@article{SchimunekSeidlElezetal.2024, author = {Schimunek, Johannes and Seidl, Philipp and Elez, Katarina and Hempel, Tim and Le, Tuan and No{\´e}, Frank and Olsson, Simon and Raich, Llu{\´i}s and Winter, Robin and Gokcan, Hatice and Gusev, Filipp and Gutkin, Evgeny M. and Isayev, Olexandr and Kurnikova, Maria G. and Narangoda, Chamali H. and Zubatyuk, Roman and Bosko, Ivan P. and Furs, Konstantin V. and Karpenko, Anna D. and Kornoushenko, Yury V. and Shuldau, Mikita and Yushkevich, Artsemi and Benabderrahmane, Mohammed B. and Bousquet-Melou, Patrick and Bureau, Ronan and Charton, Beatrice and Cirou, Bertrand C. and Gil, G{\´e}rard and Allen, William J. and Sirimulla, Suman and Watowich, Stanley and Antonopoulos, Nick and Epitropakis, Nikolaos and Krasoulis, Agamemnon and Itsikalis, Vassilis and Theodorakis, Stavros and Kozlovskii, Igor and Maliutin, Anton and Medvedev, Alexander and Popov, Petr and Zaretckii, Mark and Eghbal-Zadeh, Hamid and Halmich, Christina and Hochreiter, Sepp and Mayr, Andreas and Ruch, Peter and Widrich, Michael and Berenger, Francois and Kumar, Ashutosh and Yamanishi, Yoshihiro and Zhang, Kam Y. J. and Bengio, Emmanuel and Bengio, Yoshua and Jain, Moksh J. and Korablyov, Maksym and Liu, Cheng-Hao and Marcou, Gilles and Glaab, Enrico and Barnsley, Kelly and Iyengar, Suhasini M. and Ondrechen, Mary Jo and Haupt, V. Joachim and Kaiser, Florian and Schroeder, Michael and Pugliese, Luisa and Albani, Simone and Athanasiou, Christina and Beccari, Andrea and Carloni, Paolo and D'Arrigo, Giulia and Gianquinto, Eleonora and Goßen, Jonas and Hanke, Anton and Joseph, Benjamin P. and Kokh, Daria B. and Kovachka, Sandra and Manelfi, Candida and Mukherjee, Goutam and Mu{\~n}iz-Chicharro, Abraham and Musiani, Francesco and Nunes-Alves, Ariane and Paiardi, Giulia and Rossetti, Giulia and Sadiq, S. Kashif and Spyrakis, Francesca and Talarico, Carmine and Tsengenes, Alexandros and Wade, Rebecca C. and Copeland, Conner and Gaiser, Jeremiah and Olson, Daniel R. and Roy, Amitava and Venkatraman, Vishwesh and Wheeler, Travis J. and Arthanari, Haribabu and Blaschitz, Klara and Cespugli, Marco and Durmaz, Vedat and Fackeldey, Konstantin and Fischer, Patrick D. and Gorgulla, Christoph and Gruber, Christian and Gruber, Karl and Hetmann, Michael and Kinney, Jamie E. and Padmanabha Das, Krishna M. and Pandita, Shreya and Singh, Amit and Steinkellner, Georg and Tesseyre, Guilhem and Wagner, Gerhard and Wang, Zi-Fu and Yust, Ryan J. and Druzhilovskiy, Dmitry S. and Filimonov, Dmitry A. and Pogodin, Pavel V. and Poroikov, Vladimir and Rudik, Anastassia V. and Stolbov, Leonid A. and Veselovsky, Alexander V. and De Rosa, Maria and De Simone, Giada and Gulotta, Maria R. and Lombino, Jessica and Mekni, Nedra and Perricone, Ugo and Casini, Arturo and Embree, Amanda and Gordon, D. Benjamin and Lei, David and Pratt, Katelin and Voigt, Christopher A. and Chen, Kuang-Yu and Jacob, Yves and Krischuns, Tim and Lafaye, Pierre and Zettor, Agn{\`e}s and Rodr{\´i}guez, M. Luis and White, Kris M. and Fearon, Daren and Von Delft, Frank and Walsh, Martin A. and Horvath, Dragos and Brooks III, Charles L. and Falsafi, Babak and Ford, Bryan and Garc{\´i}a-Sastre, Adolfo and Yup Lee, Sang and Naffakh, Nadia and Varnek, Alexandre and Klambauer, G{\"u}nter and Hermans, Thomas M.}, title = {A community effort in SARS-CoV-2 drug discovery}, volume = {43}, journal = {Molecular Informatics}, number = {1}, doi = {https://doi.org/10.1002/minf.202300262}, pages = {e202300262}, year = {2024}, language = {en} } @misc{FackeldeyRoeblitzScharkoietal.2011, author = {Fackeldey, Konstantin and R{\"o}blitz, Susanna and Scharkoi, Olga and Weber, Marcus}, title = {Soft Versus Hard Metastable Conformations in Molecular Simulations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13189}, number = {11-27}, year = {2011}, abstract = {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.}, language = {en} } @misc{Fackeldey2010, author = {Fackeldey, Konstantin}, title = {Coupling Meshbased and Meshfree Methods by a Transfer Operator Approach}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11755}, number = {10-12}, year = {2010}, abstract = {In contrast to the well known meshbased methods like the finite element method, meshfree methods do not rely on a mesh. However besides their great applicability, meshfree methods are rather time consuming. Thus, it seems favorable to combine both methods, by using meshfree methods only in a small part of the domain, where a mesh is disadvantageous, and a meshbased method for the rest of the domain. We motivate, that this coupling between the two simulation techniques can be considered as saddle point problem and show the stability of this coupling. Thereby a novel transfer operator is introduced, which interacts in the transition zone, where both methods coexist.}, language = {en} } @misc{WeberFackeldey2013, author = {Weber, Marcus and Fackeldey, Konstantin}, title = {Computing the Minimal Rebinding Effect Included in a Given Kinetics}, issn = {1438-0064}, doi = {10.1137/13091124X}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17796}, year = {2013}, abstract = {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.}, language = {en} } @misc{LieFackeldeyWeber2013, author = {Lie, Han Cheng and Fackeldey, Konstantin and Weber, Marcus}, title = {A square root approximation of transition rates for a Markov State Model}, issn = {1438-0064}, doi = {10.1137/120899959}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42195}, year = {2013}, abstract = {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.}, language = {en} } @misc{NielsenFackeldeyWeber2013, author = {Nielsen, Adam and Fackeldey, Konstantin and Weber, Marcus}, title = {On a Generalized Transfer Operator}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-43162}, year = {2013}, abstract = {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.}, language = {en} } @article{FackeldeyKoltaiNeviretal.2019, author = {Fackeldey, Konstantin and Koltai, Peter and Nevir, Peter and Rust, Henning and Schild, Axel and Weber, Marcus}, title = {From metastable to coherent sets - Time-discretization schemes}, volume = {29}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, doi = {10.1063/1.5058128}, pages = {012101 -- 012101}, year = {2019}, abstract = {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.}, language = {en} } @article{ReuterFackeldeyWeber2019, author = {Reuter, Bernhard and Fackeldey, Konstantin and Weber, Marcus}, title = {Generalized Markov modeling of nonreversible molecular kinetics}, volume = {17}, journal = {The Journal of Chemical Physics}, number = {150}, doi = {10.1063/1.5064530}, pages = {174103}, year = {2019}, abstract = {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.}, language = {en} } @article{ErnstFackeldeyVolkameretal.2019, author = {Ernst, Natalia and Fackeldey, Konstantin and Volkamer, Andrea and Opatz, Oliver and Weber, Marcus}, title = {Computation of temperature-dependent dissociation rates of metastable protein-ligand complexes}, volume = {45}, journal = {Molecular Simulation}, number = {11}, doi = {10.1080/08927022.2019.1610949}, pages = {904 -- 911}, year = {2019}, abstract = {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.}, language = {en} } @misc{FackeldeySikorskiWeber2018, author = {Fackeldey, Konstantin and Sikorski, Alexander and Weber, Marcus}, title = {Spectral Clustering for Non-reversible Markov Chains}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-70218}, year = {2018}, abstract = {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.}, language = {en} } @article{FackeldeySikorskiWeber2018, author = {Fackeldey, Konstantin and Sikorski, Alexander and Weber, Marcus}, title = {Spectral Clustering for Non-Reversible Markov Chains}, volume = {37}, journal = {Computational and Applied Mathematics}, number = {5}, doi = {https://doi.org/10.1007/s40314-018-0697-0}, pages = {6376 -- 6391}, year = {2018}, abstract = {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.}, language = {en} } @article{LieFackeldeyWeber2013, author = {Lie, Han Cheng and Fackeldey, Konstantin and Weber, Marcus}, title = {A Square Root Approximation of Transition Rates for a Markov State Model}, volume = {34}, journal = {SIAM. J. Matrix Anal. Appl.}, number = {2}, doi = {10.1137/120899959}, pages = {738 -- 756}, year = {2013}, language = {en} } @article{ScharkoiFackeldeyMerkulowetal.2013, author = {Scharkoi, Olga and Fackeldey, Konstantin and Merkulow, Igor and Andrae, Karsten and Weber, Marcus and Nehls, Irene}, title = {Conformational Analysis of Alternariol on the Quantum Level}, volume = {19}, journal = {J. Mol. Model.}, number = {6}, doi = {10.1007/s00894-013-1803-2}, pages = {2567 -- 2572}, year = {2013}, language = {en} } @misc{BujotzekSchuettNielsenetal.2013, author = {Bujotzek, Alexander and Sch{\"u}tt, Ole and Nielsen, Adam and Fackeldey, Konstantin and Weber, Marcus}, title = {Efficient Conformational Analysis by Partition-of-Unity Coupling}, journal = {Math Chem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42570}, year = {2013}, abstract = {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.}, language = {en} } @misc{WeberFackeldeySchuette2017, author = {Weber, Marcus and Fackeldey, Konstantin and Sch{\"u}tte, Christof}, title = {Set-free Markov State Building}, issn = {1438-0064}, doi = {10.1063/1.4978501}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62167}, year = {2017}, abstract = {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.}, language = {en} } @incollection{DurmazFackeldeyWeber2011, author = {Durmaz, Vedat and Fackeldey, Konstantin and Weber, Marcus}, title = {A rapidly Mixing Monte Carlo Method for the Simulation of Slow Molecular Processes}, booktitle = {Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science}, editor = {Mode, Ch.}, publisher = {InTech}, year = {2011}, language = {en} } @inproceedings{FackeldeyKrauseKrause2008, author = {Fackeldey, Konstantin and Krause, Dorian and Krause, Rolf}, title = {Quadrature and Implementation of the Weak Coupling Method}, booktitle = {MMM 2008: Proceedings of the 4th International Conference on Multiscale Materials Modelling, 27-31 October 2008, Tallahassee, Fla.}, pages = {62 -- 65}, year = {2008}, language = {en} } @inproceedings{FackeldeyKrauseKrause2009, author = {Fackeldey, Konstantin and Krause, Dorian and Krause, Rolf}, title = {Weak Coupling Algorithms in Multiscale Simulations}, booktitle = {Proceedings of the third Inter. Confer. on Comp. Meth. for Coupled Problems in Science and Engrg}, pages = {1023pp}, year = {2009}, language = {en} } @inproceedings{FackeldeyKrauseKrause2010, author = {Fackeldey, Konstantin and Krause, Dorian and Krause, Rolf}, title = {Numerical Validation of Constraints Based Multiscale Methods}, booktitle = {Lecture Notes in Computational Science and Engineering}, editor = {Griebel, Michael and Schweitzer, M.}, pages = {141 -- 154}, year = {2010}, language = {en} } @article{FackeldeyKrauseKrauseetal.2011, author = {Fackeldey, Konstantin and Krause, Dorian and Krause, Rolf and Lenzen, Christoph}, title = {Coupling Molecular Dynamics and Continua with Weak Constraints}, volume = {9}, journal = {SIAM Multiscale Model. Simul.}, doi = {/10.1137/100782097}, pages = {1459 -- 1494}, year = {2011}, language = {en} } @inproceedings{FackeldeyKrauseSchweitzer2008, author = {Fackeldey, Konstantin and Krause, Rolf and Schweitzer, M.}, title = {Stability of Energy Transfer in the Weak Coupling Method}, volume = {65}, booktitle = {Meshfree Methods for Partial Differential Equations IV}, editor = {Griebel, Michael and Schweitzer, M.}, pages = {111 -- 121}, year = {2008}, language = {en} } @article{Fackeldey2011, author = {Fackeldey, Konstantin}, title = {Coupling Meshbased and Meshfree Methods by a Transfer Operator Approach}, volume = {69}, journal = {IJPAM}, number = {2}, pages = {185 -- 202}, year = {2011}, language = {en} } @article{FackeldeyKrause2009, author = {Fackeldey, Konstantin and Krause, Rolf}, title = {Multiscale Coupling in Function Space - Weak Coupling between Molecular Dynamics and Continuum Mechanics}, volume = {79}, journal = {International Journal for Numerical Methods in Engineering}, number = {12}, doi = {10.1002/nme.2626}, pages = {1517 -- 1535}, year = {2009}, language = {en} } @phdthesis{Fackeldey2009, author = {Fackeldey, Konstantin}, title = {The Weak Coupling Method for Coupling Continuum Mechanics with Molecular Dynamics}, year = {2009}, language = {en} } @inproceedings{FackeldeyKrause2007, author = {Fackeldey, Konstantin and Krause, Rolf}, title = {Solving Frictional Contact Problems with Multigrid Efficiency}, volume = {50}, booktitle = {Proc.of the 16th International Conference on Domain Decomposition Methods}, editor = {Widlund, Olof}, pages = {547 -- 554}, year = {2007}, language = {en} } @inproceedings{FackeldeyKrause2007, author = {Fackeldey, Konstantin and Krause, Rolf}, title = {Weak coupling in function space}, volume = {7}, booktitle = {Proc. Appl. Math. Mech.}, number = {1}, pages = {2020113pp}, year = {2007}, language = {en} } @inproceedings{FackeldeyKrause2008, author = {Fackeldey, Konstantin and Krause, Rolf}, title = {CM/MD Coupling - A Function Space Oriented Multiscale-Coupling Approach}, volume = {8}, booktitle = {Proc. Appl. Math. Mech.}, number = {1}, pages = {10495pp}, year = {2008}, language = {en} } @inproceedings{FackeldeyBujotzekWeber2012, author = {Fackeldey, Konstantin and Bujotzek, Alexander and Weber, Marcus}, title = {A meshless discretization method for Markov state models applied to explicit water peptide folding simulations}, volume = {89}, booktitle = {Meshfree Methods for Partial Differential Equations VI}, publisher = {Springer}, pages = {141 -- 154}, year = {2012}, language = {en} } @inproceedings{Fackeldey2012, author = {Fackeldey, Konstantin}, title = {Multiscale Methods in Time and Space}, volume = {17}, booktitle = {Progress in Industrial Mathematics at ECMI 2010}, pages = {619 -- 626}, year = {2012}, language = {en} } @article{FackeldeyKlimmWeber2012, author = {Fackeldey, Konstantin and Klimm, Martina and Weber, Marcus}, title = {A Coarse Graining Method for the Dimension Reduction of the State Space of Biomolecules}, volume = {5}, journal = {Journal of Mathematical Chemistry}, number = {9}, pages = {2623 -- 2635}, year = {2012}, language = {en} } @article{KrauseFackeldeyKrause2014, author = {Krause, Dorian and Fackeldey, Konstantin and Krause, Rolf}, title = {A Parallel Multiscale Simulation Toolbox for Coupling Molecular Dynamics and Finite Elements}, journal = {Singular Phenomena and Scaling in Mathematical Models}, editor = {Griebel, Michael}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-00786-1_14}, pages = {327 -- 346}, year = {2014}, language = {en} } @article{HaackFackeldeyRoeblitzetal.2013, author = {Haack, Fiete and Fackeldey, Konstantin and R{\"o}blitz, Susanna and Scharkoi, Olga and Weber, Marcus and Schmidt, Burkhard}, title = {Adaptive spectral clustering with application to tripeptide conformation analysis}, volume = {139}, journal = {The Journal of Chemical Physics}, doi = {10.1063/1.4830409}, pages = {110 -- 194}, year = {2013}, language = {en} } @article{ReuterWeberFackeldeyetal.2018, author = {Reuter, Bernhard and Weber, Marcus and Fackeldey, Konstantin and R{\"o}blitz, Susanna and Garcia, Martin E.}, title = {Generalized Markov State Modeling Method for Nonequilibrium Biomolecular Dynamics: Exemplified on Amyloid β Conformational Dynamics Driven by an Oscillating Electric Field}, volume = {14}, journal = {Journal of Chemical Theory and Computation}, number = {7}, doi = {10.1021/acs.jctc.8b00079}, pages = {3579 -- 3594}, year = {2018}, abstract = {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.}, language = {en} } @article{GorgullaBoeszoermnyiWangetal.2020, author = {Gorgulla, Christoph and Boeszoermnyi, Andras and Wang, Zi-Fu and Fischer, Patrick D. and Coote, Paul and Das, Krishna M. Padmanabha and Malets, Yehor S. and Radchenko, Dmytro S. and Moroz, Yurii and Scott, David A. and Fackeldey, Konstantin and Hoffmann, Moritz and Iavniuk, Iryna and Wagner, Gerhard and Arthanari, Haribabu}, title = {An open-source drug discovery platform enables ultra-large virtual screens}, volume = {580}, journal = {Nature}, publisher = {Springer Nature}, doi = {https://doi.org/10.1038/s41586-020-2117-z}, pages = {663 -- 668}, year = {2020}, abstract = {On average, an approved drug today costs \$2-3 billion and takes over ten years to develop1. In part, this is due to expensive and time-consuming wet-lab experiments, poor initial hit compounds, and the high attrition rates in the (pre-)clinical phases. Structure-based virtual screening (SBVS) has the potential to mitigate these problems. With SBVS, the quality of the hits improves with the number of compounds screened2. However, despite the fact that large compound databases exist, the ability to carry out large-scale SBVSs on computer clusters in an accessible, efficient, and flexible manner has remained elusive. Here we designed VirtualFlow, a highly automated and versatile open-source platform with perfect scaling behaviour that is able to prepare and efficiently screen ultra-large ligand libraries of compounds. VirtualFlow is able to use a variety of the most powerful docking programs. Using VirtualFlow, we have prepared the largest and freely available ready-to-dock ligand library available, with over 1.4 billion commercially available molecules. To demonstrate the power of VirtualFlow, we screened over 1 billion compounds and discovered a small molecule inhibitor (iKeap1) that engages KEAP1 with nanomolar affinity (Kd = 114 nM) and disrupts the interaction between KEAP1 and the transcription factor NRF2. We also identified a set of structurally diverse molecules that bind to KEAP1 with submicromolar affinity. This illustrates the potential of VirtualFlow to access vast regions of the chemical space and identify binders with high affinity for target proteins.}, language = {en} } @article{GorgullaFackeldeyWagneretal.2020, author = {Gorgulla, Christoph and Fackeldey, Konstantin and Wagner, Gerhard and Arthanari, Haribabu}, title = {Accounting of Receptor Flexibility in Ultra-Large Virtual Screens with VirtualFlow Using a Grey Wolf Optimization Method}, volume = {7}, journal = {Supercomputing Frontiers and Innovations}, number = {3}, doi = {10.14529/jsfi200301}, pages = {4 -- 12}, year = {2020}, abstract = {Structure-based virtual screening approaches have the ability to dramatically reduce the time and costs associated to the discovery of new drug candidates. Studies have shown that the true hit rate of virtual screenings improves with the scale of the screened ligand libraries. Therefore, we have recently developed an open source drug discovery platform (VirtualFlow), which is able to routinely carry out ultra-large virtual screenings. One of the primary challenges of molecular docking is the circumstance when the protein is highly dynamic or when the structure of the protein cannot be captured by a static pose. To accommodate protein dynamics, we report the extension of VirtualFlow to allow the docking of ligands using a grey wolf optimization algorithm using the docking program GWOVina, which substantially improves the quality and efficiency of flexible receptor docking compared to AutoDock Vina. We demonstrate the linear scaling behavior of VirtualFlow utilizing GWOVina up to 128 000 CPUs. The newly supported docking method will be valuable for drug discovery projects in which protein dynamics and flexibility play a significant role.}, language = {en} } @article{FackeldeyRoehmNiknejadetal.2021, author = {Fackeldey, Konstantin and R{\"o}hm, Jonas and Niknejad, Amir and Chewle, Surahit and Weber, Marcus}, title = {Analyzing Raman Spectral Data without Separabiliy Assumption}, volume = {3}, journal = {Journal of Mathematical Chemistry}, number = {59}, publisher = {Springer}, arxiv = {http://arxiv.org/abs/2007.06428}, doi = {10.1007/s10910-020-01201-7}, pages = {575 -- 596}, year = {2021}, abstract = {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.}, language = {en} } @article{RoehlWeberFackeldey2021, author = {R{\"o}hl, Susanne and Weber, Marcus and Fackeldey, Konstantin}, title = {Computing the minimal rebinding effect for non-reversible processes}, volume = {19}, journal = {Multiscale Modeling and Simulation}, number = {1}, arxiv = {http://arxiv.org/abs/2007.08403}, doi = {https://doi.org/10.1137/20M1334966}, pages = {460 -- 477}, year = {2021}, abstract = {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.}, language = {en} } @article{GorgullaDasLeighetal.2021, author = {Gorgulla, Christoph and Das, Krishna M. Padmanabha and Leigh, Kendra E and Cespugli, Marco and Fischer, Patrick D. and Wang, Zi-Fu and Tesseyre, Guilhem and Pandita, Shreya and Shnapir, Alex and Calderaio, Anthony and Hutcheson, Colin and Gechev, Minko and Rose, Alexander and Lewis, Noam and Yaffe, Erez and Luxenburg, Roni and Herce, Henry D. and Durmaz, Vedat and Halazonetis, Thanos D. and Fackeldey, Konstantin and Patten, Justin J. and Chuprina, Alexander and Dziuba, Igor and Plekhova, Alla and Moroz, Yurii and Radchenko, Dmytro and Tarkhanova, Olga and Yavnyuk, Irina and Gruber, Christian C. and Yust, Ryan and Payne, Dave and N{\"a}{\"a}r, Anders M. and Namchuk, Mark N. and Davey, Robert A. and Wagner, Gerhard and Kinney, Jamie and Arthanari, Haribabu}, title = {A Multi-Pronged Approach Targeting SARS-CoV-2 Proteins Using Ultra-Large Virtual Screening}, volume = {24}, journal = {iScience}, number = {2}, publisher = {CellPress}, doi = {10.26434/chemrxiv.12682316}, pages = {102021}, year = {2021}, abstract = {Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), previously known as 2019 novel coronavirus (2019-nCoV), has spread rapidly across the globe, creating an unparalleled global health burden and spurring a deepening economic crisis. As of July 7th, 2020, almost seven months into the outbreak, there are no approved vaccines and few treatments available. Developing drugs that target multiple points in the viral life cycle could serve as a strategy to tackle the current as well as future coronavirus pandemics. Here we leverage the power of our recently developed in silico screening platform, VirtualFlow, to identify inhibitors that target SARS-CoV-2. VirtualFlow is able to efficiently harness the power of computing clusters and cloud-based computing platforms to carry out ultra-large scale virtual screens. In this unprecedented structure-based multi-target virtual screening campaign, we have used VirtualFlow to screen an average of approximately 1 billion molecules against each of 40 different target sites on 17 different potential viral and host targets in the cloud. In addition to targeting the active sites of viral enzymes, we also target critical auxiliary sites such as functionally important protein-protein interaction interfaces. This multi-target approach not only increases the likelihood of finding a potent inhibitor, but could also help identify a collection of anti-coronavirus drugs that would retain efficacy in the face of viral mutation. Drugs belonging to different regimen classes could be combined to develop possible combination therapies, and top hits that bind at highly conserved sites would be potential candidates for further development as coronavirus drugs. Here, we present the top 200 in silico hits for each target site. While in-house experimental validation of some of these compounds is currently underway, we want to make this array of potential inhibitor candidates available to researchers worldwide in consideration of the pressing need for fast-tracked drug development.}, language = {en} } @article{FackeldeyOsterSallandtetal.2022, author = {Fackeldey, Konstantin and Oster, Mathias and Sallandt, Leon and Schneider, Reinhold}, title = {Approximative Policy Iteration for Exit Time Feedback Control Problems driven by Stochastic Differential Equations using Tensor Train format}, volume = {20}, journal = {SIAM Journal on Multiscale Modeling and Simulation}, number = {1}, arxiv = {http://arxiv.org/abs/2010.04465}, doi = {10.1137/20M1372500}, pages = {379 -- 403}, year = {2022}, abstract = {We consider a stochastic optimal exit time feedback control problem. The Bellman equation is solved approximatively via the Policy Iteration algorithm on a polynomial ansatz space by a sequence of linear equations. As high degree multi-polynomials are needed, the corresponding equations suffer from the curse of dimensionality even in moderate dimensions. We employ tensor-train methods to account for this problem. The approximation process within the Policy Iteration is done via a Least-Squares ansatz and the integration is done via Monte-Carlo methods. Numerical evidences are given for the (multi dimensional) double well potential and a three-hole potential.}, language = {en} } @misc{WeberFackeldey2015, author = {Weber, Marcus and Fackeldey, Konstantin}, title = {G-PCCA: Spectral Clustering for Non-reversible Markov Chains}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-55505}, year = {2015}, abstract = {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.}, language = {en} } @article{AndraeMerkelDurmazetal.2014, author = {Andrae, Karsten and Merkel, Stefan and Durmaz, Vedat and Fackeldey, Konstantin and K{\"o}ppen, Robert and Weber, Marcus and Koch, Matthias}, title = {Investigation of the Ergopeptide Epimerization Process}, volume = {2}, journal = {Computation}, number = {3}, doi = {10.3390/computation2030102}, pages = {102 -- 111}, year = {2014}, abstract = {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.}, language = {en} } @article{WeberFackeldey2014, author = {Weber, Marcus and Fackeldey, Konstantin}, title = {Computing the Minimal Rebinding Effect Included in a Given Kinetics}, volume = {12}, journal = {Multiscale Model. Simul.}, number = {1}, doi = {10.1137/13091124X}, pages = {318 -- 334}, year = {2014}, abstract = {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.}, language = {en} } @article{WeberFackeldeySchuette2017, author = {Weber, Marcus and Fackeldey, Konstantin and Sch{\"u}tte, Christof}, title = {Set-Free Markov State Model Building}, volume = {146}, journal = {Journal of Chemical Physics}, number = {12}, doi = {10.1063/1.4978501}, year = {2017}, language = {en} } @article{FackeldeyNiknejadWeber2017, author = {Fackeldey, Konstantin and Niknejad, Amir and Weber, Marcus}, title = {Finding Metastabilities in Reversible Markov Chains based on Incomplete Sampling: Case of Molecular Simulation}, journal = {Special Matrices}, number = {5/1}, doi = {10.1515/spma-2017-0006}, pages = {73 -- 81}, year = {2017}, language = {en} } @article{FackeldeyWeber2017, author = {Fackeldey, Konstantin and Weber, Marcus}, title = {GenPCCA -- Markov State Models for Non-Equilibrium Steady States}, journal = {Big data clustering: Data preprocessing, variable selection, and dimension reduction. WIAS Report No. 29}, doi = {10.20347/WIAS.REPORT.29}, pages = {70 -- 80}, year = {2017}, language = {en} } @inproceedings{FackeldeyBujotzek2014, author = {Fackeldey, Konstantin and Bujotzek, Alexander}, title = {Local Quantum-Like Updates in Classical Molecular Simulation Realized Within an Uncoupling-Coupling Approach}, volume = {19}, booktitle = {Progress in Industrial Mathematics at ECMI 2012}, doi = {10.1007/978-3-319-05365-3_42}, pages = {309 -- 313}, year = {2014}, abstract = {In this article a method to improve the precision of the classical molecular dynamics force field by solving an approximation problem with scattered quantum mechanical data is presented. This novel technique is based on two steps. In the first step a partition of unity scheme is used for partitioning the state space by meshfree basis functions. As a consequence the potential can be localized for each basis function. In a second step, for one state in each meshfree basis function, the precise QM-based charges are computed. These local QM-based charges are then used, to optimize the local potential function. The performance of this method is shown for the alanine tripeptide.}, language = {en} } @misc{KrauseFackeldeyKrause2013, author = {Krause, Dorian and Fackeldey, Konstantin and Krause, Rolf}, title = {A parallel multiscale simulation toolbox for coupling molecular dynamics and finite elements}, issn = {1438-0064}, doi = {10.1007/978-3-319-00786-1_14}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42354}, year = {2013}, abstract = {It is the ultimate goal of concurrent multiscale methods to provide computational tools that allow to simulation physical processes with the accuracy of micro-scale and the computational speed of macro-scale models. As a matter of fact, the efficient and scalable implementation of concurrent multiscale methods on clusters and supercomputers is a complicated endeavor. In this article we present the parallel multiscale simulation tool MACI which has been designed for efficient coupling between molecular dynamics and finite element codes. We propose a specification for a thin yet versatile interface for the coupling of molecular dynamics and finite element codes in a modular fashion. Further we discuss the parallelization strategy pursued in MACI, in particular, focusing on the parallel assembly of transfer operators and their efficient execution.}, language = {en} } @article{BujotzekSchuettNielsenetal.2014, author = {Bujotzek, Alexander and Sch{\"u}tt, Ole and Nielsen, Adam and Fackeldey, Konstantin and Weber, Marcus}, title = {ZIBgridfree: Efficient Conformational Analysis by Partition-of-Unity Coupling}, volume = {52}, journal = {Journal of Mathematical Chemistry}, number = {3}, doi = {10.1007/s10910-013-0265-1}, pages = {781 -- 804}, year = {2014}, language = {de} } @article{WeberFackeldey2014, author = {Weber, Marcus and Fackeldey, Konstantin}, title = {Local Refinements in Classical Molecular Dynamics Simulations}, volume = {490}, journal = {J. Phys. Conf. Ser.}, pages = {012016}, year = {2014}, language = {en} } @article{AndraeDurmazFackeldeyetal.2013, author = {Andrae, Karsten and Durmaz, Vedat and Fackeldey, Konstantin and Scharkoi, Olga and Weber, Marcus}, title = {Medizin aus dem Computer}, volume = {62}, journal = {Der Anaesthesist}, number = {7}, publisher = {Springer}, doi = {10.1007/s00101-013-2202-x}, pages = {561 -- 557}, 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} } @misc{Fackeldey2010, author = {Fackeldey, Konstantin}, title = {Challenges in Atomistic-to-Continuum Coupling}, volume = {2010}, journal = {ZIB Report}, edition = {10-12}, doi = {10.1155/2015/834517}, year = {2010}, abstract = {This paper is concerned with the design, analysis, and implementation of concurrent coupling approaches where different (atomic and continuous) models are used simultaneously within a single simulation process. Thereby, several problems or pitfalls can happen, for example, the reflection of molecular movements at the "boundary" between the atomic and continuum regions which leads to an unphysical increase in energy in the atomic model. We investigate the problems with the aim of giving an introduction into this field and preventing errors for scientists starting their research towards multiscale methods.}, language = {en} } @phdthesis{Fackeldey2015, author = {Fackeldey, Konstantin}, title = {Crossing the Scales in Structural Mechanics and Molecular Research}, year = {2015}, 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{GorgullaCınaroğluFischeretal.2021, author = {Gorgulla, Christoph and {\c{C}}{\i}naroğlu, S{\"u}leyman and Fischer, Patrick D. and Fackeldey, Konstantin and Wagner, Gerhard and Arthanari, Haribabu}, title = {VirtualFlow Ants—Ultra-Large Virtual Screenings with Artificial Intelligence Driven Docking Algorithm Based on Ant Colony Optimization}, volume = {22}, journal = {Special Issue Artificial Intelligence \& Deep Learning Approaches for Structural Bioinformatics}, number = {11}, doi = {https://doi.org/10.3390/ijms22115807}, pages = {5807}, year = {2021}, abstract = {The docking program PLANTS, which is based on ant colony optimization (ACO) algorithm, has many advanced features for molecular docking. Among them are multiple scoring functions, the possibility to model explicit displaceable water molecules, and the inclusion of experimental constraints. Here, we add support of PLANTS to VirtualFlow (VirtualFlow Ants), which adds a valuable method for primary virtual screenings and rescoring procedures. Furthermore, we have added support of ligand libraries in the MOL2 format, as well as on the fly conversion of ligand libraries which are in the PDBQT format to the MOL2 format to endow VirtualFlow Ants with an increased flexibility regarding the ligand libraries. The on the fly conversion is carried out with Open Babel and the program SPORES. We applied VirtualFlow Ants to a test system involving KEAP1 on the Google Cloud up to 128,000 CPUs, and the observed scaling behavior is approximately linear. Furthermore, we have adjusted several central docking parameters of PLANTS (such as the speed parameter or the number of ants) and screened 10 million compounds for each of the 10 resulting docking scenarios. We analyzed their docking scores and average docking times, which are key factors in virtual screenings. The possibility of carrying out ultra-large virtual screening with PLANTS via VirtualFlow Ants opens new avenues in computational drug discovery.}, 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{GorgullaNigamKoopetal.2023, author = {Gorgulla, Christoph and Nigam, AkshatKumar and Koop, Matt and Selim {\c{C}}{\i}naroğlu, S{\"u}leyman and Secker, Christopher and Haddadnia, Mohammad and Kumar, Abhishek and Malets, Yehor and Hasson, Alexander and Li, Minkai and Tang, Ming and Levin-Konigsberg, Roni and Radchenko, Dmitry and Kumar, Aditya and Gehev, Minko and Aquilanti, Pierre-Yves and Gabb, Henry and Alhossary, Amr and Wagner, Gerhard and Aspuru-Guzik, Al{\´a}n and Moroz, Yurii S. and Fackeldey, Konstantin and Arthanari, Haribabu}, title = {VirtualFlow 2.0 - The Next Generation Drug Discovery Platform Enabling Adaptive Screens of 69 Billion Molecules}, journal = {bioRxiv}, doi = {10.1101/2023.04.25.537981}, year = {2023}, 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{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{NitzkeFackeldeyVrabec2021, author = {Nitzke, Isabel and Fackeldey, Konstantin and Vrabec, Jadran}, title = {Long range corrections for inhomogeneous fluids containing a droplet or a bubble}, journal = {Molecular Simulation}, doi = {https://doi.org/10.1080/08927022.2021.1954639}, pages = {1 -- 14}, year = {2021}, abstract = {Long range corrections for molecular simulations of inhomogeneous fluids with a spherical interface are presented. Correction terms for potential energy, force and virial are derived for the monatomic Lennard-Jones fluid. The method is generalised to the Mie potential and arbitrary molecular structures, employing a numerically efficient centre of mass cut-off scheme. The results are validated by a series of droplet simulations for one-centre and two-centre Lennard-Jones fluids with different cut-off radii rc. Systems with rc=8σ provide a check of self-consistence. Further, a system containing a bubble is investigated for the one-centre Lennard-Jones fluid. The equilibrium properties are almost completely independent on the cut-off radius. In comparison with vapour-liquid equilibrium data for systems without a curved interface, all properties show the expected behaviour. Simulation data are used to approximate the surface tension, which is in good agreement with the findings for planar interfaces, thus verifying the present corrections.}, 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{GorgullaJayarajFackeldeyetal.2022, author = {Gorgulla, Christoph and Jayaraj, Abhilash and Fackeldey, Konstantin and Arthanari, Haribabu}, title = {Emerging frontiers in virtual drug discovery: From quantum mechanical methods to deep learning approaches}, volume = {69}, journal = {Current Opinion in Chemical Biology}, doi = {10.1016/j.cbpa.2022.102156}, pages = {102156 -- 102156-12}, year = {2022}, abstract = {Virtual screening-based approaches to discover initial hit and lead compounds have the potential to reduce both the cost and time of early drug discovery stages, as well as to find inhibitors for even challenging target sites such as protein-protein interfaces. Here in this review, we provide an overview of the progress that has been made in virtual screening methodology and technology on multiple fronts in recent years. The advent of ultra-large virtual screens, in which hundreds of millions to billions of compounds are screened, has proven to be a powerful approach to discover highly potent hit compounds. However, these developments are just the tip of the iceberg, with new technologies and methods emerging to propel the field forward. Examples include novel machine-learning approaches, which can reduce the computational costs of virtual screening dramatically, while progress in quantum-mechanical approaches can increase the accuracy of predictions of various small molecule properties.}, 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{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} } @misc{WitzigBeckenbachEifleretal.2016, author = {Witzig, Jakob and Beckenbach, Isabel and Eifler, Leon and Fackeldey, Konstantin and Gleixner, Ambros and Grever, Andreas and Weber, Marcus}, title = {Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes}, issn = {1438-0064}, doi = {10.1137/16M1091162}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60353}, year = {2016}, abstract = {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.}, language = {en} } @article{WitzigBeckenbachEifleretal.2018, author = {Witzig, Jakob and Beckenbach, Isabel and Eifler, Leon and Fackeldey, Konstantin and Gleixner, Ambros and Grever, Andreas and Weber, Marcus}, title = {Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes}, volume = {16}, journal = {Multiscale Modeling and Simulation}, number = {1}, issn = {1438-0064}, doi = {10.1137/16M1091162}, pages = {248 -- 265}, year = {2018}, abstract = {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.}, language = {en} } @article{GorgullaGarzaKapiletal.2025, author = {Gorgulla, Christoph and Garza, Alejandro J. and Kapil, Venkat and Fackeldey, Konstantin}, title = {QUASAR: A Flexible QM-MM Method for Biomolecular Systems based on Restraining Spheres}, volume = {320}, journal = {Computer Physics Communications}, issn = {0010-4655}, doi = {10.1016/j.cpc.2025.109949}, year = {2025}, abstract = {Quantum mechanical models of molecules theoretically offer unprecedented accuracy in predicting values associated with these systems, including the free energy of interaction between two molecules. However, high-accuracy quantum mechanical methods are computationally too expensive to be applied to larger systems, including most biomolecular systems such as proteins. To circumvent this challenge, the hybrid quantum mechanics/molecular mechanics (QM/MM) method was developed, allowing one to treat only the most important part of the system on the quantum mechanical level and the remaining part on the classical level. To date, QM/MM simulations for biomolecular systems have been carried out almost exclusively on the electronic structure level, neglecting nuclear quantum effects (NQEs). Yet NQEs can play a major role in biomolecular systems [1]. Here, we present i-QI, a QM/MM client for the path integral molecular dynamics (PIMD) software i-PI [2, 3, 4]. i-QI allows for carrying out QM/MM simulations simultaneously, allowing for the inclusion of electronic as well as nuclear quantum effects. i-QI implements a new QM/MM scheme based on constraining potentials called QUASAR, which allows handling diffusive systems, such as biomolecules solvated in water solvent. The QUASAR method is suitable in particular when the properties of interest are equilibrium properties, such as the free energy of binding. i-QI is freely available and open source, and we demonstrate it on a test system.}, language = {en} } @article{GonnermannMuellerHaaseLeinsetal.2026, author = {Gonnermann-M{\"u}ller, Jana and Haase, Jennifer and Leins, Nicolas and Igel, Moritz and Fackeldey, Konstantin and Pokutta, Sebastian}, title = {FACET: Multi-Agent AI Supporting Teachers in Scaling Differentiated Learning for Diverse Students}, journal = {arXiv}, arxiv = {http://arxiv.org/abs/2601.22788}, doi = {https://arxiv.org/abs/2601.22788}, year = {2026}, abstract = {Classrooms are becoming increasingly heterogeneous, comprising learners with diverse performance and motivation levels, language proficiencies, and learning differences such as dyslexia and ADHD. While teachers recognize the need for differentiated instruction, growing workloads create substantial barriers, making differentiated instruction an ideal that is often unrealized in practice. Current AI educational tools, which promise differentiated materials, are predominantly student-facing and performance-centric, ignoring other aspects that shape learning outcomes. We introduce FACET, a teacher-facing multi-agent framework designed to address these gaps by supporting differentiation that accounts for motivation, performance, and learning differences. Developed with educational stakeholders from the outset, the framework coordinates four specialized agents, including learner simulation, diagnostic assessment, material generation, and evaluation within a teacher-in-the-loop design. School principals (N = 30) shaped system requirements through participatory workshops, while in-service K-12 teachers (N = 70) evaluated material quality. Mixed-methods evaluation demonstrates strong perceived value for inclusive differentiation. Practitioners emphasized both the urgent need arising from classroom heterogeneity and the importance of maintaining pedagogical autonomy as a prerequisite for adoption. We discuss implications for future school deployment and outline partnerships for longitudinal classroom implementation.}, language = {en} } @article{GonnermannMuellerHaaseFackeldeyetal.2025, author = {Gonnermann-M{\"u}ller, Jana and Haase, Jennifer and Fackeldey, Konstantin and Pokutta, Sebastian}, title = {FACET: Teacher-Centred LLM-Based Multi-Agent Systems-Towards Personalized Educational Worksheets}, arxiv = {http://arxiv.org/abs/2508.11401}, year = {2025}, abstract = {The increasing heterogeneity of student populations poses significant challenges for teachers, particularly in mathematics education, where cognitive, motivational, and emotional differences strongly influence learning outcomes. While AI-driven personalization tools have emerged, most remain performance-focused, offering limited support for teachers and neglecting broader pedagogical needs. This paper presents the FACET framework, a teacher-facing, large language model (LLM)-based multi-agent system designed to generate individualized classroom materials that integrate both cognitive and motivational dimensions of learner profiles. The framework comprises three specialized agents: (1) learner agents that simulate diverse profiles incorporating topic proficiency and intrinsic motivation, (2) a teacher agent that adapts instructional content according to didactical principles, and (3) an evaluator agent that provides automated quality assurance. We tested the system using authentic grade 8 mathematics curriculum content and evaluated its feasibility through a) automated agent-based assessment of output quality and b) exploratory feedback from K-12 in-service teachers. Results from ten internal evaluations highlighted high stability and alignment between generated materials and learner profiles, and teacher feedback particularly highlighted structure and suitability of tasks. The findings demonstrate the potential of multi-agent LLM architectures to provide scalable, context-aware personalization in heterogeneous classroom settings, and outline directions for extending the framework to richer learner profiles and real-world classroom trials.}, language = {en} }