Abstract
Synaptic plasticity serves as an essential mechanism underlying cognitive processes as learning and memory. For a better understanding detailed theoretical models combine experimental underpinnings of synaptic plasticity and match experimental results. However, these models are mathematically complex impeding the comprehensive investigation of their link to cognitive processes generally executed on the neuronal network level. Here, we derive a mathematical framework enabling the simplification of such detailed models of synaptic plasticity facilitating further mathematical analyses. By this framework we obtain a compact, firing-rate-dependent mathematical formulation, which includes the essential dynamics of the detailed model and, thus, of experimentally verified properties of synaptic plasticity. Amongst others, by testing our framework by abstracting the dynamics of two well-established calcium-dependent synaptic plasticity models, we derived that the synaptic changes depend on the square of the presynaptic firing rate, which is in contrast to previous assumptions. Thus, the here-presented framework enables the derivation of biologically plausible but simple mathematical models of synaptic plasticity allowing to analyze the underlying dependencies of synaptic dynamics from neuronal properties such as the firing rate and to investigate their implications in complex neuronal networks.
Highlights
Synaptic plasticity serves as an essential mechanism of neuronal networks being linked to diverse functional properties such as the cognitive mechanisms of learning and memory (Hebb, 1949; Martin et al, 2000)
We consider a well-established calcium-based synaptic plasticity model, which describes a multitude of plasticity effects based on the underlying molecular dynamics of calcium currents in the postsynaptic dendritic spine (Graupner and Brunel, 2012; Graupner et al, 2016)
We develop a simple, compact mathematical model by inferring the neuronal firing rate dependency of synaptic plasticity from a detailed, calcium-based synaptic plasticity model (Graupner and Brunel, 2012; Graupner et al, 2016)
Summary
Synaptic plasticity serves as an essential mechanism of neuronal networks being linked to diverse functional properties such as the cognitive mechanisms of learning and memory (Hebb, 1949; Martin et al, 2000). To understand the details of this link between synaptic plasticity and functional properties of a neuronal system, theoretical or mathematical models of synaptic plasticity are formulated and investigated (Dayan and Abbott, 2001; Gerstner et al, 2012, 2014). To investigate the link between synaptic plasticity and functional properties of neuronal systems, compact, simple theoretical models of synaptic plasticity are developed neglecting the underlying biological details (Tsodyks and Feigelman, 1988; Gerstner and Kistler, 2002; Tetzlaff et al, 2011, 2013; Knoblauch and Sommer, 2016). The detailed formulation of these compact models are rather phenomenological and they are only loosely linked to the detailed biological models
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