Oscillations via Spike-Timing Dependent Plasticity in a Feed-Forward Model
Fig 4
Numerical simulation of STDP-driven synaptic dynamics of a population of 120 excitatory synapses providing feed-forward input onto a single conductance based post-synaptic neuron (see e.g. Fig 3 and Methods for details).
The pre-synaptic activity followed an inhomogeneous Poisson process with a time-varying intensity by eq (17), using N = 120, D = 10Sp/sec, A = 10Sp/sec, ν = 2π·10Hz. We simulated the temporally anti-symmetric exponential STDP rule (eq (4) with τ± = 20ms), with α = 1.1, μ = 0.1, using a learning rate constant λ = 5·10−4. (A and B) The synaptic weight profile w(φ, t) as a function of φ is shown for different times t = 0, 35,…80min by the different colors. The solid lines show the temporal average of w(φ, t) on the interval [t,t+1min]. (C) Traces showing the dynamics of all 120 synapses, each shown in a different color: black for the 60th synapse (φ60 = π), magenta for 120th synapse (φ120 = 2π), shades of blue for synapses 1–59 and shades of red for synapses 61–119. (D) The dynamics of the order parameter (eq (22)) shown in red (x100 scaled), and the oscillation amplitude of post-synaptic activity Apost (eq (6)) shown in black and measured in Sp/sec, binned in time-bins of 1 minute. (E) The dynamics of the order parameter ψ (eq (22)) shown in red (calculated in time-bins of 1 sec), and the oscillation phase of post-synaptic activity φpost (calculated in time-bins of 1 min). (F) The distribution of synaptic weights of all 120 synapses, calculated using the second half of the simulation (after convergence to a limit cycle solution). The vertical cyan line denotes the mean value of the distribution. (G) The characteristic shape of the propagating wave, calculated from synaptic weights during the second half of the simulation. Error bars depict the standard error of the mean (calculated from measurements binned at 1sec during the second half of the simulation). The calculation of φpost was obtained using time-bins of 1 min. The vertical magenta line shows the mean phase difference between pre- and post- synaptic activity.