89 research outputs found
Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium
Measurements of protein motion in living cells and membranes consistently
report transient anomalous diffusion (subdiffusion) which converges back to a
Brownian motion with reduced diffusion coefficient at long times, after the
anomalous diffusion regime. Therefore, slowed-down Brownian motion could be
considered the macroscopic limit of transient anomalous diffusion. On the other
hand, membranes are also heterogeneous media in which Brownian motion may be
locally slowed-down due to variations in lipid composition. Here, we
investigate whether both situations lead to a similar behavior for the
reversible ligand-binding reaction in 2d. We compare the (long-time)
equilibrium properties obtained with transient anomalous diffusion due to
obstacle hindrance or power-law distributed residence times (continuous-time
random walks) to those obtained with space-dependent slowed-down Brownian
motion. Using theoretical arguments and Monte-Carlo simulations, we show that
those three scenarios have distinctive effects on the apparent affinity of the
reaction. While continuous-time random walks decrease the apparent affinity of
the reaction, locally slowed-down Brownian motion and local hinderance by
obstacles both improve it. However, only in the case of slowed-down Brownian
motion, the affinity is maximal when the slowdown is restricted to a subregion
of the available space. Hence, even at long times (equilibrium), these
processes are different and exhibit irreconcilable behaviors when the area
fraction of reduced mobility changes.Comment: Biophysical Journal (2013
Generic principles of active transport
Nonequilibrium collective motion is ubiquitous in nature and often results in
a rich collection of intringuing phenomena, such as the formation of shocks or
patterns, subdiffusive kinetics, traffic jams, and nonequilibrium phase
transitions. These stochastic many-body features characterize transport
processes in biology, soft condensed matter and, possibly, also in nanoscience.
Inspired by these applications, a wide class of lattice-gas models has recently
been considered. Building on the celebrated {\it totally asymmetric simple
exclusion process} (TASEP) and a generalization accounting for the exchanges
with a reservoir, we discuss the qualitative and quantitative nonequilibrium
properties of these model systems. We specifically analyze the case of a
dimeric lattice gas, the transport in the presence of pointwise disorder and
along coupled tracks.Comment: 21 pages, 10 figures. Pedagogical paper based on a lecture delivered
at the conference on "Stochastic models in biological sciences" (May 29 -
June 2, 2006 in Warsaw). For the Banach Center Publication
Anomalous Diffusion and Non-classical Reaction Kinetics in Crowded Fluids
This thesis investigates the underlying mechanism and the effects of anomalous diffusion in crowded fluids by means of computer simulations. In order to elucidate the mechanism behind crowding-induced subdiffusion we discuss the average shape of tracer trajectories as a potential criterion that allows to reliably discriminate between frequently proposed models. Our simulations show that measurement errors inherent to single particle tracking generally impair the determination of the underlying random process from experimental data. We propose a particle-based model for the crowded cytoplasm that incorporates soft-core repulsion and weak attraction between globular proteins of various sizes. Under these prerequisites simulations reveal transient subdiffusion of proteins. On experimental time scales, however, diffusion is normal indicating that realistic, microscopic models of crowded fluids require further detail of the relevant interactions. In the second part of this thesis, the impact of subdiffusion on biochemical reactions is studied via mesoscopic, stochastic simulations. Due to their compact trajectories subdiffusive reactants get increasingly segregated over time. This results in anomalous kinetics that differs strongly from classical theories. Moreover, for a two-step reaction scheme relying on an intermediate dissociation-association event, subdiffusion can substantially improve the overall productivity because spatio-temporal correlations are exploited with high efficiency
Modeling of solvent flow effects in enzyme catalysis under physiological conditions
A stochastic model for the dynamics of enzymatic catalysis in explicit,
effective solvents under physiological conditions is presented.
Analytically-computed first passage time densities of a diffusing particle in a
spherical shell with absorbing boundaries are combined with densities obtained
from explicit simulation to obtain the overall probability density for the
total reaction cycle time of the enzymatic system. The method is used to
investigate the catalytic transfer of a phosphoryl group in a phosphoglycerate
kinase-ADP-bis phosphoglycerate system, one of the steps of glycolysis. The
direct simulation of the enzyme-substrate binding and reaction is carried out
using an elastic network model for the protein, and the solvent motions are
described by multiparticle collision dynamics, which incorporates hydrodynamic
flow effects. Systems where solvent-enzyme coupling occurs through explicit
intermolecular interactions, as well as systems where this coupling is taken
into account by including the protein and substrate in the multiparticle
collision step, are investigated and compared with simulations where
hydrodynamic coupling is absent. It is demonstrated that the flow of solvent
particles around the enzyme facilitates the large-scale hinge motion of the
enzyme with bound substrates, and has a significant impact on the shape of the
probability densities and average time scales of substrate binding for
substrates near the enzyme, the closure of the enzyme after binding, and the
overall time of completion of the cycle.Comment: 15 pages in double column forma
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