Stochastic and delayed stochastic models of gene expression and regulation

Stochastic switching of delayed feedback suppresses oscillations in genetic regulatory systems

Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates the effect of delayed feedback. To do so, we consider a hybrid model where stochastic delays evolve by a continuous-time Markov chain, and between switching events, the system of interest evolves via a deterministic delay equation. Our main contribution is the calculation of an effective delay equation in the fast switching limit. This effective equation maintains the influence of all subsystem delays and cannot be replaced with a single effective delay. To illustrate the relevance of this calculation, we investigate a simple model of stochastically switching delayed feedback motivated by gene regulation. We show that sufficiently fast switching between two oscillatory subsystems can yield stable dynamics.

Somatic Variants and Exon-Level Copy Number Changes in Five Hyperplastic Oral Leukoplakias

Oral leukoplakia (OL), an oral potentially malignant disorder, begins with a hyperplastic/hyperkeratotic stage at which no genome-scale somatic single nucleotide variant profiles have been described so far. We performed exome sequencing of five cases at this stage with no evidence of dysplasia to identify genetic alterations (exon-level copy number alterations, indels, and single nucleotide variants), their association with transcript levels, and relationship with oral cancer susceptibility. Pathway enrichment analysis of genes associated with tobacco chewing and age-related mutation signatures, transcripts with variants predicted to be functionally damaging and those with significantly altered levels all indicated the involvement of focal adhesion, ECM-receptor interactions, regulation of cytoskeleton, and DNA repair. Two novel mutations identified in FAT1 tumor suppressor gene were associated with decreased transcript levels. In addition, 16 expressed cancer driver genes contained functionally damaging variants. Many of the affected genes were also reported in dysplastic OL lesions. The presence of variants in cancer driver genes and those shared with oral dysplasias possibly provides a basis for further progression and increased susceptibility to oral cancer.

Stochastic models coupling gene expression and partitioning in cell division in Escherichia coli

Regulation of future RNA and protein numbers is a key process by which cells continuously best fit the environment. In bacteria, RNA and proteins exist in small numbers and their regulatory processes are stochastic. Consequently, there is cell-to-cell variability in these numbers, even between sister cells. Traditionally, the two most studied sources of this variability are gene expression and RNA and protein degradation, with evidence suggesting that the latter is subject to little regulation, when compared to the former. However, time-lapse microscopy and single molecule fluorescent tagging have produced evidence that cell division can also be a significant source of variability due to asymmetries in the partitioning of RNA and proteins. Relevantly, the impact of this noise differs from noise in production and degradation since, unlike these, it is not continuous. Rather, it occurs at specific time points, at which moment it can introduce major fluctuations. Several models have now been proposed that integrate noise from cell division, in addition to noise in gene expression, to mimic the dynamics of RNA and protein numbers of cell lineages. This is expected to be particularly relevant in genetic circuits, where significant fluctuations in one component protein, at specific time moments, are expected to perturb near-equilibrium states of the circuits, which can have long-lasting consequences. Here we review stochastic models coupling these processes in Escherichia coli, from single genes to small circuits.

A single nucleotide variant of human PARP1 determines response to PARP inhibitors

The introduction of novel cancer drugs and innovative treatments brings great hope for cancer patients, but also an urgent need to match drugs to suitable patients, since certain drugs that benefit one patient may actually harm others. The newly developed poly-ADP ribose polymerase (PARP) inhibitors (PARPis) are a group of pharmacological enzyme inhibitors used clinically for multiple indications. Several forms of cancer tend to be PARP dependent, making PARP an attractive target for cancer therapy. Specifically, PARPis are commonly used in BRCA-associated breast cancers patients, since unrepaired single-strand breaks are converted into double-strand breaks and BRCA-associated tumors cannot repair them by homologous recombination so that PARPi leads to tumor cell death, by a mechanism called “Synthetic Lethality”. Unfortunately, not all patients respond to PARPi, and it is not currently possible to predict who will or will not respond. Here, we present a specific genomic marker, which reflects a single-nucleotide polymorphism of human PARP1 and correlates in vitro with response to PARPi, throughout all indications. In addition, we report that this SNP is associated with re-shaping mRNA, and mRNA levels, and influences the final protein structure to expose new binding sites while hiding others. The status of the SNP is therefore critical to patients’ care, as it relates responses to PARPi to the PARP1-SNP carried.

The FLAME-accelerated signalling tool (FaST) for facile parallelisation of flexible agent-based models of cell signalling

Agent-based modelling is particularly adept at modelling complex features of cell signalling pathways, where heterogeneity, stochastic and spatial effects are important, thus increasing our understanding of decision processes in biology in such scenarios. However, agent-based modelling often is computationally prohibitive to implement. Parallel computing, either on central processing units (CPUs) or graphical processing units (GPUs), can provide a means to improve computational feasibility of agent-based applications but generally requires specialist coding knowledge and extensive optimisation. In this paper, we address these challenges through the development and implementation of the FLAME-accelerated signalling tool (FaST), a software that permits easy creation and parallelisation of agent-based models of cell signalling, on CPUs or GPUs. FaST incorporates validated new agent-based methods, for accurate modelling of reaction kinetics and, as proof of concept, successfully converted an ordinary differential equation (ODE) model of apoptosis execution into an agent-based model. We finally parallelised this model through FaST on CPUs and GPUs resulting in an increase in performance of 5.8× (16 CPUs) and 53.9×, respectively. The FaST takes advantage of the communicating X-machine approach used by FLAME and FLAME GPU to allow easy alteration or addition of functionality to parallel applications, but still includes inherent parallelisation optimisation. The FaST, therefore, represents a new and innovative tool to easily create and parallelise bespoke, robust, agent-based models of cell signalling.

Chemical Langevin Equation for Complex Reactions

The stochastic dynamical behaviors of an elementary reaction system can be investigated by the chemical Langevin equation (CLE). However, most of the reactions in engineering belong to complex reactions. It is not appropriate to describe the random evolution process of a complex chemical reaction system by directly using CLE because the foundation of the deviation of CLE is the equilibrium equation of the number of molecules in elementary reaction systems. In the study, the chemical Langevin equation for complex reactions (CLE-CR) is proposed based on the random process theory by introducing the extent of reactions to express the reaction rates of complex reactions. The reaction rates of complex reactions are regarded as some random variables following Poisson distribution. To illustrate the essential consistency of CLE-CR and CLE, the physical meaning of the propensity function in CLE is comprehensively discussed. A numerical example from chemical engineering is employed to demonstrate the effectiveness of CLE-CR and the solving procedure. The results show that CLE-CR can be conveniently applied into engineering to investigate the stochastic dynamical behaviors of complex reaction systems, giving the probabilistic information of the concentration evolution of chemical constituents.

Added value of autoregulation and multi-step kinetics of transcription initiation

Bacterial gene expression regulation occurs mostly during transcription, which has two main rate-limiting steps: the close complex formation, when the RNA polymerase binds to an active promoter, and the subsequent open complex formation, after which it follows elongation. Tuning these steps' kinetics by the action of e.g. transcription factors, allows for a wide diversity of dynamics. For example, adding autoregulation generates single-gene circuits able to perform more complex tasks. Using stochastic models of transcription kinetics with empirically validated parameter values, we investigate how autoregulation and the multi-step transcription initiation kinetics of single-gene autoregulated circuits can be combined to fine-tune steady state mean and cell-to-cell variability in protein expression levels, as well as response times. Next, we investigate how they can be jointly tuned to control complex behaviours, namely, time counting, switching dynamics and memory storage. Overall, our finding suggests that, in bacteria, jointly regulating a single-gene circuit's topology and the transcription initiation multi-step dynamics allows enhancing complex task performance.

Kinetics of lipid-nanoparticle-mediated intracellular mRNA delivery and function

mRNA delivery into cells forms the basis for one of the new and promising ways to treat various diseases. Among suitable carriers, lipid nanoparticles (LNPs) with a size of about 100 nm are now often employed. Despite high current interest in this area, the understanding of the basic details of LNP-mediated mRNA delivery and function is limited. To clarify the kinetics of mRNA release from LNPs, the author uses three generic models implying (i) exponential, (ii) diffusion-controlled, and (iii) detachment-controlled kinetic regimes, respectively. Despite the distinct differences in these kinetics, the associated transient kinetics of mRNA translation to the corresponding protein and its degradation are shown to be not too sensitive to the details of the mRNA delivery by LNPs (or other nanocarriers). In addition, the author illustrates how this protein may temporarily influence the expression of one gene or a few equivalent genes. The analysis includes positive or negative regulation of the gene transcription via the attachment of the protein without or with positive or negative feedback in the gene expression. Stable, bistable, and oscillatory schemes have been scrutinized in this context.

Stochastic modeling of biochemical systems with multistep reactions using state-dependent time delay

To deal with the growing scale of molecular systems, sophisticated modelling techniques have been designed in recent years to reduce the complexity of mathematical models. Among them, a widely used approach is delayed reaction for simplifying multistep reactions. However, recent research results suggest that a delayed reaction with constant time delay is unable to describe multistep reactions accurately. To address this issue, we propose a novel approach using state-dependent time delay to approximate multistep reactions. We first use stochastic simulations to calculate time delay arising from multistep reactions exactly. Then we design algorithms to calculate time delay based on system dynamics precisely. To demonstrate the power of proposed method, two processes of mRNA degradation are used to investigate the function of time delay in determining system dynamics. In addition, a multistep pathway of metabolic synthesis is used to explore the potential of the proposed method to simplify multistep reactions with nonlinear reaction rates. Simulation results suggest that the state-dependent time delay is a promising and accurate approach to reduce model complexity and decrease the number of unknown parameters in the models.

Stochastic Regulation of her1/7 Gene Expression Is the Source of Noise in the Zebrafish Somite Clock Counteracted by Notch Signalling

The somite segmentation clock is a robust oscillator used to generate regularly-sized segments during early vertebrate embryogenesis. It has been proposed that the clocks of neighbouring cells are synchronised via inter-cellular Notch signalling, in order to overcome the effects of noisy gene expression. When Notch-dependent communication between cells fails, the clocks of individual cells operate erratically and lose synchrony over a period of about 5 to 8 segmentation clock cycles (2-3 hours in the zebrafish). Here, we quantitatively investigate the effects of stochasticity on cell synchrony, using mathematical modelling, to investigate the likely source of such noise. We find that variations in the transcription, translation and degradation rate of key Notch signalling regulators do not explain the in vivo kinetics of desynchronisation. Rather, the analysis predicts that clock desynchronisation, in the absence of Notch signalling, is due to the stochastic dissociation of Her1/7 repressor proteins from the oscillating her1/7 autorepressed target genes. Using in situ hybridisation to visualise sites of active her1 transcription, we measure an average delay of approximately three minutes between the times of activation of the two her1 alleles in a cell. Our model shows that such a delay is sufficient to explain the in vivo rate of clock desynchronisation in Notch pathway mutant embryos and also that Notch-mediated synchronisation is sufficient to overcome this stochastic variation. This suggests that the stochastic nature of repressor/DNA dissociation is the major source of noise in the segmentation clock.

Time-Delayed Models of Gene Regulatory Networks

We discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternative modelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems.

A model for aryl hydrocarbon receptor-activated gene expression shows potency and efficacy changes and predicts squelching due to competition for transcription co-activators

A stochastic model of nuclear receptor-mediated transcription was developed based on activation of the aryl hydrocarbon receptor (AHR) by 2,3,7,8-tetrachlorodibenzodioxin (TCDD) and subsequent binding the activated AHR to xenobiotic response elements (XREs) on DNA. The model was based on effects observed in cells lines commonly used as in vitro experimental systems. Following ligand binding, the AHR moves into the cell nucleus and forms a heterodimer with the aryl hydrocarbon nuclear translocator (ARNT). In the model, a requirement for binding to DNA is that a generic coregulatory protein is subsequently bound to the AHR-ARNT dimer. Varying the amount of coregulator available within the nucleus altered both the potency and efficacy of TCDD for inducing for transcription of CYP1A1 mRNA, a commonly used marker for activation of the AHR. Lowering the amount of available cofactor slightly increased the EC50 for the transcriptional response without changing the efficacy or maximal response. Further reduction in the amount of cofactor reduced the efficacy and produced non-monotonic dose-response curves (NMDRCs) at higher ligand concentrations. The shapes of these NMDRCs were reminiscent of the phenomenon of squelching. Resource limitations for transcriptional machinery are becoming apparent in eukaryotic cells. Within single cells, nuclear receptor-mediated gene expression appears to be a stochastic process; however, intercellular communication and other aspects of tissue coordination may represent a compensatory process to maintain an organism’s ability to respond on a phenotypic level to various stimuli within an inconstant environment.

Stochastic thermodynamics of Langevin systems under time-delayed feedback control: Second-law-like inequalities

Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small stochastic systems governed by an underdamped Langevin equation and driven out of equilibrium by a time-delayed continuous feedback control. In their normal operating regime, these systems settle in a nonequilibrium steady state in which work is permanently extracted from the surrounding heat bath. By using the Fokker-Planck representation of the dynamics, we derive a set of second-law-like inequalities that provide bounds to the rate of extracted work. These inequalities involve additional contributions characterizing the reduction of entropy production due to the continuous measurement process. We also show that the non-Markovian nature of the dynamics requires a modification of the basic relation linking dissipation to the breaking of time-reversal symmetry at the level of trajectories. The modified relation includes a contribution arising from the acausal character of the reverse process. This, in turn, leads to another second-law-like inequality. We illustrate the general formalism with a detailed analytical and numerical study of a harmonic oscillator driven by a linear feedback, which describes actual experimental setups.

Effects of elongation delay in transcription dynamics

In the transcription process, elongation delay is induced by the movement of RNA polymerases (RNAP) along the DNA sequence, and can result in changes in the transcription dynamics. This paper studies the transcription dynamics that involved the elongation delay and effects of cell division and DNA replication. The stochastic process of gene expression is modeled with delay chemical master equation with periodic coefficients, and is studied numerically through the stochastic simulation algorithm with delay. We show that the average transcription level approaches to a periodic dynamics over cell cycles at homeostasis, and the elongation delay can reduce the transcription level and increase the transcription noise. Moreover, the transcription elongation can induce bimodal distribution of mRNA levels that can be measured by the techniques of flow cytometry.

Stochastic gene expression with delay

The expression of genes usually follows a two-step procedure. First, a gene (encoded in the genome) is transcribed resulting in a strand of (messenger) RNA. Afterwards, the RNA is translated into protein. We extend the classical stochastic jump model by adding delays (with arbitrary distributions) to transcription and translation. Already in the classical model, production of RNA and protein comes in bursts by activation and deactivation of the gene, resulting in a large variance of the number of RNA and proteins in equilibrium. We derive precise formulas for this second-order structure with the model including delay in equilibrium.

Kinetics of gene expression in bacteria — From models to measurements, and back again

Dennis Salahub has contributed to several scientific areas. Likely, one of the lesser known contributions is the one on the study of the kinetics of gene expression in prokaryotes, which resulted in a delayed stochastic model of transcription and translation dynamics in bacteria. The model has become the basis for modeling stochastic genetic circuits and has provided a framework for interpreting recent measurements of transcripts production dynamics in live cells, one event at a time. Here, we review the contributions by Salahub and colleagues to the modeling strategies of gene expression as a multi-delayed stochastic process. Next, we describe recent findings, which build upon this work and provide experimental validation of the models. Finally, we discuss potential future developments in this field of research.

Toggle switch: noise determines the winning gene

Bistable regulatory elements enhance heterogeneity in cell populations and, in multicellular organisms, allow cells to specialize and specify their fate. Our study demonstrates that in a system of bistable genetic switch, the noise characteristics control in which of the two epigenetic attractors the cell population will settle. We focus on two types of noise: the gene switching noise and protein dimerization noise. We found that the change of magnitudes of these noise components for one of the two competing genes introduces a large asymmetry of the protein stationary probability distribution and changes the relative probability of individual gene activation. Interestingly, an increase of noise associated with a given gene can either promote or suppress the activation of the gene, depending on the type of noise. Namely, each gene is repressed by an increase of its gene switching noise and activated by an increase of its protein-product dimerization noise. The observed effect was found robust to the large, up to fivefold deviations of the model parameters. In summary, we demonstrated that noise itself may determine the relative strength of the epigenetic attractors, which may provide a unique mode of control of cell fate decisions.

Effects of gene length on the dynamics of gene expression

In Escherichia coli, the nucleotide length of a gene is bound to affect its expression dynamics. From simulations of a stochastic model of gene expression at the nucleotide and codon levels we show that, within realistic parameter values, the nucleotide length affects RNA and protein mean levels, as well as the expected transient time for RNA and protein numbers to change, following a signal. Fluctuations in RNA and protein numbers are found to be minimized for a small range of lengths, which matches the means of the distributions of lengths found in E. coli of both essential and non-essential genes. The variance of the length distribution for essential genes is found to be smaller than for non-essential genes, implying that these distributions are far from random. Finally, gene lengths are shown to affect the kinetics of a genetic switch, namely, the correlation between temporal proteins numbers, the stability of the two noisy attractors of the switch, and how biased is the choice of noisy attractor. The stability increases with gene length due to increased 'memory' about the previous states of the switch. We argue that, by affecting the dynamics of gene expression and of genetic circuits, gene lengths are subject to selection.

Modeling stochasticity and variability in gene regulatory networks

Modeling stochasticity in gene regulatory networks is an important and complex problem in molecular systems biology. To elucidate intrinsic noise, several modeling strategies such as the Gillespie algorithm have been used successfully. This article contributes an approach as an alternative to these classical settings. Within the discrete paradigm, where genes, proteins, and other molecular components of gene regulatory networks are modeled as discrete variables and are assigned as logical rules describing their regulation through interactions with other components. Stochasticity is modeled at the biological function level under the assumption that even if the expression levels of the input nodes of an update rule guarantee activation or degradation there is a probability that the process will not occur due to stochastic effects. This approach allows a finer analysis of discrete models and provides a natural setup for cell population simulations to study cell-to-cell variability. We applied our methods to two of the most studied regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex.

Systems vaccinology: its promise and challenge for HIV vaccine development

PURPOSE OF REVIEW

The use of systems biology approaches to understand and predict vaccine-induced immunity promises to revolutionize vaccinology. For centuries vaccines were developed empirically, with very little understanding of the mechanisms by which they mediate protective immunity. The so-called systems vaccinology approach employs high-throughput technologies (e.g. microarrays, RNA-seq and mass spectrometry-based proteomics and metabolomics) and computational modeling to describe the complex interactions between all the parts of immune system, with a view to elucidating new biological rules capable of predicting the behavior of the system.

RECENT FINDINGS

Systems biology successfully applied to yellow-fever and influenza vaccines has led to the discovery of signatures that predict vaccine immunogenicity, and promises to advance basic immunology research by providing novel mechanistic insights about immune regulation. However a major challenge of systems vaccinology concerns the analyses and interpretation of the large and noisy data sets generated by high-throughput techniques. Overcoming these issues, we envision that systems vaccinology will have a potential impact on vaccine development, including HIV vaccines.

SUMMARY

High-throughput technologies allow the investigation of vaccine-induced immune responses at system and molecular levels. These are currently being used to unravel new molecular insights about the immune system, and are on the verge of being integrated into clinical trials to enable rational vaccine design and development.

Evolving kinetics of gene expression in stochastic environments

Recent studies have shown that the in vivo dynamics of RNA numbers in bacteria is regulated, to a great extent, by the kinetics of rate limiting steps in transcription. Strong evidence suggests that the kinetics of these steps is sequence dependent. We investigate the selective advantages of rate limiting steps of differing kinetics. For that, we model the kinetics of expression of a gene responsible for promoting cell division at the expense of resources in the environment in individual cells of a population. We model mutations that affect the kinetics of the rate limiting steps and selective pressure in various environmental conditions. Depletion of resources leads to cell death. We find that small changes in the evolutionary constraints can favor widely different noise levels in RNA and protein numbers. Increasing the cost in nutrients for division favors noisier expression. The results provide a better understanding of why different genes differ in the kinetics of production of RNA and proteins.

Dynamics of a genetic toggle switch at the nucleotide and codon levels

We study the dynamics of a model stochastic two-gene switch at the nucleotide and codon levels. First, we show that its stability, the mean lifetime of the noisy attractors, differs from that of a model where transcription and translation elongation are modeled as single-step delayed events, indicating the need of detailed models to study the dynamics of switches. Next, we vary the coupling between the two genes by varying the affinity of repressor proteins to the promoters and measure the mutual information between the two proteins times series. We find that there is a degree of coupling that maximizes information propagation between the two genes. This is explained by the effects of the coupling on mean and entropy of RNA and protein numbers of each gene, as well as correlation, 2-tuple entropy between the two proteins numbers, and, finally, the stability of the noisy attractors. We also find that increasing the rate of translation initiation increases the correlation between RNA and protein numbers and between the two proteins, due to increased stability of the noisy attractors. Increasing the rate of transcription or decreasing RNA degradation causes opposite effects to the correlation between RNA and proteins of each gene and the stability of the noisy attractors. Finally, we add a sequence-dependent transcription pause site and show that both its probability of occurrence, as well as its mean time length, affects the dynamics of the switch, further demonstrating the dependence of the dynamics of this circuit on sequence level events.

Cell-to-cell diversity in protein levels of a gene driven by a tetracycline inducible promoter

BACKGROUND

Gene expression in Escherichia coli is regulated by several mechanisms. We measured in single cells the expression level of a single copy gene coding for green fluorescent protein (GFP), integrated into the genome and driven by a tetracycline inducible promoter, for varying induction strengths. Also, we measured the transcriptional activity of a tetracycline inducible promoter controlling the transcription of a RNA with 96 binding sites for MS2-GFP.

RESULTS

The distribution of GFP levels in single cells is found to change significantly as induction reaches high levels, causing the Fano factor of the cells' protein levels to increase with mean level, beyond what would be expected from a Poisson-like process of RNA transcription. In agreement, the Fano factor of the cells' number of RNA molecules target for MS2-GFP follows a similar trend. The results provide evidence that the dynamics of the promoter complex formation, namely, the variability in its duration from one transcription event to the next, explains the change in the distribution of expression levels in the cell population with induction strength.

CONCLUSIONS

The results suggest that the open complex formation of the tetracycline inducible promoter, in the regime of strong induction, affects significantly the dynamics of RNA production due to the variability of its duration from one event to the next.

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.

Stochastic sequence-level model of coupled transcription and translation in prokaryotes

Background

In prokaryotes, transcription and translation are dynamically coupled, as the latter starts before the former is complete. Also, from one transcript, several translation events occur in parallel. To study how events in transcription elongation affect translation elongation and fluctuations in protein levels, we propose a delayed stochastic model of prokaryotic transcription and translation at the nucleotide and codon level that includes the promoter open complex formation and alternative pathways to elongation, namely pausing, arrests, editing, pyrophosphorolysis, RNA polymerase traffic, and premature termination. Stepwise translation can start after the ribosome binding site is formed and accounts for variable codon translation rates, ribosome traffic, back-translocation, drop-off, and trans-translation.

Results

First, we show that the model accurately matches measurements of sequence-dependent translation elongation dynamics. Next, we characterize the degree of coupling between fluctuations in RNA and protein levels, and its dependence on the rates of transcription and translation initiation. Finally, modeling sequence-specific transcriptional pauses, we find that these affect protein noise levels.

Conclusions

For parameter values within realistic intervals, transcription and translation are found to be tightly coupled in Escherichia coli, as the noise in protein levels is mostly determined by the underlying noise in RNA levels. Sequence-dependent events in transcription elongation, e.g. pauses, are found to cause tangible effects in the degree of fluctuations in protein levels.

Inference of kinetic parameters of delayed stochastic models of gene expression using a markov chain approximation

We propose a Markov chain approximation of the delayed stochastic simulation algorithm to infer properties of the mechanisms in prokaryote transcription from the dynamics of RNA levels. We model transcription using the delayed stochastic modelling strategy and realistic parameter values for rate of transcription initiation and RNA degradation. From the model, we generate time series of RNA levels at the single molecule level, from which we use the method to infer the duration of the promoter open complex formation. This is found to be possible even when adding external Gaussian noise to the RNA levels.

Information propagation within the Genetic Network of Saccharomyces cerevisiae

Background

A gene network's capacity to process information, so as to bind past events to future actions, depends on its structure and logic. From previous and new microarray measurements in Saccharomyces cerevisiae following gene deletions and overexpressions, we identify a core gene regulatory network (GRN) of functional interactions between 328 genes and the transfer functions of each gene. Inferred connections are verified by gene enrichment.

Results

We find that this core network has a generalized clustering coefficient that is much higher than chance. The inferred Boolean transfer functions have a mean p-bias of 0.41, and thus similar amounts of activation and repression interactions. However, the distribution of p-biases differs significantly from what is expected by chance that, along with the high mean connectivity, is found to cause the core GRN of S. cerevisiae's to have an overall sensitivity similar to critical Boolean networks. In agreement, we find that the amount of information propagated between nodes in finite time series is much higher in the inferred core GRN of S. cerevisiae than what is expected by chance.

Conclusions

We suggest that S. cerevisiae is likely to have evolved a core GRN with enhanced information propagation among its genes.