Statistical and Biological Physics

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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

In modern research, a new class of gaseous systems, so-called active gases arouses the interest of many scientists. Unlike gas molecules at thermal equilibrium, the constituent particles of active gases are self-propelled, and mutual interactions are typically highly dissipative. Such systems are far from thermal equilibrium and exhibit a wealth of patterns on macroscopic scales, which ultimately arise as a consequence of activity and dissipation at the microscopic level. Its distinctive capabilities to mediate between the microscopic and macroscopic views on physical systems therefore makes the Boltzmann equation a conceptually highly appealing tool in understanding the unusual collective dynamics of such active systems. more