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

The interplay between metabolic stochasticity and cAMP-CRP regulation in single E. coli cells

The inherent stochasticity of metabolism raises a critical question for understanding homeostasis: are cellular processes regulated in response to internal fluctuations? Here, we show that, in E. coli cells under constant external conditions, catabolic enzyme expression continuously responds to metabolic fluctuations. The underlying regulatory feedback is enabled by the cyclic AMP (cAMP) and cAMP receptor protein (CRP) system, which controls catabolic enzyme expression based on metabolite concentrations. Using single-cell microscopy, genetic constructs in which this feedback is disabled, and mathematical modeling, we show how fluctuations circulate through the metabolic and genetic network at sub-cell-cycle timescales. Modeling identifies four noise propagation modes, including one specific to CRP regulation. Together, these modes correctly predict noise circulation at perturbed cAMP levels. The cAMP-CRP system may thus have evolved to control internal metabolic fluctuations in addition to external growth conditions. We conjecture that second messengers may more broadly function to achieve cellular homeostasis.

Reversible 2'-OH acylation enhances RNA stability

The presence of a hydroxyl group at the 2'-position in its ribose makes RNA susceptible to hydrolysis. Stabilization of RNAs for storage, transport and biological application thus remains a serious challenge, particularly for larger RNAs that are not accessible by chemical synthesis. Here we present reversible 2'-OH acylation as a general strategy to preserve RNA of any length or origin. High-yield polyacylation of 2'-hydroxyls ('cloaking') by readily accessible acylimidazole reagents effectively shields RNAs from both thermal and enzymatic degradation. Subsequent treatment with water-soluble nucleophilic reagents removes acylation adducts quantitatively ('uncloaking') and recovers a remarkably broad range of RNA functions, including reverse transcription, translation and gene editing. Furthermore, we show that certain α-dimethylamino- and α-alkoxy- acyl adducts are spontaneously removed in human cells, restoring messenger RNA translation with extended functional half-lives. These findings support the potential of reversible 2'-acylation as a simple and general molecular solution for enhancing RNA stability and provide mechanistic insights for stabilizing RNA regardless of length or origin.

Evaluating single-cell variability in proteasomal decay

Gene expression is a stochastic process that leads to variability in mRNA and protein abundances even within an isogenic population of cells grown in the same environment. This variation, often called gene-expression noise, has typically been attributed to transcriptional and translational processes while ignoring the contributions of protein decay variability across cells. Here we estimate the single-cell protein decay rates of two degron GFPs in Saccharomyces cerevisiae using time-lapse microscopy. We find substantial cell-to-cell variability in the decay rates of the degron GFPs. We evaluate cellular features that explain the variability in the proteasomal decay and find that the amount of 20s catalytic beta subunit of the proteasome marginally explains the observed variability in the degron GFP half-lives. We propose alternate hypotheses that might explain the observed variability in the decay of the two degron GFPs. Overall, our study highlights the importance of studying the kinetics of the decay process at single-cell resolution and that decay rates vary at the single-cell level, and that the decay process is stochastic. A complex model of decay dynamics must be included when modeling stochastic gene expression to estimate gene expression noise.

Out-of-equilibrium gene expression fluctuations in the presence of extrinsic noise

Cell-to-cell variability in protein concentrations is strongly affected by extrinsic noise, especially for highly expressed genes. Extrinsic noise can be due to fluctuations of several possible cellular factors connected to cell physiology and to the level of key enzymes in the expression process. However, how to identify the predominant sources of extrinsic noise in a biological system is still an open question. This work considers a general stochastic model of gene expression with extrinsic noise represented as fluctuations of the different model rates, and focuses on the out-of-equilibrium expression dynamics. Combining analytical calculations with stochastic simulations, we characterize how extrinsic noise shapes the protein variability during gene activation or inactivation, depending on the prevailing source of extrinsic variability, on its intensity and timescale. In particular, we show that qualitatively different noise profiles can be identified depending on which are the fluctuating parameters. This indicates an experimentally accessible way to pinpoint the dominant sources of extrinsic noise using time-coarse experiments.

Genome-Wide Analysis of Gene Expression Noise Brought About by Transcriptional Regulation in Pseudomonas aeruginosa

The part of expression noise that is brought about by transcriptional regulation (represented here as NTR) is an important criterion for estimating the regulatory mode of a gene. However, characterization of NTR is an under-explored area, and there is little knowledge regarding the genome-wide NTR in the model pathogen Pseudomonas aeruginosa. Here, with a library of dual-color transcriptional reporters, we estimated the NTR for over 90% of the promoters in P. aeruginosa. Most promoters exhibit low NTR, while 42 and 115 promoters with high NTR were screened out in the exponential and the stationary growth phases, respectively. Specifically, a rearrangement of NTR was found in promoters involved in amino acid metabolism when bacteria enter the exponential phase. In addition, during the stationary phase, high NTR was found in a wide range of iron-related promoters involving siderophore synthesis and heme uptake, ExsA-regulated promoters involving bacterial virulence, and FleQ-regulated promoters involving biofilm development. We also found a large-scale negative dependence of transcriptional regulation between high-NTR promoters belonging to different functional categories. Our findings offer a global view of transcriptional heterogeneity in P. aeruginosa. IMPORTANCE The phenotypic diversity of Pseudomonas aeruginosa is frequently observed in research, suggesting that bacteria adopt strategies such as bet-hedging to survive ever-changing environments. Gene expression noise (GEN) is the major source of phenotypic diversity. Large GEN from transcriptional regulation (represented as NTR) represent an evolutionary necessity to maintain the copy number diversity of certain proteins in the population. Here, we provide a system-wide view of NTR in P. aeruginosa under nutrient-rich and stressed conditions. High NTR was found in genes involved in flagella biosynthesis and amino acid metabolism under both conditions. Specially, iron acquisition genes exhibited high NTR in the stressed condition, suggesting a great diversity of iron physiology in P. aeruginosa. We further revealed a global negative dependence of transcriptional regulation between those high-NTR genes under the stressed condition, suggesting a mutually exclusive relationship between different bacterial survival strategies.

Noise suppression in stochastic genetic circuits using PID controllers

Inside individual cells, protein population counts are subject to molecular noise due to low copy numbers and the inherent probabilistic nature of biochemical processes. We investigate the effectiveness of proportional, integral and derivative (PID) based feedback controllers to suppress protein count fluctuations originating from two noise sources: bursty expression of the protein, and external disturbance in protein synthesis. Designs of biochemical reactions that function as PID controllers are discussed, with particular focus on individual controllers separately, and the corresponding closed-loop system is analyzed for stochastic controller realizations. Our results show that proportional controllers are effective in buffering protein copy number fluctuations from both noise sources, but this noise suppression comes at the cost of reduced static sensitivity of the output to the input signal. In contrast, integral feedback has no effect on the protein noise level from stochastic expression, but significantly minimizes the impact of external disturbances, particularly when the disturbance comes at low frequencies. Counter-intuitively, integral feedback is found to amplify external disturbances at intermediate frequencies. Next, we discuss the design of a coupled feedforward-feedback biochemical circuit that approximately functions as a derivate controller. Analysis using both analytical methods and Monte Carlo simulations reveals that this derivative controller effectively buffers output fluctuations from bursty stochastic expression, while maintaining the static input-output sensitivity of the open-loop system. In summary, this study provides a systematic stochastic analysis of biochemical controllers, and paves the way for their synthetic design and implementation to minimize deleterious fluctuations in gene product levels.

In the noisy cellular environment, biochemical species such as genes, RNAs and proteins that often occur at low molecular counts, are subject to considerable stochastic fluctuations in copy numbers over time. How cellular biochemical processes function reliably in the face of such randomness is an intriguing fundamental problem. Increasing evidence suggests that random fluctuations (noise) in protein copy numbers play important functional roles, such as driving genetically identical cells to different cell fates. Moreover, many disease states have been attributed to elevated noise levels in specific proteins. Here we systematically investigate design of biochemical systems that function as proportional, integral and derivative-based feedback controllers to suppress protein count fluctuations arising from bursty expression of the protein and external disturbance in protein synthesis. Our results show that different controllers are effective in buffering different noise components, and identify ranges of feedback gain for minimizing deleterious fluctuations in protein levels.

Partitioning stable and unstable expression level variation in cell populations: A theoretical framework and its application to the T cell receptor

Phenotypic variation in the copy number of gene products expressed by cells or tissues has been the focus of intense investigation. To what extent the observed differences in cellular expression levels are persistent or transient is an intriguing question. Here, we develop a quantitative framework that resolves the expression variation into stable and unstable components. The difference between the expression means in two cohorts isolated from any cell population is shown to converge to an asymptotic value, with a characteristic time, τ_T, that measures the timescale of the unstable dynamics. The asymptotic difference in the means, relative to the initial value, measures the stable proportion of the original population variance Rα2. Empowered by this insight, we analysed the T-cell receptor (TCR) expression variation in CD4 T cells. About 70% of TCR expression variance is stable in a diverse polyclonal population, while over 80% of the variance in an isogenic TCR transgenic population is volatile. In both populations the TCR levels fluctuate with a characteristic time of 32 hours. This systematic characterisation of the expression variation dynamics, relying on time series of cohorts’ means, can be combined with technologies that measure gene or protein expression in single cells or in bulk.

No two cells are identical. Even isogenic cells, living in the same environment and expressing the same set of genes display measurable differences or variation in the expression level of any of these genes. How much of the differences in expression levels are permanent and how much of these differences vanish in time has intrigued us for generations. We develop a theoretical framework based on a stochastic model and put it to work in the analysis of T cell receptor expression level in CD4 T cells. We show that T cell populations with genetically diverse receptors display stable variation in receptor expression but, surprisingly, we detect persistent differences in receptor levels among uniform transgenic T cells. The analysis, being based on the mean cohort expression levels logarithm, can be applied to techniques that measure expression at single-cell level and also to the myriad of genomics and proteomics techniques that measure expression in bulk populations.

Enhancement of gene expression noise from transcription factor binding to genomic decoy sites

The genome contains several high-affinity non-functional binding sites for transcription factors (TFs) creating a hidden and unexplored layer of gene regulation. We investigate the role of such “decoy sites” in controlling noise (random fluctuations) in the level of a TF that is synthesized in stochastic bursts. Prior studies have assumed that decoy-bound TFs are protected from degradation, and in this case decoys function to buffer noise. Relaxing this assumption to consider arbitrary degradation rates for both bound/unbound TF states, we find rich noise behaviors. For low-affinity decoys, noise in the level of unbound TF always monotonically decreases to the Poisson limit with increasing decoy numbers. In contrast, for high-affinity decoys, noise levels first increase with increasing decoy numbers, before decreasing back to the Poisson limit. Interestingly, while protection of bound TFs from degradation slows the time-scale of fluctuations in the unbound TF levels, the decay of bound TFs leads to faster fluctuations and smaller noise propagation to downstream target proteins. In summary, our analysis reveals stochastic dynamics emerging from nonspecific binding of TFs and highlights the dual role of decoys as attenuators or amplifiers of gene expression noise depending on their binding affinity and stability of the bound TF.

Mammalian gene expression variability is explained by underlying cell state

Gene expression variability in mammalian systems plays an important role in physiological and pathophysiological conditions. This variability can come from differential regulation related to cell state (extrinsic) and allele-specific transcriptional bursting (intrinsic). Yet, the relative contribution of these two distinct sources is unknown. Here, we exploit the qualitative difference in the patterns of covariance between these two sources to quantify their relative contributions to expression variance in mammalian cells. Using multiplexed error robust RNA fluorescent in situ hybridization (MERFISH), we measured the multivariate gene expression distribution of 150 genes related to Ca2+ signaling coupled with the dynamic Ca2+ response of live cells to ATP. We show that after controlling for cellular phenotypic states such as size, cell cycle stage, and Ca2+ response to ATP, the remaining variability is effectively at the Poisson limit for most genes. These findings demonstrate that the majority of expression variability results from cell state differences and that the contribution of transcriptional bursting is relatively minimal.

Cell Size-Based Decision-Making of a Viral Gene Circuit

Latently infected T cells able to reinitiate viral propagation throughout the body remain a major barrier to curing HIV. Distinguishing between latently infected cells and uninfected cells will advance efforts for viral eradication. HIV decision-making between latency and active replication is stochastic, and drug cocktails that increase bursts of viral gene expression enhance reactivation from latency. Here, we show that a larger host-cell size provides a natural cellular mechanism for enhancing burst size of viral expression and is necessary to destabilize the latent state and bias viral decision-making. Latently infected Jurkat and primary CD4+ T cells reactivate exclusively in larger activated cells, while smaller cells remain silent. In addition, reactivation is cell-cycle dependent and can be modulated with cell-cycle-arresting compounds. Cell size and cell-cycle dependent decision-making of viral circuits may guide stochastic design strategies and applications in synthetic biology and may provide important determinants to advance diagnostics and therapies.

Bohn-Wippert et al. investigate reactivation of T cells latently infected with HIV. They discover that only larger cells exit latency, while smaller cells remain silent. Viral expression bursts are cell size and cell-cycle dependent, presenting dynamic cell states, capable of active control, as sources of viral fate determination.

Stochastic transcription in the p53-mediated response to DNA damage is modulated by burst frequency

Discontinuous transcription has been described for different mammalian cell lines and numerous promoters. However, our knowledge of how the activity of individual promoters is adjusted by dynamic signaling inputs from transcription factors is limited. To address this question, we characterized the activity of selected target genes that are regulated by pulsatile accumulation of the tumor suppressor p53 in response to ionizing radiation. We performed time-resolved measurements of gene expression at the single-cell level by smFISH and used the resulting data to inform a mathematical model of promoter activity. We found that p53 target promoters are regulated by frequency modulation of stochastic bursting and can be grouped along three archetypes of gene expression. The occurrence of these archetypes cannot solely be explained by nuclear p53 abundance or promoter binding of total p53. Instead, we provide evidence that the time-varying acetylation state of p53's C-terminal lysine residues is critical for gene-specific regulation of stochastic bursting.

Effects of mRNA Degradation and Site-Specific Transcriptional Pausing on Protein Expression Noise

Genetically identical cells exhibit diverse phenotypes even when experiencing the same environment. This phenomenon in part originates from cell-to-cell variability (noise) in protein expression. Although various kinetic schemes of stochastic transcription initiation are known to affect gene expression noise, how posttranscription initiation events contribute to noise at the protein level remains incompletely understood. To address this question, we developed a stochastic simulation-based model of bacterial gene expression that integrates well-known dependencies between transcription initiation, transcription elongation dynamics, mRNA degradation, and translation. We identified realistic conditions under which mRNA lifetime and transcriptional pauses modulate the protein expression noise initially introduced by the promoter architecture. For instance, we found that the short lifetime of bacterial mRNAs facilitates the production of protein bursts. Conversely, RNA polymerase (RNAP) pausing at specific sites during transcription elongation can attenuate protein bursts by fluidizing the RNAP traffic to the point of erasing the effect of a bursty promoter. Pause-prone sites, if located close to the promoter, can also affect noise indirectly by reducing both transcription and translation initiation due to RNAP and ribosome congestion. Our findings highlight how the interplay between transcription initiation, transcription elongation, translation, and mRNA degradation shapes the distribution in protein numbers. They also have implications for our understanding of gene evolution and suggest combinatorial strategies for modulating phenotypic variability by genetic engineering.

Fine-tuning of noise in gene expression with nucleosome remodeling

Engineering stochastic fluctuations of gene expression (or “noise”) is integral to precisely bias cellular-fate decisions and statistical phenotypes in both single-cell and multi-cellular systems. Epigenetic regulation has been shown to constitute a large source of noise, and thus, engineering stochasticity is deeply intertwined with epigenetics. Here, utilizing chromatin remodeling, we report that Caffeic acid phenethyl ester (CA) and Pyrimethamine (PYR), two inhibitors of BAF250a, a subunit of the Brahma-associated factor (BAF) nucleosome remodeling complex, enable differential and tunable control of noise in transcription and translation from the human immunodeficiency virus long terminal repeat promoter in a dose and time-dependent manner. CA conserves noise levels while increasing mean abundance, resulting in direct tuning of the transcriptional burst size, while PYR strictly increases transcriptional initiation frequency while conserving a constant transcriptional burst size. Time-dependent treatment with CA reveals non-continuous tuning with noise oscillating at a constant mean abundance at early time points and the burst size increasing for treatments after 5 h. Treatments combining CA and Protein Kinase C agonists result in an even larger increase of abundance while conserving noise levels with a highly non-linear increase in variance of up to 63× untreated controls. Finally, drug combinations provide non-antagonistic combinatorial tuning of gene expression noise and map a noise phase space for future applications with viral and synthetic gene vectors. Active remodeling of nucleosomes and BAF-mediated control of gene expression noise expand a toolbox for the future design and engineering of stochasticity in living systems.

Stochastic system identification without an a priori chosen kinetic model-exploring feasible cell regulation with piecewise linear functions

Kinetic models are at the heart of system identification. A priori chosen rate functions may, however, be unfitting or too restrictive for complex or previously unanticipated regulation. We applied general purpose piecewise linear functions for stochastic system identification in one dimension using published flow cytometry data on E.coli and report on identification results for equilibrium state and dynamic time series. In metabolic labelling experiments during yeast osmotic stress response, we find mRNA production and degradation to be strongly co-regulated. In addition, mRNA degradation appears overall uncorrelated with mRNA level. Comparison of different system identification approaches using semi-empirical synthetic data revealed the superiority of single-cell tracking for parameter identification. Generally, we find that even within restrictive error bounds for deviation from experimental data, the number of viable regulation types may be large. Indeed, distinct regulation can lead to similar expression behaviour over time. Our results demonstrate that molecule production and degradation rates may often differ from classical constant, linear or Michaelis–Menten type kinetics.

Classical cell-regulation models are often imperfectly fitting or even inconsistent with experimental data suggesting inappropriate model assumptions. Martin Hoffmann from Fraunhofer ITEM Regensburg and Jörg Galle from IZBI Leipzig analysed different protein and gene expression data using general purpose piecewise linear functions for system identification. They assessed data corresponding to various experimental techniques for their potential to determine the parameters of their models. Single-cell recordings of expression values over time were most effective for parameter identification. Generally, different and often non-classical cell-regulation models were consistent with the experimental data, even for restrictive error bounds. The authors used virtual treatment experiments to demonstrate that precise knowledge of cell regulation is important for assessing therapy effects. Their findings clearly argue in favour of system identification being performed without an a priori chosen kinetic model.

Mean-Independent Noise Control of Cell Fates via Intermediate States

Stochasticity affects accurate signal detection and robust generation of correct cell fates. Although many known regulatory mechanisms may reduce fluctuations in signals, most simultaneously influence their mean dynamics, leading to unfaithful cell fates. Through analysis and computation, we demonstrate that a reversible signaling mechanism acting through intermediate states can reduce noise while maintaining the mean. This mean-independent noise control (MINC) mechanism is investigated in the context of an intracellular binding protein that regulates retinoic acid (RA) signaling during zebrafish hindbrain development. By comparing our models with experimental data, we find that the MINC mechanism allows for sharp boundaries of gene expression without sacrificing boundary accuracy. In addition, this MINC mechanism can modulate noise to levels that we show are beneficial to spatial patterning through noise-induced cell fate switching. These results reveal a design principle that may be important for noise regulation in many systems that control cell fate determination.

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Mean-independent noise control allows noise attenuation without affecting the mean

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Intermediate states enable such control through proportional coupling

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This controls spatial gene expression noise without shifting boundary locations

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Specific noise levels are required for successful downstream boundary sharpening

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.

Transient Thresholding: A Mechanism Enabling Noncooperative Transcriptional Circuitry to Form a Switch

Threshold generation in fate-selection circuits is often achieved through deterministic bistability, which requires cooperativity (i.e., nonlinear activation) and associated hysteresis. However, the Tat positive-feedback loop that controls HIV's fate decision between replication and proviral latency lacks self-cooperativity and deterministic bistability. Absent cooperativity, it is unclear how HIV can temporarily remain in an off-state long enough for the kinetically slower epigenetic silencing mechanisms to act-expression fluctuations should rapidly trigger active positive feedback and replication, precluding establishment of latency. Here, using flow cytometry and single-cell imaging, we find that the Tat circuit exhibits a transient activation threshold. This threshold largely disappears after ∼40 h-accounting for the lack of deterministic bistability-and promoter activation shortens the lifetime of this transient threshold. Continuous differential equation models do not recapitulate this phenomenon. However, chemical reaction (master equation) models where the transcriptional transactivator and promoter toggle between inactive and active states can recapitulate the phenomenon because they intrinsically create a single-molecule threshold transiently requiring excess molecules in the inactive state to achieve at least one molecule (rather than a continuous fractional value) in the active state. Given the widespread nature of promoter toggling and transcription factor modifications, transient thresholds may be a general feature of inducible promoters.

Universal attenuators and their interactions with feedback loops in gene regulatory networks

Using a combination of mathematical modelling, statistical simulation and large-scale data analysis we study the properties of linear regulatory chains (LRCs) within gene regulatory networks (GRNs). Our modelling indicates that downstream genes embedded within LRCs are highly insulated from the variation in expression of upstream genes, and thus LRCs act as attenuators. This observation implies a progressively weaker functionality of LRCs as their length increases. When analyzing the preponderance of LRCs in the GRNs of Escherichia coli K12 and several other organisms, we find that very long LRCs are essentially absent. In both E. coli and M. tuberculosis we find that four-gene LRCs are intimately linked to identical feedback loops that are involved in potentially chaotic stress response, indicating that the dynamics of these potentially destabilising motifs are strongly restrained under homeostatic conditions. The same relationship is observed in a human cancer cell line (K562), and we postulate that four-gene LRCs act as ‘universal attenuators’. These findings suggest a role for long LRCs in dampening variation in gene expression, thereby protecting cell identity, and in controlling dramatic shifts in cell-wide gene expression through inhibiting chaos-generating motifs.

Effects of cell-cycle-dependent expression on random fluctuations in protein levels

Expression of many genes varies as a cell transitions through different cell-cycle stages. How coupling between stochastic expression and cell cycle impacts cell-to-cell variability (noise) in the level of protein is not well understood. We analyse a model where a stable protein is synthesized in random bursts, and the frequency with which bursts occur varies within the cell cycle. Formulae quantifying the extent of fluctuations in the protein copy number are derived and decomposed into components arising from the cell cycle and stochastic processes. The latter stochastic component represents contributions from bursty expression and errors incurred during partitioning of molecules between daughter cells. These formulae reveal an interesting trade-off: cell-cycle dependencies that amplify the noise contribution from bursty expression also attenuate the contribution from partitioning errors. We investigate the existence of optimum strategies for coupling expression to the cell cycle that minimize the stochastic component. Intriguingly, results show that a zero production rate throughout the cell cycle, with expression only occurring just before cell division, minimizes noise from bursty expression for a fixed mean protein level. By contrast, the optimal strategy in the case of partitioning errors is to make the protein just after cell division. We provide examples of regulatory proteins that are expressed only towards the end of the cell cycle, and argue that such strategies enhance robustness of cell-cycle decisions to the intrinsic stochasticity of gene expression.

Intercellular Variability in Protein Levels from Stochastic Expression and Noisy Cell Cycle Processes

Inside individual cells, expression of genes is inherently stochastic and manifests as cell-to-cell variability or noise in protein copy numbers. Since proteins half-lives can be comparable to the cell-cycle length, randomness in cell-division times generates additional intercellular variability in protein levels. Moreover, as many mRNA/protein species are expressed at low-copy numbers, errors incurred in partitioning of molecules between two daughter cells are significant. We derive analytical formulas for the total noise in protein levels when the cell-cycle duration follows a general class of probability distributions. Using a novel hybrid approach the total noise is decomposed into components arising from i) stochastic expression; ii) partitioning errors at the time of cell division and iii) random cell-division events. These formulas reveal that random cell-division times not only generate additional extrinsic noise, but also critically affect the mean protein copy numbers and intrinsic noise components. Counter intuitively, in some parameter regimes, noise in protein levels can decrease as cell-division times become more stochastic. Computations are extended to consider genome duplication, where transcription rate is increased at a random point in the cell cycle. We systematically investigate how the timing of genome duplication influences different protein noise components. Intriguingly, results show that noise contribution from stochastic expression is minimized at an optimal genome-duplication time. Our theoretical results motivate new experimental methods for decomposing protein noise levels from synchronized and asynchronized single-cell expression data. Characterizing the contributions of individual noise mechanisms will lead to precise estimates of gene expression parameters and techniques for altering stochasticity to change phenotype of individual cells.

Inside individual cells, gene products often occur at low molecular counts and are subject to considerable stochastic fluctuations (noise) in copy numbers over time. An important consequence of noisy expression is that the level of a protein can vary considerably even among genetically identical cells exposed to the same environment. Such non-genetic phenotypic heterogeneity is physiologically relevant and critically influences diverse cellular processes. In addition to noise sources inherent in gene product synthesis, recent experimental studies have uncovered additional noise mechanisms that critically effect expression. For example, the time within the cell cycle when a gene duplicates, and the time taken to complete cell cycle are governed by random processes. The key contribution of this work is development of novel mathematical results quantifying how cell cycle-related noise sources combine with stochastic expression to drive intercellular variability in protein molecular counts. Derived formulas lead to many counterintuitive results, such as increasing randomness in the timing of cell division can lower noise in the level of a protein. Finally, these results inform experimental strategies to systematically dissect the contributions of different noise sources in the expression of a gene of interest.

Transcriptional Bursting Explains the Noise-Versus-Mean Relationship in mRNA and Protein Levels

Recent analysis demonstrates that the HIV-1 Long Terminal Repeat (HIV LTR) promoter exhibits a range of possible transcriptional burst sizes and frequencies for any mean-expression level. However, these results have also been interpreted as demonstrating that cell-to-cell expression variability (noise) and mean are uncorrelated, a significant deviation from previous results. Here, we re-examine the available mRNA and protein abundance data for the HIV LTR and find that noise in mRNA and protein expression scales inversely with the mean along analytically predicted transcriptional burst-size manifolds. We then experimentally perturb transcriptional activity to test a prediction of the multiple burst-size model: that increasing burst frequency will cause mRNA noise to decrease along given burst-size lines as mRNA levels increase. The data show that mRNA and protein noise decrease as mean expression increases, supporting the canonical inverse correlation between noise and mean.

A mechanistic stochastic framework for regulating bacterial cell division

How exponentially growing cells maintain size homeostasis is an important fundamental problem. Recent single-cell studies in prokaryotes have uncovered the adder principle, where cells add a fixed size (volume) from birth to division, irrespective of their size at birth. To mechanistically explain the adder principle, we consider a timekeeper protein that begins to get stochastically expressed after cell birth at a rate proportional to the volume. Cell-division time is formulated as the first-passage time for protein copy numbers to hit a fixed threshold. Consistent with data, the model predicts that the noise in division timing increases with size at birth. Intriguingly, our results show that the distribution of the volume added between successive cell-division events is independent of the newborn cell size. This was dramatically seen in experimental studies, where histograms of the added volume corresponding to different newborn sizes collapsed on top of each other. The model provides further insights consistent with experimental observations: the distribution of the added volume when scaled by its mean becomes invariant of the growth rate. In summary, our simple yet elegant model explains key experimental findings and suggests a mechanism for regulating both the mean and fluctuations in cell-division timing for controlling size.

The HIV-1 Tat Protein Is Monomethylated at Lysine 71 by the Lysine Methyltransferase KMT7

The HIV-1 transactivator protein Tat is a critical regulator of HIV transcription primarily enabling efficient elongation of viral transcripts. Its interactions with RNA and various host factors are regulated by ordered, transient post-translational modifications. Here, we report a novel Tat modification, monomethylation at lysine 71 (K71). We found that Lys-71 monomethylation (K71me) is catalyzed by KMT7, a methyltransferase that also targets lysine 51 (K51) in Tat. Using mass spectrometry, in vitro enzymology, and modification-specific antibodies, we found that KMT7 monomethylates both Lys-71 and Lys-51 in Tat. K71me is important for full Tat transactivation, as KMT7 knockdown impaired the transcriptional activity of wild type (WT) Tat but not a Tat K71R mutant. These findings underscore the role of KMT7 as an important monomethyltransferase regulating HIV transcription through Tat.

Minimal moment equations for stochastic models of biochemical reaction networks with partially finite state space

Many stochastic models of biochemical reaction networks contain some chemical species for which the number of molecules that are present in the system can only be finite (for instance due to conservation laws), but also other species that can be present in arbitrarily large amounts. The prime example of such networks are models of gene expression, which typically contain a small and finite number of possible states for the promoter but an infinite number of possible states for the amount of mRNA and protein. One of the main approaches to analyze such models is through the use of equations for the time evolution of moments of the chemical species. Recently, a new approach based on conditional moments of the species with infinite state space given all the different possible states of the finite species has been proposed. It was argued that this approach allows one to capture more details about the full underlying probability distribution with a smaller number of equations. Here, I show that the result that less moments provide more information can only stem from an unnecessarily complicated description of the system in the classical formulation. The foundation of this argument will be the derivation of moment equations that describe the complete probability distribution over the finite state space but only low-order moments over the infinite state space. I will show that the number of equations that is needed is always less than what was previously claimed and always less than the number of conditional moment equations up to the same order. To support these arguments, a symbolic algorithm is provided that can be used to derive minimal systems of unconditional moment equations for models with partially finite state space.

Distinct promoter activation mechanisms modulate noise-driven HIV gene expression

Latent human immunodeficiency virus (HIV) infections occur when the virus occupies a transcriptionally silent but reversible state, presenting a major obstacle to cure. There is experimental evidence that random fluctuations in gene expression, when coupled to the strong positive feedback encoded by the HIV genetic circuit, act as a ‘molecular switch’ controlling cell fate, i.e., viral replication versus latency. Here, we implemented a stochastic computational modeling approach to explore how different promoter activation mechanisms in the presence of positive feedback would affect noise-driven activation from latency. We modeled the HIV promoter as existing in one, two, or three states that are representative of increasingly complex mechanisms of promoter repression underlying latency. We demonstrate that two-state and three-state models are associated with greater variability in noisy activation behaviors, and we find that Fano factor (defined as variance over mean) proves to be a useful noise metric to compare variability across model structures and parameter values. Finally, we show how three-state promoter models can be used to qualitatively describe complex reactivation phenotypes in response to therapeutic perturbations that we observe experimentally. Ultimately, our analysis suggests that multi-state models more accurately reflect observed heterogeneous reactivation and may be better suited to evaluate how noise affects viral clearance.

A minimal fate-selection switch

To preserve fitness in unpredictable, fluctuating environments, a range of biological systems probabilistically generate variant phenotypes--a process often referred to as 'bet-hedging', after the financial practice of diversifying assets to minimize risk in volatile markets. The molecular mechanisms enabling bet-hedging have remained elusive. Here, we review how HIV makes a bet-hedging decision between active replication and proviral latency, a long-lived dormant state that is the chief barrier to an HIV cure. The discovery of a virus-encoded bet-hedging circuit in HIV revealed an ancient evolutionary role for latency and identified core regulatory principles, such as feedback and stochastic 'noise', that enable cell-fate decisions. These core principles were later extended to fate selection in stem cells and cancer, exposed new therapeutic targets for HIV, and led to a potentially broad strategy of using 'noise modulation' to redirect cell fate.

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.

Stochastic sensitivity analysis and kernel inference via distributional data

Cellular processes are noisy due to the stochastic nature of biochemical reactions. As such, it is impossible to predict the exact quantity of a molecule or other attributes at the single-cell level. However, the distribution of a molecule over a population is often deterministic and is governed by the underlying regulatory networks relevant to the cellular functionality of interest. Recent studies have started to exploit this property to infer network states. To facilitate the analysis of distributional data in a general experimental setting, we introduce a computational framework to efficiently characterize the sensitivity of distributional output to changes in external stimuli. Further, we establish a probability-divergence-based kernel regression model to accurately infer signal level based on distribution measurements. Our methodology is applicable to any biological system subject to stochastic dynamics and can be used to elucidate how population-based information processing may contribute to organism-level functionality. It also lays the foundation for engineering synthetic biological systems that exploit population decoding to more robustly perform various biocomputation tasks, such as disease diagnostics and environmental-pollutant sensing.

Conditional Moment Closure Schemes for Studying Stochastic Dynamics of Genetic Circuits

Inside individual cells, stochastic expression drives random fluctuations in gene product copy numbers, which corrupts functioning of both natural and synthetic genetic circuits. Dynamic models of genetic circuits are formulated stochastically using the chemical master equation framework. Since obtaining probability distributions can be computationally expensive in these models, noise is typically investigated through lower-order statistical moments (mean, variance, correlation, skewness, etc.) of mRNA/proteins levels. However, due to the nonlinearities in genetic circuits, this moment dynamics is typically not closed, in the sense that the time derivative of the lower-order statistical moments depends on high-order moments. Moment equations are closed by expressing higher-order moments as nonlinear functions of lower-order moments, a technique commonly referred to as moment closure. We provide a new moment closure scheme for studying stochastic dynamics of genetic circuits, where genes randomly toggle between transcriptionally active and inactive states. The method is based on conditioning protein levels on active states of genes and then expressing higher-order moments as functions of lower-order conditional moments. The conditional closure scheme is illustrated on different circuit motifs and found to outperform existing closure techniques. Rapid computation of stochasticity through closure methods will enable improved characterization and design of synthetic circuits that exhibit robust performance in spite of noisy expression of underlying genes.

Transient changes in intercellular protein variability identify sources of noise in gene expression

Protein levels differ considerably between otherwise identical cells, and these differences significantly affect biological function and phenotype. Previous work implicated various noise mechanisms that drive variability in protein copy numbers across an isogenic cell population. For example, transcriptional bursting of mRNAs has been shown to be a major source of noise in the expression of many genes. Additional expression variability, referred to as extrinsic noise, arises from intercellular variations in mRNA transcription and protein translation rates attributed to cell-to-cell differences in cell size, abundance of ribosomes, etc. We propose a method to determine the magnitude of different noise sources in a given gene of interest. The method relies on blocking transcription and measuring changes in protein copy number variability over time. Our results show that this signal has sufficient information to quantify both the extent of extrinsic noise and transcription bursting in gene expression. Moreover, if the mean mRNA count is known, then the relative contributions of transcription versus translation rate fluctuations to extrinsic noise can also be determined. In summary, our study provides an easy-to-implement method for characterizing noisy protein expression that complements existing techniques for studying stochastic dynamics of genetic circuits.

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.

Iterative experiment design guides the characterization of a light-inducible gene expression circuit

Systems biology rests on the idea that biological complexity can be better unraveled through the interplay of modeling and experimentation. However, the success of this approach depends critically on the informativeness of the chosen experiments, which is usually unknown a priori. Here, we propose a systematic scheme based on iterations of optimal experiment design, flow cytometry experiments, and Bayesian parameter inference to guide the discovery process in the case of stochastic biochemical reaction networks. To illustrate the benefit of our methodology, we apply it to the characterization of an engineered light-inducible gene expression circuit in yeast and compare the performance of the resulting model with models identified from nonoptimal experiments. In particular, we compare the parameter posterior distributions and the precision to which the outcome of future experiments can be predicted. Moreover, we illustrate how the identified stochastic model can be used to determine light induction patterns that make either the average amount of protein or the variability in a population of cells follow a desired profile. Our results show that optimal experiment design allows one to derive models that are accurate enough to precisely predict and regulate the protein expression in heterogeneous cell populations over extended periods of time.

Integrating single-molecule experiments and discrete stochastic models to understand heterogeneous gene transcription dynamics

The production and degradation of RNA transcripts is inherently subject to biological noise that arises from small gene copy numbers in individual cells. As a result, cellular RNA levels can exhibit large fluctuations over time and from one cell to the next. This article presents a range of precise single-molecule experimental techniques, based upon RNA fluorescence in situ hybridization, which can be used to measure the fluctuations of RNA at the single-cell level. A class of models for gene activation and deactivation is postulated in order to capture complex stochastic effects of chromatin modifications or transcription factor interactions. A computational tool, known as the finite state projection approach, is introduced to accurately and efficiently analyze these models in order to predict how probability distributions of RNA change over time in response to changing environmental conditions. These single-molecule experiments, discrete stochastic models, and computational analyses are systematically integrated to identify models of gene regulation dynamics. To illustrate the power and generality of our integrated experimental and computational approach, we explore cases that include different models for three different RNA types (sRNA, mRNA and nascent RNA), three different experimental techniques and three different biological species (bacteria, yeast and human cells).

Roles of factorial noise in inducing bimodal gene expression

Some gene regulatory systems can exhibit bimodal distributions of mRNA or protein although the deterministic counterparts are monostable. This noise-induced bimodality is an interesting phenomenon and has important biological implications, but it is unclear how different sources of expression noise (each source creates so-called factorial noise that is defined as a component of the total noise) contribute separately to this stochastic bimodality. Here we consider a minimal model of gene regulation, which is monostable in the deterministic case. Although simple, this system contains factorial noise of two main kinds: promoter noise due to switching between gene states and transcriptional (or translational) noise due to synthesis and degradation of mRNA (or protein). To better trace the roles of factorial noise in inducing bimodality, we also analyze two limit models, continuous and adiabatic approximations, apart from the exact model. We show that in the case of slow gene switching, the continuous model where only promoter noise is considered can exhibit bimodality; in the case of fast switching, the adiabatic model where only transcriptional or translational noise is considered can also exhibit bimodality but the exact model cannot; and in other cases, both promoter noise and transcriptional or translational noise can cooperatively induce bimodality. Since slow gene switching and large protein copy numbers are characteristics of eukaryotic cells, whereas fast gene switching and small protein copy numbers are characteristics of prokaryotic cells, we infer that eukaryotic stochastic bimodality is induced mainly by promoter noise, whereas prokaryotic stochastic bimodality is induced primarily by transcriptional or translational noise.

A hardwired HIV latency program

Biological circuits can be controlled by two general schemes: environmental sensing or autonomous programs. For viruses such as HIV, the prevailing hypothesis is that latent infection is controlled by cellular state (i.e., environment), with latency simply an epiphenomenon of infected cells transitioning from an activated to resting state. However, we find that HIV expression persists despite the activated-to-resting cellular transition. Mathematical modeling indicates that HIV's Tat positive-feedback circuitry enables this persistence and strongly controls latency. To overcome the inherent crosstalk between viral circuitry and cellular activation and to directly test this hypothesis, we synthetically decouple viral dependence on cellular environment from viral transcription. These circuits enable control of viral transcription without cellular activation and show that Tat feedback is sufficient to regulate latency independent of cellular activation. Overall, synthetic reconstruction demonstrates that a largely autonomous, viral-encoded program underlies HIV latency—potentially explaining why cell-targeted latency-reversing agents exhibit incomplete penetrance.

Systems biology approach to understanding post-traumatic stress disorder

This review paper presents known biological facts about PTSD and the mathematical/systems biology tools used to understand the underpinning molecular principles.

Modeling dynamics of cell-to-cell variability in TRAIL-induced apoptosis explains fractional killing and predicts reversible resistance

Isogenic cells sensing identical external signals can take markedly different decisions. Such decisions often correlate with pre-existing cell-to-cell differences in protein levels. When not neglected in signal transduction models, these differences are accounted for in a static manner, by assuming randomly distributed initial protein levels. However, this approach ignores the a priori non-trivial interplay between signal transduction and the source of this cell-to-cell variability: temporal fluctuations of protein levels in individual cells, driven by noisy synthesis and degradation. Thus, modeling protein fluctuations, rather than their consequences on the initial population heterogeneity, would set the quantitative analysis of signal transduction on firmer grounds. Adopting this dynamical view on cell-to-cell differences amounts to recast extrinsic variability into intrinsic noise. Here, we propose a generic approach to merge, in a systematic and principled manner, signal transduction models with stochastic protein turnover models. When applied to an established kinetic model of TRAIL-induced apoptosis, our approach markedly increased model prediction capabilities. One obtains a mechanistic explanation of yet-unexplained observations on fractional killing and non-trivial robust predictions of the temporal evolution of cell resistance to TRAIL in HeLa cells. Our results provide an alternative explanation to survival via induction of survival pathways since no TRAIL-induced regulations are needed and suggest that short-lived anti-apoptotic protein Mcl1 exhibit large and rare fluctuations. More generally, our results highlight the importance of accounting for stochastic protein turnover to quantitatively understand signal transduction over extended durations, and imply that fluctuations of short-lived proteins deserve particular attention.

Quantifying gene expression variability arising from randomness in cell division times

The level of a given mRNA or protein exhibits significant variations from cell-to-cell across a homogeneous population of living cells. Much work has focused on understanding the different sources of noise in the gene-expression process that drive this stochastic variability in gene-expression. Recent experiments tracking growth and division of individual cells reveal that cell division times have considerable inter-cellular heterogeneity. Here we investigate how randomness in the cell division times can create variability in population counts. We consider a model by which mRNA/protein levels in a given cell evolve according to a linear differential equation and cell divisions occur at times spaced by independent and identically distributed random intervals. Whenever the cell divides the levels of mRNA and protein are halved. For this model, we provide a method for computing any statistical moment (mean, variance, skewness, etcetera) of the mRNA and protein levels. The key to our approach is to establish that the time evolution of the mRNA and protein statistical moments is described by an upper triangular system of Volterra equations. Computation of the statistical moments for physiologically relevant parameter values shows that randomness in the cell division process can be a major factor in driving difference in protein levels across a population of cells.

Stochastic holin expression can account for lysis time variation in the bacteriophage λ

The inherent stochastic nature of biochemical processes can drive differences in gene expression between otherwise identical cells. While cell-to-cell variability in gene expression has received much attention, randomness in timing of events has been less studied. We investigate event timing at the single-cell level in a simple system, the lytic pathway of the bacterial virus phage λ. In individual cells, lysis occurs on average at 65 min, with an s.d. of 3.5 min. Interestingly, mutations in the lysis protein, holin, alter both the lysis time (LT) mean and variance. In our analysis, LT is formulated as the first-passage time (FPT) for cellular holin levels to cross a critical threshold. Exact analytical formulae for the FPT moments are derived for stochastic gene expression models. These formulae reveal how holin transcription and translation efficiencies independently modulate the LT mean and variation. Analytical expressions for the LT moments are used to evaluate previously published single-cell LT data for λ phages with mutations in the holin sequence or its promoter. Our results show that stochastic holin expression is sufficient to account for the intercellular LT differences in both wild-type phages, and phage variants where holin transcription and the threshold for lysis have been experimentally altered. Finally, our analysis reveals regulatory motifs that enhance the robustness of lysis timing to cellular noise.

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.

Entrainment to periodic initiation and transition rates in a computational model for gene translation

Periodic oscillations play an important role in many biomedical systems. Proper functioning of biological systems that respond to periodic signals requires the ability to synchronize with the periodic excitation. For example, the sleep/wake cycle is a manifestation of an internal timing system that synchronizes to the solar day. In the terminology of systems theory, the biological system must entrain or phase-lock to the periodic excitation. Entrainment is also important in synthetic biology. For example, connecting several artificial biological systems that entrain to a common clock may lead to a well-functioning modular system. The cell-cycle is a periodic program that regulates DNA synthesis and cell division. Recent biological studies suggest that cell-cycle related genes entrain to this periodic program at the gene translation level, leading to periodically-varying protein levels of these genes. The ribosome flow model (RFM) is a deterministic model obtained via a mean-field approximation of a stochastic model from statistical physics that has been used to model numerous processes including ribosome flow along the mRNA. Here we analyze the RFM under the assumption that the initiation and/or transition rates vary periodically with a common period . We show that the ribosome distribution profile in the RFM entrains to this periodic excitation. In particular, the protein synthesis pattern converges to a unique periodic solution with period . To the best of our knowledge, this is the first proof of entrainment in a mathematical model for translation that encapsulates aspects such as initiation and termination rates, ribosomal movement and interactions, and non-homogeneous elongation speeds along the mRNA. Our results support the conjecture that periodic oscillations in tRNA levels and other factors related to the translation process can induce periodic oscillations in protein levels, and may suggest a new approach for re-engineering genetic systems to obtain a desired, periodic, protein synthesis rate.

Transcriptional control of HIV latency: cellular signaling pathways, epigenetics, happenstance and the hope for a cure

Replication-competent latent HIV-1 proviruses that persist in the genomes of a very small subset of resting memory T cells in infected individuals under life-long antiretroviral therapy present a major barrier towards viral eradication. Multiple molecular mechanisms are required to repress the viral trans-activating factor Tat and disrupt the regulatory Tat feedback circuit leading to the establishment of the latent viral reservoir. In particular, latency is due to a combination of transcriptional silencing of proviruses via host epigenetic mechanisms and restrictions on the expression of P-TEFb, an essential co-factor for Tat. Induction of latent proviruses in the presence of antiretroviral therapy is expected to enable clearance of latently infected cells by viral cytopathic effects and host antiviral immune responses. An in-depth comprehensive understanding of the molecular control of HIV-1 transcription should inform the development of optimal combinatorial reactivation strategies that are intended to purge the latent viral reservoir.

Integrating phenotypic plasticity within an Ecological Genomics framework: recent insights from the genomics, evolution, ecology, and fitness of plasticity

E.B. Ford's 1964 book Ecological Genetics was a call for biologists to engage in multidisciplinary work in order to elucidate the link between genotype, phenotype, and fitness for ecologically relevant traits. In this review, we argue that the integration of an ecological genomics framework in studies of phenotypic plasticity is a promising approach to elucidate the causal links between genes and the environment, particularly during colonization of novel environments, environmental change, and speciation. This review highlights some of the questions and hypotheses generated from a mechanistic, evolutionary, and ecological perspective, in order to direct the continued and future use of genomic tools in the study of phenotypic plasticity.

Quantifying intrinsic and extrinsic variability in stochastic gene expression models

Genetically identical cell populations exhibit considerable intercellular variation in the level of a given protein or mRNA. Both intrinsic and extrinsic sources of noise drive this variability in gene expression. More specifically, extrinsic noise is the expression variability that arises from cell-to-cell differences in cell-specific factors such as enzyme levels, cell size and cell cycle stage. In contrast, intrinsic noise is the expression variability that is not accounted for by extrinsic noise, and typically arises from the inherent stochastic nature of biochemical processes. Two-color reporter experiments are employed to decompose expression variability into its intrinsic and extrinsic noise components. Analytical formulas for intrinsic and extrinsic noise are derived for a class of stochastic gene expression models, where variations in cell-specific factors cause fluctuations in model parameters, in particular, transcription and/or translation rate fluctuations. Assuming mRNA production occurs in random bursts, transcription rate is represented by either the burst frequency (how often the bursts occur) or the burst size (number of mRNAs produced in each burst). Our analysis shows that fluctuations in the transcription burst frequency enhance extrinsic noise but do not affect the intrinsic noise. On the contrary, fluctuations in the transcription burst size or mRNA translation rate dramatically increase both intrinsic and extrinsic noise components. Interestingly, simultaneous fluctuations in transcription and translation rates arising from randomness in ATP abundance can decrease intrinsic noise measured in a two-color reporter assay. Finally, we discuss how these formulas can be combined with single-cell gene expression data from two-color reporter experiments for estimating model parameters.

Designing experiments to understand the variability in biochemical reaction networks

Exploiting the information provided by the molecular noise of a biological process has proved to be valuable in extracting knowledge about the underlying kinetic parameters and sources of variability from single-cell measurements. However, quantifying this additional information a priori, to decide whether a single-cell experiment might be beneficial, is currently only possible in systems where either the chemical master equation is computationally tractable or a Gaussian approximation is appropriate. Here, we provide formulae for computing the information provided by measured means and variances from the first four moments and the parameter derivatives of the first two moments of the underlying process. For stochastic kinetic models for which these moments can be either computed exactly or approximated efficiently, the derived formulae can be used to approximate the information provided by single-cell distribution experiments. Based on this result, we propose an optimal experimental design framework which we employ to compare the utility of dual-reporter and perturbation experiments for quantifying the different noise sources in a simple model of gene expression. Subsequently, we compare the information content of a set of experiments which have been performed in an engineered light-switch gene expression system in yeast and show that well-chosen gene induction patterns may allow one to identify features of the system which remain hidden in unplanned experiments.