Extending the effects of spike-timing-dependent plasticity to behavioral timescales

Abstract

Activity-dependent modification of synaptic strengths due to spike-timing-dependent plasticity (STDP) is sensitive to correlations between pre- and postsynaptic firing over timescales of tens of milliseconds. Temporal associations typically encountered in behavioral tasks involve times on the order of seconds. To relate the learning of such temporal associations to STDP, we must account for this large discrepancy in timescales. We show that the gap between synaptic and behavioral timescales can be bridged if the stimuli being associated generate sustained responses that vary appropriately in time. Synapses between neurons that fire this way can be modified by STDP in a manner that depends on the temporal ordering of events separated by several seconds even though the underlying plasticity has a much smaller temporal window.

Fig. 1

STDP and conditioned responses. (A) The fractional strengthening or weakening of a synapse per spike pair as a function of the time difference between the pre- and postsynaptic action potentials, also known as the STDP window function. (B) The learning index, which indicates a fly's attraction to or avoidance of an odor that previously had been paired with a shock as a function of the time interval between the presentation of the odor and the shock during training. [Adapted with permission from ref. (Copyright 2004, Macmillan Publishers, Ltd.).] (C) The amount of synaptic modification as a function of the interstimulus interval produced by each single trial, from the analytic formula given in the text. Parameter values are A₊ = A₋ = 0.5%, τ₊ = τ₋ = 20 ms, R_pre = R_post = 50 Hz, τ_pre = 30 s, and τ_post = 80 s.

Fig. 2

Cross-correlations resulting from decaying firing patterns. Inset shows the firing rates of two neurons (one presynaptic and one postsynaptic), and the two panels indicate the resulting cross-correlations, normalized to the value for synchronous spikes. (Left) When the decay of the firing of the presynaptic neuron coincides with the activation of the postsynaptic neuron, the pre–post cross-correlation shows more pre-before-post than post-before-pre spike ordering. (Right) When the decay of the firing of the postsynaptic neuron coincides with the activation of the presynaptic neuron, the pre–post cross-correlation shows post-before-pre more than pre-before-post spike ordering.

Fig. 3

Development of a conditioned response. A CS drives the afferents to a postsynaptic neuron at 45 Hz from time 1s to 2s, followed by an exponential decay of afferent rates with a decay time constant of 2 s. The postsynaptic neuron is driven by a US, represented by a constant current from time 6–7 s that drives it at 45 Hz, followed by a 2-s time-constant exponential decay of the current to zero. (Left) Shows the membrane potential of the postsynaptic neuron. For clarity, the dots over the action potentials indicate every 11th action potential. (Right) Shows distributions of the strengths of the 1,000 excitatory synaptic conductances between the afferents and the postsynaptic neuron relative to their maximal allowed value. (A) At the beginning of the simulation, all synapses are set to zero strength, and the postsynaptic neuron responds only to the US. (B) After 20 trials, some of the synapses have strengthened causing the postsynaptic neuron to depolarize in response to the CS. (C) After 40 trials, the synapses have grown strong enough to make the postsynaptic neuron fire in response to both stimuli.

Fig. 4

Effect of timing and order on the conditioned response. The format and procedures are identical to those in Fig. 3 except for the timing and ordering between the CS and the US. All results are after 40 trials. (A) When the CS precedes the US by 4 s (rather than 5 s as in Fig. 3), synaptic strengths are stronger, and the postsynaptic neuron responds more strongly to the CS than in Fig. 3. (B) When the CS precedes the US by 6 s, the postsynaptic neuron is depolarized but fails to fire in response to the CS after 40 trials. Synaptic strengths are weaker than in Fig. 3 and A. (C) When the US precedes the CS by 5 s, no synaptic strengthening occurs.