Stochastic networks for the clock were identified by ensemble methods using genetic algorithms that captured the amplitude and period variation in single cell oscillators of
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Abstract Neurospora crassa . The genetic algorithms were at least an order of magnitude faster than ensemble methods using parallel tempering and appeared to provide a globally optimum solution from a random start in the initial guess of model parameters (i.e., rate constants and initial counts of molecules in a cell). The resulting goodness of fit was roughly halved versus solutions produced by ensemble methods using parallel tempering, and the resulting$${x}^{2}$$ ${x}^{2}$ per data point was only$${x}^{2}$$ ${x}^{2}$ = 2,708.05/953 = 2.84. The fitted model ensemble was robust to variation in proxies for “cell size”. The fitted neutral models without cellular communication between single cells isolated by microfluidics provided evidence for only$${\chi }^{2}/n$$ ${\chi}^{2}/n$one Stochastic Resonance at one common level of stochastic intracellular noise across days from 6 to 36 h of light/dark (L/D) or in a D/D experiment. When the lightdriven phase synchronization was strong as measured by the Kuramoto (K), there was degradation in the single cell oscillations away from the stochastic resonance. The rate constants for the stochastic clock network are consistent with those determined on a macroscopic scale of 10^{7}cells. 
Four interrelated measures of phase are described to study the phase synchronization of cellular oscillators, and computation of these measures is described and illustrated on single cell fluorescence data from the model filamentous fungus, Neurospora crassa. One of these four measures is the phase shift ϕ in a sinusoid of the form x(t) = A(cos(ωt + ϕ), where t is time. The other measures arise by creating a replica of the periodic process x(t) called the Hilbert transform x̃(t), which is 90 degrees out of phase with the original process x(t). The second phase measure is the phase angle FH(t) between the replica x̃(t) and X(t), taking values between π and π. At extreme values the Hilbert Phase is discontinuous, and a continuous form FC(t) of the Hilbert Phase is used, measuring time on the nonnegative real axis (t). The continuous Hilbert Phase FC(t) is used to define the phase MC(t1,t0) for an experiment beginning at time t0 and ending at time t1. In that phase differences at time t0 are often of ancillary interest, the Hilbert Phase FC(t0) is subtracted from FC(t1). This difference is divided by 2π to obtain the phase MC(t1,t0) in cycles. Both the Hilbert Phasemore »

In previous work we reconstructed the entire transcriptional network for all 2,418 clockassociated genes in the model filamentous fungus, N. crassa. Several authors have suggested that there is extensive posttranscriptional control in the genomewide clock network (IEEE 3: 27, 2015). Here we have successfully reconstructed the entire clock network in N. crassa with a Variable Topology Ensemble Method (VTENS), assigning each clockassociated gene to the regulation of one or more of 5 transcription factors as well as to 6 RNA operons. The resulting network provides a unifying framework to explore the clock’s linkage to metabolism through posttranscriptional regulation, in which ~850 genes are predicted to fall under the regulatory control of an RNA operon. A unique feature of all of the RNA operons inferred is their functional connection to genes connected to the ribosome. We have been successful in distinguishing several hypotheses about regulatory topologies of the clock network through protein profiling of the regulators.