Elucidating interplay of speed and accuracy in biological error correction

Live tracking of replisomes reveals nutrient-dependent regulation of replication elongation rates in Caulobacter crescentus

In bacteria, commitment to genome replication (initiation) is intricately linked to nutrient availability. Whether growth conditions affect other stages of replication beyond initiation remains to be systematically studied. To address this, we assess the replication dynamics of Caulobacter crescentus, a bacterium that undergoes only a single round of replication per cell cycle, by tracking the replisome across various growth phases and nutrient conditions. We find that the replication elongation rates slow down as cells transition from exponential (high-nutrient) to stationary (low-nutrient) phase, and this contributes significantly to the overall cell-cycle delay. Although elongation rates are correlated with growth rates, both properties are differentially influenced by nutrient status. This slowdown in replication progression is reversed via supplementation with dNTPs and is not associated with increased mutagenesis or upregulation of the DNA damage responses. We conclude that growth conditions not only dictate the commitment to replication but also the rates of genome duplication. Such regulation appears to be distinct from stress-induced replication slowdown and likely serves as an adaptive mechanism to cope with fluctuations in nutrient availability in the environment.

Ligand-induced receptor multimerization achieves specificity enhancement of kinetic proofreading without associated costs

Kinetic proofreading (KPR) is a commonly invoked mechanism for specificity enhancement of receptor signaling. However, specificity enhancement comes at a cost of nonequilibrium energy input and signal attenuation. We show that ligand-induced multimeric receptor assembly can enhance receptor specificity to the same degree as KPR, yet without the need for out-of-equilibrium energy expenditure and signal loss. We show how multimeric receptor specificity enhancement arises from the amplification of affinity differences via sequential progression down a free energy landscape. We also show that multimeric receptor ligand recognition is more robust to stochastic fluctuations and molecular noise than KPR receptors. Finally, we show that multimeric receptors perform signaling tasks beyond specificity enhancement like absolute discrimination and aspects of ligand antagonism. Our results suggest that multimeric receptors may serve as a potent mechanism of ligand discrimination comparable to and potentially with more advantages than traditional proofreading.

High-Speed Combinatorial Polymerization through Kinetic-Trap Encoding

Like the letters in the alphabet forming words, reusing components of a heterogeneous mixture is an efficient strategy for assembling a large number of target structures. Examples range from synthetic DNA origami to proteins self-assembling into complexes. The standard self-assembly paradigm views target structures as free-energy minima of a mixture. While this is an appealing picture, at high speed structures may be kinetically trapped in local minima, reducing self-assembly accuracy. How then can high speed, high accuracy, and combinatorial usage of components coexist? We propose to reconcile these three concepts not by avoiding kinetic traps, but by exploiting them to encode target structures. This can be achieved by sculpting the kinetic pathways of the mixture, instead of its free-energy landscape. We formalize these ideas in a minimal toy model, for which we analytically estimate the encoding capacity and kinetic characteristics, in agreement with simulations. Our results may be generalized to other soft-matter systems capable of computation, such as liquid mixtures or elastic networks, and pave the way for high-dimensional information processing far from equilibrium.

Steady-state solution of Markov jump processes in terms of arrival probabilities

Several dynamical processes can be modeled as Markov jump processes among a finite number N of sites (the distinct physical states). Here we consider strongly connected networks with time-independent site-to-site jump rate constants, and focus on the steady-state occupation probabilities of the sites. We provide a physically framed expression of the steady-state distribution in terms of arrival probabilities, here defined as the probabilities of going from starting sites to target sites with a given number of jumps (regardless of the time required). In particular, the full set of return probabilities (for all the sites of the network) up to N-1 jumps is necessary and sufficient. A few examples illustrate the outcomes, including the case of stochastic chemical kinetics.

Where physics and biology meet

As part of this special issue on physics and biology, we invited several leading experts that bridge these disciplines to provide their views on the reciprocal contributions of each field and the benefits and challenges of working across physics and biology: introduction provided by Wallace Marshall.

Direct and indirect selection in a proofreading polymerase

The traits that affect evolvability are subject to indirect selection, as these traits affect the course of evolution over many generations rather than the direct replicative fitness of an individual. However, the evolution of evolvability-determining traits is often difficult to study because putative evolvability alleles often have confounding direct fitness effects of unknown origin and size. Here, we study theoretically and experimentally the evolution of mutation rates in proofreading polymerases with orthogonal control of direct and indirect selection. Mutagenic DNA polymerases enjoy a long-time fitness advantage by enhancing the rate of acquiring beneficial mutations. However, this is offset by a short-time fitness penalty, which we trace to a counterintuitive trade-off between mutation rates and activity in proofreading polymerases. Since these fitness effects act on different timescales, no one number characterizes the fitness of a mutator allele. We find unusual dynamic features in the resulting evolutionary dynamics, such as kinetic exclusion, selection by dynamic environments, and Rock-Paper-Scissors dynamics in the absence of ecology. Our work has implications for the evolution of mutation rates and more broadly, evolution in the context of an anti-correlation between mutation rates and short term fitness.

Transcript errors generate amyloid-like proteins in huwman cells

Aging is characterized by the accumulation of proteins that display amyloid-like behavior. However, the molecular mechanisms by which these proteins arise remain unclear. Here, we demonstrate that amyloid-like proteins are produced in a variety of human cell types, including stem cells, brain organoids and fully differentiated neurons by mistakes that occur in messenger RNA molecules. Some of these mistakes generate mutant proteins already known to cause disease, while others generate proteins that have not been observed before. Moreover, we show that these mistakes increase when cells are exposed to DNA damage, a major hallmark of human aging. When taken together, these experiments suggest a mechanistic link between the normal aging process and age-related diseases.

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.

Linear-Decoupling Enables Accurate Speed and Accuracy Predictions for Copolymerization Processes

Biological processes exhibit remarkable accuracy and speed and can be theoretically explored through various approaches. The Markov-chain copolymerization theory, describing polymer growth kinetics as a Markov chain, provides an exact set of equations to solve for error and speed. Still, due to nonlinearity, these equations are hard to solve. Alternatively, the enzyme-kinetics approach, which formulates a set of linear equations, simplifies the biological processes as transitions between discrete chemical states, but generally, it might not be accurate. Here, we show that the enzyme-kinetic approach can lead to inaccurate fluxes, even for first-order polymerization processes. To address the problem, we propose a simplified linear-decoupling approximation for steady-state probabilities of higher-order copolymer chains under biologically relevant conditions. Our findings demonstrate that the stationary speed and error rate obtained from the linear-decoupling method align closely with exact values from the Markov-chain (nonlinear) approximation. Extending the technique to higher-order processes with proofreading and internal states shows that it works equally well to describe trade-offs between speed and accuracy for DNA replication and transcription elongation. Our work underscores the proposed linear-decoupling approximation's efficacy in addressing the nonlinear behavior of the Markov-chain approach and the enzyme-kinetic approach's limitations, ensuring accurate predictions for high-fidelity biological processes.

Mutual Linearity of Nonequilibrium Network Currents

For continuous-time Markov chains and open unimolecular chemical reaction networks, we prove that any two stationary currents are linearly related upon perturbations of a single edge's transition rates, arbitrarily far from equilibrium. We extend the result to nonstationary currents in the frequency domain, provide and discuss an explicit expression for the current-current susceptibility in terms of the network topology, and discuss possible generalizations. In practical scenarios, the mutual linearity relation has predictive power and can be used as a tool for inference or model proof testing.

Steady-state probabilities for Markov jump processes in terms of powers of the transition rate matrix

Several types of dynamics at stationarity can be described in terms of a Markov jump process among a finite number N of representative sites. Before dealing with the dynamical aspects, one basic problem consists in expressing the a priori steady-state occupation probabilities of the sites. In particular, one wishes to go beyond the mere black-box computational tools and find expressions in which the jump rate constants appear explicitly, therefore allowing for a potential design/control of the network. For strongly connected networks admitting a unique stationary state with all sites populated, here we express the occupation probabilities in terms of a formula that involves powers of the transition rate matrix up to order N - 1. We also provide an expression of the derivatives with respect to the jump rate constants, possibly useful in sensitivity analysis frameworks. Although we refer to dynamics in (bio)chemical networks at thermal equilibrium or under nonequilibrium steady-state conditions, the results are valid for any Markov jump process under the same assumptions.

Insights into Error Control Mechanisms in Biological Processes: Copolymerization and Enzyme-Kinetics Revisited

The high fidelity observed in biological information processing ranging from replication to translation has stimulated significant research efforts to clarify the underlying microscopic picture. Theoretically, several approaches to analyze the error rates have been proposed. The copolymerization theory describes the addition and removal of monomers at the growing tip of a copolymer, leading to a closed set of nonlinear equations. On the other hand, enzyme-kinetics approaches formulate linear equations of biochemical networks, describing transitions between discrete chemical states. However, it is still unclear whether the error values computed by the two approaches agree. Moreover, there are conflicting interpretations on whether the error is under thermodynamic or kinetic discrimination control. In this work, we examine the error rate in persistent copying biochemical processes by specifically analyzing both theoretical approaches. The initial disagreement of the results between the two theories motivated us to rederive the formula for the error rate in the kinetic model. The error computed with the new method resulted in excellent agreement between both theoretical approaches and with Monte Carlo simulations. Furthermore, our theoretical analysis shows that the kinetic discrimination controls the error, even when the energy difference between adding the right and wrong products is very small. Our theoretical investigation gives important insights into the physical-chemical properties of complex biological processes by providing the quantitative framework to evaluate them.

Reliable ligand discrimination in stochastic multistep kinetic proofreading: First passage time vs. product counting strategies

Cellular signaling, crucial for biological processes like immune response and homeostasis, relies on specificity and fidelity in signal transduction to accurately respond to stimuli amidst biological noise. Kinetic proofreading (KPR) is a key mechanism enhancing signaling specificity through time-delayed steps, although its effectiveness is debated due to intrinsic noise potentially reducing signal fidelity. In this study, we reformulate the theory of kinetic proofreading (KPR) by convolving multiple intermediate states into a single state and then define an overall "processing" time required to traverse these states. This simplification allows us to succinctly describe kinetic proofreading in terms of a single waiting time parameter, facilitating a more direct evaluation and comparison of KPR performance across different biological contexts such as DNA replication and T cell receptor (TCR) signaling. We find that loss of fidelity for longer proofreading steps relies on the specific strategy of information extraction and show that in the first-passage time (FPT) discrimination strategy, longer proofreading steps can exponentially improve the accuracy of KPR at the cost of speed. Thus, KPR can still be an effective discrimination mechanism in the high noise regime. However, in a product concentration-based discrimination strategy, longer proofreading steps do not necessarily lead to an increase in performance. However, by introducing activation thresholds on product concentrations, can we decompose the product-based strategy into a series of FPT-based strategies to better resolve the subtleties of KPR-mediated product discrimination. Our findings underscore the importance of understanding KPR in the context of how information is extracted and processed in the cell.

Rapid adaptation of cellular metabolic rate to the MicroRNA complements of mammals and its relevance to the evolution of endothermy

The metabolic efficiency of mammalian cells depends on the attenuation of intrinsic translation noise by microRNAs. We devised a metric of cellular metabolic rate (cMR), rMR/Mexp optimally fit to the number of microRNA families (mirFam), that is robust to variation in mass and sensitive to body temperature (Tb), consistent with the heat dissipation limit theory of Speakman and Król (2010). Using mirFam as predictor, an Ornstein-Uhlenbeck process of stabilizing selection, with an adaptive shift at the divergence of Boreoeutheria, accounted for 95% of the variation in cMR across mammals. Branchwise rates of evolution of cMR, mirFam and Tb concurrently increased 6- to 7-fold at the divergence of Boreoeutheria, independent of mass. Cellular MR variation across placental mammals was also predicted by the sum of model conserved microRNA-target interactions, revealing an unexpected degree of integration of the microRNA-target apparatus into the energy economy of the mammalian cell.

The linear framework II: using graph theory to analyse the transient regime of Markov processes

The linear framework uses finite, directed graphs with labelled edges to model biomolecular systems. Graph vertices represent chemical species or molecular states, edges represent reactions or transitions and edge labels represent rates that also describe how the system is interacting with its environment. The present paper is a sequel to a recent review of the framework that focussed on how graph-theoretic methods give insight into steady states as rational algebraic functions of the edge labels. Here, we focus on the transient regime for systems that correspond to continuous-time Markov processes. In this case, the graph specifies the infinitesimal generator of the process. We show how the moments of the first-passage time distribution, and related quantities, such as splitting probabilities and conditional first-passage times, can also be expressed as rational algebraic functions of the labels. This capability is timely, as new experimental methods are finally giving access to the transient dynamic regime and revealing the computations and information processing that occur before a steady state is reached. We illustrate the concepts, methods and formulas through examples and show how the results may be used to illuminate previous findings in the literature.

The divergence of mutation rates and spectra across the Tree of Life

Owing to advances in genome sequencing, genome stability has become one of the most scrutinized cellular traits across the Tree of Life. Despite its centrality to all things biological, the mutation rate (per nucleotide site per generation) ranges over three orders of magnitude among species and several-fold within individual phylogenetic lineages. Within all major organismal groups, mutation rates scale negatively with the effective population size of a species and with the amount of functional DNA in the genome. This relationship is most parsimoniously explained by the drift-barrier hypothesis, which postulates that natural selection typically operates to reduce mutation rates until further improvement is thwarted by the power of random genetic drift. Despite this constraint, the molecular mechanisms underlying DNA replication fidelity and repair are free to wander, provided the performance of the entire system is maintained at the prevailing level. The evolutionary flexibility of the mutation rate bears on the resolution of several prior conundrums in phylogenetic and population-genetic analysis and raises challenges for future applications in these areas.

Proofreading does not result in more reliable ligand discrimination in receptor signaling due to its inherent stochasticity

Kinetic proofreading (KPR) has been used as a paradigmatic explanation for the high specificity of ligand discrimination by cellular receptors. KPR enhances the difference in the mean receptor occupancy between different ligands compared to a nonproofread receptor, thus potentially enabling better discrimination. On the other hand, proofreading also attenuates the signal and introduces additional stochastic receptor transitions relative to a nonproofreading receptor. This increases the relative magnitude of noise in the downstream signal, which can interfere with reliable ligand discrimination. To understand the effect of noise on ligand discrimination beyond the comparison of the mean signals, we formulate the task of ligand discrimination as a problem of statistical estimation of the receptor affinity of ligands based on the molecular signaling output. Our analysis reveals that proofreading typically worsens ligand resolution compared to a nonproofread receptor. Furthermore, the resolution decreases further with more proofreading steps under most commonly biologically considered conditions. This contrasts with the usual notion that KPR universally improves ligand discrimination with additional proofreading steps. Our results are consistent across a variety of different proofreading schemes and metrics of performance, suggesting that they are inherent to the KPR mechanism itself rather than any particular model of molecular noise. Based on our results, we suggest alternative roles for KPR schemes such as multiplexing and combinatorial encoding in multi-ligand/multi-output pathways.

Synergy among Pausing, Intrinsic Proofreading, and Accessory Proteins Results in Optimal Transcription Speed and Tolerable Accuracy

Cleavage of dinucleotides after the misincorporational pauses serves as a proofreading mechanism that increases transcriptional elongation accuracy. The accuracy is further improved by accessory proteins such as GreA and TFIIS. However, it is not clear why RNAP pauses and why cleavage-factor-assisted proofreading is necessary despite transcriptional errors in vitro being of the same order as those in downstream translation. Here, we developed a chemical-kinetic model that incorporates most relevant features of transcriptional proofreading and uncovers how the balance between speed and accuracy is achieved. We found that long pauses are essential for high accuracy, whereas cleavage-factor-stimulated proofreading optimizes speed. Moreover, in comparison to the cleavage of a single nucleotide or three nucleotides, RNAP backtracking and dinucleotide cleavage improve both speed and accuracy. Our results thereby show how the molecular mechanism and the kinetic parameters of the transcriptional process were evolutionarily optimized to achieve maximal speed and tolerable accuracy.

A universal method for analyzing copolymer growth

Polymers consisting of more than one type of monomer, known as copolymers, are vital to both living and synthetic systems. Copolymerization has been studied theoretically in a number of contexts, often by considering a Markov process in which monomers are added or removed from the growing tip of a long copolymer. To date, the analysis of the most general models of this class has necessitated simulation. We present a general method for analyzing such processes without resorting to simulation. Our method can be applied to models with an arbitrary network of sub-steps prior to addition or removal of a monomer, including non-equilibrium kinetic proofreading cycles. Moreover, the approach allows for a dependency of addition and removal reactions on the neighboring site in the copolymer and thermodynamically self-consistent models in which all steps are assumed to be microscopically reversible. Using our approach, thermodynamic quantities such as chemical work; kinetic quantities such as time taken to grow; and statistical quantities such as the distribution of monomer types in the growing copolymer can be directly derived either analytically or numerically from the model definition.

Bridging ribosomal synthesis to cell growth through the lens of kinetics

Understanding prokaryotic cell growth requires a multiscale modeling framework from the kinetics perspective. The detailed kinetics pathway of ribosomes exhibits features beyond the scope of the classical Hopfield kinetics model. The complexity of the molecular responses to various nutrient conditions poses additional challenge to elucidate the cell growth. Herein, a kinetics framework is developed to bridge ribosomal synthesis to cell growth. For the ribosomal synthesis kinetics, the competitive binding between cognate and near-cognate tRNAs for ribosomes can be modulated by Mg2+. This results in distinct patterns of the speed - accuracy relation comprising "trade-off" and "competition" regimes. Furthermore, the cell growth rate is optimized by varying the characteristics of ribosomal synthesis through cellular responses to different nutrient conditions. In this scenario, cellular responses to nutrient conditions manifest by two quadratic scaling relations: one for nutrient flux versus cell mass, the other for ribosomal number versus growth rate. Both are in quantitative agreement with experimental measurements.

Proteome diversification by mRNA translation in cancer

mRNA translation is a highly conserved and tightly controlled mechanism for protein synthesis and is well known to be altered by oncogenes to promote cancer development. This distorted mRNA translation is accompanied by the vulnerability of cancer to inhibitors of key mRNA translation components. Novel studies also suggest that these alternations could be utilized for immunotherapy. Ribosome heterogeneity and alternative responses to nutrient shortages, which aid cancer growth and spread, are proposed to elicit aberrant protein production but may also result in previously unidentified therapeutic targets, such as the presentation of cancer-specific peptides at the surface of cancer cells (neoepitopes). This review will assess the driving forces in tRNA and ribosome function that underlie proteome diversification due to alterations in mRNA translation in cancer cells.

Cells as the first data scientists

The concepts that we generally associate with the field of data science are strikingly descriptive of the way that life, in general, processes information about its environment. The 'information life cycle', which enumerates the stages of information treatment in data science endeavours, also captures the steps of data collection and handling in biological systems. Similarly, the 'data-information-knowledge ecosystem', developed to illuminate the role of informatics in translating raw data into knowledge, can be a framework for understanding how information is constantly being transferred between life and the environment. By placing the principles of data science in a broader biological context, we see the activities of data scientists as the latest development in life's ongoing journey to better understand and predict its environment. Finally, we propose that informatics frameworks can be used to understand the similarities and differences between abiotic complex evolving systems and life.

Understanding the Target Search by Multiple Transcription Factors on Nucleosomal DNA

The association of multiple Transcription Factors (TFs) in the cis-regulatory region is imperative for developmental changes in eukaryotes. The underlying process is exceedingly complex, and it is not at all clear what orchestrates the overall search process by multiple TFs. In this study, by developing a theoretical model based on a discrete-state stochastic approach, we investigated the target search mechanism of multiple TFs on nucleosomal DNA. Experimental kinetic rate constants of different TFs are taken as input to estimate the Mean-First-Passage time to recognize the binding motifs by two TFs on a dynamic nucleosome model. The theory systematically analyzes when the TFs search their binding motifs hierarchically and when simultaneously by proceeding via the formation of a protein-protein complex. Our results, validated by extensive Monte Carlo simulations, elucidate the molecular basis of the complex target search phenomenon of multiple TFs on nucleosomal DNA.

Speed variations of bacterial replisomes

Replisomes are multi-protein complexes that replicate genomes with remarkable speed and accuracy. Despite their importance, their dynamics is poorly characterized, especially in vivo. In this paper, we present an approach to infer the replisome dynamics from the DNA abundance distribution measured in a growing bacterial population. Our method is sensitive enough to detect subtle variations of the replisome speed along the genome. As an application, we experimentally measured the DNA abundance distribution in Escherichia coli populations growing at different temperatures using deep sequencing. We find that the average replisome speed increases nearly five-fold between 17°C and 37°C. Further, we observe wave-like variations of the replisome speed along the genome. These variations correlate with previously observed variations of the mutation rate, suggesting a common dynamical origin. Our approach has the potential to elucidate replication dynamics in E. coli mutants and in other bacterial species.

The optimal strategy balancing risk and speed predicts DNA damage checkpoint override times

Checkpoints arrest biological processes allowing time for error correction. The phenomenon of checkpoint override (also known as checkpoint adaptation, slippage, or leakage), during cellular self-replication is biologically critical but currently lacks a quantitative, functional, or system-level understanding. To uncover fundamental laws governing error-correction systems, we derived a general theory of optimal checkpoint strategies, balancing the trade-off between risk and self-replication speed. Mathematically, the problem maps onto the optimization of an absorbing boundary for a random walk. We applied the theory to the DNA damage checkpoint (DDC) in budding yeast, an intensively researched model checkpoint. Using novel reporters for double-strand DNA breaks (DSBs), we first quantified the probability distribution of DSB repair in time including rare events and, secondly, the survival probability after override. With these inputs, the optimal theory predicted remarkably accurately override times as a function of DSB numbers, which we measured precisely for the first time. Thus, a first-principles calculation revealed undiscovered patterns underlying highly noisy override processes. Our multi-DSB measurements revise well-known past results and show that override is more general than previously thought.

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.

The energy cost and optimal design of networks for biological discrimination

Many biological processes discriminate between correct and incorrect substrates through the kinetic proofreading mechanism that enables lower error at the cost of higher energy dissipation. Elucidating physico-chemical constraints for global minimization of dissipation and error is important for understanding enzyme evolution. Here, we identify theoretically a fundamental error-cost bound that tightly constrains the performance of proofreading networks under any parameter variations preserving the rate discrimination between substrates. The bound is kinetically controlled, i.e. completely determined by the difference between the transition state energies on the underlying free energy landscape. The importance of the bound is analysed for three biological processes. DNA replication by T7 DNA polymerase is shown to be nearly optimized, i.e. its kinetic parameters place it in the immediate proximity of the error-cost bound. The isoleucyl-tRNA synthetase (IleRS) of E. coli also operates close to the bound, but further optimization is prevented by the need for reaction speed. In contrast, E. coli ribosome operates in a high-dissipation regime, potentially in order to speed up protein production. Together, these findings establish a fundamental error-dissipation relation in biological proofreading networks and provide a theoretical framework for studying error-dissipation trade-off in other systems with biological discrimination.

Diffusion control in biochemical specificity

Biochemical specificity is critical in enzyme function, evolution, and engineering. Here we employ an established kinetic model to dissect the effects of reactant geometry and diffusion on product formation speed and accuracy in the presence of cognate (correct) and near-cognate (incorrect) substrates. Using this steady-state model for spherical geometries, we find that, for distinct kinetic regimes, the speed and accuracy of the reactions are optimized on different regions of the geometric landscape. From this model we deduce that accuracy can be strongly dependent on reactant geometric properties even for chemically limited reactions. Notably, substrates with a specific geometry and reactivity can be discriminated by the enzyme with higher efficacy than others through purely diffusive effects. For similar cognate and near-cognate substrate geometries (as is the case for polymerases or the ribosome), we observe that speed and accuracy are maximized in opposing regions of the geometric landscape. We also show that, in relevant environments, diffusive effects on accuracy can be substantial even far from extreme kinetic conditions. Finally, we find how reactant chemical discrimination and diffusion can be related to simultaneously optimize steady-state flux and accuracy. These results highlight how diffusion and geometry can be employed to enhance reaction speed and discrimination, and similarly how they impose fundamental restraints on these quantities.

Kinetic origin of nucleosome invasion by pioneer transcription factors

Recently, a cryo-electron microscopy study has captured different stages of nucleosome breathing dynamics that show partial unwrapping of DNA from histone core to permit transient access to the DNA sites by transcription factors. In practice, however, only a subset of transcription factors named pioneer factors can invade nucleosomes and bind to specific DNA sites to trigger essential DNA metabolic processes. We propose a discrete-state stochastic model that considers the interplay of nucleosome breathing and protein dynamics explicitly and estimate the mean time to search the target DNA sites. It is found that the molecular principle governing the search process on nucleosome is very different compared to that on naked DNA. The pioneer factors minimize their search times on nucleosomal DNA by compensating their nucleosome association rates by dissociation rates. A fine balance between the two presents a tradeoff between their nuclear mobility and error associated with the search process.

Accuracy and speed of elongation in a minimal model of DNA replication

Being a dual purpose enzyme, the DNA polymerase is responsible for elongation of the newly formed DNA strand as well as cleaving the erroneous growth in case of a misincorporation. The efficiency of replication depends on the coordination of the polymerization and exonuclease activity of DNA polymerase. Here, we propose and analyze a minimal kinetic model of DNA replication and determine exact expressions for the velocity of elongation and the accuracy of replication. We first analyze the case without exonuclease activity. In that case, accuracy is determined by a kinetic competition between stepping and unbinding, with discrimination between correct and incorrect nucleotides in both transitions. We then include exonuclease activity and ask how different modes of additional discrimination in the exonuclease pathway can improve the accuracy while limiting the detrimental effect of exonuclease on the speed of replication. In this way, we ask how the kinetic parameters of the model have to be set to coordinate the two activities of the enzyme for high accuracy and high speed. The analysis also shows that the design of a replication system does not universally have to follow the speed-accuracy trade-off rule, although it does in the biologically realized parameter range. The accuracy of the process is mainly controlled by the crucial role of stepping after erroneous incorporation, which has impact on both polymerase and exonuclease activities of DNA polymerase.

Plasmid hypermutation using a targeted artificial DNA replisome

Extensive exploration of a protein's sequence space for improved or new molecular functions requires in vivo evolution with large populations. But disentangling the evolution of a target protein from the rest of the proteome is challenging. Here, we designed a protein complex of a targeted artificial DNA replisome (TADR) that operates in live cells to processively replicate one strand of a plasmid with errors. It enhanced mutation rates of the target plasmid up to 2.3 × 10⁵-fold with only a 78-fold increase in off-target mutagenesis. It was used to evolve itself to increase error rate and increase the efficiency of an efflux pump while simultaneously expanding the substrate repertoire. TADR enables multiple simultaneous substitutions to discover functions inaccessible by accumulating single substitutions, affording potential for solving hard problems in molecular evolution and developing biologic drugs and industrial catalysts.

Pleiotropy enables specific and accurate signaling in the presence of ligand cross talk

Living cells sense their environment through the binding of extracellular molecular ligands to cell surface receptors. Puzzlingly, vast numbers of signaling pathways exhibit a high degree of cross talk between different signals whereby different ligands act through the same receptor or shared components downstream. It remains unclear how a cell can accurately process information from the environment in such cross-wired pathways. We show that a feature which commonly accompanies cross talk-signaling pleiotropy (the ability of a receptor to produce multiple outputs)-offers a solution to the cross-talk problem. In a minimal model we show that a single pleiotropic receptor can simultaneously identify and accurately sense the concentrations of arbitrary unknown ligands present individually or in a mixture. We calculate the fundamental limits of the signaling specificity and accuracy of such signaling schemes. The model serves as an elementary "building block" toward understanding more complex cross-wired receptor-ligand signaling networks.

The role of energy cost on accuracy, sensitivity, specificity, speed and adaptation of T cell foreign and self recognition

The critical role of energy consumption in biological systems including T cell discrimination process has been investigated in various ways. The kinetic proofreading (KPR) in T cell recognition involving different levels of energy dissipation influences functional outcomes such as error rates and specificity. In this work, we study quantitatively how the energy cost influences error fractions, sensitivity, specificity, kinetic speed in terms of Mean First Passage Time (MFPT) and adaption errors. These provide the background to adequately understand T cell dynamics. It is found that energy plays a central role in the system that aims to achieve minimum error fractions and maximum sensitivity and specificity with the fastest speed under our kinetic scheme for which numerical values of kinetic parameters are specially chosen, but such a condition can be broken with varying data. Starting with the application of steady state approximation (SSA) to the evaluation of the concentration of each complex produced associated with KPR, which is used to quantify various observables, we present both analytical and numerical results in detail.

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.

Theoretical Analysis Reveals the Cost and Benefit of Proofreading in Coronavirus Genome Replication

Severe acute respiratory syndrome coronaviruses have unusually large RNA genomes replicated by a multiprotein complex containing an RNA-dependent RNA polymerase (RdRp). Exonuclease activity enables the RdRp complex to remove wrongly incorporated bases via proofreading, a process not utilized by other RNA viruses. However, it is unclear why the RdRp complex needs proofreading and what the associated trade-offs are. Here we investigate the interplay among the accuracy, speed, and energetic cost of proofreading in the RdRp complex using a kinetic model and bioinformatics analysis. We find that proofreading nearly optimizes the rate of functional virus production. However, we find that further optimization would lead to a significant increase in the proofreading cost. Unexpected importance of the cost minimization is further supported by other global analyses. We speculate that cost optimization could help avoid cell defense responses. Thus, proofreading is essential for the production of functional viruses, but its rate is limited by energy costs.

Nonequilibrium Thermodynamics in Biochemical Systems and Its Application

Living systems are open systems, where the laws of nonequilibrium thermodynamics play the important role. Therefore, studying living systems from a nonequilibrium thermodynamic aspect is interesting and useful. In this review, we briefly introduce the history and current development of nonequilibrium thermodynamics, especially that in biochemical systems. We first introduce historically how people realized the importance to study biological systems in the thermodynamic point of view. We then introduce the development of stochastic thermodynamics, especially three landmarks: Jarzynski equality, Crooks' fluctuation theorem and thermodynamic uncertainty relation. We also summarize the current theoretical framework for stochastic thermodynamics in biochemical reaction networks, especially the thermodynamic concepts and instruments at nonequilibrium steady state. Finally, we show two applications and research paradigms for thermodynamic study in biological systems.

Do We Understand the Mechanisms Used by Biological Systems to Correct Their Errors?

Most cellular processes involved in biological information processing display a surprisingly low error rate despite the stochasticity of the underlying biochemical reactions and the presence of competing chemical species. Such high fidelity is the result of nonequilibrium kinetic proofreading mechanisms, i.e., the existence of dissipative pathways for correcting the reactions that went in the wrong direction. While proofreading was often studied from the perspective of error minimization, a number of recent studies have demonstrated that the underlying mechanisms need to consider the interplay of other characteristic properties such as speed, energy dissipation, and noise reduction. Here, we present current views and new insights on the mechanisms of error-correction phenomena and various trade-off scenarios in the optimization of the functionality of biological systems. Existing challenges and future directions are also discussed.

Relaxation Times of Ligand-Receptor Complex Formation Control T Cell Activation

One of the most important functions of immune T cells is to recognize the presence of the pathogen-derived ligands and to quickly respond to them while at the same time not responding to its own ligands. This is known as absolute discrimination, and it is one of the most challenging phenomena to explain. The effectiveness of pathogen detection by T cell receptor is limited by chemical similarity of foreign and self-peptides and very low concentrations of foreign ligands. We propose a new mechanism of how absolute discrimination by T cells might function. It is suggested that the decision to activate or not to activate the immune response is controlled by the time to reach the stationary concentration of the T-cell-receptor-ligand-activated complex, which transfers the signal to downstream cellular biochemical networks. Our theoretical method models T cell receptor phosphorylation events as a sequence of stochastic transitions between discrete biochemical states, and this allows us to explicitly describe the dynamical properties of the system. It is found that the proposed criterion on the relaxation times is able to explain available experimental observations. In addition, we suggest that the level of stochastic noise might be an additional factor in the activation mechanisms. Furthermore, our theoretical approach explicitly analyzes the relationships between speed, sensitivity, and specificity of T cell functioning, which are the main characteristics of the process. Thus, it clarifies the molecular picture of T cell activation in immune response.

A systems-biology approach to molecular machines: Exploration of alternative transporter mechanisms

Motivated by growing evidence for pathway heterogeneity and alternative functions of molecular machines, we demonstrate a computational approach for investigating two questions: (1) Are there multiple mechanisms (state-space pathways) by which a machine can perform a given function, such as cotransport across a membrane? (2) How can additional functionality, such as proofreading/error-correction, be built into machine function using standard biochemical processes? Answers to these questions will aid both the understanding of molecular-scale cell biology and the design of synthetic machines. Focusing on transport in this initial study, we sample a variety of mechanisms by employing Metropolis Markov chain Monte Carlo. Trial moves adjust transition rates among an automatically generated set of conformational and binding states while maintaining fidelity to thermodynamic principles and a user-supplied fitness/functionality goal. Each accepted move generates a new model. The simulations yield both single and mixed reaction pathways for cotransport in a simple environment with a single substrate along with a driving ion. In a “competitive” environment including an additional decoy substrate, several qualitatively distinct reaction pathways are found which are capable of extremely high discrimination coupled to a leak of the driving ion, akin to proofreading. The array of functional models would be difficult to find by intuition alone in the complex state-spaces of interest.

Molecular machines, which operate on the nanoscale, are proteins/complexes that perform remarkable tasks such as the selective absorption of nutrients into the cell by transporters. These complex machines are often described using a fairly simple set of states and transitions that may not account for the stochasticity and heterogeneity generally expected at the nanoscale at body temperature. New tools are needed to study the full array of possibilities. This study presents a novel in silico method to systematically generate testable molecular-machine kinetic models and explore alternative mechanisms, applied first to membrane transport proteins. Our initial results suggest these transport machines may contain mechanisms which ‘detoxify’ the cell of an unwanted toxin, as well as significantly discriminate against the import of the toxin. This novel approach should aid the experimental study of key physiological processes such as renal glucose re-absorption, rational drug design, and potentially the development of synthetic machines.

A kinetic mechanism for enhanced selectivity of membrane transport

Membrane transport is generally thought to occur via an alternating access mechanism in which the transporter adopts at least two states, accessible from two different sides of the membrane to exchange substrates from the extracellular environment and the cytoplasm or from the cytoplasm and the intracellular matrix of the organelles (only in eukaryotes). In recent years, a number of high resolution structures have supported this general framework for a wide class of transport molecules, although additional states along the transport pathway are emerging as critically important. Given that substrate binding is often weak in order to enhance overall transport rates, there exists the distinct possibility that transporters may transport the incorrect substrate. This is certainly the case for many pharmaceutical compounds that are absorbed in the gut or cross the blood brain barrier through endogenous transporters. Docking studies on the bacterial sugar transporter vSGLT reveal that many highly toxic compounds are compatible with binding to the orthosteric site, further motivating the selective pressure for additional modes of selectivity. Motivated by recent work in which we observed failed substrate delivery in a molecular dynamics simulation where the energized ion still goes down its concentration gradient, we hypothesize that some transporters evolved to harness this 'slip' mechanism to increase substrate selectivity and reduce the uptake of toxic molecules. Here, we test this idea by constructing and exploring a kinetic transport model that includes a slip pathway. While slip reduces the overall productive flux, when coupled with a second toxic molecule that is more prone to slippage, the overall substrate selectivity dramatically increases, suppressing the accumulation of the incorrect compound. We show that the mathematical framework for increased substrate selectivity in our model is analogous to the classic proofreading mechanism originally proposed for tRNA synthase; however, because the transport cycle is reversible we identified conditions in which the selectivity is essentially infinite and incorrect substrates are exported from the cell in a 'detoxification' mode. The cellular consequences of proofreading and membrane slippage are discussed as well as the impact on future drug development.

Trade-Offs between Speed, Accuracy, and Dissipation in tRNAIle Aminoacylation

Living systems maintain a high fidelity in information processing through kinetic proofreading, a mechanism for preferentially removing incorrect substrates at the cost of energy dissipation and slower speed. Proofreading mechanisms must balance their demand for higher speed, fewer errors, and lower dissipation, but it is unclear how rates of individual reaction steps are evolutionarily tuned to balance these needs, especially when multiple proofreading mechanisms are present. Here, using a discrete-state stochastic model, we analyze the optimization strategies in Escherichia coli isoleucyl-tRNA synthetase. Surprisingly, this enzyme adopts an economic proofreading strategy and improves speed and dissipation as long as the error is tolerable. Through global parameter sampling, we reveal a fundamental dissipation-error relation that bounds the enzyme's optimal performance and explains the importance of the post-transfer editing mechanism. The proximity of native system parameters to this bound demonstrates the importance of energy dissipation as an evolutionary force affecting fitness.

Kinetic control of stationary flux ratios for a wide range of biochemical processes

One of the most intriguing features of biological systems is their ability to regulate the steady-state fluxes of the underlying biochemical reactions; however, the regulatory mechanisms and their physicochemical properties are not fully understood. Fundamentally, flux regulation can be explained with a chemical kinetic formalism describing the transitions between discrete states, with the reaction rates defined by an underlying free energy landscape. Which features of the energy landscape affect the flux distribution? Here we prove that the ratios of the steady-state fluxes of quasi-first-order biochemical processes are invariant to energy perturbations of the discrete states and are only affected by the energy barriers. In other words, the nonequilibrium flux distribution is under kinetic and not thermodynamic control. We illustrate the generality of this result for three biological processes. For the network describing protein folding along competing pathways, the probabilities of proceeding via these pathways are shown to be invariant to the stability of the intermediates or to the presence of additional misfolded states. For the network describing protein synthesis, the error rate and the energy expenditure per peptide bond is proven to be independent of the stability of the intermediate states. For molecular motors such as myosin-V, the ratio of forward to backward steps and the number of adenosine 5'-triphosphate (ATP) molecules hydrolyzed per step is demonstrated to be invariant to energy perturbations of the intermediate states. These findings place important constraints on the ability of mutations and drug perturbations to affect the steady-state flux distribution for a wide class of biological processes.

Thermodynamic Cost, Speed, Fluctuations, and Error Reduction of Biological Copy Machines

Due to large fluctuations in cellular environments, transfer of information in biological processes without regulation is error-prone. The mechanistic details of error-reducing mechanisms in biological copying processes have been a subject of active research; however, how error reduction of a process is balanced with its thermodynamic cost and dynamical properties remain largely unexplored. Here, we study the error reducing strategies in light of the recently discovered thermodynamic uncertainty relation (TUR) that sets a physical bound to the cost-precision trade-off for dissipative processes. We found that the two representative copying processes, DNA replication by the exonuclease-deficient T7 DNA polymerase and mRNA translation by the E. coli ribosome, reduce the error rates to biologically acceptable levels while also optimizing the processes close to the physical limit dictated by TUR.

Global mistranslation increases cell survival under stress in Escherichia coli

Mistranslation is typically deleterious for cells, although specific mistranslated proteins can confer a short-term benefit in a particular environment. However, given its large overall cost, the prevalence of high global mistranslation rates remains puzzling. Altering basal mistranslation levels of Escherichia coli in several ways, we show that generalized mistranslation enhances early survival under DNA damage, by rapidly activating the SOS response. Mistranslating cells maintain larger populations after exposure to DNA damage, and thus have a higher probability of sampling critical beneficial mutations. Both basal and artificially increased mistranslation increase the number of cells that are phenotypically tolerant and genetically resistant under DNA damage; they also enhance survival at high temperature. In contrast, decreasing the normal basal mistranslation rate reduces cell survival. This wide-ranging stress resistance relies on Lon protease, which is revealed as a key effector that induces the SOS response in addition to alleviating proteotoxic stress. The new links between error-prone protein synthesis, DNA damage, and generalised stress resistance indicate surprising coordination between intracellular stress responses and suggest a novel hypothesis to explain high global mistranslation rates.

Promiscuous Ribozymes and Their Proposed Role in Prebiotic Evolution

The ability of enzymes, including ribozymes, to catalyze side reactions is believed to be essential to the evolution of novel biochemical activities. It has been speculated that the earliest ribozymes, whose emergence marked the origin of life, were low in activity but high in promiscuity, and that these early ribozymes gave rise to specialized descendants with higher activity and specificity. Here, we review the concepts related to promiscuity and examine several cases of highly promiscuous ribozymes. We consider the evidence bearing on the question of whether de novo ribozymes would be quantitatively more promiscuous than later evolved ribozymes or protein enzymes. We suggest that while de novo ribozymes appear to be promiscuous in general, they are not obviously more promiscuous than more highly evolved or active sequences. Promiscuity is a trait whose value would depend on selective pressures, even during prebiotic evolution.

Kinetic proofreading and the limits of thermodynamic uncertainty

To mitigate errors induced by the cell's heterogeneous noisy environment, its main information channels and production networks utilize the kinetic proofreading (KPR) mechanism. Here, we examine two extensively studied KPR circuits, DNA replication by the T7 DNA polymerase and translation by the E. coli ribosome. Using experimental data, we analyze the performance of these two vital systems in light of the fundamental bounds set by the recently discovered thermodynamic uncertainty relation (TUR), which places an inherent trade-off between the precision of a desirable output and the amount of energy dissipation required. We show that the DNA polymerase operates close to the TUR lower bound, while the ribosome operates ∼5 times farther from this bound. This difference originates from the enhanced binding discrimination of the polymerase which allows it to operate effectively as a reduced reaction cycle prioritizing correct product formation. We show that approaching this limit also decouples the thermodynamic uncertainty factor from speed and error, thereby relaxing the accuracy-speed trade-off of the system. Altogether, our results show that operating near this reduced cycle limit not only minimizes thermodynamic uncertainty, but also results in global performance enhancement of KPR circuits.

Allostery and Kinetic Proofreading

Kinetic proofreading is an error correction mechanism present in the processes of the central dogma and beyond and typically requires the free energy of nucleotide hydrolysis for its operation. Though the molecular players of many biological proofreading schemes are known, our understanding of how energy consumption is managed to promote fidelity remains incomplete. In our work, we introduce an alternative conceptual scheme called "the piston model of proofreading" in which enzyme activation through hydrolysis is replaced with allosteric activation achieved through mechanical work performed by a piston on regulatory ligands. Inspired by Feynman's ratchet and pawl mechanism, we consider a mechanical engine designed to drive the piston actions powered by a lowering weight, whose function is analogous to that of ATP synthase in cells. Thanks to its mechanical design, the piston model allows us to tune the "knobs" of the driving engine and probe the graded changes and trade-offs between speed, fidelity, and energy dissipation. It provides an intuitive explanation of the conditions necessary for optimal proofreading and reveals the unexpected capability of allosteric molecules to beat the Hopfield limit of fidelity by leveraging the diversity of states available to them. The framework that we have built for the piston model can also serve as a basis for additional studies of driven biochemical systems.

Assembly of heteropolymers via a network of reaction coordinates

In biochemistry, heteropolymers encoding biological information are assembled out of equilibrium by sequentially incorporating available monomers found in the environment. Current models of polymerization treat monomer incorporation as a sequence of discrete chemical reactions between intermediate metastable states. In this paper, we use ideas from reaction rate theory and describe nonequilibrium assembly of a heteropolymer via a continuous reaction coordinate. Our approach allows for estimating the copy error and incorporation speed from the Gibbs free energy landscape of the process. We apply our theory to several examples from a simple reaction characterized by a free energy barrier to more complex cases incorporating error correction mechanisms, such as kinetic proofreading.

Theory of Nonequilibrium Free Energy Transduction by Molecular Machines

Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they face a distinct set of challenges compared with more familiar human-engineered macroscopic machines. Here we review central questions in their performance as free energy transducers, outline theoretical and modeling approaches to understand these questions, identify both physical limits on their operational characteristics and design principles for improving performance, and discuss emerging areas of research.