statistics)
Canonical forms, reductions, classification
Classification and discrimination; cluster analysis [See also 68T10]
Numerical Mathematics
Fackeldey, Konstantin
Weber, Marcus
NonequiMSM
Sikorski, Alexander
https://opus4.kobv.de/opus4-zib/files/7021/GenPCCA_FSW.pdf
6262
2017
eng
12
146
article
0
--
--
--
Set-Free Markov State Model Building
Journal of Chemical Physics
10.1063/1.4978501
yes
urn:nbn:de:0297-zib-62167
Marcus Weber
Erlinda Körnig
Konstantin Fackeldey
Christof Schütte
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Schütte, Christof
Weber, Marcus
SFB1114-A5
1318
eng
reportzib
0
2011-06-22
2011-06-22
--
Soft Versus Hard Metastable Conformations in Molecular Simulations
Particle methods have become indispensible in conformation dynamics to
compute transition rates in protein folding, binding processes and
molecular design, to mention a few.
Conformation dynamics requires at a decomposition of a molecule's position
space into metastable conformations.
In this paper, we show how this decomposition
can be obtained via the design of either ``soft'' or ``hard''
molecular conformations.
We show, that the soft approach results in a larger metastabilitiy of
the decomposition and is thus more advantegous. This is illustrated
by a simulation of Alanine Dipeptide.
11-27
urn:nbn:de:0297-zib-13189
Konstantin Fackeldey
Konstantin Fackeldey
Susanna Röblitz
Olga Scharkoi
Marcus Weber
ZIB-Report
11-27
deu
uncontrolled
Proteins, Conformation Space, Meshfree Methods
Mathematics of Computing
ATOMIC AND MOLECULAR PHYSICS
NUMERICAL ANALYSIS
BIOLOGY AND OTHER NATURAL SCIENCES
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Röblitz, Susanna
Weber, Marcus
https://opus4.kobv.de/opus4-zib/files/1318/ZR-11-27.pdf
4660
2014
eng
012016
490
article
0
--
--
--
Local Refinements in Classical Molecular Dynamics Simulations
J. Phys. Conf. Ser.
yes
http://iopscience.iop.org/1742-6596/490/1/012016/pdf/1742-6596_490_1_012016.pdf
Marcus Weber
Adam Nielsen
Konstantin Fackeldey
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
Matheon-A19
MIP_FORMATION
Salsa-Klimm
7040
2018
eng
6376
6391
5
37
article
0
--
--
--
Spectral Clustering for Non-Reversible Markov Chains
Spectral clustering methods are based on solving eigenvalue problems for the identification of clusters, e.g., the identification of metastable subsets of a Markov chain. Usually, real-valued eigenvectors are mandatory for this type of algorithms. The Perron Cluster Analysis (PCCA+) is a well-known spectral clustering method of Markov chains. It is applicable for reversible Markov chains, because reversibility implies a real-valued spectrum. We also extend this spectral clustering method to non-reversible Markov chains and give some illustrative examples. The main idea is to replace the eigenvalue problem by a real-valued Schur decomposition. By this extension non-reversible Markov chains can be analyzed. Furthermore, the chains do not need to have a positive stationary distribution. In addition to metastabilities, dominant cycles and sinks can also be identified. This novel method is called GenPCCA (i.e., generalized PCCA), since it includes the case of non-reversible processes. We also apply the method to real-world eye-tracking data.
Computational and Applied Mathematics
https://doi.org/10.1007/s40314-018-0697-0
yes
2018/08/22
urn:nbn:de:0297-zib-70218
Konstantin Fackeldey
Marcus Weber
Alexander Sikorski
Marcus Weber
eng
uncontrolled
Spectral clustering
eng
uncontrolled
Markov chain
eng
uncontrolled
Non-reversible
eng
uncontrolled
Schur decomposition
eng
uncontrolled
GenPCCA
Numerical Mathematics
Fackeldey, Konstantin
Weber, Marcus
EyeTracking
SFB1114-A5
Sikorski, Alexander
7315
2019
eng
904
911
11
45
article
0
--
--
--
Computation of temperature-dependent dissociation rates of metastable protein–ligand complexes
Molecular simulations are often used to analyse the stability of protein–ligand complexes. The stability can be characterised by exit rates or using the exit time approach, i.e. by computing the expected holding time of the complex before its dissociation. However determining exit rates by straightforward molecular dynamics methods can be challenging for stochastic processes in which the exit event occurs very rarely. Finding a low variance procedure for collecting rare event statistics is still an open problem. In this work we discuss a novel method for computing exit rates which uses results of Robust Perron Cluster Analysis (PCCA+). This clustering method gives the possibility to define a fuzzy set by a membership function, which provides additional information of the kind ‘the process is being about to leave the set’. Thus, the derived approach is not based on the exit event occurrence and, therefore, is also applicable in case of rare events. The novel method can be used to analyse the temperature effect of protein–ligand systems through the differences in exit rates, and, thus, open up new drug design strategies and therapeutic applications.
Molecular Simulation
10.1080/08927022.2019.1610949
yes
Natalia Ernst
Konstantin Fackeldey
Konstantin Fackeldey
Andrea Volkamer
Oliver Opatz
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
BB3R
Ernst, Natalia
7893
2021
eng
575
596
59
3
article
Springer
0
--
--
--
Analyzing Raman Spectral Data without Separabiliy Assumption
Raman spectroscopy is a well established tool for the analysis of vibration spectra, which then allow for the determination of individual substances in a chemical sample, or for their phase transitions. In the Time-Resolved-Raman-Sprectroscopy the vibration spectra of a chemical sample are recorded sequentially over a time interval, such that conclusions for intermediate products (transients) can be drawn within a chemical process. The observed data-matrix M from a Raman spectroscopy can be regarded as a matrix product of two unknown matrices W and H, where the first is representing the contribution of the spectra and the latter represents the chemical spectra. One approach for obtaining W and H is the non-negative matrix factorization. We propose a novel approach, which does not need the commonly used separability assumption. The performance of this approach is shown on a real world chemical example.
Journal of Mathematical Chemistry
2007.06428
10.1007/s10910-020-01201-7
yes
2020-11-25
Konstantin Fackeldey
Marcus Weber
Jonas Röhm
Amir Niknejad
Surahit Chewle
Marcus Weber
Numerical Mathematics
Fackeldey, Konstantin
Weber, Marcus
NonequiMSM
Mathematics for Life and Materials Science
Modeling and Simulation of Complex Processes
Chewle, Surahit
7223
2019
eng
012101
012101
11
29
article
0
--
--
--
From metastable to coherent sets - Time-discretization schemes
In this article, we show that these well-established spectral algorithms (like PCCA+, Perron Cluster Cluster Analysis) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-time-discretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.
Chaos: An Interdisciplinary Journal of Nonlinear Science
10.1063/1.5058128
yes
2019-01-28
urn:nbn:de:0297-zib-66074
Konstantin Fackeldey
Marcus Weber
Peter Koltai
Peter Nevir
Henning Rust
Axel Schild
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
SFB1114-A5
8752
2022
eng
13402
12
article
0
--
--
--
Parameter estimation on multivalent ITC data sets
The Wiseman fitting can be used to extract binding parameters from ITC data sets, such as heat of binding, number of binding sites, and the overall dissociation rate. The classical Wiseman fitting assumes a direct binding process and neglects the possibility of intermediate binding steps. In principle, it only provides thermodynamic information and not the kinetics of the process. In this article we show that a concentration dependent dissociation constant could possibly stem from intermediate binding steps. The mathematical form of this dependency can be exploited with the aid of the Robust Perron Cluster Cluster Analysis method. Our proposed extension of the Wiseman fitting rationalizes the concentration dependency, and can probably also be used to determine the kinetic parameters of intermediate binding steps of a multivalent binding process. The novelty of this paper is to assume that the binding rate varies per titration step due to the change of the ligand concentration and to use this information in the Wiseman fitting. We do not claim to produce the most accurate values of the binding parameters, we rather present a novel method of how to approach multivalent bindings from a different angle.
Scientific Reports
10.1038/s41598-022-17188-x
yes
2022-08-04
publish
false
true
Franziska Erlekam
Marcus Weber
Maximilian Zumbansen
Marcus Weber
Weber, Marcus
SFB765-C2
Mathematics for Life and Materials Science
Modeling and Simulation of Complex Processes
5173
2014
eng
318
334
1
12
article
0
--
--
--
Computing the Minimal Rebinding Effect Included in a Given Kinetics
The rebinding effect is a phenomenon which occurs when observing a ligand-receptor binding process. On the macro scale this process comprises the Markov property. This Makovian view is spoiled when switching to the atomistic scale of a binding process. We therefore suggest a model which accurately describes the rebinding effect on the atomistic scale by allowing ''intermediate'' bound states. This allows us to define an indicator for the magnitude of rebinding and to formulate an optimization problem. The results form our examples show good agreement with data form laboratory.
Multiscale Model. Simul.
10.1137/13091124X
yes
urn:nbn:de:0297-zib-17796
Marcus Weber
Adam Nielsen
Konstantin Fackeldey
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
BMS-Nielsen
EyeTracking
Matheon-A19
SFB765-C2
4658
2014
deu
781
804
3
52
article
0
--
--
--
ZIBgridfree: Efficient Conformational Analysis by Partition-of-Unity Coupling
Journal of Mathematical Chemistry
10.1007/s10910-013-0265-1
yes
urn:nbn:de:0297-zib-42570
Alexander Bujotzek
Adam Nielsen
Ole Schütt
Adam Nielsen
Konstantin Fackeldey
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
BMS-Nielsen
Matheon-A19
MIP_FORMATION
NAMPAR
Salsa-Klimm
SFB1114-A5
SFB765-C2
2815
2013
2013
eng
738
756
2
34
article
0
--
--
--
A Square Root Approximation of Transition Rates for a Markov State Model
SIAM. J. Matrix Anal. Appl.
10.1137/120899959
urn:nbn:de:0297-zib-42195
yes
Han Cheng Lie
Konstantin Fackeldey
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
BMS-Nielsen
Matheon-A19
SFB765-C2
4640
2013
eng
110
194
139
article
0
--
--
--
Adaptive spectral clustering with application to tripeptide conformation analysis
The Journal of Chemical Physics
10.1063/1.4830409
yes
Fiete Haack
Adam Nielsen
Konstantin Fackeldey
Susanna Röblitz
Olga Scharkoi
Marcus Weber
Burkhard Schmidt
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Fackeldey, Konstantin
Röblitz, Susanna
Weber, Marcus
BMS-Nielsen
EyeTracking
Matheon-A19
NAMPAR
2637
2012
2012
eng
2623
2635
9
5
article
0
--
--
--
A Coarse Graining Method for the Dimension Reduction of the State Space of Biomolecules
Journal of Mathematical Chemistry
yes
Konstantin Fackeldey
Martina Klimm
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
Matheon-A19
Salsa-Klimm
1779
eng
reportzib
0
2013-02-22
2013-02-22
--
Computing the Minimal Rebinding Effect Included in a Given Kinetics
The rebinding effect is a phenomenon which occurs when observing a ligand-receptor binding process.
On the macro scale this process comprises the Markov property.
This Makovian view is spoiled when switching to the atomistic scale of a binding process.
We therefore suggest a model which accurately describes the rebinding effect on the atomistic scale by allowing ''intermediate'' bound states.
This allows us to define an indicator for the magnitude of rebinding and to formulate an optimization problem.
The results form our examples show good agreement with data form laboratory.
1438-0064
urn:nbn:de:0297-zib-17796
10.1137/13091124X
Appeared in: Multiscale Model. Simul., 12 (2014) 318–334
yes
Marcus Weber
Konstantin Fackeldey
Konstantin Fackeldey
ZIB-Report
13-12
eng
uncontrolled
Rebinding
eng
uncontrolled
Molecular Kinetics
eng
uncontrolled
Conformation Dynamics
Computational Markov chains
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
BMS-Nielsen
EyeTracking
Matheon-A19
SFB765-C2
https://opus4.kobv.de/opus4-zib/files/1779/ZR13-12.pdf
6392
2017
eng
73
81
5/1
article
0
--
--
--
Finding Metastabilities in Reversible Markov Chains based on Incomplete Sampling: Case of Molecular Simulation
Special Matrices
10.1515/spma-2017-0006
yes
Konstantin Fackeldey
Julia Boltze
Amir Niknejad
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
SFB1114-A5
8864
2022
eng
article
0
--
--
--
Qualitative Euclidean embedding of Disjoint Sets of Points
We consider two disjoint sets of points with a distance metric, or a
proximity function, associated with each set. If each set can be separately
embedded into separate Euclidean spaces, then we provide sufficient conditions
for the two sets to be jointly embedded in one Euclidean space. In this joint
Euclidean embedding, the distances between the points are generated by a
specific relation-preserving function. Consequently, the mutual distances
between two points of the same set are specific qualitative transformations of
their mutual distances in their original space; the pairwise distances between
the points of different sets can be constructed from an arbitrary proximity
function (might require scaling).
https://arxiv.org/abs/2212.00058
no
publish
false
false
Creative Commons - CC BY-NC-SA - Namensnennung - Nicht kommerziell - Weitergabe unter gleichen Bedingungen 4.0 International
N. Alexia Raharinirina
N. Alexia Raharinirina
Konstantin Fackeldey
Marcus Weber
Fackeldey, Konstantin
Weber, Marcus
Modeling and Simulation of Complex Processes
MathPlus EF5-4_Ancient-Egyptian
8257
2021
eng
researchdata
0
--
--
--
Different Tools and Results for Correspondence Analysis
This is a list of codes generated from ancient egyptian texts. The codes are used for a correspondence analysis (CA). Codes and CA software are available from the linked webpage.
10.12752/8257
A detailed description of the software can be found in the code repository at https://github.com/AlexiaNomena/Correspondence_Analysis_User_Friendly (repository version of CA software might include updates).
no
Collection
publish
https://www.zib.de/ext-data/correspondence/
N. Alexia Raharinirina
N. Alexia Raharinirina
Marcus Weber
Ralph Birk
Konstantin Fackeldey
Sarah M. Klasse
Tonio Sebastian Richter
Numerical Mathematics
Fackeldey, Konstantin
Weber, Marcus
Mathematics for Life and Materials Science
Modeling and Simulation of Complex Processes
MathPlus EF5-4_Ancient-Egyptian
Klasse, Sarah Michelle
9101
2023
deu
T1/2023
book
DWA / GDCh
0
--
--
--
Handlungsempfehlung zur integrativen Bewertung der weitergehenden Abwasserbehandlung von kommunalen Kläranlagen
Das vorliegende Statuspapier beschreibt ein Konzept zur weitergehenden Abwasserbehandlung für
die Bewertung von Aufbereitungsverfahren, sowohl in einer Pilotphase zur Auswahl von Verfah-
rensoptionen als auch für die Bewertung großtechnischer Anlagen.
978-3-96862-563-8
DWA-Themen
yes
publish
Thomas Ternes
Marcus Weber
Christian Wilhelm
Karl-Heinz Bauer
Frank Brauer
Jörg Drewes
Adriano Joss
Georg Hiller
Kevin Jewell
Jörg Oehlmann
Michael Radke
Ulrike Schulte-Oehlmann
Thomas Schwartz
Peter Seel
Jeanette Völker
Lilo Weber
Marcus Weber
Weber, Marcus
MathPlusAA1-1
Modeling and Simulation of Complex Processes
MathPlusAA1-15
8711
2022
deu
40
43
1
article
0
--
--
--
Die mathematische Forschungsdateninitiative in der NFDI: MaRDI (Mathematical Research Data Initiative)
GAMM Rundbrief
no
Peter Benner
Marco Reidelbach
Michael Burger
Dominik Göddeke
Christiane Görgen
Christian Himpe
Jan Heiland
Thomas Koprucki
Mario Ohlberger
Stephan Rave
Marco Reidelbach
Jens Saak
Anita Schöbel
Karsten Tabelow
Marcus Weber
Weber, Marcus
Modeling and Simulation of Complex Processes
Reidelbach, Marco
MaRDI-TA4
8382
2021
eng
e202100102
21
article
0
--
--
--
MSM building and projection for the analysis of time-resolved spectra
Understanding the kinetics between the components of time-resolved spectra is a crucial step in the study of photo-activatedprocesses. However, modeling the kinetics requires usually some a priori knowledge about the system. In our approach, webuild a Markov State Model (MSM) from the spectral data, and obtain a Koopman transition matrix K(t). With genPCCA,an invariant subspace projection, we project the process into its metastable components. The result of the application of gen-PCCA is a transition matrix Kc(t), from which we can read the transition probability between the metastable components of the reaction. We discuss the application of this analysis method to the transient absorption spectrum of brominated Al-corrole
Proceedings in Applied Mathematics and Mechanics
https://doi.org/10.1002/pamm.202100102
https://onlinelibrary.wiley.com/doi/10.1002/pamm.202100102
yes
2021-09-20
publish
Renata Sechi
Marcus Weber
Marcus Weber
Karsten Heyne
Computational Molecular Design
Weber, Marcus
SFB1114-A5
Modeling and Simulation of Complex Processes
8015
2020
2021
eng
758
774
2
19
article
SIAM
0
2021-04-27
--
--
Estimation of the Koopman Generator by Newton's Extrapolation
This article addresses the problem of estimating the Koopman generator of a Markov process. The direct computation of the infinitesimal generator is not easy because of the discretization of the state space, in particular because of the trade-off inherent in the choice of the best lag time to study the process. Short lag times implies a strong discretization of the state space and a consequent loss of Markovianity. Large lag times bypass events on fast timescales. We propose a method to approximate the generator with the computation of the Newton polynomial extrapolation. This technique is a multistep approach which uses as its input Koopman transfer operators evaluated for a series of lag times. Thus, the estimated infinitesimal generator combines information from different time resolutions and does not bias only fast- or slow-decaying dynamics. We show that the multi-scale Newton method can improve the estimation of the generator in comparison to the computation using finite difference or matrix logarithm methods.
Multiscale Modeling and Simulation
10.1137/20M1333006
yes
2021-02-09
Renata Sechi
Alexander Sikorski
Alexander Sikorski
Marcus Weber
Numerical Mathematics
Weber, Marcus
SFB1114-A5
Sikorski, Alexander
Modeling and Simulation of Complex Processes
6709
2018
eng
7
article
0
--
--
--
Mathematical modeling of the spreading of innovations in the ancient world
eTopoi. Journal for Ancient Studies
ISSN 2192-2608
10.17171/4-7-1
yes
http://journal.topoi.org/index.php/etopoi/index
Natasa Djurdjevac Conrad
Erlinda Koernig
Daniel Fuerstenau
Ana Grabundzija
Luzie Helfmann
Martin Park
Wolfram Schier
Brigitta Schütt
Christof Schütte
Marcus Weber
Niklas Wulkow
Johannes Zonker
Numerical Mathematics
Schütte, Christof
Weber, Marcus
Conrad, Natasa
Helfmann, Luzie
Zonker, Johannes
INNOSPREAD
9228
2023
eng
6737
6746
Crystal Growth & Design
9
23
article
American Chemical Society
0
2023-08-15
2023-09-06
--
Revealing Kinetics of Paracetamol Crystallization Using Time-Resolved Raman Spectroscopy, Orthogonal Time-Lapse Photography, and Non-Negative Matrix Factorization (OSANO)
Crystallization is a complex phenomenon with far-reaching implications for the production and formulation of active pharmaceutical ingredients. Understanding this process is critical for achieving control over key physicochemical properties that can affect, for example, the bioavailability and stability of a drug. In this study, we were able to reveal intricate and diverse dynamics of the formation of metastable intermediates of paracetamol crystallization varying with the choice of solvent. We demonstrate the efficacy of our novel approach utilizing an objective function-based non-negative matrix factorization technique for the analysis of time-resolved Raman spectroscopy data, in conjunction with time-lapse photography. Furthermore, we emphasize the crucial importance of integrating Raman spectroscopy with supplementary experimental instrumentation for the mathematical analysis of the obtained spectra.
Crystal Growth & Design
10.1021/acs.cgd.3c00617
yes
2023-08-15
publish
Surahit Chewle
Surahit Chewle
Marcus Weber
Franziska Emmerling
Weber, Marcus
Import
Modeling and Simulation of Complex Processes
Chewle, Surahit
CCMAI
Zuse Institute Berlin (ZIB)
4316
eng
reportzib
0
2013-11-26
2013-11-26
--
On a Generalized Transfer Operator
We introduce a generalized operator for arbitrary stochastic processes by using a pre-kernel, which is a generalization of the Markov kernel. For deterministic processes, such an operator is already known as the Frobenius-Perron operator, which is defined for a large class of measures. For Markov processes, there exists transfer operators being only well defined for stationary measures in $L^2$. Our novel generalized transfer operator is well defined for arbitrary stochastic processes, in particular also for deterministic ones. We can show that this operator is acting on $L^1$. For stationary measures, this operator is also an endomorphism of $L^2$ and, therefore, allows for a mathematical analysis in Hilbert spaces.
1438-0064
urn:nbn:de:0297-zib-43162
Adam Nielsen
Konstantin Fackeldey
Konstantin Fackeldey
Marcus Weber
ZIB-Report
13-74
eng
uncontrolled
Transfer Operator
eng
uncontrolled
Pre Kernel
eng
uncontrolled
Perron Frobenius Generalization
Stochastic processes (NEW)
Electronic structure of atoms and molecules: theory
DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
Applications in probability theory and statistics
Stochastic processes
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
BMS-Nielsen
EyeTracking
Matheon-A19
https://opus4.kobv.de/opus4-zib/files/4316/NFW_13.pdf
2116
2011
2011
eng
bookpart
InTech
0
--
--
--
A rapidly Mixing Monte Carlo Method for the Simulation of Slow Molecular Processes
Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science
yes
Vedat Durmaz
Ch. Mode
Konstantin Fackeldey
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Durmaz, Vedat
Fackeldey, Konstantin
Weber, Marcus
8507
2021
deu
40
46
11
article
0
--
2021-10-13
--
Neue Medikamente dank Supercomputern
Die aktuelle Pandemie verdeutlicht, wie wichtig es ist, rasch geeignete Arzneimittel zu finden. In Computersimulationen gelingt das erheblich schneller als im Labor. Gegen das Coronavirus ließen sich auf diese Weise bereits Wirkstoffkandidaten identifizieren.
Spektrum der Wissenschaft
publish
no
Konstantin Fackeldey
Konstantin Fackeldey
Christoph Gorgulla
Marcus Weber
Numerical Mathematics
Fackeldey, Konstantin
Weber, Marcus
BB3R
Modeling and Simulation of Complex Processes
Gorgulla, Christoph
4219
eng
reportzib
0
2013-08-28
2013-08-28
--
A square root approximation of transition rates for a Markov State Model
Trajectory- or mesh-based methods for analyzing the dynamical behavior of large molecules tend to be impractical due to the curse of dimensionality - their computational cost increases exponentially with the size of the molecule. We propose a method to break the curse by a novel square root approximation of transition rates, Monte Carlo quadrature and a discretization approach based on solving linear programs. With randomly sampled points on the molecular energy landscape and randomly generated discretizations of the molecular configuration space as our initial data, we construct a matrix describing the transition rates between adjacent discretization regions. This transition rate matrix yields a Markov State Model of the molecular dynamics. We use Perron cluster analysis and coarse-graining techniques in order to identify metastable sets in configuration space and approximate the transition rates between the metastable sets. Application of our method to a simple energy landscape on a two-dimensional configuration space provides proof of concept and an example for which we compare the performance of different discretizations. We show that the computational cost of our method grows only polynomially with the size of the molecule. However, finding discretizations of higher-dimensional configuration spaces in which metastable sets can be identified remains a challenge.
1438-0064
10.1137/120899959
urn:nbn:de:0297-zib-42195
Appeared in: SIAM J. Matrix Anal. Appl. 34 (2013) pp. 738 - 756
Han Cheng Lie
Konstantin Fackeldey
Konstantin Fackeldey
Marcus Weber
ZIB-Report
13-43
eng
uncontrolled
Markov State Models
eng
uncontrolled
Markov chains
eng
uncontrolled
meshfree methods
eng
uncontrolled
metastability
eng
uncontrolled
Voronoi
eng
uncontrolled
linear programming
Mathematics of Computing
ATOMIC AND MOLECULAR PHYSICS
Markov chains (discrete-time Markov processes on discrete state spaces)
Computational methods in Markov chains [See also 65C40]
Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
BMS-Nielsen
Matheon-A19
SFB765-C2
https://opus4.kobv.de/opus4-zib/files/4219/zibtitlepage.pdf
6607
eng
reportzib
0
--
2017-12-08
--
From Metastable to Coherent Sets - time-discretization schemes
Given a time-dependent stochastic process with trajectories x(t) in a space $\Omega$, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable sets M are defined in space $M\subset\Omega$, coherent sets $M(t)\subset\Omega$ are defined in space and time. Hence, if we extend the space by the time-variable t, coherent sets are metastable sets in $\Omega\times[0,\infty]$. This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article we show that these well-established spectral algorithms (like PCCA+) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-timediscretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.
1438-0064
urn:nbn:de:0297-zib-66074
Konstantin Fackeldey
Paulina Bressel
Péter Koltai
Peter Névir
Henning Rust
Axel Schild
Marcus Weber
ZIB-Report
17-74
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
SFB1114-A5
https://opus4.kobv.de/opus4-zib/files/6607/ZIB-Report_17-74.pdf
6922
2018
2018
eng
3579
3594
7
14
article
0
2018-05-29
2018-07-10
--
Generalized Markov State Modeling Method for Nonequilibrium Biomolecular Dynamics: Exemplified on Amyloid β Conformational Dynamics Driven by an Oscillating Electric Field
Markov state models (MSMs) have received an unabated increase in popularity in recent years, as they are very
well suited for the identification and analysis of metastable states and related kinetics. However, the state-of-the-art Markov state modeling methods and tools enforce the fulfillment of a
detailed balance condition, restricting their applicability to equilibrium MSMs. To date, they are unsuitable to deal with
general dominant data structures including cyclic processes, which are essentially associated with nonequilibrium systems.
To overcome this limitation, we developed a generalization of the common robust Perron Cluster Cluster Analysis (PCCA+) method, termed generalized PCCA (G-PCCA). This method handles equilibrium and nonequilibrium simulation data, utilizing Schur vectors instead of eigenvectors. G-PCCA is not limited to the detection of metastable states but enables the identification of dominant structures in a general sense, unraveling cyclic processes. This is exemplified by application of G-PCCA on nonequilibrium molecular dynamics data of the Amyloid β (1−40) peptide, periodically driven by an oscillating electric field.
Journal of Chemical Theory and Computation
10.1021/acs.jctc.8b00079
yes
29.05.2018
Bernhard Reuter
Bernhard Reuter
Marcus Weber
Konstantin Fackeldey
Susanna Röblitz
Martin E. Garcia
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Röblitz, Susanna
Weber, Marcus
NonequiMSM
6216
eng
reportzib
0
--
2017-03-03
--
Set-free Markov State Building
Molecular dynamics (MD) simulations face challenging problems since
the timescales of interest often are much longer than what is possible
to simulate and even if sufficiently long simulation are possible the complex
nature of the resulting simulation data makes interpretation difficult.
Markov State Models (MSMs) help to overcome these problems by making
experimentally relevant timescales accessible via coarse grained representations
that also allows for convenient interpretation. However, standard
set-based MSMs exhibit some caveats limiting their approximation quality
and statistical significance. One of the main caveats results from the fact
that typical MD trajectories repeatedly re-cross the boundary between
the sets used to build the MSM which causes statistical bias in estimating
the transition probabilities between these sets. In this article, we present
a set-free approach to MSM building utilizing smooth overlapping ansatz
functions instead of sets and an adaptive refinement approach. This kind
of meshless discretization helps to overcome the recrossing problem and
yields an adaptive refinement procedure that allows to improve the quality
of the model while exploring state space and inserting new ansatz
functions into the MSM.
1438-0064
urn:nbn:de:0297-zib-62167
10.1063/1.4978501
Appeared in: Journal of Chemical Physics 146/12 (2017)
Marcus Weber
Julia Boltze
Konstantin Fackeldey
Christof Schütte
ZIB-Report
17-10
Numerical Mathematics
Fackeldey, Konstantin
Schütte, Christof
Weber, Marcus
SFB1114-A5
https://opus4.kobv.de/opus4-zib/files/6216/ZR-17-10.pdf
4653
2011
deu
899
909
article
0
--
--
--
Soft Versus Hard Metastable Conformations in Molecular Simulations
Particle Methods II, Fundamentals and Applications, Barcelona, Spain 26-28 Oct. 2011, E. Onate and D.R.J. Owen (eds.)
yes
urn:nbn:de:0297-zib-13189
Adam Nielsen
Konstantin Fackeldey
Susanna Röblitz
O. Scharkoi
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
6395
2017
eng
70
80
article
0
--
--
--
GenPCCA -- Markov State Models for Non-Equilibrium Steady States
Big data clustering: Data preprocessing, variable selection, and dimension reduction. WIAS Report No. 29
10.20347/WIAS.REPORT.29
Yes
Konstantin Fackeldey
Julia Boltze
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
SFB1114-A5
5172
2014
eng
102
111
3
2
article
0
--
--
--
Investigation of the Ergopeptide Epimerization Process
Ergopeptides, like ergocornine and a-ergocryptine, exist in an S- and in an R-configuration. Kinetic experiments imply that certain configurations are preferred depending on the solvent. The experimental methods are explained in this article. Furthermore, computational methods are used to understand this configurational preference. Standard quantum chemical methods can predict the favored configurations by using minimum energy calculations on the potential energy landscape. However, the explicit role of the solvent is not revealed by this type of methods. In order to better understand its influence, classical mechanical molecular simulations are applied. It appears from our research that “folding” the ergopeptide molecules into an intermediate state (between the S- and the R-configuration) is mechanically hindered for the preferred configurations.
Computation
10.3390/computation2030102
yes
Karsten Andrae
Adam Nielsen
Stefan Merkel
Vedat Durmaz
Konstantin Fackeldey
Robert Köppen
Marcus Weber
Matthias Koch
Numerical Mathematics
Computational Molecular Design
Durmaz, Vedat
Fackeldey, Konstantin
Weber, Marcus
BAM-Ergoline
4645
2013
deu
561
557
7
62
article
Springer
0
--
--
--
Medizin aus dem Computer
Der Anaesthesist
10.1007/s00101-013-2202-x
no
Karsten Andrae
Adam Nielsen
Vedat Durmaz
Konstantin Fackeldey
Olga Scharkoi
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Durmaz, Vedat
Fackeldey, Konstantin
Weber, Marcus
NAMPAR
Salsa-Klimm
TransRisk
2816
2013
2013
eng
2567
2572
6
19
article
0
--
--
--
Conformational Analysis of Alternariol on the Quantum Level
J. Mol. Model.
10.1007/s00894-013-1803-2
yes
Olga Scharkoi
Konstantin Fackeldey
Igor Merkulow
Karsten Andrae
Marcus Weber
Irene Nehls
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
BAM-ZEN
4972
eng
reportzib
0
--
2014-04-23
--
Applications of the cross-entropy method to importance sampling and optimal control of diffusions
We study the cross-entropy method for diffusions. One of the results is a versatile cross-entropy algorithm that can be used to design efficient importance sampling strategies for rare events or to solve optimal control problems. The approach is based on the minimization of a suitable cross-entropy functional, with a parametric family of exponentially tilted probability distributions. We illustrate the new algorithm with several numerical examples and discuss algorithmic issues and possible extensions of the method.
1438-0064
urn:nbn:de:0297-zib-49720
10.1137/14096493X
yes
Appeared in: Siam Journal on Scientific Computing 36 (2014) A 2654-A2672
Wei Zhang
Erlinda Körnig
Han Wang
Carsten Hartmann
Marcus Weber
Christof Schütte
ZIB-Report
14-10
eng
uncontrolled
important sampling
eng
uncontrolled
optimal control
eng
uncontrolled
cross-entropy method
eng
uncontrolled
rare events
eng
uncontrolled
change of measure
Monte Carlo methods
Optimal stochastic control
Measures of information, entropy
Numerical Mathematics
Schütte, Christof
Weber, Marcus
NonequiMSM
SFB1114-A5
https://opus4.kobv.de/opus4-zib/files/4972/ZIB-Report_14-10.pdf
6177
2017
eng
1
52
article
0
--
--
--
Importance sampling in path space for diffusion processes with slow-fast variables
Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sampling in the framework of diffusion process and consider the change of measure which is realized by adding a control force to the original dynamics. For certain exponential type expectation, the corresponding control force of the optimal change of measure leads to a zero-variance estimator and is related to the solution of a Hamilton–Jacobi–Bellmann equation. We focus on certain diffusions with both slow and fast variables, and the main result is that we obtain an upper bound of the relative error for the importance sampling estimators with control obtained from the limiting dynamics. We demonstrate our approximation strategy with an illustrative numerical example.
Probability Theory and Related Fields
10.1007/s00440-017-0755-3
http://rdcu.be/oA51
If you are not subscribing to the journal please use the http link below as part of the Springer Nature SharedIt initiative
yes
Carsten Hartmann
Regine Kossick
Christof Schütte
Marcus Weber
Wei Zhang
Numerical Mathematics
Computational Molecular Design
Schütte, Christof
Weber, Marcus
NonequiMSM
SFB1114-A5
5167
2014
eng
A2654
A2672
6
36
article
0
--
--
--
Applications of the cross-entropy method to importance sampling and optimal control of diffusions
Siam Journal on Scientific Computing
10.1137/14096493X
yes
urn:nbn:de:0297-zib-49720
Wei Zhang
Erlinda Körnig
Han Wang
Carsten Hartmann
Marcus Weber
Christof Schütte
Numerical Mathematics
Computational Molecular Design
Schütte, Christof
Weber, Marcus
MIP_FORMATION
NonequiMSM
SFB1114-A5
8869
2023
eng
40
47
130
article
0
2023-09-21
--
--
Research-Data Management Planning in the German Mathematical Community
In this paper we discuss the notion of research data for the field of mathematics and report on the status quo of research-data management and planning. A number of decentralized approaches are presented and compared to needs and challenges faced in three use cases from different mathematical subdisciplines. We highlight the importance of tailoring research-data management plans to mathematicians’ research processes and discuss their usage all along the data life cycle.
Eur. Math. Soc. Mag.
10.4171/mag/152
yes
epub ahead of print
publish
Tobias Boege
Christiane Görgen
René Fritze
Christiane Görgen
Jeroen Hanselmann
Dorothea Iglezakis
Lars Kastner
Thomas Koprucki
Tabea Krause
Christoph Lehrenfeld
Silvia Polla
Marco Reidelbach
Christian Riedel
Jens Saak
Björn Schembera
Karsten Tabelow
Marcus Weber
Weber, Marcus
Modeling and Simulation of Complex Processes
Reidelbach, Marco
MaRDI-TA4
8586
2021
eng
article
0
--
--
--
Inferring cultural and social processes based on patterns of statistical relationships between Synodal texts
In this paper, we explore the relationship patterns between Ancient Egyptian texts of the corpus ``Synodal decrees'', which are originating between 243 and 185 BCE, during the Ptolemaic period. Particularly, we are interested in analyzing the grammatical features of the different texts. Conventional data analysis methods such as correspondence Analysis are very useful to explore the patterns of statistical interdependence between categories of variables. However, it is based on a PCA-like dimension-reduction method and turned out to be unsuitable for our dataset due to the high dimensionality of our data representations. Additionally, the similarity between pairs of texts and pairs of grammatical features is observed through the distance between their representation, but the degree of association between a particular grammatical feature and a text is not. Here, we applied a qualitative Euclidean embedding method that provides a new Euclidean representation of the categories of variables. This new representation of the categories is constructed in such a way that all the patterns of statistical interdependence, similarity, and association, are seen through the Euclidean distance between them. Nevertheless, the PCA-like dimension-reduction method also performed poorly on our new representation. Therefore, we obtained a two-dimensional visualization using non-linear methods such UMAP or t-SNE. Although these dimension-reduction methods reduced the interpretability of interpoint distances, we were still able to identify important similarity patterns between the Synodal text as well as their association patterns with the grammatical features.
yes
in progress
publish
false
true
Ralph Birk
N. Alexia Raharinirina
N. Alexia Raharinirina
Konstantin Fackeldey
Tonio Sebastian Richter
Marcus Weber
Fackeldey, Konstantin
Weber, Marcus
Sunkara, Vikram
Modeling and Simulation of Complex Processes
MathPlus EF5-4_Ancient-Egyptian
9158
2023
eng
23
article
0
2023-10-04
--
--
Efficient Estimation of Transition Rates as Functions of pH
Extracting the kinetic properties of a system whose dynamics depend on the pH of the environment with which it exchanges energy and atoms requires sampling the Grand Canonical Ensemble. As an alternative, we present a novel strategy that requires simulating only the most recurrent Canonical Ensembles that compose the Grand Canonical Ensemble. The simulations are used to estimate the Gran Canonical distribution for a specific pH value by reweighting and to construct the transition rate matrix by discretizing the Fokker-Planck equation by Square Root Approximation and robust Perron Cluster Cluster Analysis. As an application, we have studied the tripeptide Ala-Asp-Ala.
Proceedings in Applied Mathematics & Mechanics
2307.04439
10.1002/pamm.202300264
publish
yes
epub ahead of print
Luca Donati
Luca Donati
Marcus Weber
Weber, Marcus
Modeling and Simulation of Complex Processes
MathPlusAA1-15
Donati, Luca
9066
2023
2024
eng
367
385
62
article
0
2023-11-14
--
--
Augmented ant colony algorithm for virtual drug discovery
Docking is a fundamental problem in computational biology and drug discovery that seeks to predict a ligand’s binding mode and affinity to a target protein. However, the large search space size and the complexity of the underlying physical interactions make docking a challenging task. Here, we review a docking method, based on the ant colony optimization algorithm, that ranks a set of candidate ligands by solving a minimization problem for each ligand individually. In addition, we propose an augmented version that takes into account all energy functions collectively, allowing only one minimization problem to be solved. The results show that our modification outperforms in accuracy and efficiency.
Journal of Mathematical Chemistry
10.1007/s10910-023-01549-6
epub ahead of print
publish
yes
Luca Donati
Luca Donati
Konstantin Fackeldey
Marcus Weber
Fackeldey, Konstantin
Weber, Marcus
Modeling and Simulation of Complex Processes
AI in Society, Science, and Technology
Parallel and Distributed Computing
MathPlusAA1-15
Donati, Luca
9452
2024
eng
article
0
--
--
--
The Kramers turnover in terms of a macro-state projection on phase space
We analyze how Langevin dynamics is affected by the friction coefficient using an invariant subspace projection of the associated Koopman operator. This provides the friction-dependent metastable macro-states of the dynamical system as well as the transition rates in the entire phase space. We used the algorithm ISOKANN for a wide range of friction coefficient values and reproduced results consistent with the Kramers turnover.
Submitted to Molecular Physics
10.48550/arXiv.2402.00211
yes
under review
publish
Luca Donati
Luca Donati
Christof Schütte
Marcus Weber
Schütte, Christof
Weber, Marcus
SFB-1114-B3
Modeling and Simulation of Complex Processes
MathPlusAA1-15
Donati, Luca
9027
2023
eng
15
article
0
--
--
--
Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists
Opioids are essential pharmaceuticals due to their analgesic properties, however, lethal side effects, addiction, and opioid tolerance are extremely challenging. The development of novel molecules targeting the μ-opioid receptor (MOR) in inflamed, but not in healthy tissue, could significantly reduce these unwanted effects. Finding such novel molecules can be achieved by maximizing the binding affinity to the MOR at acidic pH while minimizing it at neutral pH, thus combining two conflicting objectives. Here, this multi-objective optimal affinity approach is presented, together with a virtual drug discovery pipeline for its practical implementation. When applied to finding pH-specific drug candidates, it combines protonation state-dependent structure and ligand preparation with high-throughput virtual screening. We employ this pipeline to characterize a set of MOR agonists identifying a morphine-like opioid derivative with higher predicted binding affinities to the MOR at low pH compared to neutral pH. Our results also confirm existing experimental evidence that NFEPP, a previously described fentanyl derivative with reduced side effects, and recently reported β-fluorofentanyls and -morphines show an increased specificity for the MOR at acidic pH when compared to fentanyl and morphine. We further applied our approach to screen a >50K ligand library identifying novel molecules with pH-specific predicted binding affinities to the MOR. The presented differential docking pipeline can be applied to perform multi-objective affinity optimization to identify safer and more specific drug candidates at large scale.
Journal of Cheminformatics
10.1186/s13321-023-00746-4
publish
yes
2023-08-23
Christopher Secker
Ekaterina Engel
Konstantin Fackeldey
Marcus Weber
Sourav Ray
Christoph Gorgulla
Christof Schütte
Numerical Mathematics
Fackeldey, Konstantin
Schütte, Christof
Weber, Marcus
MODAL-MedLab
SFB1114-C3
MODAL-Gesamt
Modeling and Simulation of Complex Processes
Mathematical Algorithmic Intelligence
Parallel and Distributed Computing
Gorgulla, Christoph
MathPlusAA1-15
Secker, Christopher
8274
2023
eng
607
13
article
0
--
2023-01-12
--
Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design
We previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. The design process of NFEPP was based on mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands, recognizing that GPCRs function differently under pathological versus healthy conditions. We now present an additional and novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels and their dependence on parameters of inflamed and healthy tissue (pH, radicals). The model is validated against in vitro experimental data for the ligands NFEPP and fentanyl at different pH values and radical concentrations. We observe markedly reduced binding affinity and calcium channel inhibition for NFEPP at normal pH compared to lower pH, in contrast to the effect of fentanyl. For increasing radical concentrations, we find enhanced constitutive G-protein activation but reduced ligand binding affinity. Assessing the different effects, the results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.
Scientific Reports
10.1038/s41598-023-27699-w
yes
publish
2023-01-06
Arne Thies
Erlinda Körnig
Vikram Sunkara
Sourav Ray
Hanna Wulkow
M. Özgür Celik
Fatih Yergöz
Christof Schütte
Christoph Stein
Marcus Weber
Stefanie Winkelmann
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Schütte, Christof
Weber, Marcus
SFB1114-C3
Winkelmann, Stefanie
Sunkara, Vikram
MathPlusAA1-1
Mathematics for Life and Materials Science
Modeling and Simulation of Complex Processes
MathPlusAA1-15
7939
2020
2020
eng
1443
1452
18
46
article
Taylor and Francis
0
2020-11-08
2020-11-08
--
How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs
Molecular simulations of ligand–receptor interactions are a computational challenge, especially when their association- (‘on’-rate) and dissociation- (‘off’-rate) mechanisms are working on vastly differing timescales. One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)-N-phenyl propionamide (NFEPP) in a μ-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab.
Molecular Simulation
10.1080/08927022.2020.1839660
yes
publish
urn:nbn:de:0297-zib-78437
Sourav Ray
Erlinda Körnig
Vikram Sunkara
Christof Schütte
Marcus Weber
Numerical Mathematics
Schütte, Christof
Weber, Marcus
MODAL-MedLab
Sunkara, Vikram
MODAL-Gesamt
Mathematics for Life and Materials Science
Modeling and Simulation of Complex Processes
8886
2023
eng
263
275
2
3
article
0
--
--
--
Coarse Grained MD Simulations of Opioid interactions with the µ-opioid receptor and the surrounding lipid membrane
In our previous studies, a new opioid (NFEPP) was developed to only selectively bind to the 𝜇-opoid receptor (MOR) in inflamed tissue and thus avoid the severe side effects of fentanyl. We know that NFEPP has a reduced binding affinity to MOR in healthy tissue. Inspired by the modelling and simulations performed by Sutcliffe et al., we present our own results of coarse-grained molecular dynamics simulations of fentanyl and NFEPP with regards to their interaction with the 𝜇-opioid receptor embedded within the lipid cell membrane. For technical reasons, we have slightly modified Sutcliffe’s parametrisation of opioids. The pH-dependent opioid simulations are of interest because while fentanyl is protonated at the physiological pH, NFEPP is deprotonated due to its lower pKa value than that of fentanyl. Here, we analyse for the first time whether pH changes have an effect on the dynamical behaviour of NFEPP when it is inside the cell membrane. Besides these changes, our analysis shows a possible alternative interaction of NFEPP at pH 7.4 outside the binding region of the MOR. The interaction potential of NFEPP with MOR is also depicted by analysing the provided statistical molecular dynamics simulations with the aid of an eigenvector analysis of a transition rate matrix. In our modelling, we see differences in the XY-diffusion profiles of NFEPP compared with fentanyl in the cell membrane.
Biophysica
10.3390/biophysica3020017
yes
publish
Sourav Ray
Marcus Weber
Konstantin Fackeldey
Christoph Stein
Marcus Weber
Fackeldey, Konstantin
Weber, Marcus
MathPlusAA1-1
Modeling and Simulation of Complex Processes
Mathematical Algorithmic Intelligence
Parallel and Distributed Computing
MathPlusAA1-15
7961
2020
eng
114109
11
153
article
0
--
--
--
ISOKANN: Invariant subspaces of Koopman operators learned by a neural network
The problem of determining the rate of rare events in dynamical systems is quite well-known but still difficult to solve. Recent attempts to overcome this problem exploit the fact that dynamic systems can be represented by a linear operator, such as the Koopman operator. Mathematically, the rare event problem comes down to the difficulty in finding invariant subspaces of these Koopman operators K. In this article, we describe a method to learn basis functions of invariant subspaces using an artificial neural Network.
The Journal of Chemical Physics
10.1063/5.0015132
yes
Robert Julian Rabben
Marcus Weber
Sourav Ray
Marcus Weber
Numerical Mathematics
Weber, Marcus
Rabben, Robert Julian
MathPlusAA1-1
Modeling and Simulation of Complex Processes
8279
eng
reportzib
0
--
2021-07-07
--
Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design
Initiated by mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands in normal versus diseased (inflamed) environments, we previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. Uniquely, this design recognised that GPCRs function differently under pathological versus healthy conditions.
We now present a novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels associated with parameters of inflamed tissue (pH, radicals). By means of molecular dynamics simulations, we also assessed qualitative changes of the reaction rates due to additional disulfide bridges inside the GPCR binding pocket and used these rates for stochastic simulations of the corresponding reaction jump process.
The modelling results were validated with in vitro experiments measuring calcium currents and G-protein activation.
We found markedly reduced G-protein dissociation and calcium channel inhibition induced by NFEPP at normal pH, and enhanced constitutive G-protein activation but lower probability of ligand binding with increasing radical concentrations.
These results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.
1438-0064
urn:nbn:de:0297-zib-82797
publish
Sourav Ray
Stefanie Winkelmann
Arne Thies
Vikram Sunkara
Hanna Wulkow
Özgür Celik
Fatih Yergöz
Christof Schütte
Christoph Stein
Marcus Weber
Stefanie Winkelmann
ZIB-Report
21-19
Numerical Mathematics
Schütte, Christof
Weber, Marcus
Winkelmann, Stefanie
Sunkara, Vikram
MathPlusAA1-1
Modeling and Simulation of Complex Processes
https://opus4.kobv.de/opus4-zib/files/8279/ZIB-Report.pdf
7843
eng
reportzib
0
--
2020-06-03
--
How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs
Molecular simulations of ligand-receptor interactions are a computational challenge, especially when their association- (``on''-rate) and dissociation- (``off''-rate) mechanisms are working on vastly differing timescales. In addition, the timescale of the simulations themselves is, in practice, orders of magnitudes smaller than that of the mechanisms; which further adds to the complexity of observing these mechanisms, and of drawing meaningful and significant biological insights from the simulation.
One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)- N-phenyl propionamide (NFEPP) in a $\mu$-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab, who investigated the influence of pH on the inhibitory constant of fentanyl and NFEPP (Spahn et al. 2017).
MD simulations are far more accessible and cost-effective than in vitro and in vivo studies. Especially in the context of the current opioid crisis, MD simulations can aid in unravelling molecular functionality and assist in clinical decision-making; the approaches presented in this paper are a pertinent step forward in this direction.
1438-0064
10.1080/08927022.2020.1839660
urn:nbn:de:0297-zib-78437
Molecular Simulation, 46:18, 1443-1452
Vikram Sunkara
Sourav Ray
Vikram Sunkara
Christof Schütte
Marcus Weber
ZIB-Report
20-18
eng
uncontrolled
Opioid, Ligand-Receptor Interaction, Binding Kinetics, Molecular Dynamics, Metadynamics, SQRA
Schütte, Christof
Weber, Marcus
Sunkara, Vikram
MathPlusAA1-1
MathPlus - AA6
Modeling and Simulation of Complex Processes
https://opus4.kobv.de/opus4-zib/files/7843/Ray et al_06_2020.pdf
9555
2024
eng
article
0
--
--
--
Capturing the Macroscopic Behaviour of Molecular Dynamics with Membership Functions
Markov processes serve as foundational models in many scientific disciplines,
such as molecular dynamics, and their simulation forms a common basis for
analysis. While simulations produce useful trajectories, obtaining macroscopic
information directly from microstate data presents significant challenges. This
paper addresses this gap by introducing the concept of membership functions
being the macrostates themselves. We derive equations for the holding times of
these macrostates and demonstrate their consistency with the classical definition.
Furthermore, we discuss the application of the ISOKANN method for learning
these quantities from simulation data. In addition, we present a novel method
for extracting transition paths based on the ISOKANN results and demonstrate
its efficacy by applying it to simulations of the 𝜇-opioid receptor. With this
approach we provide a new perspective on analyzing the macroscopic behaviour
of Markov systems.
under review
publish
Alexander Sikorski
Alexander Sikorski
Robert Julian Rabben
Surahit Chewle
Marcus Weber
Weber, Marcus
Sikorski, Alexander
SFB-1114-B3
Rabben, Robert Julian
Modeling and Simulation of Complex Processes
Chewle, Surahit
NHR@ZIB
CCMAI
9553
2024
eng
article
0
--
--
--
Tensor-SqRA: Modeling the transition rates of interacting molecular systems in terms of potential energies
Estimating the rate of rare conformational changes in molecular systems is one of the goals of molecular dynamics simulations. In the past few decades, a lot of progress has been done in data-based approaches toward this problem. In contrast, model-based methods, such as the Square Root Approximation (SqRA), directly derive these quantities from the potential energy functions. In this article, we demonstrate how the SqRA formalism naturally blends with the tensor structure obtained by coupling multiple systems, resulting in the tensor-based Square Root Approximation (tSqRA). It enables efficient treatment of high-dimensional systems using the SqRA and provides an algebraic expression of the impact of coupling energies between molecular subsystems. Based on the tSqRA, we also develop the projected rate estimation, a hybrid data-model-based algorithm that efficiently estimates the slowest rates for coupled systems. In addition, we investigate the possibility of integrating low-rank approximations within this framework to maximize the potential of the tSqRA.
Journal of Chemical Physics
2311.09779
https://doi.org/10.1063/5.0187792
yes
2024-02-19
publish
Alexander Sikorski
Alexander Sikorski
Amir Niknejad
Marcus Weber
Luca Donati
Weber, Marcus
Sikorski, Alexander
SFB-1114-B3
Modeling and Simulation of Complex Processes
MathPlusAA1-15
Donati, Luca