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Experimental and numerical study of heterogeneous pressure-temperature-induced lethal and sublethal injury of Lactococcus lactis in a medium scale high-pressure autoclave.

The present contribution is dedicated to experimental and theoretical assessment of microbiological process heterogeneities of the high-pressure (HP) inactivation of Lactococcus lactis ssp. cremoris MG 1363. The inactivation kinetics are determined in dependence of pressure, process time, temperature and absence or presence of co-solutes in the buffer system namely 4 M sodium chloride and 1.5 M sucrose. The kinetic analysis is carried out in a 0.1-L autoclave in order to minimise thermal and convective effects. Upon these data, a deterministic inactivation model is formulated with the logistic equation. Its independent variables represent the counts of viable cells (viable but injured) and of the stress-resistant cells (viable and not injured). This model is then coupled to a thermo-fluiddynamical simulation method, high-pressure computer fluid dynamics technique (HP-CFD), which yields spatiotemporal temperature and flow fields occurring during the HP application inside any considered autoclave. Besides the thermo-fluiddynamic quantities, the coupled model predicts also the spatiotemporal distribution of both viable (VC) and stress-resistant cell counts (SRC). In order to assess the process non-uniformity of the microbial inactivation in a 3.3-L autoclave experimentally, microbial samples are placed at two distinct locations and are exposed to various process conditions. It can be shown with both, experimental and theoretical models that thermal heterogeneities induce process non-uniformities of more than one decimal power in the counts of the viable cells at the end of the treatment.

Biotechnology↗

Experimental observation of stochastic resonance in a linear electronic array.

We report the experimental observation of array-enhanced stochastic resonance, spatiotemporal synchronization, and noise-enhanced propagation in a simple coupled linear array of bistable electronic triggers. In addition, we highlight an analogy between charge density wave (CDW) like conductivity and spatiotemporal synchronization in stochastic resonances, several aspects of which are supported by the experimental evidence presented here. This may prove to be important in the understanding of nonlinear conductivity in CDW solids.

Journal Article↗

Stimulus-secretion coupling and Ca2+ dynamics in pancreatic acinar cells.

1. Unique spatiotemporal dynamics in cytosolic Ca2+ concentration, [Ca2+]c, were characterized in various cell types. In pancreatic acinar cells, physiological concentrations of cholecystokinin octapeptide, CCK-8, (< 10 pM) induce repetitive [Ca2+]c spikes commonly termed Ca2+ oscillation, whereas relatively higher concentrations (30 pM-1 nM) evoke biphasic [Ca2+]c dynamics; a rapid transient peak followed by a sustained increase. Much higher concentrations (> 1 nM) induce a large transient followed by a steep decay. 2. These [Ca2+]c dynamics correspond to secretory responses. Repetitive [Ca2+]c change is attributable to the upstroke of the bell-shaped dose-response relationship and the biphasic change is responsible for the downstroke of the relation (so called high-dose inhibited secretion). The large transient [Ca2+]c increase is associated with morphological changes such as bleb formation. 3. Possible interrelation between dose of secretagogues, secretory responses, [Ca2+]c dynamics, IP3 production, receptor occupation and morphological change will be discussed from both pharmacological and physiological points of view.

Animals↗

How does a periodic rotating wave emerge from high-dimensional chaos in a ring of coupled chaotic oscillators?

A route to typical rotating waves from high-dimensional chaos is investigated in diffusively coupled chaotic Rössler oscillators. By increasing the coupling from zero, a high-dimensional spatiotemporal chaos changes into a coherent state, which is periodic in time and well ordered in space, through consecutive transitions. A crossover transition from spatially random chaos to spatially ordered chaos with phase locking and orientational equality (for two directions) breaking is a crucial step for establishing the typical spatial order of the rotating wave.

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Dynamic characterizers of spatiotemporal intermittency.

We study spatiotemporal intermittency (STI) in a system of coupled sine circle maps. The phase diagram of the system shows parameter regimes where the STI lies in the directed percolation (DP) class, as well as regimes which show pure spatial intermittency (where the temporal behavior is regular) which do not belong to the DP class. Thus both DP and non-DP behavior can be seen in the same system. The signature of DP and non-DP behavior can be seen in the dynamic characterizers, viz. the spectrum of eigenvalues of the linear stability matrix of the evolution equation, as well as in the multifractal spectrum of the eigenvalue distribution. The eigenvalue spectrum of the system in the DP regimes is continuous, whereas it shows evidence of level repulsion in the form of gaps in the spectrum in the non-DP regime. The multifractal spectrum of the eigenvalue distribution also shows the signature of DP and non-DP behavior. These results have implications for the manner in which correlations build up in extended systems.

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Dynamics of strongly-coupled spiking neurons.

We present a dynamical theory of integrate-and-fire neurons with strong synaptic coupling. We show how phase-locked states that are stable in the weak coupling regime can destabilize as the coupling is increased, leading to states characterized by spatiotemporal variations in the interspike intervals (ISIs). The dynamics is compared with that of a corresponding network of analog neurons in which the outputs of the neurons are taken to be mean firing rates. A fundamental result is that for slow interactions, there is good agreement between the two models (on an appropriately defined timescale). Various examples of desynchronization in the strong coupling regime are presented. First, a globally coupled network of identical neurons with strong inhibitory coupling is shown to exhibit oscillator death in which some of the neurons suppress the activity of others. However, the stability of the synchronous state persists for very large networks and fast synapses. Second, an asymmetric network with a mixture of excitation and inhibition is shown to exhibit periodic bursting patterns. Finally, a one-dimensional network of neurons with long-range interactions is shown to desynchronize to a state with a spatially periodic pattern of mean firing rates across the network. This is modulated by deterministic fluctuations of the instantaneous firing rate whose size is an increasing function of the speed of synaptic response.

Animals↗

Control of chaotic spatiotemporal spiking by time-delay autosynchronization.

A global time-delayed feedback control is applied to a globally coupled reaction-diffusion system describing charge transport in a bistable semiconductor. We demonstrate that a variety of spatiotemporal unstable periodic orbits (UPOs) embedded in a chaotic attractor of the spatially extended system can be stabilized using an extended time-delay autosynchronization algorithm. These UPOs correspond to spiking current filaments. We critically evaluate analytical approximations for the limits of control originally developed for low-dimensional temporal chaos and show that the delay time can be extrapolated with high accuracy, while the theoretical limit for the control of UPOs in terms of the product of the period and the largest Lyapunov exponent is not reached. If the global feedback is modified by a spatial filter, we achieve stabilization of different spatial patterns.

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Linking cell division to cell growth in a spatiotemporal model of the cell cycle.

Cell division must be tightly coupled to cell growth in order to maintain cell size, yet the mechanisms linking these two processes are unclear. It is known that almost all proteins involved in cell division shuttle between cytoplasm and nucleus during the cell cycle; however, the implications of this process for cell cycle dynamics and its coupling to cell growth remains to be elucidated. We developed mathematical models of the cell cycle which incorporate protein translocation between cytoplasm and nucleus. We show that protein translocation between cytoplasm and nucleus not only modulates temporal cell cycle dynamics, but also provides a natural mechanism coupling cell division to cell growth. This coupling is mediated by the effect of cytoplasmic-to-nuclear size ratio on the activation threshold of critical cell cycle proteins, leading to the size-sensing checkpoint (sizer) and the size-independent clock (timer) observed in many cell cycle experiments.

Animals↗

Synchronized chaotic intermittent and spiking behavior in coupled map chains.

We study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type-I intermittent behavior. Two types of parameter distribution, linear and random, are considered. The typical phenomena are the onset and existence of global (all-to-all) and cluster (partial) synchronization with increase of coupling. Increase of coupling strength can also lead to desynchronization phenomena, i.e., global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states. Then a regime of a fully incoherent nonsynchronous state (spatiotemporal intermittency) appears. Synchronization-desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one: a chain of coupled maps replicating the spiking behavior of neurobiological networks.

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Transverse coupling of chemical waves.

The transverse coupling of chemical waves is investigated using a model scheme for excitable media. Chemical waves supported on the surfaces of a semipermeable membrane couple via diffusion through the membrane, resulting in new types of spatiotemporal behavior. The model studies show that spontaneous wave sources may develop from interacting planar waves, giving rise to a complex sequence of patterns accessible only by perturbation. Coupled circular waves result in the spontaneous formation of spiral waves, which subsequently develop patterns in distinct domains with characteristic features. The long time entrainment behavior of coupled spiral waves reveals regions of 1:2 phase locking.

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Lyapunov spectrum and synchronization of piecewise linear map lattices with power-law coupling.

We study the synchronization properties of a lattice of chaotic piecewise linear maps. The coupling strength decreases with the lattice distance in a power-law fashion. We obtain the Lyapunov spectrum of the coupled map lattice and investigate the relation between spatiotemporal chaos and synchronization of amplitudes and phases, using suitable numerical diagnostics.

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Estimating model parameters by chaos synchronization.

Using chaos synchronization and a proposed iterative method of parameter adaptation, we precisely estimate the model parameters of chaotic systems and synchronize two chaotic systems with originally mismatching model parameters. This parameter adaptation method can be applied to a spatiotemporal chaotic system with a one-way-coupled map lattice. As a biomedical application, this method is capable of estimating the asymmetric tension parameter of a vocal fold model.

Biophysical Phenomena↗

Finite wavelength instabilities in a slow mode coupled complex ginzburg-landau equation

In this Letter, we discuss the effect of slow real modes in reaction-diffusion systems close to a supercritical Hopf bifurcation. The spatiotemporal effects of the slow mode cannot be captured by traditional descriptions in terms of a single complex Ginzburg-Landau equation (CGLE). We show that the slow mode coupling to the CGLE introduces a novel set of finite wavelength instabilities not present in the CGLE. For spiral waves, these instabilities highly affect the location of regions for convective and absolute instability. These new instability boundaries are consistent with transitions to spatiotemporal chaos found by simulation of the corresponding coupled amplitude equations.

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Spatiotemporal nonlinear dynamics of a magnetoelastic ribbon.

Magnetoelastic materials have a strong coupling between strain and magnetization, so applying a magnetic field to a magnetoelastic material can change its shape. This coupling leads to interesting dynamics. We have studied the dynamics of a wide ribbon of Metglass 2605sc which was driven by a magnetic field. The ribbon was suspended as a pendulum in a set of Helmholtz coils, which provided both dc and ac magnetic fields. Laser light was reflected off the ribbon to measure its angular displacement. Two points on the ribbon could be simultaneously illuminated, and one of the laser beams could be scanned over the ribbon. We observed quasiperiodic bifurcations in the motion of the ribbon, and characterized the spatial aspect of the motion with some recently developed statistics.

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Spatial bistability: a source of complex dynamics. From spatiotemporal reaction-diffusion patterns to chemomechanical structures.

We show experimentally and theoretically that reaction systems characterized by a slow induction period followed by a fast evolution to equilibrium can readily generate "spatial bistability" when operated in thin gel reactors diffusively fed from one side. This phenomenon which corresponds to the coexistence of two different stable steady states, not breaking the symmetry of the boundary conditions, can be at the origin of diverse reaction-diffusion instabilities. Using different chemical reactions, we show how stationary pulses, labyrinthine patterns or spatiotemporal oscillations can be generated. Beyond simple reaction-diffusion instabilities, we also demonstrate that the cross coupling of spatial bistability with the size responsiveness of a chemosensitive gel can give rise to autonomous spatiotemporal shape patterns, referred to as chemomechanical structures.

Catalysis↗

A hierarchy of global coupling induced cluster patterns during the oscillatory H2-electrooxidation reaction on a Pt ring-electrode.

We report experimental results on spatiotemporal pattern formation during the oscillatory hydrogen electrooxidation reaction on a Pt ring-electrode under negative (desynchronizing) global coupling (GC). Spatially one-dimensional profiles of the interfacial potential drop along the angular direction of the ring electrode are recorded by means of a potential probe. The dynamics is investigated as a function of two control parameters, the applied voltage U and the strength of the global coupling. The latter is adjusted either by varying the distance between the working electrode (WE) and the reference electrode (RE) or by inserting a negative impedance device in series with the WE. In the absence of global coupling, uniform oscillations were destabilized by migration coupling, and electrochemical turbulence developed at large values of U (H. Varela, C. Beta, A. Bonnefont and K. Krischer, Phys. Rev. Lett., 2005, 94, 174104; ). Already low global coupling strengths sufficed to suppress turbulence. Instead, regular two-phase clusters formed. At higher coupling strength, a second type of two-phase cluster was observed as well as two types of irregular cluster patterns, which were connected with an irregular motion of the cluster boundaries and the emergence and disappearance of clusters through splitting and merging of the boundaries, respectively. Upon increasing the coupling strength even further, five-phase clusters were stabilized and at the highest coupling strength applied the cluster patterns transformed into strongly modulated pulses. The two types of two-phase clusters and the five-phase clusters are analyzed employing several signal processing techniques.

Journal Article↗

Empirical determinants of measles metapopulation dynamics in England and Wales.

A key issue in metapopulation dynamics is the relative impact of internal patch dynamics and coupling between patches. This problem can be addressed by analysing large spatiotemporal data sets, recording the local and global dynamics of metapopulations. In this paper, we analyse the dynamics of measles meta-populations in a large spatiotemporal case notification data set, collected during the pre-vaccination era in England and Wales. Specifically, we use generalized linear statistical models to quantify the relative importance of local influences (birth rate and population size) and regional coupling on local epidemic dynamics. Apart from the proportional effect of local population size on case totals, the models indicate patterns of local and regional dynamic influences which depend on the current state of epidemics. Birth rate and geographic coupling are not associated with the size of major epidemics. By contrast, minor epidemics--and especially the incidence of local extinction of infection--are influenced both by birth rate and geographical coupling. Birth rate at a lag of four years provides the best fit, reflecting the delayed recruitment of susceptibles to school cohorts. A hierarchical index of spatial coupling to large centres provides the best spatial model. The model also indicates that minor epidemics and extinction patterns are more strongly influenced by this regional effect than the local impact of birth rate.

Disease Outbreaks↗

Synchronizing spatiotemporal chaos.

We show analytically and numerically that a pair of uni-directionally coupled spatially extended systems can synchronize. For the case of partial differential equations the synchronization can be achieved by applying the scalar driving signals only at finite number of space points. Our approach is very general and can be useful for practical applications since the synchronization is achieved via feeding in the response system only the information from certain (discrete) spatial locations of the drive system. We also stress some open problems in the field of synchronization of spatiotemporal chaos. (c) 1997 American Institute of Physics.

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