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Hydrodynamic interactions (HI) give rise to collective motions between molecules, which are known to be important in the dynamics of random coil polymers and colloids. However, their role in the biological self-assembly of many molecule systems has not been investigated. Here, using Brownian dynamics simulations, we evaluate the importance of HI on the kinetics of self-assembly of lipid membranes. One-thousand coarse-grained lipid molecules in periodic simulation boxes were allowed to assemble into stable bilayers in the presence and absence of intermolecular HI. Hydrodynamic interactions reduce the monomer-monomer association rate by 50%. In contrast, the rate of association of lipid clusters is much faster in the presence of intermolecular HI. In fact, with intermolecular HI, the membrane self-assembly rate is 3–10 times faster than that without intermolecular HI. We introduce an analytical model to describe the size dependence of the diffusive encounter rate of particle clusters, which can qualitatively explain our simulation results for the early stage of the membrane self-assembly process. These results clearly suggest that HI greatly affects the kinetics of self-assembly and that simulations without HI will significantly underestimate the kinetic parameters of such processes.

The effect of macromolecular crowding on protein diffusion has been extensively studied in order to understand the protein dynamics in cellular environments. Previous studies have generally focused on proteins as crowding agents as they are known to occupy 20-30% of the cell volume. The volume fraction of the nucleoid in bacterial cells is also significant, around 10-20%, but the effect of chromosomal DNA as a crowding agent on protein diffusion has drawn relatively limited attention. Using recently build high-resolution models of bacterial nucleoids, Brownian and Stokesian dynamics simulations of coarse-grained model systems containing chromosomal DNA and proteins were carried out to investigate the effect of nucleoid crowding on protein diffusion. The coarse-grained model for the nucleoid is an experimentally-derived 3D model of the Caulobacter crescentus chromosome at base-pair resolution built by combining topological information of chromosomal DNA with distance restraints obtained from high-throughput Chromosome Conformation Capture (HiC) experiments, while proteins in the systems are modeled as hard-spheres. Results show that diffusion of proteins are slower around the nucleoid compared to in protein crowding and that there is size-dependent exclusion of proteins from the chromosome interior. Further analysis was carried to examine the degree of anomalous diffusion at different time and length scales.

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.