SUMMARYAllosteric 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.

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 that the energetic effects of the mutations can be categorized into several classes which have characteristic curves as a function of the inducer concentration. We experimentally test these diagnostic predictions using the well-characterized LacI repressor ofEscherichia coli, probing several mutations in the DNA binding and inducer binding domains. We find that the change in gene expression due to a point mutation can be captured by modifying only the model parameters that describe the respective domain of the wild-type protein. These parameters appear to be insulated, with mutations in the DNA binding domain altering only the DNA affinity and those in the inducer binding domain altering only the allosteric parameters. Changing these subsets of parameters tunes the free energy of the system in a way that is concordant with theoretical expectations. Finally, we show that the induction profiles and resulting free energies associated with pairwise double mutants can be predicted with quantitative accuracy given knowledge of the single mutants, providing an avenue for identifying and quantifying epistatic interactions.

It is tempting to believe that we now own the genome. The ability to read and re-write 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 don't know how to interpret it. 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, have 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.

Given the stochastic nature of gene expression, genetically identical cells exposed to the same environmental inputs will produce different outputs. This heterogeneity has been hypothesized to have consequences for how cells are able to survive in changing environments. Recent work has explored the use of information theory as a framework to understand the accuracy with which cells can ascertain the state of their surroundings. Yet the predictive power of these approaches is limited and has not been rigorously tested using precision measurements. To that end, we generate a minimal model for a simple genetic circuit in which all parameter values for the model come from independently published data sets. We then predict the information processing capacity of the genetic circuit for a suite of biophysical parameters such as protein copy number and protein-DNA affinity. We compare these parameter-free predictions with an experimental determination of protein expression distributions and the resulting information processing capacity of E. coli cells. We find that our minimal model captures the scaling of the cell-to-cell variability in the data and the inferred information processing capacity of our simple genetic circuit up to a systematic deviation.

9Given the stochastic nature of gene expression, genetically identical cells exposed to the same 10 environmental inputs will produce di↵erent outputs. This heterogeneity has consequences for how 11 cells are able to survive in changing environments. Recent work has explored the use of information 12 theory as a framework to understand the accuracy with which cells can ascertain the state of their 13 surroundings. Yet the predictive power of these approaches is limited and has not been rigorously 14 tested using precision measurements. To that end, we generate a minimal model for a simple genetic 15 circuit in which all parameter values for the model come from independently published data sets. 16 We then predict the information processing capacity of the genetic circuit for a suite of biophysical 17 parameters such as protein copy number and protein-DNA a nity. We compare these parameter-18 free predictions with an experimental determination of the information processing capacity of E. 19 coli cells, and find that our minimal model accurately captures the experimental data. 20 As living organisms thrive in some given environment, they are faced with constant changes in their 21 surroundings. From abiotic conditions such as temperature fluctuations or changes in osmotic pressure, 22 to biological interactions such as cell-to-cell communication in a tissue or in a bacterial biofilm, living 23 organisms of all types sense and respond to external signals. Fig. 1(A) shows a schematic of this 24 process for a bacterial cell sensing a concentration of an extracellular chemical. At the molecular 25 level where signal transduction unfolds mechanistically, there are physical constraints on the accuracy 26 and precision of these responses given by intrinsic stochastic fluctuations [1]. This means that two 27 genetically identical cells exposed to the same stimulus will not have an identical response [2]. 28The implication of this biological noise is that cells do not have an infinite resolution to distinguish 29 signals and, as a consequence, there is a one-to-many mapping between inputs and outputs. Further-30 more, given the limited number of possible outputs, there are overlapping responses between di↵erent 31 inputs. In that sense, one might think of cells performing a Bayesian inference of the state of the 32 environment given their phenotypic response, as schematized in Fig. 1(B). The question then becomes 33 how to analyze this probabilistic rather than deterministic relationship between inputs and outputs? 34The abstract answer to this question was worked out in 1948 by Claude Shannon who, in his seminal 35 work, founded the field of information theory [3]. Shannon developed a general framework for how 36 to analyze information transmission through noisy communication channels. In his work, Shannon 37 showed that the only quantity that satisfies simple conditions of how a metric for information should 38 behave, was of the same functional form as the thermodynamic entropy -thereby christening his ...

The study of transcription remains one of the centerpieces of modern biology with implications in settings from development to metabolism to evolution to disease. Precision measurements using a host of different techniques including fluorescence and sequencing readouts have raised the bar for what it means to quantitatively understand transcriptional regulation. In particular our understanding of the simplest genetic circuit is sufficiently refined both experimentally and theoretically that it has become possible to carefully discriminate between different conceptual pictures of how this regulatory system works. This regulatory motif, originally posited by Jacob and Monod in the 1960s, consists of a single transcriptional repressor binding to a promoter site and inhibiting transcription. In this paper, we show how seven distinct models of this so-called simple-repression motif, based both on thermodynamic and kinetic thinking, can be used to derive the predicted levels of gene expression and shed light on the often surprising past success of the thermodynamic models. These different models are then invoked to confront a variety of different data on mean, variance and full gene expression distributions, illustrating the extent to which such models can and cannot be distinguished, and suggesting a two-state model with a distribution of burst sizes as the most potent of the seven for describing the simple-repression motif.

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 promoter region.

Apart from addressing humanity’s growing demand for fuels, pharmaceuticals, plastics and other value added chemicals, metabolic engineering of microbes can serve as a powerful tool to address questions concerning the characteristics of cellular metabolism. Along these lines, we developed an in vivo metabolic strategy that conclusively identifies the product specificity of glycerate kinase. By deleting E. coli’s phosphoglycerate mutases, we divide its central metabolism into an ‘upper’ and ’lower’ metabolism, each requiring its own carbon source for the bacterium to grow. Glycerate can serve to replace the upper or lower carbon source depending on the product of glycerate kinase. Using this strategy we show that while glycerate kinase from Arabidopsis thaliana produces 3-phosphoglycerate, both E. coli’s enzymes generate 2-phosphoglycerate. This strategy represents a general approach to decipher enzyme specificity under physiological conditions.