Pseudo-anticipated Synchronization in a Biologically Plausible Model of a Ubiquitous Neuronal Motif

In a broad region in parameter space (K, τ ) the slave system can anticipate the master system: y(t) = x(t+ τ) [1, 2]. A recent series of papers have extended these results to a setup in which the dynamical system is nonautonomous (e.g. fed by noise) and f models an excitable neuron (FitzHugh-Nagumo or Hodgkin-Huxley model) [3, 4]. The fact that anticipated synchronization is verified also in this 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 the enhancement or diminution of synaptic weight [respectively long term potentiation (LTP) and long term depression (LTD)] depending on the relative timing between the spikes of the preand 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) [5]. The idea is that if anticipated synchronization leads to an inversion in the timing of the preand post-synaptic spikes, then by appropriately controlling this effect one could dynamically toggle between synaptic strengthening and weakening. This could be potentially linked with modelling of large-scale ascending feedback modulation from reward systems. Here we investigate whether anticipated synchronization can occur in biophysically plausible models. Differently from Eqs. 1, in chemical synapses (where STDP takes place) a post-synaptic neuron is not coupled directly to the membrane potential of a pre-synaptic neuron, but rather receives indirect information about it via neurotransmitters (this is precisely the role of the synapse!). Similarly, a negative feedback loop via an inhibitory interneuron can play the role of Figure 1 – Example of a neuronal motif in the spinal cord circuitry with a master neuron (the muscle sensor), a slave neuron (the motor neuron) and an interneuron (the Renshaw cell).