Transcriptional control of noise in gene expression.
ABSTRACT: Cis-regulatory control of transcription is the dominant form of regulation of gene expression. Recent experimental results suggest that, in addition to the mean expression level, cell-to-cell variability might also be transcriptionally regulated. Here, we develop a stochastic model of transcriptional regulation that allows us to calculate closed-form analytical expressions for the mean and variance of the protein and mRNA distributions for an arbitrarily complex cis-regulatory motif. Our model allows us to investigate how noise may be transcriptionally regulated independently from the mean expression. We show that our approach is in excellent agreement with stochastic simulations and experiment, and leads to an experimentally testable formula for the noise in gene expression as a function of inducer-molecule concentrations.
Project description:Gene expression is subject to stochastic variation which leads to fluctuations in the rate of protein production. Recently, a study in yeast at a genomic scale showed that, in some cases, gene expression variability alters phenotypes while, in other cases, these remain unchanged despite fluctuations in the expression of other genes. These studies suggested that noise in gene expression is a physiologically relevant trait and, to prevent harmful stochastic variation in the expression levels of some genes, it can be subject to minimisation. However, the mechanisms for noise minimisation are still unclear. In the present work, we analysed how noise expression depends on the architecture of the cis-regulatory system, in particular on the number of regulatory binding sites. Using analytical calculations and stochastic simulations, we found that the fluctuation level in noise expression decreased with the number of regulatory sites when regulatory transcription factors interacted with only one other bound transcription factor. In contrast, we observed that there was an optimal number of binding sites when transcription factors interacted with many bound transcription factors. This finding suggested a new mechanism for preventing large fluctuations in the expression of genes which are sensitive to the concentration of regulators.
Project description:Gene expression is an intrinsically stochastic process. Fluctuations in transcription and translation lead to cell-to-cell variations in mRNA and protein levels affecting cellular function and cell fate. Here, using fluorescence time-lapse microscopy, we quantify noise dynamics in an artificial operon in Escherichia coli, which is based on the native operon of ColicinE2, a toxin. In the natural system, toxin expression is controlled by a complex regulatory network; upon induction of the bacterial SOS response, ColicinE2 is produced (cea gene) and released (cel gene) by cell lysis. Using this ColicinE2-based operon, we demonstrate that upon induction of the SOS response noise of cells expressing the operon is significantly lower for the (mainly) transcriptionally regulated gene cea compared to the additionally post-transcriptionally regulated gene cel. Likewise, we find that mutations affecting the transcriptional regulation by the repressor LexA do not significantly alter the population noise, whereas specific mutations to post-transcriptionally regulating units, strongly influence noise levels of both genes. Furthermore, our data indicate that global factors, such as the plasmid copy number of the operon encoding plasmid, affect gene expression noise of the entire operon. Taken together, our results provide insights on how noise in a native toxin-producing operon is controlled and underline the importance of post-transcriptional regulation for noise control in this system.
Project description:Gene expression noise arises from stochastic variation in the synthesis and degradation of mRNA and protein molecules and creates differences in protein numbers across populations of genetically identical cells. Such variability can lead to imprecision and reduced performance of both native and synthetic networks. In principle, gene expression noise can be controlled through the rates of transcription, translation and degradation, such that different combinations of those rates lead to the same protein concentrations but at different noise levels. Here, we present a "noise tuner" which allows orthogonal control over the transcription and the mRNA degradation rates by two different inducer molecules. Combining experiments with theoretical analysis, we show that in this system the noise is largely determined by the transcription rate, whereas the mean expression is determined by both the transcription rate and mRNA stability and can thus be decoupled from the noise. This noise tuner enables 2-fold changes in gene expression noise over a 5-fold range of mean protein levels. We demonstrated the efficacy of the noise tuner in a complex regulatory network by varying gene expression noise in the mating pathway of Saccharomyces cerevisiae, which allowed us to control the output noise and the mutual information transduced through the pathway. The noise tuner thus represents an effective tool of gene expression noise control, both to interrogate noise sensitivity of natural networks and enhance performance of synthetic circuits.
Project description:Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Thus, it is important to understand how regularity can emerge from noise. Here, we study the stochastic dynamics of a self-repressing gene with arbitrarily long or short response time. We find that when the mRNA and protein half-lives are approximately equal to the gene response time, fluctuations can induce relatively regular oscillations in the protein concentration. To gain insight into this phenomenon at the crossroads of determinism and stochasticity, we use an intermediate theoretical approach, based on a moment-closure approximation of the master equation, which allows us to take into account the binary character of gene activity. We thereby obtain differential equations that describe how nonlinearity can feed-back fluctuations into the mean-field equations to trigger oscillations. Finally, our results suggest that the self-repressing Hes1 gene circuit exploits this phenomenon to generate robust oscillations, inasmuch as its time constants satisfy precisely the conditions we have identified.
Project description:We present a data-driven approach to determine the memory kernel and random noise in generalized Langevin equations. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. We show that such an approximation can be constructed to arbitrarily high order and the resulting generalized Langevin dynamics can be embedded in an extended stochastic model without explicit memory. We demonstrate how to introduce the stochastic noise so that the second fluctuation-dissipation theorem is exactly satisfied. Results from several numerical tests are presented to demonstrate the effectiveness of the proposed method.
Project description:The process of transcription is highly stochastic leading to cell-to-cell variations and noise in gene expression levels. However, key essential genes have to be precisely expressed at the correct amount and time to ensure proper cellular development and function. Studies in yeast and bacterial systems have shown that gene expression noise decreases as mean expression levels increase, a relationship that is controlled by promoter DNA sequence. However, the function of distal cis-regulatory modules (CRMs), an evolutionary novelty of metazoans, in controlling transcriptional robustness and variability is poorly understood. In this study, we used live cell imaging of transfected reporters combined with a mathematical modelling and statistical inference scheme to quantify the function of conserved Msx1 CRMs and promoters in modulating single-cell real-time transcription rates in C2C12 mouse myoblasts. The results show that the mean expression-noise relationship is solely promoter controlled for this key pluripotency regulator. In addition, we demonstrate that CRMs modulate single-cell basal promoter rate distributions in a graded manner across a population of cells. This extends the rheostatic model of CRM action to provide a more detailed understanding of CRM function at single-cell resolution. We also identify a novel CRM transcriptional filter function that acts to reduce intracellular variability in transcription rates and show that this can be phylogenetically separable from rate modulating CRM activities. These results are important for understanding how the expression of key vertebrate developmental transcription factors is precisely controlled both within and between individual cells.
Project description:The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.
Project description:A major challenge in biology is that genetically identical cells in the same environment can display gene expression stochasticity (noise), which contributes to bet-hedging, drug tolerance, and cell-fate switching. The magnitude and timescales of stochastic fluctuations can depend on the gene regulatory network. Currently, it is unclear how gene expression noise of specific networks impacts the evolution of drug resistance in mammalian cells. Answering this question requires adjusting network noise independently from mean expression. Here, we develop positive and negative feedback-based synthetic gene circuits to decouple noise from the mean for Puromycin resistance gene expression in Chinese Hamster Ovary cells. In low Puromycin concentrations, the high-noise, positive-feedback network delays long-term adaptation, whereas it facilitates adaptation under high Puromycin concentration. Accordingly, the low-noise, negative-feedback circuit can maintain resistance by acquiring mutations while the positive-feedback circuit remains mutation-free and regains drug sensitivity. These findings may have profound implications for chemotherapeutic inefficiency and cancer relapse.
Project description:From observations of colloidal tracer particles in fibrin undergoing gelation, we introduce an analytical framework that allows the determination of the probability density function for a stochastic process beyond fractional Brownian motion. Using passive microrheology via videomicroscopy, mean square displacements of tracer particles suspended in fibrin at different ageing times are obtained. The anomalous diffusion is then described by a damped white noise process with memory, with analytical results closely matching experimental plots of mean square displacements and probability density function. We further show that the white noise functional stochastic approach applied to passive microrheology reveals the existence of a gelation parameter ? which elucidates the dynamics of constrained tracer particles embedded in a time-dependent soft material. In addition, we found that microstructural heterogeneity of particle environments decreases as the ageing time increases. This study offers experimental insights on the ageing of fibrin gels while presenting a white noise functional stochastic approach that could be applied to other systems exhibiting non-Markovian diffusive behavior.
Project description:Gene regulatory interactions are context dependent, active in some cellular states but not in others. Stochastic fluctuations, or 'noise', in gene expression propagate through active, but not inactive, regulatory links. Thus, correlations in gene expression noise could provide a noninvasive means to probe the activity states of regulatory links. However, global, 'extrinsic', noise sources generate correlations even without direct regulatory links. Here we show that single-cell time-lapse microscopy, by revealing time lags due to regulation, can discriminate between active regulatory connections and extrinsic noise. We demonstrate this principle mathematically, using stochastic modeling, and experimentally, using simple synthetic gene circuits. We then use this approach to analyze dynamic noise correlations in the galactose metabolism genes of Escherichia coli. We find that the CRPGalS-GalE feed-forward loop is inactive in standard conditions but can become active in a GalR mutant. These results show how noise can help analyze the context dependence of regulatory interactions in endogenous gene circuits.