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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.

Unbounded CaDP. Without imposing any methods to curb potentiation, synaptic weights will continue to increase without limit.

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.

Metaplasticity with CaDP stabilizes synaptic weights. Here we depict the stabilization of synaptic weights with the scaling of a = 1 (left) and a = 4 (right).

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] .

NMDAR conductance in Metaplasticity. Metaplasticity involves slow insertion and removal of NMDAR receptors. Increased firing causes removal of NMDAR receptors in lap 20, reaching a new equilibrium conductance.

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.

Unbounded Backward Shift. Plot depicts the number of spikes for cell 60 on each degree of the track during each lap. Note consistent firing within place field until lap 20, when place field expands to cover the entire track.

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Source:  OpenStax, The art of the pfug. OpenStax CNX. Jun 05, 2013 Download for free at http://cnx.org/content/col10523/1.34
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