Abstract
The brain is a dynamical system, wherein neural activity evolves according to the present state of neurons' excitability and the connectivity between them. This connectivity is shaped over time through synaptic plasticity. Hebbian plasticity causes strengthening of connections between co-active neurons, leading to the formation of clustered, attractor-like circuits. Encoding distinct memories with uncorrelated neural representations results in effectively random connections between different neuronal clusters. In this dissertation, we examine the dynamics of networks possessing this kind of random clustered connectivity. In chapter 1, we introduce the idea of random clustered connectivity and briefly review the literature on its formation and function. Such connectivity is prevalent throughout the brain in vivo, develops spontaneously in cultured neurons, and naturally arises from biologically based plasticity rules in simulations of model recurrent networks.
In chapter 2, we apply the idea of random clustered connectivity to modeling hippocampal dynamics. The hippocampus exhibits spontaneous sequential neural activity corresponding to recently experienced spatial trajectories. We show that random clustered networks can produce key signatures of hippocampal activity observed experimentally, including place field tuning and reactivation of trajectories, without assuming structured, environment-specific recurrent connectivity. Such networks may represent the default state of the hippocampus with respect to a novel environment, which would then be shaped by plasticity through experience in the environment.
In chapter 3, we consider multistability in randomly connected attractor networks. Under certain conditions, networks of randomly connected firing-rate units can store multiple memories as distinct stable attractor states. We extend previous results to show that both finite-size effects and more biologically realistic firing rate functions lead to multistability in parameter regimes not previously predicted to have multistability. Such multistability is a hallmark of many cortical and subcortical regions and is the basis for autoassociative memory retrieval.
In chapter 4, we summarize and review our results. We consider future directions needed to further develop our understanding of the functional role of preexisting connectivity in the brain. We focus our discussion of future directions on questions regarding the role of ongoing experience-dependent plasticity in shaping the intrinsic dynamics that result from a random preexisting structure.