Single-molecule approaches to stochastic gene expression

Quantitative measurement of single cell dynamics

Over the past 20 years luminescent and fluorescent imaging assays have been developed to report on the dynamics of transcription and protein translocation in single cells. The combination of these measurements with mathematical analysis is having an increasingly significant impact on cell biology. There is an urgent need to translate these assays to the study of cells and tissues in vivo, which requires new tools and technologies. Emergence of these new tools and techniques will further the understanding of the role of signalling and transcriptional dynamics in the generation of cellular heterogeneity and the control of cell fate.

Stochastic steady state gain in a gene expression process with mRNA degradation control

Recent analyses with high-resolution single-molecule experimental methods have shown highly irregular and variable bursting of mRNA in a wide range of organisms. Noise in gene expression is thought to be beneficial in cell fate specifications, as it can lay a foundation for phenotypic diversification of isogenetic cells in the homogeneous environment. However, because the stability of proteins is, in many cases, higher than that of mRNAs, noise from transcriptional bursting can be considerably buffered at the protein level, limiting the effect of noisy mRNAs at a more global regulation level. This raises a question as to what constructive role noisy mRNAs can play in the system-level dynamics. In this study, we have addressed this question using the computational models that extend the conventional transcriptional bursting model with a post-transcriptional regulation step. Surprisingly, by comparing this stochastic model with the corresponding deterministic model, we find that intrinsic fluctuations can substantially increase the expected mRNA level. Because effects of a higher mRNA level can be transmitted to the protein level even with slow protein degradation rates, this finding suggests that an increase in the protein level is another potential effect of transcriptional bursting. Here, we show that this striking steady state increase is caused by the asynchronous nature of molecular reactions, which allows the transcriptional regulation model to create additional modes of qualitatively distinct dynamics. Our results illustrate non-intuitive effects of reaction asynchronicity on system dynamics that cannot be captured by the traditional deterministic framework. Because molecular reactions are intrinsically stochastic and asynchronous, these findings may have broad implications in modelling and understanding complex biological systems.

Fluorescence correlation spectroscopy: past, present, future

In recent years fluorescence correlation spectroscopy (FCS) has become a routine method for determining diffusion coefficients, chemical rate constants, molecular concentrations, fluorescence brightness, triplet state lifetimes, and other molecular parameters. FCS measures the spatial and temporal correlation of individual molecules with themselves and so provides a bridge between classical ensemble and contemporary single-molecule measurements. It also provides information on concentration and molecular number fluctuations for nonlinear reaction systems that complement single-molecule measurements. Typically implemented on a fluorescence microscope, FCS samples femtoliter volumes and so is especially useful for characterizing small dynamic systems such as biological cells. In addition to its practical utility, however, FCS provides a window on mesoscopic systems in which fluctuations from steady states not only provide the basis for the measurement but also can have important consequences for the behavior and evolution of the system. For example, a new and potentially interesting field for FCS studies could be the study of nonequilibrium steady states, especially in living cells.

Comparison and calibration of different reporters for quantitative analysis of gene expression

Absolute levels of gene expression in bacteria are observed to vary over as much as six orders of magnitude. Thermodynamic models have been proposed as a tool to describe the expression levels of a given transcriptional circuit. In this context, it is essential to understand both the limitations and linear range of the different methods for measuring gene expression and to determine to what extent measurements from different reporters can be directly compared with one aim being the stringent testing of theoretical descriptions of gene expression. In this article, we compare two protein reporters by measuring both the absolute level of expression and fold-change in expression using the fluorescent protein EYFP and the enzymatic reporter β-galactosidase. We determine their dynamic and linear range and show that they are interchangeable for measuring mean levels of expression over four orders of magnitude. By calibrating these reporters such that they can be interpreted in terms of absolute molecular counts, we establish limits for their applicability: autofluorescence on the lower end of expression for EYFP (at ∼10 molecules per cell) and interference with cellular growth on the high end for β-galactosidase (at ∼20,000 molecules per cell). These qualities make the reporters complementary and necessary when trying to experimentally verify the predictions from the theoretical models.

Single-molecule transcript counting of stem-cell markers in the mouse intestine

Determining the molecular identities of adult stem cells requires technologies for sensitive transcript detection in tissues. In mouse intestinal crypts, lineage-tracing studies indicated that different genes uniquely mark spatially distinct stem-cell populations, residing either at crypt bases or at position +4, but a detailed analysis of their spatial co-expression has not been feasible. Here we apply three-colour single-molecule fluorescent in situ hybridization to study a comprehensive panel of intestinal stem-cell markers during homeostasis, ageing and regeneration. We find that the expression of all markers overlaps at crypt-base cells. This co-expression includes Lgr5, Bmi1 and mTert, genes previously suggested to mark distinct stem cells. Strikingly, Dcamkl1 tuft cells, distributed throughout the crypt axis, co-express Lgr5 and other stem-cell markers that are otherwise confined to crypt bases. We also detect significant changes in the expression of some of the markers following irradiation, indicating their potential role in the regeneration process. Our approach can enable the sensitive detection of putative stem cells in other tissues and in tumours, guiding complementary functional studies to evaluate their stem-cell properties.

An interacting multiple model filter-based autofocus strategy for confocal time-lapse microscopy

Gene expression and other cellular processes are stochastic, thus their study requires observing multiple events in multiple cells. Therefore, confocal microscopy cell imaging has recently gained much interest. In time-lapse imaging, adjustments are needed at short intervals to compensate for focus drift. There are several automated methods for this purpose. In general, before acquiring higher resolution images, software-based autofocus algorithms require a set of low-resolution images along the z-axis to determine the plane for which a predefined focusing function is maximized. These algorithms require 10-100 z-slices each time, and there is no fixed number or upper limit of required z-slices that ensures optimal focusing. The higher is this number, the stronger is photo bleaching, hampering the feasibility of long-time series measurements. We propose a new focusing strategy in time-lapse imaging. The algorithm relies on the nature and predictability of the focus drift. We first show that the focus drift curve is predictable within a small error bound in standard experimental setups. We, then, exploit the interacting multiple model filter algorithm to predict the drift at time, t, based on the measurement at time t-1. This allows a drastic reduction of the number of required z-slices for focus drift correction, largely overcoming the problem of photo bleaching. In addition, we propose a new set of functions for focusing in time-lapse imaging, derived from preexisting ones. We demonstrate the method's efficiency in time-lapse imaging of Escherichia coli cells expressing MS2d-GFP tagged RNA molecules.

Multiscale stochastic modelling of gene expression

Stochastic phenomena in gene regulatory networks can be modelled by the chemical master equation for gene products such as mRNA and proteins. If some of these elements are present in significantly higher amounts than the rest, or if some of the reactions between these elements are substantially faster than others, it is often possible to reduce the master equation to a simpler problem using asymptotic methods. We present examples of such a procedure and analyse the relationship between the reduced models and the original.

A novel method for producing mono-biotinylated, biologically active neurotrophic factors: an essential reagent for single molecule study of axonal transport

In this report, we describe a novel method for producing mature and biologically active mono-biotinylated nerve growth factors (mBtNGF) that can be used for single molecule studies of real-time movement of neurotrophins within axons of neurons. We inserted an AviTag sequence into the C-terminal of the full length mouse preproNGF cDNA and cloned the fusion construct into a pcDNA3.1 mammalian expression vector. We also subcloned the Escherichia coli biotin ligase, BirA, into a pcDNA3.1 vector. These two plasmids were then transiently co-expressed in HEK293FT cells. As a result, the AviTag located in the C-terminal of preproNGF was selectively ligated to a single biotin by BirA. The prepro sequence of NGF was subsequently cleaved within the cell. Mature mono-biotinylated NGF (mBtNGF) was secreted into cell culture media and was purified using Ni resin. We carried out activity assays and our results showed that mBtNGF retained biological activities that were comparable to normal NGF purified from mouse sub maxillary glands. We further verified the biotinylation efficiency of mBtNGF and the level of non-biotinylated NGF was virtually undetectable in the final preparation. Finally, by conjugating to quantum-dot streptavidin, mBtNGF was successfully used for single molecule study of axonal NGF trafficking in neurons.

Mechanosignaling to the cell nucleus and gene regulation

Cells integrate physicochemical signals on the nanoscale from the local microenvironment, resulting in altered functional nuclear landscape and gene expression. These alterations regulate diverse biological processes including stem cell differentiation, establishing robust developmental genetic programs and cellular homeostatic control systems. The mechanisms by which these signals are integrated into the 3D spatiotemporal organization of the cell nucleus to elicit differential gene expression programs are poorly understood. In this review I analyze our current understanding of mechanosignal transduction mechanisms to the cell nucleus to induce differential gene regulation. A description of both physical and chemical coupling, resulting in a prestressed nuclear organization, is emphasized. I also highlight the importance of spatial dimension in chromosome assembly, as well as the temporal filtering and stochastic processes at gene promoters that may be important in understanding the biophysical design principles underlying mechanoregulation of gene transcription.

Quantifying negative feedback regulation by micro-RNAs

Micro-RNAs (miRNAs) play a crucial role in post-transcriptional gene regulation by pairing with target mRNAs to repress protein production. It has been shown that over one-third of human genes are targeted by miRNA. Although hundreds of miRNAs have been identified in mammalian genomes, the function of miRNA-based repression in the context of gene regulation networks still remains unclear. In this study, we explore the functional roles of feedback regulation by miRNAs. In a model where repression of translation occurs by sequestration of mRNA by miRNA, we find that miRNA and mRNA levels are anti-correlated, resulting in larger fluctuation in protein levels than theoretically expected assuming no correlation between miRNA and mRNA levels. If miRNA repression is due to a catalytic suppression of translation rates, we analytically show that the protein fluctuations can be strongly repressed with miRNA regulation. We also discuss how either of these modes may be relevant for cell function.

Regulation by small RNAs via coupled degradation: mean-field and variational approaches

Regulatory genes called small RNAs (sRNAs) are known to play critical roles in cellular responses to changing environments. For several sRNAs, regulation is effected by coupled stoichiometric degradation with messenger RNAs (mRNAs). The nonlinearity inherent in this regulatory scheme indicates that exact analytical solutions for the corresponding stochastic models are intractable. Here, we present a variational approach to analyze a well-studied stochastic model for regulation by sRNAs via coupled degradation. The proposed approach is efficient and provides accurate estimates of mean mRNA levels as well as higher-order terms. Results from the variational ansatz are in excellent agreement with data from stochastic simulations for a wide range of parameters, including regions of parameter space where mean-field approaches break down. The proposed approach can be applied for quantitative modeling of stochastic gene expression in complex regulatory networks.

Measuring cell identity in noisy biological systems

Global gene expression measurements are increasingly obtained as a function of cell type, spatial position within a tissue and other biologically meaningful coordinates. Such data should enable quantitative analysis of the cell-type specificity of gene expression, but such analyses can often be confounded by the presence of noise. We introduce a specificity measure Spec that quantifies the information in a gene's complete expression profile regarding any given cell type, and an uncertainty measure dSpec, which measures the effect of noise on specificity. Using global gene expression data from the mouse brain, plant root and human white blood cells, we show that Spec identifies genes with variable expression levels that are nonetheless highly specific of particular cell types. When samples from different individuals are used, dSpec measures genes’ transcriptional plasticity in each cell type. Our approach is broadly applicable to mapped gene expression measurements in stem cell biology, developmental biology, cancer biology and biomarker identification. As an example of such applications, we show that Spec identifies a new class of biomarkers, which exhibit variable expression without compromising specificity. The approach provides a unifying theoretical framework for quantifying specificity in the presence of noise, which is widely applicable across diverse biological systems.

Quantification noise in single cell experiments

In quantitative single-cell studies, the critical part is the low amount of nucleic acids present and the resulting experimental variations. In addition biological data obtained from heterogeneous tissue are not reflecting the expression behaviour of every single-cell. These variations can be derived from natural biological variance or can be introduced externally. Both have negative effects on the quantification result. The aim of this study is to make quantitative single-cell studies more transparent and reliable in order to fulfil the MIQE guidelines at the single-cell level. The technical variability introduced by RT, pre-amplification, evaporation, biological material and qPCR itself was evaluated by using RNA or DNA standards. Secondly, the biological expression variances of GAPDH, TNFα, IL-1β, TLR4 were measured by mRNA profiling experiment in single lymphocytes. The used quantification setup was sensitive enough to detect single standard copies and transcripts out of one solitary cell. Most variability was introduced by RT, followed by evaporation, and pre-amplification. The qPCR analysis and the biological matrix introduced only minor variability. Both conducted studies impressively demonstrate the heterogeneity of expression patterns in individual cells and showed clearly today's limitation in quantitative single-cell expression analysis.

Exact and approximate distributions of protein and mRNA levels in the low-copy regime of gene expression

Gene expression at the single-cell level incorporates reaction mechanisms which are intrinsically stochastic as they involve molecular species present at low copy numbers. The dynamics of these mechanisms can be described quantitatively using stochastic master-equation modelling; in this paper we study a generic gene-expression model of this kind which explicitly includes the representations of the processes of transcription and translation. For this model we determine the generating function of the steady-state distribution of mRNA and protein counts and characterise the underlying probability law using a combination of analytic, asymptotic and numerical approaches, finding that the distribution may assume a number of qualitatively distinct forms. The results of the analysis are suitable for comparison with single-molecule resolution gene-expression data emerging from recent experimental studies.

RNA sequencing reveals two major classes of gene expression levels in metazoan cells

The expression level of a gene is often used as a proxy for determining whether the protein or RNA product is functional in a cell or tissue. Therefore, it is of fundamental importance to understand the global distribution of gene expression levels, and to be able to interpret it mechanistically and functionally. Here we use RNA sequencing (RNA-seq) of mouse Th2 cells, coupled with a range of other techniques, to show that all genes can be separated, based on their expression abundance, into two distinct groups: one group comprised of lowly expressed and putatively non-functional mRNAs, and the other of highly expressed mRNAs with active chromatin marks at their promoters. These observations are confirmed in many other microarray and RNA-seq data sets of metazoan cell types.

Transcriptional regulation: effects of promoter proximal pausing on speed, synchrony and reliability

Recent whole genome polymerase binding assays in the Drosophila embryo have shown that a substantial proportion of uninduced genes have pre-assembled RNA polymerase-II transcription initiation complex (PIC) bound to their promoters. These constitute a subset of promoter proximally paused genes for which mRNA elongation instead of promoter access is regulated. This difference can be described as a rearrangement of the regulatory topology to control the downstream transcriptional process of elongation rather than the upstream transcriptional initiation event. It has been shown experimentally that genes with the former mode of regulation tend to induce faster and more synchronously, and that promoter-proximal pausing is observed mainly in metazoans, in accord with a posited impact on synchrony. However, it has not been shown whether or not it is the change in the regulated step per se that is causal. We investigate this question by proposing and analyzing a continuous-time Markov chain model of PIC assembly regulated at one of two steps: initial polymerase association with DNA, or release from a paused, transcribing state. Our analysis demonstrates that, over a wide range of physical parameters, increased speed and synchrony are functional consequences of elongation control. Further, we make new predictions about the effect of elongation regulation on the consistent control of total transcript number between cells. We also identify which elements in the transcription induction pathway are most sensitive to molecular noise and thus possibly the most evolutionarily constrained. Our methods produce symbolic expressions for quantities of interest with reasonable computational effort and they can be used to explore the interplay between interaction topology and molecular noise in a broader class of biochemical networks. We provide general-purpose code implementing these methods.

Gene activation is an inherently random process because numerous diffusing proteins and DNA must first interact by random association before transcription can begin. For many genes the necessary protein–DNA associations only begin after activation, but it has recently been noted that a large class of genes in multicellular organisms can assemble the initiation complex of proteins on the core promoter prior to activation. For these genes, activation merely releases polymerase from the preassembled complex to transcribe the gene. It has been proposed on the basis of experiments that such a mechanism, while possibly costly, increases both the speed and the synchrony of the process of gene transcription. We study a realistic model of gene transcription, and show that this conclusion holds for all but a tiny fraction of the space of physical rate parameters that govern the process. The improved control of cell-to-cell variations afforded by regulation through a paused polymerase may help multicellular organisms achieve the high degree of coordination required for development. Our approach has also generated tools with which one can study the effects of analogous changes in other molecular networks and determine the relative importance of various molecular binding rates to particular system properties.

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

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

Advances in the molecular detection of ABC transporters involved in multidrug resistance in cancer

ATP-Binding Cassette (ABC) transporters are important mediators of multidrug resistance (MDR) in patients with cancer. Although their role in MDR has been extensively studied in vitro, their value in predicting response to chemotherapy has yet to be fully determined. Establishing a molecular diagnostic assay dedicated to the quantitation of ABC transporter genes is therefore critical to investigate their involvement in clinical MDR. In this article, we provide an overview of the methodologies that have been applied to analyze the mRNA expression levels of ABC transporters, by describing the technology, its pros and cons, and the experimental protocols that have been followed. We also discuss recent studies performed in our laboratory that assess the ability of the currently available high-throughput gene expression profiling platforms to discriminate between highly homologous genes. This work led to the conclusion that high-throughput TaqMan-based qRT-PCR platforms provide standardized clinical assays for the molecular detection of ABC transporters and other families of highly homologous MDR-linked genes encoding, for example, the uptake transporters (solute carriers-SLCs) and the phase I and II metabolism enzymes.

Mammalian genes are transcribed with widely different bursting kinetics

In prokaryotes and eukaryotes, most genes appear to be transcribed during short periods called transcriptional bursts, interspersed by silent intervals. We describe how such bursts generate gene-specific temporal patterns of messenger RNA (mRNA) synthesis in mammalian cells. To monitor transcription at high temporal resolution, we established various gene trap cell lines and transgenic cell lines expressing a short-lived luciferase protein from an unstable mRNA, and recorded bioluminescence in real time in single cells. Mathematical modeling identified gene-specific on- and off-switching rates in transcriptional activity and mean numbers of mRNAs produced during the bursts. Transcriptional kinetics were markedly altered by cis-regulatory DNA elements. Our analysis demonstrated that bursting kinetics are highly gene-specific, reflecting refractory periods during which genes stay inactive for a certain time before switching on again.

A quantitative comparison of cell-type-specific microarray gene expression profiling methods in the mouse brain

Expression profiling of restricted neural populations using microarrays can facilitate neuronal classification and provide insight into the molecular bases of cellular phenotypes. Due to the formidable heterogeneity of intermixed cell types that make up the brain, isolating cell types prior to microarray processing poses steep technical challenges that have been met in various ways. These methodological differences have the potential to distort cell-type-specific gene expression profiles insofar as they may insufficiently filter out contaminating mRNAs or induce aberrant cellular responses not normally present in vivo. Thus we have compared the repeatability, susceptibility to contamination from off-target cell-types, and evidence for stress-responsive gene expression of five different purification methods - Laser Capture Microdissection (LCM), Translating Ribosome Affinity Purification (TRAP), Immunopanning (PAN), Fluorescence Activated Cell Sorting (FACS), and manual sorting of fluorescently labeled cells (Manual). We found that all methods obtained comparably high levels of repeatability, however, data from LCM and TRAP showed significantly higher levels of contamination than the other methods. While PAN samples showed higher activation of apoptosis-related, stress-related and immediate early genes, samples from FACS and Manual studies, which also require dissociated cells, did not. Given that TRAP targets actively translated mRNAs, whereas other methods target all transcribed mRNAs, observed differences may also reflect translational regulation.

Noise regulation by quorum sensing in low mRNA copy number systems

Background

Cells must face the ubiquitous presence of noise at the level of signaling molecules. The latter constitutes a major challenge for the regulation of cellular functions including communication processes. In the context of prokaryotic communication, the so-called quorum sensing (QS) mechanism relies on small diffusive molecules that are produced and detected by cells. This poses the intriguing question of how bacteria cope with the fluctuations for setting up a reliable information exchange.

Results

We present a stochastic model of gene expression that accounts for the main biochemical processes that describe the QS mechanism close to its activation threshold. Within that framework we study, both numerically and analytically, the role that diffusion plays in the regulation of the dynamics and the fluctuations of signaling molecules. In addition, we unveil the contribution of different sources of noise, intrinsic and transcriptional, in the QS mechanism.

Conclusions

The interplay between noisy sources and the communication process produces a repertoire of dynamics that depends on the diffusion rate. Importantly, the total noise shows a non-monotonic behavior as a function of the diffusion rate. QS systems seems to avoid values of the diffusion that maximize the total noise. These results point towards the direction that bacteria have adapted their communication mechanisms in order to improve the signal-to-noise ratio.

Origins of regulated cell-to-cell variability

Single-cell measurements and lineage-tracing experiments are revealing that phenotypic cell-to-cell variability is often the result of deterministic processes, despite the existence of intrinsic noise in molecular networks. In most cases, this determinism represents largely uncharacterized molecular regulatory mechanisms, which places the study of cell-to-cell variability in the realm of molecular cell biology. Further research in the field will be important to advance quantitative cell biology because it will provide new insights into the mechanisms by which cells coordinate their intracellular activities in the spatiotemporal context of the multicellular environment.

Origins of stochastic intracellular processes and consequences for cell-to-cell variability and cellular survival strategies

Quantitative analyses of the dynamics of single cells have become a powerful approach in current cell biology. They give us an unprecedented opportunity to study dynamics of molecular networks at a high level of accuracy in living single cells. Genetically identical cells, growing in the same environment and sharing the same growth history, can differ remarkably in their molecular makeup and physiological behaviors. The origins of this cell-to-cell variability have in many cases been traced to the inevitable stochasticity of molecular reactions. Those mechanisms can cause isogenic cells to have qualitatively different life histories. Many studies indicate that molecular noise can be exploited by cell populations to enhance survival prospects in uncertain environments. On the other hand, cells have evolved noise-suppression mechanisms to cope with the inevitable noise in their functioning so as to reduce the hazardous effects of noise. In this chapter, we discuss key experiments, theoretical results, and physiological consequences of molecular stochasticity to introduce this exciting field to a broader community of (systems) biologists.

Grand challenge commentary: Exploiting single-cell variation for new antibiotics

Variations between single members of a bacterial population can lead to antibiotic resistance that is not gene based. The future of effective infectious disease management might depend on a better understanding of this phenomenon and the potential to manipulate both it and microbial population dynamics in general.

Transcription by the numbers redux: experiments and calculations that surprise

The study of transcription has witnessed an explosion of quantitative effort both experimentally and theoretically. In this article we highlight some of the exciting recent experimental efforts in the study of transcription with an eye to the demands that such experiments put on theoretical models of transcription. From a modeling perspective, we focus on two broad classes of models: the so-called thermodynamic models that use statistical mechanics to reckon the level of gene expression as probabilities of promoter occupancy, and rate-equation treatments that focus on the temporal evolution of the activity of a given promoter and that make it possible to compute the distributions of messenger RNA and proteins. We consider several appealing case studies to illustrate how quantitative models have been used to dissect transcriptional regulation.

Random discrete competing events vs. dynamic bistable switches in cell proliferation in differentiation

Several recent experiments related to fundamental aspects of cell behaviour, such as passing of the restriction point of cell cycle, which are generally interpreted in accordance with the dynamic paradigm implying the use of differential equations operating with the concentrations of cellular components and rate constants of their interactions, are shown in the present paper to be consistent with a simple model based on discrete competing stochastic events interpreted as assembly of alternative complexes of transcription factors at gene promoters. The model conforms to the transition probability model of cell cycle and to the stochastic approaches to cell differentiation and integrates them with the restriction point concept.

Finite-size effects in dynamics of zero-range processes

The finite-size effects prominent in zero-range processes exhibiting a condensation transition are studied by using continuous-time Monte Carlo simulations. We observe that, well above the thermodynamic critical point, both static and dynamic properties display fluidlike behavior up to a density ρc(L), which is the finite-size counterpart of the critical density ρc=ρc(L→∞). We determine this density from the crossover behavior of the average size of the largest cluster. We then show that several dynamical characteristics undergo a qualitative change at this density. In particular, the size distribution of the largest cluster at the moment of relocation, the persistence properties of the largest cluster, and the correlations in its motion are studied.

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

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

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

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

Numbers on the edges: a simplified and scalable method for quantifying the gene regulation function

The gene regulation function (GRF) provides an operational description of a promoter behavior as a function of the concentration of one of its transcriptional regulators. Behind this apparently trivial definition lies a central concept in biological control: the GRF provides the input/output relationship of each edge in a transcriptional network, independently from the molecular interactions involved. Here we discuss how existing methods allow direct measurement of the GRF, and how several trade-offs between scalability and accuracy have hindered its application to relatively large networks. We discuss the theoretical and technical requirements for obtaining the GRF. Based on these requirements, we introduce a simplified and easily scalable method that is able to capture the significant parameters of the GRF. The GRF is able to predict the behavior of a simple genetic circuit, illustrating how addressing the quantitative nature of gene regulation substantially increases our comprehension on the mechanisms of gene control.

Variability in the control of cell division underlies sepal epidermal patterning in Arabidopsis thaliana

How growth and proliferation are precisely controlled in organs during development and how the regulation of cell division contributes to the formation of complex cell type patterns are important questions in developmental biology. Such a pattern of diverse cell sizes is characteristic of the sepals, the outermost floral organs, of the plant Arabidopsis thaliana. To determine how the cell size pattern is formed in the sepal epidermis, we iterate between generating predictions from a computational model and testing these predictions through time-lapse imaging. We show that the cell size diversity is due to the variability in decisions of individual cells about when to divide and when to stop dividing and enter the specialized endoreduplication cell cycle. We further show that altering the activity of cell cycle inhibitors biases the timing and changes the cell size pattern as our model predicts. Models and observations together demonstrate that variability in the time of cell division is a major determinant in the formation of a characteristic pattern.

Visualization of individual Scr mRNAs during Drosophila embryogenesis yields evidence for transcriptional bursting

The detection and counting of transcripts within single cells via fluorescent in situ hybridization (FISH) has allowed researchers to ask quantitative questions about gene expression at the level of individual cells. This method is often preferable to quantitative RT-PCR, because it does not necessitate destruction of the cells being probed and maintains spatial information that may be of interest. Until now, studies using FISH at single-molecule resolution have only been rigorously carried out in isolated cells (e.g., yeast cells or mammalian cell culture). Here, we describe the detection and counting of transcripts within single cells of fixed, whole-mount Drosophila embryos via a combination of FISH, immunohistochemistry, and image segmentation. Our method takes advantage of inexpensive, long RNA probes detected with antibodies, and we present novel evidence to show that we can robustly detect single mRNA molecules. We use this method to characterize transcription at the endogenous locus of the Hox gene Sex combs reduced (Scr), by comparing a stably expressing group of cells to a group that only transiently expresses the gene. Our data provide evidence for transcriptional bursting, as well for divergent "accumulation" and "maintenance" phases of gene activity at the Scr locus.

An integrative paradigm to impart quality to correlative science

Correlative studies are a primary mechanism through which insights can be obtained about the bioactivity and potential efficacy of candidate therapeutics evaluated in early-stage clinical trials. Accordingly, well designed and performed early-stage correlative studies have the potential to strongly influence further clinical development of candidate therapeutic agents, and correlative data obtained from early stage trials has the potential to provide important guidance on the design and ultimate successful evaluation of products in later stage trials, particularly in the context of emerging clinical trial paradigms such as adaptive trial design.

Historically the majority of early stage trials have not generated meaningful correlative data sets that could guide further clinical development of the products under evaluation. In this review article we will discuss some of the potential limitations with the historical approach to performing correlative studies that might explain at least in part the to-date overall failure of such studies to adequately support clinical trial development, and present emerging thought and approaches related to comprehensiveness and quality that hold the promise to support the development of correlative plans which will provide meaningful correlative data that can effectively guide and support the clinical development path for candidate therapeutic agents.

Messenger RNA fluctuations and regulatory RNAs shape the dynamics of a negative feedback loop

Single-cell experiments of simple regulatory networks can markedly differ from cell population experiments. Such differences arise from stochastic events in individual cells that are averaged out in cell populations. For instance, while individual cells may show sustained oscillations in the concentrations of some proteins, such oscillations may appear damped in the population average. In this paper we investigate the role of RNA stochastic fluctuations as a leading force to produce a sustained excitatory behavior at the single-cell level. As opposed to some previous models, we build a fully stochastic model of a negative feedback loop that explicitly takes into account the RNA stochastic dynamics. We find that messenger RNA random fluctuations can be amplified during translation and produce sustained pulses of protein expression. Motivated by the recent appreciation of the importance of noncoding regulatory RNAs in post-transcription regulation, we also consider the possibility that a regulatory RNA transcript could bind to the messenger RNA and repress translation. Our findings show that the regulatory transcript helps reducing gene expression variability both at the single-cell level and at the cell population level.

Single-molecule DNA analysis

The ability to detect single molecules of DNA or RNA has led to an extremely rich area of exploration of the single most important biomolecule in nature. In cases in which the nucleic acid molecules are tethered to a solid support, confined to a channel, or simply allowed to diffuse into a detection volume, novel techniques have been developed to manipulate the DNA and to examine properties such as structural dynamics and protein-DNA interactions. Beyond the analysis of the properties of nucleic acids themselves, single-molecule detection has enabled dramatic improvements in the throughput of DNA sequencing and holds promise for continuing progress. Both optical and nonoptical detection methods that use surfaces, nanopores, and zero-mode waveguides have been attempted, and one optically based instrument is already commercially available. The breadth of literature related to single-molecule DNA analysis is vast; this review focuses on a survey of efforts in molecular dynamics and nucleic acid sequencing.