Defining time in a minimal hippocampal CA3 model by matching time-span of associative synaptic modification and input pattern duration

This paper quantifies the time shifting of neuronal codes in a sparse, randomly connected neural network model of hippocampal region CA3. As this network is trained to learn a sequence, the neurons that encode portions of this sequence characteristically fire earlier and earlier over the course of training. Here we systematically investigate the effects of the N-methyl-D-aspartate (NMDA)-governed time-span of synaptic associativity on this shifting process and how this time-span interacts with the duration of each successive external input. The results show that there is an interaction between this synaptic time-span and externally applied pattern duration such that the early shifting effect approaches a maximum asymptotically and that this maximum is very nearly produced when the e-fold decay time-span of synaptic associativity is matched to the duration of individual input patterns. The performance of this model as a sequence prediction device varies with the time-span selected. If too long a time-span is used, overly strong attractors evolve and destroy the sequence prediction ability of the network. Local context cell firing-the learned repetitive firing of neurons that code for a specific subsequence - also varies in duration with these two parameters. Importantly, if the associative time-span is matched to the longevity of each individual external pattern and if time-shifting and local context length are normalized by this same external pattern duration, then time-shifting and local context length are constant across simulations with different parameters. This constancy supports the idea that real time can be mapped into a network of McCulloch-Pitts neurons that lack a time scale for excitation and resetting.