(42f) Coarse Modeling of Circadian Rhythms in Heterogeneous Neural Networks

The suprachiasmatic nucleus (SCN) of the hypothalamus contains about 15,000 neurons in mammals, and is the source of a light-independent 24-hour rhythm which serves as a central clock governing daily rhythms throughout the rest of the body. This rhythm is the result of a set of gene repression/promotion feedback loops occurring in each neuron. Though, in isolation, cells exhibit a range of free-running periods distributed around 24 hours, their coupling in a complex network allows for synchronization, and entrainment to an external zeitgeber.

Our work on coarse-graining the dynamics of synchronized populations uses the emergent smooth dependence of cellsâ?? states in this synchronized group on the particular parameters of each cell--such as natural period. Such parameters are heterogeneous across the population, but unchanging with time. Under the assumption that this dependence is smooth (and that the cells synchronize at least partially in frequency), this coarse-graining constitutes a significant dimensionality reduction of our description of the system state.

We use this reduced-dimension representation to perform optimizations of drug dosing schedules to treat non-24-hour sleep/wake disorders or to aid with entrainment to an industrial non-24-hour shift schedule.