Interacting stochastic oscillators

Synchronization and clustering of synthetic genetic networks: a role for cis-regulatory modules

The effect of signal integration through cis-regulatory modules (CRMs) on synchronization and clustering of populations of two-component genetic oscillators coupled with quorum sensing is investigated in detail. We find that the CRMs play an important role in achieving synchronization and clustering. For this, we investigate six possible cis-regulatory input functions with AND, OR, ANDN, ORN, XOR, and EQU types of responses in two possible kinds of cell-to-cell communications: activator-regulated communication (i.e., the autoinducer regulates the activator) and repressor-regulated communication (i.e., the autoinducer regulates the repressor). Both theoretical analysis and numerical simulation show that different CRMs drive fundamentally different cellular patterns, such as complete synchronization, various cluster-balanced states and several cluster-nonbalanced states.

Neurotransmitter-Mediated Collective Rhythms in Grouped Drosophila Circadian Clocks

Over the past decades, fly Drosophila melanogaster has being used as a premier model organism to study molecular and genetic bases of circadian rhythms. Here the authors propose a multicellular heterogeneous model for which the network of Drosophila circadian oscillators consists of two groups, the self-sustained lateral neurons (LNs) communicating to each other and the damped dorsal neurons (DNs) receiving neurotransmitters only from the LNs without interaction within this group. By simulating different experimental conditions, the authors find that the proposed model, except for being capable of reproducing some known experimental results well, also can predict some interesting phenomena: 1) The DNs need neuronal projections from the LNs to be rhythmic and to synchronize; 2) the effect of communication on mean amplitude and mean period of two oscillatory groups is different; 3) communication delay can facilitate the network synchronization of the LNs; and 4) only the LNs lose rhythmicity under constant light conditions. These results reveal the mechanism of an integrated pacemaker that would govern behavioral and physiological rhythmicity of the model organism.

Coherence, collective rhythm, and phase difference distribution in populations of stochastic genetic oscillators with cellular communication

An ensemble of stochastic genetic relaxation oscillators via phase-attractive or repulsive cell-to-cell communication are investigated. In the phase-attractive coupling case, it is found that cellular communication can enhance self-induced stochastic resonance as well as collective rhythms, and that different intensities of noise resulting from the fluctuation of intrinsic chemical reactions or the extrinsic environment can induce stochastic limit cycles with different amplitudes for a large cell density. In contrast, in the phase-repulsive coupling case, the distribution of phase differences among the stochastic oscillators can display such characteristic as unimodality, bimodality or polymodality, depending on both noise intensity and cell number, but the modality of phase difference distribution almost keeps invariant for an arbitrary noise intensity as the cell number is beyond a threshold.

Synchronization of genetic oscillators

Synchronization of genetic or cellular oscillators is a central topic in understanding the rhythmicity of living organisms at both molecular and cellular levels. Here, we show how a collective rhythm across a population of genetic oscillators through synchronization-induced intercellular communication is achieved, and how an ensemble of independent genetic oscillators is synchronized by a common noisy signaling molecule. Our main purpose is to elucidate various synchronization mechanisms from the viewpoint of dynamics, by investigating the effects of various biologically plausible couplings, several kinds of noise, and external stimuli. To have a comprehensive understanding on the synchronization of genetic oscillators, we consider three classes of genetic oscillators: smooth oscillators (exhibiting sine-like oscillations), relaxation oscillators (displaying jump dynamics), and stochastic oscillators (noise-induced oscillation). For every class, we further study two cases: with intercellular communication (including phase-attractive and repulsive coupling) and without communication between cells. We find that an ensemble of smooth oscillators has different synchronization phenomena from those in the case of relaxation oscillators, where noise plays a different but key role in synchronization. To show differences in synchronization between them, we make comparisons in many aspects. We also show that a population of genetic stochastic oscillators have their own synchronization mechanisms. In addition, we present interesting phenomena, e.g., for relaxation-type stochastic oscillators coupled to a quorum-sensing mechanism, different noise intensities can induce different periodic motions (i.e., inhomogeneous limit cycles).