Nucleosomal proofreading of activator-promoter interactions

Trade-offs and thermodynamics of energy-relay proofreading

Biological processes that are able to discriminate between different molecules consume energy and dissipate heat, using a mechanism known as proofreading. In this work, we thoroughly analyse the thermodynamic properties of one of the most important proofreading mechanisms, namely Hopfield's energy-relay proofreading. We discover several trade-off relations and scaling laws between several kinetic and thermodynamic observables. These trade-off relations are obtained both analytically and numerically through Pareto optimal fronts. We show that the scheme is able to operate in three distinct regimes: an energy-relay regime, a mixed relay-Michaelis-Menten (MM) regime and a Michaelis-Menten regime, depending on the kinetic and energetic parameters that tune transitions between states. The mixed regime features a dynamical phase transition in the error-entropy production Pareto trade-off, while the pure energy-relay regime contains a region where this type of proofreading energetically outperforms standard kinetic proofreading.

The method in the madness: Transcriptional control from stochastic action at the single-molecule scale

Cell states result from the ordered activation of gene expression by transcription factors. Transcription factors face opposing design constraints: they need to be dynamic to trigger rapid cell state transitions, but also stable enough to maintain terminal cell identities indefinitely. Recent progress in live-cell single-molecule microscopy has helped define the biophysical principles underlying this paradox. Beyond transcription factor activity, single-molecule experiments have revealed that at nearly every level of transcription regulation, control emerges from multiple short-lived stochastic interactions, rather than deterministic, stable interactions typical of other biochemical pathways. This architecture generates consistent outcomes that can be rapidly choreographed. Here, we highlight recent results that demonstrate how order in transcription regulation emerges from the apparent molecular-scale chaos and discuss remaining conceptual challenges.

Single gene analysis in yeast suggests nonequilibrium regulatory dynamics for transcription

Fluctuations in the initiation rate of transcription, the first step in gene expression, ensue from the stochastic behavior of the molecular process that controls transcription. In steady state, the regulatory process is often assumed to operate reversibly, i.e., in equilibrium. However, reversibility imposes fundamental limits to information processing. For instance, the assumption of equilibrium is difficult to square with the precision with which the regulatory process executes its task in eukaryotes. Here we provide evidence - from microscopic analyses of the transcription dynamics at a single gene copy of yeast - that the regulatory process for transcription is cyclic and irreversible (out of equilibrium). The necessary coupling to reservoirs of free energy occurs via sequence-specific transcriptional activators and the recruitment, in part, of ATP-dependent chromatin remodelers. Our findings may help explain how eukaryotic cells reconcile the dual but opposing requirements for fast regulatory kinetics and high regulatory specificity.

Connecting Chromatin Structures to Gene Regulation Using Dynamic Polymer Simulations

The transfer of regulatory information between distal loci on chromatin is thought to involve physical proximity, but key biophysical features of these contacts remain unclear. For instance, it is unknown how close and for how long two loci need to be in order to productively interact. The main challenge is that it is currently impossible to measure chromatin dynamics with high spatiotemporal resolution at scale. Polymer simulations provide an accessible and rigorous way to test biophysical models of chromatin regulation, yet there is a lack of simple and general methods for extracting the values of model parameters. Here we adapt the Nelder-Mead simplex optimization algorithm to select the best polymer model matching a given Hi-C dataset, using the MYC locus as an example. The model's biophysical parameters predict a compartmental rearrangement of the MYC locus in leukemia, which we validate with single-cell measurements. Leveraging trajectories predicted by the model, we find that loci with similar Hi-C contact frequencies can exhibit widely different contact dynamics. Interestingly, the frequency of productive interactions between loci exhibits a non-linear relationship with their Hi-C contact frequency when we enforce a specific capture radius and contact duration. These observations are consistent with recent experimental observations and suggest that the dynamic ensemble of chromatin configurations, rather than average contact matrices, is required to fully predict productive long-range chromatin interactions.

The Hill function is the universal Hopfield barrier for sharpness of input-output responses

The Hill functions, [Formula: see text], have been widely used in biology for over a century but, with the exception of [Formula: see text], they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, coregulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalizes most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, [Formula: see text], for any equilibrium model with [Formula: see text] input binding sites. [Formula: see text] exhibits a cusp which approaches, but never exceeds, the sharpness of [Formula: see text], but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers, and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, [Formula: see text], whose structure may be of mathematical interest, and suggest the importance of characterizing Hopfield barriers for other forms of cellular information processing.

Governing principles of transcriptional logic out of equilibrium

To survive, adapt, and develop, cells respond to external and internal stimuli by tightly regulating transcription. Transcriptional regulation involves the combinatorial binding of a repertoire of transcription factors to DNA, which often results in switch-like binary outputs akin to Boolean logic gates. Recent experimental studies have demonstrated that in eukaryotes, transcription factor binding to DNA often involves energy expenditure, thereby driving the system out of equilibrium. The governing principles of transcriptional logic operations out of equilibrium remain unexplored. Here, we employ a simple two-input, single-locus model of transcription that can accommodate both equilibrium and nonequilibrium mechanisms. Using this model, we find that nonequilibrium regimes can give rise to all the logic operations accessible in equilibrium. Strikingly, energy expenditure alters the regulatory function of the two transcription factors in a mutually exclusive manner. This allows for the emergence of new logic operations that are inaccessible in equilibrium. Overall, our results show that energy expenditure can expand the range of cellular decision-making without the need for more complex promoter architectures.

The Hill function is the universal Hopfield barrier for sharpness of input-output responses

The Hill functions, ℋ h ( x ) = x h / 1 + x h , have been widely used in biology for over a century but, with the exception of ℋ 1 , they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, co-regulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalises most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, Ω m ⊂ ℝ + 2 , for any equilibrium model with m input binding sites. Ω m exhibits a cusp which approaches, but never exceeds, the sharpness of ℋ m but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, Ω m , whose structure may be of mathematical interest, and suggest the importance of characterising Hopfield barriers for other forms of cellular information processing.

Transcription Factor Dynamics: One Molecule at a Time

Cells must tightly regulate their gene expression programs and yet rapidly respond to acute biochemical and biophysical cues within their environment. This information is transmitted to the nucleus through various signaling cascades, culminating in the activation or repression of target genes. Transcription factors (TFs) are key mediators of these signals, binding to specific regulatory elements within chromatin. While live-cell imaging has conclusively proven that TF-chromatin interactions are highly dynamic, how such transient interactions can have long-term impacts on developmental trajectories and disease progression is still largely unclear. In this review, we summarize our current understanding of the dynamic nature of TF functions, starting with a historical overview of early live-cell experiments. We highlight key factors that govern TF dynamics and how TF dynamics, in turn, affect downstream transcriptional bursting. Finally, we conclude with open challenges and emerging technologies that will further our understanding of transcriptional regulation.

Chromatin accessibility in the Drosophila embryo is determined by transcription factor pioneering and enhancer activation

Chromatin accessibility is integral to the process by which transcription factors (TFs) read out cis-regulatory DNA sequences, but it is difficult to differentiate between TFs that drive accessibility and those that do not. Deep learning models that learn complex sequence rules provide an unprecedented opportunity to dissect this problem. Using zygotic genome activation in Drosophila as a model, we analyzed high-resolution TF binding and chromatin accessibility data with interpretable deep learning and performed genetic validation experiments. We identify a hierarchical relationship between the pioneer TF Zelda and the TFs involved in axis patterning. Zelda consistently pioneers chromatin accessibility proportional to motif affinity, whereas patterning TFs augment chromatin accessibility in sequence contexts where they mediate enhancer activation. We conclude that chromatin accessibility occurs in two tiers: one through pioneering, which makes enhancers accessible but not necessarily active, and the second when the correct combination of TFs leads to enhancer activation.

Dynamic epistasis analysis reveals how chromatin remodeling regulates transcriptional bursting

Transcriptional bursting has been linked to the stochastic positioning of nucleosomes. However, how bursting is regulated by the remodeling of promoter nucleosomes is unknown. Here, we use single-molecule live-cell imaging of GAL10 transcription in Saccharomyces cerevisiae to measure how bursting changes upon combined perturbations of chromatin remodelers, the transcription factor Gal4 and preinitiation complex components. Using dynamic epistasis analysis, we reveal how the remodeling of different nucleosomes regulates transcriptional bursting parameters. At the nucleosome covering the Gal4 binding sites, RSC and Gal4 binding synergistically facilitate each burst. Conversely, nucleosome remodeling at the TATA box controls only the first burst upon galactose induction. At canonical TATA boxes, the nucleosomes are displaced by TBP binding to allow for transcription activation even in the absence of remodelers. Overall, our results reveal how promoter nucleosome remodeling together with Gal4 and preinitiation complex binding regulates transcriptional bursting.

Flexibility and sensitivity in gene regulation out of equilibrium

Cells adapt to environments and tune gene expression by controlling the concentrations of proteins and their kinetics in regulatory networks. In both eukaryotes and prokaryotes, experiments and theory increasingly attest that these networks can and do consume bio-chemical energy. How does this dissipation enable cellular behaviors unobtainable in equilibrium? This open question demands quantitative models that transcend thermodynamic equilibrium. Here we study the control of a simple, ubiquitous gene regulatory motif to explore the consequences of departing equilibrium in kinetic cycles. Employing graph theory, we find that dissipation unlocks nonmonotonicity and enhanced sensitivity of gene expression with respect to a transcription factor's concentration. These features allow a single transcription factor to act as both a repressor and activator at different levels or achieve outputs with multiple concentration regions of locally-enhanced sensitivity. We systematically dissect how energetically-driving individual transitions within regulatory networks, or pairs of transitions, generates more adjustable and sensitive phenotypic responses. Our findings quantify necessary conditions and detectable consequences of energy expenditure. These richer mathematical behaviors-feasibly accessed using biological energy budgets and rates-may empower cells to accomplish sophisticated regulation with simpler architectures than those required at equilibrium.

Significance Statement

Growing theoretical and experimental evidence demonstrates that cells can (and do) spend biochemical energy while regulating their genes. Here we explore the impact of departing from equilibrium in simple regulatory cycles, and learn that beyond increasing sensitivity, dissipation can unlock more flexible input-output behaviors that are otherwise forbidden without spending energy. These more complex behaviors could enable cells to perform more sophisticated functions using simpler systems than those needed at equilibrium.

Competing constraints shape the nonequilibrium limits of cellular decision-making

Gene regulation is central to cellular function. Yet, despite decades of work, we lack quantitative models that can predict how transcriptional control emerges from molecular interactions at the gene locus. Thermodynamic models of transcription, which assume that gene circuits operate at equilibrium, have previously been employed with considerable success in the context of bacterial systems. However, the presence of ATP-dependent processes within the eukaryotic transcriptional cycle suggests that equilibrium models may be insufficient to capture how eukaryotic gene circuits sense and respond to input transcription factor concentrations. Here, we employ simple kinetic models of transcription to investigate how energy dissipation within the transcriptional cycle impacts the rate at which genes transmit information and drive cellular decisions. We find that biologically plausible levels of energy input can lead to significant gains in how rapidly gene loci transmit information but discover that the regulatory mechanisms underlying these gains change depending on the level of interference from noncognate activator binding. When interference is low, information is maximized by harnessing energy to push the sensitivity of the transcriptional response to input transcription factors beyond its equilibrium limits. Conversely, when interference is high, conditions favor genes that harness energy to increase transcriptional specificity by proofreading activator identity. Our analysis further reveals that equilibrium gene regulatory mechanisms break down as transcriptional interference increases, suggesting that energy dissipation may be indispensable in systems where noncognate factor interference is sufficiently large.

Kinetic Proofreading

Biochemistry and molecular biology rely on the recognition of structural complementarity between molecules. Molecular interactions must be both quickly reversible, i.e., tenuous, and specific. How the cell reconciles these conflicting demands is the subject of this article. The problem and its theoretical solution are discussed within the wider theoretical context of the thermodynamics of stochastic processes (stochastic thermodynamics). The solution-an irreversible reaction cycle that decreases internal error at the expense of entropy export into the environment-is shown to be widely employed by biological processes that transmit genetic and regulatory information. Expected final online publication date for the Annual Review of Biochemistry, Volume 91 is June 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Thermodynamic uncertainty relation to assess biological processes

We review the trade-offs between speed, fluctuations, and thermodynamic cost involved with biological processes in nonequilibrium states and discuss how optimal these processes are in light of the universal bound set by the thermodynamic uncertainty relation (TUR). The values of the uncertainty product Q of TUR, which can be used as a measure of the precision of enzymatic processes realized for a given thermodynamic cost, are suboptimal when the substrate concentration is at the Michaelis constant, and some of the key biological processes are found to work around this condition. We illustrate the utility of Q in assessing how close the molecular motors and biomass producing machineries are to the TUR bound, and for the cases of biomass production (or biological copying processes), we discuss how their optimality quantified in terms of Q is balanced with the error rate in the information transfer process. We also touch upon the trade-offs in other error-minimizing processes in biology, such as gene regulation and chaperone-assisted protein folding. A spectrum of Q recapitulating the biological processes surveyed here provides glimpses into how biological systems are evolved to optimize and balance the conflicting functional requirements.

Kinetic sculpting of the seven stripes of the Drosophila even-skipped gene

We used live imaging to visualize the transcriptional dynamics of the Drosophila melanogaster even-skipped gene at single-cell and high-temporal resolution as its seven stripe expression pattern forms, and developed tools to characterize and visualize how transcriptional bursting varies over time and space. We find that despite being created by the independent activity of five enhancers, even-skipped stripes are sculpted by the same kinetic phenomena: a coupled increase of burst frequency and amplitude. By tracking the position and activity of individual nuclei, we show that stripe movement is driven by the exchange of bursting nuclei from the posterior to anterior stripe flanks. Our work provides a conceptual, theoretical and computational framework for dissecting pattern formation in space and time, and reveals how the coordinated transcriptional activity of individual nuclei shapes complex developmental patterns.

A matter of time: Using dynamics and theory to uncover mechanisms of transcriptional bursting

Eukaryotic transcription generally occurs in bursts of activity lasting minutes to hours; however, state-of-the-art measurements have revealed that many of the molecular processes that underlie bursting, such as transcription factor binding to DNA, unfold on timescales of seconds. This temporal disconnect lies at the heart of a broader challenge in physical biology of predicting transcriptional outcomes and cellular decision-making from the dynamics of underlying molecular processes. Here, we review how new dynamical information about the processes underlying transcriptional control can be combined with theoretical models that predict not only averaged transcriptional dynamics, but also their variability, to formulate testable hypotheses about the molecular mechanisms underlying transcriptional bursting and control.

Job Opening for Nucleosome Mechanic: Flexibility Required

The nucleus has been studied for well over 100 years, and chromatin has been the intense focus of experiments for decades. In this review, we focus on an understudied aspect of chromatin biology, namely the chromatin fiber polymer’s mechanical properties. In recent years, innovative work deploying interdisciplinary approaches including computational modeling, in vitro manipulations of purified and native chromatin have resulted in deep mechanistic insights into how the mechanics of chromatin might contribute to its function. The picture that emerges is one of a nucleus that is shaped as much by external forces pressing down upon it, as internal forces pushing outwards from the chromatin. These properties may have evolved to afford the cell a dynamic and reversible force-induced communication highway which allows rapid coordination between external cues and internal genomic function.