8.6 Mathematical models of hippocampal spatial memory  (Page 9/13)

The behavior of metaplasticity is aimed to depress the amount of available NMDA receptors when the cell voltage is at consistently high levels. That is, upon increased firing rates, less NMDA receptors would be available for calcium influx, resulting in less synaptic weight change to the point where the synaptic weights stabilize. As such, we expect that the implementation of metaplasticity should allow us to limit the increase in synaptic weights without having to implement a fixed upper weight bound. Note that metaplasticity does not modify the characteristics of LTD under normal firing rates, meaning that we must still implement a fixed lower weight bound in our plasticity model.

Spike-time dependence of cadp

In order to analyze the spike-time dependence of the CaDP model, we implement a regime of paired stimulation in which we induce cell firing at prespecified times and monitor the synaptic weights. We use 50 pre-post spike pairs stimulated at a constant rate of 1 Hz.

When plotting synaptic weight against the difference in spike times, we find that the CaDP curve emulates the STDP curve: we observe LTP when presynaptic firing precedes postsynaptic firing ( $\Delta t>0$ , where $\Delta t=t_{post}-t_{pre}$ ) and LTD when postsynaptic firing precedes presynaptic firing ( $\Delta t\le 0$ ). However, with the CaDP model, we also get a second region of LTD when the spike interval becomes too large (see [link] ). The existence of a second depression window has been highly debated and supported by some recent research [link] , [link] .

Calcium dependent plasticity involves a higher order of complexity in its dynamics and synaptic weight modifications in comparison to STDP. When implementing CaDP alongside the Integrate and Fire model, there appear to be redundancies: even though they may be related, we separate synaptic voltage from membrane voltage, NMDAR conductance from synaptic conductance, etc. It still incorporates presynaptic and postsynaptic spike times via the use of the $f$ function and BPAP, respectively. While we do not discuss it in depth, it also incorporates some aspects of rate-dependent plasticity: higher spiking frequencies result in more potentiation of weights, whereas in STDP, the frequency of spike-pairs is disregarded. We will discuss more of the similarities and differences between the two plasticity models in the next chapter.

Comparison: stdp vs. cadp

Having introduced both Spike-time Dependent Plasticity and Calcium Dependent Plasticity, we now compare the two models in their ability to explain the phenomena associated with spatial memory. We focus on two of these phenomena: (1) the backward shift of Hippocampal place fields and (2) the final stabilization of place fields.