@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{VillatoroZuehlkeRiebeetal.2016, author = {Villatoro, Jose and Z{\"u}hlke, Martin and Riebe, Daniel and Riedel, Jens and Beitz, Toralf and L{\"o}hmannsr{\"o}ben, Hans-Gerd}, title = {IR-MALDI ion mobility spectrometry}, volume = {408}, journal = {Analytical and Bioanalytical Chemistry}, number = {23}, doi = {10.1007/s00216-016-9739-x}, pages = {6259 -- 6268}, year = {2016}, 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{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} } @article{PrasadTiwariRayetal.2022, author = {Prasad, Anup K. and Tiwari, Chandni and Ray, Sourav and Holden, Stephanie and Armstrong, David A. and Rosengren, K. Johan and Rodger, Alison and Panwar, Ajay S. and Martin, Lisandra L.}, title = {Secondary Structure Transitions for a Family of Amyloidogenic, Antimircobial Uperin 3 Peptides in Contact with Sodium Dodecyl Sulfate}, volume = {87}, journal = {ChemPlusChem}, doi = {10.1002/cplu.202100408}, pages = {e202100408}, year = {2022}, 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{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{TrepteSeckerOlivetetal.2024, author = {Trepte, Philipp and Secker, Christopher and Olivet, Julien and Blavier, Jeremy and Kostova, Simona and Maseko, Sibusiso B and Minia, Igor and Silva Ramos, Eduardo and Cassonnet, Patricia and Golusik, Sabrina and Zenkner, Martina and Beetz, Stephanie and Liebich, Mara J and Scharek, Nadine and Sch{\"u}tz, Anja and Sperling, Marcel and Lisurek, Michael and Wang, Yang and Spirohn, Kerstin and Hao, Tong and Calderwood, Michael A and Hill, David E and Landthaler, Markus and Choi, Soon Gang and Twizere, Jean-Claude and Vidal, Marc and Wanker, Erich E}, title = {AI-guided pipeline for protein-protein interaction drug discovery identifies a SARS-CoV-2 inhibitor}, volume = {20}, journal = {Molecular Systems Biology}, number = {4}, publisher = {Springer Science and Business Media LLC}, issn = {1744-4292}, doi = {https://doi.org/10.1038/s44320-024-00019-8}, pages = {428 -- 457}, year = {2024}, abstract = {Protein-protein interactions (PPIs) offer great opportunities to expand the druggable proteome and therapeutically tackle various diseases, but remain challenging targets for drug discovery. Here, we provide a comprehensive pipeline that combines experimental and computational tools to identify and validate PPI targets and perform early-stage drug discovery. We have developed a machine learning approach that prioritizes interactions by analyzing quantitative data from binary PPI assays or AlphaFold-Multimer predictions. Using the quantitative assay LuTHy together with our machine learning algorithm, we identified high-confidence interactions among SARS-CoV-2 proteins for which we predicted three-dimensional structures using AlphaFold-Multimer. We employed VirtualFlow to target the contact interface of the NSP10-NSP16 SARS-CoV-2 methyltransferase complex by ultra-large virtual drug screening. Thereby, we identified a compound that binds to NSP10 and inhibits its interaction with NSP16, while also disrupting the methyltransferase activity of the complex, and SARS-CoV-2 replication. Overall, this pipeline will help to prioritize PPI targets to accelerate the discovery of early-stage drug candidates targeting protein complexes and pathways.}, 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} } @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{LelievreStoltzZhang2022, author = {Lelievre, Tony and Stoltz, Gabriel and Zhang, Wei}, title = {Multiple projection MCMC algorithms on submanifolds}, journal = {IMA Journal of Numerical Analysis}, arxiv = {http://arxiv.org/abs/2003.09402}, doi = {10.1093/imanum/drac006}, year = {2022}, abstract = {We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for this generalization is that the numerical solvers used to project proposed moves to the submanifold of interest may find several solutions. We show that the new algorithms indeed sample the target probability measure correctly, thanks to some carefully enforced reversibility property. We demonstrate the interest of the new MCMC algorithms on illustrative numerical examples.}, language = {en} } @article{ZhangLiSchuette2022, author = {Zhang, Wei and Li, Tiejun and Sch{\"u}tte, Christof}, title = {Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks}, volume = {465}, journal = {Journal of Computational Physics}, arxiv = {http://arxiv.org/abs/2110.14523}, doi = {10.1016/j.jcp.2022.111377}, year = {2022}, abstract = {In this paper, we consider the eigenvalue PDE problem of the infinitesimal generators of metastable diffusion processes. We propose a numerical algorithm based on training artificial neural networks for solving the leading eigenvalues and eigenfunctions of such high-dimensional eigenvalue problem. The algorithm is useful in understanding the dynamical behaviors of metastable processes on large timescales. We demonstrate the capability of our algorithm on a high-dimensional model problem, and on the simple molecular system alanine dipeptide.}, language = {en} }