Promoter architecture dictates cell-to-cell variability in gene expression

Information Processing in Biochemical Networks

Living systems are characterized by controlled flows of matter, energy, and information. While the biophysics community has productively engaged with the first two, addressing information flows has been more challenging, with some scattered success in evolutionary theory and a more coherent track record in neuroscience. Nevertheless, interdisciplinary work of the past two decades at the interface of biophysics, quantitative biology, and engineering has led to an emerging mathematical language for describing information flows at the molecular scale. This is where the central processes of life unfold: from detection and transduction of environmental signals to the readout or copying of genetic information and the triggering of adaptive cellular responses. Such processes are coordinated by complex biochemical reaction networks that operate at room temperature, are out of equilibrium, and use low copy numbers of diverse molecular species with limited interaction specificity. Here we review how flows of information through biochemical networks can be formalized using information-theoretic quantities, quantified from data, and computed within various modeling frameworks. Optimization of information flows is presented as a candidate design principle that navigates the relevant time, energy, crosstalk, and metabolic constraints to predict reliable cellular signaling and gene regulation architectures built of individually noisy components.

A differentiable Gillespie algorithm for simulating chemical kinetics, parameter estimation, and designing synthetic biological circuits

The Gillespie algorithm is commonly used to simulate and analyze complex chemical reaction networks. Here, we leverage recent breakthroughs in deep learning to develop a fully differentiable variant of the Gillespie algorithm. The differentiable Gillespie algorithm (DGA) approximates discontinuous operations in the exact Gillespie algorithm using smooth functions, allowing for the calculation of gradients using backpropagation. The DGA can be used to quickly and accurately learn kinetic parameters using gradient descent and design biochemical networks with desired properties. As an illustration, we apply the DGA to study stochastic models of gene promoters. We show that the DGA can be used to: (1) successfully learn kinetic parameters from experimental measurements of mRNA expression levels from two distinct Escherichia coli promoters and (2) design nonequilibrium promoter architectures with desired input-output relationships. These examples illustrate the utility of the DGA for analyzing stochastic chemical kinetics, including a wide variety of problems of interest to synthetic and systems biology.

Optimisation of gene expression noise for cellular persistence against lethal events

Bacterial cell persistence, crucial for survival under adverse conditions like antibiotic exposure, is intrinsically linked to stochastic fluctuations in gene expression. Certain genes, while inhibiting growth under normal circumstances, confer tolerance to antibiotics at elevated expression levels. The occurrence of antibiotic events lead to instantaneous cellular responses with varied survival probabilities correlated with gene expression levels. Notably, cells with lower protein concentrations face higher mortality rates. This study aims to elucidate an optimal strategy for protein expression conducive to cellular survival. Through comprehensive mathematical analysis, we determine the optimal burst size and frequency that maximise cell proliferation. Furthermore, we explore how the optimal expression distribution changes as the cost of protein expression to growth escalates. Our model reveals a hysteresis phenomenon, characterised by discontinuous transitions between deterministic and stochastic optima. Intriguingly, stochastic optima possess a noise floor, representing the minimal level of fluctuations essential for optimal cellular resilience.

A differentiable Gillespie algorithm for simulating chemical kinetics, parameter estimation, and designing synthetic biological circuits

The Gillespie algorithm is commonly used to simulate and analyze complex chemical reaction networks. Here, we leverage recent breakthroughs in deep learning to develop a fully differentiable variant of the Gillespie algorithm. The differentiable Gillespie algorithm (DGA) approximates discontinuous operations in the exact Gillespie algorithm using smooth functions, allowing for the calculation of gradients using backpropagation. The DGA can be used to quickly and accurately learn kinetic parameters using gradient descent and design biochemical networks with desired properties. As an illustration, we apply the DGA to study stochastic models of gene promoters. We show that the DGA can be used to: (i) successfully learn kinetic parameters from experimental measurements of mRNA expression levels from two distinct E. coli promoters and (ii) design nonequilibrium promoter architectures with desired input-output relationships. These examples illustrate the utility of the DGA for analyzing stochastic chemical kinetics, including a wide variety of problems of interest to synthetic and systems biology.

A differentiable Gillespie algorithm for simulating chemical kinetics, parameter estimation, and designing synthetic biological circuits

The Gillespie algorithm is commonly used to simulate and analyze complex chemical reaction networks. Here, we leverage recent breakthroughs in deep learning to develop a fully differentiable variant of the Gillespie algorithm. The differentiable Gillespie algorithm (DGA) approximates discontinuous operations in the exact Gillespie algorithm using smooth functions, allowing for the calculation of gradients using backpropagation. The DGA can be used to quickly and accurately learn kinetic parameters using gradient descent and design biochemical networks with desired properties. As an illustration, we apply the DGA to study stochastic models of gene promoters. We show that the DGA can be used to: (i) successfully learn kinetic parameters from experimental measurements of mRNA expression levels from two distinct E. coli promoters and (ii) design nonequilibrium promoter architectures with desired input-output relationships. These examples illustrate the utility of the DGA for analyzing stochastic chemical kinetics, including a wide variety of problems of interest to synthetic and systems biology.

Anti-correlation of LacI association and dissociation rates observed in living cells

The rate at which transcription factors (TFs) bind their cognate sites has long been assumed to be limited by diffusion, and thus independent of binding site sequence. Here, we systematically test this assumption using cell-to-cell variability in gene expression as a window into the in vivo association and dissociation kinetics of the model transcription factor LacI. Using a stochastic model of the relationship between gene expression variability and binding kinetics, we performed single-cell gene expression measurements to infer association and dissociation rates for a set of 35 different LacI binding sites. We found that both association and dissociation rates differed significantly between binding sites, and moreover observed a clear anticorrelation between these rates across varying binding site strengths. These results contradict the long-standing hypothesis that TF binding site strength is primarily dictated by the dissociation rate, but may confer the evolutionary advantage that TFs do not get stuck in near-operator sequences while searching.

A mathematical model clarifies the ABC Score formula used in enhancer-gene prediction

Enhancers are discrete DNA elements that regulate the expression of eukaryotic genes. They are important not only for their regulatory function, but also as loci that are frequently associated with disease traits. Despite their significance, our conceptual understanding of how enhancers work remains limited. CRISPR-interference methods have recently provided the means to systematically screen for enhancers in cell culture, from which a formula for predicting whether an enhancer regulates a gene, the Activity-by-Contact (ABC) Score, has emerged and has been widely adopted. While useful as a binary classifier, it is less effective at predicting the quantitative effect of an enhancer on gene expression. It is also unclear how the algebraic form of the ABC Score arises from the underlying molecular mechanisms and what assumptions are needed for it to hold. Here, we use the graph-theoretic linear framework, previously introduced to analyze gene regulation, to formulate the default model, a mathematical model of how multiple enhancers independently regulate a gene. We show that the algebraic form of the ABC Score arises from this model. However, the default model assumptions also imply that enhancers act additively on steady-state gene expression. This is known to be false for certain genes and we show how modifying the assumptions can accommodate this discrepancy. Overall, our approach lays a rigorous, biophysical foundation for future studies of enhancer-gene regulation.

Flexibility and sensitivity in gene regulation out of equilibrium

Cells adapt to environments and tune gene expression by controlling the concentrations of proteins and their kinetics in regulatory networks. In both eukaryotes and prokaryotes, experiments and theory increasingly attest that these networks can and do consume biochemical energy. How does this dissipation enable cellular behaviors forbidden in equilibrium? This open question demands quantitative models that transcend thermodynamic equilibrium. Here, we study the control of simple, ubiquitous gene regulatory networks to explore the consequences of departing equilibrium in transcription. Employing graph theory to model a set of especially common regulatory motifs, we find that dissipation unlocks nonmonotonicity and enhanced sensitivity of gene expression with respect to a transcription factor's concentration. These features allow a single transcription factor to act as both a repressor and activator at different concentrations or achieve outputs with multiple concentration regimes of locally enhanced sensitivity. We systematically dissect how energetically driving individual transitions within regulatory networks, or pairs of transitions, generates a wide range of more adjustable and sensitive phenotypic responses than in equilibrium. These results generalize to more complex regulatory scenarios, including combinatorial control by multiple transcription factors, which we relate and often find collapse to simple mathematical behaviors. Our findings quantify necessary conditions and detectable consequences of energy expenditure. These richer mathematical behaviors-feasibly accessed using biological energy budgets and rates-may empower cells to accomplish sophisticated regulation with simpler architectures than those required at equilibrium.

Unravelling the Roles of Bacterial Nanomachines Bistability in Pathogens' Life Cycle

Bacterial nanomachines represent remarkable feats of evolutionary engineering, showcasing intricate molecular mechanisms that enable bacteria to perform a diverse array of functions essential to persist, thrive, and evolve within ecological and pathological niches. Injectosomes and bacterial flagella represent two categories of bacterial nanomachines that have been particularly well studied both at the molecular and functional levels. Among the diverse functionalities of these nanomachines, bistability emerges as a fascinating phenomenon, underscoring their dynamic and complex regulation as well as their contribution to shaping the bacterial community behavior during the infection process. In this review, we examine two closely related bacterial nanomachines, the type 3 secretion system, and the flagellum, to explore how the bistability of molecular-scale devices shapes the bacterial eco-pathological life cycle.

Nascent RNA kinetics with complex promoter architecture: Analytic results and parameter inference

Transcription is a stochastic process that involves several downstream operations which make it difficult to model and infer transcription kinetics from mature RNA numbers in individual cell. However, recent advances in single-cell technologies have enabled a more precise measurement of the fluctuations of nascent RNA that closely reflect transcription kinetics. In this paper we introduce a general stochastic model to mimic nascent RNA kinetics with complex promoter architecture. We derive the exact distribution and moments of nascent RNA using queuing theory techniques, which provide valuable insights into the effect of the molecular memory created by the multistep activation and deactivation on the stochastic kinetics of nascent RNA. Moreover, based on the analytical results, we develop a statistical method to infer the promoter memory from stationary nascent RNA distributions. Data analysis of synthetic data and a realistic example, the HIV-1 gene, verifies the validity of this inference method.

Gene activity fully predicts transcriptional bursting dynamics

Transcription commonly occurs in bursts, with alternating productive (ON) and quiescent (OFF) periods, governing mRNA production rates. Yet, how transcription is regulated through bursting dynamics remains unresolved. Here, we conduct real-time measurements of endogenous transcriptional bursting with single-mRNA sensitivity. Leveraging the diverse transcriptional activities in early fly embryos, we uncover stringent relationships between bursting parameters. Specifically, we find that the durations of ON and OFF periods are linked. Regardless of the developmental stage or body-axis position, gene activity levels predict individual alleles' average ON and OFF periods. Lowly transcribing alleles predominantly modulate OFF periods (burst frequency), while highly transcribing alleles primarily tune ON periods (burst size). These relationships persist even under perturbations of cis-regulatory elements or trans-factors and account for bursting dynamics measured in other species. Our results suggest a novel mechanistic constraint governing bursting dynamics rather than a modular control of distinct parameters by distinct regulatory processes.

What can we learn when fitting a simple telegraph model to a complex gene expression model?

In experiments, the distributions of mRNA or protein numbers in single cells are often fitted to the random telegraph model which includes synthesis and decay of mRNA or protein, and switching of the gene between active and inactive states. While commonly used, this model does not describe how fluctuations are influenced by crucial biological mechanisms such as feedback regulation, non-exponential gene inactivation durations, and multiple gene activation pathways. Here we investigate the dynamical properties of four relatively complex gene expression models by fitting their steady-state mRNA or protein number distributions to the simple telegraph model. We show that despite the underlying complex biological mechanisms, the telegraph model with three effective parameters can accurately capture the steady-state gene product distributions, as well as the conditional distributions in the active gene state, of the complex models. Some effective parameters are reliable and can reflect realistic dynamic behaviors of the complex models, while others may deviate significantly from their real values in the complex models. The effective parameters can also be applied to characterize the capability for a complex model to exhibit multimodality. Using additional information such as single-cell data at multiple time points, we provide an effective method of distinguishing the complex models from the telegraph model. Furthermore, using measurements under varying experimental conditions, we show that fitting the mRNA or protein number distributions to the telegraph model may even reveal the underlying gene regulation mechanisms of the complex models. The effectiveness of these methods is confirmed by analysis of single-cell data for E. coli and mammalian cells. All these results are robust with respect to cooperative transcriptional regulation and extrinsic noise. In particular, we find that faster relaxation speed to the steady state results in more precise parameter inference under large extrinsic noise.

Balanced implicit Patankar-Euler methods for positive solutions of stochastic differential equations of biological regulatory systems

Stochastic differential equations (SDEs) are a powerful tool to model fluctuations and uncertainty in complex systems. Although numerical methods have been designed to simulate SDEs effectively, it is still problematic when numerical solutions may be negative, but application problems require positive simulations. To address this issue, we propose balanced implicit Patankar-Euler methods to ensure positive simulations of SDEs. Instead of considering the addition of balanced terms to explicit methods in existing balanced methods, we attempt the deletion of possible negative terms from the explicit methods to maintain positivity of numerical simulations. The designed balanced terms include negative-valued drift terms and potential negative diffusion terms. The proposed method successfully addresses the issue of divisions with very small denominators in our recently designed stochastic Patankar method. Stability analysis shows that the balanced implicit Patankar-Euler method has much better stability properties than our recently designed composite Patankar-Euler method. Four SDE systems are used to examine the effectiveness, accuracy, and convergence properties of balanced implicit Patankar-Euler methods. Numerical results suggest that the proposed balanced implicit Patankar-Euler method is an effective and efficient approach to ensure positive simulations when any appropriate stepsize is used in simulating SDEs of biological regulatory systems.

Power-law behavior of transcriptional bursting regulated by enhancer-promoter communication

Revealing how transcriptional bursting kinetics are genomically encoded is challenging because genome structures are stochastic at the organization level and are suggestively linked to gene transcription. To address this challenge, we develop a generic theoretical framework that integrates chromatin dynamics, enhancer-promoter (E-P) communication, and gene-state switching to study transcriptional bursting. The theory predicts that power law can be a general rule to quantitatively describe bursting modulations by E-P spatial communication. Specifically, burst frequency and burst size are up-regulated by E-P communication strength, following power laws with positive exponents. Analysis of the scaling exponents further reveals that burst frequency is preferentially regulated. Bursting kinetics are down-regulated by E-P genomic distance with negative power-law exponents, and this negative modulation desensitizes at large distances. The mutual information between burst frequency (or burst size) and E-P spatial distance further reveals essential characteristics of the information transfer from E-P communication to transcriptional bursting kinetics. These findings, which are in agreement with experimental observations, not only reveal fundamental principles of E-P communication in transcriptional bursting but also are essential for understanding cellular decision-making.

Using steady-state formula to estimate time-dependent parameters of stochastic gene transcription models

When studying stochastic gene transcription, it is important to understand how system parameters are temporally modulated in response to varying environments. Experimentally, the dynamic distribution data of RNA copy numbers measured at multiple time points are often fitted to stochastic transcription models to estimate time-dependent parameters. However, current methods require determining which parameters are time-dependent, as well as their analytical formulas, before the optimal fit. In this study, we developed a method to estimate time-dependent parameters in a classical two-state model without prior assumptions regarding the system parameters. At each measured time point, the method fitted the dynamic distribution data using a steady-state distribution formula, in which the estimated constant parameters were approximated as time-dependent parameter values at the measured time point. The accuracy of this method can be guaranteed for RNA molecules with relatively high degradation rates and genes with relatively slow responses to induction. We quantify the accuracy of the method and implemented this method on two sets of dynamic distribution data from prokaryotic and eukaryotic cells, and revealed the temporal modulation of transcription burst size in response to environmental changes.

Chemical Reaction Models in Synthetic Promoter Design in Bacteria

We discuss the formalism of chemical reaction networks (CRNs) as a computer-aided design interface for using formal methods in engineering living technologies. We set out by reviewing formal methods within a broader view of synthetic biology. Based on published results, we illustrate, step by step, how mathematical and computational techniques on CRNs can be used to study the structural and dynamic properties of the designed systems. As a case study, we use an E. coli two-component system that relays the external inorganic phosphate concentration signal to genetic components. We show how CRN models can scan and explore phenotypic regimes of synthetic promoters with varying detection thresholds, thereby providing a means for fine-tuning the promoter strength to match the specification.

Gene expression in growing cells: A biophysical primer

Cell growth and gene expression, two essential elements of all living systems, have long been the focus of biophysical interrogation. Advances in experimental single-cell methods have invigorated theoretical studies into these processes. However, until recently, there was little dialog between the two areas of study. In particular, most theoretical models for gene regulation assumed gene activity to be oblivious to the progression of the cell cycle between birth and division. But, in fact, there are numerous ways in which the periodic character of all cellular observables can modulate gene expression. The molecular factors required for transcription and translation-RNA polymerase, transcription factors, ribosomes-increase in number during the cell cycle, but are also diluted due to the continuous increase in cell volume. The replication of the genome changes the dosage of those same cellular players but also provides competing targets for regulatory binding. Finally, cell division reduces their number again, and so forth. Stochasticity is inherent to all these biological processes, manifested in fluctuations in the synthesis and degradation of new cellular components as well as the random partitioning of molecules at each cell division event. The notion of gene expression as stationary is thus hard to justify. In this review, we survey the emerging paradigm of cell-cycle regulated gene expression, with an emphasis on the global expression patterns rather than gene-specific regulation. We discuss recent experimental reports where cell growth and gene expression were simultaneously measured in individual cells, providing first glimpses into the coupling between the two, and motivating several questions. How do the levels of gene expression products - mRNA and protein - scale with the cell volume and cell-cycle progression? What are the molecular origins of the observed scaling laws, and when do they break down to yield non-canonical behavior? What are the consequences of cell-cycle dependence for the heterogeneity ("noise") in gene expression within a cell population? While the experimental findings, not surprisingly, differ among genes, organisms, and environmental conditions, several theoretical models have emerged that attempt to reconcile these differences and form a unifying framework for understanding gene expression in growing cells.

Effects of microRNA-mediated negative feedback on gene expression noise

MicroRNAs (miRNAs) are small noncoding RNAs that regulate gene expression post-transcriptionally in eukaryotes by binding with target mRNAs and preventing translation. miRNA-mediated feedback motifs are ubiquitous in various genetic networks that control cellular decision making. A key question is how such a feedback mechanism may affect gene expression noise. To answer this, we have developed a mathematical model to study the effects of a miRNA-dependent negative-feedback loop on mean expression and noise in target mRNAs. Combining analytics and simulations, we show the existence of an expression threshold demarcating repressed and expressed regimes in agreement with earlier studies. The steady-state mRNA distributions are bimodal near the threshold, where copy numbers of mRNAs and miRNAs exhibit enhanced anticorrelated fluctuations. Moreover, variation of negative-feedback strength shifts the threshold locations and modulates the noise profiles. Notably, the miRNA-mRNA binding affinity and feedback strength collectively shape the bimodality. We also compare our model with a direct auto-repression motif, where a gene produces its own repressor. Auto-repression fails to produce bimodal mRNA distributions as found in miRNA-based indirect repression, suggesting the crucial role of miRNAs in creating phenotypic diversity. Together, we demonstrate how miRNA-dependent negative feedback modifies the expression threshold and leads to a broader parameter regime of bimodality compared to the no-feedback case.

BurstDECONV: a signal deconvolution method to uncover mechanisms of transcriptional bursting in live cells

Monitoring transcription in living cells gives access to the dynamics of this complex fundamental process. It reveals that transcription is discontinuous, whereby active periods (bursts) are separated by one or several types of inactive periods of distinct lifetimes. However, decoding temporal fluctuations arising from live imaging and inferring the distinct transcriptional steps eliciting them is a challenge. We present BurstDECONV, a novel statistical inference method that deconvolves signal traces into individual transcription initiation events. We use the distribution of waiting times between successive polymerase initiation events to identify mechanistic features of transcription such as the number of rate-limiting steps and their kinetics. Comparison of our method to alternative methods emphasizes its advantages in terms of precision and flexibility. Unique features such as the direct determination of the number of promoter states and the simultaneous analysis of several potential transcription models make BurstDECONV an ideal analytic framework for live cell transcription imaging experiments. Using simulated realistic data, we found that our method is robust with regards to noise or suboptimal experimental designs. To show its generality, we applied it to different biological contexts such as Drosophila embryos or human cells.

The minimal intrinsic stochasticity of constitutively expressed eukaryotic genes is sub-Poissonian

Gene expression inherently gives rise to stochastic variation ("noise") in the production of gene products. Minimizing noise is crucial for ensuring reliable cellular functions. However, noise cannot be suppressed below a certain intrinsic limit. For constitutively expressed genes, this limit is typically assumed to be Poissonian noise, wherein the variance in mRNA numbers is equal to their mean. Here, we demonstrate that several cell division genes in fission yeast exhibit mRNA variances significantly below this limit. The reduced variance can be explained by a gene expression model incorporating multiple transcription and mRNA degradation steps. Notably, in this sub-Poissonian regime, distinct from Poissonian or super-Poissonian regimes, cytoplasmic noise is effectively suppressed through a higher mRNA export rate. Our findings redefine the lower limit of eukaryotic gene expression noise and uncover molecular requirements for achieving ultralow noise, which is expected to be important for vital cellular functions.

Flexibility and sensitivity in gene regulation out of equilibrium

Cells adapt to environments and tune gene expression by controlling the concentrations of proteins and their kinetics in regulatory networks. In both eukaryotes and prokaryotes, experiments and theory increasingly attest that these networks can and do consume bio-chemical energy. How does this dissipation enable cellular behaviors unobtainable in equilibrium? This open question demands quantitative models that transcend thermodynamic equilibrium. Here we study the control of a simple, ubiquitous gene regulatory motif to explore the consequences of departing equilibrium in kinetic cycles. Employing graph theory, we find that dissipation unlocks nonmonotonicity and enhanced sensitivity of gene expression with respect to a transcription factor's concentration. These features allow a single transcription factor to act as both a repressor and activator at different levels or achieve outputs with multiple concentration regions of locally-enhanced sensitivity. We systematically dissect how energetically-driving individual transitions within regulatory networks, or pairs of transitions, generates more adjustable and sensitive phenotypic responses. Our findings quantify necessary conditions and detectable consequences of energy expenditure. These richer mathematical behaviors-feasibly accessed using biological energy budgets and rates-may empower cells to accomplish sophisticated regulation with simpler architectures than those required at equilibrium.

Significance Statement

Growing theoretical and experimental evidence demonstrates that cells can (and do) spend biochemical energy while regulating their genes. Here we explore the impact of departing from equilibrium in simple regulatory cycles, and learn that beyond increasing sensitivity, dissipation can unlock more flexible input-output behaviors that are otherwise forbidden without spending energy. These more complex behaviors could enable cells to perform more sophisticated functions using simpler systems than those needed at equilibrium.

BCH1 expression pattern contributes to the fruit carotenoid diversity between peach and apricot

Peach (Prunus persica L. Batsch) and apricot (Prunus armeniaca L.) are two species of economic importance for fruit production in the genus Prunus. Peach and apricot fruits exhibit significant differences in carotenoid levels and profiles. HPLC-PAD analysis showed that a greater content of β-carotene in mature apricot fruits is primarily responsible for orange color, while peach fruits showed a prominent accumulation of xanthophylls (violaxanthin and cryptoxanthin) with yellow color. There are two β-carotene hydroxylase genes in both peach and apricot genomes. Transcriptional analysis revealed that BCH1 expresses highly in peach but lowly in apricot fruit, showing a correlation with peach and apricot fruit carotenoid profiles. By using a carotenoid engineered bacterial system, it was demonstrated that there was no difference in the BCH1 enzymatic activity between peach and apricot. Comparative analysis about the putative cis-acting regulatory elements between peach and apricot BCH1 promoters provided important information for our understanding of the differences in promoter activity of the BCH1 genes in peach and apricot. Therefore, we investigated the promoter activity of BCH1 gene through a GUS detection system, and confirmed that the difference in the transcription level of the BCH1 gene resulted from the difference of the promoter function. This study provides important perspective to understanding the diversity of carotenoid accumulation in Prunus fruits such as peach and apricot. In particular, BCH1 gene is proposed as a main predictor for β-carotene content in peach and apricot fruits during the ripening process.

The minimal intrinsic stochasticity of constitutively expressed eukaryotic genes is sub-Poissonian

Stochastic variation in gene products ("noise") is an inescapable by-product of gene expression. Noise must be minimized to allow for the reliable execution of cellular functions. However, noise cannot be suppressed beyond an intrinsic lower limit. For constitutively expressed genes, this limit is believed to be Poissonian, meaning that the variance in mRNA numbers cannot be lower than their mean. Here, we show that several cell division genes in fission yeast have mRNA variances significantly below this limit, which cannot be explained by the classical gene expression model for low-noise genes. Our analysis reveals that multiple steps in both transcription and mRNA degradation are essential to explain this sub-Poissonian variance. The sub-Poissonian regime differs qualitatively from previously characterized noise regimes, a hallmark being that cytoplasmic noise is reduced when the mRNA export rate increases. Our study re-defines the lower limit of eukaryotic gene expression noise and identifies molecular requirements for ultra-low noise which are expected to support essential cell functions.

Critical points for the design and application of RNA silencing constructs for plant virus resistance

Control of plant virus diseases is a big challenge in agriculture as is resistance in plant lines to infection by viruses. Recent progress using advanced technologies has provided fast and durable alternatives. One of the most promising techniques against plant viruses that is cost-effective and environmentally safe is RNA silencing or RNA interference (RNAi), a technology that could be used alone or along with other control methods. To achieve the goals of fast and durable resistance, the expressed and target RNAs have been examined in many studies, with regard to the variability in silencing efficiency, which is regulated by various factors such as target sequences, target accessibility, RNA secondary structures, sequence variation in matching positions, and other intrinsic characteristics of various small RNAs. Developing a comprehensive and applicable toolbox for the prediction and construction of RNAi helps researchers to achieve the acceptable performance level of silencing elements. Although the attainment of complete prediction of RNAi robustness is not possible, as it also depends on the cellular genetic background and the nature of the target sequences, some important critical points have been discerned. Thus, the efficiency and robustness of RNA silencing against viruses can be improved by considering the various parameters of the target sequence and the construct design. In this review, we provide a comprehensive treatise regarding past, present and future prospective developments toward designing and applying RNAi constructs for resistance to plant viruses.

Genome-wide inference reveals that feedback regulations constrain promoter-dependent transcriptional burst kinetics

Gene expression in mammalian cells is highly variable and episodic, resulting in a series of discontinuous bursts of mRNAs. A challenge is to understand how static promoter architecture and dynamic feedback regulations dictate bursting on a genome-wide scale. Although single-cell RNA sequencing (scRNA-seq) provides an opportunity to address this challenge, effective analytical methods are scarce. We developed an interpretable and scalable inference framework, which combined experimental data with a mechanistic model to infer transcriptional burst kinetics (sizes and frequencies) and feedback regulations. Applying this framework to scRNA-seq data generated from embryonic mouse fibroblast cells, we found Simpson's paradoxes, i.e. genome-wide burst kinetics exhibit different characteristics in two cases without and with distinguishing feedback regulations. We also showed that feedbacks differently modulate burst frequencies and sizes and conceal the effects of transcription start site distributions on burst kinetics. Notably, only in the presence of positive feedback, TATA genes are expressed with high burst frequencies and enhancer-promoter interactions mainly modulate burst frequencies. The developed inference method provided a flexible and efficient way to investigate transcriptional burst kinetics and the obtained results would be helpful for understanding cell development and fate decision.

Allelic correlation is a marker of trade-offs between barriers to transmission of expression variability and signal responsiveness in genetic networks

Genetic networks should respond to signals but prevent the transmission of spontaneous fluctuations. Limited data from mammalian cells suggest that noise transmission is uncommon, but systematic claims about noise transmission have been limited by the inability to directly measure it. Here, we build a mathematical framework modeling allelic correlation and noise transmission, showing that allelic correlation and noise transmission correspond across model parameters and network architectures. Limiting noise transmission comes with the trade-off of being unresponsive to signals, and within responsive regimes, there is a further trade-off between response time and basal noise transmission. Analysis of allele-specific single-cell RNA-sequencing data revealed that genes encoding upstream factors in signaling pathways and cell-type-specific factors have higher allelic correlation than downstream factors, suggesting they are more subject to regulation. Overall, our findings suggest that some noise transmission must result from signal responsiveness, but it can be minimized by trading off for a slower response. A record of this paper's transparent peer review process is included in the supplemental information.

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.

m6A RNA methylation impairs gene expression variability and reproductive thermotolerance in Arabidopsis

Heat-imposed crop failure is often attributed to reduced thermotolerance of floral tissues; however, the underlying mechanism remains unknown. Here, we demonstrate that m⁶A RNA methylation increases in Arabidopsis flowers and negatively regulates gene expression variability. Stochastic gene expression provides flexibility to cope with environmental stresses. We find that reduced transcriptional fluctuation is associated with compromised activation of heat-responsive genes. Moreover, disruption of an RNA demethylase AtALKBH10B leads to lower gene expression variability, suppression of heat-activated genes, and strong reduction of plant fertility. Our work proposes a novel role for RNA methylation in the bet-hedging strategy of heat stress response.

Molecular Origins of Transcriptional Heterogeneity in Diazotrophic Klebsiella oxytoca

Phenotypic heterogeneity in clonal bacterial batch cultures has been shown for a range of bacterial systems; however, the molecular origins of such heterogeneity and its magnitude are not well understood. Under conditions of extreme low-nitrogen stress in the model diazotroph Klebsiella oxytoca, we found remarkably high heterogeneity of nifHDK gene expression, which codes for the structural genes of nitrogenase, one key enzyme of the global nitrogen cycle. This heterogeneity limited the bulk observed nitrogen-fixing capacity of the population. Using dual-probe, single-cell RNA fluorescent in situ hybridization, we correlated nifHDK expression with that of nifLA and glnK-amtB, which code for the main upstream regulatory components. Through stochastic transcription models and mutual information analysis, we revealed likely molecular origins for heterogeneity in nitrogenase expression. In the wild type and regulatory variants, we found that nifHDK transcription was inherently bursty, but we established that noise propagation through signaling was also significant. The regulatory gene glnK had the highest discernible effect on nifHDK variance, while noise from factors outside the regulatory pathway were negligible. Understanding the basis of inherent heterogeneity of nitrogenase expression and its origins can inform biotechnology strategies seeking to enhance biological nitrogen fixation. Finally, we speculate on potential benefits of diazotrophic heterogeneity in natural soil environments. IMPORTANCE Nitrogen is an essential micronutrient for both plant and animal life and naturally exists in both reactive and inert chemical forms. Modern agriculture is heavily reliant on nitrogen that has been "fixed" into a reactive form via the energetically expensive Haber-Bosch process, with significant environmental consequences. Nitrogen-fixing bacteria provide an alternative source of fixed nitrogen for use in both biotechnological and agricultural settings, but this relies on a firm understanding of how the fixation process is regulated within individual bacterial cells. We examined the cell-to-cell variability in the nitrogen-fixing behavior of Klebsiella oxytoca, a free-living bacterium. The significance of our research is in identifying not only the presence of marked variability but also the specific mechanisms that give rise to it. This understanding gives insight into both the evolutionary advantages of variable behavior as well as strategies for biotechnological applications.

Eukaryotic gene regulation at equilibrium, or non?

Models of transcriptional regulation that assume equilibrium binding of transcription factors have been less successful at predicting gene expression from sequence in eukaryotes than in bacteria. This could be due to the non-equilibrium nature of eukaryotic regulation. Unfortunately, the space of possible non-equilibrium mechanisms is vast and predominantly uninteresting. The key question is therefore how this space can be navigated efficiently, to focus on mechanisms and models that are biologically relevant. In this review, we advocate for the normative role of theory-theory that prescribes rather than just describes-in providing such a focus. Theory should expand its remit beyond inferring mechanistic models from data, towards identifying non-equilibrium gene regulatory schemes that may have been evolutionarily selected, despite their energy consumption, because they are precise, reliable, fast, or otherwise outperform regulation at equilibrium. We illustrate our reasoning by toy examples for which we provide simulation code.

A spatially resolved stochastic model reveals the role of supercoiling in transcription regulation

In Escherichia coli, translocation of RNA polymerase (RNAP) during transcription introduces supercoiling to DNA, which influences the initiation and elongation behaviors of RNAP. To quantify the role of supercoiling in transcription regulation, we developed a spatially resolved supercoiling model of transcription. The integrated model describes how RNAP activity feeds back with the local DNA supercoiling and how this mechanochemical feedback controls transcription, subject to topoisomerase activities and stochastic topological domain formation. This model establishes that transcription-induced supercoiling mediates the cooperation of co-transcribing RNAP molecules in highly expressed genes, and this cooperation is achieved under moderate supercoiling diffusion and high topoisomerase unbinding rates. It predicts that a topological domain could serve as a transcription regulator, generating substantial transcriptional noise. It also shows the relative orientation of two closely arranged genes plays an important role in regulating their transcription. The model provides a quantitative platform for investigating how genome organization impacts transcription.

Tunable transcription factor library for robust quantification of regulatory properties in Escherichia coli

Predicting the quantitative regulatory function of transcription factors (TFs) based on factors such as binding sequence, binding location, and promoter type is not possible. The interconnected nature of gene networks and the difficulty in tuning individual TF concentrations make the isolated study of TF function challenging. Here, we present a library of Escherichia coli strains designed to allow for precise control of the concentration of individual TFs enabling the study of the role of TF concentration on physiology and regulation. We demonstrate the usefulness of this resource by measuring the regulatory function of the zinc-responsive TF, ZntR, and the paralogous TF pair, GalR/GalS. For ZntR, we find that zinc alters ZntR regulatory function in a way that enables activation of the regulated gene to be robust with respect to ZntR concentration. For GalR and GalS, we are able to demonstrate that these paralogous TFs have fundamentally distinct regulatory roles beyond differences in binding affinity.

Quantification of transcription noise’s impact on cell fate commitment with digital resolutions

Motivation

Gene transcription is a random and noisy process. Tremendous efforts in single cell studies have been mapping transcription noises to phenotypic variabilities between isogenic cells. However, the exact role of the noise in cell fate commitment remains largely descriptive or even controversial.

Results

For a specified cell fate, we define the jumping digit I of a critical gene as a statistical threshold that a single cell has approximately an equal chance to commit the fate as to have at least I transcripts of the gene. When the transcription is perturbed by a noise enhancer without changing the basal transcription level E  0, we find a crossing digit k such that the noise catalyzes cell fate change when I > k while stabilizes the current state when I < k; k remains stable against enormous variations of kinetic rates. We further test the reactivation of latent HIV in 22 integration sites by noise enhancers paired with transcriptional activators. Strong synergistic actions are observed when the activators increase transcription burst frequency, whereas no synergism, but antagonism, is often observed if activators increase burst size. The synergistic efficiency can be predicted accurately by the ratio I / E0. When the noise enhancers double the noise, the activators double the burst frequency, and I / E0 ≥ 7, their combination is 10 times more effective than their additive effects across all 22 sites.

Availability and implementation

The jumping digit I may provide a novel probe to explore the phenotypic consequences of transcription noise in cell functions. Code is freely available at http://cam.gzhu.edu.cn/info/1014/1223.htm.

Supplementary information

Supplementary data are available at Bioinformatics online.

Sequence-dependent model of genes with dual σ factor preference

Escherichia coli uses σ factors to quickly control large gene cohorts during stress conditions. While most of its genes respond to a single σ factor, approximately 5% of them have dual σ factor preference. The most common are those responsive to both σ⁷⁰, which controls housekeeping genes, and σ³⁸, which activates genes during stationary growth and stresses. Using RNA-seq and flow-cytometry measurements, we show that 'σ⁷⁰⁺³⁸ genes' are nearly as upregulated in stationary growth as 'σ³⁸ genes'. Moreover, we find a clear quantitative relationship between their promoter sequence and their response strength to changes in σ³⁸ levels. We then propose and validate a sequence dependent model of σ⁷⁰⁺³⁸ genes, with dual sensitivity to σ³⁸ and σ⁷⁰, that is applicable in the exponential and stationary growth phases, as well in the transient period in between. We further propose a general model, applicable to other stresses and σ factor combinations. Given this, promoters controlling σ⁷⁰⁺³⁸ genes (and variants) could become important building blocks of synthetic circuits with predictable, sequence-dependent sensitivity to transitions between the exponential and stationary growth phases.

Sequence specificity in DNA binding is mainly governed by association

Sequence-specific binding of proteins to DNA is essential for accessing genetic information. We derive a model that predicts an anticorrelation between the macroscopic association and dissociation rates of DNA binding proteins. We tested the model for thousands of different lac operator sequences with a protein binding microarray and by observing kinetics for individual lac repressor molecules in single-molecule experiments. We found that sequence specificity is mainly governed by the efficiency with which the protein recognizes different targets. The variation in probability of recognizing different targets is at least 1.7 times as large as the variation in microscopic dissociation rates. Modulating the rate of binding instead of the rate of dissociation effectively reduces the risk of the protein being retained on nontarget sequences while searching.

Exact distributions for stochastic gene expression models with arbitrary promoter architecture and translational bursting

Gene expression in individual cells is inherently variable and sporadic, leading to cell-to-cell variability in mRNA and protein levels. Recent single-cell and single-molecule experiments indicate that promoter architecture and translational bursting play significant roles in controlling gene expression noise and generating the phenotypic diversity that life exhibits. To quantitatively understand the impact of these factors, it is essential to construct an accurate mathematical description of stochastic gene expression and find the exact analytical results, which is a formidable task. Here, we develop a stochastic model of bursty gene expression, which considers the complex promoter architecture governing the variability in mRNA expression and a general distribution characterizing translational burst. We derive the analytical expression for the corresponding protein steady-state distribution and all moment statistics of protein counts. We show that the total protein noise can be decomposed into three parts: the low-copy noise of protein due to probabilistic individual birth and death events, the noise due to stochastic switching between promoter states, and the noise resulting from translational busting. The theoretical results derived provide quantitative insights into the biochemical mechanisms of stochastic gene expression.

Genome-wide gene expression noise in Escherichia coli is condition-dependent and determined by propagation of noise through the regulatory network

Although it is well appreciated that gene expression is inherently noisy and that transcriptional noise is encoded in a promoter’s sequence, little is known about the extent to which noise levels of individual promoters vary across growth conditions. Using flow cytometry, we here quantify transcriptional noise in Escherichia coli genome-wide across 8 growth conditions and find that noise levels systematically decrease with growth rate, with a condition-dependent lower bound on noise. Whereas constitutive promoters consistently exhibit low noise in all conditions, regulated promoters are both more noisy on average and more variable in noise across conditions. Moreover, individual promoters show highly distinct variation in noise across conditions. We show that a simple model of noise propagation from regulators to their targets can explain a significant fraction of the variation in relative noise levels and identifies TFs that most contribute to both condition-specific and condition-independent noise propagation. In addition, analysis of the genome-wide correlation structure of various gene properties shows that gene regulation, expression noise, and noise plasticity are all positively correlated genome-wide and vary independently of variations in absolute expression, codon bias, and evolutionary rate. Together, our results show that while absolute expression noise tends to decrease with growth rate, relative noise levels of genes are highly condition-dependent and determined by the propagation of noise through the gene regulatory network.

Genome-wide flow cytometry measurements reveal that gene expression noise in bacteria is highly condition-dependent; while absolute noise levels of all genes decrease with growth-rate, theoretical modeling shows that the relative noise levels of different genes are determined by the propagation of noise through the gene regulatory network (GRN). Thus GRN structure controls not only mean expression but also noise levels.

Exploiting Noise, Non-Linearity, and Feedback for Differential Control of Multiple Synthetic Cells with a Single Optogenetic Input

Synthetic biology seeks to develop modular biocircuits that combine to produce complex, controllable behaviors. These designs are often subject to noisy fluctuations and uncertainties, and most modern synthetic biology design processes have focused to create robust components to mitigate the noise of gene expression and reduce the heterogeneity of single-cell responses. However, a deeper understanding of noise can achieve control goals that would otherwise be impossible. We explore how an "Optogenetic Maxwell Demon" could selectively amplify noise to control multiple cells using single-input-multiple-output (SIMO) feedback. Using data-constrained stochastic model simulations and theory, we show how an appropriately selected stochastic SIMO controller can drive multiple different cells to different user-specified configurations irrespective of initial conditions. We explore how controllability depends on cells' regulatory structures, the amount of information available to the controller, and the accuracy of the model used. Our results suggest that gene regulation noise, when combined with optogenetic feedback and non-linear biochemical auto-regulation, can achieve synergy to enable precise control of complex stochastic processes.

Co-Delivery of mRNA and pDNA Using Thermally Stabilized Coacervate-Based Core-Shell Nanosystems

Co-delivery of different species of protein-encoding polynucleotides, e.g., messenger RNA (mRNA) and plasmid DNA (pDNA), using the same nanocarrier is an interesting topic that remains scarcely researched in the field of nucleic acid delivery. The current study hence aims to explore the possibility of the simultaneous delivery of mRNA (mCherry) and pDNA (pAmCyan) using a single nanocarrier. The latter is based on gelatin type A, a biocompatible, and biodegradable biopolymer of broad pharmaceutical application. A core-shell nanostructure is designed with a thermally stabilized gelatin-pDNA coacervate in its center. Thermal stabilization enhances the core's colloidal stability and pDNA shielding effect against nucleases as confirmed by nanoparticle tracking analysis and gel electrophoresis, respectively. The stabilized, pDNA-loaded core is coated with the cationic peptide protamine sulfate to enable additional surface-loading with mRNA. The dual-loaded core-shell system transfects murine dendritic cell line DC2.4 with both fluorescent reporter mRNA and pDNA simultaneously, showing a transfection efficiency of 61.4 ± 21.6% for mRNA and 37.6 ± 19.45% for pDNA, 48 h post-treatment, whereas established commercial, experimental, and clinical transfection reagents fail. Hence, the unique co-transfectional capacity and the negligible cytotoxicity of the reported system may hold prospects for vaccination among other downstream applications.

Cis-Regulatory Logic Produces Gene-Expression Noise Describing Phenotypic Heterogeneity in Bacteria

Gene transcriptional process is random. It occurs in bursts and follows single-molecular kinetics. Intermittent bursts are measured based on their frequency and size. They influence temporal fluctuations in the abundance of total mRNA and proteins by generating distinct transcriptional variations referred to as “noise”. Noisy expression induces uncertainty because the association between transcriptional variation and the extent of gene expression fluctuation is ambiguous. The promoter architecture and remote interference of different cis-regulatory elements are the crucial determinants of noise, which is reflected in phenotypic heterogeneity. An alternative perspective considers that cellular parameters dictating genome-wide transcriptional kinetics follow a universal pattern. Research on noise and systematic perturbations of promoter sequences reinforces that both gene-specific and genome-wide regulation occur across species ranging from bacteria and yeast to animal cells. Thus, deciphering gene-expression noise is essential across different genomics applications. Amidst the mounting conflict, it is imperative to reconsider the scope, progression, and rational construction of diversified viewpoints underlying the origin of the noise. Here, we have established an indication connecting noise, gene expression variations, and bacterial phenotypic variability. This review will enhance the understanding of gene-expression noise in various scientific contexts and applications.

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

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

Approximating gene transcription dynamics using steady-state formulas

Understanding how genes in a single cell respond to dynamically changing signals has been a central question in stochastic gene transcription research. Recent studies have generated massive steady-state or snapshot mRNA distribution data of individual cells, and inferred a large spectrum of kinetic transcription parameters under varying conditions. However, there have been few algorithms to convert these static data into the temporal variation of kinetic rates. Real-time imaging has been developed to monitor stochastic transcription processes at the single-cell level, but the immense technicality has prevented its application to most endogenous loci in mammalian cells. In this article, we introduced a stochastic gene transcription model with variable kinetic rates induced by unstable cellular conditions. We approximated the transcription dynamics using easily obtained steady-state formulas in the model. We tested the approximation against experimental data in both prokaryotic and eukaryotic cells and further solidified the conditions that guarantee the robustness of the method. The method can be easily implemented to provide convenient tools for quantifying dynamic kinetics and mechanisms underlying the widespread static transcription data, and may shed a light on circumventing the limitation of current bursting data on transcriptional real-time imaging.

Stochastic Simulations as a Tool for Assessing Signal Fidelity in Gene Expression in Synthetic Promoter Design

Simple Summary

Synthetic biology is an emerging discipline, offering new perspectives in many industrial fields, from pharma and row-material production to renewable energy. Developing synthetic biology applications is often a lengthy and expensive process with extensive and tedious trial-and-error runs. Computational models can direct the engineering of biological circuits in a computer-aided design setting. By providing a virtual lab environment, in silico models of synthetic circuits can contribute to a quantitative understanding of the underlying molecular pathways before a wet-lab implementation. Here, we illustrate this notion from the point of view of signal fidelity and noise relationship. Noise in gene expression can undermine signal fidelity with implications on the well-functioning of the engineered organisms. For our analysis, we use a specific biological circuit that regulates the gene expression in bacterial inorganic phosphate economy. Applications that use this circuit include those in pollutant detection and wastewater treatment. We provide computational models with different levels of molecular detail as virtual labs. We show that inherent fluctuations in the gene expression machinery can be predicted via stochastic simulations to introduce control in the synthetic promoter design process. Our analysis suggests that noise in the system can be alleviated by strong synthetic promoters with slow unbinding rates. Overall, we provide a recipe for the computer-aided design of synthetic promoter libraries with specific signal to noise characteristics.

Abstract

The design and development of synthetic biology applications in a workflow often involve connecting modular components. Whereas computer-aided design tools are picking up in synthetic biology as in other areas of engineering, the methods for verifying the correct functioning of living technologies are still in their infancy. Especially, fine-tuning for the right promoter strength to match the design specifications is often a lengthy and expensive experimental process. In particular, the relationship between signal fidelity and noise in synthetic promoter design can be a key parameter that can affect the healthy functioning of the engineered organism. To this end, based on our previous work on synthetic promoters for the E. coli PhoBR two-component system, we make a case for using chemical reaction network models for computational verification of various promoter designs before a lab implementation. We provide an analysis of this system with extensive stochastic simulations at a single-cell level to assess the signal fidelity and noise relationship. We then show how quasi-steady-state analysis via ordinary differential equations can be used to navigate between models with different levels of detail. We compare stochastic simulations with our full and reduced models by using various metrics for assessing noise. Our analysis suggests that strong promoters with low unbinding rates can act as control tools for filtering out intrinsic noise in the PhoBR context. Our results confirm that even simpler models can be used to determine promoters with specific signal to noise characteristics.

First-principles prediction of the information processing capacity of a simple genetic circuit

Given the stochastic nature of gene expression, genetically identical cells exposed to the same environmental inputs will produce different outputs. This heterogeneity has been hypothesized to have consequences for how cells are able to survive in changing environments. Recent work has explored the use of information theory as a framework to understand the accuracy with which cells can ascertain the state of their surroundings. Yet the predictive power of these approaches is limited and has not been rigorously tested using precision measurements. To that end, we generate a minimal model for a simple genetic circuit in which all parameter values for the model come from independently published data sets. We then predict the information processing capacity of the genetic circuit for a suite of biophysical parameters such as protein copy number and protein-DNA affinity. We compare these parameter-free predictions with an experimental determination of protein expression distributions and the resulting information processing capacity of E. coli cells. We find that our minimal model captures the scaling of the cell-to-cell variability in the data and the inferred information processing capacity of our simple genetic circuit up to a systematic deviation.

Non-Genetic Diversity in Chemosensing and Chemotactic Behavior

Non-genetic phenotypic diversity plays a significant role in the chemotactic behavior of bacteria, influencing how populations sense and respond to chemical stimuli. First, we review the molecular mechanisms that generate phenotypic diversity in bacterial chemotaxis. Next, we discuss the functional consequences of phenotypic diversity for the chemosensing and chemotactic performance of single cells and populations. Finally, we discuss mechanisms that modulate the amount of phenotypic diversity in chemosensory parameters in response to changes in the environment.

Real-time single-cell characterization of the eukaryotic transcription cycle reveals correlations between RNA initiation, elongation, and cleavage

The eukaryotic transcription cycle consists of three main steps: initiation, elongation, and cleavage of the nascent RNA transcript. Although each of these steps can be regulated as well as coupled with each other, their in vivo dissection has remained challenging because available experimental readouts lack sufficient spatiotemporal resolution to separate the contributions from each of these steps. Here, we describe a novel application of Bayesian inference techniques to simultaneously infer the effective parameters of the transcription cycle in real time and at the single-cell level using a two-color MS2/PP7 reporter gene and the developing fruit fly embryo as a case study. Our method enables detailed investigations into cell-to-cell variability in transcription-cycle parameters as well as single-cell correlations between these parameters. These measurements, combined with theoretical modeling, suggest a substantial variability in the elongation rate of individual RNA polymerase molecules. We further illustrate the power of this technique by uncovering a novel mechanistic connection between RNA polymerase density and nascent RNA cleavage efficiency. Thus, our approach makes it possible to shed light on the regulatory mechanisms in play during each step of the transcription cycle in individual, living cells at high spatiotemporal resolution.

Scaling of intrinsic noise in an autocratic reaction network

Biochemical reactions in living cells often produce stochastic trajectories due to the fluctuations of the finite number of the macromolecular species present inside the cell. A significant number of computational and theoretical studies have previously investigated stochasticity in small regulatory networks to understand its origin and regulation. At the systems level regulatory networks have been determined to be hierarchical resembling social networks. In order to determine the stochasticity in networks with hierarchical architecture, here we computationally investigated intrinsic noise in an autocratic reaction network in which only the upstream regulators regulate the downstream regulators. We studied the effects of the qualitative and quantitative nature of regulatory interactions on the stochasticity in the network. We established an unconventional scaling of noise with average abundance in which the noise passes through a minimum indicating that the network can be noisy both in the low and high abundance regimes. We determined that the bursty kinetics of the trajectories are responsible for such scaling. The scaling of noise remains intact for a mixed network that includes democratic subnetworks within the autocratic network.

Interplay between genetic, epigenetic, and gene expression variability: Considering complexity in evolvability

Genetic variability, epigenetic variability, and gene expression variability (noise) are generally considered independently in their relationship with phenotypic variation. However, they appear to be intrinsically interconnected and influence it in combination. The study of the interplay between genetic and epigenetic variability has the longest history. This article rather considers the introduction of gene expression variability in its relationships with the two others and reviews for the first time experimental evidences over the four relationships connected to gene expression noise. They show how introducing this third source of variability complicates the way of thinking evolvability and the emergence of biological novelty. Finally, cancer cells are proposed to be an ideal model to decipher the dynamic interplay between genetic, epigenetic, and gene expression variability when one of them is either experimentally increased or therapeutically targeted. This interplay is also discussed in an evolutionary perspective in the context of cancer cell drug resistance.

Stochastic Differential Equations for Practical Simulation of Gene Circuits

The Chemical Langevin Equation approach allows simple stochastic simulation of gene circuits under many practical situations where the number of molecules of the species involved is not extremely low. Here, we describe methods and a computational framework to simulate a population of cells containing gene circuits of interest. These methods account for both intrinsic and extrinsic noise sources, and allow us to have both individual cell-related species and population-related ones. The protocol covers aspects related to proper description of the system and setting the software tools. It also helps to deal with the optimization of data storage and the simulation precision versus computational time issue. Finally, it also gives practical tests to assess the validity of the underlying technical assumptions.

smiFISH and embryo segmentation for single-cell multi-gene RNA quantification in arthropods

Recently, advances in fluorescent in-situ hybridization techniques and in imaging technology have enabled visualization and counting of individual RNA molecules in single cells. This has greatly enhanced the resolution in our understanding of transcriptional processes. Here, we adapt a recently published smiFISH protocol (single-molecule inexpensive fluorescent in-situ hybridization) to whole embryos across a range of arthropod model species, and also to non-embryonic tissues. Using multiple fluorophores with distinct spectra and white light laser confocal imaging, we simultaneously detect and separate single RNAs from up to eight different genes in a whole embryo. We also combine smiFISH with cell membrane immunofluorescence, and present an imaging and analysis pipeline for 3D cell segmentation and single-cell RNA counting in whole blastoderm embryos. Finally, using whole embryo single-cell RNA count data, we propose two alternative single-cell variability measures to the commonly used Fano factor, and compare the capacity of these three measures to address different aspects of single-cell expression variability.

Here, the authors combine single-molecule inexpensive FISH (smiFISH) with cell membrane immunofluorescence and mathematical methods to enable whole embryo segmentation in 3D image stacks and mRNA quantification of multiple genes in each cell of the embryo.