9 research outputs found
First passage behaviour of fractional Brownian motion in two-dimensional wedge domains
We study the survival probability and the corresponding first passage time
density of fractional Brownian motion confined to a two-dimensional open wedge
domain with absorbing boundaries. By analytical arguments and numerical
simulation we show that in the long time limit the first passage time density
scales as t**{-1+pi*(2H-2)/(2*Theta)} in terms of the Hurst exponent H and the
wedge angle Theta. We discuss this scaling behaviour in connection with the
reaction kinetics of FBM particles in a one-dimensional domain.Comment: 6 pages, 4 figure
Non-Markovian polymer reaction kinetics
Describing the kinetics of polymer reactions, such as the formation of loops
and hairpins in nucleic acids or polypeptides, is complicated by the structural
dynamics of their chains. Although both intramolecular reactions, such as
cyclization, and intermolecular reactions have been studied extensively, both
experimentally and theoretically, there is to date no exact explicit analytical
treatment of transport-limited polymer reaction kinetics, even in the case of
the simplest (Rouse) model of monomers connected by linear springs. We
introduce a new analytical approach to calculate the mean reaction time of
polymer reactions that encompasses the non-Markovian dynamics of monomer
motion. This requires that the conformational statistics of the polymer at the
very instant of reaction be determined, which provides, as a by-product, new
information on the reaction path. We show that the typical reactive
conformation of the polymer is more extended than the equilibrium conformation,
which leads to reaction times significantly shorter than predicted by the
existing classical Markovian theory.Comment: Main text (7 pages, 5 figures) + Supplemantary Information (13 pages,
2 figures
First-passage problem for the Rouse polymer chain: An exact solution
We solve the first-passage problem of a non-Markovian process
arising in the reaction diffusion theory of polymer chains. By
considering the Rouse chain, a free-draining dynamic model of a
polymer where the chain monomers are represented by beads and the
chain connectivity by harmonic springs, we develop an exact
analytical method for describing the kinetics of end-chain
reactions. Our analytical results illuminate the approximations used
previously and are in perfect agreement with numerical stochastic
simulations
Ligand−Receptor Interactions in Chains of Colloids: When Reactions Are Limited by Rotational Diffusion
First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect
Mean first-passage times in confined media: from Markovian to non-Markovian processes
We review recent theoretical works that enable the accurate evaluation of the mean first passage time (MFPT) of a random walker to a target in confinement for Markovian (memory-less) and non-Markovian walkers. For the Markovian problem, we present a general theory which allows one to accurately evaluate the MFPT and its extensions to related first-passage observables such as splitting probabilities and occupation times. We show that this analytical approach provides a universal scaling dependence of the MFPT on both the volume of the confining domain and the source target distance in the case of general scale-invariant processes. This analysis is applicable to a broad range of stochastic processes characterized by length scale-invariant properties, and reveals the key role that can be played by the starting position of the random walker. We then present an extension to non-Markovian walks by taking the specific example of a tagged monomer of a polymer chain looking for a target in confinement. We show that the MFPT can be calculated accurately by computing the distribution of the positions of all the monomers in the chain at the instant of reaction. Such a theory can be used to derive asymptotic relations that generalize the scaling dependence with the volume and the initial distance to the target derived for Markovian walks. Finally, we present an application of this theory to the problem of the first contact time between the two ends of a polymer chain, and review the various theoretical approaches of this non-Markovian problem.First-passage times and optimization of target search strategie