Extrinsic noise passing through a Michaelis-Menten reaction: A universal response of a genetic switch

The study of biochemical pathways usually focuses on a small section of a protein interactions network. Two distinct sources contribute to the noise in such a system: intrinsic noise, inherent in the studied reactions, and extrinsic noise generated in other parts of the network or in the environment. We study the effect of extrinsic noise entering the system through a nonlinear uptake reaction which acts as a nonlinear filter. Varying input noise intensity varies the mean of the noise after the passage through the filter, which changes the stability properties of the system. The steady-state displacement due to small noise is independent on the kinetics of the system but it only depends on the nonlinearity of the input function.For monotonically increasing and concave input functions such as the Michaelis-Menten uptake rate, we give a simple argument based on the small-noise expansion, which enables qualitative predictions of the steady-state displacement only by inspection of experimental data: when weak and rapid noise enters the system through a Michaelis-Menten reaction, then the graph of the system's steady states vs. the mean of the input signal always shifts to the right as noise intensity increases.We test the predictions on two models of lac operon, where TMG/lactose uptake is driven by a Michaelis-Menten enzymatic process. We show that as a consequence of the steady state displacement due to fluctuations in extracellular TMG/lactose concentration the lac switch responds in an asymmetric manner: as noise intensity increases, switching off lactose metabolism becomes easier and switching it on becomes more difficult.     

Subpopulations of sensorless bacteria drive fitness in fluctuating environments

Populations of bacteria often undergo a lag in growth when switching conditions. Because growth lags can be large compared to typical doubling times, variations in growth lag are an important but often overlooked component of bacterial fitness in fluctuating environments. We here explore how growth lag variation is determined for the archetypical switch from glucose to lactose as a carbon source in Escherichia coli. First, we show that single-cell lags are bimodally distributed and controlled by a single-molecule trigger. That is, gene expression noise causes the population before the switch to divide into subpopulations with zero and nonzero lac operon expression. While “sensorless” cells with zero preexisting lac expression at the switch have long lags because they are unable to sense the lactose signal, any nonzero lac operon expression suffices to ensure a short lag. Second, we show that the growth lag at the population level depends crucially on the fraction of sensorless cells and that this fraction in turn depends sensitively on the growth condition before the switch. Consequently, even small changes in basal expression can significantly affect the fraction of sensorless cells, thereby population lags and fitness under switching conditions, and may thus be subject to significant natural selection. Indeed, we show that condition-dependent population lags vary across wild E. coli isolates. Since many sensory genes are naturally low expressed in conditions where their inducer is not present, bimodal responses due to subpopulations of sensorless cells may be a general mechanism inducing phenotypic heterogeneity and controlling population lags in switching environments. This mechanism also illustrates how gene expression noise can turn even a simple sensory gene circuit into a bet hedging module and underlines the profound role of gene expression noise in regulatory responses.

Is ignorance bliss for some bacterial cells? Single-cell analysis of the archetypical switch from glucose to lactose as a carbon source in E. coli shows that bacteria can exhibit stochastic bimodal responses to external stimuli because the corresponding sensory circuit is so lowly expressed that some cells are effectively blind to the stimulus.     

Memory and Fitness Optimization of Bacteria under Fluctuating Environments

Bacteria prudently regulate their metabolic phenotypes by sensing the availability of specific nutrients, expressing the required genes for their metabolism, and repressing them after specific metabolites are depleted. It is unclear, however, how genetic networks maintain and transmit phenotypic states between generations under rapidly fluctuating environments. By subjecting bacteria to fluctuating carbon sources (glucose and lactose) using microfluidics, we discover two types of non-genetic memory in Escherichia coli and analyze their benefits. First, phenotypic memory conferred by transmission of stable intracellular lac proteins dramatically reduces lag phases under cyclical fluctuations with intermediate timescales (1–10 generations). Second, response memory, a hysteretic behavior in which gene expression persists after removal of its external inducer, enhances adaptation when environments fluctuate over short timescales (<1 generation). Using a mathematical model we analyze the benefits of memory across environmental fluctuation timescales. We show that memory mechanisms provide an important class of survival strategies in biology that improve long-term fitness under fluctuating environments. These results can be used to understand how organisms adapt to fluctuating levels of nutrients, antibiotics, and other environmental stresses.     

Population models in a periodically fluctuating environment

Summary We investigate the behavior of population models in the presence of a periodically fluctuating environment. We consider in particular single-species models and models of interspecific competition. It is shown that the fluctuations cause constant equilibrium states to be replaced by periodic equilibrium states, with a shift in the mean value relative to the constant-environment state. It is shown also that the locations of points of exchange of stability may be changed as a result of the fluctuations.     

Dip listening or modulation masking? Call recognition by green treefrogs (Hyla cinerea) in temporally fluctuating noise

Despite the importance of perceptually separating signals from background noise, we still know little about how nonhuman animals solve this problem. Dip listening, an ability to catch meaningful ‘acoustic glimpses’ of a target signal when fluctuating background noise levels momentarily drop, constitutes one possible solution. Amplitude-modulated noises, however, can sometimes impair signal recognition through a process known as modulation masking. We asked whether fluctuating noise simulating a breeding chorus affects the ability of female green treefrogs (Hyla cinerea) to recognize male advertisement calls. Our analysis of recordings of the sounds of green treefrog choruses reveal that their levels fluctuate primarily at rates below 10?Hz. In laboratory phonotaxis tests, we found no evidence for dip listening or modulation masking. Mean signal recognition thresholds in the presence of fluctuating chorus-like noises were never statistically different from those in the presence of a non-fluctuating control. An analysis of statistical effects sizes indicates that masker fluctuation rates, and the presence versus absence of fluctuations, had negligible effects on subject behavior. Together, our results suggest that females listening in natural settings should receive no benefits, nor experience any additional constraints, as a result of level fluctuations in the soundscape of green treefrog choruses.     

The role of migration in the evolution of phenotypic switching

Stochastic switching is an example of phenotypic bet hedging, where an individual can switch between different phenotypic states in a fluctuating environment. Although the evolution of stochastic switching has been studied when the environment varies temporally, there has been little theoretical work on the evolution of phenotypic switching under both spatially and temporally fluctuating selection pressures. Here, we explore the interaction of temporal and spatial change in determining the evolutionary dynamics of phenotypic switching. We find that spatial variation in selection is important; when selection pressures are similar across space, migration can decrease the rate of switching, but when selection pressures differ spatially, increasing migration between demes can facilitate the evolution of higher rates of switching. These results may help explain the diverse array of non-genetic contributions to phenotypic variability and phenotypic inheritance observed in both wild and experimental populations.     

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

Background  

Bistability, 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.     

Metastable behavior in Markov processes with internal states

A perturbation framework is developed to analyze metastable behavior in stochastic processes with random internal and external states. The process is assumed to be under weak noise conditions, and the case where the deterministic limit is bistable is considered. A general analytical approximation is derived for the stationary probability density and the mean switching time between metastable states, which includes the pre exponential factor. The results are illustrated with a model of gene expression that displays bistable switching. In this model, the external state represents the number of protein molecules produced by a hypothetical gene. Once produced, a protein is eventually degraded. The internal state represents the activated or unactivated state of the gene; in the activated state the gene produces protein more rapidly than the unactivated state. The gene is activated by a dimer of the protein it produces so that the activation rate depends on the current protein level. This is a well studied model, and several model reductions and diffusion approximation methods are available to analyze its behavior. However, it is unclear if these methods accurately approximate long-time metastable behavior (i.e., mean switching time between metastable states of the bistable system). Diffusion approximations are generally known to fail in this regard.     

Analysis of noise in quorum sensing

Noise may play a pivotal role in gene circuit functionality, as demonstrated for the genetic switch in the bacterial phage lambda. Like the lambda switch, bacterial quorum sensing (QS) systems operate within a population and contain a bistable switching element, making it likely that noise plays a functional role in QS circuit operation. Therefore, a detailed analysis of the noise behavior of QS systems is needed. We have developed a set of tools generally applicable to the analysis of gene circuits, with an emphasis on investigations in the frequency domain (FD), that we apply here to the QS system in the marine bacterium Vibrio fischeri. We demonstrate that a tight coupling between exact stochastic simulation and FD analysis provides insights into the structure/function relationships in the QS circuit. Furthermore, we argue that a noise analysis is incomplete without consideration of the power spectral densities (PSDs) of the important molecular output signals. As an example we consider reversible reactions in the QS circuit, and show through analysis and exact stochastic simulation that these circuits make significant and dynamic modifications to the noise spectra. In particular, we demonstrate a "whitening" effect, which occurs as the noise is processed through these reversible reactions.     

Optimal resting-growth strategies of microbial populations in fluctuating environments

Bacteria spend most of their lifetime in non-growing states which allow them to survive extended periods of stress and starvation. When environments improve, they must quickly resume growth to maximize their share of limited nutrients. Cells with higher stress resistance often survive longer stress durations at the cost of needing more time to resume growth, a strong disadvantage in competitive environments. Here we analyze the basis of optimal strategies that microorganisms can use to cope with this tradeoff. We explicitly show that the prototypical inverse relation between stress resistance and growth rate can explain much of the different types of behavior observed in stressed microbial populations. Using analytical mathematical methods, we determine the environmental parameters that decide whether cells should remain vegetative upon stress exposure, downregulate their metabolism to an intermediate optimum level, or become dormant. We find that cell-cell variability, or intercellular noise, is consistently beneficial in the presence of extreme environmental fluctuations, and that it provides an efficient population-level mechanism for adaption in a deteriorating environment. Our results reveal key novel aspects of responsive phenotype switching and its role as an adaptive strategy in changing environments.     

Fluctuating Environments Maintain Genetic Diversity through Neutral Fitness Effects and Balancing Selection

Genetic variation is the raw material upon which selection acts. The majority of environmental conditions change over time and therefore may result in variable selective effects. How temporally fluctuating environments impact the distribution of fitness effects and in turn population diversity is an unresolved question in evolutionary biology. Here, we employed continuous culturing using chemostats to establish environments that switch periodically between different nutrient limitations and compared the dynamics of selection to static conditions. We used the pooled Saccharomyces cerevisiae haploid gene deletion collection as a synthetic model for populations comprising thousands of unique genotypes. Using barcode sequencing, we find that static environments are uniquely characterized by a small number of high-fitness genotypes that rapidly dominate the population leading to dramatic decreases in genetic diversity. By contrast, fluctuating environments are enriched in genotypes with neutral fitness effects and an absence of extreme fitness genotypes contributing to the maintenance of genetic diversity. We also identified a unique class of genotypes whose frequencies oscillate sinusoidally with a period matching the environmental fluctuation. Oscillatory behavior corresponds to large differences in short-term fitness that are not observed across long timescales pointing to the importance of balancing selection in maintaining genetic diversity in fluctuating environments. Our results are consistent with a high degree of environmental specificity in the distribution of fitness effects and the combined effects of reduced and balancing selection in maintaining genetic diversity in the presence of variable selection.     

Positive feedback exists and drives the glucose-mediated repression in Escherichia coli

The expression of the lac operon of E. coli is subject to positive feedback during growth in the presence of gratuitous inducers, but its existence in the presence of lactose remains controversial. The key question in this debate is: Do the lactose enzymes, Lac permease and β-galactosidase, promote accumulation of allolactose? If so, positive feedback exists since allolactose does stimulate synthesis of the lactose enzymes. Here, we addressed the above question by developing methods for determining the intracellular allolactose concentration as well as the kinetics of enzyme induction and dilution. We show that, during lac induction in the presence of lactose, the intracellular allolactose concentration increases with the lactose enzyme level, which implies that lactose enzymes promote allolactose accumulation, and positive feedback exists. We also show that, during lac repression in the presence of lactose + glucose, the intracellular allolactose concentration decreases with the lactose enzyme levels, which suggests that, under these conditions, the positive feedback loop turns in the reverse direction. The induction and dilution rates derived from the transient data show that the positive feedback loop is reversed due to a radical shift of the steady-state induction level. This is formally identical to the mechanism driving catabolite repression in the presence of TMG + glucose.     

Predicting population genetic change in an autocorrelated random environment: Insights from a large automated experiment

Most natural environments exhibit a substantial component of random variation, with a degree of temporal autocorrelation that defines the color of environmental noise. Such environmental fluctuations cause random fluctuations in natural selection, affecting the predictability of evolution. But despite long-standing theoretical interest in population genetics in stochastic environments, there is a dearth of empirical estimation of underlying parameters of this theory. More importantly, it is still an open question whether evolution in fluctuating environments can be predicted indirectly using simpler measures, which combine environmental time series with population estimates in constant environments. Here we address these questions by using an automated experimental evolution approach. We used a liquid-handling robot to expose over a hundred lines of the micro-alga Dunaliella salina to randomly fluctuating salinity over a continuous range, with controlled mean, variance, and autocorrelation. We then tracked the frequencies of two competing strains through amplicon sequencing of nuclear and choloroplastic barcode sequences. We show that the magnitude of environmental fluctuations (determined by their variance), but also their predictability (determined by their autocorrelation), had large impacts on the average selection coefficient. The variance in frequency change, which quantifies randomness in population genetics, was substantially higher in a fluctuating environment. The reaction norm of selection coefficients against constant salinity yielded accurate predictions for the mean selection coefficient in a fluctuating environment. This selection reaction norm was in turn well predicted by environmental tolerance curves, with population growth rate against salinity. However, both the selection reaction norm and tolerance curves underestimated the variance in selection caused by random environmental fluctuations. Overall, our results provide exceptional insights into the prospects for understanding and predicting genetic evolution in randomly fluctuating environments.     

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.