Abstract
When entering a synapse, presynaptic pulse trains are filtered according to the recent pulse history at the synapse and also with respect to their own pulse time course. Various behavioral models have tried to reproduce these complex filtering properties. In particular, the quantal model of neurotransmitter release has been shown to be highly selective for particular presynaptic pulse patterns. However, since the original, pulse-iterative quantal model does not lend itself to mathematical analysis, investigations have only been carried out via simulations. In contrast, we derive a comprehensive explicit expression for the quantal model. We show the correlation between the parameters of this explicit expression and the preferred spike train pattern of the synapse. In particular, our analysis of the transmission of modulated pulse trains across a dynamic synapse links the original parameters of the quantal model to the transmission efficacy of two major spiking regimes, that is, bursting and constant-rate ones.
Highlights
The main computational function of artificial neural networks has traditionally been modeled as an adjustment of the coupling weight between neurons. This coupling weight is provided by the synapse, where an incoming pulse causes a release of neurotransmitters, which in turn generate a postsynaptic current (PSC) that charges the postsynaptic neuron membrane [1]
Since the optimal spike trains of [10] differ from our modulated pulse rate assumption, we have to validate that the sum over the product uR, that is, the PSC efficacy criterion, has the same quantitative and qualitative behavior for the modulated rate as for the optimized spike train
An initial validation can be done by extracting a sample spike train for a single parameter set from [10], applying a jitter to account for extraction errors, and comparing it to a modulated spike train which is parameterized to exhibit a similar burstiness
Summary
The main computational function of artificial neural networks has traditionally been modeled as an adjustment of the coupling weight between neurons. Dynamic synapses interact in a complex manner with another important component of neural information transmission, modulated pulse trains [7, 8], that is, spike trains characterized by regular shifts between high and low pulse rates [9]. This is especially interesting since biological synapses show very complex interdependences between their state variables and behavior [15, 16]; so an analytical expression of the biophysical model in [11] could be employed to identify the governing variables and mechanisms To derive this expression, we show that for regular pulse rates, the model by Markram et al can be expressed explicitly as an exponential decay function. We extend the optimality analysis of [10] to a wider parameter spectrum and give an explanation for the favored transmission of modulated spike trains in dynamic synapses
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