Inherent regulatory asymmetry emanating from network architecture in a prevalent autoregulatory motif

Exploring the mono-/bistability range of positively autoregulated signaling systems in the presence of competing transcription factor binding sites

Binding of transcription factor (TF) proteins to regulatory DNA sites is key to accurate control of gene expression in response to environmental stimuli. Theoretical modeling of transcription regulation is often focused on a limited set of genes of interest, while binding of the TF to other genomic sites is seldom considered. The total number of TF binding sites (TFBSs) affects the availability of TF protein molecules and sequestration of a TF by TFBSs can promote bistability. For many signaling systems where a graded response is desirable for continuous control over the input range, biochemical parameters of the regulatory proteins need be tuned to avoid bistability. Here we analyze the mono-/bistable parameter range for positively autoregulated two-component systems (TCSs) in the presence of different numbers of competing TFBSs. TCS signaling, one of the major bacterial signaling strategies, couples signal perception with output responses via protein phosphorylation. For bistability, competition for TF proteins by TFBSs lowers the requirement for high fold change of the autoregulated transcription but demands high phosphorylation activities of TCS proteins. We show that bistability can be avoided with a low phosphorylation capacity of TCSs, a high TF affinity for the autoregulated promoter or a low fold change in signaling protein levels upon induction. These may represent general design rules for TCSs to ensure uniform graded responses. Examining the mono-/bistability parameter range allows qualitative prediction of steady-state responses, which are experimentally validated in the E. coli CusRS system.

Tunable transcription factor library for robust quantification of regulatory properties in Escherichia coli

Predicting the quantitative regulatory function of transcription factors (TFs) based on factors such as binding sequence, binding location, and promoter type is not possible. The interconnected nature of gene networks and the difficulty in tuning individual TF concentrations make the isolated study of TF function challenging. Here, we present a library of Escherichia coli strains designed to allow for precise control of the concentration of individual TFs enabling the study of the role of TF concentration on physiology and regulation. We demonstrate the usefulness of this resource by measuring the regulatory function of the zinc-responsive TF, ZntR, and the paralogous TF pair, GalR/GalS. For ZntR, we find that zinc alters ZntR regulatory function in a way that enables activation of the regulated gene to be robust with respect to ZntR concentration. For GalR and GalS, we are able to demonstrate that these paralogous TFs have fundamentally distinct regulatory roles beyond differences in binding affinity.

Sequence specificity in DNA binding is mainly governed by association

Sequence-specific binding of proteins to DNA is essential for accessing genetic information. We derive a model that predicts an anticorrelation between the macroscopic association and dissociation rates of DNA binding proteins. We tested the model for thousands of different lac operator sequences with a protein binding microarray and by observing kinetics for individual lac repressor molecules in single-molecule experiments. We found that sequence specificity is mainly governed by the efficiency with which the protein recognizes different targets. The variation in probability of recognizing different targets is at least 1.7 times as large as the variation in microscopic dissociation rates. Modulating the rate of binding instead of the rate of dissociation effectively reduces the risk of the protein being retained on nontarget sequences while searching.

Predictive landscapes hidden beneath biological cellular automata

To celebrate Hans Frauenfelder's achievements, we examine energy(-like) "landscapes" for complex living systems. Energy landscapes summarize all possible dynamics of some physical systems. Energy(-like) landscapes can explain some biomolecular processes, including gene expression and, as Frauenfelder showed, protein folding. But energy-like landscapes and existing frameworks like statistical mechanics seem impractical for describing many living systems. Difficulties stem from living systems being high dimensional, nonlinear, and governed by many, tightly coupled constituents that are noisy. The predominant modeling approach is devising differential equations that are tailored to each living system. This ad hoc approach faces the notorious "parameter problem": models have numerous nonlinear, mathematical functions with unknown parameter values, even for describing just a few intracellular processes. One cannot measure many intracellular parameters or can only measure them as snapshots in time. Another modeling approach uses cellular automata to represent living systems as discrete dynamical systems with binary variables. Quantitative (Hamiltonian-based) rules can dictate cellular automata (e.g., Cellular Potts Model). But numerous biological features, in current practice, are qualitatively described rather than quantitatively (e.g., gene is (highly) expressed or not (highly) expressed). Cellular automata governed by verbal rules are useful representations for living systems and can mitigate the parameter problem. However, they can yield complex dynamics that are difficult to understand because the automata-governing rules are not quantitative and much of the existing mathematical tools and theorems apply to continuous but not discrete dynamical systems. Recent studies found ways to overcome this challenge. These studies either discovered or suggest an existence of predictive "landscapes" whose shapes are described by Lyapunov functions and yield "equations of motion" for a "pseudo-particle." The pseudo-particle represents the entire cellular lattice and moves on the landscape, thereby giving a low-dimensional representation of the cellular automata dynamics. We outline this promising modeling strategy.

A balancing act in transcription regulation by response regulators: titration of transcription factor activity by decoy DNA binding sites

Studies of transcription regulation are often focused on binding of transcription factors (TFs) to a small number of promoters of interest. It is often assumed that TFs are in great excess to their binding sites (TFBSs) and competition for TFs between DNA sites is seldom considered. With increasing evidence that TFBSs are exceedingly abundant for many TFs and significant variations in TF and TFBS numbers occur during growth, the interplay between a TF and all TFBSs should not be ignored. Here, we use additional decoy DNA sites to quantitatively analyze how the relative abundance of a TF to its TFBSs impacts the steady-state level and onset time of gene expression for the auto-activated Escherichia coli PhoB response regulator. We show that increasing numbers of decoy sites progressively delayed transcription activation and lowered promoter activities. Perturbation of transcription regulation by additional TFBSs did not require extreme numbers of decoys, suggesting that PhoB is approximately at capacity for its DNA sites. Addition of decoys also converted a graded response to a bi-modal response. We developed a binding competition model that captures the major features of experimental observations, providing a quantitative framework to assess how variations in TFs and TFBSs influence transcriptional responses.

Quantifying the regulatory role of individual transcription factors in Escherichia coli

Gene regulation often results from the action of multiple transcription factors (TFs) acting at a promoter, obscuring the individual regulatory effect of each TF on RNA polymerase (RNAP). Here we measure the fundamental regulatory interactions of TFs in E. coli by designing synthetic target genes that isolate individual TFs' regulatory effects. Using a thermodynamic model, each TF's regulatory interactions are decoupled from TF occupancy and interpreted as acting through (de)stabilization of RNAP and (de)acceleration of transcription initiation. We find that the contribution of each mechanism depends on TF identity and binding location; regulation immediately downstream of the promoter is insensitive to TF identity, but the same TFs regulate by distinct mechanisms upstream of the promoter. These two mechanisms are uncoupled and can act coherently, to reinforce the observed regulatory role (activation/repression), or incoherently, wherein the TF regulates two distinct steps with opposing effects.

Making mechanistic sense: are we teaching students what they need to know?

Evaluating learning outcomes depends upon objective and actionable measures of what students know - that is, what can they do with what they have learned. In the context of a developmental biology course, a capstone of many molecular biology degree programs, I asked students to predict the behaviors of temporal and spatial signaling gradients. Their responses led me to consider an alternative to conventional assessments, namely a process in which students are asked to build and apply plausible explanatory mechanistic models ("PEMMs"). A salient point is not whether students' models are correct, but whether they "work" in a manner consistent with underlying scientific principles. Analyzing such models can reveal the extent to which students recognize and accurately apply relevant ideas. An emphasis on model building, analysis and revision, an authentic scientific practice, can be expected to have transformative effects on course and curricular design as well as on student engagement and learning outcomes.

Tunability enhancement of gene regulatory motifs through competition for regulatory protein resources

Gene regulatory networks (GRNs) orchestrate the spatiotemporal levels of gene expression, thereby regulating various cellular functions ranging from embryonic development to tissue homeostasis. Some patterns called "motifs" recurrently appear in the GRNs. Owing to the prevalence of these motifs they have been subjected to much investigation, both in the context of understanding cellular decision making and engineering synthetic circuits. Mounting experimental evidence suggests that (1) the copy number of genes associated with these motifs varies, and (2) proteins produced from these genes bind to decoy binding sites on the genome as well as promoters driving the expression of other genes. Together, these two processes engender competition for protein resources within a cell. To unravel how competition for protein resources affects the dynamical properties of regulatory motifs, we propose a simple kinetic model that explicitly incorporates copy number variation (CNV) of genes and decoy binding of proteins. Using quasi-steady-state approximations, we theoretically investigate the transient and steady-state properties of three of the commonly found motifs: Autoregulation, toggle switch, and repressilator. While protein resource competition alters the timescales to reach the steady state for all these motifs, the dynamical properties of the toggle switch and repressilator are affected in multiple ways. For toggle switch, the basins of attraction of the known attractors are dramatically altered if one set of proteins binds to decoys more frequently than the other, an effect which gets suppressed as the copy number of the toggle switch is enhanced. For repressilators, protein sharing leads to an emergence of oscillation in regions of parameter space that were previously nonoscillatory. Intriguingly, both the amplitude and frequency of oscillation are altered in a nonlinear manner through the interplay of CNV and decoy binding. Overall, competition for protein resources within a cell provides an additional layer of regulation of gene regulatory motifs.

Inherent regulatory asymmetry emanating from network architecture in a prevalent autoregulatory motif

Predicting gene expression from DNA sequence remains a major goal in the field of gene regulation. A challenge to this goal is the connectivity of the network, whose role in altering gene expression remains unclear. Here, we study a common autoregulatory network motif, the negative single-input module, to explore the regulatory properties inherited from the motif. Using stochastic simulations and a synthetic biology approach in E. coli, we find that the TF gene and its target genes have inherent asymmetry in regulation, even when their promoters are identical; the TF gene being more repressed than its targets. The magnitude of asymmetry depends on network features such as network size and TF-binding affinities. Intriguingly, asymmetry disappears when the growth rate is too fast or too slow and is most significant for typical growth conditions. These results highlight the importance of accounting for network architecture in quantitative models of gene expression.