The influence of hydrodynamic interactions on protein dynamics in confined and crowded spaces-assessment in simple models

We consider several systems that are confined within a softly repulsive sphere. The first one is a model protein, crambin, which is described by a structure-based coarse grained model. We demonstrate that the folding process is accelerated by the hydrodynamic interactions (HI) in a way that depends on the radius of the sphere. The tighter the encompassing sphere, the smaller the effect, independent of the nature of the starting conformations. The second system is a protein surrounded by protein-like softly repulsive spheres that make the confined space crowded. In this case, the HI shorten the folding times in a way which depends on the degree of crowdedness only weakly. The third system is a collection of spheres that are meant to represent molecules. We show that confinement increases association times. We also observe that the HI either facilitate or obstruct association of two spheres depending on the crowding conditions. The dependence of the association time on crowdedness in the confining sphere is qualitatively distinct from that derived by Wieczorek and Zielenkiewicz for a cube with the periodic boundary conditions.