Ab initio thermodynamic modeling of distal multisite transcription regulation

The unreasonable effectiveness of equilibrium gene regulation through the cell cycle

Systems like the prototypical lac operon can reliably hold repression of transcription upon DNA replication across cell cycles with just 10 repressor molecules per cell and behave as if they were at equilibrium. The origin of this phenomenology is still an unresolved question. Here, we develop a general theory to analyze strong perturbations in quasi-equilibrium systems and use it to quantify the effects of DNA replication in gene regulation. We find a scaling law linking actual with predicted equilibrium transcription via a single kinetic parameter. We show that even the lac operon functions beyond the physical limits of naive regulation through compensatory mechanisms that suppress non-equilibrium effects. Synthetic systems without adjuvant activators, such as the cAMP receptor protein (CRP), lack this reliability. Our results provide a rationale for the function of CRP, beyond just being a tunable activator, as a mitigator of cell cycle perturbations.

Multi-landmark alignment of genomic signals reveals conserved expression patterns across transcription start sites

The prevalent one-dimensional alignment of genomic signals to a reference landmark is a cornerstone of current methods to study transcription and its DNA-dependent processes but it is prone to mask potential relations among multiple DNA elements. We developed a systematic approach to align genomic signals to multiple locations simultaneously by expanding the dimensionality of the genomic-coordinate space. We analyzed transcription in human and uncovered a complex dependence on the relative position of neighboring transcription start sites (TSSs) that is consistently conserved among cell types. The dependence ranges from enhancement to suppression of transcription depending on the relative distances to the TSSs, their intragenic position, and the transcriptional activity of the gene. Our results reveal a conserved hierarchy of alternative TSS usage within a previously unrecognized level of genomic organization and provide a general methodology to analyze complex functional relationships among multiple types of DNA elements.

Predicting bacterial promoter function and evolution from random sequences

Predicting function from sequence is a central problem of biology. Currently, this is possible only locally in a narrow mutational neighborhood around a wildtype sequence rather than globally from any sequence. Using random mutant libraries, we developed a biophysical model that accounts for multiple features of σ⁷⁰ binding bacterial promoters to predict constitutive gene expression levels from any sequence. We experimentally and theoretically estimated that 10–20% of random sequences lead to expression and ~80% of non-expressing sequences are one mutation away from a functional promoter. The potential for generating expression from random sequences is so pervasive that selection acts against σ⁷⁰-RNA polymerase binding sites even within inter-genic, promoter-containing regions. This pervasiveness of σ⁷⁰-binding sites implies that emergence of promoters is not the limiting step in gene regulatory evolution. Ultimately, the inclusion of novel features of promoter function into a mechanistic model enabled not only more accurate predictions of gene expression levels, but also identified that promoters evolve more rapidly than previously thought.

Anticipating response function in gene regulatory networks

The origin of an ordered genetic response of a complex and noisy biological cell is intimately related to the detailed mechanism of protein-DNA interactions present in a wide variety of gene regulatory (GR) systems. However, the quantitative prediction of genetic response and the correlation between the mechanism and the response curve is poorly understood. Here, we report in silico binding studies of GR systems to show that the transcription factor (TF) binds to multiple DNA sites with high cooperativity spreads from specific binding sites into adjacent non-specific DNA and bends the DNA. Our analysis is not limited only to the isolated model system but also can be applied to a system containing multiple interacting genes. The controlling role of TF oligomerization, TF-ligand interactions, and DNA looping for gene expression has been also characterized. The predictions are validated against detailed grand canonical Monte Carlo simulations and published data for the lac operon system. Overall, our study reveals that the expression of target genes can be quantitatively controlled by modulating TF-ligand interactions and the bending energy of DNA.

Gene Regulation in and out of Equilibrium

Determining whether and how a gene is transcribed are two of the central processes of life. The conceptual basis for understanding such gene regulation arose from pioneering biophysical studies in eubacteria. However, eukaryotic genomes exhibit vastly greater complexity, which raises questions not addressed by this bacterial paradigm. First, how is information integrated from many widely separated binding sites to determine how a gene is transcribed? Second, does the presence of multiple energy-expending mechanisms, which are absent from eubacterial genomes, indicate that eukaryotes are capable of improved forms of genetic information processing? An updated biophysical foundation is needed to answer such questions. We describe the linear framework, a graph-based approach to Markov processes, and show that it can accommodate many previous studies in the field. Under the assumption of thermodynamic equilibrium, we introduce a language of higher-order cooperativities and show how it can rigorously quantify gene regulatory properties suggested by experiment. We point out that fundamental limits to information processing arise at thermodynamic equilibrium and can only be bypassed through energy expenditure. Finally, we outline some of the mathematical challenges that must be overcome to construct an improved biophysical understanding of gene regulation.

Figure 1 Theory Meets Figure 2 Experiments in the Study of Gene Expression

It is tempting to believe that we now own the genome. The ability to read and rewrite it at will has ushered in a stunning period in the history of science. Nonetheless, there is an Achilles' heel exposed by all of the genomic data that has accrued: We still do not know how to interpret them. Many genes are subject to sophisticated programs of transcriptional regulation, mediated by DNA sequences that harbor binding sites for transcription factors, which can up- or down-regulate gene expression depending upon environmental conditions. This gives rise to an input-output function describing how the level of expression depends upon the parameters of the regulated gene-for instance, on the number and type of binding sites in its regulatory sequence. In recent years, the ability to make precision measurements of expression, coupled with the ability to make increasingly sophisticated theoretical predictions, has enabled an explicit dialogue between theory and experiment that holds the promise of covering this genomic Achilles' heel. The goal is to reach a predictive understanding of transcriptional regulation that makes it possible to calculate gene expression levels from DNA regulatory sequence. This review focuses on the canonical simple repression motif to ask how well the models that have been used to characterize it actually work. We consider a hierarchy of increasingly sophisticated experiments in which the minimal parameter set learned at one level is applied to make quantitative predictions at the next. We show that these careful quantitative dissections provide a template for a predictive understanding of the many more complex regulatory arrangements found across all domains of life.

Multi-Factor Regulation of the Master Modulator LeuO for the Cyclic-(Phe-Pro) Signaling Pathway in Vibrio vulnificus

LeuO plays the role of a master regulator in the cyclic-L-phenylalanine-L-proline (cFP)-dependent signaling pathway in Vibrio vulnificus. cFP, as shown through isothermal titration calorimetry analysis, binds specifically to the periplasmic domain of ToxR. Binding of cFP triggers a change in the cytoplasmic domain of ToxR, which then activates transcription of leuO encoding a LysR-type regulator. LeuO binds to the region upstream of its own coding sequence, inhibiting its own transcription and maintaining a controlled level of expression. A five-bp deletion in this region abolished expression of LeuO, but a ten-bp deletion did not, suggesting that a DNA bending mechanism is involved in the regulation. Furthermore, binding of RNA polymerase was significantly lower both in the deletion of the ToxR binding site and in the five-bp deletion, but not in the ten-bp deletion, as shown in pull-down assays using an antibody against RNA polymerase subunit α. In summary, multiple factors are involved in control of the expression of LeuO, a master regulator that orchestrates downstream regulators to modulate factors required for survival and pathogenicity of the pathogen.

Tuning Transcriptional Regulation through Signaling: A Predictive Theory of Allosteric Induction

Allosteric regulation is found across all domains of life, yet we still lack simple, predictive theories that directly link the experimentally tunable parameters of a system to its input-output response. To that end, we present a general theory of allosteric transcriptional regulation using the Monod-Wyman-Changeux model. We rigorously test this model using the ubiquitous simple repression motif in bacteria by first predicting the behavior of strains that span a large range of repressor copy numbers and DNA binding strengths and then constructing and measuring their response. Our model not only accurately captures the induction profiles of these strains, but also enables us to derive analytic expressions for key properties such as the dynamic range and [EC₅₀]. Finally, we derive an expression for the free energy of allosteric repressors that enables us to collapse our experimental data onto a single master curve that captures the diverse phenomenology of the induction profiles.

Acceleration of bursty multiprotein target search kinetics on DNA by colocalisation

Proteins are capable of locating specific targets on DNA by employing a facilitated diffusion process with intermittent 1D and 3D search steps. We here uncover the implications of colocalisation of protein production and DNA binding sites via computer simulations.

Self-consistent theory of transcriptional control in complex regulatory architectures

Individual regulatory proteins are typically charged with the simultaneous regulation of a battery of different genes. As a result, when one of these proteins is limiting, competitive effects have a significant impact on the transcriptional response of the regulated genes. Here we present a general framework for the analysis of any generic regulatory architecture that accounts for the competitive effects of the regulatory environment by isolating these effects into an effective concentration parameter. These predictions are formulated using the grand-canonical ensemble of statistical mechanics and the fold-change in gene expression is predicted as a function of the number of transcription factors, the strength of interactions between the transcription factors and their DNA binding sites, and the effective concentration of the transcription factor. The effective concentration is set by the transcription factor interactions with competing binding sites within the cell and is determined self-consistently. Using this approach, we analyze regulatory architectures in the grand-canonical ensemble ranging from simple repression and simple activation to scenarios that include repression mediated by DNA looping of distal regulatory sites. It is demonstrated that all the canonical expressions previously derived in the case of an isolated, non-competing gene, can be generalised by a simple substitution to their grand canonical counterpart, which allows for simple intuitive incorporation of the influence of multiple competing transcription factor binding sites. As an example of the strength of this approach, we build on these results to present an analytical description of transcriptional regulation of the lac operon.

On the mechanistic nature of epistasis in a canonical cis-regulatory element

Understanding the relation between genotype and phenotype remains a major challenge. The difficulty of predicting individual mutation effects, and particularly the interactions between them, has prevented the development of a comprehensive theory that links genotypic changes to their phenotypic effects. We show that a general thermodynamic framework for gene regulation, based on a biophysical understanding of protein-DNA binding, accurately predicts the sign of epistasis in a canonical cis-regulatory element consisting of overlapping RNA polymerase and repressor binding sites. Sign and magnitude of individual mutation effects are sufficient to predict the sign of epistasis and its environmental dependence. Thus, the thermodynamic model offers the correct null prediction for epistasis between mutations across DNA-binding sites. Our results indicate that a predictive theory for the effects of cis-regulatory mutations is possible from first principles, as long as the essential molecular mechanisms and the constraints these impose on a biological system are accounted for.

DOI:http://dx.doi.org/10.7554/eLife.25192.001

Mutations are changes to DNA that provide the raw material upon which evolution can act. Therefore, to understand evolution, we need to know the effects of mutations, and how those mutations interact with each other (a phenomenon referred to as epistasis). So far, few mathematical models allow scientists to predict the effects of mutations, and even fewer are able to predict epistasis.

Biological systems are complex and consist of many proteins and other molecules. Genes are the sections of DNA that provide the instructions needed to produce these molecules, and some genes encode proteins that can bind to DNA to control whether other genes are switched on or off. Lagator, Paixão et al. have now used mathematical models and experiments to understand how the environment inside the cells of a bacterium known as E. coli, specifically the amount of particular proteins, affects epistasis.

These mathematical models are able to predict interactions between mutations in the most abundant class of DNA-binding sites in proteins. This approach found that the nature of the interaction between mutations can be explained through biophysical laws, combined with the basic knowledge of the logic of how genes regulate each other’s activities. Furthermore, the models allow Lagator, Paixão et al. to predict interactions between mutations in several different environments, such as the presence of a new food source or a toxin, defined by the amounts of relevant DNA-binding proteins in cells.

By providing new ways of understanding how genes are regulated in bacteria, and how gene regulation is affected by mutations, these findings contribute to our understanding of how organisms evolve. In addition, this work may help us to build artificial networks of genes that interact with each other to produce a desired response, such as more efficient production of fuel from ethanol or the break down of hazardous chemicals.

DOI:http://dx.doi.org/10.7554/eLife.25192.002

Three-dimensional modeling of single stranded DNA hairpins for aptamer-based biosensors

Aptamers consist of short oligonucleotides that bind specific targets. They provide advantages over antibodies, including robustness, low cost, and reusability. Their chemical structure allows the insertion of reporter molecules and surface-binding agents in specific locations, which have been recently exploited for the development of aptamer-based biosensors and direct detection strategies. Mainstream use of these devices, however, still requires significant improvements in optimization for consistency and reproducibility. DNA aptamers are more stable than their RNA counterparts for biomedical applications but have the disadvantage of lacking the wide array of computational tools for RNA structural prediction. Here, we present the first approach to predict from sequence the three-dimensional structures of single stranded (ss) DNA required for aptamer applications, focusing explicitly on ssDNA hairpins. The approach consists of a pipeline that integrates sequentially building ssDNA secondary structure from sequence, constructing equivalent 3D ssRNA models, transforming the 3D ssRNA models into ssDNA 3D structures, and refining the resulting ssDNA 3D structures. Through this pipeline, our approach faithfully predicts the representative structures available in the Nucleic Acid Database and Protein Data Bank databases. Our results, thus, open up a much-needed avenue for integrating DNA in the computational analysis and design of aptamer-based biosensors.

Supercoiling Effects on Short-Range DNA Looping in E. coli

DNA-protein loops can be essential for gene regulation. The Escherichia coli lactose (lac) operon is controlled by DNA-protein loops that have been studied for decades. Here we adapt this model to test the hypothesis that negative superhelical strain facilitates the formation of short-range (6-8 DNA turns) repression loops in E. coli. The natural negative superhelicity of E. coli DNA is regulated by the interplay of gyrase and topoisomerase enzymes, adding or removing negative supercoils, respectively. Here, we measured quantitatively DNA looping in three different E. coli strains characterized by different levels of global supercoiling: wild type, gyrase mutant (gyrB226), and topoisomerase mutant (ΔtopA10). DNA looping in each strain was measured by assaying repression of the endogenous lac operon, and repression of ten reporter constructs with DNA loop sizes between 70-85 base pairs. Our data are most simply interpreted as supporting the hypothesis that negative supercoiling facilitates gene repression by small DNA-protein loops in living bacteria.

Suppression and enhancement of transcriptional noise by DNA looping

DNA looping has been observed to enhance and suppress transcriptional noise but it is uncertain which of these two opposite effects is to be expected for given conditions. Here, we derive analytical expressions for the main quantifiers of transcriptional noise in terms of the molecular parameters and elucidate the role of DNA looping. Our results rationalize paradoxical experimental observations and provide the first quantitative explanation of landmark individual-cell measurements at the single molecule level on the classical lac operon genetic system [Choi, L. Cai, K. Frieda, and X. S. Xie, Science 322, 442 (2008)].

Comparison of the theoretical and real-world evolutionary potential of a genetic circuit

With the development of next-generation sequencing technologies, many large scale experimental efforts aim to map genotypic variability among individuals. This natural variability in populations fuels many fundamental biological processes, ranging from evolutionary adaptation and speciation to the spread of genetic diseases and drug resistance. An interesting and important component of this variability is present within the regulatory regions of genes. As these regions evolve, accumulated mutations lead to modulation of gene expression, which may have consequences for the phenotype. A simple model system where the link between genetic variability, gene regulation and function can be studied in detail is missing. In this article we develop a model to explore how the sequence of the wild-type lac promoter dictates the fold-change in gene expression. The model combines single-base pair resolution maps of transcription factor and RNA polymerase binding energies with a comprehensive thermodynamic model of gene regulation. The model was validated by predicting and then measuring the variability of lac operon regulation in a collection of natural isolates. We then implement the model to analyze the sensitivity of the promoter sequence to the regulatory output, and predict the potential for regulation to evolve due to point mutations in the promoter region.

Systems biophysics of gene expression

Gene expression is a process central 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 to the use of 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 review recent advances in the description of gene regulation as a system of biophysical processes that extend from specific protein-DNA interactions to the combinatorial assembly of nucleoprotein complexes. There is now basic mechanistic understanding on how promoters controlled by multiple, local and distal, DNA binding sites for transcription factors can actively control transcriptional noise, cell-to-cell variability, and other properties of gene regulation, including precision and flexibility of the transcriptional responses.

Reliable prediction of complex phenotypes from a modular design in free energy space: an extensive exploration of the lac operon

The basic methodology for designing, altering, and constructing biological systems is increasingly relying on well-established engineering principles to move forward from trial and error approaches to reliably predicting the system behavior from the properties of the components and their interactions. The inherent complexity of even the simplest biological systems, however, often precludes achieving such predictive power. A prototypical example is the lac operon, one of the best-characterized genetic systems, which still poses serious challenges for understanding the results of combining its parts into novel setups. The reason is the pervasive complex hierarchy of events involved in gene regulation that extend from specific protein-DNA interactions to the combinatorial assembly of nucleoprotein complexes. Here, we integrate such complexity into a few-parameter model to accurately predict gene expression from a few simple rules to connect the parts. The model accurately reproduces the observed transcriptional activity of the lac operon over a 10,000-fold range for 21 different operator setups, different repressor concentrations, and tetrameric and dimeric forms of the repressor. Incorporation of the calibrated model into more complex scenarios accurately captures the induction curves for key operator configurations and the temporal evolution of the β-galactosidase activity of cell populations.

Stochastic models of transcription: from single molecules to single cells

Genes in prokaryotic and eukaryotic cells are typically regulated by complex promoters containing multiple binding sites for a variety of transcription factors leading to a specific functional dependence between regulatory inputs and transcriptional outputs. With increasing regularity, the transcriptional outputs from different promoters are being measured in quantitative detail in single-cell experiments thus providing the impetus for the development of quantitative models of transcription. We describe recent progress in developing models of transcriptional regulation that incorporate, to different degrees, the complexity of multi-state promoter dynamics, and its effect on the transcriptional outputs of single cells. The goal of these models is to predict the statistical properties of transcriptional outputs and characterize their variability in time and across a population of cells, as a function of the input concentrations of transcription factors. The interplay between mathematical models of different regulatory mechanisms and quantitative biophysical experiments holds the promise of elucidating the molecular-scale mechanisms of transcriptional regulation in cells, from bacteria to higher eukaryotes.

Theoretical and experimental dissection of DNA loop-mediated repression

Transcriptional networks across all domains of life feature a wide range of regulatory architectures. Theoretical models now make clear predictions about how key parameters describing those architectures modulate gene expression, and the ability to construct genetic circuits with tunable parameters enables precise tests of such models. We dissect gene regulation through DNA looping by tuning network parameters such as repressor copy number, DNA binding strengths, and loop length in both thermodynamic models and experiments. Our results help clarify the short-length mechanical properties of DNA.

DNA looping in prokaryotes: experimental and theoretical approaches

Transcriptional regulation is at the heart of biological functions such as adaptation to a changing environment or to new carbon sources. One of the mechanisms which has been found to modulate transcription, either positively (activation) or negatively (repression), involves the formation of DNA loops. A DNA loop occurs when a protein or a complex of proteins simultaneously binds to two different sites on DNA with looping out of the intervening DNA. This simple mechanism is central to the regulation of several operons in the genome of the bacterium Escherichia coli, like the lac operon, one of the paradigms of genetic regulation. The aim of this review is to gather and discuss concepts and ideas from experimental biology and theoretical physics concerning DNA looping in genetic regulation. We first describe experimental techniques designed to show the formation of a DNA loop. We then present the benefits that can or could be derived from a mechanism involving DNA looping. Some of these are already experimentally proven, but others are theoretical predictions and merit experimental investigation. Then, we try to identify other genetic systems that could be regulated by a DNA looping mechanism in the genome of Escherichia coli. We found many operons that, according to our set of criteria, have a good chance to be regulated with a DNA loop. Finally, we discuss the proposition recently made by both biologists and physicists that this mechanism could also act at the genomic scale and play a crucial role in the spatial organization of genomes.

The physics of protein-DNA interaction networks in the control of gene expression

Protein-DNA interaction networks play a central role in many fundamental cellular processes. In gene regulation, physical interactions and reactions among the molecular components together with the physical properties of DNA control how genes are turned on and off. A key player in all these processes is the inherent flexibility of DNA, which provides an avenue for long-range interactions between distal DNA elements through DNA looping. Such versatility enables multiple interactions and results in additional complexity that is remarkably difficult to address with traditional approaches. This topical review considers recent advances in statistical physics methods to study the assembly of protein-DNA complexes with loops, their effects in the control of gene expression, and their explicit application to the prototypical lac operon genetic system of the E. coli bacterium. In the last decade, it has been shown that the underlying physical properties of DNA looping can actively control transcriptional noise, cell-to-cell variability, and other properties of gene regulation, including the balance between robustness and sensitivity of the induction process. These physical properties are largely dependent on the free energy of DNA looping, which accounts for DNA bending and twisting effects. These new physical methods have also been used in reverse to uncover the actual in vivo free energy of looping double-stranded DNA in living cells, which was not possible with existing experimental techniques. The results obtained for DNA looping by the lac repressor inside the E. coli bacterium showed a more malleable DNA than expected as a result of the interplay of the simultaneous presence of two distinct conformations of looped DNA.

Non-transcriptional regulatory processes shape transcriptional network dynamics

Information about the extra- or intracellular environment is often captured as biochemical signals that propagate through regulatory networks. These signals eventually drive phenotypic changes, typically by altering gene expression programmes in the cell. Reconstruction of transcriptional regulatory networks has given a compelling picture of bacterial physiology, but transcriptional network maps alone often fail to describe phenotypes. Cellular response dynamics are ultimately determined by interactions between transcriptional and non-transcriptional networks, with dramatic implications for physiology and evolution. Here, we provide an overview of non-transcriptional interactions that can affect the performance of natural and synthetic bacterial regulatory networks.

Deterministic and stochastic population-level simulations of an artificial lac operon genetic network

BACKGROUND

The lac operon genetic switch is considered as a paradigm of genetic regulation. This system has a positive feedback loop due to the LacY permease boosting its own production by the facilitated transport of inducer into the cell and the subsequent de-repression of the lac operon genes. Previously, we have investigated the effect of stochasticity in an artificial lac operon network at the single cell level by comparing corresponding deterministic and stochastic kinetic models.

RESULTS

This work focuses on the dynamics of cell populations by incorporating the above kinetic scheme into two Monte Carlo (MC) simulation frameworks. The first MC framework assumes stochastic reaction occurrence, accounts for stochastic DNA duplication, division and partitioning and tracks all daughter cells to obtain the statistics of the entire cell population. In order to better understand how stochastic effects shape cell population distributions, we develop a second framework that assumes deterministic reaction dynamics. By comparing the predictions of the two frameworks, we conclude that stochasticity can create or destroy bimodality, and may enhance phenotypic heterogeneity.

CONCLUSIONS

Our results show how various sources of stochasticity act in synergy with the positive feedback architecture, thereby shaping the behavior at the cell population level. Further, the insights obtained from the present study allow us to construct simpler and less computationally intensive models that can closely approximate the dynamics of heterogeneous cell populations.

The RpiR-like repressor IolR regulates inositol catabolism in Sinorhizobium meliloti

Sinorhizobium meliloti, the nitrogen-fixing symbiont of alfalfa, has the ability to catabolize myo-, scyllo-, and D-chiro-inositol. Functional inositol catabolism (iol) genes are required for growth on these inositol isomers, and they play a role during plant-bacterium interactions. The inositol catabolism genes comprise the chromosomally encoded iolA (mmsA) and the iolY(smc01163)RCDEB genes, as well as the idhA gene located on the pSymB plasmid. Reverse transcriptase assays showed that the iolYRCDEB genes are transcribed as one operon. The iol genes were weakly expressed without induction, but their expression was strongly induced by myo-inositol. The putative transcriptional regulator of the iol genes, IolR, belongs to the RpiR-like repressor family. Electrophoretic mobility shift assays demonstrated that IolR recognized a conserved palindromic sequence (5'-GGAA-N6-TTCC-3') in the upstream regions of the idhA, iolY, iolR, and iolC genes. Complementation assays found IolR to be required for the repression of its own gene and for the downregulation of the idhA-encoded myo-inositol dehydrogenase activity in the presence and absence of inositol. Further expression studies indicated that the late pathway intermediate 2-keto-5-deoxy-D-gluconic acid 6-phosphate (KDGP) functions as the true inducer of the iol genes. The iolA (mmsA) gene encoding methylmalonate semialdehyde dehydrogenase was not regulated by IolR. The S. meliloti iolA (mmsA) gene product seems to be involved in more than only the inositol catabolic pathway, since it was also found to be essential for valine catabolism, supporting its more recent annotation as mmsA.

Theory on the dynamic memory in the transcription-factor-mediated transcription activation

We develop a theory to explain the origin of the static and dynamical memory effects in transcription-factor-mediated transcription activation. Our results suggest that the following inequality conditions should be satisfied to observe such memory effects: (a) τ(L)≫max(τ(R),τ(E)), (b) τ(LT)≫τ(T), and (c) τ(I)≥(τ(EL)+τ(TR)) where τ(L) is the average time required for the looping-mediated spatial interactions of enhancer-transcription-factor complex with the corresponding promoter--RNA-polymerase or eukaryotic RNA polymerase type II (PolII in eukaryotes) complex that is located L base pairs away from the cis-acting element, (τ(R),τ(E)) are respectively the search times required for the site-specific binding of the RNA polymerase and the transcription factor with the respective promoter and the cis-regulatory module, τ(LT) is the time associated with the relaxation of the looped-out segment of DNA that connects the cis-acting site and promoter, τ(T) is the time required to generate a complete transcript, τ(I) is the transcription initiation time, τ(EL) is the elongation time, and τ(TR) is the termination time. We have theoretically derived the expressions for the various searching, looping, and loop-relaxation time components. Using the experimentally determined values of various time components we further show that the dynamical memory effects cannot be experimentally observed whenever the segment of DNA that connects the cis-regulatory element with the promoter is not loaded with bulky histone bodies. Our analysis suggests that the presence of histone-mediated compaction of the connecting segment of DNA can result in higher values of looping and loop-relaxation times, which is the origin of the static memory in the transcription activation that is mediated by the memory gene loops in eukaryotes.

Control of gene expression by modulated self-assembly

Numerous transcription factors self-assemble into different order oligomeric species in a way that is actively regulated by the cell. Until now, no general functional role has been identified for this widespread process. Here, we capture the effects of modulated self-assembly in gene expression with a novel quantitative framework. We show that this mechanism provides precision and flexibility, two seemingly antagonistic properties, to the sensing of diverse cellular signals by systems that share common elements present in transcription factors like p53, NF-κB, STATs, Oct and RXR. Applied to the nuclear hormone receptor RXR, this framework accurately reproduces a broad range of classical, previously unexplained, sets of gene expression data and corroborates the existence of a precise functional regime with flexible properties that can be controlled both at a genome-wide scale and at the individual promoter level.

Accurate prediction of gene expression by integration of DNA sequence statistics with detailed modeling of transcription regulation

Gene regulation involves a hierarchy of events that extend from specific protein-DNA interactions to the combinatorial assembly of nucleoprotein complexes. The effects of DNA sequence on these processes have typically been studied based either on its quantitative connection with single-domain binding free energies or on empirical rules that combine different DNA motifs to predict gene expression trends on a genomic scale. The middle-point approach that quantitatively bridges these two extremes, however, remains largely unexplored. Here, we provide an integrated approach to accurately predict gene expression from statistical sequence information in combination with detailed biophysical modeling of transcription regulation by multidomain binding on multiple DNA sites. For the regulation of the prototypical lac operon, this approach predicts within 0.3-fold accuracy transcriptional activity over a 10,000-fold range from DNA sequence statistics for different intracellular conditions.

Rational design of modular circuits for gene transcription: A test of the bottom-up approach

BACKGROUND

Most of synthetic circuits developed so far have been designed by an ad hoc approach, using a small number of components (i.e. LacI, TetR) and a trial and error strategy. We are at the point where an increasing number of modular, inter-changeable and well-characterized components is needed to expand the construction of synthetic devices and to allow a rational approach to the design.

RESULTS

We used interchangeable modular biological parts to create a set of novel synthetic devices for controlling gene transcription, and we developed a mathematical model of the modular circuits. Model parameters were identified by experimental measurements from a subset of modular combinations. The model revealed an unexpected feature of the lactose repressor system, i.e. a residual binding affinity for the operator site by induced lactose repressor molecules. Once this residual affinity was taken into account, the model properly reproduced the experimental data from the training set. The parameters identified in the training set allowed the prediction of the behavior of networks not included in the identification procedure.

CONCLUSIONS

This study provides new quantitative evidences that the use of independent and well-characterized biological parts and mathematical modeling, what is called a bottom-up approach to the construction of gene networks, can allow the design of new and different devices re-using the same modular parts.

Modeling reveals bistability and low-pass filtering in the network module determining blood stem cell fate

Combinatorial regulation of gene expression is ubiquitous in eukaryotes with multiple inputs converging on regulatory control elements. The dynamic properties of these elements determine the functionality of genetic networks regulating differentiation and development. Here we propose a method to quantitatively characterize the regulatory output of distant enhancers with a biophysical approach that recursively determines free energies of protein-protein and protein-DNA interactions from experimental analysis of transcriptional reporter libraries. We apply this method to model the Scl-Gata2-Fli1 triad—a network module important for cell fate specification of hematopoietic stem cells. We show that this triad module is inherently bistable with irreversible transitions in response to physiologically relevant signals such as Notch, Bmp4 and Gata1 and we use the model to predict the sensitivity of the network to mutations. We also show that the triad acts as a low-pass filter by switching between steady states only in response to signals that persist for longer than a minimum duration threshold. We have found that the auto-regulation loops connecting the slow-degrading Scl to Gata2 and Fli1 are crucial for this low-pass filtering property. Taken together our analysis not only reveals new insights into hematopoietic stem cell regulatory network functionality but also provides a novel and widely applicable strategy to incorporate experimental measurements into dynamical network models.

Hematopoiesis—blood cell development—has long served as a model for study of cellular differentiation and its control by underlying gene regulatory networks. The Scl-Gata2-Fli1 triad is a network module essential for the development of hematopoietic stem cells but its mechanistic role is not well understood. The transcription factors Scl, Gata2 and Fli1 act in combination to upregulate transcription of each other via distal enhancer site binding. Similar network architectures are essential in other multipotent cell lines. We propose a method that uses experimental results to circumvent the difficulties of mathematically modeling the combinatorial regulation of this triad module. Using this dynamical model we show that the triad exhibits robust bistable behavior. Environmental signals can irreversibly switch the triad between stable states in a manner that reflects the unidirectional switching in the formation and subsequent differentiation of hematopoietic stem cells. We also show that the triad makes reliable decisions in noisy environments by only switching in response to transient signals that persist longer than the threshold duration. These results suggest that the Scl-Gata2-Fli1 module possibly functions as a control switch for hematopoietic stem cell development. The proposed method can be extended for quantitative characterization of other combinatorial gene regulatory modules.