Quantitative dissection of the simple repression input–output function

We present a quantitative case study of transcriptional regulation in which we carry out a systematic dialogue between theory and measurement for an important and ubiquitous regulatory motif in bacteria, namely, that of simple repression. This architecture is realized by a single repressor binding site overlapping the promoter. From the theory point of view, this motif is described by a single gene regulation function based upon only a few parameters that are convenient theoretically and accessible experimentally. The usual approach is turned on its side by using the mathematical description of these regulatory motifs as a predictive tool to determine the number of repressors in a collection of strains with a large variation in repressor copy number. The predictions and corresponding measurements are carried out over a large dynamic range in both expression fold change (spanning nearly four orders of magnitude) and repressor copy number (spanning about two orders of magnitude). The predictions are tested by measuring the resulting level of gene expression and are then validated by using quantitative immunoblots. The key outcomes of this study include a systematic quantitative analysis of the limits and validity of the input–output relation for simple repression, a precise determination of the in vivo binding energies for DNA–repressor interactions for several distinct repressor binding sites, and a repressor census for Lac repressor in Escherichia coli

A First Exposure to Statistical Mechanics for Life Scientists

Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a clue that it might have some bearing on the analysis of the molecules of living matter. As a result of data on biological systems becoming increasingly quantitative, there is a concomitant demand that the models set forth to describe biological systems be themselves quantitative. We describe how statistical mechanics is part of the quantitative toolkit that is needed to respond to such data. The power of statistical mechanics is not limited to traditional physical and chemical problems and there are a host of interesting ways in which these ideas can be applied in biology. This article reports on our efforts to teach statistical mechanics to life science students and provides a framework for others interested in bringing these tools to a nontraditional audience in the life sciences.Comment: 27 pages, 16 figures. Submitted to American Journal of Physic

Statistical Mechanics of Monod–Wyman–Changeux (MWC) Models

The 50th anniversary of the classic Monod–Wyman–Changeux (MWC) model provides an opportunity to survey the broader conceptual and quantitative implications of this quintessential biophysical model. With the use of statistical mechanics, the mathematical implementation of the MWC concept links problems that seem otherwise to have no ostensible biological connection including ligand–receptor binding, ligand-gated ion channels, chemotaxis, chromatin structure and gene regulation. Hence, a thorough mathematical analysis of the MWC model can illuminate the performance limits of a number of unrelated biological systems in one stroke. The goal of our review is twofold. First, we describe in detail the general physical principles that are used to derive the activity of MWC molecules as a function of their regulatory ligands. Second, we illustrate the power of ideas from information theory and dynamical systems for quantifying how well the output of MWC molecules tracks their sensory input, giving a sense of the “design” constraints faced by these receptors

First-principles calculation of DNA looping in tethered particle experiments

We calculate the probability of DNA loop formation mediated by regulatory proteins such as Lac repressor (LacI), using a mathematical model of DNA elasticity. Our model is adapted to calculating quantities directly observable in Tethered Particle Motion (TPM) experiments, and it accounts for all the entropic forces present in such experiments. Our model has no free parameters; it characterizes DNA elasticity using information obtained in other kinds of experiments. [...] We show how to compute both the "looping J factor" (or equivalently, the looping free energy) for various DNA construct geometries and LacI concentrations, as well as the detailed probability density function of bead excursions. We also show how to extract the same quantities from recent experimental data on tethered particle motion, and then compare to our model's predictions. [...] Our model successfully reproduces the detailed distributions of bead excursion, including their surprising three-peak structure, without any fit parameters and without invoking any alternative conformation of the LacI tetramer. Indeed, the model qualitatively reproduces the observed dependence of these distributions on tether length (e.g., phasing) and on LacI concentration (titration). However, for short DNA loops (around 95 basepairs) the experiments show more looping than is predicted by the harmonic-elasticity model, echoing other recent experimental results. Because the experiments we study are done in vitro, this anomalously high looping cannot be rationalized as resulting from the presence of DNA-bending proteins or other cellular machinery. We also show that it is unlikely to be the result of a hypothetical "open" conformation of the LacI tetramer.Comment: See the supplement at http://www.physics.upenn.edu/~pcn/Ms/TowlesEtalSuppl.pdf . This revised version accepted for publication at Physical Biolog

Using synthetic biology to make cells tomorrow's test tubes

The main tenet of physical biology is that biological phenomena can be subject to the same quantitative and predictive understanding that physics has afforded in the context of inanimate matter. However, the inherent complexity of many of these biological processes often leads to the derivation of complex theoretical descriptions containing a plethora of unknown parameters. Such complex descriptions pose a conceptual challenge to the establishment of a solid basis for predictive biology. In this article, we present various exciting examples of how synthetic biology can be used to simplify biological systems and distill these phenomena down to their essential features as a means to enable their theoretical description. Here, synthetic biology goes beyond previous efforts to engineer nature and becomes a tool to bend nature to understand it. We discuss various recent and classic experiments featuring applications of this synthetic approach to the elucidation of problems ranging from bacteriophage infection, to transcriptional regulation in bacteria and in developing embryos, to evolution. In all of these examples, synthetic biology provides the opportunity to turn cells into the equivalent of a test tube, where biological phenomena can be reconstituted and our theoretical understanding put to test with the same ease that these same phenomena can be studied in the in vitro setting

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

Operator Sequence Alters Gene Expression Independently of Transcription Factor Occupancy in Bacteria

A canonical quantitative view of transcriptional regulation holds that the only role of operator sequence is to set the probability of transcription factor binding, with operator occupancy determining the level of gene expression. In this work, we test this idea by characterizing repression in vivo and the binding of RNA polymerase in vitro in experiments where operators of various sequences were placed either upstream or downstream from the promoter in Escherichia coli. Surprisingly, we find that operators with a weaker binding affinity can yield higher repression levels than stronger operators. Repressor bound to upstream operators modulates promoter escape, and the magnitude of this modulation is not correlated with the repressor-operator binding affinity. This suggests that operator sequences may modulate transcription by altering the nature of the interaction of the bound transcription factor with the transcriptional machinery, implying a new layer of sequence dependence that must be confronted in the quantitative understanding of gene expression

Concentration and Length Dependence of DNA Looping in Transcriptional Regulation

In many cases, transcriptional regulation involves the binding of transcription factors at sites on the DNA that are not immediately adjacent to the promoter of interest. This action at a distance is often mediated by the formation of DNA loops: Binding at two or more sites on the DNA results in the formation of a loop, which can bring the transcription factor into the immediate neighborhood of the relevant promoter. These processes are important in settings ranging from the historic bacterial examples (bacterial metabolism and the lytic-lysogeny decision in bacteriophage), to the modern concept of gene regulation to regulatory processes central to pattern formation during development of multicellular organisms. Though there have been a variety of insights into the combinatorial aspects of transcriptional control, the mechanism of DNA looping as an agent of combinatorial control in both prokaryotes and eukaryotes remains unclear. We use single-molecule techniques to dissect DNA looping in the lac operon. In particular, we measure the propensity for DNA looping by the Lac repressor as a function of the concentration of repressor protein and as a function of the distance between repressor binding sites. As with earlier single-molecule studies, we find (at least) two distinct looped states and demonstrate that the presence of these two states depends both upon the concentration of repressor protein and the distance between the two repressor binding sites. We find that loops form even at interoperator spacings considerably shorter than the DNA persistence length, without the intervention of any other proteins to prebend the DNA. The concentration measurements also permit us to use a simple statistical mechanical model of DNA loop formation to determine the free energy of DNA looping, or equivalently, the J-factor for looping