Zhanjiang Yuan

Noise-induced switches in network systems of the genetic toggle switch

BackgroundBistability, the capacity to achieve two distinct stable steady states in response to a set of external stimuli, arises within biological systems ranging from the λ phage switch in bacteria to cellular signal transduction pathways in mammalian cells. On the other hand, more and more experimental evidence in the form of bimodal population distribution has indicated that noise plays a very important role in the switching of bistable systems. However, the physiological mechanism underling noise-induced switching behaviors remains to be fully understood.ResultsIn this paper, we investigate the effect of noises on switching in single and coupled genetic toggle switch systems in Escherichia coli. In the case of the single toggle switch, we show that the multiplicative noises resulting from stochastic fluctuations in degradation rates can induce switching. In the case of the toggle switches interfaced by a quorum-sensing signaling pathway, we find that stochastic fluctuations in degradation rates inside cells, i.e., intracellular noises, can induce synchronized switching, whereas the extracellular noise additive to the common medium can not only entrain all the individual systems to switch in a synchronous manner but also enhance this ordering behavior efficiently, leading a robust collective rhythm in this interacting system.ConclusionThese insights on the effect of noises would be beneficial to understanding the basic mechanism of how living systems optimally facilitate to function under various fluctuated environments.

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).

Effects of promoter leakage on dynamics of gene expression

BackgroundQuantitative analysis of simple molecular networks is an important step forward understanding fundamental intracellular processes. As network motifs occurring recurrently in complex biological networks, gene auto-regulatory circuits have been extensively studied but gene expression dynamics remain to be fully understood, e.g., how promoter leakage affects expression noise is unclear.ResultsIn this work, we analyze a gene model with auto regulation, where the promoter is assumed to have one active state with highly efficient transcription and one inactive state with very lowly efficient transcription (termed as promoter leakage). We first derive the analytical distribution of gene product, and then analyze effects of promoter leakage on expression dynamics including bursting kinetics. Interestingly, we find that promoter leakage always reduces expression noise and that increasing the leakage rate tends to simplify phenotypes. In addition, higher leakage results in fewer bursts.ConclusionsOur results reveal the essential role of promoter leakage in controlling expression dynamics and further phenotype. Specifically, promoter leakage is a universal mechanism of reducing expression noise, controlling phenotypes in different environments and making the gene produce generate fewer bursts.

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.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.

Architecture-Dependent Robustness and Bistability in a Class of Genetic Circuits

Understanding the relationship between genotype and phenotype is a challenge in systems biology. An interesting yet related issue is why a particular circuit topology is present in a cell when the same function can supposedly be obtained from an alternative architecture. Here we analyzed two topologically equivalent genetic circuits of coupled positive and negative feedback loops, named NAT and ALT circuits, respectively. The computational search for the oscillation volume of the entire biologically reasonable parameter region through large-scale random samplings shows that the NAT circuit exhibits a distinctly larger fraction of the oscillatory region than the ALT circuit. Such a global robustness difference between two circuits is supplemented by analyzing local robustness, including robustness to parameter perturbations and to molecular noise. In addition, detailed dynamical analysis shows that the molecular noise of both circuits can induce transient switching of the different mechanism between a stable steady state and a stable limit cycle. Our investigation on robustness and dynamics through examples provides insights into the relationship between network architecture and its function.

Physical limits of feedback noise-suppression in biological networks

Feedback is a ubiquitous control mechanism of biological networks, and has also been identified in a variety of regulatory systems and organisms. It has been shown that, for a given gain and with negligible intrinsic noise, negative feedback impairs noise buffering whereas positive feedback enhances noise buffering. We further investigate the influence of negative and positive feedback on noise in output signals by considering both intrinsic and extrinsic noise as well as operator noise. We find that, while maintaining the system sensitivity, either there exists a minimum of the output noise intensity corresponding to a biologically feasible feedback strength, or the output noise intensity is a monotonic function of feedback strength bounded by both biological and dynamical constraints. In both cases, feedback noise-suppression is physically limited. In other words, noise suppressed by negative or positive feedback cannot be reduced without limitation even in the case of slow transcription.

External Stimuli Mediate Collective Rhythms: Artificial Control Strategies

The artificial intervention of biological rhythms remains an exciting challenge. Here, we proposed artificial control strategies that were developed to mediate the collective rhythms emerging in multicellular structures. Based on noisy repressilators and by injecting a periodic control amount to the extracellular medium, we introduced two typical kinds of control models. In one, there are information exchanges among cells, where signaling molecules receive the injected stimulus that freely diffuses toward/from the intercellular medium. In the other, there is no information exchange among cells, but signaling molecules also receive the stimulus that directionally diffuses into each cell from the common environment. We uncovered physical mechanisms for how the stimulus induces, enhances or ruins collective rhythms. We found that only when the extrinsic period is close to an integer multiplicity of the averaged intrinsic period can the collective behaviors be induced/enhanced; otherwise, the stimulus possibly ruins the achieved collective behaviors. Such entrainment properties of these oscillators to external signals would be exploited by realistic living cells to sense external signals. Our results not only provide a new perspective to the understanding of the interplays between extrinsic stimuli and intrinsic physiological rhythms, but also would lead to the development of medical therapies or devices.

Decomposition and tunability of expression noise in the presence of coupled feedbacks

Expression noise results in cell-to-cell variability in expression levels, and feedback regulation may complicate the tracing of sources of this noise. Using a representative model of gene expression with feedbacks, we analytically show that the expression noise (or the total noise) is decomposed into three parts: feedback-dependent promoter noise determined by a continuous approximation, birth-death noise determined by a simple Poisson process, and correlation noise induced by feedbacks. We clarify confused relationships between feedback and noise in previous studies, by showing that feedback-regulated noisy sources have different contributions to the total noise in different cases of promoter switching (it is an essential reason resulting in confusions). More importantly, we find that there is a tradeoff between response time and expression noise. In addition, we show that in contrast to single feedbacks, coupled positive and negative feedbacks can perform better in tuning expression noise, controlling expression levels, and maintaining response time. The overall analysis implies that living organisms would utilize coupled positive and negative feedbacks for better survival in complex and fluctuating environments.

Mechanisms of information decoding in a cascade system of gene expression.

Biotechnology advances have allowed investigation of heterogeneity of cellular responses to stimuli on the single-cell level. Functionally, this heterogeneity can compromise cellular responses to environmental signals, and it can also enlarge the repertoire of possible cellular responses and hence increase the adaptive nature of cellular behaviors. However, the mechanism of how this response heterogeneity is generated remains elusive. Here, by systematically analyzing a representative cellular signaling system, we show that (1) the upstream activator always amplifies the downstream burst frequency (BF) but the noiseless activator performs better than the noisy one, remarkably for small or moderate input signal strengths, and the repressor always reduces the downstream BF but the difference in the reducing effect between noiseless and noise repressors is very small; (2) both the downstream burst size and mRNA mean are a monotonically increasing function of the activator strength but a monotonically decreasing function of the repressor strength; (3) for repressor-type input, there is a noisy signal strength such that the downstream mRNA noise arrives at an optimal level, but for activator-type input, the output noise intensity is fundamentally a monotonically decreasing function of the input strength. Our results reveal the essential mechanisms of both signal information decoding and cellular response heterogeneity, whereas our analysis provides a paradigm for analyzing dynamics of noisy biochemical signaling systems.