5 - “Fluctuation” of Intracellular Dynamics

Summary

This chapter quantitatively examines molecule numbers and reaction rates within a cell, along with thermal fluctuations and Brownian motion, from a mesoscopic perspective. Thermal fluctuations of molecules are pivotal in chemical reactions, protein folding, molecular motor systems, and so on. We introduce estimations of cell size and molecule numbers within cells, highlighting the possible significance of the minority of molecules. Describing their behaviors necessitates dealing with stochastic fluctuations, and the Gillespie algorithm, widely employed in Monte Carlo simulations for stochastic chemical reactions, is described. We elaborate on extrinsic and intrinsic noise in cells, and on why understanding how cells process fluctuations for sensing is crucial. To facilitate this comprehension, we revisit the fundamentals of statistics, including the law of large numbers and the central limit theorem. We derive the diffusion equation from random walk and confirm the dimensionality dependence of random walks, and elucidate Brownian motion as the continuous limit of random walk and explain the Einstein relation. As examples of the physiological significance of fluctuations in cell biology, we estimate the diffusion constant of proteins inside cells, diffusion-limited reactions, and introduce bacterial random walks and chemotaxis, and amoeboid movements of eukaryotic cells.