Modeling and Analysis of Electrical Network Activity in Neuronal Systems.

Abstract

Electrical activity in networks of neurons is an essential part of most brain functions. This dissertation deals with two different aspects in modeling and analysis of such activity in neuronal systems. Part I develops the first detailed mathematical model of the electrophysiology of the specific neuronal network responsible for the generation of circadian (~24-hour) rhythms in mammals. Part II is concerned with methods for inferring the functional connectivity of neuronal networks from multi-neuronal spike train data.

Mammalian circadian rhythms are controlled by a group of about 20,000 neurons in the hypothalamus called the suprachiasmatic nucleus (SCN). We have developed a model of action potential firing in the SCN network. With this model we can simulate and track the action potentials of thousands of model SCN neurons, while experimentally it is only possible to record the activity of a few dozen SCN neurons at the same time. Our simulations predict that subgroups, or clusters, of SCN neurons form, within which neurons synchronize their firing at a millisecond time scale. Furthermore, our simulations demonstrate how this clustering leads to the silencing or adjustment of neurons whose firing is out of phase with the rest of the population at the 24-hour time scale, giving insight into how the circadian clock may operate at the network level.

Temporal patterns of firing that are more complex than synchrony, such as precise firing sequences with fixed time delays between neurons, have been observed in multi-neuronal recordings from other brain areas. To determine whether the patterns detected are meaningful, it is important to know whether they are occurring more or less often than would be expected due to chance alone. To address this question, we have developed statistical methods for assessing when the number of occurrences of a precise firing sequence is significantly different from randomness and for estimating the magnitude of the connection strength. Our approach is computationally efficient and can discover patterns involving many neurons. The significant patterns discovered in multi-neuronal spike trains can be used to infer the functional connectivity between neurons and potentially identify circuits in the underlying neural tissue.