Nonidentifiability of the source of intrinsic noise in gene expression from single-burst data

Estimates of differential toxin expression governing heterogeneous intracellular lifespans of Streptococcus pneumoniae

Following invasion of the host cell, pore-forming toxins secreted by pathogens compromise vacuole integrity and expose the microbe to diverse intracellular defence mechanisms. However, the quantitative correlation between toxin expression levels and consequent pore dynamics, fostering the intracellular life of pathogens, remains largely unexplored. In this study, using Streptococcus pneumoniae and its secreted pore-forming toxin pneumolysin (Ply) as a model system, we explored various facets of host-pathogen interactions in the host cytosol. Using time-lapse fluorescence imaging, we monitored pore formation dynamics and lifespans of different pneumococcal subpopulations inside host cells. Based on experimental histograms of various event timescales such as pore formation time, vacuolar death or cytosolic escape time and total degradation time, we developed a mathematical model based on first-passage processes that could correlate the event timescales to intravacuolar toxin accumulation. This allowed us to estimate Ply production rate, burst size and threshold Ply quantities that trigger these outcomes. Collectively, we present a general method that illustrates a correlation between toxin expression levels and pore dynamics, dictating intracellular lifespans of pathogens.

Pathway dynamics can delineate the sources of transcriptional noise in gene expression

Single-cell expression profiling opens up new vistas on cellular processes. Extensive cell-to-cell variability at the transcriptomic and proteomic level has been one of the stand-out observations. Because most experimental analyses are destructive we only have access to snapshot data of cellular states. This loss of temporal information presents significant challenges for inferring dynamics, as well as causes of cell-to-cell variability. In particular, we typically cannot separate dynamic variability from within cells ('intrinsic noise') from variability across the population ('extrinsic noise'). Here, we make this non-identifiability mathematically precise, allowing us to identify new experimental set-ups that can assist in resolving this non-identifiability. We show that multiple generic reporters from the same biochemical pathways (e.g. mRNA and protein) can infer magnitudes of intrinsic and extrinsic transcriptional noise, identifying sources of heterogeneity. Stochastic simulations support our theory, and demonstrate that 'pathway-reporters' compare favourably to the well-known, but often difficult to implement, dual-reporter method.

Protein hourglass: Exact first passage time distributions for protein thresholds

Protein thresholds have been shown to act as an ancient timekeeping device, such as in the time to lysis of Escherichia coli infected with bacteriophage λ. The time taken for protein levels to reach a particular threshold for the first time is defined as the first passage time (FPT) of the protein synthesis system, which is a stochastic quantity. The first few moments of the distribution of first passage times were known earlier, but an analytical expression for the full distribution was not available. In this work, we derive an analytical expression for the first passage times for a long-lived protein. This expression allows us to calculate the full distribution not only for cases of no self-regulation, but also for both positive and negative self-regulation of the threshold protein. We show that the shape of the distribution matches previous experimental data on λ-phage lysis time distributions. We also provide analytical expressions for the FPT distribution with non-zero degradation in Laplace space. Furthermore, we study the noise in the precision of the first passage times described by coefficient of variation (CV) of the distribution as a function of the protein threshold value. We show that under conditions of positive self-regulation, the CV declines monotonically with increasing protein threshold, while under conditions of linear negative self-regulation, there is an optimal protein threshold that minimizes the noise in the first passage times.

Extrinsic Noise and Heavy-Tailed Laws in Gene Expression

Noise in gene expression is one of the hallmarks of life at the molecular scale. Here we derive analytical solutions to a set of models describing the molecular mechanisms underlying transcription of DNA into RNA. Our ansatz allows us to incorporate the effects of extrinsic noise-encompassing factors external to the transcription of the individual gene-and discuss the ramifications for heterogeneity in gene product abundance that has been widely observed in single cell data. Crucially, we are able to show that heavy-tailed distributions of RNA copy numbers cannot result from the intrinsic stochasticity in gene expression alone, but must instead reflect extrinsic sources of variability.

Modulation of first-passage time for bursty gene expression via random signals

The stochastic nature of cell-specific signal molecules (such as transcription factor, ribosome, etc.) and the intrinsic stochastic nature of gene expression process result in cell-to-cell variations at protein levels. Increasing experimental evidences suggest that cell phenotypic variations often depend on the accumulation of some special proteins. Hence, a natural and fundamental question is: How does input signal affect the timing of protein count up to a given threshold? To this end, we study effects of input signal on the first-passage time (FPT), the time at which the number of proteins crosses a given threshold. Input signal is distinguished into two types: constant input signal and random input signal, regulating only burst frequency (or burst size) of gene expression. Firstly, we derive analytical formulae for FPT moments in each case of constant signal regulation and random signal regulation. Then, we find that random input signal tends to increases the mean and noise of FPT compared with constant input signal. Finally, we observe that different regulation ways of random signal have different effects on FPT, that is, burst size modulation tends to decrease the mean of FPT and increase the noise of FPT compared with burst frequency modulation. Our findings imply a fundamental mechanism that random fluctuating environment may prolong FPT. This can provide theoretical guidance for studies of some cellular key events such as latency of HIV and lysis time of bacteriophage λ. In conclusion, our results reveal impacts of external signal on FPT and aid understanding the regulation mechanism of gene expression.

An efficient and assumption-free method to approximate protein level distribution in the two-states gene expression model

Stochastic fluctuations at each step of gene expression might influence protein levels distributions across cell populations. However, current methods to model protein distribution of intrinsic gene expression dynamics are either computationally inefficient or rely on ad hoc assumptions, e.g., that the gene is always active. Taking advantage of the simple form of lower-order moments of distribution, we developed an efficient and assumption-free protein distribution approximation method (EFPD), for the two state gene expression model to accurately approximate the distribution. By EFPD, we computed nearly identical intensity of gene expression regulation at mRNA and protein level, implying a profound link between transcription and translation. Finally, by extending EFPD to approximate the distribution of protein level at any arbitrary temporal state, we proposed an explanation for the role of stochastic noise in gene expression in the context of a continuously changing environment. EFPD can be a powerful tool for modeling the particular molecular mechanisms of targeted gene expression pattern.

Control mechanisms for stochastic biochemical systems via computation of reachable sets

Controlling the behaviour of cells by rationally guiding molecular processes is an overarching aim of much of synthetic biology. Molecular processes, however, are notoriously noisy and frequently nonlinear. We present an approach to studying the impact of control measures on motifs of molecular interactions that addresses the problems faced in many biological systems: stochasticity, parameter uncertainty and nonlinearity. We show that our reachability analysis formalism can describe the potential behaviour of biological (naturally evolved as well as engineered) systems, and provides a set of bounds on their dynamics at the level of population statistics: for example, we can obtain the possible ranges of means and variances of mRNA and protein expression levels, even in the presence of uncertainty about model parameters.

Information processing by simple molecular motifs and susceptibility to noise

Biological organisms rely on their ability to sense and respond appropriately to their environment. The molecular mechanisms that facilitate these essential processes are however subject to a range of random effects and stochastic processes, which jointly affect the reliability of information transmission between receptors and, for example, the physiological downstream response. Information is mathematically defined in terms of the entropy; and the extent of information flowing across an information channel or signalling system is typically measured by the 'mutual information', or the reduction in the uncertainty about the output once the input signal is known. Here, we quantify how extrinsic and intrinsic noise affects the transmission of simple signals along simple motifs of molecular interaction networks. Even for very simple systems, the effects of the different sources of variability alone and in combination can give rise to bewildering complexity. In particular, extrinsic variability is apt to generate 'apparent' information that can, in extreme cases, mask the actual information that for a single system would flow between the different molecular components making up cellular signalling pathways. We show how this artificial inflation in apparent information arises and how the effects of different types of noise alone and in combination can be understood.

Exploiting Natural Fluctuations to Identify Kinetic Mechanisms in Sparsely Characterized Systems

From biochemistry to ecology, many biological systems are stochastic, complex, and sparsely characterized. In such systems, each component may respond to changes in any directly or indirectly connected components, thus requiring knowledge of the whole to predict the dynamics of the parts. Here, we address this challenge by deriving relations between properties of fluctuations that only reflect local interactions between a subset of components but are invariant to all indirectly connected dynamics. This greatly reduces the number of assumptions when evaluating dynamic models experimentally. We illustrate the approach by revisiting systematic single-cell gene expression data, and we show that the observed fluctuations contradict the assumptions made in most published models of stochastic gene expression, even when accounting for the possibility of systematic experimental artifacts.

Transcriptional Bursting in Gene Expression: Analytical Results for General Stochastic Models

Gene expression in individual cells is highly variable and sporadic, often resulting in the synthesis of mRNAs and proteins in bursts. Such bursting has important consequences for cell-fate decisions in diverse processes ranging from HIV-1 viral infections to stem-cell differentiation. It is generally assumed that bursts are geometrically distributed and that they arrive according to a Poisson process. On the other hand, recent single-cell experiments provide evidence for complex burst arrival processes, highlighting the need for analysis of more general stochastic models. To address this issue, we invoke a mapping between general stochastic models of gene expression and systems studied in queueing theory to derive exact analytical expressions for the moments associated with mRNA/protein steady-state distributions. These results are then used to derive noise signatures, i.e. explicit conditions based entirely on experimentally measurable quantities, that determine if the burst distributions deviate from the geometric distribution or if burst arrival deviates from a Poisson process. For non-Poisson arrivals, we develop approaches for accurate estimation of burst parameters. The proposed approaches can lead to new insights into transcriptional bursting based on measurements of steady-state mRNA/protein distributions.

One of the fundamental problems in biology is understanding how phenotypic variations arise among individuals in a population. Recent research has shown that phenotypic variations can arise due to probabilistic cell-fate decisions driven by inherent randomness (noise) in the process of gene expression. One of the manifestations of such stochasticity in gene expression is the production of mRNAs and proteins in bursts. Bursting in gene expression is known to impact cell-fate in diverse systems ranging from latency in HIV-1 viral infections to cellular differentiation. Recent single-cell experiments provide evidence for complex arrival processes leading to bursting, however an analytical framework connecting such burst arrival processes with the corresponding higher moments of mRNA/protein distributions is currently lacking. We address this issue by invoking a mapping between general models of gene expression and systems studied in queueing theory. The framework developed and the results derived lead to new approaches for testing commonly used assumptions in modeling gene expression and for accurate estimation of burst parameters. Notably, the phenomenon of stochastic bursting has been observed in a wide range of disciplines ranging from neuroscience and finance to cell biology. The approaches developed and results obtained in this work will thus contribute towards quantitative characterization of burst processes in diverse systems of current interest.

A computational framework for analyzing stochasticity in gene expression

Stochastic fluctuations in gene expression give rise to distributions of protein levels across cell populations. Despite a mounting number of theoretical models explaining stochasticity in protein expression, we lack a robust, efficient, assumption-free approach for inferring the molecular mechanisms that underlie the shape of protein distributions. Here we propose a method for inferring sets of biochemical rate constants that govern chromatin modification, transcription, translation, and RNA and protein degradation from stochasticity in protein expression. We asked whether the rates of these underlying processes can be estimated accurately from protein expression distributions, in the absence of any limiting assumptions. To do this, we (1) derived analytical solutions for the first four moments of the protein distribution, (2) found that these four moments completely capture the shape of protein distributions, and (3) developed an efficient algorithm for inferring gene expression rate constants from the moments of protein distributions. Using this algorithm we find that most protein distributions are consistent with a large number of different biochemical rate constant sets. Despite this degeneracy, the solution space of rate constants almost always informs on underlying mechanism. For example, we distinguish between regimes where transcriptional bursting occurs from regimes reflecting constitutive transcript production. Our method agrees with the current standard approach, and in the restrictive regime where the standard method operates, also identifies rate constants not previously obtainable. Even without making any assumptions we obtain estimates of individual biochemical rate constants, or meaningful ratios of rate constants, in 91% of tested cases. In some cases our method identified all of the underlying rate constants. The framework developed here will be a powerful tool for deducing the contributions of particular molecular mechanisms to specific patterns of gene expression.

Proteins, the molecular machines encoded by our genes, serve essential roles in every living cell. Investigators were therefore surprised to find widely variable levels of a particular protein within populations of genetically identical cells. This variation in protein level, called stochasticity, arises from the chemical nature of the processes that underlie protein production. The “central dogma” of biology dictates that the DNA encoding a particular gene transmits information via RNA to molecular factories called ribosomes in order to create proteins. Each step in transcription and translation introduces some variation, or stochasticity, into the production of the protein. In the current work, we tackled how one might learn more about the machinery responsible for creating proteins by the character of the stochasticity in the central dogma process. We find that many different mechanisms can explain any given stochastic protein signature. Even though there were many explanations for any particular pattern of stochasticity, the set of explanations still inform on how a given gene creates its protein. Our mathematical and computational framework will permit others to better understand how the machinery that expresses genes works. This, in turn, will enable investigators to better predict how a given mutation is likely to affect gene expression.

Time scales in epigenetic dynamics and phenotypic heterogeneity of embryonic stem cells

A remarkable feature of the self-renewing population of embryonic stem cells (ESCs) is their phenotypic heterogeneity: Nanog and other marker proteins of ESCs show large cell-to-cell variation in their expression level, which should significantly influence the differentiation process of individual cells. The molecular mechanism and biological implication of this heterogeneity, however, still remain elusive. We address this problem by constructing a model of the core gene-network of mouse ESCs. The model takes account of processes of binding/unbinding of transcription factors, formation/dissolution of transcription apparatus, and modification of histone code at each locus of genes in the network. These processes are hierarchically interrelated to each other forming the dynamical feedback loops. By simulating stochastic dynamics of this model, we show that the phenotypic heterogeneity of ESCs can be explained when the chromatin at the Nanog locus undergoes the large scale reorganization in formation/dissolution of transcription apparatus, which should have the timescale similar to the cell cycle period. With this slow transcriptional switching of Nanog, the simulated ESCs fluctuate among multiple transient states, which can trigger the differentiation into the lineage-specific cell states. From the simulated transitions among cell states, the epigenetic landscape underlying transitions is calculated. The slow Nanog switching gives rise to the wide basin of ESC states in the landscape. The bimodal Nanog distribution arising from the kinetic flow running through this ESC basin prevents transdifferentiation and promotes the definite decision of the cell fate. These results show that the distribution of timescales of the regulatory processes is decisively important to characterize the fluctuation of cells and their differentiation process. The analyses through the epigenetic landscape and the kinetic flow on the landscape should provide a guideline to engineer cell differentiation.

Embryonic stem cells (ESCs) can proliferate indefinitely by keeping pluripotency, i.e., the ability to differentiate into any cell-lineage. ESCs, therefore, have been the focus of intense biological and medical interests. A remarkable feature of ESCs is their phenotypic heterogeneity: ESCs show large cell-to-cell fluctuation in the expression level of Nanog, which is a key factor to maintain pluripotency. Since Nanog regulates many genes in ESCs, this fluctuation should seriously affect individual cells when they start differentiation. In this paper we analyze this phenotypic fluctuation by simulating the stochastic dynamics of gene network in ESCs. The model takes account of the mutually interrelated processes of gene regulation such as binding/unbinding of transcription factors, formation/dissolution of transcription apparatus, and histone-code modification. We show the distribution of timescales of these processes is decisively important to characterize the dynamical behavior of the gene network, and that the slow formation/dissolution of transcription apparatus at the Nanog locus explains the observed large fluctuation of ESCs. The epigenetic landscapes are calculated based on the stochastic simulation, and the role of the phenotypic fluctuation in the differentiation process is analyzed through the landscape picture.

A hierarchical model of transcriptional dynamics allows robust estimation of transcription rates in populations of single cells with variable gene copy number

Motivation:cis-regulatory DNA sequence elements, such as enhancers and silencers, function to control the spatial and temporal expression of their target genes. Although the overall levels of gene expression in large cell populations seem to be precisely controlled, transcription of individual genes in single cells is extremely variable in real time. It is, therefore, important to understand how these cis-regulatory elements function to dynamically control transcription at single-cell resolution. Recently, statistical methods have been proposed to back calculate the rates involved in mRNA transcription using parameter estimation of a mathematical model of transcription and translation. However, a major complication in these approaches is that some of the parameters, particularly those corresponding to the gene copy number and transcription rate, cannot be distinguished; therefore, these methods cannot be used when the copy number is unknown.

Results: Here, we develop a hierarchical Bayesian model to estimate biokinetic parameters from live cell enhancer–promoter reporter measurements performed on a population of single cells. This allows us to investigate transcriptional dynamics when the copy number is variable across the population. We validate our method using synthetic data and then apply it to quantify the function of two known developmental enhancers in real time and in single cells.

Availability: Supporting information is submitted with the article.

Contact:d.j.woodcock@warwick.ac.uk

Supplementary information:Supplementary data are available at Bioinformatics online.

Evaluation of gene association methods for coexpression network construction and biological knowledge discovery

BACKGROUND

Constructing coexpression networks and performing network analysis using large-scale gene expression data sets is an effective way to uncover new biological knowledge; however, the methods used for gene association in constructing these coexpression networks have not been thoroughly evaluated. Since different methods lead to structurally different coexpression networks and provide different information, selecting the optimal gene association method is critical.

METHODS AND RESULTS

In this study, we compared eight gene association methods - Spearman rank correlation, Weighted Rank Correlation, Kendall, Hoeffding's D measure, Theil-Sen, Rank Theil-Sen, Distance Covariance, and Pearson - and focused on their true knowledge discovery rates in associating pathway genes and construction coordination networks of regulatory genes. We also examined the behaviors of different methods to microarray data with different properties, and whether the biological processes affect the efficiency of different methods.

CONCLUSIONS

We found that the Spearman, Hoeffding and Kendall methods are effective in identifying coexpressed pathway genes, whereas the Theil-sen, Rank Theil-Sen, Spearman, and Weighted Rank methods perform well in identifying coordinated transcription factors that control the same biological processes and traits. Surprisingly, the widely used Pearson method is generally less efficient, and so is the Distance Covariance method that can find gene pairs of multiple relationships. Some analyses we did clearly show Pearson and Distance Covariance methods have distinct behaviors as compared to all other six methods. The efficiencies of different methods vary with the data properties to some degree and are largely contingent upon the biological processes, which necessitates the pre-analysis to identify the best performing method for gene association and coexpression network construction.

Stochastic modeling of regulation of gene expression by multiple small RNAs

A wealth of new research has highlighted the critical roles of small noncoding RNAs (sRNAs) in diverse processes, such as quorum sensing and cellular responses to stress. The pathways controlling these processes often have a central motif composed of a master regulator protein whose expression is controlled by multiple sRNAs. However, the stochastic gene expression of a single target gene regulated by multiple sRNAs is currently not well understood. To address this issue, we analyze a stochastic model of regulation of gene expression by multiple sRNAs. For this model, we derive exact analytic results for the regulated protein distribution, including compact expressions for its mean and variance. The derived results provide insights into the roles of multiple sRNAs in fine-tuning the noise in gene expression. In particular, we show that, in contrast to regulation by a single sRNA, multiple sRNAs provide a mechanism for independently controlling the mean and variance of the regulated protein distribution.

Dynamics of protein noise can distinguish between alternate sources of gene-expression variability

Within individual cells, two molecular processes have been implicated as sources of noise in gene expression: (i) Poisson fluctuations in mRNA abundance arising from random birth and death of individual mRNA transcripts or (ii) promoter fluctuations arising from stochastic promoter transitions between different transcriptional states. Steady-state measurements of variance in protein levels are insufficient to discriminate between these two mechanisms, and mRNA single-molecule fluorescence in situ hybridization (smFISH) is challenging when cellular mRNA concentrations are high. Here, we present a perturbation method that discriminates mRNA birth/death fluctuations from promoter fluctuations by measuring transient changes in protein variance and that can operate in the regime of high molecular numbers. Conceptually, the method exploits the fact that transcriptional blockage results in more rapid increases in protein variability when mRNA birth/death fluctuations dominate over promoter fluctuations. We experimentally demonstrate the utility of this perturbation approach in the HIV-1 model system. Our results support promoter fluctuations as the primary noise source in HIV-1 expression. This study illustrates a relatively simple method that complements mRNA smFISH hybridization and can be used with existing GFP-tagged libraries to include or exclude alternate sources of noise in gene expression.

Connecting protein and mRNA burst distributions for stochastic models of gene expression

The intrinsic stochasticity of gene expression can lead to large variability in protein levels for genetically identical cells. Such variability in protein levels can arise from infrequent synthesis of mRNAs which in turn give rise to bursts of protein expression. Protein expression occurring in bursts has indeed been observed experimentally and recent studies have also found evidence for transcriptional bursting, i.e. production of mRNAs in bursts. Given that there are distinct experimental techniques for quantifying the noise at different stages of gene expression, it is of interest to derive analytical results connecting experimental observations at different levels. In this work, we consider stochastic models of gene expression for which mRNA and protein production occurs in independent bursts. For such models, we derive analytical expressions connecting protein and mRNA burst distributions which show how the functional form of the mRNA burst distribution can be inferred from the protein burst distribution. Additionally, if gene expression is repressed such that observed protein bursts arise only from single mRNAs, we show how observations of protein burst distributions (repressed and unrepressed) can be used to completely determine the mRNA burst distribution. Assuming independent contributions from individual bursts, we derive analytical expressions connecting means and variances for burst and steady-state protein distributions. Finally, we validate our general analytical results by considering a specific reaction scheme involving regulation of protein bursts by small RNAs. For a range of parameters, we derive analytical expressions for regulated protein distributions that are validated using stochastic simulations. The analytical results obtained in this work can thus serve as useful inputs for a broad range of studies focusing on stochasticity in gene expression.

Effect of promoter architecture on the cell-to-cell variability in gene expression

According to recent experimental evidence, promoter architecture, defined by the number, strength and regulatory role of the operators that control transcription, plays a major role in determining the level of cell-to-cell variability in gene expression. These quantitative experiments call for a corresponding modeling effort that addresses the question of how changes in promoter architecture affect variability in gene expression in a systematic rather than case-by-case fashion. In this article we make such a systematic investigation, based on a microscopic model of gene regulation that incorporates stochastic effects. In particular, we show how operator strength and operator multiplicity affect this variability. We examine different modes of transcription factor binding to complex promoters (cooperative, independent, simultaneous) and how each of these affects the level of variability in transcriptional output from cell-to-cell. We propose that direct comparison between in vivo single-cell experiments and theoretical predictions for the moments of the probability distribution of mRNA number per cell can be used to test kinetic models of gene regulation. The emphasis of the discussion is on prokaryotic gene regulation, but our analysis can be extended to eukaryotic cells as well.

Applications of Little's Law to stochastic models of gene expression

The intrinsic stochasticity of gene expression can lead to large variations in protein levels across a population of cells. To explain this variability, different sources of messenger RNA (mRNA) fluctuations ("Poisson" and "telegraph" processes) have been proposed in stochastic models of gene expression. Both Poisson and telegraph scenario models explain experimental observations of noise in protein levels in terms of "bursts" of protein expression. Correspondingly, there is considerable interest in establishing relations between burst and steady-state protein distributions for general stochastic models of gene expression. In this work, we address this issue by considering a mapping between stochastic models of gene expression and problems of interest in queueing theory. By applying a general theorem from queueing theory, Little's Law, we derive exact relations which connect burst and steady-state distribution means for models with arbitrary waiting-time distributions for arrival and degradation of mRNAs and proteins. The derived relations have implications for approaches to quantify the degree of transcriptional bursting and hence to discriminate between different sources of intrinsic noise in gene expression. To illustrate this, we consider a model for regulation of protein expression bursts by small RNAs. For a broad range of parameters, we derive analytical expressions (validated by stochastic simulations) for the mean protein levels as the levels of regulatory small RNAs are varied. The results obtained show that the degree of transcriptional bursting can, in principle, be determined from changes in mean steady-state protein levels for general stochastic models of gene expression.

Post-transcriptional regulation of noise in protein distributions during gene expression

The intrinsic stochasticity of gene expression can lead to a large variability of protein levels across a population of cells. Variability (or noise) in protein distributions can be modulated by cellular mechanisms of gene regulation; in particular, there is considerable interest in understanding the role of post-transcriptional regulation. To address this issue, we propose and analyze a stochastic model for post-transcriptional regulation of gene expression. The analytical solution of the model provides insight into the effects of different mechanisms of post-transcriptional regulation on the noise in protein distributions. The results obtained also demonstrate how different sources of intrinsic noise in gene expression can be discriminated based on observations of regulated protein distributions.

Biological role of noise encoded in a genetic network motif

Genetic circuits that regulate distinct cellular processes can differ in their wiring pattern of interactions (architecture) and susceptibility to stochastic fluctuations (noise). Whether the link between circuit architecture and noise is of biological importance remains, however, poorly understood. To investigate this problem, we performed a computational study of gene expression noise for all possible circuit architectures of feed-forward loop (FFL) motifs. Results revealed that FFL architectures fall into two categories depending on whether their ON (stimulated) or OFF (unstimulated) steady states exhibit noise. To explore the biological importance of this difference in noise behavior, we analyzed 858 documented FFLs in Escherichia coli that were divided into 39 functional categories. The majority of FFLs were found to regulate two subsets of functional categories. Interestingly, these two functional categories associated with FFLs of opposite noise behaviors. This opposite noise preference revealed two noise-based strategies to cope with environmental constraints where cellular responses are either initiated or terminated stochastically to allow probabilistic sampling of alternative states. FFLs may thus be selected for their architecture-dependent noise behavior, revealing a biological role for noise that is encoded in gene circuit architectures.

Quantifying mRNA synthesis and decay rates using small RNAs

Regulation of mRNA decay is a critical component of global cellular adaptation to changing environments. The corresponding changes in mRNA lifetimes can be coordinated with changes in mRNA transcription rates to fine-tune gene expression. Current approaches for measuring mRNA lifetimes can give rise to secondary effects due to transcription inhibition and require separate experiments to estimate changes in mRNA transcription rates. Here, we propose an approach for simultaneous determination of changes in mRNA transcription rate and lifetime using regulatory small RNAs (sRNAs) to control mRNA decay. We analyze a stochastic model for coupled degradation of mRNAs and sRNAs and derive exact results connecting RNA lifetimes and transcription rates to mean abundances. The results obtained are then generalized to include nonstoichiometric coupled degradation of sRNAs. Our analysis suggests experimental protocols for determining parameters controlling the efficiency of stoichiometric regulation by small RNAs and for analyzing factors and processes regulating changes in mRNA transcription and decay.

Effects of the promoter open complex formation on gene expression dynamics

Little is known about the biological mechanisms that shape the distribution of intervals between the completion of RNA molecules (T(p)RNA) , and thus transcriptional noise. We characterize numerically and analytically how the promoter open complex delay (tau(P)) and the transcription initiation rate (k(t)) shape T(p)RNA. From this, we assess the noise and mean of transcript levels and show that these can be tuned both independently and simultaneously by tau(P) and k(t). Finally, we characterize how tau(P) affects bursting in RNA production and show that the tau(P) measured for a lac promoter best fits independent measurements of the burst distribution of the same promoter. Since tau(P) affects noise in gene expression, and given that it is sequence dependent, it is likely to be evolvable.