We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ode's representing the reaction kinetics, and by stochastic simulations employing the Gillespie algorithm. We elucidate the different results both approaches can deliver, depending on the network under study, and in particular depending on the level of detail retained in the respective description. Two examples are addressed in detail: the repressilator, a transcriptional clock based on a three-gene network realized experimentally in E. coli, and a bistable two-gene circuit under external driving, a transcriptional network motif recently proposed to play a role in cellular development.
The set of regulatory interactions between genes, mediated by transcription factors, forms a species' transcriptional regulatory network (TRN). By comparing this network with measured gene expression data one can identify functional properties of the TRN and gain general insight into transcriptional control. We define the subnet of a node as the subgraph consisting of all nodes topologically downstream of the node, including itself. Using a large set of microarray expression data of the bacterium Escherichia coli, we find that the gene expression in different subnets exhibits a structured patt…
Recently, there has been a lot of effort in understanding sRNA mediated regulation of gene expression and how this mode of regulation differs from transcriptional regulation.In E.coli, in the presence of oxidative stress, the synthesis of sigma^s is regulated through an interesting mechanism involving both transcriptional and sRNA-mediated translational regulation. The key regulatory factors involved in transcriptional and translational regulation are ArcA and ArcB proteins and ArcZ sRNA, respectively. Phosphorylated ArcA, in a feedforward mechanism, represses the transcriptions sigma^s and Ar…
We investigate the dynamical properties of the transcriptional regulation of gene expression in the yeast Saccharomyces Cerevisiae within the framework of a synchronously and deterministically updated Boolean network model. By means of a dynamically determinant subnetwork, we explore the robustness of transcriptional regulation as a function of the type of Boolean functions used in the model that mimic the influence of regulating agents on the transcription level of a gene. We compare the results obtained for the actual yeast network with those from two different model networks, one with simil…
Gene expression is controlled primarily by interactions between transcription factor proteins (TFs) and the regulatory DNA sequence, a process that can be captured well by thermodynamic models of regulation. These models, however, neglect regulatory crosstalk: the possibility that non-cognate TFs could initiate transcription, with potentially disastrous effects for the cell. Here we estimate the importance of crosstalk, suggest that its avoidance strongly constrains equilibrium models of TF binding, and propose an alternative non-equilibrium scheme that implements kinetic proofreading to suppr…
The intrinsic stochasticity of gene expression can lead to 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 n…
Transcriptional regulation by transcription factors and post-transcriptional regulation by microRNAs constitute two major modes of regulation of gene expression. While gene expression motifs incorporating solely transcriptional regulation are well investigated, the dynamics of motifs with dual strategies of regulation, i.e., both transcriptional and post-transcriptional regulation, have not been studied as extensively. In this paper, we probe the dynamics of a four-gene motif with dual strategies of regulation of gene expression. Some of the functional characteristics are compared with those o…
Mixed feedback loops combining transcriptional and post-transcriptional regulations are common in cellular regulatory networks. They consist of two genes, encoding a transcription factor and a small non-coding RNA (sRNA), which mutually regulate each other's expression. We present a theoretical and numerical study of coherent mixed feedback loops of this type, in which both regulations are negative. Under suitable conditions, these feedback loops are expected to exhibit bistability, namely two stable states, one dominated by the transcriptional repressor and the other dominated by the sRNA. We…
Over the past few years, microRNAs (miRNAs) have emerged as a new prominent class of gene regulatory factors that negatively regulate expression of approximately one-third of the genes in animal genomes at post-transcriptional level. However, it is still unclear why some genes are regulated by miRNAs but others are not, i.e. what principles govern miRNA regulation in animal genomes. In this study, we systematically analyzed the relationship between transcription factors (TFs) and miRNAs in gene regulation. We found that the genes with more TF-binding sites have a higher probability of being ta…
A novel information-theoretic method for reconstruction of interaction networks is introduced. We prove that the method is exact for some class of networks. Performance tests on large synthetic transcriptional regulatory networks produce very encouraging results.
The precision of biochemical signaling is limited by randomness in the diffusive arrival of molecules at their targets. For proteins binding to the specific sites on the DNA and regulating transcription, the ability of the proteins to diffuse in one dimension by sliding along the length of the DNA, in addition to their diffusion in bulk solution, would seem to generate a larger target for DNA binding, consequently reducing the noise in the occupancy of the regulatory site. Here we show that this effect is largely cancelled by the enhanced temporal correlations in one dimensional diffusion. Wit…
We have performed a statistical analysis of the spatial distribution of operons in the transcriptional regulation network of Escherichia coli. The analysis reveals that operons that regulate each other and operons that are coregulated tend to lie next to each other on the genome. Moreover, these pairs of operons tend to be transcribed in diverging directions. This spatial arrangement of operons allows the upstream regulatory regions to interfere with each other. This affords additional regulatory control, as illustrated by a mean-field analysis of a feed-forward loop. Our results suggest that …
The past decade has seen great advances in our understanding of the role of noise in gene regulation and the physical limits to signaling in biological networks. Here we introduce the spectral method for computation of the joint probability distribution over all species in a biological network. The spectral method exploits the natural eigenfunctions of the master equation of birth-death processes to solve for the joint distribution of modules within the network, which then inform each other and facilitate calculation of the entire joint distribution. We illustrate the method on a ubiquitous ca…
MicroRNA-mediated regulation of gene expression is characterised by some distinctive features that set it apart from unregulated and transcription factor-regulated gene expression. Recently, a mathematical model has been proposed to describe the dynamics of post-transcriptional regulation by microRNAs. The model explains the observations made in single cell experiments quite well. In this paper, we introduce some additional features into the model and consider two specific cases. In the first case, a non-cooperative positive feedback loop is included in the transcriptional regulation of the ta…
Identity, response to external stimuli, and spatial architecture of a living system are central topics of molecular biology. Presently, they are largely seen as a result of the interplay between a gene repertoire and the regulatory machinery of the cell. At the transcriptional level, the cis-regulatory regions establish sets of interdependencies between transcription factors and genes, including other transcription factors. These ``transcription networks'' are too large to be approached globally with a detailed dynamical model. In this paper, we describe an approach to this problem that focuse…
With the increasing amount of experimental data on gene expression and regulation, there is a growing need for quantitative models to describe the data and relate them to the different contexts. The thermodynamic models reviewed in the preceding paper provide a useful framework for the quantitative analysis of bacterial transcription regulation. We review a number of well-characterized bacterial promoters that are regulated by one or two species of transcription factors, and apply the thermodynamic framework to these promoters. We show that the framework allows one to quantify vastly different…
Even under constant external conditions, the expression levels of genes fluctuate. Much emphasis has been placed on the components of this noise that are due to randomness in transcription and translation; here we analyze the role of noise associated with the inputs to transcriptional regulation, the random arrival and binding of transcription factors to their target sites along the genome. This noise sets a fundamental physical limit to the reliability of genetic control, and has clear signatures, but we show that these are easily obscured by experimental limitations and even by conventional …
Artificial neurons built on synthetic gene networks have potential applications ranging from complex cellular decision-making to bioreactor regulation. Furthermore, due to the high information throughput of natural systems, it provides an interesting candidate for biologically-based supercomputing and analog simulations of traditionally intractable problems. In this paper, we propose an architecture for constructing multicellular neural networks and programmable nonlinear systems. We design an artificial neuron based on gene regulatory networks and optimize its dynamics for modularity. Using g…
We build a simple model for feedback systems involving small RNA (sRNA) molecules based on the iron metabolism system in the bacterium E. coli, and compare it with the corresponding system in H. pylori which uses purely transcriptional regulation. This reveals several unique features of sRNA based regulation that could be exploited by cells. Firstly, we show that sRNA regulation can maintain a smaller turnover of target mRNAs than transcriptional regulation, without sacrificing the speed of response to external shocks. Secondly, we propose that a single sRNA can prioritize the usage of differe…
The transcriptional regulation of gene expression is orchestrated by complex networks of interacting genes. Increasing evidence indicates that these transcriptional regulatory networks (TRNs) in bacteria have an inherently hierarchical architecture, although the design principles and the specific advantages offered by this type of organization have not yet been fully elucidated. In this study, we focussed on the hierarchical structure of the TRN of the gram-positive bacterium Bacillus subtilis and performed a comparative analysis with the TRN of the gram-negative bacterium Escherichia coli. Us…
The formation of DNA loops by proteins and protein complexes that bind at distal DNA sites plays a central role in many cellular processes, such as transcription, recombination, and replication. Here we review the basic thermodynamic concepts underlying the assembly of macromolecular complexes on looped DNA and the effects that this process has in the properties of gene regulation. Beyond the traditional view of DNA looping as a mechanism to increase the affinity of regulatory molecules for their cognate sites, recent developments indicate that DNA looping can also lead to the suppression of c…
To regulate a particular gene, a transcription factor (TF) needs to bind a specific genome location. How is this genome address specified amid the presence of ~10^6-10^9 decoy sites? Our analysis of 319 known TF binding motifs clearly demonstrates that prokaryotes and eukaryotes use strikingly different strategies to target TFs to specific genome locations; eukaryotic TFs exhibit widespread nonfunctional binding and require clustering of sites in regulatory regions for specificity.
The diffusive arrival of transcription factors at the promoter sites on the DNA sets a lower bound on how accurately a cell can regulate its protein levels. Using results from the literature on diffusion-influenced reactions, we derive an analytical expression for the lower bound on the precision of transcriptional regulation. In our theory, transcription factors can perform multiple rounds of 1D diffusion along the DNA and 3D diffusion in the cytoplasm before binding to the promoter. Comparing our expression for the lower bound on the precision against results from Green's Function Reaction D…
The study of gene regulation and expression is often discussed in quantitative terms. In particular, the expression of genes is regularly characterized with respect to how much, how fast, when and where. Whether discussing the level of gene expression in a bacterium or its precise location within a developing embryo, the natural language for these experiments is that of numbers. Such quantitative data demands quantitative models. We review a class of models ("thermodynamic models") which exploit statistical mechanics to compute the probability that RNA polymerase is at the appropriate promoter…
In early development, regulation of transcription results in precisely positioned and highly reproducible expression patterns that specify cellular identities. How transcription, a fundamentally noisy molecular process, is regulated to achieve reliable embryonic patterning remains unclear. In particular, it is unknown how gene-specific regulation mechanisms affect kinetic rates of transcription, and whether there are common, global features that govern these rates across a genetic network. Here, we measure nascent transcriptional activity in the gap gene network of early Drosophila embryos and…
In the simplest view of transcriptional regulation, the expression of a gene is turned on or off by changes in the concentration of a transcription factor (TF). We use recent data on noise levels in gene expression to show that it should be possible to transmit much more than just one regulatory bit. Realizing this optimal information capacity would require that the dynamic range of TF concentrations used by the cell, the input/output relation of the regulatory module, and the noise levels of binding and transcription satisfy certain matching relations. This parameter-free prediction is in goo…
BACKGROUND. Signal recognition and information processing is a fundamental cellular function, which in part involves comprehensive transcriptional regulatory (TR) mechanisms carried out in response to complex environmental signals in the context of the cell's own internal state. However, the network topological basis of developing such integrated responses remains poorly understood. RESULTS. By studying the TR network of the yeast Saccharomyces cerevisiae we show that an intermediate layer of transcription factors naturally segregates into distinct subnetworks. In these topological units trans…
It is well known that, under suitable conditions, microRNAs are able to fine tune the relative concentration of their targets to any desired value. We show that this function is particularly effective when one of the targets is a Transcription Factor (TF) which regulates the other targets. This combination defines a new class of feed-forward loops (FFLs) in which the microRNA plays the role of master regulator. Using both deterministic and stochastic equations we show that these FFLs are indeed able not only to fine-tune the TF/target ratio to any desired value as a function of the miRNA conce…
A detailed stochastic model of single-gene auto-regulation is established and its solutions are explored when mRNA dynamics is fast compared with protein dynamics and in the opposite regime. The model includes all the sources of randomness that are intrinsic to the auto-regulation process and it considers both transcriptional and post transcriptional regulation. The timescale separation allows the derivation of analytic expressions for the equilibrium distributions of protein and mRNA. These distributions are generally well described in the continuous approximation, which is used to discuss th…
We revisit the dynamics of a gene repressed by its own protein in the case where the transcription rate does not adapt instantaneously to protein concentration but is a dynamical variable. We derive analytical criteria for the appearance of sustained oscillations and find that they require degradation mechanisms much less nonlinear than for infinitely fast regulation. Deterministic predictions are also compared with stochastic simulations of this minimal genetic oscillator.
Recent whole genome polymerase binding assays have shown that a large proportion of unexpressed genes have pre-assembled RNA pol II transcription initiation complex stably bound to their promoters. Some such promoter proximally paused genes are regulated at transcription elongation rather than at initiation; it has been proposed that this difference allows these genes to both express faster and achieve more synchronous expression across populations of cells, thus overcoming molecular "noise" arising from low copy number factors. It has been established experimentally that genes which are regul…
Mutation is a critical mechanism by which evolution explores the functional landscape of proteins. Despite our ability to experimentally inflict mutations at will, it remains difficult to link sequence-level perturbations to systems-level responses. Here, we present a framework centered on measuring changes in the free energy of the system to link individual mutations in an allosteric transcriptional repressor to the parameters which govern its response. We find the energetic effects of the mutations can be categorized into several classes which have characteristic curves as a function of the …
When small RNAs are loaded onto Argonaute proteins they can form the RNA-induced silencing complexes (RISCs), which mediate RNA interference. RISC-formation is dependent on a shared pool of Argonaute proteins and RISC loading factors, and is thus susceptible to competition among small RNAs for loading. We present a mathematical model that aims to understand how small RNA competition for the PTR resources affects target gene repression. We discuss that small RNA activity is limited by RISC-formation, RISC-degradation and the availability of Argonautes. Together, these observations explain a num…
Transcriptional delay can significantly impact the dynamics of gene networks. Here we examine how such delay affects bistable systems. We investigate several stochastic models of bistable gene networks and find that increasing delay dramatically increases the mean residence times near stable states. To explain this, we introduce a non-Markovian, analytically tractable reduced model. The model shows that stabilization is the consequence of an increased number of failed transitions between stable states. Each of the bistable systems that we simulate behaves in this manner.
We study a stochastic model of biosynthesis of proteins in generic bacterial operons. The stochasticity arises from two different processes, namely from `bursting' production of either mRNA and/or protein (in the transcription/translation process) and from standard diffusive fluctuations. The amount of protein follows the Feller diffusion, while the bursting introduces random jumps between trajectories of the diffusion process. The combined effect leads to a process commonly known as a diffusion process with jumps. We study existence of invariant densities and the long time behavior of distrib…
Transcription of genes is the focus of most forms of regulation of gene expression. Even though careful biochemical experimentation has revealed the molecular mechanisms of transcription initiation for a number of different promoters in vitro, the dynamics of this process in cells is still poorly understood. One approach has been to measure the transcriptional output (fluorescently labeled messenger RNAs or proteins) from single cells in a genetically identical population, which could then be compared to predictions from models that incorporate different molecular mechanisms of transcription i…
In unicellular organisms such as bacteria the same acquired mutations beneficial in one environment can be restrictive in another. However, evolving Escherichia coli populations demonstrate remarkable flexibility in adaptation. The mechanisms sustaining genetic flexibility remain unclear. In E. coli the transcriptional regulation of gene expression involves both dedicated regulators binding specific DNA sites with high affinity and also global regulators - abundant DNA architectural proteins of the bacterial chromoid binding multiple low affinity sites and thus modulating the superhelical dens…
Small, non-coding RNAs (sRNAs) play important roles as genetic regulators in prokaryotes. sRNAs act post-transcriptionally via complementary pairing with target mRNAs to regulate protein expression. We use a quantitative approach to compare and contrast sRNAs with conventional transcription factors (TFs) to better understand the advantages of each form of regulation. In particular, we calculate the steady-state behavior, noise properties, frequency-dependent gain (amplification), and dynamical response to large input signals of both forms of regulation. While the mean steady-state behavior of …
We investigate the structural and dynamical properties of the transcriptional regulatory network of the yeast {\it Saccharomyces cerevisiae} and compare it with two unbiased ensembles: one obtained by reshuffling the edges and the other generated by mimicking the transcriptional regulation mechanism within the cell. Both ensembles reproduce the degree distributions (the first -by construction- exactly and the second approximately), degree-degree correlations and the $k$-core structure observed in Yeast. An exceptionally large dynamically relevant core network found in Yeast in comparison with …
The intrinsic stochasticity of gene expression is usually mitigated in higher eukaryotes by post-transcriptional regulation channels that stabilise the output layer, most notably protein levels. The discovery of small non-coding RNAs (miRNAs) in specific motifs of the genetic regulatory network has led to identifying noise buffering as the possible key function they exert in regulation. Recent in vitro} and in silico studies have corroborated this hypothesis. It is however also known that miRNA-mediated noise reduction is hampered by transcriptional bursting in simple topologies. Here, using s…
Gene expression is a fundamental process in a living system. The small RNAs (sRNAs) is widely observed as a global regulator in gene expression. The inherent nonlinearity in this regulatory process together with the bursty production of messenger RNA (mRNA), sRNA and protein make the exact solution for this stochastic process intractable. This is particularly the case when quantifying the protein noise level, which has great impact on multiple cellular processes. Here we propose an approximate yet reasonably accurate solution for the gene expression noise with infrequent burst and strong regul…
Transcription factors are proteins that regulate gene activity by activating or repressing gene transcription. A special class of transcriptional repressors operates via a short-range mechanism, making local DNA regions inaccessible to binding by activators, and thus providing an indirect repressive action on the target gene. This mechanism is commonly modeled assuming that repressors interact with DNA under thermodynamic equilibrium and neglecting some configurations of the gene regulatory region. We elaborate on a more general nonequilibrium model of short-range repression using the graph fo…
Motivation: Cell-biological processes are regulated through a complex network of interactions between genes and their products. The processes, their activating conditions, and the associated transcriptional responses are often unknown. Organism-wide modeling of network activation can reveal unique and shared mechanisms between physiological conditions, and potentially as yet unknown processes. We introduce a novel approach for organism-wide discovery and analysis of transcriptional responses in interaction networks. The method searches for local, connected regions in a network that exhibit coo…
According to the `ceRNA hypothesis', microRNAs (miRNAs) may act as mediators of an effective positive interaction between long coding or non-coding RNA molecules, carrying significant potential implications for a variety of biological processes. Here, inspired by recent work providing a quantitative description of small regulatory elements as information-conveying channels, we characterize the effectiveness of miRNA-mediated regulation in terms of the optimal information flow achievable between modulator (transcription factors) and target nodes (long RNAs). Our findings show that, while a suff…
Genome-scale metabolic models have become a fundamental tool for examining metabolic principles. However, metabolism is not solely characterized by the underlying biochemical reactions and catalyzing enzymes, but also affected by regulatory events. Since the pioneering work of Covert and co-workers as well as Shlomi and co-workers it is debated, how regulation and metabolism synergistically characterize a coherent cellular state. The first approaches started from metabolic models which were extended by the regulation of the encoding genes of the catalyzing enzymes. By now, bioinformatics datab…
Gene expression is a central process to any form of life. It involves multiple temporal and functional scales that extend from specific protein-DNA interactions to the coordinated regulation of multiple genes in response to intracellular and extracellular changes. This diversity in scales poses fundamental challenges among traditional approaches to fully understand even the simplest gene expression systems. Recent advances in computational systems biophysics have provided promising avenues to reliably integrate the molecular detail of biophysical process into the system behavior. Here, we revi…
Gene expression in individual cells is highly variable and sporadic, often resulting in the synthesis of mRNAs and proteins in bursts. Bursting in gene expression is known to impact cell-fate in diverse systems ranging from latency in HIV-1 viral infections to cellular differentiation. It is generally assumed that bursts are geometrically distributed and that they arrive according to a Poisson process. On the other hand, recent single-cell experiments provide evidence for complex burst arrival processes, highlighting the need for more general stochastic models. To address this issue, we invoke…
Stochasticity in gene expression can result in fluctuations in gene product levels. Recent experiments indicated that feedback regulation plays an important role in controlling the noise in gene expression. A quantitative understanding of the feedback effect on gene expression requires analysis of the corresponding stochastic model. However, for stochastic models of gene expression with general regulation functions, exact analytical results for gene product distributions have not been given so far. Here, we propose a technique to solve a generalized ON-OFF model of stochastic gene expression w…
The structure and dynamics of a typical biological system are complex due to strong and inhomogeneous interactions between its constituents. The investigation of such systems with classical mathematical tools, such as differential equations for their dynamics, is not always suitable. The graph theoretical models may serve as a rough but powerful tool in such cases. In this thesis, I first consider the network modeling for the representation of the biological systems. Both the topological and dynamical investigation tools are developed and applied to the various model networks. In particular, t…
In this work we focus on how noise propagates in biochemical reaction networks and affects sensitivities of the system. We discover that the stochastic fluctuations can enhance sensitivities in one region of the value of control parameters by reducing sensitivities in another region. Based on this compensation principle, we designed a concentration detector in which enhanced amplification is achieved by an incoherent feedforward reaction network.
Focusing on the DNA-bridging nucleoid proteins Fis and H-NS, and integrating several independent experimental and bioinformatic data sources, we investigate the links between chromosomal spatial organization and global transcriptional regulation. By means of a novel multi-scale spatial aggregation analysis, we uncover the existence of contiguous clusters of nucleoid-perturbation sensitive genes along the genome, whose expression is affected by a combination of topological DNA state and nucleoid-shaping protein occupancy. The clusters correlate well with the macrodomain structure of the genome.…
