Putative Role of Connectivity in the Generation of Spontaneous Bursting Activity in an Excitatory Neuron Population

Population-wide synchronized rhythmic bursts of electrical activity are present in a \nvariety of neural circuits. The proposed general mechanisms for \nrhythmogenesis are often attributed to intrinsic and synaptic properties. For example,\nthe recurrent excitation through excitatory synaptic connections determines \nburst initiation, and the slower kinetics of ionic currents or synaptic depression\nresults in burst termination. In such theories, a slow recovery process is essential \nfor the slow dynamics associated with bursting.\n\nThis thesis presents a new hypothesis that depends on \nthe connectivity pattern among neurons rather than a slow kinetic process to achieve \nthe network-wide bursting. The thesis \nbegins with an introduction of bursts of electrical activity in a purely excitatory \nneural network and existing theories explaining this phenomenon. It then covers \nthe small-world approach, which is applied to modify the network structure in the simulation,\nand the Morris-Lecar (ML) neuron model, which is used as the component cells in the network.\nSimulation results of the dependence of bursting activity on network connectivity, \nas well as the inherent network properties explaining this dependence are described. \nThis work shows that the network-wide bursting activity emerges in the small-world network\nregime but not in the regular or random networks, and this small-world bursting primarily results\nfrom the uniform random distribution of long-range connections in the network, as well as \nthe unique dynamics in the ML model. Both attributes foster progressive synchronization in\nfiring activity throughout the network during a burst, and this synchronization may terminate a burst in the absence of an obvious slow recovery process. The thesis concludes with possible future work.