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Biomedical subjects

K Pakdaman

Publications and source records attributed to K Pakdaman.

34 records · Page 2Linked to original sources
PubMed1999

Response of coupled noisy excitable systems to weak stimulation.

It is known that coupling can enhance the response of noisy bistable devices to weak periodic modulation. This work examines whether a similar phenomenon occurs in the active rotator model for excitable systems. We study the dynamics of assemblies of weakly periodically modulated active rotators. The addition of noise to these brings about a number of behaviors that have no counterpart in networks of bistable systems. The analysis of the dynamics of the solution of the Fokker-Planck equation of active rotator networks shows that these new behaviors are similar to generic responses of periodically forced autonomous oscillators. This is because noise alone, in the absence of other inputs, can regularize the dynamics of single active rotators through coherence resonance, and lead to regular synchronous activity at the level of networks. We argue that similar phenomena take place in a broad class of excitable systems.

Acoustic Stimulation↗
PubMed1999

Rate coding in a chain of pulse-coupled oscillators.

The input-output relation of a chain of pulse-coupled oscillators is examined. The oscillators capture the essential aspect of the dynamics of pacemaker neurons. Inputs consist of pacemaker, and noisy trains impinging upon the first unit in the chain. The response of the chain is defined as the spike train emitted by the last unit. We observe two important phenomena in the response of the chain for a given input train, whether pacemaker or noisy. First, the mean output rate of the chain is equal to the mean input rate in the range of input rate in which one input pulse corresponds to one output spike without phase locking (1:1 alternation). Second, for the same input range, the output interspike intervals tend to the average of the input interpulse intervals in a long chain of oscillators. This behavior contrasts with the fact that the response of a single unit depends on both input rate and pattern. We show that the response of the chain is reproduced by the phase transition curve which represents the phase shift due to a single isolated pulse stimulus. This analysis reveals that the averaging of the output interspike intervals is due to the geometrical aspect of the phase transition curve. This geometrical aspect causes the dependence of the response of a single unit on input pattern.

Biological Clocks↗
PubMed1999

Metastability for delayed differential equations.

In systems at phase transitions, two phases of the same substance may coexist for a long time before one of them dominates. We show that a similar phenomenon occurs in systems with delayed feedback, where short-term stable oscillatory patterns can also have very long lifetimes before vanishing into constant or periodic steady states.

Journal Article↗
PubMed1999

Response of an ensemble of noisy neuron models to a single input.

Spike timing precision in response to a subthreshold stimulation can be enhanced by noise in ensembles of neurons [X. Pei, L. Wilkens, and F. Moss, Phys. Rev. Lett. 77, 4679 (1996)]. We elucidate the mechanism underlying this phenomenon by computing the membrane potential distributions of ensembles of Hodgkin-Huxley neuron models. For small noise amplitudes, the membrane potential distribution takes on a Gaussian form centered on the resting potential, while for large fluctuations, there is a significant spread to lower potentials. These two regimes are separated by a relatively narrow band where the distributions transit rapidly from the Gaussian-like shapes to the spread ones. We argue that the optimal noise that maximizes the spike timing precision is situated close to this boundary.

Action Potentials↗
PubMed1999

Mean discharge frequency locking in the response of a noisy neuron model to subthreshold periodic stimulation.

Leaky integrate-and-fire neuron models display stochastic resonance-like behavior when stimulated by subthreshold periodic signal and noise. Previous works have shown that matching between the time scales of the noise induced discharges and the modulation period can account for this phenomenon at low modulation amplitudes, but not large subthreshold modulation amplitude. In order to examine the discharge patterns of the model in this regime, we introduce a method for the computation of the power spectral density of the discharge train. Using this method, we clarify the role of the distribution of the input phase at discharge times. Finally, we argue that for large subthreshold inputs, mean discharge frequency locking accounts for the enhanced response.

Animals↗
PubMed1998

Reduction of a model for an Onchidium pacemaker neuron.

The eight-variable model for the giant neuron localized in the esophageal ganglia of the marine pulmonate mollusk Onchidium verruculatum is reduced to four- and-three-dimensional systems by regrouping variables with similar time scales. These reduced models replicate the complex behavior including beating, periodic bursting and aperiodic bursting displayed by the original full model when the parameter Iext representing the intensity of the constant DC current stimulation is varied across a wide range. The complex behavior of the full model arises from the interaction of fast and slow dynamics, and depends on the time scale Cs of the slow dynamics. The four-variable reduced model is constructed independently from the parameter Cs so that it reproduces the two-dimensional bifurcation structure of the full model for the two parameters Iext and Cs. The three-variable reduced model is derived for a specific value of Cs. The parameters of this model are tuned so that its one-parameter bifurcation diagram for Iext closely matches that of the full model. Correspondence between bifurcation structures ensures that both reduced models reproduce the various discharge patterns of the full model. Similarity between the full and reduced models is also confirmed by comparing mean firing frequencies and membrane potential waveforms in various regimes. The reduction exposes the factors essential for reproducing the dynamics of the full model; indeed, it shows that the eight variables representing the membrane potential and seven gating variables of six ionic currents in the full model account, in fact, for three basic processes responsible for excitability, post-discharge refractoriness and slow membrane modulation.

Animals↗
PubMed1998

Effect of delay on the boundary of the basin of attraction in a system of two neurons.

The behavior of neural networks may be influenced by transmission delays and many studies have derived constraints on parameters such as connection weights and output functions which ensure that the asymptotic dynamics of a network with delay remains similar to that of the corresponding system without delay. However, even when the delay does not affect the asymptotic behavior of the system, it may influence other important features in the system's dynamics such as the boundary of the basin of attraction of the stable equilibria. In order to better understand such effects, we study the dynamics of a system constituted by two neurons interconnected through delayed excitatory connections. We show that the system with delay has exactly the same stable equilibrium points as the associated system without delay, and that, in both the network with delay and the corresponding one without delay, most trajectories converge to these stable equilibria. Thus, the asymptotic behavior of the network with delay and that of the corresponding system without delay are similar. We obtain a theoretical characterization of the boundary separating the basins of attraction of two stable equilibria, which enables us to estimate the boundary. Our numerical investigations show that, even in this simple system, the boundary separting the basins of attraction of two stable equilibrium points depends on the value of the delays. The extension of these results to networks with an arbritrary number of units is discussed.

Journal Article↗
PubMed1997

Effect of delay on the boundary of the basin of attraction in a self-excited single graded-response neuron.

Little attention has been paid in the past to the effects of interunit transmission delays (representing axonal and synaptic delays) on the boundary of the basin of attraction of stable equilibrium points in neural networks. As a first step toward a better understanding of the influence of delay, we study the dynamics of a single graded-response neuron with a delayed excitatory self-connection. The behavior of this system is representative of that of a family of networks composed of graded-response neurons in which most trajectories converge to stable equilibrium points for any delay value. It is shown that changing the delay modifies the "location" of the boundary of the basin of attraction of the stable equilibrium points without affecting the stability of the equilibria. The dynamics of trajectories on the boundary are also delay dependent and influence the transient regime of trajectories within the adjacent basins. Our results suggest that when dealing with networks with delay, it is important to study not only the effect of the delay on the asymptotic convergence of the system but also on the boundary of the basins of attraction of the equilibria.

Animals↗
PubMed1997

Single neuron model with recurrent excitation: response to slow periodic modulation.

The influence of a recurrent excitatory connection on the response of three neuron models to slow periodic modulation is analyzed. The models are the graded response model and the threshold model with and without adaptation. Lissajous displays of the system's output (discharge rate) as a function of the instantaneous input value show hysteresis in all three models. Hence, the outputs are different depending on whether the input is increasing or decreasing. Recurrent excitation increases the width of the hysteresis with (i) the frequency of the periodic modulation, (ii) the transmission delay of the recurrent connection, and (iii) the connection strength.

Action Potentials↗
PubMed1997

Complex responses of living neurons to pacemaker inhibition: a comparison of dynamical models.

A neuron can respond to periodic inhibitory input with a variety of complex behaviors, periodic and aperiodic. We present a succession of models to test hypotheses for mechanisms underlying complex behavior generation. Model comparison using non-linear dynamics techniques indicates that long-duration IPSP aftereffects and spiking behavior are necessary for most of the basic response properties, though not sufficient for some of their more subtle aspects.

Action Potentials↗
PubMed1997

XNBC: a simulation tool. Application to the study of neural coding using hybrid networks.

XNBC is a software package for simulating biological neural networks. Two neuron models are available, a leaky integrator model and an ion-conductance model. Inputs to the simulated neurons can be provided by experimental data stored in files, allowing the creation of 'hybrid' networks. Graphic tools are used to describe the modeled neurons as well as the network. Neuron and network parameters can be modified during the simulation, to mimic electrical stimulations and drugs action. The temporal evolution of the network and of selected neurons can be visualized. A point process, frequency or dynamic analysis of the simulator output can be performed. The successive stages of the creation of a hybrid network are explained.

Computer Graphics↗
PubMedDate not supplied

Computational model of the jamming avoidance response in the electric fish Gymnotus carapo.

The unperturbed electric organ discharges of Gymnotus carapo fish are highly periodic with interpulse intervals around 40 ms. The 'jamming avoidance response' happens when fish interact and is a transitory interval shortening in the fish with the faster discharge that decreases the likelihood that pulses from it and the other fish will coincide. Our model's basic components match certain experimentally demonstrated facts. First, recurrence equations reproduce the periodic unperturbed discharges. Secondly, when an isolated pulse arrives, the two intervals following that with the pulse are shortened by amounts that decrease up to a minimum and then increase. Simulations demonstrated that this model reproduces satisfactorily the jamming avoidance response. Two additional conditions were demonstrably necessary: (i) one was that every pulse arrive within the hot cophase window (and not elsewhere); (ii) the other condition was that, along successive pulses, the respective cophases decrease by moderate amounts. In short, we conclude that the fish's jamming avoidance response can involve the simple computational rules implied by the proposed equations.

Animals↗
PubMedDate not supplied

A discrete map for the dynamics of recurrent excitatory neural networks in the presence of noise.

We investigate the effect of the neuron characteristics on the behavior of a recurrent excitatory neural network model. First, we present the different types of dynamics obtained with simulations of a network of coupled excitatory spike-response neuron models placed under the influence of noise. Then, we derive a discrete map describing the dynamics of large fully connected networks. By studying the bifurcation structure of this map, we can determine for which ranges of the neuron model parameters the network will display collective oscillations or other types of dynamics.

Action Potentials↗
PubMedDate not supplied

Analysis of the response of a pacemaker neuron model to transient inputs.

The response of a pacemaker neuron model to a train of transient inhibitory impulsive perturbations is examined. The model reproduces the heterogeneous discharge forms and abrupt switchings displayed by the crayfish slowly adapting stretch receptor organ (Segundo et al., 1994, Neuroscience 62(2), pp. 459-480). The non-monotonous aspect of the instantaneous firing rate of the model reflects the fact that in some regimes input and output rates are both increasing, despite the inhibitory effect of the former. We determine how such paradoxical acceleration takes place by analyzing the response of the model using its phase transition curve. We show that paradoxical acceleration results from the fact that the phase transition curve exhibits a large slowly increasing, almost linear section similar to that of living preparations.

Biological Clocks↗
PubMedDate not supplied

An analysis of the reliability phenomenon in the FitzHugh-Nagumo model.

The reliability of single neurons on realistic stimuli has been experimentally confirmed in a wide variety of animal preparations. We present a theoretical study of the reliability phenomenon in the FitzHugh-Nagumo model on white Gaussian stimulation. The analysis of the model's dynamics is performed in three regimes-the excitable, bistable, and oscillatory ones. We use tools from the random dynamical systems theory, such as the pullbacks and the estimation of the Lyapunov exponents and rotation number. The results show that for most stimulus intensities, trajectories converge to a single stochastic equilibrium point, and the leading Lyapunov exponent is negative. Consequently, in these regimes the discharge times are reliable in the sense that repeated presentation of the same aperiodic input segment evokes similar firing times after some transient time. Surprisingly, for a certain range of stimulus intensities, unreliable firing is observed due to the onset of stochastic chaos, as indicated by the estimated positive leading Lyapunov exponents. For this range of stimulus intensities, stochastic chaos occurs in the bistable regime and also expands in adjacent parts of the excitable and oscillating regimes. The obtained results are valuable in the explanation of experimental observations concerning the reliability of neurons stimulated with broad-band Gaussian inputs. They reveal two distinct neuronal response types. In the regime where the first Lyapunov has negative values, such inputs eventually lead neurons to reliable firing, and this suggests that any observed variance of firing times in reliability experiments is mainly due to internal noise. In the regime with positive Lyapunov exponents, the source of unreliable firing is stochastic chaos, a novel phenomenon in the reliability literature, whose origin and function need further investigation.

Computer Simulation↗