@misc{DeuflhardHuisingaJahnkeetal.2007, author = {Deuflhard, Peter and Huisinga, Wilhelm and Jahnke, Tobias and Wulkow, Michael}, title = {Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9471}, number = {07-04}, year = {2007}, abstract = {\begin{abstract} In systems biology, the stochastic description of biochemical reaction kinetics is increasingly being employed to model gene regulatory networks and signalling pathways. Mathematically speaking, such models require the numerical solution of the underlying evolution equat ion, also known as the chemical master equation (CME). Up to now, the CME has almost exclusively been treated by Monte-Carlo techniques, the most prominent of which is the simulation algorithm suggest ed by Gillespie in 1976. Since this algorithm requires an update for each single reaction event, realizations can be computationally very costly. As an alternative, we here propose a novel approach, which focuses on the discrete partial differential equation (PDE) structure of the CME and thus allows to adopt ideas from adaptive discrete Galerkin methods (as designed by two of the present authors in 1989), which have proven to be highly efficient in the mathematical modelling of polyreaction kinetics. Among the two different options of discretizing the CME as a discrete PDE, the method of lines approach (first space, then time) and the Rothe method (first time, then space), we select the latter one for clear theoretical and algorithmic reasons. First numeric al experiments at a challenging model problem illustrate the promising features of the proposed method and, at the same time, indicate lines of necessary further research. \end{abstract}}, language = {en} } @article{HuisingaBestCordesetal.1999, author = {Huisinga, Wilhelm and Best, Christoph and Cordes, Frank and Roitzsch, Rainer and Sch{\"u}tte, Christof}, title = {Identification of Molecular Conformations via Statistical Analysis of Simulation Data}, volume = {20}, journal = {Comp. Chem.}, pages = {1760 -- 1774}, year = {1999}, language = {en} } @article{HuisingaTelgmannWulkow2006, author = {Huisinga, Wilhelm and Telgmann, R. and Wulkow, Michael}, title = {The virtual lab approach to pharmacokinetic}, volume = {11}, journal = {Drug Discov Today}, pages = {800 -- 805}, year = {2006}, language = {en} } @article{HuisingaBestRoitzschetal.1999, author = {Huisinga, Wilhelm and Best, Christoph and Roitzsch, Rainer and Sch{\"u}tte, Christof and Cordes, Frank}, title = {From Simulation Data to Conformational Ensembles}, volume = {20}, journal = {J. Comp. Chem.}, number = {16}, pages = {1760 -- 1774}, year = {1999}, language = {en} } @inproceedings{GalliatHuisingaDeuflhard2000, author = {Galliat, Tobias and Huisinga, Wilhelm and Deuflhard, Peter}, title = {Self-Organizing Maps Combined with Eigenmode Analysis for Automated Cluster Identification}, booktitle = {Neural Computation, ICSC Academic Press}, editor = {H. Bothe, R.}, pages = {227 -- 232}, year = {2000}, language = {en} } @article{SchuetteFischerHuisingaetal.1999, author = {Sch{\"u}tte, Christof and Fischer, Alexander and Huisinga, Wilhelm and Deuflhard, Peter}, title = {A Direct Approach to Conformational Dynamics Based on Hybrid Monte Carlo}, volume = {151}, journal = {J. Comput. Phys.}, pages = {146 -- 168}, year = {1999}, language = {en} } @incollection{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, Bernold}, publisher = {Berlin: Springer}, pages = {191 -- 223}, year = {2001}, language = {en} } @article{vonKleistMenzStockeretal.2011, author = {von Kleist, Max and Menz, Stephan and Stocker, Hartmut and Arasteh, Keikawus and Huisinga, Wilhelm and Sch{\"u}tte, Christof}, title = {HIV Quasispecies Dynamics during Pro-active Treatment Switching}, volume = {6}, journal = {Plos One}, number = {3}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0018204}, pages = {e18204}, year = {2011}, language = {en} } @article{MenzLatorreSchuetteetal.2012, author = {Menz, Stephan and Latorre, J. and Sch{\"u}tte, Christof and Huisinga, Wilhelm}, title = {Hybrid Stochastic--Deterministic Solution of the Chemical Master Equation}, volume = {10}, journal = {SIAM Interdisciplinary Journal Multiscale Modeling and Simulation (MMS)}, number = {4}, doi = {10.1137/110825716}, pages = {1232 -- 1262}, year = {2012}, language = {en} } @article{DeuflhardHuisingaJahnkeetal.2008, author = {Deuflhard, Peter and Huisinga, Wilhelm and Jahnke, Tobias and Wulkow, Michael}, title = {Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation}, volume = {30}, journal = {SIAM J. Sci. Comput}, number = {6}, pages = {2990 -- 3011}, year = {2008}, language = {en} } @article{DeuflhardHuisingaFischeretal.2000, author = {Deuflhard, Peter and Huisinga, Wilhelm and Fischer, Alexander and Sch{\"u}tte, Christof}, title = {Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains}, volume = {315}, journal = {Lin. Alg. Appl.}, number = {1-3}, doi = {10.1016/S0024-3795(00)00095-1}, pages = {39 -- 59}, year = {2000}, language = {en} } @inproceedings{SchuetteHuisinga2000, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm}, title = {On Conformational Dynamics induced by Langevin Processes}, volume = {2}, booktitle = {Equadiff 99}, editor = {Fiedler, B. and Grger, K. and Sprekels, J{\"u}rgen}, publisher = {World Scientific}, doi = {10.1142/9789812792617_0234}, pages = {1247 -- 1262}, year = {2000}, language = {en} } @article{SchuetteFischerHuisingaetal.1999, author = {Sch{\"u}tte, Christof and Fischer, Alexander and Huisinga, Wilhelm and Deuflhard, Peter}, title = {A Direct Approach to Conformational Dynamics based on Hybrid Monte Carlo}, volume = {151}, journal = {J. Comp. Phys}, number = {1}, doi = {10.1006/jcph.1999.6231}, pages = {146 -- 168}, year = {1999}, language = {en} } @article{HuisingaBestRoitzschetal.1999, author = {Huisinga, Wilhelm and Best, Christoph and Roitzsch, Rainer and Sch{\"u}tte, Christof and Cordes, Frank}, title = {From Simulation Data to Conformational Ensembles}, volume = {20}, journal = {J. Comp. Chem.}, number = {16}, doi = {10.1002/(SICI)1096-987X(199912)20:16<1760::AID-JCC8>3.0.CO;2-2}, pages = {1760 -- 1774}, year = {1999}, language = {en} } @article{HorenkoLorenzSchuetteetal.2005, author = {Horenko, Illia and Lorenz, S. and Sch{\"u}tte, Christof and Huisinga, Wilhelm}, title = {Adaptive Approach for Non-Linear Sensitivity Analysis of Reaction Kinetics}, volume = {26}, journal = {J. Comp. Chem.}, number = {9}, doi = {10.1002/jcc.20234}, pages = {941 -- 948}, year = {2005}, language = {en} } @article{SchuetteWalterHartmannetal.2004, author = {Sch{\"u}tte, Christof and Walter, J. and Hartmann, Carsten and Huisinga, Wilhelm}, title = {An Averaging Principle for Fast Degrees of Freedom Exhibiting Long-Term Correlations}, volume = {2}, journal = {Multiscale Model. Simul.}, number = {3}, doi = {10.1137/030600308}, pages = {501 -- 526}, year = {2004}, language = {en} } @article{NettesheimHuisingaSchuette1996, author = {Nettesheim, Peter and Huisinga, Wilhelm and Sch{\"u}tte, Christof}, title = {Chebyshev-Approximation for Wavepacket-Dynamics}, journal = {preprint}, year = {1996}, language = {en} } @article{HuisingaMeynSchuette2004, author = {Huisinga, Wilhelm and Meyn, S. and Sch{\"u}tte, Christof}, title = {Phase Transitions and Metastability in Markovian and Molecular Systems}, volume = {14}, journal = {Ann. Appl. Prob.}, number = {1}, doi = {10.1214/aoap/1075828057}, pages = {419 -- 458}, year = {2004}, language = {en} } @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} }