## C03 - Multiscale modelling and simulation for spatiotemporal master equations

**Head(s):** Prof. Dr. Felix Höfling (FU Berlin), Prof. Dr. Frank Noé (FU Berlin), Prof. Dr. Christof Schütte (FU Berlin)

**Project member(s):** Dr. Rainald Ehrig, Christoph Fröhner, Dr. Daniela Frömberg, Luigi Sbailò, Dr. Arthur Straube, Dr. Stefanie Winkelmann

**Participating institution(s):** FU Berlin, ZIB

### Project Summary

Chemical reactions cover many length scales from the formation of chemical bonds at the atomistic scale up to the physiological response of a whole cell or the size of a chemical reactor. Concomitantly, copy numbers may vary drastically between molecular species and as a function of time, covering many orders of magnitude. In biological and technological applications, complex geometrical landscapes may arise from cellular crowding or nanoporous grains. Simulations of such situations are thus facing a number of challenges, which need to be overcome by efficient modelling.

In C03 we want to push the methodological boundaries of modelling reaction kinetics in different regimes of the scaling cascades (low and high particle concentrations, fast and slow diffusion), and the scaling transitions between them. In the first funding period, significant progress has been achieved regarding models for different levels of resolution (mathematical foundations, new hybrid models coupling different levels, and their algorithmic realisation and practical use).

In the subsequent funding period, we aim at (i) a seamless integration of models for specific scaling regimes into hybrid models for real-life systems where population numbers may vary dramatically; (ii) developing rigorous particle-based reaction dynamics schemes with particle interaction forces and characterising the effect of molecular crowding on reaction kinetics; (iii) derive effective particle-based reaction dynamics schemes that account for crowded media and establish the coarse-graining transition to the spatiotemporal Master equation; (iv) bridging particle-based reaction dynamics with molecular dynamics (MD), both in order to obtain kinetic parameters for the reaction dynamics simulation, and to form a multiscale simulation method.

### Project publications

Scherer, M. K. and Husic, B.E. and Hoffmann, M. and Paul, F. and Wu, H. and Noé, F.
(2018)
*Variational Selection of Features for Molecular Kinetics.*
SFB 1114 Preprint in arXiv:1811.11714
.
pp. 1-12.
(Unpublished)

Wehmeyer, C. and Scherer, M. K. and Hempel, T. and Husic, B.E. and Olsson, S. and Noé, F.
(2018)
*Introduction to Markov state modeling with the PyEMMA software — v1.0.*
LiveCoMS, 1
(1).
pp. 1-12.
ISSN E-ISSN: 2575-6524
(Unpublished)

del Razo, M.J. and Qian, H. and Noé, F.
(2018)
*Grand canonical diffusion-influenced reactions: a stochastic theory with applications to multiscale reaction-diffusion simulations.*
J. Chem. Phys., 149
(4).
ISSN 0021-9606, ESSN: 1089-7690

Sadeghi, M. and Weikl, T. and Noé, F.
(2018)
*Particle-based membrane model for mesoscopic simulation of cellular dynamics.*
J. Chem. Phys., 148
(4).
044901.

Paul, F. and Wehmeyer, C. and Abualrous, E. T. and Wu, H. and Crabtree, M. D. and Schöneberg, J. and Clarke, J. and Freund, C. and Weikl, T. and Noé, F.
(2017)
*Protein-peptide association kinetics beyond the seconds timescale from atomistic simulations.*
Nat. Comm., 8
(1095).

Winkelmann, S. and Schütte, Ch.
(2017)
*Hybrid models for chemical reaction networks: Multiscale theory
and application to gene regulatory systems.*
Journal of Chemical Physics, 147
(11).
pp. 1-18.

Olsson, Simon and Wu, H. and Paul, F. and Clementi, C. and Noé, F.
(2017)
*Combining experimental and simulation data of molecular processes via augmented Markov models.*
Proc. Natl. Acad. Sci. USA, 114
.
pp. 8265-8270.

Pinamonti, G. and Zhao, J. and Condon, D. and Paul, F. and Noé, F. and Turner, D. and Bussi, G.
(2017)
*Predicting the kinetics of RNA oligonucleotides using Markov state models.*
J. Chem. Theory Comput., 13
(2).
pp. 926-934.

Schöneberg, J. and Lehmann, M. and Ullrich, A. and Posor, Y. and Lo, W.-T. and Lichtner, G. and Schmoranzer, J. and Haucke, V. and Noé, F.
(2017)
*Lipid-mediated PX-BAR domain recruitment couples local membrane constriction to endocytic vesicle fission.*
Nat. Comm., 8
.
p. 15873.

Winkelmann, S. and Schütte, Ch.
(2016)
*The spatiotemporal master equation: approximation of reaction-diffusion dynamics via Markov state modeling.*
Journal of Chemical Physics, 145
(21).
p. 214107.

Albrecht, D. and Winterflood, C. M. and Sadeghi, M. and Tschager, T. and Noé, F. and Ewers, H.
(2016)
*Nanoscopic compartmentalization of membrane protein motion at the axon initial segment.*
J. Cell Biol., 215
(1).
pp. 37-46.

Wu, H. and Paul, F. and Wehmeyer, C. and Noé, F.
(2016)
*Multiensemble Markov models of molecular thermodynamics and kinetics.*
Proceedings of the National Academy of Sciences, 113
(23).
E3221-E3230 .
ISSN 0027-8424

Trendelkamp-Schroer, B. and Wu, H. and Paul, F. and Noé, F.
(2015)
*Estimation and uncertainty of reversible Markov models.*
J. Chem. Phys., 143
(17).
p. 174101.

Scherer, M. K. and Trendelkamp-Schroer, B. and Paul, F. and Pérez-Hernández, G. and Hoffmann, M. and Plattner, N. and Wehmeyer, C. and Prinz, J.-H. and Noé, F.
(2015)
*PyEMMA 2: A Software Package for Estimation, Validation, and Analysis of Markov Models.*
J. Chem. Theory Comput., 11
(11).
pp. 5525-5542.