Speaker
Description
All-atom and coarse-grained molecular dynamics~\cite{ref1}, Langevin dynamics~\cite{ref2}, Brownian dynamics~\cite{ref3,ref4}, and compartment-based stochastic reaction–diffusion models~\cite{ref4,ref5} are computational methodologies that have been applied to the spatio-temporal modelling of numerous intracellular processes. They differ in the level of biological detail they can capture and in the computational intensity of the resulting simulations. In some cases, it is possible to establish rigorous connections between these modelling frameworks by deriving a macroscopic (coarse-grained) description from the detailed one. I will discuss these connections, with a focus on the development, analysis, and applications of multi-resolution methods, which combine detailed (high-resolution) simulations in localized regions of particular interest (where accuracy and microscopic detail are crucial) with a coarser stochastic model in other regions where accuracy may be traded for computational efficiency. I will illustrate applications of multi-resolution methodologies to modelling intracellular calcium dynamics, actin dynamics, and DNA dynamics.
Bibliography
@article{ref1,
title={Asymmetric periodic boundary conditions for all-atom molecular dynamics and coarse-grained simulations of nucleic acids},
author={Erban, R. and Togashi, Y.},
journal={Journal of Physical Chemistry B},
volume={127},
number={38},
pages={8257--8267},
year={2023}
}
@article{ref2,
title={Langevin dynamics for a heavy particle immersed within a flow of light particles},
author={Erban, R. and Van Gorder, R.},
journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
volume={480},
number={2301},
year={2024}
}
@article{ref3,
title={From {B}rownian dynamics to {P}oisson-{N}ernst-{P}lanck equations: multi-resolution simulations of ions},
author={Zhang, J. and Erban, R.},
journal={arXiv preprint arXiv:2506.19738},
year={2026}
}
@book{ref4,
title={Stochastic {M}odelling of {R}eaction-{D}iffusion {P}rocesses},
author={Erban, R. and Chapman, S. J.},
ISBN = {9781108498128},
doi = {10.1017/9781108628389},
year={2020},
publisher={Cambridge University Press}
}
@article{ref5,
title={Multi-grid reaction-diffusion master equation: applications to morphogen gradient modelling},
author={Erban, R. and Winkelmann, S.},
journal={Bulletin of Mathematical Biology},
volume={87},
number={1},
pages={6},
year={2025}
}
