Bistability in feedback circuits as a byproduct of evolution of evolvability

Noisy bistable dynamics in gene regulation can underlie stochastic switching and is demonstrated to be beneficial under fluctuating environments. It is not known, however, if fluctuating selection alone can result in bistable dynamics. Using a stochastic model of simple feedback networks, we apply fluctuating selection on gene expression and run in silico evolutionary simulations. We find that independent of the specific nature of the environment–fitness relationship, the main outcome of fluctuating selection is the evolution of increased evolvability in the network; system parameters evolve toward a nonlinear regime where phenotypic diversity is increased and small changes in genotype cause large changes in expression level. In the presence of noise, the evolution of increased nonlinearity results in the emergence and maintenance of bistability. Our results provide the first direct evidence that bistability and stochastic switching in a gene regulatory network can emerge as a mechanism to cope with fluctuating environments. They strongly suggest that such emergence occurs as a byproduct of evolution of evolvability and exploitation of noise by evolution.     

Internal noise enhanced oscillation in a delayed circadian pacemaker

The effect of internal noise in a delayed circadian oscillator is studied by using both chemical Langevin equations and stochastic normal form theory. It is found that internal noise can induce circadian oscillation even if the delay time τ is below the deterministic Hopf bifurcation τ_h. We use signal-to-noise ratio (SNR) to quantitatively characterize the performance of such noise induced oscillations and a threshold value of SNR is introduced to define the so-called effective oscillation. Interestingly, the τ-range for effective stochastic oscillation, denoted as Δτ_EO, shows a bell-shaped dependence on the intensity of internal noise which is inversely proportional to the system size. We have also investigated how the rates of synthesis and degradation of the clock protein influence the SNR and thus Δτ_EO. The decay rate K_d could significantly affect Δτ_EO, while varying the gene expression rate K_e has no obvious effect if K_e is not too small. Stochastic normal form analysis and numerical simulations are in good consistency with each other. This work provides us comprehensive understandings of how internal noise and time delay work cooperatively to influence the dynamics of circadian oscillations.     

System-size resonance for intracellular and intercellular calcium signaling

Dynamical behaviors of unidirectionally, linearly coupled as well as isolated calcium subsystems are investigated by taking into account the internal noise resulting from finite system size and thus small numbers of interacting molecules. For an isolated calcium system, the internal noise can induce stochastic oscillations for a steady state close to the Hopf-bifurcation point, and the regularity of those stochastic oscillations depends resonantly on the system size, exhibiting system-size resonance. For the coupled system consisting of two subsystems, the system-size resonance effect observed in the subsystem subject to coupling is significantly amplified due to the nontrivial effects of coupling.     

Adjusting phenotypes by noise control

Genetically identical cells can show phenotypic variability. This is often caused by stochastic events that originate from randomness in biochemical processes involving in gene expression and other extrinsic cellular processes. From an engineering perspective, there have been efforts focused on theory and experiments to control noise levels by perturbing and replacing gene network components. However, systematic methods for noise control are lacking mainly due to the intractable mathematical structure of noise propagation through reaction networks. Here, we provide a numerical analysis method by quantifying the parametric sensitivity of noise characteristics at the level of the linear noise approximation. Our analysis is readily applicable to various types of noise control and to different types of system; for example, we can orthogonally control the mean and noise levels and can control system dynamics such as noisy oscillations. As an illustration we applied our method to HIV and yeast gene expression systems and metabolic networks. The oscillatory signal control was applied to p53 oscillations from DNA damage. Furthermore, we showed that the efficiency of orthogonal control can be enhanced by applying extrinsic noise and feedback. Our noise control analysis can be applied to any stochastic model belonging to continuous time Markovian systems such as biological and chemical reaction systems, and even computer and social networks. We anticipate the proposed analysis to be a useful tool for designing and controlling synthetic gene networks.     

Stochastic S-system modeling of gene regulatory network

Microarray gene expression data can provide insights into biological processes at a system-wide level and is commonly used for reverse engineering gene regulatory networks (GRN). Due to the amalgamation of noise from different sources, microarray expression profiles become inherently noisy leading to significant impact on the GRN reconstruction process. Microarray replicates (both biological and technical), generated to increase the reliability of data obtained under noisy conditions, have limited influence in enhancing the accuracy of reconstruction . Therefore, instead of the conventional GRN modeling approaches which are deterministic, stochastic techniques are becoming increasingly necessary for inferring GRN from noisy microarray data. In this paper, we propose a new stochastic GRN model by investigating incorporation of various standard noise measurements in the deterministic S-system model. Experimental evaluations performed for varying sizes of synthetic network, representing different stochastic processes, demonstrate the effect of noise on the accuracy of genetic network modeling and the significance of stochastic modeling for GRN reconstruction . The proposed stochastic model is subsequently applied to infer the regulations among genes in two real life networks: (1) the well-studied IRMA network, a real-life in-vivo synthetic network constructed within the Saccharomycescerevisiae yeast, and (2) the SOS DNA repair network in Escherichiacoli.     

生物钟体系中色噪音诱导的日夜节律振荡和内信号随机共振

利用脉孢菌生物钟体系,研究了色噪音对其进行诱导所产生的日夜节律振荡信号及其内信号随机共振的行为．结果表明,色噪音的相关时间对该体系内信号随机共振的强弱起较大的影响作用．当无外信号存在时,色噪音的相关时间对体系内信号随机共振强度起抑制的作用,且随相关时间的增大,抑制作用增强．当外信号加到体系中时,由于相关时间和外信号的协同作用,相关时间不仅对其内信号随机共振强度起抑制的作用,而且还影响内信号随机共振峰的数目,即随相关时间的增大,可使单峰随机共振变为随机双共振．存在最佳的外信号频率使体系的内信号随机共振强度得到最大的增强,而其他频率的外信号却起抑制作用．色内噪音和色外噪音相比,前者对该体系进行诱导所得的内信号随机共振强度比后者的更强,而且体系对前者更敏感．另外,存在极限的噪音强度使白噪音和色噪音对该体系内信号随机共振的影响差异得以消失．所得结果可为治疗生物钟紊乱综合症提供理论依据,同时可更好地理解其他节奏机理,如心脏搏动节奏、呼吸节奏以及荷尔蒙水平的波动节奏等．     

Stable stochastic dynamics in yeast cell cycle

Chemical reactions in cells are subject to intense stochastic fluctuations. An important question is how the fundamental physiological behavior of the cell is kept stable against those noisy perturbations. In this study, a stochastic model of the cell cycle of budding yeast was constructed to analyze the effects of noise on the cell-cycle oscillation. The model predicts intense noise in levels of mRNAs and proteins, and the simulated protein levels explain the observed statistical tendency of noise in populations of synchronous and asynchronous cells. Despite intense noise in levels of proteins and mRNAs, the cell cycle is stable enough to bring the largely perturbed cells back to the physiological cyclic oscillation. The model shows that consecutively appearing fixed points are the origin of this stability of the cell cycle.     

Noise-Induced Coherence and Network Oscillations in a Reduced Bursting Model

The dynamics of the Hindmarsh-Rose (HR) model of bursting thalamic neurons is reduced to a system of two linear differential equations that retains the subthreshold resonance properties of the HR model. Introducing a reset mechanism after a threshold crossing, we turn this system into a resonant integrate-and-fire (RIF) model. Using Monte-Carlo simulations and mathematical analysis, we examine the effects of noise and the subthreshold dynamic properties of the RIF model on the occurrence of coherence resonance (CR). Synchronized burst firing occurs in a network of such model neurons with excitatory pulse-coupling. The coherence level of the network oscillations shows a stochastic resonance-like dependence on the noise level. Stochastic analysis of the equations shows that the slow recovery from the spike-induced inhibition is crucial in determining the frequencies of the CR and the subthreshold resonance in the original HR model. In this particular type of CR, the oscillation frequency strongly depends on the intrinsic time scales but changes little with the noise intensity. We give analytical quantities to describe this CR mechanism and illustrate its influence on the emerging network oscillations. We discuss the profound physiological roles this kind of CR may have in information processing in neurons possessing a subthreshold resonant frequency and in generating synchronized network oscillations with a frequency that is determined by intrinsic properties of the neurons. PACS 05.45.-a, 05.40.Ca, 87.18.Sn, 87.19     

Toward a Rosetta stone for the stem cell genome: Stochastic gene expression, network architecture, and external influences

We review literature relating to three types of factors known to influence stem cell behavior. These factors are stochastic gene expression, regulatory network architecture, and the influence of external signals, such as those emanating from the niche. Although these factors are considered separately, their shared evolutionary history necessitates integration. Stochastic gene expression pervades network components; network architecture controls, modulates, or exploits this noise while performing additional computation; and such complexity also interplays with factors external to cells. Adequate understanding of each of these components, and how they interact, will lead to a conceptual model of the stem cell regulatory system that can be used to drive hypothesis-driven research and facilitate interpretation of experimental data.     

Single effective neuron: dendritic coupling effects and stochastic resonance

We consider a model of a neuron coupled with a surrounding dendritic network subject to Langevin noise and a weak periodic modulation. Through an adiabatic elimination procedure, the single-neuron dynamics are extracted from the coupled stochastic differential equations describing the network of dendrodendritic interactions.Our approach yields areduced neuron model whose dynamics may correspond to neurophysiologically realistic behavior for certain ranges of soma and bath parameters. Cooperative effects (e.g., stochastic resonance) arising from the interplay between the noise and modulation are discussed in detail.     

Stochastic Simulation of Delay-Induced Circadian Rhythms in Drosophila

Circadian rhythms are ubiquitous in all eukaryotes and some prokaryotes. Several computational models with or without time delays have been developed for circadian rhythms. Exact stochastic simulations have been carried out for several models without time delays, but no exact stochastic simulation has been done for models with delays. In this paper, we proposed a detailed and a reduced stochastic model with delays for circadian rhythms in Drosophila based on two deterministic models of Smolen et al. and employed exact stochastic simulation to simulate circadian oscillations. Our simulations showed that both models can produce sustained oscillations and that the oscillation is robust to noise in the sense that there is very little variability in oscillation period although there are significant random fluctuations in oscillation peeks. Moreover, although average time delays are essential to simulation of oscillation, random changes in time delays within certain range around fixed average time delay cause little variability in the oscillation period. Our simulation results also showed that both models are robust to parameter variations and that oscillation can be entrained by light/dark circles. Our simulations further demonstrated that within a reasonable range around the experimental result, the rates that dclock and per promoters switch back and forth between activated and repressed sites have little impact on oscillation period.     

Spatial coherence resonance in excitable biochemical media induced by internal noise

We show that in a spatially extended excitable medium, presently modelled with diffusively coupled FitzHugh-Nagumo neurons, internal stochasticity is able to extract a characteristic spatial frequency of waves on the spatial grid. Internal noise is introduced via a stochastic simulation method and is the only agent acting on the system. Remarkably, the spatial periodicity is best pronounced at an intermediate level of internal stochasticity. Thus, the reported phenomenon is an observation of internal noise spatial coherence resonance in excitable biochemical media.     

Quantifying Stochastic Noise in Cultured Circadian Reporter Cells

Stochastic noise at the cellular level has been shown to play a fundamental role in circadian oscillations, influencing how groups of cells entrain to external cues and likely serving as the mechanism by which cell-autonomous rhythms are generated. Despite this importance, few studies have investigated how clock perturbations affect stochastic noise—even as increasing numbers of high-throughput screens categorize how gene knockdowns or small molecules can change clock period and amplitude. This absence is likely due to the difficulty associated with measuring cell-autonomous stochastic noise directly, which currently requires the careful collection and processing of single-cell data. In this study, we show that the damping rate of population-level bioluminescence recordings can serve as an accurate measure of overall stochastic noise, and one that can be applied to future and existing high-throughput circadian screens. Using cell-autonomous fibroblast data, we first show directly that higher noise at the single-cell results in faster damping at the population level. Next, we show that the damping rate of cultured cells can be changed in a dose-dependent fashion by small molecule modulators, and confirm that such a change can be explained by single-cell noise using a mathematical model. We further demonstrate the insights that can be gained by applying our method to a genome-wide siRNA screen, revealing that stochastic noise is altered independently from period, amplitude, and phase. Finally, we hypothesize that the unperturbed clock is highly optimized for robust rhythms, as very few gene perturbations are capable of simultaneously increasing amplitude and lowering stochastic noise. Ultimately, this study demonstrates the importance of considering the effect of circadian perturbations on stochastic noise, particularly with regard to the development of small-molecule circadian therapeutics.     

Noise enhances subthreshold oscillations in injured primary sensory neurons

Noise can play a constructive role in the detection of weak signals in various kinds of peripheral receptors and neurons. What the mechanism underlying the effect of noise is remains unclear. Here, the perforated patch-clamp technique was used on isolated cells from chronic compression of the dorsal root ganglion (DRG) model. Our data provided new insight indicating that, under conditions without external signals, noise can enhance subthreshold oscillations, which was observed in a certain type of neurons with high-frequency (20-100 Hz) intrinsic resonance from injured DRG neurons. The occurrence of subthreshold oscillation considerably decreased the threshold potential for generating repetitive firing. The above effects of noise can be abolished by blocking the persistent sodium current (I(Na, P)). Utilizing a mathematical neuron model we further simulated the effect of noise on subthreshold oscillation and firing, and also found that noise can enhance the electrical activity through autonomous stochastic resonance. Accordingly, we propose a new concept of the effects of noise on neural intrinsic activity, which suggests that noise may be an important factor for modulating the excitability of neurons and generation of chronic pain signals.     

Stochastic resonance induced by fluctuation in liquid membrane oscillator without input signals

We investigated numerically the dynamic behavior of the oil/water liquid membrane, which is a promising model for excitable bio-membrane. When we use noise to modulate the parameters in simulation, noise-induced coherent oscillation is observed. With the increment of the noise intensity, the coherence of noise-induced oscillation can go through a maximum, which indicating the occurrence of stochastic resonance (SR) without input signals. We compared the SR effects under the condition that noise is added to different control parameters. When noise was added to both of the parameters, a complicated SR-like phenomemon was observed. The interaction of coherent SRs induced by two independent noises is discussed. The possibly constructive role of noise in some sensory cells is discussed also.