Regulation of noise in the expression of a single gene

Dissecting splicing decisions and cell-to-cell variability with designed sequence libraries

Most human genes are alternatively spliced, allowing for a large expansion of the proteome. The multitude of regulatory inputs to splicing limits the potential to infer general principles from investigating native sequences. Here, we create a rationally designed library of >32,000 splicing events to dissect the complexity of splicing regulation through systematic sequence alterations. Measuring RNA and protein splice isoforms allows us to investigate both cause and effect of splicing decisions, quantify diverse regulatory inputs and accurately predict (R² = 0.73–0.85) isoform ratios from sequence and secondary structure. By profiling individual cells, we measure the cell-to-cell variability of splicing decisions and show that it can be encoded in the DNA and influenced by regulatory inputs, opening the door for a novel, single-cell perspective on splicing regulation.

Alternative splicing is regulated by multiple mechanisms. Here the authors employed designed splice site libraries and massively parallel reporter assays to dissect the regulatory complexity and cell-to-cell variability of splicing decisions and to build accurate predictive models.

Discontinuous transcription

Numerous studies based on new single-cell and single-gene techniques show that individual genes can be transcribed in short bursts or pulses accompanied by changes in pulsing frequencies. Since so many examples of such discontinuous or fluctuating transcription have been found from prokaryotes to mammals, it now seems to be a common mode of gene expression. In this review we discuss the occurrence of the transcriptional fluctuations, the techniques used for their detection, their putative causes, kinetic characteristics, and probable physiological significance.

Frequency spectrum of chemical fluctuation: A probe of reaction mechanism and dynamics

Even in the steady-state, the number of biomolecules in living cells fluctuates dynamically, and the frequency spectrum of this chemical fluctuation carries valuable information about the dynamics of the reactions creating these biomolecules. Recent advances in single-cell techniques enable direct monitoring of the time-traces of the protein number in each cell; however, it is not yet clear how the stochastic dynamics of these time-traces is related to the reaction mechanism and dynamics. Here, we derive a rigorous relation between the frequency-spectrum of the product number fluctuation and the reaction mechanism and dynamics, starting from a generalized master equation. This relation enables us to analyze the time-traces of the protein number and extract information about dynamics of mRNA number and transcriptional regulation, which cannot be directly observed by current experimental techniques. We demonstrate our frequency spectrum analysis of protein number fluctuation, using the gene network model of luciferase expression under the control of the Bmal 1a promoter in mouse fibroblast cells. We also discuss how the dynamic heterogeneity of transcription and translation rates affects the frequency-spectra of the mRNA and protein number.

Molecular Filters for Noise Reduction

Living systems are inherently stochastic and operate in a noisy environment, yet despite all these uncertainties, they perform their functions in a surprisingly reliable way. The biochemical mechanisms used by natural systems to tolerate and control noise are still not fully understood, and this issue also limits our capacity to engineer reliable, quantitative synthetic biological circuits. We study how representative models of biochemical systems propagate and attenuate noise, accounting for intrinsic as well as extrinsic noise. We investigate three molecular noise-filtering mechanisms, study their noise-reduction capabilities and limitations, and show that nonlinear dynamics such as complex formation are necessary for efficient noise reduction. We further suggest that the derived molecular filters are widespread in gene expression and regulation and, particularly, that microRNAs can serve as such noise filters. To our knowledge, our results provide new insight into how biochemical networks control noise and could be useful to build robust synthetic circuits.

Challenges in measuring and understanding biological noise

Biochemical reactions are intrinsically stochastic, leading to variation in the production of mRNAs and proteins within cells. In the scientific literature, this source of variation is typically referred to as 'noise'. The observed variability in molecular phenotypes arises from a combination of processes that amplify and attenuate noise. Our ability to quantify cell-to-cell variability in numerous biological contexts has been revolutionized by recent advances in single-cell technology, from imaging approaches through to 'omics' strategies. However, defining, accurately measuring and disentangling the stochastic and deterministic components of cell-to-cell variability is challenging. In this Review, we discuss the sources, impact and function of molecular phenotypic variability and highlight future directions to understand its role.

Single-cell RNA sequencing for the study of development, physiology and disease

An ongoing technological revolution is continually improving our ability to carry out very high-resolution studies of gene expression patterns. Current technology enables the global gene expression profiles of single cells to be defined, facilitating dissection of heterogeneity in cell populations that was previously hidden. In contrast to gene expression studies that use bulk RNA samples and provide only a virtual average of the diverse constituent cells, single-cell studies enable the molecular distinction of all cell types within a complex population mix, such as a tumour or developing organ. For instance, single-cell gene expression profiling has contributed to improved understanding of how histologically identical, adjacent cells make different differentiation decisions during development. Beyond development, single-cell gene expression studies have enabled the characteristics of previously known cell types to be more fully defined and facilitated the identification of novel categories of cells, contributing to improvements in our understanding of both normal and disease-related physiological processes and leading to the identification of new treatment approaches. Although limitations remain to be overcome, technology for the analysis of single-cell gene expression patterns is improving rapidly and beginning to provide a detailed atlas of the gene expression patterns of all cell types in the human body.

Analytical Expressions and Physics for Single-Cell mRNA Distributions of the lac Operon of E. coli

Mechanistic models of stochastic gene expression are of considerable interest, but their complexity often precludes tractable analytical expressions for messenger RNA (mRNA) and protein distributions. The lac operon of Escherichia coli is a model system with regulatory elements such as multiple operators and DNA looping that are shared by many operons. Although this system is complex, intuition suggests that fast DNA looping may simplify it by causing the repressor-bound states of the operon to equilibrate rapidly, thus ensuring that the subsequent dynamics are governed by slow transitions between the repressor-free and the equilibrated repressor-bound states. Here, we show that this intuition is correct by applying singular perturbation theory to a mechanistic model of lac transcription with the scaled time constant of DNA looping as the perturbation parameter. We find that at steady state, the repressor-bound states satisfy detailed balance and are dominated by the looped states; moreover, the interaction between the repressor-free and the equilibrated repressor-bound states is described by an extension of the Peccoud-Ycart two-state model in which both (repressor-free and repressor-bound) states support transcription. The solution of this extended two-state model reveals that the steady-state mRNA distribution is a mixture of the Poisson and negative hypergeometric distributions, which reflects mRNAs obtained by transcription from the repressor-bound and repressor-free states. Finally, we show that the physics revealed by perturbation theory makes it easy to derive the extended two-state model equations for complex regulatory architectures.

Fluorescence Tools Adapted for Real-Time Monitoring of the Behaviors of Streptococcus Species

Tagging of bacteria with fluorescent proteins has become an essential component of modern microbiology. Fluorescent proteins can be used to monitor gene expression and biofilm growth and to visualize host-pathogen interactions. Here, we developed a collection of fluorescent protein reporter plasmids for Streptococcus mutans UA159 and other oral streptococci. Using superfolder green fluorescent protein (sfGFP) as a reporter for transcriptional activity, we were able to characterize four strong constitutive promoters in S. mutans These promoter-sfgfp fusions worked both for single-copy chromosomal integration and on a multicopy plasmid, with the latter being segregationally stable in the absence of selective pressure under the conditions tested. We successfully labeled S. mutans UA159, Streptococcus gordonii DL1, and Streptococcus sp. strain A12 with sfGFP, DsRed-Express2 (red), and citrine (yellow). To test these plasmids under more challenging conditions, we performed mixed-species biofilm experiments and separated fluorescent populations using fluorescence-activated cell sorting (FACS). This allowed us to visualize two streptococci at a time and quantify the amounts of each species simultaneously. These fluorescent reporter plasmids add to the genetic toolbox available for the study of oral streptococci.IMPORTANCE Oral streptococci are the most abundant bacteria in the mouth and have a major influence on oral health and disease. In this study, we designed and optimized the expression of fluorescent proteins in Streptococcus mutans and other oral streptococci. We monitored the levels of expression and noise (the variability in fluorescence across the population). We then created several fluorescent protein delivery systems (green, yellow, and red) for use in oral streptococci. The data show that we can monitor bacterial growth and interactions in situ, differentiating between different bacteria growing in biofilms, the natural state of the organisms in the human mouth. These new tools will allow researchers to study these bacteria in novel ways to create more effective diagnostic and therapeutic tools for ubiquitous infectious diseases.

Exact and efficient hybrid Monte Carlo algorithm for accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts

Single cells exhibit a significant amount of variability in transcript levels, which arises from slow, stochastic transitions between gene expression states. Elucidating the nature of these states and understanding how transition rates are affected by different regulatory mechanisms require state-of-the-art methods to infer underlying models of gene expression from single cell data. A Bayesian approach to statistical inference is the most suitable method for model selection and uncertainty quantification of kinetic parameters using small data sets. However, this approach is impractical because current algorithms are too slow to handle typical models of gene expression. To solve this problem, we first show that time-dependent mRNA distributions of discrete-state models of gene expression are dynamic Poisson mixtures, whose mixing kernels are characterized by a piecewise deterministic Markov process. We combined this analytical result with a kinetic Monte Carlo algorithm to create a hybrid numerical method that accelerates the calculation of time-dependent mRNA distributions by 1000-fold compared to current methods. We then integrated the hybrid algorithm into an existing Monte Carlo sampler to estimate the Bayesian posterior distribution of many different, competing models in a reasonable amount of time. We demonstrate that kinetic parameters can be reasonably constrained for modestly sampled data sets if the model is known a priori. If there are many competing models, Bayesian evidence can rigorously quantify the likelihood of a model relative to other models from the data. We demonstrate that Bayesian evidence selects the true model and outperforms approximate metrics typically used for model selection.

Empirical mean-noise fitness landscapes reveal the fitness impact of gene expression noise

The effects of cell-to-cell variation (noise) in gene expression have proven difficult to quantify because of the mechanistic coupling of noise to mean expression. To independently quantify the effects of changes in mean expression and noise we determine the fitness landscapes in mean-noise expression space for 33 genes in yeast. For most genes, short-lived (noise) deviations away from the expression optimum are nearly as detrimental as sustained (mean) deviations. Fitness landscapes can be classified by a combination of each gene’s sensitivity to protein shortage or surplus. We use this classification to explore evolutionary scenarios for gene expression and find that certain landscape topologies can break the mechanistic coupling of mean and noise, thus promoting independent optimization of both properties. These results demonstrate that noise is detrimental for many genes and reveal non-trivial consequences of mean-noise-fitness topologies for the evolution of gene expression systems.

Quantifying the effects of noise in gene expression is difficult since noise and mean expression are coupled. Here the authors determine fitness landscapes in mean-noise expression space to uncouple these two parameters and show that changes in noise and mean expression are similarly detrimental to fitness.

The causes of evolvability and their evolution

Evolvability is the ability of a biological system to produce phenotypic variation that is both heritable and adaptive. It has long been the subject of anecdotal observations and theoretical work. In recent years, however, the molecular causes of evolvability have been an increasing focus of experimental work. Here, we review recent experimental progress in areas as different as the evolution of drug resistance in cancer cells and the rewiring of transcriptional regulation circuits in vertebrates. This research reveals the importance of three major themes: multiple genetic and non-genetic mechanisms to generate phenotypic diversity, robustness in genetic systems, and adaptive landscape topography. We also discuss the mounting evidence that evolvability can evolve and the question of whether it evolves adaptively.

Clustering and classification methods for single-cell RNA-sequencing data

Appropriate ways to measure the similarity between single-cell RNA-sequencing (scRNA-seq) data are ubiquitous in bioinformatics, but using single clustering or classification methods to process scRNA-seq data is generally difficult. This has led to the emergence of integrated methods and tools that aim to automatically process specific problems associated with scRNA-seq data. These approaches have attracted a lot of interest in bioinformatics and related fields. In this paper, we systematically review the integrated methods and tools, highlighting the pros and cons of each approach. We not only pay particular attention to clustering and classification methods but also discuss methods that have emerged recently as powerful alternatives, including nonlinear and linear methods and descending dimension methods. Finally, we focus on clustering and classification methods for scRNA-seq data, in particular, integrated methods, and provide a comprehensive description of scRNA-seq data and download URLs.

Post-Transcriptional Noise Control

Recent evidence indicates that transcriptional bursts are intrinsically amplified by messenger RNA cytoplasmic processing to generate large stochastic fluctuations in protein levels. These fluctuations can be exploited by cells to enable probabilistic bet-hedging decisions. But large fluctuations in gene expression can also destabilize cell-fate commitment. Thus, it is unclear if cells temporally switch from high to low noise, and what mechanisms enable this switch. Here, the discovery of a post-transcriptional mechanism that attenuates noise in HIV is reviewed. Early in its life cycle, HIV amplifies transcriptional fluctuations to probabilistically select alternate fates, whereas at late times, HIV utilizes a post-transcriptional feedback mechanism to commit to a specific fate. Reanalyzing various reported post-transcriptional negative feedback architectures reveals that they attenuate noise more efficiently than classic transcriptional autorepression, leading to the derivation of an assay to detect post-transcriptional motifs. It is hypothesized that coupling transcriptional and post-transcriptional autoregulation enables efficient temporal noise control to benefit developmental bet-hedging decisions.

Analytical results for a generalized model of bursty gene expression with molecular memory

The activation of a gene is a complex biochemical process and could involve small steps, creating a memory between individual events. However, the effect of this molecular memory was often neglected in previous work. How the molecular memory affects gene expression remains not fully explored. We analyze a stochastic model of bursty gene expression, where the waiting time from inactivation to activation is assumed to follow a nonexponential (in fact, Erlang) distribution. We derive the analytical expression for the gene-product distribution, which explicitly traces the effect of molecule memory. Interestingly, we find that the effect of molecular memory is equivalent to the introduction of feedback. In addition, we analytically show that the stationary distribution is always super-Poissonian, independent of the detail of the waiting-time distribution, and there is the optimal step size that minimizes the Fano factor for any given mean burst size and is a decreasing function of the mean burst size. These analytical results indicate that molecular memory is an unneglectable factor affecting gene expression.

Defining Division of Labor in Microbial Communities

In order to survive and reproduce, organisms must perform a multitude of tasks. However, trade-offs limit their ability to allocate energy and resources to all of these different processes. One strategy to solve this problem is to specialize in some traits and team up with other organisms that can help by providing additional, complementary functions. By reciprocally exchanging metabolites and/or services in this way, both parties benefit from the interaction. This phenomenon, which has been termed functional specialization or division of labor, is very common in nature and exists on all levels of biological organization. Also, microorganisms have evolved different types of synergistic interactions. However, very often, it remains unclear whether or not a given example represents a true case of division of labor. Here we aim at filling this gap by providing a list of criteria that clearly define division of labor in microbial communities. Furthermore, we propose a set of diagnostic experiments to verify whether a given interaction fulfills these conditions. In contrast to the common use of the term, our analysis reveals that both intraspecific and interspecific interactions meet the criteria defining division of labor. Moreover, our analysis identified non-cooperators of intraspecific public goods interactions as growth specialists that divide labor with conspecific producers, rather than being social parasites. By providing a conceptual toolkit, our work will help to unambiguously identify cases of division of labor and stimulate more detailed investigations of this important and widespread type of inter-microbial interaction.

Dichotomous Nature of Bistability Generated by Negative Cooperativity in Receptor-Ligand Binding

Positive cooperativity in receptor-ligand binding plays an important role in cell signaling as it generates an ultrasensitive response, a requirement for nonlinear phenomena such as bistability and oscillations in feedback regulated reaction networks. On the other hand, negative cooperativity typically produces a hyperbolic response and is thus less explored. However, recently negative cooperativity was shown to generate an ultrasensitive response under the condition of strong ligand affinity. In this work, we have used mathematical modeling to investigate the effect of negative cooperativity in receptor-ligand interaction on the bistability in a positive feedback regulatory motif. We systematically investigated the effect of negative cooperativity, modifying the two equilibrium constants of the receptor-ligand binding, on the robustness and tunability of bistability. We show that in the regime where negative cooperativity exhibits robust bistability, positive cooperativity results in poor bistability and vice versa. Further we find that the robustness and tunability of bistability depend crucially on the stability of singly and doubly engaged receptors. Our modeling highlights the ability of negative cooperativity to produce complex phenomena with potential applications in designing synthetic devices or in explaining experimental observations in cell biology.

Intracellular Noise Level Determines Ratio Control Strategy Confined by Speed-Accuracy Trade-off

Robust and precise ratio control of heterogeneous phenotypes within an isogenic population is an essential task, especially in the development and differentiation of a large number of cells such as bacteria, sensory receptors, and blood cells. However, the mechanisms of such ratio control are poorly understood. Here, we employ experimental and mathematical techniques to understand the combined effects of signal induction and gene expression stochasticity on phenotypic multimodality. We identify two strategies to control phenotypic ratios from an initially homogeneous population, suitable roughly to high-noise and low-noise intracellular environments, and we show that both can be used to generate precise fractional differentiation. In noisy gene expression contexts, such as those found in bacteria, induction within the circuit's bistable region is enough to cause noise-induced bimodality within a feasible time frame. However, in less noisy contexts, such as tightly controlled eukaryotic systems, spontaneous state transitions are rare and hence bimodality needs to be induced with a controlled pulse of induction that falls outside the bistable region. Finally, we show that noise levels, system response time, and ratio tuning accuracy impose trade-offs and limitations on both ratio control strategies, which guide the selection of strategy alternatives.

Is the cell really a machine?

It has become customary to conceptualize the living cell as an intricate piece of machinery, different to a man-made machine only in terms of its superior complexity. This familiar understanding grounds the conviction that a cell's organization can be explained reductionistically, as well as the idea that its molecular pathways can be construed as deterministic circuits. The machine conception of the cell owes a great deal of its success to the methods traditionally used in molecular biology. However, the recent introduction of novel experimental techniques capable of tracking individual molecules within cells in real time is leading to the rapid accumulation of data that are inconsistent with an engineering view of the cell. This paper examines four major domains of current research in which the challenges to the machine conception of the cell are particularly pronounced: cellular architecture, protein complexes, intracellular transport, and cellular behaviour. It argues that a new theoretical understanding of the cell is emerging from the study of these phenomena which emphasizes the dynamic, self-organizing nature of its constitution, the fluidity and plasticity of its components, and the stochasticity and non-linearity of its underlying processes.

Multivariate information processing characterizes fitness of a cascaded gene-transcription machinery

We report that a genetic two-step activation cascade processes diverse flavors of information, e.g., synergy, redundancy, and unique information. Our computations measuring reduction in Shannon entropies and reduction in variances produce differently behaving absolute magnitudes of these informational flavors. We find that similarity can be brought in if these terms are evaluated in fractions with respect to corresponding total information. Each of the input signal and final gene-product is found to generate common or redundant information fractions (mostly) to predict each other, whereas they also complement one another to harness synergistic information fraction, predicting the intermediate biochemical species. For an optimally growing signal to maintain fixed steady-state abundance of activated downstream gene-products, the interaction information fractions for this cascade module shift from net-redundancy to information-independence.

Imaging and Analysis of Cellular Locations in Three-Dimensional Tissue Models

The absence of quantitative in vitro cell-extracellular matrix models represents an important bottleneck for basic research and human health. Randomness of cellular distributions provides an opportunity for the development of a quantitative in vitro model. However, quantification of the randomness of random cell distributions is still lacking. In this paper, we have imaged cellular distributions in an alginate matrix using a multiview light sheet microscope and developed quantification metrics of randomness by modeling it as a Poisson process, a process that has constant probability of occurring in space or time. We imaged fluorescently labeled human mesenchymal stem cells embedded in an alginate matrix of thickness greater than 5 mm with axial resolution, the mean full width at half maximum of the axial intensity profiles of fluorescent particles. Simulated randomness agrees well with the experiments. Quantification of distributions and validation by simulations will enable quantitative study of cell-matrix interactions in tissue models.

Phenotypic Heterogeneity in Bacterial Quorum Sensing Systems

Quorum sensing is usually thought of as a collective behavior in which all members of a population partake. However, over the last decade, several reports of phenotypic heterogeneity in quorum sensing-related gene expression have been put forward, thus challenging this view. In the respective systems, cells of isogenic populations did not contribute equally to autoinducer production or target gene activation, and in some cases, the fraction of contributing cells was modulated by environmental factors. Here, we look into potential origins of these incidences and into how initial cell-to-cell variations might be amplified to establish distinct phenotypic heterogeneity. We furthermore discuss potential functions heterogeneity in bacterial quorum sensing systems could serve: as a preparation for environmental fluctuations (bet hedging), as a more cost-effective way of producing public goods (division of labor), as a loophole for genotypic cooperators when faced with non-contributing mutants (cheat protection), or simply as a means to fine-tune the output of the population as a whole (output modulation). We illustrate certain aspects of these recent developments with the model organisms Sinorhizobium meliloti, Sinorhizobium fredii and Bacillus subtilis, which possess quorum sensing systems of different complexity, but all show phenotypic heterogeneity therein.

Coculturing Bacteria Leads to Reduced Phenotypic Heterogeneities

Isogenic bacterial populations are known to exhibit phenotypic heterogeneity at the single-cell level. Because of difficulties in assessing the phenotypic heterogeneity of a single taxon in a mixed community, the importance of this deeper level of organization remains relatively unknown for natural communities. In this study, we have used membrane-based microcosms that allow the probing of the phenotypic heterogeneity of a single taxon while interacting with a synthetic or natural community. Individual taxa were studied under axenic conditions, as members of a coculture with physical separation, and as a mixed culture. Phenotypic heterogeneity was assessed through both flow cytometry and Raman spectroscopy. Using this setup, we investigated the effect of microbial interactions on the individual phenotypic heterogeneities of two interacting drinking water isolates. Through flow cytometry we have demonstrated that interactions between these bacteria lead to a reduction of their individual phenotypic diversities and that this adjustment is conditional on the bacterial taxon. Single-cell Raman spectroscopy confirmed a taxon-dependent phenotypic shift due to the interaction. In conclusion, our data suggest that bacterial interactions may be a general driver of phenotypic heterogeneity in mixed microbial populations.IMPORTANCE Laboratory studies have shown the impact of phenotypic heterogeneity on the survival and functionality of isogenic populations. Because phenotypic heterogeneity plays an important role in pathogenicity and virulence, antibiotic resistance, biotechnological applications, and ecosystem properties, it is crucial to understand its influencing factors. An unanswered question is whether bacteria in mixed communities influence the phenotypic heterogeneity of their community partners. We found that coculturing bacteria leads to a reduction in their individual phenotypic heterogeneities, which led us to the hypothesis that the individual phenotypic diversity of a taxon is dependent on the community composition.

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.

Mathematical modeling of movement on fitness landscapes

Background

Movement of populations on fitness landscapes has been a problem of interest for a long time. While the subject has been extensively developed theoretically, reconciliation of the theoretical work with recent experimental data has not yet happened. In this work, we develop a computational framework and study evolution of the simplest transcription network between a single regulator, R and a single target protein, T.

Results

Through our simulations, we track evolution of this transcription network and comment on its dynamics and statistics of this movement. Significantly, we report that there exists a critical parameter which controls the ability of a network to reach the global fitness peak on the landscape. This parameter is the fraction of all permissible values of a biochemical parameter that can be accessed from its current value via a single mutation.

Conclusions

Overall, through this work, we aim to present a general framework for analysis of movement of populations (and particularly regulatory networks) on landscapes.

Electronic supplementary material

The online version of this article (10.1186/s12918-019-0704-0) contains supplementary material, which is available to authorized users.

Efficient anticorrelated variance reduction for stochastic simulation of biochemical reactions

We investigate the computational challenge of improving the accuracy of the stochastic simulation estimation by inducing negative correlation through the anticorrelated variance reduction technique. A direct application of the technique to the stochastic simulation algorithm (SSA), employing the inverse transformation, is not efficient for simulating large networks because its computational cost is similar to the sum of independent simulation runs. We propose in this study a new algorithm that employs the propensity bounds of reactions, introduced recently in their rejection-based SSA, to correlate and synchronise the trajectories during the simulation. The selection of reaction firings by our approach is exact due to the rejection-based mechanism. In addition, by applying the anticorrelated variance technique to select reaction firings, our approach can induce substantial correlation between realisations, hence reducing the variance of the estimator. The computational advantage of our rejection-based approach in comparison with the traditional inverse transformation is that it only needs to maintain a single data structure storing propensity bounds of reactions, which is updated infrequently, hence achieving better performance.

Mapping DNA sequence to transcription factor binding energy in vivo

Despite the central importance of transcriptional regulation in biology, it has proven difficult to determine the regulatory mechanisms of individual genes, let alone entire gene networks. It is particularly difficult to decipher the biophysical mechanisms of transcriptional regulation in living cells and determine the energetic properties of binding sites for transcription factors and RNA polymerase. In this work, we present a strategy for dissecting transcriptional regulatory sequences using in vivo methods (massively parallel reporter assays) to formulate quantitative models that map a transcription factor binding site’s DNA sequence to transcription factor-DNA binding energy. We use these models to predict the binding energies of transcription factor binding sites to within 1 k_BT of their measured values. We further explore how such a sequence-energy mapping relates to the mechanisms of trancriptional regulation in various promoter contexts. Specifically, we show that our models can be used to design specific induction responses, analyze the effects of amino acid mutations on DNA sequence preference, and determine how regulatory context affects a transcription factor’s sequence specificity.

It has been said that we live in the “genomic era,” a time where we can readily sequence full genomes at will. However, it remains difficult to interpret much of the information within a genome. This is especially true of non-coding sequences such as promoters, which contain a number of features such as transcription factor binding sites that determine how genes are regulated. There is no straightforward regulatory “code” that tells us how transcription factor binding sites are organized within a promoter. In this work we examine how DNA sequence determines one of the most important features of a promoter, the strength with which a transcription factor binds to its DNA binding site. We discuss an approach to modeling DNA sequence-specific transcription factor binding energies in vivo using a massively parellel reporter assay. We develop models that allow us to predict the binding energy between a transcription factor and a mutated version of its binding site. We then show that this modeling technique can be used to address a number of scientific and design questions, such as engineering the behavior of genetic circuit elements or examining how transcription factors and their binding sites co-evolve.

An algebraic method to calculate parameter regions for constrained steady-state distribution in stochastic reaction networks

Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression. Because biochemical reactions occur at the cellular level, they are affected by unavoidable fluctuations. Although several methods have been proposed to detect and analyze the stability of steady states for deterministic models, these methods cannot be applied to stochastic reaction networks. In this paper, we propose an algorithm based on algebraic computations to calculate parameter regions for constrained steady-state distribution of stochastic reaction networks, in which the means and variances satisfy some given inequality constraints. To evaluate our proposed method, we perform computer simulations for three typical chemical reactions and demonstrate that the results obtained with our method are consistent with the simulation results.

Regulatory Network of the Scoliosis-Associated Genes Establishes Rostrocaudal Patterning of Somites in Zebrafish

Gene regulatory networks govern pattern formation and differentiation during embryonic development. Segmentation of somites, precursors of the vertebral column among other tissues, is jointly controlled by temporal signals from the segmentation clock and spatial signals from morphogen gradients. To explore how these temporal and spatial signals are integrated, we combined time-controlled genetic perturbation experiments with computational modeling to reconstruct the core segmentation network in zebrafish. We found that Mesp family transcription factors link the temporal information of the segmentation clock with the spatial action of the fibroblast growth factor signaling gradient to establish rostrocaudal (head to tail) polarity of segmented somites. We further showed that cells gradually commit to patterning by the action of different genes at different spatiotemporal positions. Our study provides a blueprint of the zebrafish segmentation network, which includes evolutionarily conserved genes that are associated with the birth defect congenital scoliosis in humans.

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A core network establishes rostrocaudal polarity of segmented somites in zebrafish

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mesp genes link the segmentation clock with the FGF signaling gradient

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Gradual patterning is done by the action of different genes at different positions

Maximum Caliber Can Build and Infer Models of Oscillation in a Three-Gene Feedback Network

Single-cell protein expression time trajectories provide rich temporal data quantifying cellular variability and its role in dictating fitness. However, theoretical models to analyze and fully extract information from these measurements remain limited for three reasons: (i) gene expression profiles are noisy, rendering models of averages inapplicable, (ii) experiments typically measure only a few protein species while leaving other molecular actors-necessary to build traditional bottom-up models-unnoticed, and (iii) measured data are in fluorescence, not particle number. We recently addressed these challenges in an alternate top-down approach using the principle of Maximum Caliber (MaxCal) to model genetic switches with one and two protein species. In the present work we address scalability and broader applicability of MaxCal by extending to a three-gene (A, B, C) feedback network that exhibits oscillation, commonly known as the repressilator. We test MaxCal's inferential power by using synthetic data of noisy protein number time traces-serving as a proxy for experimental data-generated from a known underlying model. We notice that the minimal MaxCal model-accounting for production, degradation, and only one type of symmetric coupling between all three species-reasonably infers several underlying features of the circuit such as the effective production rate, degradation rate, frequency of oscillation, and protein number distribution. Next, we build models of higher complexity including different levels of coupling between A, B, and C and rigorously assess their relative performance. While the minimal model (with four parameters) performs remarkably well, we note that the most complex model (with six parameters) allowing all possible forms of crosstalk between A, B, and C slightly improves prediction of rates, but avoids ad hoc assumption of all the other models. It is also the model of choice based on Bayesian information criteria. We further analyzed time trajectories in arbitrary fluorescence (using synthetic trajectories) to mimic realistic data. We conclude that even with a three-protein system including both fluorescence noise and intrinsic gene expression fluctuations, MaxCal can faithfully infer underlying details of the network, opening future directions to model other network motifs with many species.

Central dogma rates and the trade-off between precision and economy in gene expression

Steady-state protein abundance is set by four rates: transcription, translation, mRNA decay and protein decay. A given protein abundance can be obtained from infinitely many combinations of these rates. This raises the question of whether the natural rates for each gene result from historical accidents, or are there rules that give certain combinations a selective advantage? We address this question using high-throughput measurements in rapidly growing cells from diverse organisms to find that about half of the rate combinations do not exist: genes that combine high transcription with low translation are strongly depleted. This depletion is due to a trade-off between precision and economy: high transcription decreases stochastic fluctuations but increases transcription costs. Our theory quantitatively explains which rate combinations are missing, and predicts the curvature of the fitness function for each gene. It may guide the design of gene circuits with desired expression levels and noise.

Inferring Cell-State Transition Dynamics from Lineage Trees and Endpoint Single-Cell Measurements

As they proliferate, living cells undergo transitions between specific molecularly and developmentally distinct states. Despite the functional centrality of these transitions in multicellular organisms, it has remained challenging to determine which transitions occur and at what rates without perturbations and cell engineering. Here, we introduce kin correlation analysis (KCA) and show that quantitative cell-state transition dynamics can be inferred, without direct observation, from the clustering of cell states on pedigrees (lineage trees). Combining KCA with pedigrees obtained from time-lapse imaging and endpoint single-molecule RNA-fluorescence in situ hybridization (RNA-FISH) measurements of gene expression, we determined the cell-state transition network of mouse embryonic stem (ES) cells. This analysis revealed that mouse ES cells exhibit stochastic and reversible transitions along a linear chain of states ranging from 2C-like to epiblast-like. Our approach is broadly applicable and may be applied to systems with irreversible transitions and non-stationary dynamics, such as in cancer and development.

Diffusion-dynamics laws in stochastic reaction networks

Many biological activities are induced by cellular chemical reactions of diffusing reactants. The dynamics of such systems can be captured by stochastic reaction networks. A recent numerical study has shown that diffusion can significantly enhance the fluctuations in gene regulatory networks. However, the universal relation between diffusion and stochastic system dynamics remains veiled. Within the approximation of reaction-diffusion master equation (RDME), we find general relation that the steady-state distribution in complex balanced networks is diffusion-independent. Here, complex balance is the nonequilibrium generalization of detailed balance. We also find that for a diffusion-included network with a Poisson-like steady-state distribution, the diffusion can be ignored at steady state. We then derive a necessary and sufficient condition for networks holding such steady-state distributions. Moreover, we show that for linear reaction networks the RDME reduces to the chemical master equation, which implies that the stochastic dynamics of networks is unaffected by diffusion at any arbitrary time. Our findings shed light on the fundamental question of when diffusion can be neglected, or (if nonnegligible) its effects on the stochastic dynamics of the reaction network.

Noise in bacterial gene expression

The expression level of a gene can fluctuate significantly between individuals within a population of genetically identical cells. The resultant phenotypic heterogeneity could be exploited by bacteria to adapt to changing environmental conditions. Noise is hence a genome-wide phenomenon that arises from the stochastic nature of the biochemical reactions that take place during gene expression and the relatively low abundance of the molecules involved. The production of mRNA and proteins therefore occurs in bursts, with alternating episodes of high and low activity during transcription and translation. Single-cell and single-molecule studies demonstrated that noise within gene expression is influenced by a combination of both intrinsic and extrinsic factors. However, our mechanistic understanding of this process at the molecular level is still rather limited. Further investigation is necessary that takes into account the detailed knowledge of gene regulation gained from biochemical studies.

Stochastic protein multimerization, activity, and fitness

Many proteins assemble into homomultimeric structures, with a number of subunits that can vary substantially among phylogenetic lineages. As protein-protein interactions require productive encounters among subunits, such variation might partially be explained by variation in cellular protein abundance. Protein abundance in turn depends on the intrinsic rates of production and decay of mRNA and protein molecules, as well as rates of cell growth and division. Using a stochastic framework for prediction of the multimeric state of a protein as a function of these processes and the free energy associated with interface-interface binding, we demonstrate agreement with a wide class of proteins using E. coli proteome data. As such, this platform, which links protein quaternary structure with biochemical rates governing gene expression, protein association and dissociation, and cell growth and division, can be extended to evolutionary models for the emergence and diversification of multimers. While it is tempting to think of multimerization as adaptive, the diversity of multimeric states raises the question of its functional role and impact on fitness. As a force driving selection, we consider the possible increase in enzymatic activity of proteins arising strictly as a consequence of interface-interface binding-namely, enhanced stability to degradation, substrate binding affinity, or catalytic rate of multimers with respect to monomers without invoking further conformational changes, as in allostery. For fixed cost of protein production, we find a benefit conferred by multimers that is dependent on context and can therefore become different in diverging lineages.

Buffering and Amplifying Transcriptional Noise During Cell Fate Specification

The molecular processes that drive gene transcription are inherently noisy. This noise often manifests in the form of transcriptional bursts, producing fluctuations in gene activity over time. During cell fate specification, this noise is often buffered to ensure reproducible developmental outcomes. However, sometimes noise is utilized as a “bet-hedging” mechanism to diversify functional roles across a population of cells. Studies of bacteria, yeast, and cultured cells have provided insights into the nature and roles of noise in transcription, yet we are only beginning to understand the mechanisms by which noise influences the development of multicellular organisms. Here we discuss the sources of transcriptional noise and the mechanisms that either buffer noise to drive reproducible fate choices or amplify noise to randomly specify fates.

Evolutionary stability of the lysis-lysogeny decision: Why be virulent?

Lytic viruses infect and kill host cells, producing a large number of viral copies. Temperate viruses, in contrast, are able to integrate viral genetic material into the host cell DNA, leaving a viable host cell. The evolutionary advantage of this strategy, lysogeny, has been demonstrated in complex environments that include spatial structure, oscillating population dynamics, or periodic environmental collapse. Here, we examine the evolutionary stability of the lysis-lysogeny decision, that is, we predict the long-term outcome of the evolution of lysogeny rates. We demonstrate that viruses with high rates of lysogeny are stable against invasion by more virulent viral strains even in simple environments, as long as the pool of susceptible hosts is not unlimited. This mirrors well-known results in both r-K selection theory and virulence evolution: although virulent viruses have a faster potential growth rate, temperate strains are able to maintain positive growth on a lower density of the limiting resource, susceptible hosts. We then outline scenarios in which the rate of lysogeny is predicted to evolve either toward full lysogeny or full lysis. Finally, we demonstrate conditions under which intermediate rates of lysogeny, as observed in temperate viruses in nature, can be sustained long-term. In general, intermediate lysogeny rates persist when the coupling between susceptible host density and virus density is relaxed.

Efficient finite-difference method for computing sensitivities of biochemical reactions

Sensitivity analysis of biochemical reactions aims at quantifying the dependence of the reaction dynamics on the reaction rates. The computation of the parameter sensitivities, however, poses many computational challenges when taking stochastic noise into account. This paper proposes a new finite-difference method for efficiently computing sensitivities of biochemical reactions. We employ propensity bounds of reactions to couple the simulation of the nominal and perturbed processes. The exactness of the simulation is preserved by applying the rejection-based mechanism. For each simulation step, the nominal and perturbed processes under our coupling strategy are synchronized and often jump together, increasing their positive correlation and hence reducing the variance of the estimator. The distinctive feature of our approach in comparison with existing coupling approaches is that it only needs to maintain a single data structure storing propensity bounds of reactions during the simulation of the nominal and perturbed processes. Our approach allows to compute sensitivities of many reaction rates simultaneously. Moreover, the data structure does not require to be updated frequently, hence improving the computational cost. This feature is especially useful when applied to large reaction networks. We benchmark our method on biological reaction models to prove its applicability and efficiency.

Single cell protein analysis for systems biology

The cellular abundance of proteins can vary even between isogenic single cells. This variability between single-cell protein levels can have regulatory roles, such as controlling cell fate during apoptosis induction or the proliferation/quiescence decision. Here, we review examples connecting protein levels and their dynamics in single cells to cellular functions. Such findings were made possible by the introduction of antibodies, and subsequently fluorescent proteins, for tracking protein levels in single cells. However, in heterogeneous cell populations, such as tumors or differentiating stem cells, cellular decisions are controlled by hundreds, even thousands of proteins acting in concert. Characterizing such complex systems demands measurements of thousands of proteins across thousands of single cells. This demand has inspired the development of new methods for single-cell protein analysis, and we discuss their trade-offs, with an emphasis on their specificity and coverage. We finish by highlighting the potential of emerging mass-spec methods to enable systems-level measurement of single-cell proteomes with unprecedented coverage and specificity. Combining such methods with methods for quantitating the transcriptomes and metabolomes of single cells will provide essential data for advancing quantitative systems biology.

Quantifying phenotypes in single cells using droplet microfluidics

This book chapter describes the use of droplet microfluidics to phenotype single cells. The basic process flow includes the encapsulation of single cells with a specific probe into aqueous micro-droplets suspended in a biocompatible oil. The probe is chosen to measure the phenotype of interest. After incubation, the encapsulated cell turns the probe fluorescent and renders the entire droplet fluorescent. Enumerating drops that are fluorescent quantifies the concentration of cells possessing the phenotype of interest. Examining the distribution of fluorescence further allows one to quantify the heterogeneity among the cell population.

Cytoplasmic Amplification of Transcriptional Noise Generates Substantial Cell-to-Cell Variability

Transcription is an episodic process characterized by probabilistic bursts, but how the transcriptional noise from these bursts is modulated by cellular physiology remains unclear. Using simulations and single-molecule RNA counting, we examined how cellular processes influence cell-to-cell variability (noise). The results show that RNA noise is higher in the cytoplasm than the nucleus in ∼85% of genes across diverse promoters, genomic loci, and cell types (human and mouse). Measurements show further amplification of RNA noise in the cytoplasm, fitting a model of biphasic mRNA conversion between translation- and degradation-competent states. This multi-state translation-degradation of mRNA also causes substantial noise amplification in protein levels, ultimately accounting for ∼74% of intrinsic protein variability in cell populations. Overall, the results demonstrate how noise from transcriptional bursts is intrinsically amplified by mRNA processing, leading to a large super-Poissonian variability in protein levels.

Multi-component gene network design as a survival strategy in diverse environments

Background

Gene-environment interactions are often mediated though gene networks in which gene expression products interact with other network components to dictate network activity levels, which in turn determines the fitness of the host cell in specific environments. Even though a gene network is the right context for studying gene-environment interactions, we have little understanding on how systematic genetic perturbations affects fitness in the context of a gene network.

Results

Here we examine the effect of combinatorial gene dosage alterations on gene network activity and cellular fitness. Using the galactose utilization pathway as a model network in diploid yeast, we reduce the copy number of four regulatory genes (GAL2, GAL3, GAL4, GAL80) from two to one, and measure the activity of the perturbed networks. We integrate these results with competitive fitness measurements made in six different rationally-designed environments containing different galactose concentrations representing the natural induction spectrum of the galactose network. In the lowest galactose environment, we find a nonlinear relationship between gene expression and fitness while high galactose environments lead to a linear relationship between the two with a saturation regime reached at a sufficiently high galactose concentration. We further uncover environment-specific relevance of the different network components for dictating the relationship between the network activity and organismal fitness, indicating that none of the network components are redundant.

Conclusions

These results provide experimental support to the hypothesis that dynamic changes in the environment throughout natural evolution is key to structuring natural gene networks in a multi-component fashion, which robustly provides protection against population extinction in different environments.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0609-3) contains supplementary material, which is available to authorized users.

The Insight into Protein-Ligand Interactions, a Novel Way of Buffering Protein Noise in Gene Expression

Random fluctuations are often considered detrimental in the context of gene regulation. Studies aimed at discovering the noise-buffering strategies are important. In this study, we demonstrated a novel design of attenuating noise at protein-level. The protein-ligand interaction dramatically reduced noise so that the coefficient of variation (COV) became roughly 1/3. Remarkably, in comparison to the other two noise-buffering methods, the negative feedback control and the incoherent feedforward loop, the COV of the target protein in the case of protein-ligand interaction appeared to be less than 1/2 of that of the other two methods. The high correlation of the target protein and the ligand grants the present method great ability to buffer noise. Further, it buffers noise at the stage after translation so it is also capable of attenuating the noise inherited from the process of translation.

Influence of global gene regulatory networks on single cell heterogeneity of green fluorescent protein production in Bacillus subtilis

BACKGROUND

Gram-positive bacterium Bacillus subtilis has been extensively studied as a microbial cell factory for high-level producing a wide range of interesting products. Green fluorescent protein (GFP) is commonly used as a marker for determining the strength of a given promoter or for the subcellular localization of a fusion protein. However, the inherent heterogeneity of GFP expression among individual cells that can arise from global regulation differences in the expression host, has not yet been systematically assessed. B. subtilis strains with single mutation(s) in the two major transcriptional regulators CcpA and/or CodY were earlier found to improve overall heterologous protein production levels. Here, we investigate the dynamic production performance of GFP in the reporter strains with chromosomally integrated Physpank-sfGFP(Sp).

RESULTS

The mutation R214C in the DNA-binding domain of CodY effectively enhances GFP production at the population level relative to two other strains, i.e. wildtype (WT) and CcpAT19S. During the late stationary phase, the high- and low-level GFP-producing cells coexist in the WT population, while the CodYR214C population at the single-cell level shows higher phenotypic homogeneity of fluorescence signals.

CONCLUSION

Expression of GFP is prominently heterogeneous in the WT B. subtilis cells, and this phenotypic heterogeneity can be significantly reduced by CodYR214C mutation. The rates of production heterogeneity show a high correlation to the overall GFP yields. Moreover, the toolkit of flow cytometry and fluorescence microscopy that can achieve real-time profiles of GFP production performance in various strains may facilitate the further use of B. subtilis as a cell factory.

Single neuron serotonin receptor subtype gene expression correlates with behaviour within and across three molluscan species

The marine mollusc, Pleurobranchaea californica varies daily in whether it swims and this correlates with whether serotonin (5-HT) enhances the strength of synapses made by the swim central pattern generator neuron, A1/C2. Another species, Tritonia diomedea, reliably swims and does not vary in serotonergic neuromodulation. A third species, Hermissenda crassicornis, never produces this behaviour and lacks the neuromodulation. We found that expression of particular 5-HT receptor subtype (5-HTR) genes in single neurons correlates with swimming. Orthologues to seven 5-HTR genes were identified from whole-brain transcriptomes. We isolated individual A1/C2 neurons and sequenced their RNA or measured 5-HTR gene expression using absolute quantitative PCR. A1/C2 neurons isolated from Pleurobranchaea that produced a swim motor pattern just prior to isolation expressed 5-HT2a and 5-HT7 receptor genes, as did all Tritonia samples. These subtypes were absent from A1/C2 isolated from Pleurobranchaea that did not swim on that day and from Hermissenda A1/C2 neurons. Expression of other receptors was not correlated with swimming. This suggests that these 5-HTRs may mediate the modulation of A1/C2 synaptic strength and play an important role in swimming. Furthermore, it suggests that regulation of receptor expression could underlie daily changes in behaviour as well as evolution of behaviour.