Hydrodynamically enforced entropic trapping of Brownian particles

We study the transport of Brownian particles through a corrugated channel caused by a force field containing curl-free (scalar potential) and divergence-free (vector potential) parts. We develop a generalized Fick-Jacobs approach leading to an effective one-dimensional description involving the potential of mean force. As an application, the interplay of a pressure-driven flow and an oppositely oriented constant bias is considered. We show that for certain parameters, the particle diffusion is significantly suppressed via the property of hyrodynamically enforced entropic particle trapping.Comment: 5 pages, 4 figures, in press with Physical Review Letter

Transport of a colloidal particle driven across a temporally oscillating optical potential energy landscape

A colloidal particle is driven across a temporally oscillating one-dimensional optical potential energy landscape and its particle motion is analysed. Different modes of dynamic mode locking are observed and are confirmed with the use of phase portraits. The effect of the oscillation frequency on the mode locked step width is addressed and the results are discussed in light of a high-frequency theory and compared to simulations. Furthermore, the influence of the coupling between the particle and the optical landscape on mode locking is probed by increasing the maximum depth of the optical landscape. Stronger coupling is seen to increase the width of mode locked steps. Finally, transport across the temporally oscillating landscape is studied by measuring the effective diffusion coefficient of a mobile particle, which is seen to be highly sensitive to the driving velocity and mode locking

Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtolitres. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small sub-cellular compartment. This is achieved by applying a mesoscopic version of the quasi-steady state assumption to the exact Fokker-Planck equation associated with the Poisson Representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing sub-cellular volume, decreasing Michaelis-Menten constants and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.Comment: 13 pages, 4 figures; published in The Journal of Chemical Physic

Pattern Formation Induced by Time-Dependent Advection

We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially homogeneous state. We deal with the flows periodic in space that may have arbitrary time dependence. We propose a discrete in time model, where reaction, advection, and diffusion act as successive operators, and show that a mixing advection can lead to a pattern-forming instability in a two-component system where only one of the species is advected. Physically, this can be explained as crossing a threshold of Turing instability due to effective increase of one of the diffusion constants

A CPH-Like Picture in Two Patients with an Orbitocavernous Sinus Syndrome

Two patients with retroorbital pain syndromes with or without paresis of cranial nerves developed weeks after ipsilateral headache resembling chronic paroxysmal hemicrania (CPH) but without autonomic features. These findings might support the hypothesis that CPH may be caused by a pathological process in the region of the cavernous sinus, as has been proposed for the Tolosa-Hunt syndrome (THS)

Rigorous elimination of fast stochastic variables from the linear noise approximation using projection operators

The linear noise approximation (LNA) offers a simple means by which one can study intrinsic noise in monostable biochemical networks. Using simple physical arguments, we have recently introduced the slow-scale LNA (ssLNA) which is a reduced version of the LNA under conditions of timescale separation. In this paper, we present the first rigorous derivation of the ssLNA using the projection operator technique and show that the ssLNA follows uniquely from the standard LNA under the same conditions of timescale separation as those required for the deterministic quasi-steady state approximation. We also show that the large molecule number limit of several common stochastic model reduction techniques under timescale separation conditions constitutes a special case of the ssLNA.Comment: 10 pages, 1 figure, submitted to Physical Review E; see also BMC Systems Biology 6, 39 (2012