Hydrodynamic Collective Effects of Active Protein Machines in Solution and Lipid Bilayers

The cytoplasm and biomembranes in biological cells contain large numbers of proteins that cyclically change their shapes. They are molecular machines that can function as molecular motors or carry out many other tasks in the cell. We analyze the effects that hydrodynamic flows induced by active proteins have on other passive molecules in solution or membranes. We show that the diffusion constants of passive particles are enhanced substantially. Furthermore, when gradients of active proteins are present, a chemotaxis-like drift of passive particles takes place. In lipid bilayers, the effects are strongly nonlocal, so that active inclusions in the membrane contribute to diffusion enhancement and the drift. The results indicate that the transport properties of passive particles in systems containing active proteins machines operating under nonequilibrium conditions differ from their counterparts in systems at thermal equilibrium

Mesoscopic Multi-Particle Collision Dynamics of Reaction-Diffusion Fronts

A mesoscopic multi-particle collision model for fluid dynamics is generalized to incorporate the chemical reactions among species that may diffuse at different rates. This generalization provides a means to simulate reaction-diffusion dynamics of complex reactive systems. The method is illustrated by a study of cubic autocatalytic fronts. The mesoscopic scheme is able to reproduce the results of reaction-diffusion descriptions under conditions where the mean field equations are valid. The model is also able to incorporate the effects of molecular fluctuations on the reactive dynamics.Comment: 5 pages, 4 figure

Perturbation Theory for the Breakdown of Mean-Field Kinetics in Oscillatory Reaction-Diffusion Systems

Spatially-distributed, nonequilibrium chemical systems described by a Markov chain model are considered. The evolution of such systems arises from a combination of local birth-death reactive events and random walks executed by the particles on a lattice. The parameter \gamma, the ratio of characteristic time scales of reaction and diffusion, is used to gauge the relative contributions of these two processes to the overall dynamics. For the case of relatively fast diffusion, i.e. \gamma << 1, an approximate solution to the Markov chain in the form of a perturbation expansion in powers of \gamma is derived. Kinetic equations for the average concentrations differ from the mass-action law and contain memory terms. For a reaction- diffusion system with Willamowski-Rossler reaction mechanism, we further derive the following two results: a) in the limit of \gamma --> 0 these memory terms vanish and the mass-action law is recovered; b) the memory kernel is found to assume a simple exponential form. A comparison with numerical results from lattice gas automaton simulations is also carried out.Comment: 18 pages, 5 figures. To appear in J. Chem. Phy

{\AA}ngstr\"om-scale chemically powered motors

Like their larger micron-scale counterparts, {\AA}ngstr\"om-scale chemically self-propelled motors use asymmetric catalytic activity to produce self-generated concentration gradients that lead to directed motion. Unlike their micron-scale counterparts, the sizes of {\AA}ngstr\"om-scale motors are comparable to the solvent molecules in which they move, they are dominated by fluctuations, and they operate on very different time scales. These new features are studied using molecular dynamics simulations of small sphere dimer motors. We show that the ballistic regime is dominated by the thermal speed but the diffusion coefficients of these motors are orders of magnitude larger than inactive dimers. Such small motors may find applications in nano-confined systems or perhaps eventually in the cell.Comment: 6 pages, 8 figure