Biomedical subjects

Alexander S Mikhailov

Publications and source records attributed to Alexander S Mikhailov.

15 recordsLinked to original sources

PubMed2006

Universal finite-sample effect on the perturbation growth in chaotic dynamical systems.

The finite-sample effect on the growth of moments of the perturbation observed in numerical simulations of chaotic dynamical systems is studied. To numerically estimate the moments, only a limited number of sample trajectories can be utilized, and therefore the moments exhibit pure exponential growth only initially, and give way to relaxed growth thereafter. Such transition is a consequence of the unobservability of rare events in finite sample sets. Using the large-deviation formalism for chaotic time series, we estimate the relaxation time and derive the post-relaxation growth law. We demonstrate that even after the relaxation, each moment still obeys a universal growth law of different type, which reflects physical information on the statistics of chaotic expansion rates.

Journal Article↗

PubMed2006

Front reversals, wave traps, and twisted spirals in periodically forced oscillatory media.

A new kind of nonlinear nonequilibrium patterns--twisted spiral waves--is predicted for periodically forced oscillatory reaction-diffusion media. We show, furthermore, that, in such media, spatial regions with modified local properties may act as traps where propagating waves can be stored and released in a controlled way. Underlying both phenomena is the effect of the wavelength-dependent propagation reversal of traveling phase fronts, always possible when homogeneous oscillations are modulationally stable without forcing. The analysis is performed using as a model the complex Ginzburg-Landau equation, applicable for reaction-diffusion systems in the vicinity of a supercritical Hopf bifurcation.

Journal Article↗

PubMed2006

Nonequilibrium self-organization phenomena in active Langmuir monolayers.

Langmuir monomolecular layers, formed by amphiphilic molecules at liquid-air interfaces and containing a fraction of chiral molecules, are theoretically investigated. These monolayers can be brought out of thermal equilibrium by applying a gradient of small molecules across the interface, resulting in the leakage flow. We show that, when splay coupling between the orientation field and the local concentration of chiral molecules in the monolayer is taken into account, this nonequilibrium soft matter system can show complex wave behavior, including the development of target wave patterns, spiral waves, and dense regions filled with inwardly propagating waves.

Biophysics↗

PubMed2006

Cooperative stochastic behavior in the onset of localized corrosion.

Stochastic temporal and spatiotemporal models of metastable pitting on a metal surface are presented. A stochastic reaction-diffusion model accounts for the effects of local changes in concentration, potential drop, and oxide film damage on the nucleation of subsequent events. The cooperative interactions among events can lead to the formation of clusters of metastable pits and to an explosive growth in the total number of pits. Recent progress in the studies of such phenomena is reviewed. New results based on a mean-field analysis of the model and numerical simulations on critical nucleation effects are reported.

Journal Article↗

PubMed2005

Functional conformational motions in the turnover cycle of cholesterol oxidase.

Reexamining experimental data of single-molecule fluorescence correlation spectroscopy for cholesterol oxidase, we find that the existing Michaelis-Menten models with dynamical disorder cannot explain strong correlations between subsequent turnover cycles revealed in the diagonal feature in the joint statistical distribution of adjacent "on" times of this enzyme. We suggest that functional conformational motions representing ordered sequences of transitions between a set of conformational substates are involved, along with equilibrium conformational fluctuations in the turnover cycle of cholesterol oxidase. A two-channel model of single-enzyme dynamics, including a slow functional conformational motion in one of the channels, is proposed that allows us to reproduce such strong correlations.

Cholesterol Oxidase↗

PubMed2005

Noise-induced transition from translational to rotational motion of swarms.

We consider a model of active Brownian agents interacting via a harmonic attractive potential in a two-dimensional system in the presence of noise. By numerical simulations, we show that this model possesses a noise-induced transition characterized by the breakdown of translational motion and the onset of swarm rotation as the noise intensity is increased. Statistical properties of swarm dynamics in the weak noise limit are further analytically investigated.

Animals↗

PubMed2004

Entrainment of randomly coupled oscillator networks by a pacemaker.

Entrainment by a pacemaker, representing an element with a higher frequency, is numerically investigated for several classes of random networks which consist of identical phase oscillators. We find that the entrainment frequency window of a network decreases exponentially with its depth, defined as the mean forward distance of the elements from the pacemaker. Effectively, only shallow networks can thus exhibit frequency locking to the pacemaker. The exponential dependence is also derived analytically as an approximation for large random asymmetric networks.

Adaptation, Physiological↗

PubMed2004

Nonequilibrium orientational patterns in two-component Langmuir monolayers.

A model of a phase-separating two-component Langmuir monolayer in the presence of a photoinduced reaction interconverting two components is formulated. An interplay between phase separation, orientational ordering, and reaction is found to lead to a variety of nonequilibrium self-organized patterns, both stationary and traveling. Examples of the patterns, observed in numerical simulations, include flowing droplets, traveling stripes, wave sources, and vortex defects.

Journal Article↗

PubMed2003

Pattern formation on the edge of chaos: mathematical modeling of CO oxidation on a Pt(110) surface under global delayed feedback.

Effects of global delayed feedback on diffusion-induced turbulence are studied in a realistic model of catalytic oxidation of carbon monoxide on Pt(110). Spatiotemporal patterns resulting from numerical simulations of this model are identified and analyzed using a transformation into the phase and the amplitude of local oscillations. We find that chemical turbulence can be efficiently controlled by varying the feedback intensity and the delay time in the feedback loop. Near the transition from turbulence to uniform oscillations, various chaotic and regular spatiotemporal patterns-intermittent turbulence, two-phase clusters, cells of hexagonal symmetry, and phase turbulence-are found.

Journal Article↗

PubMed2003

Pattern formation on the edge of chaos: experiments with CO oxidation on a Pt(110) surface under global delayed feedback.

Experiments with catalytic oxidation of carbon monoxide on Pt(110) show that chemical turbulence in this system can be suppressed by application of appropriate global delayed feedback. Different spatiotemporal patterns, seen near the transition from turbulence to uniform oscillations, are investigated. Such patterns include intermittent turbulence, oscillatory standing waves, cellular structures, and phase clusters. Using a method based on the Hilbert transform, spatial distributions of local phase and amplitude in these patterns are reconstructed from the experimental data.

Journal Article↗

PubMed2003

Taming Winfree turbulence of scroll waves in excitable media.

Winfree turbulence of scroll waves is a special kind of spatiotemporal chaos that exists exclusively in three-dimensional excitable media and is currently considered one of the principal mechanisms of cardiac fibrillation. A chaotic wave pattern develops through the negative-tension instability of vortex filaments, which tend to spontaneously stretch, bend, loop, and produce an expanding tangle that fills up the volume. We demonstrate that such turbulence can readily be controlled by weak nonresonant modulation of the medium excitability. Depending on the forcing frequency, either suppression or induction of turbulence can be achieved.

Journal Article↗

PubMed2003

Statistics of rare strong bursts in autocatalytic stochastic growth with diffusion.

A general model of autocatalytic stochastic growth with diffusion is analytically and numerically investigated. Exact analytical results for the intermittency exponents and the probability of rare strong bursts in an infinite system are presented. Finite-size saturation effects, leading to the stretched exponential growth of statistical moments, are further considered. These analytical predictions are checked in numerical simulations.

Diffusion↗

PubMed2002

Conformational-relaxation models of single-enzyme kinetics.

Fluorescent spectroscopy experiments with single-enzyme molecules yield a large volume of statistical data that can be analyzed and interpreted using stochastic models of enzyme action. Here, we present two models, each based on the mechanism that an enzyme molecule must pass through a sequence of conformational transformations to complete its catalytic turnover cycle. In the simplest model, only one path leading to the release of product is present. In contrast to this, two different catalytic paths are possible in the second considered model. If a cycle is started from an active state, immediately after the previous product release, it follows a different conformational route and is much shorter. Our numerical investigations show that both models generate non-Markovian molecular statistics. However, their memory landscapes and distributions of cycle times are significantly different. The memory landscape of the double-path model bears strong similarity to the recent experimental data for horseradish peroxidase.

Catalysis↗

PubMed2002

Evolutionary reconstruction of networks.

Can a graph specifying the pattern of connections of a dynamical network be reconstructed from statistical properties of a signal generated by such a system? In this model study, we present a Metropolis algorithm for reconstruction of graphs from their Laplacian spectra. Through a stochastic process of mutations and selection, evolving test networks converge to a reference graph. Applying the method to several examples of random graphs, clustered graphs, and small-world networks, we show that the proposed stochastic evolution allows exact reconstruction of relatively small networks and yields good approximations in the case of large sizes.

Journal Article↗

PubMed2002

Traveling waves and nonequilibrium stationary patterns in two-component reactive langmuir monolayers.

A simple kinetic model of a two-component phase-separating Langmuir monolayer with a chemical reaction is proposed. Its analysis and numerical simulations show that nonequilibrium periodic stationary structures and patterns of traveling stripes can spontaneously develop. The nonequilibrium phase diagram of this system is constructed and the properties of the patterns are discussed.

Cell Membrane↗