A Computational Model for E. coli Cytoplasm: Diffusion and Hydrodynamics

Abstract

The dynamics of proteins is essential for the quantification of various cellular processes like rates of enzymatic reactions, signal transduction and protein association reactions. However, understanding the structure and dynamics of macromolecules in a cell is complicated by the highly crowded nature of the cell. It is likely that properties of macromolecules in cell may differ significantly to that measured in dilute solution. Diffusion plays important roles in many processes occurring inside the cell. The estimation of diffusion coefficient of macromolecules in a cell can be considered as a first step in understanding the complex nature of the heterogeneous environment of the cell.In this current work we developed a computational model of E. coli cytoplasm and performed extensive Brownian dynamics simulation to calculate diffusivity of proteins. Our model differs from some of the previous models of E. coli cytoplasm in the following way; (1) The proteins modeled as flexible units by considering them as a collection of spheres. (2) hydrodynamic interaction (HI), which is essential to get accurate diffusion coefficient, was considered using a mean field approach.The model predicts accurately the diffusion coefficient of Green Fluorescent Protein (GFP) in E.coli cell. We have found that HI is essential to get correct diffusion coefficient for this highly crowded system. The presence of anomalous diffusion has also been observed for short time (∼1 micro sec), which was identified using fractional Brownian motion (FBM) analysis. It was found that repulsive interaction between different proteins is the main reason for the anomalous diffusion. To understand the anomalous diffusion observed in simulations, we also formulated a one dimensional random walk model in which successive steps are biased and correlated. This analytical model can explain some of the findings from our simulation.