@article{SenneTrendelkampSchroerMeyetal.2012, author = {Senne, M. and Trendelkamp-Schroer, B. and Mey, A. and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {EMMA - A software package for Markov model building and analysis}, series = {Journal of Chemical Theory and Computation}, volume = {8}, journal = {Journal of Chemical Theory and Computation}, doi = {10.1021/ct300274u}, pages = {2223 -- 2238}, year = {2012}, language = {en} } @misc{SchuetteDeuflhardNoeetal., author = {Sch{\"u}tte, Christof and Deuflhard, Peter and No{\´e}, Frank and Weber, Marcus}, title = {Design of functional molecules}, series = {MATHEON-Mathematics for Key Technologies}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {49 -- 65}, language = {en} } @article{KoltaiWuNoeetal., author = {Koltai, Peter and Wu, Hao and No{\´e}, Frank and Sch{\"u}tte, Christof}, title = {Optimal data-driven estimation of generalized Markov state models for non-equilibrium dynamics}, series = {Computation}, volume = {6}, journal = {Computation}, number = {1}, publisher = {MDPI}, address = {Basel, Switzerland}, doi = {10.3390/computation6010022}, pages = {22}, language = {en} } @article{DibakdelRazodeSanchoetal., author = {Dibak, Manuel and del Razo, Mauricio J. and de Sancho, David and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations}, series = {Journal of Chemical Physics}, volume = {148}, journal = {Journal of Chemical Physics}, number = {21}, doi = {10.1063/1.5020294}, abstract = {Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long time-scale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large length scales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time and length scales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step toward MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B ⇌ C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.}, language = {en} } @article{KlusNueskeKoltaietal., author = {Klus, Stefan and N{\"u}ske, Feliks and Koltai, Peter and Wu, Hao and Kevrekidis, Ioannis and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {Data-driven model reduction and transfer operator approximation}, series = {Journal of Nonlinear Science}, volume = {28}, journal = {Journal of Nonlinear Science}, number = {3}, doi = {10.1007/s00332-017-9437-7}, pages = {985 -- 1010}, language = {en} } @article{KostreSchuetteNoeetal.2021, author = {Kostre, Margarita and Sch{\"u}tte, Christof and No{\´e}, Frank and del Razo Sarmina, Mauricio}, title = {Coupling Particle-Based Reaction-Diffusion Simulations with Reservoirs Mediated by Reaction-Diffusion PDEs}, series = {Multiscale Modeling \& Simulation}, volume = {19}, journal = {Multiscale Modeling \& Simulation}, number = {4}, publisher = {Society for Industrial and Applied Mathematics}, doi = {10.1137/20M1352739}, pages = {1659 -- 1683}, year = {2021}, abstract = {Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small to be relevant for life processes. Alternatively, particle-based reaction-diffusion models are currently the most accurate and computationally feasible approach at these scales. Their efficiency lies in modeling entire molecules as particles that can diffuse and interact with each other. In this work, we develop modeling and numerical schemes for particle-based reaction-diffusion in an open setting, where the reservoirs are mediated by reaction-diffusion PDEs. We derive two important theoretical results. The first one is the mean-field for open systems of diffusing particles; the second one is the mean-field for a particle-based reaction-diffusion system with second-order reactions. We employ these two results to develop a numerical scheme that consistently couples particle-based reaction-diffusion processes with reaction-diffusion PDEs. This allows modeling open biochemical systems in contact with reservoirs that are time-dependent and spatially inhomogeneous, as in many relevant real-world applications.}, language = {en} } @article{delRazoDibakSchuetteetal., author = {del Razo, Mauricio J. and Dibak, Manuel and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics}, series = {The Journal of Chemical Physics}, volume = {155}, journal = {The Journal of Chemical Physics}, number = {12}, doi = {10.1063/5.0060314}, language = {en} } @article{DibakJdelRazoDeSanchoetal., author = {Dibak, Manuel and J. del Razo, Mauricio and De Sancho, David and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations}, series = {Journal of Chemical Physics}, volume = {148}, journal = {Journal of Chemical Physics}, number = {214107}, doi = {10.1063/1.5020294}, abstract = {Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long-timescale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large lengthscales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time- and lengthscales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B <--> C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.}, language = {en} } @article{NoeSchuetteVandenEijndenetal.2009, author = {No{\´e}, Frank and Sch{\"u}tte, Christof and Vanden-Eijnden, E. and Reich, L. and Weikl, T.}, title = {Constructing the Full Ensemble of Folding Pathways from Short Off-Equilibrium Simulations}, series = {Proc. Natl. Acad. Sci. USA}, volume = {106}, journal = {Proc. Natl. Acad. Sci. USA}, number = {45}, doi = {10.1073/pnas.0905466106}, pages = {19011 -- 19016}, year = {2009}, language = {en} } @article{MetznerNoeSchuette2009, author = {Metzner, Ph. and No{\´e}, Frank and Sch{\"u}tte, Christof}, title = {Estimating the Sampling Error}, series = {Phys. Rev. E}, volume = {80}, journal = {Phys. Rev. E}, number = {2}, publisher = {American Physical Society}, doi = {10.1103/PhysRevE.80.021106}, pages = {021106}, year = {2009}, language = {en} } @article{SarichNoeSchuette2010, author = {Sarich, Marco and No{\´e}, Frank and Sch{\"u}tte, Christof}, title = {On the Approximation Quality of Markov State Models}, series = {Multiscale Model. Simul.}, volume = {8}, journal = {Multiscale Model. Simul.}, number = {4}, doi = {10.1137/090764049}, pages = {1154 -- 1177}, year = {2010}, language = {en} } @article{PrinzWuSarichetal.2011, author = {Prinz, J.-H. and Wu, Hao and Sarich, Marco and Keller, B. and Fischbach, M. and Held, M. and Chodera, J. and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {Markov models of molecular kinetics}, series = {J. Chem. Phys.}, volume = {134}, journal = {J. Chem. Phys.}, doi = {10.1063/1.3565032}, pages = {174105}, year = {2011}, language = {en} } @article{SchuetteNoeLuetal.2011, author = {Sch{\"u}tte, Christof and No{\´e}, Frank and Lu, Jianfeng and Sarich, Marco and Vanden-Eijnden, E.}, title = {Markov State Models Based on Milestoning}, series = {J. Chem. Phys.}, volume = {134}, journal = {J. Chem. Phys.}, number = {20}, doi = {10.1063/1.3590108}, pages = {204105}, year = {2011}, language = {en} } @article{NoeHorenkoSchuetteetal.2007, author = {No{\´e}, Frank and Horenko, Illia and Sch{\"u}tte, Christof and Smith, J.}, title = {Hierarchical Analysis of Conformational Dynamics in Biomolecules}, series = {J. Chem. Phys.}, volume = {126}, journal = {J. Chem. Phys.}, number = {15}, doi = {10.1063/1.2714539}, pages = {155102}, year = {2007}, language = {en} } @article{NoeSmithSchuette2007, author = {No{\´e}, Frank and Smith, J. and Sch{\"u}tte, Christof}, title = {A network-based approach to biomolecular dynamics}, series = {From Computational Biophysics to Systems Biology (CBSB07). Editors}, volume = {NIC Series 36}, journal = {From Computational Biophysics to Systems Biology (CBSB07). Editors}, publisher = {John von Neumann Institute for Computing, J{\"u}lich}, year = {2007}, language = {en} } @article{HorenkoHartmannSchuetteetal.2007, author = {Horenko, Illia and Hartmann, Carsten and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {Data-based Parameter Estimation of Generalized Multidimensional Langevin Processes}, series = {Phys. Rev. E}, volume = {76}, journal = {Phys. Rev. E}, number = {01}, doi = {10.1103/PhysRevE.76.016706}, pages = {016706}, year = {2007}, language = {en} } @article{SchuetteNoeMeerbachetal.2009, author = {Sch{\"u}tte, Christof and No{\´e}, Frank and Meerbach, E. and Metzner, Ph. and Hartmann, Carsten}, title = {Conformation Dynamics}, series = {Proceedings of the 6th International Congress on Industrial and Applied Mathematics, I. Jeltsch and G. Wanner (eds.),}, journal = {Proceedings of the 6th International Congress on Industrial and Applied Mathematics, I. Jeltsch and G. Wanner (eds.),}, publisher = {EMS publishing house}, doi = {10.4171/056-1/15}, pages = {297 -- 335}, year = {2009}, language = {en} }