Simulations of flexible membranes using a coarse-grained particle-based model with spontaneous curvature variables

We propose a simple mathematical model for lipid bilayer membranes of flexible fluid or solid state. The model consists of interacting coarse-grained particles with two extra variables. One indicates the spontaneous curvature at the particle position, and the other indicates the vector representing the direction normal to the membrane. When the spontaneous curvature variable is allowed to fluctuate significantly, the fluctuation causes a softening of the membrane and growth of large undulations as the amplitude of the fluctuation is increased. By changing the amplitude of the fluctuation in simulations, the bending rigidity of the membrane can be easily controlled. Because the proposed model includes anisotropic interactions between the particles, multilayered vesicles can be obtained through a reversible transition by weakening the strength of the anisotropic interactions.     

Rectification Efficiency of Two Harmonically Coupled Particles

Transportation properties of two harmonically coupled particles moving in a flashing or rocking ratchet potential are investigated in terms of Langevin simulation. The efficiency for rectification of non-equilibrium fluctuation is calculated by using a new definition. The results show that both the average current and efficiency of two coupled particles in the flashing ratchet are larger than that of a single particle and these quantities are non-monotonous functions of the potential remaining time.     

Coupling Effect of Ion Channel Clusters on Calcium Signalling

Based on a modified intracellular Ca^2＋ model involving diffusive coupling of two calcium ion channel dusters, the effects of coupling on calcium signalling are numerically investigated. The simulation results indicate that the diffusive coupling of dusters together with internal noise determine the calcium dynamics of single duster, and for either homogeneous or heterogeneous coupled dusters, the synchronization of dusters, which is important to calcium signalling, is enhanced by the coupling effect.     

Simulation of proliferation and differentiation of cells in a stem-cell niche

Stem-cell niches represent microscopic compartments formed of environmental cells that nurture stem cells and enable them to maintain tissue homeostasis. The spatio-temporal kinetics of proliferation and differentiation of cells in such niches depend on the specifics of the niche structure and on adhesion and communication between cells and may also be influenced by spatial constraints on cell division. We propose a generic lattice model, taking all these factors into account, and systematically illustrate their role. The model is motivated by the experimental data available for the niches located in the subventricular zone of adult mammalian brain. The general conclusions drawn from our Monte Carlo simulations are applicable to other niches as well. One of our main findings is that the kinetics under consideration are highly stochastic due to a relatively small number of cells proliferating and differentiating in a niche and the autocatalytic character of the symmetric cell division. In particular, the kinetics exhibit huge stochastic bursts especially if the adhesion between cells is taken into account. In addition, the results obtained show that despite the small number of cells present in stem-cell niches, their arrangement can be predetermined to appreciable extent provided that the adhesion of different cells is different so that they tend to segregate.     

Stochastic resonance in an ion channel following the non-Arrhenius gating rate

Stochastic resonance (SR) is a novel cooperative phenomenon occurring in nonlinear systems due to coupling of an ambient noise and an external signal. Biological systems may use SR mechanism to detect the signal efficiently from an external environment. A number of studies have addressed the SR in artificial ion channels considering external voltages as noises. More important than these external noises is the internal, thermal noise which changes the channel conformations essential for biological functions. In this work, we consider that the channel gating rates follow a non-Arrhenius temperature dependence derived from experimental data of a real biological channel. Using the Monte-Carlo simulations, we find that in this channel SR occurs near a physiological temperature in a very distinctive manner compared with that for the Arrhenius gating model.     

The nucleosome: A transparent, slippery, sticky and yet stable DNA-protein complex

Roughly three quarters of eucaryotic DNA are tightly wrapped onto protein cylinders organized in so-called nucleosomes. Despite this fact, the wrapped DNA cannot be inert since DNA is at the heart of many crucial life processes. We focus here on physical mechanisms that might allow nucleosomes to perform a great deal of such processes, specifically 1) on unwrapping fluctuations that give DNA-binding proteins access to the wrapped DNA portions without disrupting the nucleosome as a whole, 2) on corkscrew sliding along DNA and some implications and on 3) tail-bridging-induced attraction between nucleosomes as a means of controlling higher-order folding.     

A general two-cycle network model of molecular motors

Molecular motors are single macromolecules that generate forces at the piconewton range and nanometer scale. They convert chemical energy into mechanical work by moving along filamentous structures. In this paper, we study the velocity of two-head molecular motors in the framework of a mechanochemical network theory. The network model, a generalization of the recently work of Liepelt and Lipowsky [Steffen Liepelt, Reinhard Lipowsky, Kinesins network of chemomechanical motor cycles, Physical Review Letters 98 (25) (2007) 258102], is based on the discrete mechanochemical states of a molecular motor with multiple cycles. By generalizing the mathematical method developed by Fisher and Kolomeisky for a single cycle motor [Michael E. Fisher, Anatoly B. Kolomeisky, Simple mechanochemistry describes the dynamics of kinesin molecules, Proceedings of the National Academy of Sciences 98 (14) (2001) 7748-7753], we are able to obtain an explicit formula for the velocity of a molecular motor.     

Effects of the network structure and coupling strength on the noise-induced response delay of a neuronal network

The Hodgkin-Huxley (H-H) neuron model driven by stimuli just above threshold shows a noise-induced response delay with respect to time to the first spike for a certain range of noise strengths, an effect called “noise delayed decay” (NDD). We study the response time of a network of coupled H-H neurons, and investigate how the NDD can be affected by the connection topology of the network and the coupling strength. We show that the NDD effect exists for weak and intermediate coupling strengths, whereas it disappears for strong coupling strength regardless of the connection topology. We also show that although the network structure has very little effect on the NDD for a weak coupling strength, the network structure plays a key role for an intermediate coupling strength by decreasing the NDD effect with the increasing number of random shortcuts, and thus provides an additional operating regime, that is absent in the regular network, in which the neurons may also exploit a spike time code.     

Effects of Nonlinear Time-Delay on a Stochastic Asymmetric System

We numerically investigate the effects of nonlinear time-delay on the stochastic system. With the delay time increasing, it is found that the peak of probability distribution in low steady states is decreased, and the peak of probability distribution in high steady states is increased. The mean of state variable, the normalized variance, and the normalized autocorrelation function which quantifies the concentrated degree are slowly varied for small delay time. However, the mean of state variable is rapidly increased, and the normalized variance and the normalized autocorrelation function is rapidly decreased for large delay time.     

Stochastic resonance on Newman-Watts networks of Hodgkin-Huxley neurons with local periodic driving

We study the phenomenon of stochastic resonance on Newman-Watts small-world networks consisting of biophysically realistic Hodgkin-Huxley neurons with a tunable intensity of intrinsic noise via voltage-gated ion channels embedded in neuronal membranes. Importantly thereby, the subthreshold periodic driving is introduced to a single neuron of the network, thus acting as a pacemaker trying to impose its rhythm on the whole ensemble. We show that there exists an optimal intensity of intrinsic ion channel noise by which the outreach of the pacemaker extends optimally across the whole network. This stochastic resonance phenomenon can be further amplified via fine-tuning of the small-world network structure, and depends significantly also on the coupling strength among neurons and the driving frequency of the pacemaker. In particular, we demonstrate that the noise-induced transmission of weak localized rhythmic activity peaks when the pacemaker frequency matches the intrinsic frequency of subthreshold oscillations. The implications of our findings for weak signal detection and information propagation across neural networks are discussed.     

Resonant phenomena in extended chaotic systems subject to external noise: The Lorenz’96 model case

We have investigated the effects of noise on an extended chaotic system. The chosen model is the Lorenz’96, a type of “toy” model used for climate studies. Through the analysis of the system’s time evolution and its time and space correlations, we have obtained numerical evidence for two distinct stochastic resonance-like behaviors. Such behaviors are seen when both the usual and a generalized signal-to-noise ratio functions are depicted as a function of the external noise intensity, or of the system size. The underlying mechanisms seem to be associated with a noise-induced chaos reduction. The possible relevance of these and other findings for an optimal climate prediction are discussed.     

Signal propagation in stem-cell niches

Stem cells, maintaining tissue homeostasis, are nurtured in microscopic niches formed of so-called environmental cells. The kinetics of proliferation and differentiation of stem cells in such niches depend on their interaction with the messenger proteins secreted by environmental cells. We propose a generic mean-field kinetic model of the propagation of such signals. To motivate our study, we briefly describe a stem-cell niche in the Drosophila ovary. Our model is however applicable to other niches as well. In particular, it helps one to understand the necessary conditions for the niche function. For example, the model predicts that in the case of the Drosophila ovary each germline stem cell should have in the external membrane at least 700 receptors interacting with the signaling Dpp and Gpp proteins emanating from the cap cells.     

Nonlinear molecular excitations in a completely inhomogeneous DNA chain

We study the nonlinear dynamics of a completely inhomogeneous DNA chain which is governed by a perturbed sine-Gordon equation. A multiple scale perturbation analysis provides perturbed kink-antikink solitons to represent open state configuration with small fluctuation. The perturbation due to inhomogeneities changes the velocity of the soliton. However, the width of the soliton remains constant.     

Universality of level spacing distributions in classical chaos

We suggest that random matrix theory applied to a matrix of lengths of classical trajectories can be used in classical billiards to distinguish chaotic from non-chaotic behavior. We consider in 2D the integrable circular and rectangular billiard, the chaotic cardioid, Sinai and stadium billiard as well as mixed billiards from the Limaçon/Robnik family. From the spectrum of the length matrix we compute the level spacing distribution, the spectral auto-correlation and spectral rigidity. We observe non-generic (Dirac comb) behavior in the integrable case and Wignerian behavior in the chaotic case. For the Robnik billiard close to the circle the distribution approaches a Poissonian distribution. The length matrix elements of chaotic billiards display approximate GOE behavior. Our findings provide evidence for universality of level fluctuations—known from quantum chaos—to hold also in classical physics.     

Experimental observation of strange nonchaotic attractors in a driven excitable system

We report the observation of strange nonchaotic attractors in an electrochemical cell. The system parameters were chosen such that the system observable (anodic current) exhibits fixed point behavior or period one oscillations. These autonomous dynamics were thereafter subjected to external quasiperiodic forcing. Systematically varying the characteristics (frequency and amplitude) of the superimposed external signal; quasiperiodic, chaotic and strange nonchaotic behaviors in the anodic current were generated. The inception of strange nonchaotic attractors was verified using standard diagnostic techniques.     

ncRNA-mediated bistability in the synthesis of hundreds of distinct mRNAs and proteins

The kinetics of gene expression can be bistable due to the feedback between the mRNA and protein formation. In eukaryotic cells, the interplay between mRNAs and proteins can be influenced by non-coding RNAs. Some of these RNAs, e.g., microRNAs, may target hundreds of distinct mRNAs. The model presented here shows how a non-coding RNA can be used as a mediator in order to involve numerous mRNAs and proteins into a bistable network.     

Nonlinear adaptive synchronization rule for identification of a large amount of parameters in dynamical models

The existing adaptive synchronization technique based on the stability theory and invariance principle of dynamical systems, though theoretically proved to be valid for parameters identification in specific models, is always showing slow convergence rate and even failed in practice when the number of parameters becomes large. Here, for parameters update, a novel nonlinear adaptive rule is proposed to accelerate the rate. Its feasibility is validated by analytical arguments as well as by specific parameters identification in the Lotka-Volterra model with multiple species. Two adjustable factors in this rule influence the identification accuracy, which means that a proper choice of these factors leads to an optimal performance of this rule. In addition, a feasible method for avoiding the occurrence of the approximate linear dependence among terms with parameters on the synchronized manifold is also proposed.