Synchronization properties of fully connected networks of identical oscillatory neurons are studied, assuming purely excitatory interactions. We analyze their dependence on the time course of the synaptic interaction and on the response of the neurons to small depolarizations. Two types of responses are distinguished. In the first type, neurons always respond to small depolarization by advancing the next spike. In the second type, an excitatory postsynaptic potential (EPSP) received after the refractory period delays the firing of the next spike, while an EPSP received at a later time advances the firing. For these two types of responses we derive general conditions under which excitation destabilizes in-phase synchrony. We show that excitation is generally desynchronizing for neurons with a response of type I but can be synchronizing for responses of type II when the synaptic interactions are fast. These results are illustrated on three models of neurons: the Lapicque integrate-and-fire model, the model of Connor et al., and the Hodgkin-Huxley model. The latter exhibits a type II response, at variance with the first two models, that have type I responses. We then examine the consequences of these results for large networks, focusing on the states of partial coherence that emerge. Finally, we study the Lapicque model and the model of Connor et al. at large coupling and show that excitation can be desynchronizing even beyond the weak coupling regime.

We consider a network of globally coupled phase oscillators. The interaction between any two of them is derived from a simple model of weakly coupled biological neurons and is a periodic function of the phase difference with two Fourier components. The collective dynamics of this network is studied with emphasis on the existence and the stability of clustering states. Depending on a control parameter, three typical types of dynamics can be observed at large time: a fully synchronized state of the network (one-cluster state), a totally incoherent state, and a pair of two-cluster states connected by heteroclinic orbits. This last regime is particularly sensitive to noise. Indeed, adding a small noise gives rise, in large networks, to a slow periodic oscillation between the two two-cluster states. The frequency of this oscillation is proportional to the logarithm of the noise intensity. These switching states should occur frequently in networks of globally coupled oscillators.

PACS. 87.10 -General, theoretical, and mathematical biophysics (inc. logic of biosystems, quantum biology and relevant aspects of thermodynamics, information theory, cybernetics, and bionics). PACS. 05.45 -Theory and models of chaotic systems.

Multiphase averaging for classieal systems : with applications to adiabatic theorems I P. Lochak, C. Meunier : translated by H.S. Dumas. p. cm.-(Applied mathematical sciences : v. 72) Bibliography: p.

It is shown that very small time steps are required to reproduce correctly the synchronization properties of large networks of integrate-and-fire neurons when the differential system describing their dynamics is integrated with the standard Euler or second-order Runge-Kutta algorithms. The reason for that behavior is analyzed, and a simple improvement of these algorithms is proposed.

We explain the mechanism that elicits the mixed mode oscillations (MMOs) and the subprimary firing range that we recently discovered in mouse spinal motoneurons. In this firing regime, high-frequency subthreshold oscillations appear a few millivolts below the spike voltage threshold and precede the firing of a full blown spike. By combining intracellular recordings in vivo (including dynamic clamp experiments) in mouse spinal motoneurons and modeling, we show that the subthreshold oscillations are due to the spike currents and that MMOs appear each time the membrane is in a low excitability state. Slow kinetic processes largely contribute to this low excitability. The clockwise hysteresis in the I-F relationship, frequently observed in mouse motoneurons, is mainly due to a substantial slow inactivation of the sodium current. As a consequence, less sodium current is available for spiking. This explains why a large subprimary range with numerous oscillations is present in motoneurons displaying a clockwise hysteresis. In motoneurons whose I-F curve exhibits a counterclockwise hysteresis, it is likely that the slow inactivation operates on a shorter time scale and is substantially reduced by the de-inactivating effect of the afterhyperpolarization (AHP) current, thus resulting in a more excitable state. This accounts for the short subprimary firing range with only a few MMOs seen in these motoneurons. Our study reveals a new role for the AHP current that sets the membrane excitability level by counteracting the slow inactivation of the sodium current and allows or precludes the appearance of MMOs.

The emergence of synchrony in the activity of large, heterogeneous networks of spiking neurons is investigated. We define the robustness of synchrony by the critical disorder at which the asynchronous state becomes linearly unstable. We show that at low firing rates, synchrony is more robust in excitatory networks than in inhibitory networks, but excitatory networks cannot display any synchrony when the average firing rate becomes too high. We introduce a new regime where all inputs, external and internal, are strong and have opposite effects that cancel each other when averaged. In this regime, the robustness of synchrony is strongly enhanced, and robust synchrony can be achieved at a high firing rate in inhibitory networks. On the other hand, in excitatory networks, synchrony remains limited in frequency due to the intrinsic instability of strong recurrent excitation.

Why do motoneurons possess two persistent inward currents (PICs), a fast sodium current and a slow calcium current? To answer this question, we replaced the natural PICs with dynamic clamp-imposed artificial PICs at the soma of spinal motoneurons of anesthetized cats. We investigated how PICs with different kinetics (1-100 ms) amplify proprioceptive inputs. We showed that their action depends on the presence or absence of a resonance created by the I h current. In resonant motoneurons, a fast PIC enhances the resonance and amplifies the dynamic component of Ia inputs elicited by ramp-and-hold muscle stretches. This facilitates the recruitment of these motoneurons, which likely innervate fast contracting motor units developing large forces, e.g., to restore balance or produce ballistic movements. In nonresonant motoneurons, in contrast, a fast PIC easily triggers plateau potentials, which leads to a dramatic amplification of the static component of Ia inputs. This likely facilitates the recruitment of these motoneurons, innervating mostly slowly contracting and fatigue-resistant motor units, during postural activities. Finally, a slow PIC may switch a resonant motoneuron to nonresonant by counterbalancing I h , thus changing the action of the fast PIC. A modeling study shows that I h needs to be located on the dendrites to create the resonance, and it predicts that dendritic PICs amplify synaptic input in the same manner as somatic PICs.