Time evolution of interhemispheric coupling in a model of focal neocortical epilepsy in mice.

Epilepsy is characterized by substantial network rearrangements leading to spontaneous seizures and little is known on how an epileptogenic focus impacts on neural activity in the contralateral hemisphere. Here, we used a model of unilateral epilepsy induced by injection of the synaptic blocker tetanus neurotoxin (TeNT) in the mouse primary visual cortex (V1). Local field potential (LFP) signals were simultaneously recorded from both hemispheres of each mouse in acute phase (peak of toxin action) and chronic condition (completion of TeNT effects). To characterize the neural electrical activities the corresponding LFP signals were analyzed with several methods of time series analysis. For the epileptic mice, the spectral analysis showed that TeNT determines a power redistribution among the different neurophysiological bands in both acute and chronic phases. Using linear and nonlinear interdependence measures in both time and frequency domains, it was found in the acute phase that TeNT injection promotes a reduction of the interhemispheric coupling for high frequencies (12-30 Hz) and small time lag (<20 ms), whereas an increase of the coupling is present for low frequencies (0.5-4 Hz) and long time lag (>40 ms). On the other hand, the chronic period is characterized by a partial or complete recovery of the interhemispheric interdependence level. Granger causality test and symbolic transfer entropy indicate a greater driving influence of the TeNT-injected side on activity in the contralateral hemisphere in the chronic phase. Lastly, based on experimental observations, we built a computational model of LFPs to investigate the role of the ipsilateral inhibition and exicitatory interhemispheric connections in the dampening of the interhemispheric coupling. The time evolution of the interhemispheric coupling in such a relevant model of epilepsy has been addressed here.

Existence of anticorrelations for local field potentials recorded from mice reared in standard condition and environmental enrichment.

In the present paper, we analyze local field potentials (LFPs) recorded from the secondary motor cortex (M2) and primary visual cortex (V1) of freely moving mice reared in environmental enrichment (EE) and standard condition (SC). We focus on the scaling properties of the signals by using an integrated approach combining three different techniques: the Higuchi method, detrended fluctuation analysis, and power spectrum. Each technique provides direct or indirect estimations of the Hurst exponent H and this prevents spurious identification of scaling properties in time-series analysis. It is well known that the power spectrum of an LFP signal scales as 1/f(ß) with ß>0. Our results indicate the existence of a particular power spectrum scaling law 1/f(ß) with ß<0 for low frequencies (f<4 Hz) for both SC and EE rearing conditions. This type of scaling behavior is associated to the presence of anticorrelation in the corresponding LFP signals. Moreover, since EE is an experimental protocol based on the enhancement of sensorimotor stimulation, we study the possible effects of EE on the scaling properties of secondary motor cortex (M2) and primary visual cortex (V1). Notably, the difference between Hurst's exponents in EE and SC for individual cortical regions (M2) and (V1) is not statistically significant. On the other hand, using the detrended cross-correlation coefficient, we find that EE significantly reduces the functional coupling between secondary motor cortex (M2) and visual cortex (V1).

P2X7 receptor-mediated calcium dynamics in HEK293 cells: experimental characterization and modelling approach.

The P2X7 receptor (P2X7R) induces ionotropic Ca²âº signalling in different cell types. It plays an important role in the immune response and in the nervous system. Here, the mechanisms underlying intracellular Ca²âº variations evoked by 3'-O-(4-benzoyl)benzoyl-ATP (BzATP), a potent agonist of the P2X7R, in transfected HEK293 cells, are investigated both experimentally and theoretically. We propose a minimal model of P2X7R that is capable of reproducing, qualitatively and quantitatively, the experimental data. This approach was also adopted for the P2X7R variant, which lacks the entire C-terminus tail (trP2X7R). Then we introduce a biophysical model describing the Ca²âº dynamics in HEK293. Our model gives an account of the ionotropic Ca²âº influx evoked by BzATP on the basis of the kinetics model of P2X7R. To explain the complex Ca²âº responses evoked by BzATP, the model predicted that an impairment in Ca²âº extrusion flux through the plasma membrane is a key factor for Ca²âº homeostasis in HEK293 cells.

Variable renewal rate and growth properties of cell populations in colon crypts.

A nonlinear mathematical model is used to investigate the time evolution of the cell populations in colon crypts (stem, semidifferentiated and fully differentiated cells). To mimic pathological alteration of the biochemical pathways leading to abnormal proliferative activity of the population of semidifferentiated cells their renewal rate is assumed to be dependent on the population size. Then, the effects of such perturbation on the population dynamics are investigated theoretically. Using both theoretical methods and numerical simulations it is shown that the increase in the renewal rate of semidifferentiated cells strongly impacts the dynamical behavior of the cell populations.

A minimal model for the respiratory sinus arrhythmia.

The cardiac and respiratory rhythms in humans are known to be coupled by several mechanisms. In particular, the first rhythm is deeply modulated by the second. In this report we propose a simple operational model for heart rate variability which, taking such modulation into account, reproduces the main features of some experimental sequences of RR intervals recorded from healthy subjects in the resting condition. Also, peer analysis of the model performance allows us to answer the question whether the observed behaviour should be ascribed to phase synchronisation of the heart beating to the respiratory rhythm. Lastly, the changes of the model activity brought about by changing its relevant parameters are analysed and discussed.

Gap junctions promote synchronous activities in a network of inhibitory interneurons.

By using a single compartment biophysical model of a fast spiking interneuron the synchronization properties of a pair of cells, coupled by electrical and inhibitory synapses, are investigated. The inhibitory and excitatory synaptic couplings are modeled in order to reproduce the experimental time course of the corresponding currents. It is shown that increasing the conductance value of the electrical synapses enhances the synchronization between the spike trains of the two cells. Moreover, increasing either the decay time constant of the inhibitory current or the firing frequency of the cells favours the emergence of synchronous discharges.

Delayed self-synchronization in homoclinic chaos.

The chaotic spike train of a homoclinic dynamical system is self-synchronized by applying a time-delayed correction proportional to the laser output intensity. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long-periodic orbits is possible. On these orbits, the dynamics appears chaotic over a finite time, but then it repeats with a recurrence time that is slightly longer than the delay time. The effect, called delayed self-synchronization, displays analogies with neurodynamic events that occur in the buildup of long-term memories.

Autonomous bursting in a homoclinic system.

The output of a dynamical system in a regime of homoclinic chaos transforms from a continuous train of irregularly spaced spikes to clusters of regularly spaced spikes with quiescent periods in between (bursting), provided a low frequency portion of the output is fed back. We provide experimental evidence of such an autonomous bursting by a CO2 laser with feedback. The phenomena here presented are extremely robust against noise and display qualitative analogies with bursting phenomena in neurons.

Mutual information detects a decreased interdependence between RR and SAP in orthostatic intolerance after microgravity condition.

Orthostatic intolerance is the most serious symptom of cardiovascular deconditioning induced by microgravity. However, the exact mechanisms underlying these alterations have not been completely clarified. Several methods for studying the time series of systolic arterial pressure and RR interval have been proposed both in the time and in the frequency domain. However, these methods did not produce definitive results. In fact heart rate and arterial pressure show a complex pattern of global variability which is likely due to non linear feedback which involves the autonomic nervous system and to "stochastic" influences. Aim of this study was to evaluate the degree of interdependence between the mechanisms responsible for the variability of SAP and RR signals in subjects exposed to head down (HD). This quantification was achieved by using Mutual Information (MI).

Synchronization of homoclinic chaos.

Homoclinic chaos is characterized by regular geometric orbits occurring at erratic times. Phase synchronization at the average repetition frequency is achieved by a tiny periodic modulation of a control parameter. An experiment has been carried on a CO(2) laser with feedback, set in a parameter range where homoclinic chaos occurs. Any offset of the modulation frequency from the average induces phase slips over long times. Perfect phase synchronization is recovered by slow changes of the modulation frequency based upon the sign and amplitude of the slip rate. Satellite synchronization regimes are also realized, with variable numbers of homoclinic spikes per period of the modulation.

Nonlinear activity of identified Lymnaea neurons.

Two long-lasting discharges of action potentials were recorded from a buccal cell of the pond snail, respectively, before and after superfusing the preparation with low-calcium solution. The corresponding sequences of interspike intervals were then analysed by the nonlinear prediction methods. The results yield evidence of a small but clear nonlinearity only in the second of analysed tachograms. This finding is evaluated and discussed.

Heart rate and blood pressure response to short-term head-down bed rest: a nonlinear approach.

Although it is well-known that prolonged exposure to microgravity environment such as in space travel results in derangements of orthostasis, recent evidence suggests that even short-term exposure may have similar effects and parallels such common examples as prolonged bed rest. Whereas spectral analysis of heart rate and systolic blood pressure have been unable to detect changes, we hypothesized that nonlinear indexes may be better able to uncover such perturbations. Eighteen healthy subjects were exposed to 4-hour head-down tilt, and of these, 4 exhibited fainting. Two nonlinear indexes, mutual information and recurrence quantification were used to analyze the data. Only recurrence quantification was able to detect a "decoupling" of heart rate and systolic blood pressure at rest using discriminant analysis (p < 0.05). These results suggest that orthostatic intolerance may be due to a decoupling of heart rate from systolic blood pressure reflexive activity occurring at rest.

Dynamics of the neural discharge in snail neurons.

Spike trains recorded under weak sinusoidal driving from central neurons of Lymnaea stagnalis appear quite irregular and envisage the possibility of an underlying chaotic process. Therefore, the sequences of interspike intervals are analyzed in the framework of non-linear dynamics. Since, for several reasons, these sequences are rather short, the analysis is performed by using methods of non-linear forecasting. To reject the null hypothesis that the original time series is a realization of a linear stochastic process with the same autocorrelation function, the results obtained on the original data are compared with those from surrogate data sets. Some 'non-linear' predictability occurs only in narrow regions of the space of stimulus parameters and the frequency of perturbation is critical in determining it. Moreover, it is shown that such behavior can be qualitatively mimicked by the FitzHugh-Nagumo model driven by a weak sinusoidal signal plus noise. It is argued that the narrowness of the non-linear predictability regions renders quite unlikely the detection of deterministic dynamics in the activity of these neurons.

Detection of nonlinearity in the healthy heart rhythm.

Sequences of interbeat intervals from two groups of subjects, 24 in relaxed and 10 in sleeping condition were analyzed by the nonlinear predictor method as well as by a method, proposed recently, able to directly estimate the time series nonlinearity. The nonlinear predictability of the R-R intervals is tested by using surrogate data. The results obtained with both methods show that nearly all the sequences exhibit a statistically meaningful degree of nonlinearity. This raises the question whether such nonlinearity encodes information about the physiological condition of the examined subjects.

Ring wave solutions of a n+1-dimensional Sine-Gordon model.

The dynamical properties of the ring wave solutions of the model psi(tt)- nabla (n) (2)psi+sin psi+ varepsilon sin (psi/2)+alphapsi(t)=0 (00, alpha=0 (or alpha>0) the return effect of the ring wave does not occur only for well defined values of varepsilon. It will be shown numerically that the dissipative perturbation alphapsi(t) (alpha>0) stabilizes both the velocity and the wave profile of the ring wave when the return effect does not occur. (c) 1997 American Institute of Physics.