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Abstract
Circadian clock oscillators in living organisms have been studied extensively for decades. However, it is presently still not fully understood how the stochastic clock gene regulatory processes in individual cells are getting organized to produce coherent, nearly periodic clock oscillations observed at the level of large cell populations. To investigate the effects of intra-cellular stochasticity, arising from the stochastic gene regulation at the multi-cell level, we have developed a hybrid model, which combines the random clock gene flip processes with a deterministic time evolution of resulting gene products and signaling agents, subject to a quorum sensing-type inter-cellular coupling mechanism, for the microbial fungus Neurospora crassa. The cell population, with sufficient coupling strength, can generate coherent and nearly periodic average signals, whereas the dynamics of each single cells still remains irregular and incoherent. We introduce several novel non-linear time series analysis methods to study the underlying mechanism of this paradoxical collective system behavior. By using the relative signal amplitude as the synchronization order parameter, a continuous phase transition phenomenon can be observed in the system, from being non-oscillatory to oscillatory, with the population size approaching infinity.