Resumo

Objectives: Two identical dynamical systems coupled unidirectionally in a master-slave configuration can exhibit anticipated synchronization (AS) if the slave also receives a delayed negative self-feedback. A recent series of papers have extended these results to a setup in which the membrane potentials of the FitzHugh-Nagumo or Hodgkin-Huxley model neurons are directly coupled with a delay term. The fact that AS is verified also in this (biophysically nonrealistic) scenario opens new possibilities in neuronal modeling, specially regarding the bearing of collective dynamical phenomena on plasticity. The last decades have witnessed a growing literature on spike-timing dependent plasticity (STDP), which acounts for changes in the synaptic weight depending on the relative timing between the spikes of the pre- and post-synaptic neurons. Experimental data strongly suggest that if the pre-synaptic neuron fires before (after) the post-synaptic neuron, the synapse between them will be strenghtened (weakened). If AS leads to an inversion in the timing of the pre- and post-synaptic spikes, then by appropriately controlling this effect one could dynamically toggle between synaptic strengthening and weakening (potentially modelling large-scale ascending feedback modulation from reward systems). Here we investigate whether AS can occur in a biophysically plausible model. Methods: By using a fourth-order Runge-Kutta algorithm, we have numerically integrated the equations of three coupled Hodgkin-Huxley neurons in the master-slave-interneuron-slave configuration, with two excitatory synapses (from master to slave and from slave to interneuron) and one inhibitory synapse (from interneuron to slave). Synaptic gating variables obey first-order dynamics, with standard parameters describing AMPA and GABA_A receptors for excitatory and inhibitory couplings, respectively. The time-delayed negative feedback is therefore acounted for by chemical inhibition which impinges on the slave neuron some time after it has spiked, simply because synapses have characteristic time scales. Results: We have observed that if neurons are in the excitable regime, then AS cannot occur. This can be easily understood: before a pre-synaptic neuron spikes, no coupling exists with a post-synaptic neuron, because the synapse will not be activated. Therefore the slave spikes only after the master has spiked. If neurons are individually tuned to a periodic regime via application of a constant current, however, the slave neuron can spike right before the master spikes, owing to the interplay between the synaptic couplings. In this regime (which we call pseudo-anticipated synchronization, since the system is periodic), we have observed that the time interval between the slave and the master spikes ("anticipation" time) increases with the maximal conductance g_is of the inhibitory synapse. The larger the applied current (thus with higher firing frequency), the smaller the range of values of g_is in which AS occurs, which suggests that the mechanism is more easily implemented near the onset of sustained firing. Conclusions: We have verified that a biologically plausible model can exhibit an attractor in phase space where (pseudo-)anticipated synchronization is stable. The transition from the anticipated regime to the usual one (in which the master spikes before the slave) is smooth.