Computing the optimally fitted spike train for a synapse

Experimental data have shown that synapses are heterogeneous: different synapses respond with different sequences of amplitudes of postsynaptic responses to the same spike train. Neither the role of synaptic dynamics itself nor the role of the heterogeneity of synaptic dynamics for computations in neural circuits is well understood. We present in this article two computational methods that make it feasible to compute for a given synapse with known synaptic parameters the spike train that is optimally fitted to the synapse in a certain sense. With the help of these methods, one can compute, for example, the temporal pattern of a spike train (with a given number of spikes) that produces the largest sum of postsynaptic responses for a specific synapse. Several other applications are also discussed. To our surprise, we find that most of these optimally fitted spike trains match common firing patterns of specific types of neurons that are discussed in the literature. Hence, our analysis provides a possible functional explanation for the experimentally observed regularity in the combination of specific types of synapses with specific types of neurons in neural circuits.