8.6 Mathematical models of hippocampal spatial memory  (Page 11/13)

We also analyze multiplicative STDP as an improved variation of STDP. We display the forward and backward synaptic weights as a function of lap in [link] .

We observe an asymptotic trend of the weight changes in this regime as opposed to the stepwise form of weight changes in regular, additive STDP. We also depict the place field backward shift in [link] .

When using multiplicative STDP, we see a faster backward shift in earlier laps due to the faster initial increase in synaptic weight. This shift also slows down significantly in later laps due to the slowed increase in weights, leading to final place field stabilization. This trend appears to agree with the nature of the backward shift in experimental results [link] . While this is a slightly improved fit to experimental data as opposed to STDP, the weight bounds are directly incorporated into the weight modification equations, making it a better approximation of results than an explanation of the mechanisms behind synaptic plasticity.

Cadp dynamics

Having explained the advantages and disadvantages of STDP, we now look at CaDP and compare its simulation results with STDP. First, we will depict the changes in calcium concentrations in different synapses to better illustrate the mechanisms behind CaDP.

The plot above shows calcium changes in the forward connection from cell 1 to cell 2 and the two counterclockwise connections associated with cell 1. We observe that the clockwise synapse reaches a calcium level above the LTP threshold due to effective pre-post firing. We also notice that presynaptic firing without postsynaptic response results in LTD calcium levels. Also notice that the initial increase in calcium concentration from baseline levels results from the peak in the $f$ function as a result from presynaptic spiking, and the subsequent increases of calcium into the LTP region are a result from postsynaptic feedback from the back-propagating action potential. Furthermore, persistent postsynaptic cell firing following presynaptic stimulus causes a sustained LTP calcium concentration and allows for increased potentiation of synaptic weights.

The changes in calcium levels yield the following weight changes and backward shift over the simulation as depicted below in [link] .

These plots show that CaDP is able to reproduce the same weight changes and backward shift found in STDP. However, there are a couple of slight differences. The weight changes in STDP result only following the occurence of a postsynaptic spike. However, in CaDP, weights are constantly being changed as a function of calcium levels. Furthermore, we note that the depression of the backward connections occurs in an almost entirely different manner than in STDP: in STDP, LTD was an inherent part of the learning rule whenever a postsynaptic spike preceded a presynaptic spike. In CaDP, LTD results from the absence of or extended time between the postsynaptic spike following presynaptic stimulation. As such, the second LTD window is an essential consequence of the CaDP model in the depression of synaptic weights.