Quantifying the Influence of the Crowded Cytoplasm on Small Biomolecule Diffusion via Homogenization Theory

Abstract

Cytosolic crowding is known to influence the thermodynamics and kinetics of in vivo chemical reactions. Crowders, including proteins, macromolecular assemblies and intracellular organelles, reduce the volume available to a diffusing substrate and thereby lower its effective diffusion constant relative to its rate in bulk solution. However, the nature of a substrate's interaction with crowders, such as through electrostatic or van der Waals forces, can further influence the effective diffusion rate. To probe the impact of crowding over micron-scale intracellular distances, we apply a multi-scale mathematical theory, homogenization, to estimate effective diffusion rates for ions and small biomolecules diffusing in a densely-packed lattice of representative cytosolic proteins. Specifically, via the finite element method we numerically solve the homogenized diffusion equation for a nearly 1 micron cubed cytosolic fraction based on published Brownian dynamics data of the bacterial cytoplasm (McGuffee and Elcock, PLOS Computational Biology, vol. 6, no. 3, p. e1000694, Mar. 2010). Our simulations quantify how the crowded volume fraction, irregularity of protein shapes and distribution, and molecular interactions influence the diffusion rates of small molecules.