Stochastic Modeling of System Function in a Network of Biological Oscillators

Author(s): Meeker, Kirsten R. | Advisor(s): Petzold, Linda R | Abstract: Many living organisms have evolved to anticipate daily circadian cycles and changing seasons of their environment. In mammals, the suprachiasmatic nucleus (SCN) of the hypothalamus, a brain region of about 20,000 neurons, serves as the master circadian clock coordinating timing throughout the body and entraining to daily external light cycles. The remarkable precision of the SCN clock relies on intercellular signaling. In its absence, each SCN neuron and the SCN as a whole have significantly less stable oscillations. Though there are candidate signaling neuropeptides and anatomical surveys of the SCN, it is still unknown how the SCN as a whole responds to changes in the environment and regulates function in the body. We model the unstable oscillations in individual cells by developing a stochastic model based on the cell clock's gene regulatory network, then investigate the intercellular signaling properties of the SCN to understand its behavior as a whole. Though many existing deterministic models contain details of the gene regulation in the cell, their output has been compared to the behavior of the SCN as a whole, rather than to individual cells. Characterizing properties of individual cells such as period, phase, and synchronization is challenging due to their non-linear and unstable oscillations. We developed a wavelet analysis method to characterize cell behavior in biological experiments and compare with stochastic cell models. This analysis led to an examination of how period distributions could be influenced by stochastic fluctuations in a nonlinear cell oscillator model, and a hypothesis that the poor or strong oscillators observed in biological experiments could be a stochastic oscillator operating near a bifurcation point, between non-oscillatory and oscillatory conditions.It was observed in SCN tissue and in the SCN stochastic model that the oscillator is less likely to shift phase in response to a vasoactive intestinal polypeptide (VIP) dose at circadian time (CT4) than at other times. A reexamination of the behavior of the SCN as a whole, when modeled as linked stochastic oscillators, led to the hypothesis that the cells of the SCN synchronize to each other using a ``phase tumbling'' process. Our hypothesis is that the SCN synchronizes by its cells shifting with a wide phase distribution when they are perturbed at phases not near CT4. Rather than shifting in a deterministic manner, where all the cells stay synchronized and shift together to a new light schedule, they instead temporarily desynchronize then reorganize aligned to the new light/dark cycle. Within a few cycles the system can rapidly shift to a new light schedule. This rapid re-entrainment to both new light/dark and temperature schedules was confirmed in mice by first desynchronizing the SCN using a neuropeptide that has been considered a synchronizing agent, vasoactive intestinal polypeptide, or by a brief bright light exposure before exposing the animals to a new shifted schedule.Finally, since the behavior of the SCN as a whole may depend on the network topology of its intercellular connections, we applied an information theoretic measure to infer pairwise functional connections between neurons in the SCN. We first validated the method on several model networks. After inferring connection networks of three SCN's, we modeled those networks in our stochastic SCN model and confirmed that we could re-infer the bio-inspired networks. We found that the SCN, at least for these experimental samples, appears to have a small-world network topology and is scale-free. We hope that our results have helped to illuminate how stochastic fluctuations in the SCN system contribute to its behavior.