Stochastic resonance in circadian rhythms

The macroscopic limit to synchronization of cellular clocks in single cells of Neurospora crassa

We determined the macroscopic limit for phase synchronization of cellular clocks in an artificial tissue created by a “big chamber” microfluidic device to be about 150,000 cells or less. The dimensions of the microfluidic chamber allowed us to calculate an upper limit on the radius of a hypothesized quorum sensing signal molecule of 13.05 nm using a diffusion approximation for signal travel within the device. The use of a second microwell microfluidic device allowed the refinement of the macroscopic limit to a cell density of 2166 cells per fixed area of the device for phase synchronization. The measurement of averages over single cell trajectories in the microwell device supported a deterministic quorum sensing model identified by ensemble methods for clock phase synchronization. A strong inference framework was used to test the communication mechanism in phase synchronization of quorum sensing versus cell-to-cell contact, suggesting support for quorum sensing. Further evidence came from showing phase synchronization was density-dependent.

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.

Stochastic resonance and hysteresis in climate with state-dependent fluctuations

We consider two aspects in climatic science where bistability between the two stable states of the systems is observed. One is the transition between the glacial and the interglacial period in Earth's glacial cycle. Another is the thermohaline circulation in the North Atlantic ocean. Both of these phenomena can be modeled by the overdamped dynamics of a Brownian particle in a double-well potential subject to periodic forcing. For the former case, the two wells represent two different climates and the periodic forcing is sufficiently weak not to cause a transition between the two states without the effect of the noise. Whereas in case of the latter phenomenon, the two states correspond to the two different conditions of the flow and the strength of the periodic forcing is high enough to give rise to hysteresis in the system. We propose that one important component of the dynamics, short-term fluctuations related to weather, in both of these cases, depends on the current climatic state of the system. This leads to introduction of the state-dependent diffusion coefficients in the dynamics because the diffusion coefficient represents the strength of the fluctuations. We justify our argument by analyzing the δ^{18}O record for the glacial cycle model. We have shown that this consideration can produce certain features in the dynamics which agree with the real observations in case of both glacial cycles and thermohaline flow.

Noise-induced coherence in multicellular circadian clocks

In higher organisms, circadian rhythms are generated by a multicellular genetic clock that is entrained very efficiently to the 24-h light-dark cycle. Most studies done so far of these circadian oscillators have considered a perfectly periodic driving by light, in the form of either a square wave or a sinusoidal modulation. However, in natural conditions, organisms are subject to nonnegligible fluctuations in the light level all through the daily cycle. In this article, we investigate how the interplay between light fluctuations and intercellular coupling affects the dynamics of the collective rhythm in a large ensemble of nonidentical, globally coupled cellular clocks modeled as Goodwin oscillators. On the basis of experimental considerations, we assume an inverse dependence of the cell-cell coupling strength on the light intensity, in such a way that the larger the light intensity, the weaker the coupling. Our results show a noise-induced rhythm generation for constant light intensities at which the clock is arrhythmic in the noise-free case. Importantly, the rhythm shows a resonancelike phenomenon as a function of the noise intensity. Such improved coherence can be only observed at the level of the overt rhythm and not at the level of the individual oscillators, thus suggesting a cooperative effect of noise, coupling, and the emerging synchronization between the oscillators.