Seminar by Prof. Dr. Felix Höfling

Free University Berlin (Germany)

Bacterial Outer Membrane Simulations: Why Atomistic Models Remain Useful?

Cellular membranes and the interior of cells constitute densely packed and heterogeneous environments, which is commonly summarised as macromolecular crowding. Such highly heterogeneous spaces give rise to a number of anomalies in the Brownian motion of proteins, granules, or vesicles [1]. A familiar consequence is non-Markovian behaviour such as subdiffusion and persistent memory, which requires modifications of the simple diffusion model.

One example is the generalised Langevin equation, which is parametrised by a friction kernel rather than a single friction constant. Based on high-precision simulations of three prototypical, homogeneous liquids, including water, we have obtained frequency-resolved friction data from atomistic to hydrodynamic scales [2]. I will discuss the abrupt emergence of friction at the atomistic scale, persistent correlations of Brownian forces, and the status of the generalised Stokes-Einstein relation that links single-molecule and collective responses.

In the second part, I will introduce a generalised master equation (GME) for non-Markovian jump processes that result from coarse-graining of diffusion in partitioned spaces [3]. The spatial domains can differ with respect to their diffusivity, geometry, and dimensionality, but can also refer to transport modes alternating between diffusive, driven, or anomalous motion. The approach is applied to target search problems in a two-domain model, yielding first-passage time densities and an effective, scale-dependent reaction rate constant.

[1] F. Höfling and T. Franosch, Rep. Prog. Phys. 76, 046602 (2013).

[2] D. Frömberg and F. Höfling, J. Phys. A: Math. Theor. 54, 215601 (2021).

[3] A. V. Straube, B. G. Kowalik, R. R. Netz, and F. Höfling, Commun. Phys. 3, 126 (2020).