8.6 Mathematical models of hippocampal spatial memory  (Page 12/13)

In these plots, we impose the same upper weight bound that we use for STDP, leading to a similar stabilization of place field firing. The removal of this limit will allow for the unbounded increase in synaptic weight, as depicted in [link] . The problem of unbounded weight changes still remains when implementing CaDP alone. However, CaDP provides a more sophisticated, biologically accurate method by which the synaptic weight changes can occur. Additionally, we can attempt to curb the backward shift by using more realistic mechanisms, such as metaplasticity, which we explore below.

Applying metaplasticity to cadp

Now that we have demonstrated the ability of CaDP to replicate the results produced by STDP, we remove the weight bound and attempt to use metaplasticity to stabilize the final synaptic weights and place field distributions. Here we show the effect of metaplasticity on the synaptic weights over the course of the simulation.

We see that the weights stabilize at a magnitude of around 8-9, showing that metaplasticity can stabilize the final synaptic weights without implementing an upper weight bound. As depicted in [link] , an increased rate of metaplasticity causes slower potentiation/depression of weights. Note that metaplasticity only limits potentiation of weights: for depressed weights, a lower bound of zero must still be applied to avoid negative weights. The weights reach equilibrium values once the firing rate has reached a level where any increase in weight would cause an increase in firing rate that would cause the removal of NMDA receptors to outpace the insertion rate, decreasing the available NMDARs and halting any additional calcium influx and synaptic weight change. These fluctuations in NMDA receptor availability are depicted in the NMDAR conductance plot in [link] .

Note that the NMDAR conductance decreases during the periods of input to the postsynaptic cell. The decrease in NMDAR conductance slightly decreases the amount of calcium influx, limiting the potentiation/depression of weights. We witness a sharper decline in conductance upon the overlap of place fields and the increased firing rates. Once the cells fire at a rate fast enough to equal or outpace the reinsertion of NMDARs, the conductance stabilizes, allowing for a stabilization of synaptic weights.