26,713 research outputs found
Markov Chain Modeling of Polymer Translocation Through Pores
We solve the Chapman-Kolmogorov equation and study the exact splitting
probabilities of the general stochastic process which describes polymer
translocation through membrane pores within the broad class of Markov chains.
Transition probabilities which satisfy a specific balance constraint provide a
refinement of the Chuang-Kantor-Kardar relaxation picture of translocation,
allowing us to investigate finite size effects in the evaluation of dynamical
scaling exponents. We find that (i) previous Langevin simulation results can be
recovered only if corrections to the polymer mobility exponent are taken into
account and that (ii) the dynamical scaling exponents have a slow approach to
their predicted asymptotic values as the polymer's length increases. We also
address, along with strong support from additional numerical simulations, a
critical discussion which points in a clear way the viability of the Markov
chain approach put forward in this work.Comment: 17 pages, 5 figure
Effective ergodicity breaking in an exclusion process with varying system length
Stochastic processes of interacting particles with varying length are
relevant e.g. for several biological applications. We try to explore what kind
of new physical effects one can expect in such systems. As an example, we
extend the exclusive queueing process that can be viewed as a one-dimensional
exclusion process with varying length, by introducing Langmuir kinetics. This
process can be interpreted as an effective model for a queue that interacts
with other queues by allowing incoming and leaving of customers in the bulk. We
find surprising indications for breaking of ergodicity in a certain parameter
regime, where the asymptotic growth behavior depends on the initial length. We
show that a random walk with site-dependent hopping probabilities exhibits
qualitatively the same behavior.Comment: 5 pages, 7 figure
Intrinsic noise profoundly alters the dynamics and steady state of morphogen-controlled bistable genetic switches
During tissue development, patterns of gene expression determine the spatial
arrangement of cell types. In many cases, gradients of secreted signaling
molecules - morphogens - guide this process. The continuous positional
information provided by the gradient is converted into discrete cell types by
the downstream transcriptional network that responds to the morphogen. A
mechanism commonly used to implement a sharp transition between two adjacent
cell fates is the genetic toggle switch, composed of cross-repressing
transcriptional determinants. Previous analyses emphasize the steady state
output of these mechanisms. Here, we explore the dynamics of the toggle switch
and use exact numerical simulations of the kinetic reactions, the Chemical
Langevin Equation, and Minimum Action Path theory to establish a framework for
studying the effect of gene expression noise on patterning time and boundary
position. This provides insight into the time scale, gene expression
trajectories and directionality of stochastic switching events between cell
states. Taking gene expression noise into account predicts that the final
boundary position of a morphogen-induced toggle switch, although robust to
changes in the details of the noise, is distinct from that of the deterministic
system. Moreover, stochastic switching introduces differences in patterning
time along the morphogen gradient that result in a patterning wave propagating
away from the morphogen source. The velocity of this wave is influenced by
noise; the wave sharpens and slows as it advances and may never reach steady
state in a biologically relevant time. This could explain experimentally
observed dynamics of pattern formation. Together the analysis reveals the
importance of dynamical transients for understanding morphogen-driven
transcriptional networks and indicates that gene expression noise can
qualitatively alter developmental patterning
Solvent fluctuations induce non-Markovian kinetics in hydrophobic pocket-ligand binding
We investigate the impact of water fluctuations on the key-lock association
kinetics of a hydrophobic ligand (key) binding to a hydrophobic pocket (lock)
by means of a minimalistic stochastic model system. It describes the collective
hydration behavior of the pocket by bimodal fluctuations of a water-pocket
interface that dynamically couples to the diffusive motion of the approaching
ligand via the hydrophobic interaction. This leads to a set of overdamped
Langevin equations in 2D-coordinate-space, that is Markovian in each dimension.
Numerical simulations demonstrate locally increased friction of the ligand,
decelerated binding kinetics, and local non-Markovian (memory) effects in the
ligand's reaction coordinate as found previously in explicit-water molecular
dynamics studies of model hydrophobic pocket-ligand binding [1,2]. Our
minimalistic model elucidates the origin of effectively enhanced friction in
the process that can be traced back to long-time decays in the
force-autocorrelation function induced by the effective, spatially fluctuating
pocket-ligand interaction. Furthermore, we construct a generalized 1D-Langevin
description including a spatially local memory function that enables further
interpretation and a semi-analytical quantification of the results of the
coupled 2D-system
Non-Fickian Interdiffusion of Dynamically Asymmetric Species: A Molecular Dynamics Study
We use Molecular Dynamics combined with Dissipative Particle Dynamics to
construct a model of a binary mixture where the two species differ only in
their dynamic properties (friction coefficients). For an asymmetric mixture of
slow and fast particles we study the interdiffusion process. The relaxation of
the composition profile is investigated in terms of its Fourier coefficients.
While for weak asymmetry we observe Fickian behavior, a strongly asymmetric
system exhibits clear indications of anomalous diffusion, which occurs in a
crossover region between the Cases I (Fickian) and II (sharp front moving with
constant velocity), and is close to the Case II limit.Comment: to appear in J. Chem. Phy
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
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