Quantitative analysis of the transcription control mechanism

Exact burst-size distributions for gene-expression models with complex promoter structure

In prokaryotic and eukaryotic cells, most genes are transcribed in a bursty fashion on one hand and complex gene regulations may lead to complex promoter structure on the other hand. This raises an unsolved issue: how does promoter structure shape transcriptional bursting kinetics characterized by burst size and frequency? Here we analyze stochastic models of gene transcription, which consider complex regulatory mechanisms. Notably, we develop an efficient method to derive exact burst-size distributions. The analytical results show that if the promoter of a gene contains only one active state, the burst size indeed follows a geometric distribution, in agreement with the previous result derived under certain limiting conditions. However, if it contains a multitude of active states, the burst size in general obeys a non-geometric distribution, which is a linearly weighted sum of geometric distributions. This superposition principle reveals the essential feature of bursting kinetics in complex cases of transcriptional regulation although it seems that there has been no direct experimental confirmation. The derived burst-size distributions not only highlight the importance of promoter structure in regulating bursting kinetics, but can be also used in the exact inference of this kinetics based on experimental data.

Single gene analysis in yeast suggests nonequilibrium regulatory dynamics for transcription

Fluctuations in the initiation rate of transcription, the first step in gene expression, ensue from the stochastic behavior of the molecular process that controls transcription. In steady state, the regulatory process is often assumed to operate reversibly, i.e., in equilibrium. However, reversibility imposes fundamental limits to information processing. For instance, the assumption of equilibrium is difficult to square with the precision with which the regulatory process executes its task in eukaryotes. Here we provide evidence - from microscopic analyses of the transcription dynamics at a single gene copy of yeast - that the regulatory process for transcription is cyclic and irreversible (out of equilibrium). The necessary coupling to reservoirs of free energy occurs via sequence-specific transcriptional activators and the recruitment, in part, of ATP-dependent chromatin remodelers. Our findings may help explain how eukaryotic cells reconcile the dual but opposing requirements for fast regulatory kinetics and high regulatory specificity.

Transcriptional kinetic synergy: A complex landscape revealed by integrating modeling and synthetic biology

Transcription factors (TFs) control gene expression, often acting synergistically. Classical thermodynamic models offer a biophysical explanation for synergy based on binding cooperativity and regulated recruitment of RNA polymerase. Because transcription requires polymerase to transition through multiple states, recent work suggests that "kinetic synergy" can arise through TFs acting on distinct steps of the transcription cycle. These types of synergy are not mutually exclusive and are difficult to disentangle conceptually and experimentally. Here, we model and build a synthetic circuit in which TFs bind to a single shared site on DNA, such that TFs cannot synergize by simultaneous binding. We model mRNA production as a function of both TF binding and regulation of the transcription cycle, revealing a complex landscape dependent on TF concentration, DNA binding affinity, and regulatory activity. We use synthetic TFs to confirm that the transcription cycle must be integrated with recruitment for a quantitative understanding of gene regulation.

Kinetic Proofreading

Biochemistry and molecular biology rely on the recognition of structural complementarity between molecules. Molecular interactions must be both quickly reversible, i.e., tenuous, and specific. How the cell reconciles these conflicting demands is the subject of this article. The problem and its theoretical solution are discussed within the wider theoretical context of the thermodynamics of stochastic processes (stochastic thermodynamics). The solution-an irreversible reaction cycle that decreases internal error at the expense of entropy export into the environment-is shown to be widely employed by biological processes that transmit genetic and regulatory information. Expected final online publication date for the Annual Review of Biochemistry, Volume 91 is June 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Differences in evolutionary accessibility determine which equally effective regulatory motif evolves to generate pulses

Transcriptional regulatory networks (TRNs) are enriched for certain "motifs." Motif usage is commonly interpreted in adaptationist terms, i.e., that the optimal motif evolves. But certain motifs can also evolve more easily than others. Here, we computationally evolved TRNs to produce a pulse of an effector protein. Two well-known motifs, type 1 incoherent feed-forward loops (I1FFLs) and negative feedback loops (NFBLs), evolved as the primary solutions. The relative rates at which these two motifs evolve depend on selection conditions, but under all conditions, either motif achieves similar performance. I1FFLs generally evolve more often than NFBLs. Selection for a tall pulse favors NFBLs, while selection for a fast response favors I1FFLs. I1FFLs are more evolutionarily accessible early on, before the effector protein evolves high expression; when NFBLs subsequently evolve, they tend to do so from a conjugated I1FFL-NFBL genotype. In the empirical S. cerevisiae TRN, output genes of NFBLs had higher expression levels than those of I1FFLs. These results suggest that evolutionary accessibility, and not relative functionality, shapes which motifs evolve in TRNs, and does so as a function of the expression levels of particular genes.

Nucleosomal proofreading of activator-promoter interactions

Specificity in transcriptional regulation is imparted by transcriptional activators that bind to specific DNA sequences from which they stimulate transcription. Specificity may be increased by slowing down the kinetics of regulation: by increasing the energy for dissociation of the activator-DNA complex or decreasing activator concentration. In general, higher dissociation energies imply longer DNA dwell times of the activator; the activator-bound gene may not readily turn off again. Lower activator concentrations entail longer pauses between binding events; the activator-unbound gene is not easily turned on again and activated transcription occurs in stochastic bursts. We show that kinetic proofreading of activator-DNA recognition-insertion of an energy-dissipating delay step into the activation pathway for transcription-reconciles high specificity of transcriptional regulation with fast regulatory kinetics. We show that kinetic proofreading results from the stochastic removal and reformation of promoter nucleosomes, at a distance from equilibrium.

Transcriptional processes: Models and inference

Many biochemical events involve multistep reactions. One of the most important biological processes that involve multistep reaction is the transcriptional process. Models for multistep reaction necessarily need multiple states and it is a challenge to compute model parameters that best agree with experimental data. Therefore, the aim of this work is to design a multistep promoter model which accurately characterizes transcriptional bursting and is consistent with observed data. To address this issue, we develop a model for promoters with several OFF states and a single ON state using Erlang distribution. To explore the combined effects of model and data, we combine Monte Carlo extension of Expectation Maximization (MCEM) and delay Stochastic Simulation Algorithm (DSSA) and call the resultant algorithm as delay Bursty MCEM. We apply this algorithm to time-series data of endogenous mouse glutaminase promoter to validate the model assumptions and infer the kinetic parameters. Our results show that with multiple OFF states, we are able to infer and produce a model which is more consistent with experimental data. Our results also show that delay Bursty MCEM inference is more efficient.

Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise

In transcriptional regulatory networks (TRNs), a canonical 3-node feed-forward loop (FFL) is hypothesized to evolve to filter out short spurious signals. We test this adaptive hypothesis against a novel null evolutionary model. Our mutational model captures the intrinsically high prevalence of weak affinity transcription factor binding sites. We also capture stochasticity and delays in gene expression that distort external signals and intrinsically generate noise. Functional FFLs evolve readily under selection for the hypothesized function but not in negative controls. Interestingly, a 4-node “diamond” motif also emerges as a short spurious signal filter. The diamond uses expression dynamics rather than path length to provide fast and slow pathways. When there is no idealized external spurious signal to filter out, but only internally generated noise, only the diamond and not the FFL evolves. While our results support the adaptive hypothesis, we also show that non-adaptive factors, including the intrinsic expression dynamics, matter.

Feed‐forward loops (FFLs) can filter out noise, but whether their overrepresentation in GRNs reflects adaptive evolution for this function is debated. Here, the authors develop a null model of regulatory evolution and find that FFLs evolve readily under selection for the noise filtering function.

Complex signal processing in synthetic gene circuits using cooperative regulatory assemblies

Eukaryotic genes are regulated by multivalent transcription factor complexes. Through cooperative self-assembly, these complexes perform nonlinear regulatory operations involved in cellular decision-making and signal processing. In this study, we apply this design principle to synthetic networks, testing whether engineered cooperative assemblies can program nonlinear gene circuit behavior in yeast. Using a model-guided approach, we show that specifying the strength and number of assembly subunits enables predictive tuning between linear and nonlinear regulatory responses for single- and multi-input circuits. We demonstrate that assemblies can be adjusted to control circuit dynamics. We harness this capability to engineer circuits that perform dynamic filtering, enabling frequency-dependent decoding in cell populations. Programmable cooperative assembly provides a versatile way to tune the nonlinearity of network connections, markedly expanding the engineerable behaviors available to synthetic circuits.

An Optogenetic Platform for Real-Time, Single-Cell Interrogation of Stochastic Transcriptional Regulation

Transcription is a highly regulated and inherently stochastic process. The complexity of signal transduction and gene regulation makes it challenging to analyze how the dynamic activity of transcriptional regulators affects stochastic transcription. By combining a fast-acting, photo-regulatable transcription factor with nascent RNA quantification in live cells and an experimental setup for precise spatiotemporal delivery of light inputs, we constructed a platform for the real-time, single-cell interrogation of transcription in Saccharomyces cerevisiae. We show that transcriptional activation and deactivation are fast and memoryless. By analyzing the temporal activity of individual cells, we found that transcription occurs in bursts, whose duration and timing are modulated by transcription factor activity. Using our platform, we regulated transcription via light-driven feedback loops at the single-cell level. Feedback markedly reduced cell-to-cell variability and led to qualitative differences in cellular transcriptional dynamics. Our platform establishes a flexible method for studying transcriptional dynamics in single cells.

mRNA detection in budding yeast with single fluorophores

Quantitative measurement of mRNA levels in single cells is necessary to understand phenotypic variability within an otherwise isogenic population of cells. Single-molecule mRNA Fluorescence In Situ Hybridization (FISH) has been established as the standard method for this purpose, but current protocols require a long region of mRNA to be targeted by multiple DNA probes. Here, we introduce a new single-probe FISH protocol termed sFISH for budding yeast, Saccharomyces cerevisiae using a single DNA probe labeled with a single fluorophore. In sFISH, we markedly improved probe specificity and signal-to-background ratio by using methanol fixation and inclined laser illumination. We show that sFISH reports mRNA changes that correspond to protein levels and gene copy number. Using this new FISH protocol, we can detect >50% of the total target mRNA. We also demonstrate the versatility of sFISH using FRET detection and mRNA isoform profiling as examples. Our FISH protocol with single-fluorophore sensitivity significantly reduces cost and time compared to the conventional FISH protocols and opens up new opportunities to investigate small changes in RNA at the single cell level.

Role of transcription factor-mediated nucleosome disassembly in PHO5 gene expression

Studying nucleosome dynamics in promoter regions is crucial for understanding gene regulation. Nucleosomes regulate gene expression by sterically occluding transcription factors (TFs) and other non–histone proteins accessing genomic DNA. How the binding competition between nucleosomes and TFs leads to transcriptionally compatible promoter states is an open question. Here, we present a computational study of the nucleosome dynamics and organization in the promoter region of PHO5 gene in Saccharomyces cerevisiae. Introducing a model for nucleosome kinetics that takes into account ATP-dependent remodeling activity, DNA sequence effects, and kinetics of TFs (Pho4p), we compute the probability of obtaining different “promoter states” having different nucleosome configurations. Comparing our results with experimental data, we argue that the presence of local remodeling activity (LRA) as opposed to basal remodeling activity (BRA) is crucial in determining transcriptionally active promoter states. By modulating the LRA and Pho4p binding rate, we obtain different mRNA distributions—Poisson, bimodal, and long-tail. Through this work we explain many features of the PHO5 promoter such as sequence-dependent TF accessibility and the role of correlated dynamics between nucleosomes and TFs in opening/coverage of the TATA box. We also obtain possible ranges for TF binding rates and the magnitude of LRA.

From Structural Variation of Gene Molecules to Chromatin Dynamics and Transcriptional Bursting

Transcriptional activation of eukaryotic genes is accompanied, in general, by a change in the sensitivity of promoter chromatin to endonucleases. The structural basis of this alteration has remained elusive for decades; but the change has been viewed as a transformation of one structure into another, from "closed" to "open" chromatin. In contradistinction to this static and deterministic view of the problem, a dynamical and probabilistic theory of promoter chromatin has emerged as its solution. This theory, which we review here, explains observed variation in promoter chromatin structure at the level of single gene molecules and provides a molecular basis for random bursting in transcription-the conjecture that promoters stochastically transition between transcriptionally conducive and inconducive states. The mechanism of transcriptional regulation may be understood only in probabilistic terms.

Nucleosomes, transcription, and probability

Speaking of current measurements on single ion channel molecules, David Colquhoun wrote in 2006, "Individual molecules behave randomly, so suddenly we had to learn how to deal with stochastic processes." Here I describe theoretical efforts to understand recent experimental observations on the chromatin structure of single gene molecules, a molecular biologist's path toward probabilistic theories.

Chromatin structure analysis of single gene molecules by psoralen cross-linking and electron microscopy

Nucleosomes occupy a central role in regulating eukaryotic gene expression by blocking access of transcription factors to their target sites on chromosomal DNA. Analysis of chromatin structure and function has mostly been performed by probing DNA accessibility with endonucleases. Such experiments average over large numbers of molecules of the same gene, and more recently, over entire genomes. However, both digestion and averaging erase the structural variation between molecules indicative of dynamic behavior, which must be reconstructed for any theory of regulation. Solution of this problem requires the structural analysis of single gene molecules. In this chapter, we describe a method by which single gene molecules are purified from the yeast Saccharomyces cerevisiae and cross-linked with psoralen, allowing the determination of nucleosome configurations by transmission electron microscopy. We also provide custom analysis software that semi-automates the analysis of micrograph data. This single-gene technique enables detailed examination of chromatin structure at any genomic locus in yeast.

Orthogonal control of expression mean and variance by epigenetic features at different genomic loci

While gene expression noise has been shown to drive dramatic phenotypic variations, the molecular basis for this variability in mammalian systems is not well understood. Gene expression has been shown to be regulated by promoter architecture and the associated chromatin environment. However, the exact contribution of these two factors in regulating expression noise has not been explored. Using a dual-reporter lentiviral model system, we deconvolved the influence of the promoter sequence to systematically study the contribution of the chromatin environment at different genomic locations in regulating expression noise. By integrating a large-scale analysis to quantify mRNA levels by smFISH and protein levels by flow cytometry in single cells, we found that mean expression and noise are uncorrelated across genomic locations. Furthermore, we showed that this independence could be explained by the orthogonal control of mean expression by the transcript burst size and noise by the burst frequency. Finally, we showed that genomic locations displaying higher expression noise are associated with more repressed chromatin, thereby indicating the contribution of the chromatin environment in regulating expression noise.

Multiplex Eukaryotic Transcription (In)activation: Timing, Bursting and Cycling of a Ratchet Clock Mechanism

Activation of eukaryotic transcription is an intricate process that relies on a multitude of regulatory proteins forming complexes on chromatin. Chromatin modifications appear to play a guiding role in protein-complex assembly on chromatin. Together, these processes give rise to stochastic, often bursting, transcriptional activity. Here we present a model of eukaryotic transcription that aims to integrate those mechanisms. We use stochastic and ordinary-differential-equation modeling frameworks to examine various possible mechanisms of gene regulation by multiple transcription factors. We find that the assembly of large transcription factor complexes on chromatin via equilibrium-binding mechanisms is highly inefficient and insensitive to concentration changes of single regulatory proteins. An alternative model that lacks these limitations is a cyclic ratchet mechanism. In this mechanism, small protein complexes assemble sequentially on the promoter. Chromatin modifications mark the completion of a protein complex assembly, and sensitize the local chromatin for the assembly of the next protein complex. In this manner, a strict order of protein complex assemblies is attained. Even though the individual assembly steps are highly stochastic in duration, a sequence of them gives rise to a remarkable precision of the transcription cycle duration. This mechanism explains how transcription activation cycles, lasting for tens of minutes, derive from regulatory proteins residing on chromatin for only tens of seconds. Transcriptional bursts are an inherent feature of such transcription activation cycles. Bursting transcription can cause individual cells to remain in synchrony transiently, offering an explanation of transcriptional cycling as observed in cell populations, both on promoter chromatin status and mRNA levels.

Nucleosomal promoter variation generates gene expression noise

Gene product molecule numbers fluctuate over time and between cells, confounding deterministic expectations. The molecular origins of this noise of gene expression remain unknown. Recent EM analysis of single PHO5 gene molecules of yeast indicated that promoter molecules stochastically assume alternative nucleosome configurations at steady state, including the fully nucleosomal and nucleosome-free configuration. Given that distinct configurations are unequally conducive to transcription, the nucleosomal variation of promoter molecules may constitute a source of gene expression noise. This notion, however, implies an untested conjecture, namely that the nucleosomal variation arises de novo or intrinsically (i.e., that it cannot be explained as the result of the promoter's deterministic response to variation in its molecular surroundings). Here, we show--by microscopically analyzing the nucleosome configurations of two juxtaposed physically linked PHO5 promoter copies--that the configurational variation, indeed, is intrinsically stochastic and thus, a cause of gene expression noise rather than its effect.

Mechanistic stochastic model of histone modification pattern formation

BACKGROUND

The activity of a single gene is influenced by the composition of the chromatin in which it is embedded. Nucleosome turnover, conformational dynamics, and covalent histone modifications each induce changes in the structure of chromatin and its affinity for regulatory proteins. The dynamics of histone modifications and the persistence of modification patterns for long periods are still largely unknown.

RESULTS

In this study, we present a stochastic mathematical model that describes the molecular mechanisms of histone modification pattern formation along a single gene, with non-phenomenological, physical parameters. We find that diffusion and recruitment properties of histone modifying enzymes together with chromatin connectivity allow for a rich repertoire of stochastic histone modification dynamics and pattern formation. We demonstrate that histone modification patterns at a single gene can be established or removed within a few minutes through diffusion and weak recruitment mechanisms of histone modification spreading. Moreover, we show that strong synergism between diffusion and weak recruitment mechanisms leads to nearly irreversible transitions in histone modification patterns providing stable patterns. In the absence of chromatin connectivity spontaneous and dynamic histone modification boundaries can be formed that are highly unstable, and spontaneous fluctuations cause them to diffuse randomly. Chromatin connectivity destabilizes this synergistic system and introduces bistability, illustrating state switching between opposing modification states of the model gene. The observed bistable long-range and localized pattern formation are critical effectors of gene expression regulation.

CONCLUSION

This study illustrates how the cooperative interactions between regulatory proteins and the chromatin state generate complex stochastic dynamics of gene expression regulation.

Promoter-mediated transcriptional dynamics

Genes in eukaryotic cells are typically regulated by complex promoters containing multiple binding sites for a variety of transcription factors, but how promoter dynamics affect transcriptional dynamics has remained poorly understood. In this study, we analyze gene models at the transcriptional regulation level, which incorporate the complexity of promoter structure (PS) defined as transcriptional exits (i.e., ON states of the promoter) and the transition pattern (described by a matrix consisting of transition rates among promoter activity states). We show that multiple exits of transcription are the essential origin of generating multimodal distributions of mRNA, but promoters with the same transition pattern can lead to multimodality of different modes, depending on the regulation of transcriptional factors. In turn, for similar mRNA distributions in the models, the mean ON or OFF time distributions may exhibit different characteristics, thus providing the supplemental information on PS. In addition, we demonstrate that the transcriptional noise can be characterized by a nonlinear function of mean ON and OFF times. These results not only reveal essential characteristics of promoter-mediated transcriptional dynamics but also provide signatures useful for inferring PS based on characteristics of transcriptional outputs.

The yeast PHO5 promoter: from single locus to systems biology of a paradigm for gene regulation through chromatin

Chromatin dynamics crucially contributes to gene regulation. Studies of the yeast PHO5 promoter were key to establish this nowadays accepted view and continuously provide mechanistic insight in chromatin remodeling and promoter regulation, both on single locus as well as on systems level. The PHO5 promoter is a context independent chromatin switch module where in the repressed state positioned nucleosomes occlude transcription factor sites such that nucleosome remodeling is a prerequisite for and not consequence of induced gene transcription. This massive chromatin transition from positioned nucleosomes to an extensive hypersensitive site, together with respective transitions at the co-regulated PHO8 and PHO84 promoters, became a prime model for dissecting how remodelers, histone modifiers and chaperones co-operate in nucleosome remodeling upon gene induction. This revealed a surprisingly complex cofactor network at the PHO5 promoter, including five remodeler ATPases (SWI/SNF, RSC, INO80, Isw1, Chd1), and demonstrated for the first time histone eviction in trans as remodeling mode in vivo. Recently, the PHO5 promoter and the whole PHO regulon were harnessed for quantitative analyses and computational modeling of remodeling, transcription factor binding and promoter input-output relations such that this rewarding single-locus model becomes a paradigm also for theoretical and systems approaches to gene regulatory networks.

Single-cell nucleosome mapping reveals the molecular basis of gene expression heterogeneity

Nucleosomes, the basic unit of chromatin, have a critical role in the control of gene expression. Nucleosome positions have generally been determined by examining bulk populations of cells and then correlated with overall gene expression. Here, we describe a technique to determine nucleosome positioning in single cells by virtue of the ability of the nucleosome to protect DNA from GpC methylation. In the acid phosphatase inducible PHO5 gene, we find that there is significant cell-to-cell variation in nucleosome positions and shifts in nucleosome positioning correlate with changes in gene expression. However, nucleosome positioning is not absolute, and even with major shifts in gene expression, some cells fail to change nucleosome configuration. Mutations of the PHO5 promoter that introduce a poly(dA:dT) tract-stimulated gene expression under nonpermissive conditions led to shifts of positioned nucleosomes similar to induction of PHO5. By contrast, mutations that altered AA/TT/AT periodicity reduced gene expression upon PHO5 induction and stabilized nucleosomes in most cells, suggesting that enhanced nucleosome affinity for DNA antagonizes chromatin remodelers. Finally, we determined nucleosome positioning in two regions described as "fuzzy" or nucleosome-free when examined in a bulk assay. These regions consisted of distinct nucleosomes with a larger footprint for potential location and an increase population of cells lacking a nucleosome altogether. These data indicate an underlying complexity of nucleosome positioning that may contribute to the flexibility and heterogeneity of gene expression.

Mapping the fine structure of a eukaryotic promoter input-output function

The precise tuning of gene expression levels is essential for the optimal performance of transcriptional regulatory networks. We created 209 variants of the Saccharomyces cerevisiae PHO5 promoter to quantify how different binding sites for the transcription factor Pho4 affect its output. We found that transcription-factor binding affinities determined in vitro could quantitatively predict the output of a complex yeast promoter. Promoter output was precisely tunable by subtle changes in binding-site affinity of less than 3 kcal mol(-1), which are accessible by modifying 1-2 bases. Our results provide insights into how transcription-factor binding sites regulate gene expression, their possible evolution and how they can be used to precisely tune gene expression. More generally, we show that in vitro binding-energy landscapes of transcription factors can precisely predict the output of a native yeast promoter, indicating that quantitative models of transcriptional regulatory networks are feasible.

An effective method for computing the noise in biochemical networks

We present a simple yet effective method, which is based on power series expansion, for computing exact binomial moments that can be in turn used to compute steady-state probability distributions as well as the noise in linear or nonlinear biochemical reaction networks. When the method is applied to representative reaction networks such as the ON-OFF models of gene expression, gene models of promoter progression, gene auto-regulatory models, and common signaling motifs, the exact formulae for computing the intensities of noise in the species of interest or steady-state distributions are analytically given. Interestingly, we find that positive (negative) feedback does not enlarge (reduce) noise as claimed in previous works but has a counter-intuitive effect and that the multi-OFF (or ON) mechanism always attenuates the noise in contrast to the common ON-OFF mechanism and can modulate the noise to the lowest level independently of the mRNA mean. Except for its power in deriving analytical expressions for distributions and noise, our method is programmable and has apparent advantages in reducing computational cost.

Linking stochastic fluctuations in chromatin structure and gene expression

Electron microscopy of single gene molecules and mathematical modeling shows that a promoter stochastically transitions between transcriptionally favorable and unfavorable nucleosome configurations, providing a mechanism for transcriptional bursting.

The number of mRNA and protein molecules expressed from a single gene molecule fluctuates over time. These fluctuations have been attributed, in part, to the random transitioning of promoters between transcriptionally active and inactive states, causing transcription to occur in bursts. However, the molecular basis of transcriptional bursting remains poorly understood. By electron microscopy of single PHO5 gene molecules from yeast, we show that the “activated” promoter assumes alternative nucleosome configurations at steady state, including the maximally repressive, fully nucleosomal, and the maximally non-repressive, nucleosome-free, configuration. We demonstrate that the observed probabilities of promoter nucleosome configurations are obtained from a simple, intrinsically stochastic process of nucleosome assembly, disassembly, and position-specific sliding; and we show that gene expression and promoter nucleosome configuration can be mechanistically coupled, relating promoter nucleosome dynamics and gene expression fluctuations. Together, our findings suggest a structural basis for transcriptional bursting, and offer new insights into the mechanism of transcriptional regulation and the kinetics of promoter nucleosome transitions.

In eukaryotes, such as plants, fungi, and animals, the DNA is wrapped around basic protein cores called nucleosomes at more or less regular intervals. This wrapping discourages transcription, the first step in gene expression. By isolating PHO5 gene molecules from yeast cells and analyzing their structure by electron microscopy, we provide evidence that the “nucleosomes” completely unwrap and then re-wrap in an intrinsically stochastic manner. Only nucleosomes that wrap the regulatory sequences of the gene (promoter) were observed to unspool; no such unspooling was found across the body of the gene. Random unwrapping and re-wrapping generates an ensemble of alternative promoter nucleosome configurations, some conducive to transcription, others not. Mounting evidence suggests that transcription occurs in bursts, where transcripts are released in close succession, interrupted by intervals of transcriptional inactivity; this may lead to significant stochastic fluctuations in gene expression. Although the mechanism of this behavior is not understood, our findings now provide a structural basis for it, suggesting that spooling and unspooling of promoter DNA from the nucleosomes determines the fundamental frequency of transcriptional bursting.

Cell-cycle dependence of transcription dominates noise in gene expression

The large variability in mRNA and protein levels found from both static and dynamic measurements in single cells has been largely attributed to random periods of transcription, often occurring in bursts. The cell cycle has a pronounced global role in affecting transcriptional and translational output, but how this influences transcriptional statistics from noisy promoters is unknown and generally ignored by current stochastic models. Here we show that variable transcription from the synthetic tetO promoter in S. cerevisiae is dominated by its dependence on the cell cycle. Real-time measurements of fluorescent protein at high expression levels indicate tetO promoters increase transcription rate ∼2-fold in S/G2/M similar to constitutive genes. At low expression levels, where tetO promoters are thought to generate infrequent bursts of transcription, we observe random pulses of expression restricted to S/G2/M, which are correlated between homologous promoters present in the same cell. The analysis of static, single-cell mRNA measurements at different points along the cell cycle corroborates these findings. Our results demonstrate that highly variable mRNA distributions in yeast are not solely the result of randomly switching between periods of active and inactive gene expression, but instead largely driven by differences in transcriptional activity between G1 and S/G2/M.

There is an astonishing amount of variation in the number of mRNA and protein molecules generated from particular genes between genetically identical single cells grown in the same environment. Particularly for mRNA, the large variation seen from these “noisy” genes is consistent with the idea of transcriptional bursting where transcription occurs in random, intermittent periods of high activity. There is considerable experimental support for transcriptional bursting, and it is a primary feature of stochastic models of gene expression that account for variation. Still, it has long been recognized that variation, especially in protein levels, can occur because of global differences between genetically identical cells. We show that in budding yeast, mRNA variation is driven to a large extent by differences in the transcriptional activity of a noisy gene between different phases of the cell cycle. These differences are not because of specific cell-cycle regulation, and in some cases transcription appears restricted to certain phases, leading to pulses of mRNA production. These results raise new questions about the origins of transcriptional bursting and how the statistics of gene expression are regulated in a global way by the cell cycle.

The effect of an intervening promoter nucleosome on gene expression

Nucleosomes, which are the basic packaging units of chromatin, are stably positioned in promoters upstream of most stress-inducible genes. These promoter nucleosomes are generally thought to repress gene expression due to exclusion; they prevent transcription factors from accessing their target sites on the DNA. However, the role of promoter nucleosomes that do not directly occlude transcription factor binding sites is not obvious. Here, we varied the stability of a non-occluding nucleosome positioned between a transcription factor binding site and the TATA box region in an inducible yeast promoter and measured downstream gene expression level. We found that gene expression level depends on the occupancy of the non-occluding nucleosome in a non-monotonic manner. We postulated that a non-occluding nucleosome can serve both as a vehicle of and a barrier to chromatin remodeling activity and built a quantitative, nonequilibrium model to explain the observed nontrivial effect of the intervening nucleosome. Our work sheds light on the dual role of nucleosome as a repressor and an activator and expands the standard model of gene expression to include irreversible promoter chromatin transitions.

Transcription stochasticity of complex gene regulation models

Transcription is regulated by a multitude of factors that concertedly induce genes to switch between activity states. Eukaryotic transcription involves a multitude of complexes that sequentially assemble on chromatin under the influence of transcription factors and the dynamic state of chromatin. Prokaryotic transcription depends on transcription factors, sigma-factors, and, in some cases, on DNA looping. We present a stochastic model of transcription that considers these complex regulatory mechanisms. We coarse-grain the molecular details in such a way that the model can describe a broad class of gene-regulation mechanisms. We solve this model analytically for various measures of stochastic transcription and compare alternative gene-regulation designs. We find that genes with complex multiprotein regulation can have peaked burst-size distributions in contrast to the geometric distributions found for simple models of transcription regulation. Burst-size distributions are, in addition, shaped by mRNA degradation during transcription bursts. We derive the stochastic properties of genes in the limit of deterministic switch times. These genes typically have reduced transcription noise. Severe timescale separation between gene regulation and transcription initiation enhances noise and leads to bimodal mRNA copy number distributions. In general, complex mechanisms for gene regulation lead to nonexponential waiting-time distributions for gene switching and transcription initiation, which typically reduce noise in mRNA copy numbers and burst size. Finally, we discuss that qualitatively different gene regulation models can often fit the same experimental data on single-cell mRNA abundance even though they have qualitatively different burst-size statistics and regulatory parameters.

Using temporal correlations and full distributions to separate intrinsic and extrinsic fluctuations in biological systems

Studies of stochastic biological dynamics typically compare observed fluctuations to theoretically predicted variances, sometimes after separating the intrinsic randomness of the system from the enslaving influence of changing environments. But variances have been shown to discriminate surprisingly poorly between alternative mechanisms, while for other system properties no approaches exist that rigorously disentangle environmental influences from intrinsic effects. Here, we apply the theory of generalized random walks in random environments to derive exact rules for decomposing time series and higher statistics, rather than just variances. We show for which properties and for which classes of systems intrinsic fluctuations can be analyzed without accounting for extrinsic stochasticity and vice versa. We derive two independent experimental methods to measure the separate noise contributions and show how to use the additional information in temporal correlations to detect multiplicative effects in dynamical systems.

Reprogramming chromatin

Cellular reprogramming involves the artificial dedifferentiation of somatic cells to a pluripotent state. When affected by overexpressing specific transcription factors, the process is highly inefficient, as only 0.1-1% of cells typically undergo the transformation. This low efficiency has been attributed to high kinetic barriers that affect all cells equally and can only be overcome by rare stochastic events. The barriers to reprogramming are likely to involve transformations of chromatin state because (i) inhibitors of chromatin-modifying enzymes can enhance the efficiency of reprogramming and (ii) knockdown or knock-out of chromatin-modifying enzymes can lower the efficiency of reprogramming. Here, we review the relationship between chromatin state transformations (chromatin reprogramming) and cellular reprogramming, with an emphasis on transcription factors, chromatin remodeling factors, histone modifications and DNA methylation.

Teasing apart translational and transcriptional components of stochastic variations in eukaryotic gene expression

The intrinsic stochasticity of gene expression leads to cell-to-cell variations, noise, in protein abundance. Several processes, including transcription, translation, and degradation of mRNA and proteins, can contribute to these variations. Recent single cell analyses of gene expression in yeast have uncovered a general trend where expression noise scales with protein abundance. This trend is consistent with a stochastic model of gene expression where mRNA copy number follows the random birth and death process. However, some deviations from this basic trend have also been observed, prompting questions about the contribution of gene-specific features to such deviations. For example, recent studies have pointed to the TATA box as a sequence feature that can influence expression noise by facilitating expression bursts. Transcription-originated noise can be potentially further amplified in translation. Therefore, we asked the question of to what extent sequence features known or postulated to accompany translation efficiency can also be associated with increase in noise strength and, on average, how such increase compares to the amplification associated with the TATA box. Untangling different components of expression noise is highly nontrivial, as they may be gene or gene-module specific. In particular, focusing on codon usage as one of the sequence features associated with efficient translation, we found that ribosomal genes display a different relationship between expression noise and codon usage as compared to other genes. Within nonribosomal genes we found that sequence high codon usage is correlated with increased noise relative to the average noise of proteins with the same abundance. Interestingly, by projecting the data on a theoretical model of gene expression, we found that the amplification of noise strength associated with codon usage is comparable to that of the TATA box, suggesting that the effect of translation on noise in eukaryotic gene expression might be more prominent than previously appreciated.

The stochastic nature of gene expression leads to cell-to-cell differences in protein level referred to as noise. Expression noise can be disadvantageous, by affecting the precision of biological functions, but it may also be advantageous by enabling heterogeneous stress-response programs to environmental changes. Therefore various genes and gene groups might display various levels of expression noise. Importantly, gene expression is a multi-step process and the stochasticity of its individual steps, including transcription and translation, contributes to the resulting variability. Recent single cell analyses of gene expression in yeast have confirmed the theoretically predicted general trend where expression noise scales with protein abundance. However, some deviations from this basic trend have also been observed, prompting questions about the contribution of gene-specific features to such deviations. Accounting for noise heterogeneity in different gene groups, we revealed a clear relationship between noise and translation-related genomic features, specifically codon usage and 5′ UTR secondary structure. Our results suggest that the effect of translation on these deviations might be more prominent than previously appreciated, and provide important clues towards understanding expression stochasticity in yeast.

Analytical distribution and tunability of noise in a model of promoter progress

Chromatin template (CT), which accumulates over time until the promoter becomes active, determines upstream dynamics of transcription, but how upstream sequential steps impact downstream dynamics qualitatively and quantitatively is unclear. Here, we analyze a stochastic gene model with a simple yet typical CT that contains one active state and several inactive states of the promoter. We derive the analytical expressions for the noise in mRNA probability distributions governed by master equations. The derived results extend previous work by including the effects of promoter progress on variability and bimodality. Specifically, given a CT for transcription, we analytically demonstrate that inactive phases of the promoter can modulate the noise intensity to the minimum independently of the mean expression of mRNA. If one new inactive state is added to the CT, then the resulting noise will be reduced, implying that the multi-off mechanism plays a role of attenuating the noise. In contrast to the simple on-off mechanism, the multi-off mechanism can also narrow bimodal regions in a certain parameter plane and obscure two peaks, explaining why bimodal distributions are rarely observed in experiments. Our results provide insight into the role of promoter progress in determining the level of cell-to-cell variability in gene expression.

In vivo role for the chromatin-remodeling enzyme SWI/SNF in the removal of promoter nucleosomes by disassembly rather than sliding

Analysis of in vivo chromatin remodeling at the PHO5 promoter of yeast led to the conclusion that remodeling removes nucleosomes from the promoter by disassembly rather than sliding away from the promoter. The catalytic activities required for nucleosome disassembly remain unknown. Transcriptional activation of the yeast PHO8 gene was found to depend on the chromatin-remodeling complex SWI/SNF, whereas activation of PHO5 was not. Here, we show that PHO8 gene circles formed in vivo lose nucleosomes upon PHO8 induction, indicative of nucleosome removal by disassembly. Our quantitative analysis of expression noise and chromatin-remodeling data indicates that the dynamics of continual nucleosome removal and reformation at the activated promoters of PHO5 and PHO8 are closely similar. In contrast to PHO5, however, activator-stimulated transcription of PHO8 appears to be limited mostly to the acceleration of promoter nucleosome disassembly with little or no acceleration of promoter transitions following nucleosome disassembly, accounting for the markedly lower expression level of PHO8.

Separating intrinsic from extrinsic fluctuations in dynamic biological systems

From molecules in cells to organisms in ecosystems, biological populations fluctuate due to the intrinsic randomness of individual events and the extrinsic influence of changing environments. The combined effect is often too complex for effective analysis, and many studies therefore make simplifying assumptions, for example ignoring either intrinsic or extrinsic effects to reduce the number of model assumptions. Here we mathematically demonstrate how two identical and independent reporters embedded in a shared fluctuating environment can be used to identify intrinsic and extrinsic noise terms, but also how these contributions are qualitatively and quantitatively different from what has been previously reported. Furthermore, we show for which classes of biological systems the noise contributions identified by dual-reporter methods correspond to the noise contributions predicted by correct stochastic models of either intrinsic or extrinsic mechanisms. We find that for broad classes of systems, the extrinsic noise from the dual-reporter method can be rigorously analyzed using models that ignore intrinsic stochasticity. In contrast, the intrinsic noise can be rigorously analyzed using models that ignore extrinsic stochasticity only under very special conditions that rarely hold in biology. Testing whether the conditions are met is rarely possible and the dual-reporter method may thus produce flawed conclusions about the properties of the system, particularly about the intrinsic noise. Our results contribute toward establishing a rigorous framework to analyze dynamically fluctuating biological systems.

Varying virulence: epigenetic control of expression noise and disease processes

Gene expression noise is a significant source of phenotypic heterogeneity in otherwise identical populations of cells. Phenotypic heterogeneity can cause reversible drug resistance in diseased cells, and thus a better understanding of its origins might improve treatment strategies. In eukaryotes, data strongly suggest that intrinsic noise arises from transcriptional bursts caused by slow, random transitions between inactive and active gene states that are mediated by chromatin remodeling. In this review, we consider how chromatin modifications might modulate gene expression noise and lead to phenotypic diversity in diseases as varied as viral infection and cancer. Additionally, we argue that this fundamental information can be applied to develop innovative therapies that counteract 'pathogenic noise' and sensitize all diseased cells to therapeutic intervention.

General properties of transcriptional time series in Escherichia coli

Gene activity is described by the time-series of discrete, stochastic mRNA production events. This transcriptional time-series exhibits intermittent, bursty behavior. One consequence of this temporal intricacy is that gene expression can be tuned by varying different features of the time-series. What schemes for varying the transcriptional time-series are observed in the cell? Are the observed properties of these time-series optimized for cellular function? To address these questions, we characterize mRNA copy-number statistics at single-molecule resolution from multiple Escherichia coli promoters. We find that the degree of burstiness depends only on the gene expression level, while being independent of the details of gene regulation. The observed behavior is explained by the underlying variation in the duration of bursting events. Using information theory, we find that the properties of the transcriptional time series allow the cell to efficiently map the extracellular concentration of inducer molecules to intracellular levels of mRNA and proteins.

Occlusion of regulatory sequences by promoter nucleosomes in vivo

Nucleosomes are believed to inhibit DNA binding by transcription factors. Theoretical attempts to understand the significance of nucleosomes in gene expression and regulation are based upon this assumption. However, nucleosomal inhibition of transcription factor binding to DNA is not complete. Rather, access to nucleosomal DNA depends on a number of factors, including the stereochemistry of transcription factor-DNA interaction, the in vivo kinetics of thermal fluctuations in nucleosome structure, and the intracellular concentration of the transcription factor. In vitro binding studies must therefore be complemented with in vivo measurements. The inducible PHO5 promoter of yeast has played a prominent role in this discussion. It bears two binding sites for the transcriptional activator Pho4, which at the repressed promoter are positioned within a nucleosome and in the linker region between two nucleosomes, respectively. Earlier studies suggested that the nucleosomal binding site is inaccessible to Pho4 binding in the absence of chromatin remodeling. However, this notion has been challenged by several recent reports. We therefore have reanalyzed transcription factor binding to the PHO5 promoter in vivo, using ‘chromatin endogenous cleavage’ (ChEC). Our results unambiguously demonstrate that nucleosomes effectively interfere with the binding of Pho4 and other critical transcription factors to regulatory sequences of the PHO5 promoter. Our data furthermore suggest that Pho4 recruits the TATA box binding protein to the PHO5 promoter.