Identifying a stochastic clock network with light entrainment for single cells of Neurospora crassa.

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 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 [Formula: see text] was roughly halved versus solutions produced by ensemble methods using parallel tempering, and the resulting [Formula: see text] per data point was only [Formula: see text] = 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 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 light-driven 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 107 cells.

Ensemble methods for stochastic networks with special reference to the biological clock of Neurospora crassa.

A major challenge in systems biology is to infer the parameters of regulatory networks that operate in a noisy environment, such as in a single cell. In a stochastic regime it is hard to distinguish noise from the real signal and to infer the noise contribution to the dynamical behavior. When the genetic network displays oscillatory dynamics, it is even harder to infer the parameters that produce the oscillations. To address this issue we introduce a new estimation method built on a combination of stochastic simulations, mass action kinetics and ensemble network simulations in which we match the average periodogram and phase of the model to that of the data. The method is relatively fast (compared to Metropolis-Hastings Monte Carlo Methods), easy to parallelize, applicable to large oscillatory networks and large (~2000 cells) single cell expression data sets, and it quantifies the noise impact on the observed dynamics. Standard errors of estimated rate coefficients are typically two orders of magnitude smaller than the mean from single cell experiments with on the order of ~1000 cells. We also provide a method to assess the goodness of fit of the stochastic network using the Hilbert phase of single cells. An analysis of phase departures from the null model with no communication between cells is consistent with a hypothesis of Stochastic Resonance describing single cell oscillators. Stochastic Resonance provides a physical mechanism whereby intracellular noise plays a positive role in establishing oscillatory behavior, but may require model parameters, such as rate coefficients, that differ substantially from those extracted at the macroscopic level from measurements on populations of millions of communicating, synchronized cells.

Systems biology of the neurospora biological clock.

A major challenge of systems biology is explaining complex traits, such as the biological clock, in terms of the kinetics of macromolecules. The clock poses at least four challenges for systems biology: (i) identifying the genetic network to explain the clock mechanism quantitatively; (ii) specifying the clock's functional connection to a thousand or more genes and their products in the genome; (iii) explaining the clock's response to light and other environmental cues; and (iv) explaining how the clock's genetic network evolves. Here, the authors illustrate an approach to these problems by fitting an ensemble of genetic networks to microarray data derived from oligonucleotide arrays with approximately all 11 000 Neurospora crassa genes represented. A promising genetic network for the clock mechanism is identified.

An ensemble method for identifying regulatory circuits with special reference to the qa gene cluster of Neurospora crassa.

A chemical reaction network for the regulation of the quinic acid (qa) gene cluster of Neurospora crassa is proposed. An efficient Monte Carlo method for walking through the parameter space of possible chemical reaction networks is developed to identify an ensemble of deterministic kinetics models with rate constants consistent with RNA and protein profiling data. This method was successful in identifying a model ensemble fitting available RNA profiling data on the qa gene cluster.

Behavior of damage spreading in the two-dimensional Blume-Capel model.

The damage spreading technique has been used to study the general integer and half-integer spin-S Blume-Capel model on the square lattice within a Metropolis-type dynamics. For S=1 and 2 integer spins, our results suggest that there exists one multicritical point along the order-disorder transition line; for S=3/2 and 5/2 half-integer spins, our results show that this multicritical behavior does not exist for this model.

Damage spreading in the mixed spin Ising model.

We apply the damage spreading technique to study a mixed spin Ising model consisting of spin 1/2 and spin 1 with a crystal field interaction on the square lattice within a kind of Metropolis dynamics. The completely different behavior, depending on the value of the crystal field interaction, strongly suggests there may exist a dynamical tricritical point where the phase transition may change from the second order to the first order for this model.