C03 - Multiscale modelling and simulation for spatiotemporal master equations
Head(s): Prof. Dr. Christof Schütte (FU Berlin, ZIB), Dr. Stefanie Winkelmann (ZIB), Prof. Dr. Roland Netz (FU Berlin)
Project member(s): Katarina Elez, Nathalie Unger, Vikram Sunkara
Participating institution(s): FU Berlin, ZIB
This project is concerned with the modeling and analysis of spatio-temporal cellular processes that comprise cascades of scales in time, space and population size. We successfully constructed several new hybrid models that seamlessly couple different resolutions for different molecular species and spatial locations within the cell, e.g., integrating particle-based reactions diffusion (PBRD) models with spatio-temporal master equations and/or stochastic partial differential equations, or coupling PBRD models with molecular kinetics like conformational changes or membrane dynamics. Efficient algorithms for numerical simulations were proposed and their superior performance (in comparison to non-hybrid models) was demonstrated for various real-life applications.
In the third funding period we make the decisive final step: we refine our methods further and integrate external progress in the field in order to construct a hybrid model and appropriate simulation algorithms for investigating the process of receptor diffusion, co-localization, and kinetic interaction on the membrane surface of neurons. For this process, experimental data with single-molecule resolution in time and space indicates surprising cluster formation of receptors. Modeling this process requires coupling of receptor conformation kinetics with diffusion, mediated by the interaction with the membrane, and bi-molecular interaction, making it into a prototype for the interaction across a cascade of scales.