Diffusion: Membrane Permeability and the Rate of Actin Polymerization

Abstract

This chapter shows that diffusive flow from a high concentration to a low concentration is an emergent behavior of many particles, resulting from individual particles’ Brownian random walks, and how the consequences of diffusion may be quantified by means of the diffusion equation. The concept of particle number conservation will be especially important, namely that particles cannot appear or disappear without a good reason (such as that they undergo a chemical reaction). An immediate consequence of particle number conservation is that steady-state particle currents—the number of particles per unit time passing a particular point or a particular radius—are independent of position or radius. We study diffusion across membranes, which is particularly important in physiology and medicine, because the human body can be conceived as consisting of myriad membranes across which oxygen, CO², nutrients, waste, therapeutics, etc., all must pass. We will discover that the particle current through a flat membrane is proportional to the difference in concentration across the membrane, providing an example of a ”gradient flow.” Individual cells also have membranes, across which many of these same quantities must also pass. We also study ”diffusion to capture,” which reveals how essential equations of chemical and biochemical kinetics emerge from particles’ Brownian motion and their consequent diffusion, and how diffusion limits the maximum possible rate of a chemical reaction. We will also understand what are the consequences of diffusion for the size of cells, and for the efficiency with which cell surface receptors detect their binding partners.