STOCHASTIC MODELS OF NEURAL SYNAPTIC PLASTICITY

In neuroscience, learning and memory are usually associated with long-term changes in neuronal connectivity. In this context, synaptic plasticity refers to the set of mechanisms driving the dynamics of neuronal connections, called synapses and represented by a scalar value, the synaptic weight. Spike-timing-dependent plasticity (STDP) is a biologically based model representing the time evolution of the synaptic weight as a functional of the past spiking activity of adjacent neurons. Although numerous models of neuronal cells have been proposed in the mathematical literature, few of them include a variable for the time-varying strength of the connection. A new, general, mathematical framework is introduced to study synaptic plasticity associated to different STDP rules. The system composed of two neurons connected by a single synapse is investigated, and a stochastic process describing its dynamical behavior is presented and analyzed. The notion of plasticity kernel is introduced as a key component of plastic neural networks models, generalizing a notion used for pair-based models. We show that a large number of STDP rules from neuroscience and physics can be represented by this formalism. Several aspects of these models are discussed and compared to canonical models of computational neuroscience. An important subclass of plasticity kernels with a Markovian formulation is also defined and investigated. In these models, the time evolution of cellular processes such as the neuronal membrane potential and the concentrations of chemical components created/suppressed by spiking activity has the Markov property.

Automated summary

This paragraph discusses the relationship between long-term changes in neuronal connectivity and learning and memory, exploring the mechanisms of synaptic plasticity and the time evolution of synaptic weight. A new mathematical framework is introduced to study synaptic plasticity associated with different STDP rules. The concept of plasticity kernel is introduced as a key component of plastic neural network models and a subclass with a Markovian formulation is defined and investigated.