Collective dynamics of nonlocally coupled Hindmarsh-Rose neurons modified by magnetic flux

We investigate the dynamics of nonlocally coupled Hindmarsh-Rose neurons, modified by coupling the induced magnetic flux to the membrane potential with a quadratic memristor of strength k. The nonlocal coupling consists of the interaction of each neuron with its neighbors within a fixed radius, which influence the membrane potential of the neuron with coupling intensity σ. For such local dynamics and network of interactions, we investigate how variations of k and σ affect the collective dynamics. We find that when increasing k as well as when increasing σ, coherence typically increases, except for small ranges of these parameters where the opposite behavior can occur. Besides affecting coherence, varying k also affects the pattern of bursts and spikes, namely, for large enough k, burst frequency is augmented, the number and amplitude of the spikes are reduced, and quiescent periods become longer. Results are displayed for an intermediate range of interactions with radius 1/4 of the network size, but we also varied the range of interactions, ranging from first-neighbor to all-to-all couplings, observing in all cases a qualitatively similar impact of induction.

Efficiency of random search with space-dependent diffusivity

We address the problem of random search for a target in an environment with a space-dependent diffusion coefficient D(x). Considering a general form of the diffusion differential operator that includes Itô, Stratonovich, and Hänggi-Klimontovich interpretations of the associated stochastic process, we obtain and analyze the first-passage-time distribution and use it to compute the search efficiency E=〈1/t〉. For the paradigmatic power-law diffusion coefficient D(x)=D_{0}|x|^{α}, where x is the distance from the target and α<2, we show the impact of the different interpretations. For the Stratonovich framework, we obtain a closed-form expression for E, valid for arbitrary diffusion coefficient D(x). This result depends only on the distribution of diffusivity values and not on its spatial organization. Furthermore, the analytical expression predicts that a heterogeneous diffusivity profile leads to a lower efficiency than the homogeneous one with the same average level within the space between the target and the searcher initial position, but this efficiency can be exceeded for other interpretations.

Critical patch size reduction by heterogeneous diffusion

Population survival depends on a large set of factors and on how they are distributed in space. Due to landscape heterogeneity, species can occupy particular regions that provide the ideal scenario for development, working as a refuge from harmful environmental conditions. Survival occurs if population growth overcomes the losses caused by adventurous individuals that cross the patch edge. In this work, we consider a single species dynamics in a patch with a space-dependent diffusion coefficient. We show analytically, within the Stratonovich framework, that heterogeneous diffusion reduces the minimal patch size for population survival when contrasted with the homogeneous case with the same average diffusivity. Furthermore, this result is robust regardless of the particular choice of the diffusion coefficient profile. We also discuss how this picture changes beyond the Stratonovich framework. Particularly, the Itô case, which is nonanticipative, can promote the opposite effect, while Hänggi-Klimontovich interpretation reinforces the reduction effect.

Heat flux direction controlled by power-law oscillators under non-Gaussian fluctuations

Chains of particles coupled through anharmonic interactions and subject to non-Gaussian baths can exhibit paradoxical outcomes such as heat currents flowing from colder to hotter reservoirs. Aiming to explore the role of generic nonharmonicities in mediating the contributions of non-Gaussian fluctuations to the direction of heat propagation, we consider a chain of power-law oscillators, with interaction potential V(x)∝|x|^{α}, subject to Gaussian and Poissonian baths at its ends. Performing numerical simulations and addressing heuristic considerations, we show that a deformable potential has bidirectional control over heat flux.

Single-species fragmentation: The role of density-dependent feedback

Internal feedback is commonly present in biological populations and can play a crucial role in the emergence of collective behavior. To describe the temporal evolution of the distribution of a single-species population, we consider a generalization of the Fisher-KPP equation. This equation includes the elementary processes of random motion, reproduction, and, importantly, nonlocal interspecific competition, which introduces a spatial scale of interaction. In addition, we take into account feedback mechanisms in diffusion and growth processes, mimicked by power-law density dependencies. This feedback includes, for instance, anomalous diffusion, reaction to overcrowding or to the rarefaction of the population, as well as Allee-like effects. We show that, depending on the kind of feedback that takes place, the population can self-organize splitting into disconnected subpopulations, in the absence of external constraints. Through extensive numerical simulations, we investigate the temporal evolution and the characteristics of the stationary population distribution in the one-dimensional case. We discuss the crucial role that density-dependence has on pattern formation, particularly on fragmentation, which can bring important consequences to processes such as epidemic spread and speciation.

Population dynamics in an intermittent refuge

Population dynamics is constrained by the environment, which needs to obey certain conditions to support population growth. We consider a standard model for the evolution of a single species population density, which includes reproduction, competition for resources, and spatial spreading, while subject to an external harmful effect. The habitat is spatially heterogeneous, there existing a refuge where the population can be protected. Temporal variability is introduced by the intermittent character of the refuge. This scenario can apply to a wide range of situations, from a laboratory setting where bacteria can be protected by a blinking mask from ultraviolet radiation, to large-scale ecosystems, like a marine reserve where there can be seasonal fishing prohibitions. Using analytical and numerical tools, we investigate the asymptotic behavior of the total population as a function of the size and characteristic time scales of the refuge. We obtain expressions for the minimal size required for population survival, in the slow and fast time scale limits.

Metapopulation dynamics in a complex ecological landscape

We propose a general model to study the interplay between spatial dispersal and environment spatiotemporal fluctuations in metapopulation dynamics. An ecological landscape of favorable patches is generated like a Lévy dust, which allows to build a range of patterns, from dispersed to clustered ones. Locally, the dynamics is driven by a canonical model for the time evolution of the population density, consisting of a logistic expression plus multiplicative noises. Spatial coupling is introduced by means of two spreading mechanisms: diffusion and selective dispersal driven by patch suitability. We focus on the long-time population size as a function of habitat configurations, environment fluctuations, and coupling schemes. We obtain the conditions, that the spatial distribution of favorable patches and the coupling mechanisms must fulfill, to grant population survival. The fundamental phenomenon that we observe is the positive feedback between environment fluctuations and spatial spread preventing extinction.

Effect of environment fluctuations on pattern formation of single species

System-environment interactions are intrinsically nonlinear and dependent on the interplay between many degrees of freedom. The complexity may be even more pronounced when one aims to describe biologically motivated systems. In that case, it is useful to resort to simplified models relying on effective stochastic equations. A natural consideration is to assume that there is a noisy contribution from the environment, such that the parameters that characterize it are not constant but instead fluctuate around their characteristic values. From this perspective, we propose a stochastic generalization of the nonlocal Fisher-KPP equation where, as a first step, environmental fluctuations are Gaussian white noises, both in space and time. We apply analytical and numerical techniques to study how noise affects stability and pattern formation in this context. Particularly, we investigate noise-induced coherence by means of the complementary information provided by the dispersion relation and the structure function.

Dynamics of heme complexed with human serum albumin: a theoretical approach

Human serum albumin (HSA) is the most abundant protein in the blood serum. It binds several ligands and has an especially strong affinity for heme, hence becoming a natural candidate for oxygen transport. In order to analyze the interaction of HSA-heme, molecular dynamics simulations of HSA with bound heme were performed. Based on the results of X-ray diffraction, the binding site of the heme, localized in subdomain IB, was considered. We analyzed the fluctuations and their correlations along trajectories to detect collective motions. The role of H bonds and salt bridges in the stabilization of heme in its pocket was also investigated. Complementarily, the localization of water molecules in the hydrophobic pocket and the interaction with heme were discussed.

Nonparametric segmentation of nonstationary time series

The nonstationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasistationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption of stationarity, it is important to detect in real time series intervals holding that property. With that aim, we introduce a segmentation algorithm based on a fully nonparametric approach. We illustrate its applicability through the analysis of real time series presenting diverse degrees of nonstationarity, thus showing that this segmentation procedure generalizes and allows one to uncover features unresolved by previous proposals based on the discrepancy of low order statistical moments only.

Hydration of hydrophobic biological porphyrins

Explicit solvent, single solute molecular dynamics simulations of protoporphyrin IX and its Fe(2+) complex (heme) in water were performed. The relation of solute-solvent was examined through the spatial distribution functions of water molecules around the centroid of the porphyrin ring. A detailed description of the time-averaged structure of water surrounding the solutes as well as of its fluctuations is presented.

Complex dynamics of life at different scales: from genomic to global environmental issues

This introduction to the Theme Issue, Complex dynamics of life at different scales: from genomic to global environmental issues, gives a short overview on why the ideas and concepts in complexity and nonlinearity are relevant to the understanding of life in its different manifestations. Also, it discusses how life phenomena can be thought of as composing different scales of organization. Finally, the articles in this thematic publication are briefly commented on in terms of their relevance in helping to understand the complexity of life systems.

Low-sampling-rate Kramers-Moyal coefficients

We analyze the impact of the sampling interval on the estimation of Kramers-Moyal coefficients. We obtain the finite-time expressions of these coefficients for several standard processes. We also analyze extreme situations such as the independence and no-fluctuation limits that constitute useful references. Our results aim at aiding the proper extraction of information in data-driven analysis.

Exact results for the Barabási queuing model

Previous works on the queuing model introduced by Barabási to account for the heavy tailed distributions of the temporal patterns found in many human activities mainly concentrate on the extremal dynamics case and on lists of only two items. Here we obtain exact results for the general case with arbitrary values of the list length L and of the degree of randomness that interpolates between the deterministic and purely random limits. The statistically fundamental quantities are extracted from the solution of master equations. From this analysis, scaling features of the model are uncovered.

Unraveling the fluctuations of animal motor activity

Human and animal behavior exhibits power law correlations whose origin is controversial. In this work, the spontaneous motion of laboratory rodents was recorded during several days. It is found that animal motion is scale-free and that the scaling is introduced by the inactivity pauses both by its length as well as by its specific ordering. Furthermore, the scaling is also demonstrable in the rates of event's occurrence. A comparison with related results in humans is made and candidate models are discussed to provide clues for the origin of such dynamics.

Arbitrary-order corrections for finite-time drift and diffusion coefficients

We address a standard class of diffusion processes with linear drift and quadratic diffusion coefficients. These contributions to dynamic equations can be directly drawn from data time series. However, real data are constrained to finite sampling rates and therefore it is crucial to establish a suitable mathematical description of the required finite-time corrections. Based on Itô-Taylor expansions, we present the exact corrections to the finite-time drift and diffusion coefficients. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments that furnish extra theoretical checks for this class of diffusion models. The analytical predictions are compared with the numerical outcomes of representative artificial time series.

Critical scaling in standard biased random walks

The spatial coverage produced by a single discrete-time random walk, with an asymmetric jump probability p not equal 1/2 and nonuniform steps, moving on an infinite one-dimensional lattice is investigated. Analytical calculations are complemented with Monte Carlo simulations. We show that, for appropriate step sizes, the model displays a critical phenomenon, at p=p(c). Its scaling properties as well as the main features of the fragmented coverage occurring in the vicinity of the critical point are shown. In particular, in the limit p-->p(c), the distribution of fragment lengths is scale-free, with nontrivial exponents. Moreover, the spatial distribution of cracks (unvisited sites) defines a fractal set over the spanned interval. Thus, from the perspective of the covered territory, a very rich critical phenomenology is revealed in a simple one-dimensional standard model.

Long-time behavior of spreading solutions of Schrödinger and diffusion equations

We investigate the asymptotic time behavior of the solutions of a large class of linear differential equations that generalize the free-particle Schrödinger and diffusion equations, containing the standard ones as particular cases. We find general scalings that depend only on characteristic features of both the arbitrary initial condition and the Green function associated with the evolution equation. Basically, the amplitude of a long-time solution can be expressed in terms of low order moments of the initial condition (if finite) and low order spatial derivatives of the Green function. These derivatives can also be of the fractional type, which naturally arise when moments are divergent. We apply our results to a large class of differential equations that includes the fractional Schrödinger and Lévy diffusion equations. In particular, we show that, except for threshold cases, the amplitude of a packet may follow the asymptotic law t-alpha, with arbitrary positive alpha.

Additive-multiplicative stochastic models of financial mean-reverting processes

We investigate a generalized stochastic model with the property known as mean reversion, that is, the tendency to relax towards a historical reference level. Besides this property, the dynamics is driven by multiplicative and additive Wiener processes. While the former is modulated by the internal behavior of the system, the latter is purely exogenous. We focus on the stochastic dynamics of volatilities, but our model may also be suitable for other financial random variables exhibiting the mean reversion property. The generalized model contains, as particular cases, many early approaches in the literature of volatilities or, more generally, of mean-reverting financial processes. We analyze the long-time probability density function associated to the model defined through an Itô-Langevin equation. We obtain a rich spectrum of shapes for the probability function according to the model parameters. We show that additive-multiplicative processes provide realistic models to describe empirical distributions, for the whole range of data.

Escape time in anomalous diffusive media

We investigate the escape behavior of systems governed by the one-dimensional nonlinear diffusion equation theta(t)rho=theta(x)[theta(x)Urho]+Dtheta(x)2rho(nu), where the potential of the drift, U(x), presents a double well and D,nu are real parameters. For systems close to the steady state, we obtain an analytical expression of the mean first-passage time, yielding a generalization of Arrhenius law. Analytical predictions are in very good agreement with numerical experiments performed through integration of the associated Ito-Langevin equation. For nu not equal to 1, important anomalies are detected in comparison to the standard Brownian case. These results are compared to those obtained numerically for initial conditions far from the steady state.

Rotators with long-range interactions: connection with the mean-field approximation

We analyze the equilibrium properties of a chain of ferromagnetically coupled rotators which interact through a force that decays as r(-alpha) where r is the interparticle distance and alpha>/=0. By integrating the equations of motion we obtain the microcanonical time averages of both the magnetization and the kinetic energy. We detect three different regimes depending on whether alpha belongs to the intervals [0,1), (1,2), or (2,infinity). For 0<alpha<1, the microcanonical averages agree, after a scaling, with those obtained in the canonical ensemble for the mean-field case (alpha = 0). This correspondence offers a mathematically tractable way of dealing with systems governed by slowly decaying long-range interactions.

Carboxyl groups at the membrane interface as molecular targets for local anesthetics

The interaction of the tertiary amine drugs chlorpromazine and dibucaine in their cationic form with carboxyl groups at the membrane surface is studied at concentrations relevant to anesthesia. Spin-labeled stearic acid is used both to provide the carboxyl groups and to monitor binding and ionization behavior in egg lecithin liposomes. Membrane anesthetic concentrations are spectrophotometrically obtained. They are shown to determine the drug influence on carboxyl groups at the membrane surface, independently of aqueous concentrations. The intramembrane association constants (related to the usual aqueous phase ones through the partition coefficient) of the drugs with fatty acids are determined. The same value (10(2) M-1) is obtained for both drugs, suggesting that it is approximately the same for all tertiary amine local anesthetics. pH titrations of anesthetic-treated spin-labeled membranes are performed. The observed shifts in the fatty acid pK are higher than can be produced assuming uniform distribution of the drug in the membrane surface, implying that there is an increased affinity of local anesthetics for superficial carboxyl. This affinity could account for the resting block of voltage-gated Na+ channels. Under these considerations, local anesthetic binding sites at voltage-gated Na+ channels and at sarcoplasmic reticulum Ca(2+)-ATPase are proposed.

Nonlinear Dynamics of Lipid Films under Electric Forces

We study the dynamics and rupture of lipid films perturbed in the symmetric mode squeezing through an electrohydrodynamical approach. The lipid phase and the two surrounding aqueous phases are considered as incompressible Newtonian viscous fluids submitted to van der Waals, steric, and electric body forces. A nonlinear evolution equation for the film thickness, at the long-wavelength limit, is obtained for two symmetric cases: a film with equally charged surfaces with no potential drop and a neutral film submitted to an external electric field. At the long-wavelength limit, the electric term only influences the film evolution when the electric field inside the film is nonvanishing. We solve numerically, as an initial value problem with periodic boundary conditions, the nonlinear evolution equation. The rupture time is obtained and compared with analytical estimates. Sufficiently strong steric forces prevent the film from narrowing beyond a minimum thickness leading the film to a steady state different from the planar one consistently with the nonlinear analytical approach. The presence of a transmembrane electric potential destabilizes the perturbed film as predicted by the linear and nonlinear approaches; however, as expected, destabilization is not relevant at physiological values of the potential drop.

Interaction of alkanols and local anesthetics with spin-labeled Ca(2+)-ATPase of sarcoplasmic reticulum vesicles

Alkanols and tertiary amine derivative local anesthetics modify the activity of Ca(2+)-ATPase. In order to investigate the primary binding sites, associated to the functional changes, sarcoplasmic reticulum (SR) Ca(2+)-ATPase was labeled with maleimide derivative spin labels which bind covalently to SH groups of cysteine residues and allow to probe the regions of the protein close to those residues. The EPR measurements showed motional constraints induced by drug-treatment which indicate changes in the enzyme dynamics and structure. n-Alkanols are shown to affect some of the protein-bound labels by restricting their motion. There is, however, no correlation between the functional effects and the observed motional restriction, in the sense that concentrations of the different alcohols leading to the same functional effects do not induce the same degree of restriction. Dibucaine and tetracaine at functional relevant concentrations also restrict the movement of protein bound labels. But, in this case, correlation between spectral changes and functional effects is observed.

A model for nucleotide sequences

We propose a model for generating "artificial" nucleotide sequences and, by the method of mapping those sequences onto a "DNA-walk," we analyze the presence of correlation between nucleotides. Artificial sequences are constructed considering, basically, interactions between first neighbors and between more distant units. We show that long-range correlations may be favored by the occurrence of intrastrand interactions, which give a nonlinear characteristic to the sequence.

Interaction of chlorpromazine with phospholipid membranes. An EPR study of membrane surface potential effects

The interaction of chlorpromazine (CPZ) with artificial membranes (egg-yolk phosphatidylcholine liposomes) has been studied. Measurements of the surface electric potential, which is modified in the presence of the ionized form of the drug, were obtained by electron paramagnetic resonance spectroscopy (EPR) using a positively charged amphiphilic spin-probe. This probe partitions between the aqueous and lipidic phases depending on the surface potential and on the structural state of the membrane. The surface potential was measured as a function of drug concentration in the range where the spectral line-shapes are not affected by the incorporation of the drug. From these experimental results and through an appropriate formalism we obtain information on the binding of the drug to the lipid bilayer and on the ionization of the drug in the lipidic phase.

Interaction of dibucaine with the transmembrane domain of the Ca(2+)-ATPase of sarcoplasmic reticulum

The site of interaction of dibucaine with the Ca(2+)-ATPase of rabbit sarcoplasmic reticulum, an ion-transporting membrane protein, was investigated by determining the effect of dibucaine on the denaturation of the transmembrane domain and the aqueous domain containing, respectively, the high-affinity Ca2+ binding sites and the site of ATP hydrolysis. In the absence of Ca2+, a single irreversible denaturation transition with Tm approximately equal to 49 degrees C is observed for the Ca(2+)-ATPase by differential scanning calorimetry (DSC). In the presence of Ca2+, but not Mg2+, Sr2+, or Ba2+, a new high-temperature transition is observed that has been shown to be due to stabilization of the transmembrane region [Lepock, J. R., Rodahl, A. M., Zhang, C., Heynen, M. L., Waters, B., & Cheng, K. H. (1990) Biochemistry 29, 681-689]. The maximum stabilization corresponds to a shift in Tm of 13.8 degrees C, and Hill analysis indicates that the Ca2+ binding site yielding stabilization has a Kd = 2.5 x 10(-4) M with a cooperativity (n) of 1. Thus, stabilization is due to Ca2+ binding not to the high-affinity sites but to one of the previously observed sites of low or intermediate affinity, which must be located in the transmembrane or stalk subdomains. Dibucaine has little effect on the Tm of the aqueous domain, but it decreases the Tm of the transmembrane domain with Kd approximately equal to 4.1 x 10(-4) M and a cooperativity of approximately 1.6, implying that destabilization is due to the binding of dibucaine to sites of intermediate or moderately high affinity.(ABSTRACT TRUNCATED AT 250 WORDS)