Statistical and Biological Physics

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Bosons are quantum particles that like to be together. When a dilute gas of bosons is cooled to a temperature close to absolute zero, a macroscopic fraction of the bosons will occupy the energetic ground state of the system; the bosons form a Bose-Einstein condensate. Only recently has it been proposed that bosons may also group into multiple condensates when they are driven by a time-periodic force and dissipate into the environment. In our manuscript, we show that the condensation of bosons in such a nonequilibrium system corresponds to the selection of strategies in evolutionary game theory. We applied mathematical concepts of this theory to explain why and under which conditions bosons form multiple condensates. We found that the condensation dynamics follows a simple physical guiding principle: the vanishing of relative entropy production guides the selection of condensates. more

The functional relevance of regulating proteins is often restricted to specific binding sites such as the ends of microtubules or actin-filaments. A localization of proteins on these functional sites is of great importance. We present a quantitative theory for a diffusion and capture process, where proteins diffuse on a filament and stop diffusion when reaching the filament's end. It is found that end-association after one-dimensional diffusion is highly efficient as compared to direct binding from solution/cytoplasm. As a consequence, diffusion and capture substantially enhances the reaction velocity of enzymatic reactions, where proteins and filament ends are to each other as enzyme and substrate. We show that the ensuing reaction velocity can effectively be computed within an effective Michaelis-Menten framework. The presented theory is simple yet fully quantitative as it depends only on experimentally accessible parameter values such as binding constants and diffusion coefficients. We predict that diffusion and capture significantly beats the diffusion limit for the rate of direct protein end-association for practically all proteins diffusing on microtubules and actin-filaments. more