Temporal dynamics of rate-based synaptic plasticity rules in a stochastic model of spike-timing-dependent plasticity

In a recently proposed, stochastic model of spike-timing-dependent plasticity, we derived general expressions for the expected change in synaptic strength, Delta S-n, induced by a typical sequence of precisely n spikes. We found that the rules Delta S-n, n >= 3, exhibit regions of parameter space in which stable, competitive interactions between afferents are present, leading to the activity-dependent segregation of afferents on their targets. The rules Delta S-n, however, allow an indefinite period of time to elapse for the occurrence of precisely n spikes, while most measurements of changes in synaptic strength are conducted over definite periods of time during which a potentially unknown number of spikes may occur. Here, therefore, we derive an expression, Delta S(t), for the expected change in synaptic strength of a synapse experiencing an average sequence of spikes of typical length occurring during a fixed period of time, t. We find that the resulting synaptic plasticity rule Delta S(t) exhibits a number of remarkable properties. It is an entirely self-stabilizing learning rule in all regions of parameter space. Further, its parameter space is carved up into three distinct, contiguous regions in which the exhibited synaptic interactions undergo different transitions as the time t is increased. In one region, the synaptic dynamics change from noncompetitive to competitive to entirely depressing. In a second region, the dynamics change from noncompetitive to competitive without the second transition to entirely depressing dynamics. In a third region, the dynamics are always noncompetitive. The locations of these regions are not fixed in parameter space but may be modified by changing the mean presynaptic firing rates. Thus, neurons may be moved among these three different regions and so exhibit different sets of synaptic dynamics depending on their mean firing rates.