@inproceedings{SchuetteHuisinga2003, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm}, title = {Biomolecular Conformations can be Identified as Metastable Sets of Molecular Dynamics}, volume = {X}, booktitle = {Special Volume}, editor = {Ciarlet, P. and Le Bris, Claude}, publisher = {Elsevier}, pages = {699 -- 744}, year = {2003}, language = {en} } @article{HuisingaSchuetteStuart2003, author = {Huisinga, Wilhelm and Sch{\"u}tte, Christof and Stuart, Andrew}, title = {Extracting Macroscopic Stochastic Dynamics}, volume = {56}, journal = {Comm. Pure Appl. Math.}, number = {2}, doi = {10.1002/cpa.10057}, pages = {234 -- 269}, year = {2003}, language = {en} } @inproceedings{SchuetteHuisingaMeyn2003, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm and Meyn, S.}, title = {Metastability of Diffusion Processes}, volume = {110}, booktitle = {Nonlinear Stochastic Dynamics}, editor = {Namachchivaya, N. and Lin, Y.}, publisher = {Springer}, pages = {71 -- 81}, year = {2003}, language = {en} } @inproceedings{FischerSchuetteDeuflhardetal.2002, author = {Fischer, Alexander and Sch{\"u}tte, Christof and Deuflhard, Peter and Cordes, Frank}, title = {Hierarchical Uncoupling-Coupling of Metastable Conformations}, volume = {24}, booktitle = {Computational Methods for Macromolecules}, editor = {Schlick, T. and Gan, H.}, publisher = {Springer}, pages = {235 -- 259}, year = {2002}, language = {en} } @article{HorenkoSchmidtSchuette2002, author = {Horenko, Illia and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {Multidimensional Classical Liouville Dynamics with Quantum Initial Conditions}, volume = {117}, journal = {J. Chem. Phys.}, number = {10}, doi = {10.1063/1.1498467}, pages = {4643 -- 4650}, year = {2002}, language = {en} } @article{HorenkoSalzmannSchmidtetal.2002, author = {Horenko, Illia and Salzmann, Ch. and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {Quantum-Classical Liouville Approach to Molecular Dynamics}, volume = {117}, journal = {J. Chem. Phys.}, number = {24}, doi = {10.1063/1.1522712}, pages = {11075 -- 11088}, year = {2002}, language = {en} } @article{HorenkoSchmidtSchuette2001, author = {Horenko, Illia and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {A Theoretical Model for Molecules Interacting with Intense Laser Pulses}, volume = {115}, journal = {J. Chem. Phys.}, number = {13}, doi = {10.1063/1.1398577}, pages = {5733 -- 5743}, year = {2001}, language = {en} } @inproceedings{SchuetteHuisingaDeuflhard2001, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm and Deuflhard, Peter}, title = {Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems}, booktitle = {Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems}, editor = {Fiedler, B.}, publisher = {Springer}, pages = {191 -- 223}, year = {2001}, language = {en} } @inproceedings{SchuetteHuisinga2000, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm}, title = {Biomolecular Conformations as Metastable Sets of Markov Chains}, booktitle = {Proceedings of the 38th Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinoins/USA}, editor = {Sreenivas, R. and Jones, D.}, publisher = {University of Illinois at Urbana-Champaign}, pages = {1106 -- 1115}, year = {2000}, language = {en} } @misc{ZhangHartmannSchuette2016, author = {Zhang, Wei and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Effective Dynamics Along Given Reaction Coordinates, and Reaction Rate Theory}, issn = {1438-0064}, doi = {10.1039/C6FD00147E}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59706}, year = {2016}, abstract = {In molecular dynamics and related fields one considers dynamical descriptions of complex systems in full (atomic) detail. In order to reduce the overwhelming complexity of realistic systems (high dimension, large timescale spread, limited computational resources) the projection of the full dynamics onto some reaction coordinates is examined in order to extract statistical information like free energies or reaction rates. In this context, the effective dynamics that is induced by the full dynamics on the reaction coordinate space has attracted considerable attention in the literature. In this article, we contribute to this discussion: We first show that if we start with an ergodic diffusion processes whose invariant measure is unique then these properties are inherited by the effective dynamics. Then, we give equations for the effective dynamics, discuss whether the dominant timescales and reaction rates inferred from the effective dynamics are accurate approximations of such quantities for the full dynamics, and compare our findings to results from approaches like Zwanzig-Mori, averaging, or homogenization. Finally, by discussing the algorithmic realization of the effective dynamics, we demonstrate that recent algorithmic techniques like the "equation-free" approach and the "heterogeneous multiscale method" can be seen as special cases of our approach.}, language = {en} } @misc{CiccottiFerrarioSchuette2018, author = {Ciccotti, Giovanni and Ferrario, Mauro and Sch{\"u}tte, Christof}, title = {Molecular Dynamics vs. Stochastic Processes: Are We Heading Anywhere?}, volume = {20}, journal = {Special Issue: Understanding Molecular Dynamics via Stochastic Processes, Entropy}, number = {5}, doi = {10.3390/e20050348}, year = {2018}, language = {en} } @article{ZhangSchuette2017, author = {Zhang, Wei and Sch{\"u}tte, Christof}, title = {Reliable approximation of long relaxation timescales in molecular dynamics}, volume = {19}, journal = {Entropy}, number = {7}, doi = {10.3390/e19070367}, year = {2017}, language = {en} } @article{ZhangHartmannSchuette2016, author = {Zhang, Wei and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Effective dynamics along given reaction coordinates, and reaction rate theory}, journal = {Faraday Discussions}, number = {195}, doi = {10.1039/C6FD00147E}, pages = {365 -- 394}, year = {2016}, language = {en} } @article{KlebanovSikorskiSchuetteetal.2021, author = {Klebanov, Ilja and Sikorski, Alexander and Sch{\"u}tte, Christof and R{\"o}blitz, Susanna}, title = {Objective priors in the empirical Bayes framework}, volume = {48}, journal = {Scandinavian Journal of Statistics}, number = {4}, publisher = {Wiley Online Library}, doi = {10.1111/sjos.12485}, pages = {1212 -- 1233}, year = {2021}, abstract = {When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the nonparametric case, the maximum likelihood estimate is known to overfit the data, an issue that is commonly tackled by regularization. However, the majority of regularizations are ad hoc choices which lack invariance under reparametrization of the model and result in inconsistent estimates for equivalent models. We introduce a nonparametric, transformation-invariant estimator for the prior distribution. Being defined in terms of the missing information similar to the reference prior, it can be seen as an extension of the latter to the data-driven setting. This implies a natural interpretation as a trade-off between choosing the least informative prior and incorporating the information provided by the data, a symbiosis between the objective and empirical Bayes methodologies.}, language = {en} } @article{HartmannRichterSchuetteetal.2017, author = {Hartmann, Carsten and Richter, Lorenz and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Variational characterization of free energy: theory and algorithms}, volume = {19}, journal = {Entropy}, number = {11}, doi = {10.3390/e19110626}, pages = {626}, year = {2017}, language = {en} } @article{DibakJdelRazoDeSanchoetal.2018, 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}, volume = {148}, journal = {Journal of Chemical Physics}, number = {214107}, doi = {10.1063/1.5020294}, year = {2018}, 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{DjurdjevacConradHelfmannZonkeretal.2018, author = {Djurdjevac Conrad, Natasa and Helfmann, Luzie and Zonker, Johannes and Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {Human mobility and innovation spreading in ancient times: a stochastic agent-based simulation approach}, volume = {7}, journal = {EPJ Data Science}, number = {1}, edition = {EPJ Data Science}, publisher = {EPJ Data Science}, doi = {10.1140/epjds/s13688-018-0153-9}, pages = {24}, year = {2018}, abstract = {Human mobility always had a great influence on the spreading of cultural, social and technological ideas. Developing realistic models that allow for a better understanding, prediction and control of such coupled processes has gained a lot of attention in recent years. However, the modeling of spreading processes that happened in ancient times faces the additional challenge that available knowledge and data is often limited and sparse. In this paper, we present a new agent-based model for the spreading of innovations in the ancient world that is governed by human movements. Our model considers the diffusion of innovations on a spatial network that is changing in time, as the agents are changing their positions. Additionally, we propose a novel stochastic simulation approach to produce spatio-temporal realizations of the spreading process that are instructive for studying its dynamical properties and exploring how different influences affect its speed and spatial evolution.}, language = {en} } @article{MoellerIsbilirSungkawornetal.2020, author = {M{\"o}ller, Jan and Isbilir, Ali and Sungkaworn, Titiwat and Osberg, Brenda and Karathanasis, Christos and Sunkara, Vikram and Grushevsky, Eugene O and Bock, Andreas and Annibale, Paolo and Heilemann, Mike and Sch{\"u}tte, Christof and Lohse, Martin J.}, title = {Single molecule mu-opioid receptor membrane-dynamics reveal agonist-specific dimer formation with super-resolved precision}, volume = {16}, journal = {Nature Chemical Biology}, doi = {10.1038/s41589-020-0566-1}, pages = {946 -- 954}, year = {2020}, language = {en} } @article{BittracherSchuette2021, author = {Bittracher, Andreas and Sch{\"u}tte, Christof}, title = {A probabilistic algorithm for aggregating vastly undersampled large Markov chains}, volume = {416}, journal = {Physica D: Nonlinear Phenomena}, doi = {https://doi.org/10.1016/j.physd.2020.132799}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-75874}, year = {2021}, language = {en} } @article{BittracherKlusHamzietal.2021, author = {Bittracher, Andreas and Klus, Stefan and Hamzi, Boumediene and Sch{\"u}tte, Christof}, title = {Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds}, volume = {31}, journal = {Journal of Nonlinear Science}, doi = {10.1007/s00332-020-09668-z}, year = {2021}, abstract = {We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based on learning a parameterization of a low-dimensional transition manifold in a certain function space. In this article, we enhance this approach by embedding and learning this transition manifold in a reproducing kernel Hilbert space, exploiting the favorable properties of kernel embeddings. Under mild assumptions on the kernel, the manifold structure is shown to be preserved under the embedding, and distortion bounds can be derived. This leads to a more robust and more efficient algorithm compared to the previous parameterization approaches.}, language = {en} }