A Theoretical and Numerical Study of Certain Dynamical Models of Synaptic Plasticity

David Higgins 1
1 Cervellet
IBENS - Institut de biologie de l'Ecole Normale Supérieure
Abstract : Synaptic efficacy measures the ability of a presynaptic neuron to influence the membrane potential of a postsynaptic neuron. The process of changing synaptic efficacy, via plasticity, is thought to underlie learning and memory in the brain. Focusing on chemical synapses, we examine the abstract rules of synaptic plasticity which determine how changes in synaptic efficacy occur. Beginning with an atypical, non-Hebbian synapse, the parallel fibre to Purkinje cell synapse, we develop a model which explains the burst frequency and length de- pendence of this particular synaptic plasticity rule. We present a model based on underlying calcium and NO pathways which accurately unifies much of the experi- mental literature. This model will be useful in future studies of synaptic plasticity for this synapse and its simplicity will allow for numerical studies involving large numbers of synapses in a network architecture. We also examine a more typical plasticity rule for neocortical synaptic plasticity, developing analytical tools which accurately predict the behaviour of this synapse model under pre- and postsynaptic Poisson spiking. Building on this analysis we extend the theory to leaky integrate-and-fire (LIF) neurons in a network. We develop theoretical tools which can accurately describe the network response to both constant and transiently elevated noisy external inputs. Utilising these tools we examine the duration of synaptic memories under ongoing background (1/sec) spiking activity both in independent neurons and in a recurrent network. We find that lowering the extracellular calcium concentration extends memory time scales and that the further introduction of a bistability to the synaptic plasticity rule extends this memory time scale by several orders of magnitude. In all cases we provide theoretical predictions of memory time scales which match subsequent simulation comparisons. Both sets of investigations reveal insights into the processes of learning and sub- sequent forgetting in the brain. Both models reveal the joint importance of burst frequency and relative spike timing in the induction of memory changes at the synap- tic level. Adjustment of model parameters to more closely mimic in vivo conditions extends the retention time of memories, under ongoing activity, to biologically rel- evant time scales. Our work represents a coherent development right through from the biophysical processes of synaptic plasticity to the analytical mean-field level.
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David Higgins. A Theoretical and Numerical Study of Certain Dynamical Models of Synaptic Plasticity. Neurobiology. Ecole Normale Supérieure de Paris - ENS Paris, 2014. English. ⟨NNT : 158⟩. ⟨tel-01052580⟩

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