Spike timing dependent plasticity: a consequence of more fundamental learning rules

Abstract

Spike timing dependent plasticity (STDP) is a phenomenon in which the precise timing of spikes affects the sign and magnitude of changes in synaptic strength. STDP is often interpreted as the comprehensive learning rule for a synapse - the "first law" of synaptic plasticity. This interpretation is made explicit in theoretical models in which the total plasticity produced by complex spike patterns results from a superposition of the effects of all spike pairs. Although such models are appealing for their simplicity, they can fail dramatically. For example, the measured single-spike learning rule between hippocampal CA3 and CA1 pyramidal neurons does not predict the existence of long-term potentiation one of the best-known forms of synaptic plasticity. Layers of complexity have been added to the basic STDP model to repair predictive failures, but they have been outstripped by experimental data. We propose an alternate first law: neural activity triggers changes in key biochemical intermediates, which act as a more direct trigger of plasticity mechanisms. One particularly successful model uses intracellular calcium as the intermediate and can account for many observed properties of bidirectional plasticity. In this formulation, STDP is not itself the basis for explaining other forms of plasticity, but is instead a consequence of changes in the biochemical intermediate, calcium. Eventually a mechanism-based framework for learning rules should include other messengers, discrete change at individual synapses, spread of plasticity among neighboring synapses, and priming of hidden processes that change a synapse's susceptibility to future change. Mechanism-based models provide a rich framework for the computational representation of synaptic plasticity.

Keywords: STDP; calcium; learning rules; long-term depression; long-term potentiation; mechanistic models; synaptic plasticity.

Figure 1

Classical induction protocols for synaptic plasticity. (A) Changing the stimulation frequency of robust extracellular stimulation affects the sign and magnitude of synaptic plasticity. Left: high-frequency stimulation results in LTP whereas low-frequency stimulation produces LTD. Right: frequency vs. plasticity curve (from O'Connor et al., 2005a). (B) Low-frequency stimulation paired with voltage clamping of the postsynaptic cell can also result in LTP or LTD depending on the postsynaptic voltage. Left: moderate depolarization produces LTD where as large depolarization produces LTP. Right: depolarization vs. plasticity curve (from Ngezahayo et al., 2000). (C) Theta-burst stimulation tries to mimic more naturalistic conditions. In the hippocampus of awake behaving animals there is a strong theta-frequency oscillation (right). Left: In a theta-burst induction protocol, short high-frequency bursts are delivered each 200 ms, or at a frequency of 5 Hz, within the theta range (from Hirase et al., 1999). (D) STDP protocols are induced by precisely stimulating the presynaptic afferents at a specific time (Δt) before or after a postsynaptic spike. Right: The precise Δt determines the sign and magnitude of synaptic plasticity (from Bi and Poo, 1998).

Figure 2

Spike timing dependent plasticity as the first law of synaptic plasticity. (A) Measurements of synaptic plasticity for protocols in which presynaptic and postsynaptic action potentials are repeatedly separated in time by an interval Δt_ij are made to construct an STDP “kernel” (see STDP as the “first law” of synaptic plasticity? for definition) for a given synapse type. Kernel shapes have been taken to be synapse-specific representations of learning rules (for review see Abbott and Nelson, ; Wittenberg and Wang, 2006). (B) Illustration of two common methods for using STDP kernels to predict plasticity from an epoch of neural activity. Left: contributions to plasticity from all pairwise combinations of presynaptic and postsynaptic spikes are included. Right: Only nearest neighbor spike pairs are included. (C) Experiments have demonstrated that very different kernels can be measured at a single synapse. Left: At the CA3–CA1 synapse pairing single presynaptic and postsynaptic action potentials leads to an LTD-only rule. Based on the linear STDP model illustrated in (A,B), no spike pattern would ever result in LTP. Middle: By adding a second postsynaptic action potential, LTP can be induced. This is not predicted by linear STDP. Dashed vertical line corresponds to the time of the first postsynaptic action potential. Right: By decreasing the number of pairings to 20–30, the depression window disappears and an LTP-only kernel is measured. From such a kernel, the existence of LTD would not be predicted. Data from Wittenberg and Wang (2006).

Figure 3

The CaDP model can account for various forms of spike timing dependent plasticity. (A) The key functions controlling the CaDP model. Left: The Ω function controls the sign and magnitude of calcium-dependent synaptic plasticity, the gray shading marks the LTD region. Center: the η function controls the calcium-dependent rate of plasticity. Right: the shape of the back-propagating action potential with its long tail current. (B) The results of an STDP induction protocol, simulating the CaDP model with G_NMDA = 1/420 (μM/mV). Left: the calcium transients for baseline, Δt = −10 ms, 0 ms and 30 ms. Here the LTD threshold is θ_d = 0.35 and the LTP threshold is θ_p = 0.55. The LTD region is indicated by the gray shading. Right: the complete STDP curve, which exhibits, post-pre LTD, pre-post LTP and also pre-post LTD. (C) The same as (B) but with G_NMDA = 1/600 (μM/mV). Here all values of Δt produce LTD. (D) The same as (C) but with two postsynaptic spikes. The timing of the two postsynaptic spikes is indicated by the vertical lines, and the time between the two post spikes is 10 ms. Here we get a complete STDP curve with one LTP window and two LTD windows.

Figure 4

Spike timing is merely one dimension in the high-dimensional synaptic learning rule. A conceptual illustration of a learning rule in three dimensions is shown. Depending on the choice of activity parameters other than spike timing, many different STDP rules can be measured at a synapse (from Wittenberg and Wang, 2006). The second axis represents the transition from parameters that more strongly activate depression (D-rule) to parameters that more strongly activate potentiation (P-rule). By choosing parameters that activate only a single rule, the spike timing-dependence of LTP and LTD can be measured separately. At the CA3–CA1 synapse, potentiation is initiated by as few as 20 causal pairings of presynaptic action potentials with postsynaptic bursts repeated at 5 Hz or higher. Depression does not require high-frequency stimulation or postsynaptic bursts but requires more pairings than LTP. Stimulus conditions that satisfy the temporal requirements for both the potentiation rule and the depression rule lead to a bidirectional spike-timing-dependent plasticity curve. In neocortex one can shift along the P–D axis by changing the pairing frequency (Sjöström et al., 2001), or by neuromodulator concentration (Seol et al., 2007).