Tag-Trigger-Consolidation: A Model of Early and Late Long-Term-Potentiation and Depression

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Abstract
Changes in synaptic efficacies need to be long-lasting in order to serve as a substrate for memory. Experimentally, synaptic plasticity exhibits phases covering the induction of long-term potentiation and depression (LTP/LTD) during the early phase of synaptic plasticity, the setting of synaptic tags, a trigger process for protein synthesis, and a slow transition leading to synaptic consolidation during the late phase of synaptic plasticity. We present a mathematical model that describes these different phases of synaptic plasticity. The model explains a large body of experimental data on synaptic tagging and capture, cross-tagging, and the late phases of LTP and LTD. Moreover, the model accounts for the dependence of LTP and LTD induction on voltage and presynaptic stimulation frequency. The stabilization of potentiated synapses during the transition from early to late LTP occurs by protein synthesis dynamics that are shared by groups of synapses. The functional consequence of this shared process is that previously stabilized patterns of strong or weak synapses onto the same postsynaptic neuron are well protected against later changes induced by LTP/LTD protocols at individual synapses. Humans and animals learn by changing the strength of connections between neurons, a phenomenon called synaptic plasticity. These changes can be induced by rather short stimuli (lasting sometimes only a few seconds) but should then be stable for months or years in order to be useful for long-term memory. Experimentalists have shown that synapses undergo a sequence of steps that transforms the rapid change during the early phase of synaptic plasticity into a stable memory trace in the late phase. In this paper we introduce a model with a small number of equations that can describe the phenomena of induction of synaptic changes during the early phase of synaptic plasticity, the trigger process for protein synthesis, and the final stabilization. The model covers a broad range of experimental phenomena known as tagging experiments and makes testable predictions. The ability to model the stabilization of synapses is crucial to understand learning and memory processes in animals and humans and a necessary ingredient for any large-scale model of the brain.