@article{Weber2013, author = {Weber, Marcus}, title = {Adaptive Spectral Clustering in Molecular Simulation. In: Studies in Classification, Data Analysis, and Knowledge Organization}, journal = {XIV: Classification and Data Mining, A. Giusti, G. Ritter, M. Vichi (Eds.), Springer Series}, pages = {147 -- 157}, year = {2013}, language = {de} } @article{FackeldeyRoeblitzScharkoietal.2011, author = {Fackeldey, Konstantin and R{\"o}blitz, Susanna and Scharkoi, O. and Weber, Marcus}, title = {Soft Versus Hard Metastable Conformations in Molecular Simulations}, journal = {Particle Methods II, Fundamentals and Applications, Barcelona, Spain 26-28 Oct. 2011, E. Onate and D.R.J. Owen (eds.)}, pages = {899 -- 909}, year = {2011}, language = {de} } @article{ShanBujotzekAbendrothetal.2011, author = {Shan, Min and Bujotzek, Alexander and Abendroth, Frank and Seitz, Oliver and Weber, Marcus and Haag, Rainer}, title = {Conformational Analysis of Bivalent Estrogen Receptor-Ligands: From Intramolecular to Intermolecular Binding}, journal = {ChemBioChem, 12(17)}, doi = {10.1002/cbic.201100529}, pages = {2587 -- 2598}, year = {2011}, language = {en} } @phdthesis{Weber2015, author = {Weber, Britta}, title = {Reconstruction of Microtubule Centerlines from Electron Tomograms}, year = {2015}, abstract = {The organization of the mitotic spindle, a structure that separates the chromosomes during cell division, is an active research topic in molecular cell biology. It is composed of microtubules, elongated tubular macromolecules with a diameter of 25 nm. The only volumetric imaging technique that is available to a wide community and provides the required resolution to capture details about microtubules is electron tomography. However, the automatic detection of microtubules in electron tomograms is a difficult task due to the low contrast of the data. Furthermore, thick samples have to be cut into 300 nm thin sections before electron tomography can be applied. Software for automatically segmentation and stitching of the microtubules are not available and therefore these tasks have to be performed manually. Unfortunately, manual segmentation is time consuming for large samples and manual stitching of the tomograms is often infeasible due to the lack of prominent features for registration. Conclusions drawn from electron tomographic data is currently mostly based on either small samples containing few microtubules or single sections of complex structures. Consequently, simple properties, such as the length of microtubules in the spindle or their number, are still unknown for most model organisms. In this thesis, we present methods for 1) an automatic segmentation of microtubule centerlines in electron tomograms, and 2) an automatic stitching of the lines extracted from serial sections. For the centerline segmentation, we use 3D template matching and exploit knowledge about shape of microtubules and microscopy artifacts to design the templates. For the registration of the lines, we present a way to model the orientation of lines as a mixture of Fisher-Mises distributions where we estimate transformation parameters with the expectation maximization algorithm. The final line matching problem is formulated in terms of a probabilistic graphical model. To find the correct correspondences of line ends, we use belief propagation. We handle the poor convergence properties of this algorithm by detecting ambiguous and conflicting assignments of lines automatically. An expert can then influence the final output of the algorithm by solving conflicts manually. A detailed error analysis on true biological data and assessment of the reliability of the results is the prerequisite for analyzing the resulting line representations of the microtubules. To this end, the developed workflow for segmenting and stitching of microtubule centerlines is evaluated on plasticembedded samples of C. elegans early embryos and of spindles from X. laevis egg extracts. Our results suggest that the output of the presented algorithms together with little manual correction is of sufficient quality to allow a detailed analysis of dense microtubule networks. Finally, we exemplarily show results for the centrosome of a C. elegans mitotic spindle.}, language = {en} } @article{DjurdjevacConradWeberSchuette2016, author = {Djurdjevac Conrad, Natasa and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Finding dominant structures of nonreversible Markov processes}, volume = {14}, journal = {Multiscale Modeling and Simulation}, number = {4}, doi = {10.1137/15M1032272}, pages = {1319 -- 1340}, year = {2016}, language = {en} } @misc{BojarovskiHegeLieetal.2015, author = {Bojarovski, Stefan and Hege, Hans-Christian and Lie, Han Cheng and Weber, Marcus}, title = {Topological analysis and visualization of scalar functions characterizing conformational transitions of molecules on multiple time-scales}, journal = {Shape Up 2015 - Exercises in Materials Geometry and Topology, 14-18 Sept. 2015, Berlin, Germany}, year = {2015}, abstract = {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.}, language = {en} } @article{KrebekvonAchaziSollederetal.2016, author = {Krebek, von, Larissa K. S. and Achazi, Andreas J. and Solleder, Marthe and Weber, Marcus and Paulus, Beate and Schalley, Christoph A.}, title = {Allosteric and Chelate Cooperativity in Divalent Crown Ether-Ammonium Complexes with Strong Binding Enhancements}, volume = {22}, journal = {Chem. Eur. J.}, number = {43}, doi = {10.1002/chem.201603098}, pages = {15475 -- 15484}, year = {2016}, language = {en} } @misc{FackeldeyKoltaiNeviretal.2017, author = {Fackeldey, Konstantin and Koltai, P{\´e}ter and N{\´e}vir, Peter and Rust, Henning and Schild, Axel and Weber, Marcus}, title = {From Metastable to Coherent Sets - time-discretization schemes}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66074}, year = {2017}, abstract = {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.}, language = {en} } @article{IgdeRoeblitzMuelleretal.2017, author = {Igde, Sinaida and R{\"o}blitz, Susanna and M{\"u}ller, Anne and Kolbe, Katharina and Boden, Sophia and Fessele, Claudia and Lindhorst, Thisbe and Weber, Marcus and Hartmann, Laura}, title = {Linear Precision Glycomacromolecules with Varying Interligand Spacing and Linker Functionalities Binding to Concanavalin A and the Bacterial Lectin FimH}, volume = {17}, journal = {Marcomolecular Bioscience}, number = {12}, doi = {10.1002/mabi.201700198}, pages = {1700198}, year = {2017}, language = {en} } @misc{WeberGalliat2002, author = {Weber, Marcus and Galliat, Tobias}, title = {Characterization of Transition States in Conformational Dynamics using Fuzzy Sets}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6791}, number = {02-12}, year = {2002}, abstract = {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.}, language = {en} } @misc{Weber2007, author = {Weber, Marcus}, title = {Conformation-based transition state theory}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9612}, number = {07-18}, year = {2007}, abstract = {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.}, language = {en} } @misc{KubeWeber2005, author = {Kube, Susanna and Weber, Marcus}, title = {Conformation Kinetics as a Reduced Model for Transition Pathways}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8763}, number = {05-43}, year = {2005}, abstract = {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.}, language = {en} } @misc{MeyerMollCordesetal.2006, author = {Meyer, Holger and Moll, Sebastian and Cordes, Frank and Weber, Marcus}, title = {ConFlow? A new space-based Application for complete Conformational Analysis of Molecules}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9258}, number = {06-31}, year = {2006}, abstract = {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.}, language = {en} } @misc{KubeWeber2006, author = {Kube, Susanna and Weber, Marcus}, title = {Coarse Grained Molecular Kinetics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9299}, number = {06-35}, year = {2006}, abstract = {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.}, language = {en} } @misc{KubeLasserWeber2007, author = {Kube, Susanna and Lasser, Caroline and Weber, Marcus}, title = {Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9604}, number = {07-17}, year = {2007}, abstract = {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.}, language = {en} } @article{ThiesSunkaraRayetal.2023, author = {Thies, Arne and Sunkara, Vikram and Ray, Sourav and Wulkow, Hanna and Celik, M. {\"O}zg{\"u}r and Yerg{\"o}z, Fatih and Sch{\"u}tte, Christof and Stein, Christoph and Weber, Marcus and Winkelmann, Stefanie}, title = {Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design}, volume = {13}, journal = {Scientific Reports}, number = {607}, doi = {10.1038/s41598-023-27699-w}, year = {2023}, abstract = {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.}, language = {en} } @misc{RayThiesSunkaraetal.2021, author = {Ray, Sourav and Thies, Arne and Sunkara, Vikram and Wulkow, Hanna and Celik, {\"O}zg{\"u}r and Yerg{\"o}z, Fatih and Sch{\"u}tte, Christof and Stein, Christoph and Weber, Marcus and Winkelmann, Stefanie}, title = {Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-82797}, year = {2021}, abstract = {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.}, language = {en} } @article{HeidaSikorskiWeber2022, author = {Heida, Martin and Sikorski, Alexander and Weber, Marcus}, title = {Consistency and order 1 convergence of cell-centered finite volume discretizations of degenerate elliptic problems in any space dimension}, journal = {SIAM Journal on Numerical Analysis}, doi = {10.20347/WIAS.PREPRINT.2913}, year = {2022}, abstract = {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.}, language = {en} } @article{FackeldeyGorgullaWeber2021, author = {Fackeldey, Konstantin and Gorgulla, Christoph and Weber, Marcus}, title = {Neue Medikamente dank Supercomputern}, journal = {Spektrum der Wissenschaft}, number = {11}, pages = {40 -- 46}, year = {2021}, abstract = {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.}, language = {de} } @article{BirkRaharinirinaFackeldeyetal.2021, author = {Birk, Ralph and Raharinirina, N. Alexia and Fackeldey, Konstantin and Richter, Tonio Sebastian and Weber, Marcus}, title = {Inferring cultural and social processes based on patterns of statistical relationships between Synodal texts}, year = {2021}, abstract = {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.}, language = {en} } @article{SechiWeberHeyne2021, author = {Sechi, Renata and Weber, Marcus and Heyne, Karsten}, title = {MSM building and projection for the analysis of time-resolved spectra}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {21}, doi = {https://doi.org/10.1002/pamm.202100102}, url = {http://nbn-resolving.de/https://onlinelibrary.wiley.com/doi/10.1002/pamm.202100102}, pages = {e202100102}, year = {2021}, abstract = {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}, language = {en} } @article{ChewleWeberEmmerling2023, author = {Chewle, Surahit and Weber, Marcus and Emmerling, Franziska}, title = {Revealing Kinetics of Paracetamol Crystallization Using Time-Resolved Raman Spectroscopy, Orthogonal Time-Lapse Photography, and Non-Negative Matrix Factorization (OSANO)}, volume = {23}, journal = {Crystal Growth \& Design}, number = {9}, edition = {Crystal Growth \& Design}, publisher = {American Chemical Society}, doi = {10.1021/acs.cgd.3c00617}, pages = {6737 -- 6746}, year = {2023}, abstract = {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.}, language = {en} } @article{MarcoMarcus2025, author = {Marco, Reidelbach and Marcus, Weber}, title = {From Documentation to Discovery - MaRDMO and the MaRDI Ecosystem}, journal = {2nd Conference on Research Data Infrastructure (CoRDI)}, doi = {10.5281/zenodo.16735889}, year = {2025}, language = {en} } @inproceedings{ReidelbachSchemberaWeber2024, author = {Reidelbach, Marco and Schembera, Bj{\"o}rn and Weber, Marcus}, title = {Towards a FAIR Documentation of Workflows and Models in Applied Mathematics}, volume = {14749}, booktitle = {Mathematical Software - ICMS 2024}, edition = {Lecture Notes in Computer Science}, publisher = {Springer Nature Switzerland}, address = {Cham}, arxiv = {http://arxiv.org/abs/2403.17778}, doi = {10.1007/978-3-031-64529-7_27}, pages = {254 -- 262}, year = {2024}, abstract = {Modeling-Simulation-Optimization workflows play a fundamental role in applied mathematics. The Mathematical Research Data Initiative, MaRDI, responded to this by developing a FAIR and machine-interpretable template for a comprehensive documentation of such workflows. MaRDMO, a Plugin for the Research Data Management Organiser, enables scientists from diverse fields to document and publish their workflows on the MaRDI Portal seamlessly using the MaRDI template. Central to these workflows are mathematical models. MaRDI addresses them with the MathModDB ontology, offering a structured formal model description. Here, we showcase the interaction between MaRDMO and the MathModDB Knowledge Graph through an algebraic modeling workflow from the Digital Humanities. This demonstration underscores the versatility of both services beyond their original numerical domain.}, language = {en} } @article{RaharinirinaSunkaravonKleistetal.2024, author = {Raharinirina, Nomenjanahary Alexia and Sunkara, Vikram and von Kleist, Max and Fackeldey, Konstantin and Weber, Marcus}, title = {Multi-Input data ASsembly for joint Analysis (MIASA): A framework for the joint analysis of disjoint sets of variables}, volume = {19}, journal = {PLOS ONE}, number = {5}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0302425}, pages = {26}, year = {2024}, language = {en} } @article{ReidelbachFerrerWeber2023, author = {Reidelbach, Marco and Ferrer, Eloi and Weber, Marcus}, title = {MaRDMO Plugin}, volume = {1}, journal = {Proceedings of the Conference on Research Data Infrastructure}, publisher = {TIB Open Publishing}, issn = {2941-296X}, doi = {10.52825/cordi.v1i.254}, year = {2023}, abstract = {MaRDMO, a plugin for the Research Data Management Organiser, was developed in the Mathematical Research Data Initiative to document interdisciplinary workflows using a standardised scheme. Interdisciplinary workflows recorded this way are published directly on the MaRDI portal. In addition, central information is integrated into the MaRDI knowledge graph. Next to the documentation, MaRDMO offers the possibility to retrieve existing interdisciplinary workflows from the MaRDI Knowledge Graph to allow the reproduction of the initial work and to provide scientists with new researchimpulses. Thus, MaRDMO creates a community-driven knowledge loop that could help to overcome the replication crisis.}, language = {en} } @article{KlasseWeber2025, author = {Klasse, Sarah Michelle and Weber, Marcus}, title = {A Case Study of the Use of Logical Data Analysis in the Workmen's Village in Tell el-Amarna, Egypt}, volume = {66}, journal = {it - Information Technology}, number = {6}, publisher = {de Gruyter}, doi = {10.1515/itit-2024-0088}, pages = {256 -- 268}, year = {2025}, abstract = {The search for patterns in archaeological contexts is crucial to understanding ancient civilizations, including the organization of their societies and economies. This study focuses on the interdisciplinary application of mathematical logical data analysis to Egyptology, particularly examining food production in the Workmen's Village of Amarna. The introduction provides historical context about Amarna, founded by Pharaoh Akhenaten, and outlines the settlement structure and excavations of the Workmen's Village. The research utilizes archaeobotanical and archaeological data, along with digital humanities tools, to identify activity areas related to food production. The findings reveal spatial patterns in the distribution of tools such as mortars, pestles, and ovens, providing insights into the self-sufficiency and daily life of the villagers. Logical data analysis helps in finding rules and patterns in a dataset which are not visible otherwise, predicting the distribution of unexcavated areas and thus in this case enhancing our understanding of ancient Egyptian food production practices in state- planned settlements.}, language = {en} } @article{DonatiChewleStPierreetal.2025, author = {Donati, Luca and Chewle, Surahit and St. Pierre, Dominik and Natarajan, Vijay and Weber, Marcus}, title = {Topological analysis reveals multiple pathways in molecular dynamics}, volume = {21}, journal = {Journal of Chemical Theory and Computation}, number = {20}, address = {J. Chem. Theory Comput.}, arxiv = {http://arxiv.org/abs/2412.20580}, doi = {10.1021/acs.jctc.5c00819}, pages = {10385 -- 10397}, year = {2025}, abstract = {Molecular Dynamics simulations are indispensable tools for comprehending the dynamic behavior of biomolecules, yet extracting meaningful molecular pathways from these simulations remains challenging due to the vast amount of high dimensional data. In this work, we present Molecular Kinetics via Topology (MoKiTo), a novel approach that combines the ISOKANN algorithm to determine the membership function of a molecular system with a topological analysis tool inspired by the Mapper algorithm. Our strategy efficiently identifies and characterizes distinct molecular pathways, enabling the detection and visualization of critical conformational transitions and rare events. This method offers deeper insights into molecular mechanisms, facilitating the design of targeted interventions in drug discovery and protein engineering.}, language = {en} } @article{BauerWeberDiehlWieseneckeretal.2021, author = {Bauer, Wolfgang and Weber, Marcus and Diehl-Wiesenecker, Eva and Galtung, Noa and Prpic, Monika and Somasundaram, Rajan and Tauber, Rudolf and Schwenk, Jochen and Micke, Patrick and Kappert, Kai}, title = {Plasma Proteome Fingerprints Reveal Distinctiveness and Clinical Outcome of SARS-CoV-2 Infection}, volume = {13}, journal = {Viruses}, number = {12}, doi = {10.3390/v13122456}, pages = {2456}, year = {2021}, abstract = {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.}, language = {en} } @article{KontouWalterAlkaetal.2023, author = {Kontou, Eftychia E. and Walter, Axel and Alka, Oliver and Pfeuffer, Julianus and Sachsenberg, Timo and Mohite, Omkar and Nuhamunanda, Matin and Kohlbacher, Oliver and Weber, Tilmann}, title = {UmetaFlow: An untargeted metabolomics workflow for high-throughput data processing and analysis}, volume = {15}, journal = {Journal of Cheminformatics}, doi = {10.1186/s13321-023-00724-w}, year = {2023}, abstract = {Metabolomics experiments generate highly complex datasets, which are time and work-intensive, sometimes even error-prone if inspected manually. Therefore, new methods for automated, fast, reproducible, and accurate data processing and dereplication are required. Here, we present UmetaFlow, a computational workflow for untargeted metabolomics that combines algorithms for data pre-processing, spectral matching, molecular formula and structural predictions, and an integration to the GNPS workflows Feature-Based Molecular Networking and Ion Identity Molecular Networking for downstream analysis. UmetaFlow is implemented as a Snakemake workflow, making it easy to use, scalable, and reproducible. For more interactive computing, visualization, as well as development, the workflow is also implemented in Jupyter notebooks using the Python programming language and a set of Python bindings to the OpenMS algorithms (pyOpenMS). Finally, UmetaFlow is also offered as a web-based Graphical User Interface for parameter optimization and processing of smaller-sized datasets. UmetaFlow was validated with in-house LC-MS/MS datasets of actinomycetes producing known secondary metabolites, as well as commercial standards, and it detected all expected features and accurately annotated 76\% of the molecular formulas and 65\% of the structures. As a more generic validation, the publicly available MTBLS733 and MTBLS736 datasets were used for benchmarking, and UmetaFlow detected more than 90\% of all ground truth features and performed exceptionally well in quantification and discriminating marker selection.}, language = {en} } @article{DonatiWeber2023, author = {Donati, Luca and Weber, Marcus}, title = {Efficient Estimation of Transition Rates as Functions of pH}, volume = {23}, journal = {Proceedings in Applied Mathematics \& Mechanics}, arxiv = {http://arxiv.org/abs/2307.04439}, doi = {10.1002/pamm.202300264}, year = {2023}, abstract = {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.}, language = {en} } @article{DonatiWeberKeller2021, author = {Donati, Luca and Weber, Marcus and Keller, Bettina G.}, title = {Markov models from the square root approximation of the Fokker-Planck equation: calculating the grid-dependent flux}, volume = {33}, journal = {Journal of Physics: Condensed Matter}, number = {11}, doi = {10.1088/1361-648X/abd5f7}, pages = {115902}, year = {2021}, abstract = {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.}, language = {en} } @article{YousefianFrankWeberetal.2025, author = {Yousefian, Maryam and Frank, Anne-Simone and Weber, Marcus and R{\"o}blitz, Susanna}, title = {Efficient construction of Markov state models for stochastic gene regulatory networks by domain decomposition}, volume = {26}, journal = {BMC Bioinformatics}, number = {147}, doi = {10.1186/s12859-025-06174-5}, year = {2025}, abstract = {The dynamics of many gene regulatory networks (GRNs) is characterized by the occurrence of metastable phenotypes and stochastic phenotype switches. The chemical master equation (CME) is the most accurate description to model such stochastic dynamics, whereby the long-time dynamics of the system is encoded in the spectral properties of the CME operator. Markov State Models (MSMs) provide a general framework for analyzing and visualizing stochastic multistability and state transitions based on these spectral properties. Until now, however, this approach is either limited to low-dimensional systems or requires the use of high-performance computing facilities, thus limiting its usability.}, language = {en} } @inproceedings{YousefianDonatiSikorskietal.2026, author = {Yousefian, Maryam and Donati, Luca and Sikorski, Alexander and Weber, Marcus and R{\"o}blitz, Susanna}, title = {Exploring Metastable Dynamics of Gene Regulatory Networks with ISOKANN}, volume = {15959}, booktitle = {Computational Methods in Systems Biology. CMSB 2025}, doi = {10.1007/978-3-032-01436-8_8}, pages = {126 -- 149}, year = {2026}, abstract = {Stochastic dynamical systems like gene regulatory networks (GRNs) often exhibit behavior characterized by metastable sets (representing cellular phenotypes), in which trajectories remain for long times, whereas switches between these sets in the phase space are rare events. One way to capture these rare events is to infer the system's long-term behavior from the spectral characteristics (eigenvalues and eigenvectors) of its Koopman operator. For GRNs, the Koopman operator is based on the chemical master equation (CME), which provides a precise mathematical modeling framework for stochastic GRNs. Since the CME is typically analytically intractable, methods based on discretizing the CME operator have been developed. However, determining the number and location of metastable sets in the phase space as well as the transition rates between them remains computationally challenging, especially for large GRNs with many genes and interactions. A promising alternative method, called ISOKANN (invariant subspaces of Koopman operators with artificial neural networks) has been developed in the context of molecular dynamics. ISOKANN uses a combination of the power iteration and neural networks to learn the basis functions of an invariant subspace of the Koopman operator. In this paper, we extend the application of ISOKANN to the CME operator and apply it to two small GRNs: a genetic toggle switch model and a model for macrophage polarization. Our work opens a new field of application for the ISOKANN algorithm and demonstrates the potential of this algorithm for studying large GRNs.}, language = {en} } @article{BauerGaltungGesericketal.2025, author = {Bauer, Wolfgang and Galtung, Noa and Geserick, Peter and Friedrich, Katharina and Weber, Marcus and Somasundaram, Rajan and Diehl-Wiesenecker, Eva and Kappert, Kai}, title = {Pentraxin-3, MyD88, GLP-1, and PD-L1: Performance assessment and composite algorithmic analysis for sepsis identification}, volume = {91}, journal = {Journal of Infection}, number = {3}, doi = {10.1016/j.jinf.2025.106599}, pages = {106599}, year = {2025}, abstract = {This study examines nine emerging biomarkers as possible indicators for diagnosing sepsis in emergency department patient.}, language = {en} } @article{CoomberChewleSeckeretal.2025, author = {Coomber, Celvic and Chewle, Surahit and Secker, Christopher and Fackeldey, Konstantin and Weber, Marcus and Winkelmann, Stefanie and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {Investigating Endogenous Opioids Unravels the Mechanisms Behind Opioid-Induced Constipation, a Mathematical Modeling Approach}, volume = {26}, journal = {International Journal of Molecular Sciences}, number = {13}, doi = {10.3390/ijms26136207}, year = {2025}, abstract = {Endogenous opioids, such as Endomorphin-2, are not typically associated with severe constipation, unlike pharmaceutical opioids, which induce opioid-induced constipation (OIC) by activating μ-opioid receptors in the gastrointestinal tract. In this study, we present a mathematical model, which integrates the serotonergic and opioid pathways, simulating the interaction between serotonin and opioid signaling within the enteric nervous system (ENS). The model explores the mechanisms underlying OIC, with a focus on the change in adenylyl cyclase (AC) activity, cAMP accumulation, and the distinct functionalities of Endomorphin-2 compared to commonly used pharmaceutical opioids. We study the effects of Morphine, Fentanyl, and Methadone and contrast them with Endomorphin-2. Our findings reveal that opioids do not perturb the signaling of serotonin, but only the activity of AC, suggesting that serotonin levels have no influence on improving opioid-induced constipation. Furthermore, this study reveals that the primary difference between endogenous and pharmaceutical opioids is their degradation rates. This finding shows that modulating opioid degradation rates significantly improves cAMP recovery. In conclusion, our insights steer towards exploring opioid degrading enzymes, localized to the gut, as a strategy for mitigating OIC.}, language = {en} } @misc{RaharinirinaWeberBirketal.2021, author = {Raharinirina, N. Alexia and Weber, Marcus and Birk, Ralph and Fackeldey, Konstantin and Klasse, Sarah M. and Richter, Tonio Sebastian}, title = {Different Tools and Results for Correspondence Analysis}, doi = {10.12752/8257}, year = {2021}, abstract = {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.}, language = {en} } @article{FernandesChaowdharySalehetal.2022, author = {Fernandes, Rita and Chaowdhary, Suvrat and Saleh, Noureldin and Mikula, Natalia and Kanevche, Katerina and Berlepsch, Hans and Hosogi, Naoki and Heberle, Joachim and Weber, Marcus and B{\"o}ttcher, Christoph and Koksch, Beate}, title = {Cyanine Dye Coupling Mediates Self-assembly of a pH Sensitive Peptide into Novel 3D Architectures}, volume = {61}, journal = {Angewandte Chemie}, number = {48}, pages = {e202208647}, year = {2022}, abstract = {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.}, language = {en} } @article{SeckerFackeldeyWeberetal.2023, author = {Secker, Christopher and Fackeldey, Konstantin and Weber, Marcus and Ray, Sourav and Gorgulla, Christoph and Sch{\"u}tte, Christof}, title = {Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists}, volume = {15}, journal = {Journal of Cheminformatics}, doi = {10.1186/s13321-023-00746-4}, year = {2023}, abstract = {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.}, language = {en} } @article{SikorskiRiberaBorrellWeber2024, author = {Sikorski, Alexander and Ribera Borrell, Enric and Weber, Marcus}, title = {Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN}, volume = {65}, journal = {Journal of Mathematical Physics}, arxiv = {http://arxiv.org/abs/2301.00065}, doi = {10.1063/5.0140764}, pages = {013502}, year = {2024}, abstract = {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.}, language = {en} } @article{SikorskiWeberSchuette2021, author = {Sikorski, Alexander and Weber, Marcus and Sch{\"u}tte, Christof}, title = {The Augmented Jump Chain}, volume = {4}, journal = {Advanced Theory and Simulations}, number = {4}, publisher = {Wiley-VCH}, arxiv = {http://arxiv.org/abs/2008.04624}, doi = {10.1002/adts.202000274}, year = {2021}, abstract = {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.}, language = {en} } @article{SechiSikorskiWeber2021, author = {Sechi, Renata and Sikorski, Alexander and Weber, Marcus}, title = {Estimation of the Koopman Generator by Newton's Extrapolation}, volume = {19}, journal = {Multiscale Modeling and Simulation}, number = {2}, publisher = {SIAM}, doi = {10.1137/20M1333006}, pages = {758 -- 774}, year = {2021}, abstract = {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.}, language = {en} } @article{DonatiWeber2022, author = {Donati, Luca and Weber, Marcus}, title = {Assessing transition rates as functions of environmental variables}, volume = {157}, journal = {The Journal of Chemical Physics}, number = {22}, publisher = {AIP Publishing}, doi = {10.1063/5.0109555}, pages = {224103-1 -- 224103-14}, year = {2022}, abstract = {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.}, language = {en} } @article{SechiFackeldeyChewleetal.2022, author = {Sechi, Renata and Fackeldey, Konstantin and Chewle, Surahit and Weber, Marcus}, title = {SepFree NMF: A Toolbox for Analyzing the Kinetics of Sequential Spectroscopic Data}, volume = {15}, journal = {Algorithms}, number = {9}, doi = {10.3390/a15090297}, pages = {297}, year = {2022}, abstract = {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.}, language = {en} } @article{DonatiWeberKeller2022, author = {Donati, Luca and Weber, Marcus and Keller, Bettina G.}, title = {A review of Girsanov Reweighting and of Square Root Approximation for building molecular Markov State Models}, volume = {63}, journal = {Journal of Mathematical Physics}, number = {12}, publisher = {AIP Publishing}, doi = {10.1063/5.0127227}, pages = {123306-1 -- 123306-21}, year = {2022}, abstract = {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.}, language = {en} } @article{RayFackeldeySteinetal.2023, author = {Ray, Sourav and Fackeldey, Konstantin and Stein, Christoph and Weber, Marcus}, title = {Coarse Grained MD Simulations of Opioid interactions with the µ-opioid receptor and the surrounding lipid membrane}, volume = {3}, journal = {Biophysica}, number = {2}, doi = {10.3390/biophysica3020017}, pages = {263 -- 275}, year = {2023}, abstract = {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.}, language = {en} } @article{RaharinirinaFackeldeyWeber2022, author = {Raharinirina, N. Alexia and Fackeldey, Konstantin and Weber, Marcus}, title = {Qualitative Euclidean embedding of Disjoint Sets of Points}, year = {2022}, abstract = {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).}, language = {en} } @article{BoegeFritzeGoergenetal.2023, author = {Boege, Tobias and Fritze, Ren{\´e} and G{\"o}rgen, Christiane and Hanselmann, Jeroen and Iglezakis, Dorothea and Kastner, Lars and Koprucki, Thomas and Krause, Tabea and Lehrenfeld, Christoph and Polla, Silvia and Reidelbach, Marco and Riedel, Christian and Saak, Jens and Schembera, Bj{\"o}rn and Tabelow, Karsten and Weber, Marcus}, title = {Research-Data Management Planning in the German Mathematical Community}, volume = {130}, journal = {Eur. Math. Soc. Mag.}, doi = {10.4171/mag/152}, pages = {40 -- 47}, year = {2023}, abstract = {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.}, language = {en} } @misc{ReidelbachWeber2022, author = {Reidelbach, Marco and Weber, Marcus}, title = {MaRDI - The mathematical Research Data Initiative}, journal = {Aktionstag Forschungsdaten}, doi = {10.5281/zenodo.7397588}, year = {2022}, language = {en} } @article{SikorskiNiknejadWeberetal.2024, author = {Sikorski, Alexander and Niknejad, Amir and Weber, Marcus and Donati, Luca}, title = {Tensor-SqRA: Modeling the transition rates of interacting molecular systems in terms of potential energies}, volume = {160}, journal = {Journal of Chemical Physics}, arxiv = {http://arxiv.org/abs/2311.09779}, doi = {10.1063/5.0187792}, pages = {104112}, year = {2024}, abstract = {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.}, language = {en} } @inproceedings{SikorskiRabbenChewleetal.2025, author = {Sikorski, Alexander and Rabben, Robert Julian and Chewle, Surahit and Weber, Marcus}, title = {Capturing the Macroscopic Behaviour of Molecular Dynamics with Membership Functions}, booktitle = {Mathematical Optimization for Machine Learning: Proceedings of the MATH+ Thematic Einstein Semester 2023}, editor = {Fackeldey, K.}, publisher = {De Gruyter}, arxiv = {http://arxiv.org/abs/2404.10523}, doi = {10.1515/9783111376776-004}, pages = {41 -- 58}, year = {2025}, abstract = {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.}, language = {en} }