Persistence length of a polyelectrolyte in salty water: a Monte-Carlo study

We address the long standing problem of the dependence of the electrostatic persistence length $l_e$ of a flexible polyelectrolyte (PE) on the screening length $r_s$ of the solution within the linear Debye-Huckel theory. The standard Odijk, Skolnick and Fixman (OSF) theory suggests $l_e \propto r_s^2$, while some variational theories and computer simulations suggest $l_e \propto r_s$. In this paper, we use Monte-Carlo simulations to study the conformation of a simple polyelectrolyte. Using four times longer PEs than in previous simulations and refined methods for the treatment of the simulation data, we show that the results are consistent with the OSF dependence $l_e \propto r_s^2$. The linear charge density of the PE which enters in the coefficient of this dependence is properly renormalized to take into account local fluctuations.Comment: 7 pages, 6 figures. Various corrections in text and reference

Doubly stochastic coherence via noise-induced symmetry in bistable neural models

The generation of coherent dynamics due to noise in an activator-inhibitor system describing bistable neural dynamics is investigated. We show that coherence can be induced in deterministically asymmetric regimes via symmetry restoration by multiplicative noise, together with the action of additive noise which induces jumps between the two stable steady states. The phenomenon is thus doubly stochastic, because both noise sources are necessary. This effect can be understood analytically in the frame of a small-noise expansion and is confirmed experimentally in a nonlinear electronic circuit. Finally, we show that spatial coupling enhances this coherent behavior in a form of system-size coherence resonance

Noise-induced inhibitory suppression of malfunction neural oscillators

Motivated by the aim to find new medical strategies to suppress undesirable neural synchronization we study the control of oscillations in a system of inhibitory coupled noisy oscillators. Using dynamical properties of inhibition, we find regimes when the malfunction oscillations can be suppressed but the information signal of a certain frequency can be transmitted through the system. The mechanism of this phenomenon is a resonant interplay of noise and the transmission signal provided by certain value of inhibitory coupling. Analyzing a system of three or four oscillators representing neural clusters, we show that this suppression can be effectively controlled by coupling and noise amplitudes.Comment: 10 pages, 14 figure

Variational theory for a single polyelectrolyte chain revisited

We reconsider the electrostatic contribution to the persistence length, $\ell_e$, of a single, infinitely long charged polymer in the presence of screening. A Gaussian variational method is employed, taking $\ell_e$ as the only variational parameter. For weakly charged and flexible chains, crumpling occurs at small length scales because conformational fluctuations overcome electrostatic repulsion. The electrostatic persistence length depends on the square of the screening length, $\ell_e\sim\kappa^{-2}$, as first argued by Khokhlov and Khachaturian by applying the Odijk-Skolnick-Fixman (OSF) theory to a string of crumpled blobs. We compare our approach to previous theoretical works (including variational formulations) and show that the result $\ell_e\sim\kappa^{-1}$ found by several authors comes from the improper use of a cutoff at small length scales. For highly charged and stiff chains, crumpling does not occur; here we recover the OSF result and validate the perturbative calculation for slightly bent rods.Comment: 11 pages, 6 figure

The transition between stochastic and deterministic behavior in an excitable gene circuit

We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramatically different from that predicted by the ODE model. We analyze how that behavior depends on the gene copy number and find very slow convergence to the large number limit near the bifurcation point. The implications for understanding the dynamics of gene circuits and other birth-death dynamical systems with small numbers of constituents are discussed.Comment: PLoS ONE: Research Article, published 11 Apr 201

Complex and unexpected dynamics in simple genetic regulatory networks

Peer reviewedPublisher PD

Optimizing end-labeled free-solution electrophoresis by increasing the hydrodynamic friction of the drag-tag

We study the electrophoretic separation of polyelectrolytes of varying lengths by means of end-labeled free-solution electrophoresis (ELFSE). A coarse-grained molecular dynamics simulation model, using full electrostatic interactions and a mesoscopic Lattice Boltzmann fluid to account for hydrodynamic interactions, is used to characterize the drag coefficients of different label types: linear and branched polymeric labels, as well as transiently bound micelles. It is specifically shown that the label's drag coefficient is determined by its hydrodynamic size, and that the drag per label monomer is largest for linear labels. However, the addition of side chains to a linear label offers the possibility to increase the hydrodynamic size, and therefore the label efficiency, without having to increase the linear length of the label, thereby simplifying synthesis. The third class of labels investigated, transiently bound micelles, seems very promising for the usage in ELFSE, as they provide a significant higher hydrodynamic drag than the other label types. The results are compared to theoretical predictions, and we investigate how the efficiency of the ELFSE method can be improved by using smartly designed drag-tags.Comment: 32 pages, 11 figures, submitted to Macromolecule

Neutral and Charged Polymers at Interfaces

Chain-like macromolecules (polymers) show characteristic adsorption properties due to their flexibility and internal degrees of freedom, when attracted to surfaces and interfaces. In this review we discuss concepts and features that are relevant to the adsorption of neutral and charged polymers at equilibrium, including the type of polymer/surface interaction, the solvent quality, the characteristics of the surface, and the polymer structure. We pay special attention to the case of charged polymers (polyelectrolytes) that have a special importance due to their water solubility. We present a summary of recent progress in this rapidly evolving field. Because many experimental studies are performed with rather stiff biopolymers, we discuss in detail the case of semi-flexible polymers in addition to flexible ones. We first review the behavior of neutral and charged chains in solution. Then, the adsorption of a single polymer chain is considered. Next, the adsorption and depletion processes in the many-chain case are reviewed. Profiles, changes in the surface tension and polymer surface excess are presented. Mean-field and corrections due to fluctuations and lateral correlations are discussed. The force of interaction between two adsorbed layers, which is important in understanding colloidal stability, is characterized. The behavior of grafted polymers is also reviewed, both for neutral and charged polymer brushes.Comment: a review: 130 pages, 30 ps figures; final form, added reference

Effect of Network Architecture on Synchronization and Entrainment Properties of the Circadian Oscillations in the Suprachiasmatic Nucleus

In mammals, the suprachiasmatic nucleus (SCN) of the hypothalamus constitutes the central circadian pacemaker. The SCN receives light signals from the retina and controls peripheral circadian clocks (located in the cortex, the pineal gland, the liver, the kidney, the heart, etc.). This hierarchical organization of the circadian system ensures the proper timing of physiological processes. In each SCN neuron, interconnected transcriptional and translational feedback loops enable the circadian expression of the clock genes. Although all the neurons have the same genotype, the oscillations of individual cells are highly heterogeneous in dispersed cell culture: many cells present damped oscillations and the period of the oscillations varies from cell to cell. In addition, the neurotransmitters that ensure the intercellular coupling, and thereby the synchronization of the cellular rhythms, differ between the two main regions of the SCN. In this work, a mathematical model that accounts for this heterogeneous organization of the SCN is presented and used to study the implication of the SCN network topology on synchronization and entrainment properties. The results show that oscillations with larger amplitude can be obtained with scale-free networks, in contrast to random and local connections. Networks with the small-world property such as the scale-free networks used in this work can adapt faster to a delay or advance in the light/dark cycle (jet lag). Interestingly a certain level of cellular heterogeneity is not detrimental to synchronization performances, but on the contrary helps resynchronization after jet lag. When coupling two networks with different topologies that mimic the two regions of the SCN, efficient filtering of pulse-like perturbations in the entrainment pattern is observed. These results suggest that the complex and heterogeneous architecture of the SCN decreases the sensitivity of the network to short entrainment perturbations while, at the same time, improving its adaptation abilities to long term changes