8.6 Mathematical models of hippocampal spatial memory  (Page 10/13)

Experimental setup revisited

We must first revisit the experimental setup and simulation methods that we use to compare the two plasticity models. We have a rat run clockwise around a circular track. In our models, we vary the number of simulated laps from 20-30. Each of the 120 place cells used to model the ring have been evenly spaced along the track, numbered in a clockwise fashion, each with three degrees of external input. We set the duration of external stimulus for each place cell at 100 ms per lap. When the rat is within a cell's place field, the cell receives external input at a uniform rate of 50 Hz throughout (it receives synaptic input every 20 ms). The magnitude of external input, which we denote $w_{inp}$ , has a set, nonplastic value of 10. This synaptic weight is large enough to ensure cell firing whenever external input is available. Within the 120 cell ring contains bidirectional connections to neighboring cells, as previously depicted in [link] in Chapter 2. Each of these connections is plastic. We set each of these connections to an initial weight $w_{init}$ = 0.5.

Stdp dynamics

Using the parameters we defined in the previous chapters, we run the simulation and track the synaptic weights between cells 1 and 2 on the ring over each lap. A plot of this data is given in [link] .

We note that the connection from cell 1 to 2 increases in weight each lap and the reverse connection decreases each lap. This occurs because of the clockwise connection's reinforcement by the order of external input: since the rat travels through cell 1's firing field right before cell 2's, the STDP rule favors the strengthening the connection from 1 to 2 and the weakening of the connection from 2 to 1. The weights appear to change in an approximately uniform stepwise fashion each lap until they reach their extrema set by the imposed weight bounds.

As the backward shift of hippocampal place fields is of primary importance to us, we track the firing locations of the place cells during the simulation. We denote the rat's location by its angular position along the track, setting zero degrees to the position where cell 1 first receives external stimulus. We monitor the degree on the track at which the cell first fires during each lap, which we call its firing degree, over the course of the simulation. We plot cell 2's firing degree in [link] below.

The decrease in the firing degree of the cell is a result of earlier firing positions along the track and indicative of the backward shift of hippocampal place fields. The earlier firing positions are a result of the strengthening of synaptic weights: stronger weights allow for a greater increase in conductance upon presynaptic firing, allowing for faster depolarization of the postsynaptic cell and earlier firing, resulting in the backward shift.

The second point of interest in the simulation lies in the stabilization of the place fields. We notice a stabilization of place fields which coincides with the synaptic weights reaching their upper bounds. This implies that we do not achieve place field stability without applying an upper weight bound when using STDP, detracting from the feasibility of STDP as a standalone mechanism of synaptic plasticity.