Fig. 4: Predictive learning rule gives rise to spike-timing-dependent plasticity mechanisms.
From: Sequence anticipation and spike-timing-dependent plasticity emerge from a predictive learning rule
a Left: Illustration of the protocol, where a neuron receives inputs from two pre-synaptic neurons (associated with weights w1 and w2) with a delay of Δt = 4 ms. These inputs were repeated across epochs. Middle and right: Asymmetry index, computed as the difference between the initial weight vector (w1,0, w2,0) and the final vector after j epochs: (w1,j−w1,0)−(w2,j−w2,0). Positive values of the asymmetry index thus indicate that w1 increases relative to w2. Shown are the asymmetry index after 100 and 300 epochs, as a function of the initial weights. The white lines divide three regions: (1) No spike; (2) A single spike; (3) A single spike before the second input (i.e. anticipation). The right panel shows, that for all initial weight conditions, the weight of the first input showed a relative increase as compared to the second input. b In order to model classic STDP protocols with current injection, one of the two inputs (pre-synaptic neuron 2) had a strong initial weight (i.e. did evoke a spike), and the other input (pre-synaptic neuron 1) was sub-threshold (i.e. did not evoke a spike). In this simulation, the weights for both inputs could be adjusted via the predictive learning rule (see Fig. S11 when the second input has a fixed weight). The y-axis shows the weight change (in percentage relative to the initial weight) of the sub-threshold input (i.e. pre-synaptic neuron 1) as a function of the delay Δt between the two input spikes (see Methods). Negative and positive values of Δt indicate that input 1 preceded or lagged input 2, respectively. Shown are the weight changes for different membrane time constants after 60 epochs. c In this simulation, the second input contained a burst of 3 spikes, which arrived after the first input, and each triggered a spike in the post-synaptic neuron. The input from pre-synaptic neuron 1 only had a sub-threshold effect. Shown is the weights change (as in b) versus the firing frequency, i.e. 1/Δt, within the burst (total of 3 spikes per burst). The blue and purple lines refer to the case that input 1 preceded input 2 or lagged input 2, respectively. Data used with permission of Society for Neuroscience, from “Spine Ca2+ Signaling in Spike-Timing-Dependent Plasticity'', Nevian and Sakmann, Journal of Neuroscience 26(43), 2006; permission conveyed through Copyright Clearance Center, Inc. (we refer to42 for information about the sample size), RMS error: 0.868 for pre-post pairing and 0.206 for post-pre pairing. d Weights change (as in b) as a function of the number of spikes in the second input. The inputs from pre-synaptic neuron 2 each triggered a spike in the post-synaptic neuron. The input from pre-synaptic neuron 1 only had a sub-threshold effect. RMS error: 0.089. e Weights change (as in b) induced by increasing the frequency pairing. Here, the inputs from pre-synaptic neuron 2 always triggered a spike in the post-synaptic neuron, whereas the input from pre-synaptic neuron 1 only had a sub-threshold effect. The inputs from neuron 2 arrived 6 ms before the inputs from neuron 1. RMS error: 0.057. Data in panel d and e used with permission of The American Physiological Society, from `Contribution of Individual Spikes in Burst-Induced Long-Term Synaptic Modification'', Froemke et al., Journal of neurophysiology 95(3), 2006; permission conveyed through Copyright Clearance Center, Inc. (we refer to43 for information about the sample size).
