Memory Maintenance in Synapses with Calcium-Based Plasticity in the Presence of Background Activity
Figure 4
Steady-state behaviour of a recurrent network with plastic synapses between excitatory neurons.
(A) Firing rate mean-field predictions compared with network simulation results. The mean-field theory predicted firing rate is higher (black line) than the actual firing rate of the excitatory neurons (green dots) in the recurrent network of 8000 exc. and 2000 inh. LIF neurons. Network simulation with fixed synapses yield a good match with the theory (blue dots). (B) Average synaptic weight prediction compared with asymptotic average synaptic weights in the network simulation. The observed average synaptic efficacy of excitatory to excitatory connections is smaller (mustard dots) than the theoretical prediction (black line). Even when using the asymptotic firing rate of the network in the calculations (green dots), the average synaptic efficacy is overestimated by the theory. (C) Mean and standard deviation of synaptic weights vs. firing rate for independent LIF neurons (magenta), networked LIF neurons (green) and LIF neurons in a network in which actual weights are held constant but we examine how their efficacy would have evolved in the presence of observed firing (blue dots). Asymptotic synaptic weights for LIF neurons underestimate the efficacy predicted by the theory (blue line). (D) Average synaptic weight vs. firing rate for independent LIFs with different reset potentials. The analytical prediction of the asymptotic synaptic weight based on Poisson firing is shown by the blue line (same as in C). The reset potential in the LIF model, , has a marked influence on the observed average synaptic efficacy. Depolarised/hyperpolarised reset potentials (e.g. −55/−70 mV, cyan/green dots) lead to an over/under-representation of short ISIs (left/right inset) compared to Poisson neurons (red line in insets). ISI histograms in inset are shown for LIF neurons firing at 1/s.