Statistical and Biological Physics

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According to the Einstein-Stokes relation different Brownian particles of equal size must have the same diffusion constant. However, particle diffusion or motility can also originate from non-thermal, active processes. In this case equal-sized particles can indeed exhibit different diffusivities or motilities. Throughout the last 5 years the influence of size differences, shape, mass and persistent motion on phase separation of active particle systems has been intensively studied. For binary mixtures, however, former research focused on particles with pronounced persistence in motion, while the exclusive role of differences in diffusion constants remains elusive. more

Protein patterns play a major role in establishing cell polarity and guiding cell division processes. Examples include spatio-temporal oscillations in the MinCDE system of E. coli, and the formation of narrow/tightly localized protein caps in the Cdc42 system of S.cerevisiae. The formation of these patterns requires biochemical processes that sense and adapt to the geometry of the organism. Previously suggested mechanisms either require proteins that are able to directly sense membrane curvature, or are based on nonlinear diffusion-reaction systems that can generate geometry-adapted patterns. In Bacillus subtilis, there is good evidence suggesting that DivIVA recognizes negative membrane curvature directly by a mechanism which is intrinsic to this cell division protein. In contrast, enrichment of MinD at the cell poles in E. coli or formation of Cdc42 caps in S. cerevisiae is an emergent property of the collective dynamics of several proteins. A clear disadvantage of such self-organized symmetry breaking by means of a dynamical instability is that the kinetic parameters must be fine-tuned in order to allow the establishment of a stable polar pattern. This need for fine-tuning also poses a particular challenge for the utilization of functional, pattern forming modules in reconstituted synthetic systems. In the paper we show that adaptation to geometry can emerge from generic chemical dynamics without any need for parameter tuning or explicit curvature sensing. more