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 $[EC_{50}]$. Finally, we derive an expression for the free energy of allosteric repressors which enables us to collapse our experimental data onto a single master curve that captures the diverse phenomenology of the induction profiles.Comment: Substantial revisions for resubmission (3 new figures, significantly elaborated discussion); added Professor Mitchell Lewis as another author for his continuing contributions to the projec

The Energetics of Molecular Adaptation in Transcriptional Regulation

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 inducer concentration. We experimentally test these diagnostic predictions using the well-characterized LacI repressor of Escherichia 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 a subset of 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.Comment: 11 pages, 6 figures, supplemental info. available via http://rpgroup.caltech.edu/mwc_mutant

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

Sequence-Dependent Dynamics of Synthetic and Endogenous RSSs in V(D)J Recombination

Developing lymphocytes of jawed vertebrates cleave and combine distinct gene segments to assemble antigen–receptor genes. This process called V(D)J recombination that involves the RAG recombinase binding and cutting recombination signal sequences (RSSs) composed of conserved heptamer and nonamer sequences flanking less well-conserved 12- or 23-bp spacers. Little quantitative information is known about the contributions of individual RSS positions over the course of the RAG–RSS interaction. We employ a single-molecule method known as tethered particle motion to track the formation, lifetime and cleavage of individual RAG–12RSS–23RSS paired complexes (PCs) for numerous synthetic and endogenous 12RSSs. We reveal that single-bp changes, including in the 12RSS spacer, can significantly and selectively alter PC formation or the probability of RAG-mediated cleavage in the PC. We find that some rarely used endogenous gene segments can be mapped directly to poor RAG binding on their adjacent 12RSSs. Finally, we find that while abrogating RSS nicking with Ca²⁺ leads to substantially shorter PC lifetimes, analysis of the complete lifetime distributions of any 12RSS even on this reduced system reveals that the process of exiting the PC involves unidentified molecular details whose involvement in RAG–RSS dynamics are crucial to quantitatively capture kinetics in V(D)J recombination

Theoretical investigation of a genetic switch for metabolic adaptation

Membrane transporters carry key metabolites across the cell membrane and, from a resource standpoint, are hypothesized to be produced when necessary. The expression of membrane transporters in metabolic pathways is often upregulated by the transporter substrate. In E. coli, such systems include for example the lacY, araFGH, and xylFGH genes, which encode for lactose, arabinose, and xylose transporters, respectively. As a case study of a minimal system, we build a generalizable physical model of the xapABR genetic circuit, which features a regulatory feedback loop via membrane transport (positive feedback) and enzymatic degradation (negative feedback) of an inducer. Dynamical systems analysis and stochastic simulations show that the membrane transport makes the model system bistable in certain parameter regimes. Thus, it serves as a genetic “on-off” switch, enabling the cell to only produce a set of metabolic enzymes when the corresponding metabolite is present in large amounts. We find that the negative feedback from the degradation enzyme does not significantly disturb the positive feedback from the membrane transporter. We investigate hysteresis in the switching and discuss the role of cooperativity and multiple binding sites in the model circuit. Fundamentally, this work explores how a stable genetic switch for a set of enzymes is obtained from transcriptional auto-activation of a membrane transporter through its substrate

Fundamental limits on the rate of bacterial growth

Recent years have seen an experimental deluge interrogating the relationship between bacterial growth rate, cell size, and protein content, quantifying the abundance of proteins across growth conditions with unprecedented resolution. However, we still lack a rigorous understanding of what sets the scale of these quantities and when protein abundances should (or should not) depend on growth rate. Here, we seek to quantitatively understand this relationship across a collection of Escherichia coli proteomic data covering ≈ 4000 proteins and 36 growth rates. We estimate the basic requirements for steady-state growth by considering key processes in nutrient transport, cell envelope biogenesis, energy generation, and the central dogma. From these estimates, ribosome biogenesis emerges as a primary determinant of growth rate. We expand on this assessment by exploring a model of proteomic regulation as a function of the nutrient supply, revealing a mechanism that ties cell size and growth rate to ribosomal content

Fundamental limits on the rate of bacterial growth

Recent years have seen an experimental deluge interrogating the relationship between bacterial growth rate, cell size, and protein content, quantifying the abundance of proteins across growth conditions with unprecedented resolution. However, we still lack a rigorous understanding of what sets the scale of these quantities and when protein abundances should (or should not) depend on growth rate. Here, we seek to quantitatively understand this relationship across a collection of Escherichia coli proteomic data covering ≈ 4000 proteins and 36 growth rates. We estimate the basic requirements for steady-state growth by considering key processes in nutrient transport, cell envelope biogenesis, energy generation, and the central dogma. From these estimates, ribosome biogenesis emerges as a primary determinant of growth rate. We expand on this assessment by exploring a model of proteomic regulation as a function of the nutrient supply, revealing a mechanism that ties cell size and growth rate to ribosomal content