123 research outputs found
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
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
Synchronization Defect Lines in Media with Complex-Periodic Dynamics (Interfaces, Pulses and Waves in Nonlinear Dissipative Systems : RIMS Project 2000 "Reaction-diffusion systems : theory and applications")
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