The Role of Hydrodynamic Interactions in Self-Organization of Biological Molecules

Abstract

Self-organization is one of the most fundamental phenomena in biology. Elucidating the mechanisms of the self-assembly of biological molecules, such as protein folding/binding and formation of lipid bilayer membranes, have been a fascinating topic over decades in biological field. Hydrodynamic interactions (HIs) give rise to collective motions between molecules. Therefore, they may play an important role on dynamics of self-assembly. Although there are significant advances in theoretical and computational studies on thermodynamics and kinetics of self-assembling systems recent years, analysis on effects of HIs to the reactions are limited due to their high complexity. Here, by using a Brownian dynamics (BD) simulation technique, we evaluate the importance of HIs on kinetic of self-assembly in a set of examples, formation of lipid membrane and actin polymerization reaction. We first built coarse-grained models of lipid and actin monomer. A cluster of lipid molecules was represented by two particles, one is hydrophilic head group and the other is hydrophobic tail group, and attractive interaction between tail groups was applied. For actin polymerization system, each monomer was represented by two particles and an angle-dependent attractive interaction was applied to form long filaments. In BD simulations, the Rotne-Prager-Yamakawa tensor was used to account for HIs between particles. In the early stage of self-assembly, HIs between inter-monomer particles decelerated the association rate of monomers to form oligomers compared with that in the simulations without inter-monomer HIs in both systems. On the other hand, the HIs accelerate the reaction of oligomers to form a fully-assembled state or much longer polymers. This phenomenon could be explained by the Kirkwood-Riseman theory. Those results clearly suggest that HIs greatly affect kinetics of self-assembly reactions and considering the interactions is crucial for studying dynamics of biological systems.