A role for conformational changes in enzyme catalysis.

The role played by conformational changes in enzyme catalysis is controversial. In addition to examining specific enzymes, studying formal models can help identify the conditions under which conformational changes promote catalysis. Here, we present a model demonstrating how conformational changes can break a generic trade-off due to the conflicting requirements of successive steps in catalytic cycles, namely high specificity for the transition state to accelerate the chemical transformation and low affinity for the products to favor their release. The mechanism by which the trade-off is broken is a transition between conformations with different affinities for the substrate. The role of the effector that induces the transition is played by a substrate "handle," a part of the substrate that is not chemically transformed but whose interaction with the enzyme is nevertheless essential to rapidly complete the catalytic cycle. A key element of the model is the formalization of the constraints causing the trade-off that the presence of multiple states breaks, which we attribute to the strong chemical similarity between successive reaction states-substrates, transition states, and products. For the sake of clarity, we present our model for irreversible one-step unimolecular reactions. In this context, we demonstrate how the different forms that chemical similarities between reaction states can take impose limits on the overall catalytic turnover. We first analyze catalysts without internal degrees of freedom and then show how two-state catalysts can overcome their limitations. Our results recapitulate previous proposals concerning the role of conformational changes and substrate handles in a formalism that makes explicit the constraints that elicit these features. In addition, our approach establishes links with studies in the field of heterogeneous catalysis, where the same trade-offs are observed and where overcoming them is a well-recognized challenge.

On the exclusion of exponential autocatalysts by sub-exponential autocatalysts.

Selection among autocatalytic species fundamentally depends on their growth law: exponential species, whose number of copies grows exponentially, are mutually exclusive, while sub-exponential ones, whose number of copies grows polynomially, can coexist. Here we consider competitions between autocatalytic species with different growth laws and make the simple yet counterintuitive observation that sub-exponential species can exclude exponential ones while the reverse is, in principle, impossible. This observation has implications for scenarios pertaining to the emergence of natural selection.

On Kinetic Constraints That Catalysis Imposes on Elementary Processes.

Catalysis, the acceleration of product formation by a substance that is left unchanged, typically results from multiple elementary processes, including diffusion of the reactants toward the catalyst, chemical steps, and release of the products. While efforts to design catalysts are often focused on accelerating the chemical reaction on the catalyst, catalysis is a global property of the catalytic cycle that involves all processes. These are controlled by both intrinsic parameters such as the composition and shape of the catalyst and extrinsic parameters such as the concentration of the chemical species at play. We examine here the conditions that catalysis imposes on the different steps of a reaction cycle and the respective role of intrinsic and extrinsic parameters of the system on the emergence of catalysis by using an approach based on first-passage times. We illustrate this approach for various decompositions of a catalytic cycle into elementary steps, including non-Markovian decompositions, which are useful when the presence and nature of intermediate states are a priori unknown. Our examples cover different types of reactions and clarify the constraints on elementary steps and the impact of species concentrations on catalysis.

How Flexibility Can Enhance Catalysis.

Conformational changes are observed in many enzymes, but their role in catalysis is highly controversial. Here we present a theoretical model that illustrates how rigid catalysts can be fundamentally limited and how a conformational change induced by substrate binding can overcome this limitation, ultimately enabling barrier-free catalysis. The model is deliberately minimal, but the principle it illustrates is general and consistent with unique features of proteins as well as with previous informal proposals to explain the superiority of enzymes over other classes of catalysts. Implementing the discriminative switch suggested by the model could help overcome limitations currently encountered in the design of artificial catalysts.

Assessing in vivo the impact of gene context on transcription through DNA supercoiling.

Gene context can have significant impact on gene expression but is currently not integrated in quantitative models of gene regulation despite known biophysical principles and quantitative in vitro measurements. Conceptually, the simplest gene context consists of a single gene framed by two topological barriers, known as the twin transcriptional-loop model, which illustrates the interplay between transcription and DNA supercoiling. In vivo, DNA supercoiling is additionally modulated by topoisomerases, whose modus operandi remains to be quantified. Here, we bridge the gap between theory and in vivo properties by realizing in Escherichia coli the twin transcriptional-loop model and by measuring how gene expression varies with promoters and distances to the topological barriers. We find that gene expression depends on the distance to the upstream barrier but not to the downstream barrier, with a promoter-dependent intensity. We rationalize these findings with a first-principle biophysical model of DNA transcription. Our results are explained if TopoI and gyrase both act specifically, respectively upstream and downstream of the gene, with antagonistic effects of TopoI, which can repress initiation while facilitating elongation. Altogether, our work sets the foundations for a systematic and quantitative description of the impact of gene context on gene regulation.

The context of genes, particularly the arrangement of neighboring genes along the DNA, exerts an important impact on their expression. However, predicting this impact remains challenging due to the complex interplay of concurrent mechanisms. To gain a quantitative understanding, we experimentally implemented the simplest possible theoretical model, isolating a gene from its neighboring genes. This allowed us to investigate the role of DNA's mechanical and topological properties, along with the enzymes that shape these properties, including RNA polymerases and topoisomerases. Comparison of the experimental results to a mathematical model based on physical principles allowed us to parametrize the operating mode of topoisomerases. Our work paves the way towards a systematic understanding of the role of gene context in gene expression.

Multilevel selection in the evolution of sexual dimorphism in phenotypic plasticity.

Phenotypes are partly shaped by the environment, which can impact both short-term adaptation and long-term evolution. In dioecious species, the two sexes may exhibit different degrees of phenotypic plasticity and theoretical models indicate that such differences may confer an adaptive advantage when the population is subject to directional selection, either because of a systematically varying environment or a load of deleterious mutations. The effect stems from the fundamental asymmetry between the two sexes: female fertility is more limited than male fertility. Whether this asymmetry is sufficient for sexual dimorphism in phenotypic plasticity to evolve is, however, not obvious. Here, we show that even in conditions where it provides an adaptive advantage, dimorphic phenotypic plasticity may be evolutionarily unstable due to sexual selection. This is the case, in particular, for panmictic populations where mating partnerships are formed at random. However, we show that the effects of sexual selection can be counteracted when mating occurs within groups of related individuals. Under this condition, sexual dimorphism in phenotypic plasticity can not only evolve but offset the twofold cost of males. We demonstrate these points with a simple mathematical model through a combination of analytical and numerical results.

Computational design of a minimal catalyst using colloidal particles with programmable interactions.

Catalysis, the acceleration of chemical reactions by molecules that are not consumed in the process, is essential to living organisms but remains absent in physical systems that aspire to emulate biological functionalities with artificial components. Here we demonstrate how to design a catalyst using spherical building blocks interacting via programmable potentials, and show that a minimal catalyst design, a rigid dimer, can accelerate a ubiquitous elementary reaction, the cleaving of a bond. Combining coarse-grained molecular dynamics simulations and theory, and by comparing the mean reaction time for bond dissociation in the presence and absence of the catalyst, we derive geometrical and physical constraints for its design and determine the reaction conditions under which catalysis emerges in the system. The framework and design rules that we introduce are general and can be applied to experimental systems on a wide range of scales, from micron size DNA-coated colloids to magnetic handshake materials in the macroscale, opening the door to the realization of self-regulated artificial systems with bio-inspired functionalities.

Undersampling and the inference of coevolution in proteins.

Protein structure, function, and evolution depend on local and collective epistatic interactions between amino acids. A powerful approach to defining these interactions is to construct models of couplings between amino acids that reproduce the empirical statistics (frequencies and correlations) observed in sequences comprising a protein family. The top couplings are then interpreted. Here, we show that as currently implemented, this inference unequally represents epistatic interactions, a problem that fundamentally arises from limited sampling of sequences in the context of distinct scales at which epistasis occurs in proteins. We show that these issues explain the ability of current approaches to predict tertiary contacts between amino acids and the inability to obviously expose larger networks of functionally relevant, collectively evolving residues called sectors. This work provides a necessary foundation for more deeply understanding and improving evolution-based models of proteins.

Natural Selection beyond Life? A Workshop Report.

Natural selection is commonly seen not just as an explanation for adaptive evolution, but as the inevitable consequence of "heritable variation in fitness among individuals". Although it remains embedded in biological concepts, such a formalisation makes it tempting to explore whether this precondition may be met not only in life as we know it, but also in other physical systems. This would imply that these systems are subject to natural selection and may perhaps be investigated in a biological framework, where properties are typically examined in light of their putative functions. Here we relate the major questions that were debated during a three-day workshop devoted to discussing whether natural selection may take place in non-living physical systems. We start this report with a brief overview of research fields dealing with "life-like" or "proto-biotic" systems, where mimicking evolution by natural selection in test tubes stands as a major objective. We contend the challenge may be as much conceptual as technical. Taking the problem from a physical angle, we then discuss the framework of dissipative structures. Although life is viewed in this context as a particular case within a larger ensemble of physical phenomena, this approach does not provide general principles from which natural selection can be derived. Turning back to evolutionary biology, we ask to what extent the most general formulations of the necessary conditions or signatures of natural selection may be applicable beyond biology. In our view, such a cross-disciplinary jump is impeded by reliance on individuality as a central yet implicit and loosely defined concept. Overall, these discussions thus lead us to conjecture that understanding, in physico-chemical terms, how individuality emerges and how it can be recognised, will be essential in the search for instances of evolution by natural selection outside of living systems.

Sex as information processing: Optimality and evolution.

The long-term growth rate of populations in varying environments quantifies the evolutionary value of processing the information that biological individuals inherit from their ancestors and acquire from their environment. Previous models were limited to asexual reproduction with inherited information coming from a single parent with no recombination. We present a general extension to sexual reproduction and an analytical solution for a particular but important case, the infinitesimal model of quantitative genetics which assumes traits to be normally distributed. We study with this model the conditions under which sexual reproduction is advantageous and can evolve in the context of autocorrelated or directionally varying environments, mutational biases, spatial heterogeneities, and phenotypic plasticity. Our results generalize and unify previous analyses. We also examine the proposal made by Geodakyan that the presence of two phenotypically distinct sexes permits an optimal adaptation to varying environments. We verify that conditions exists where sexual dimorphism is adaptive but find that its evolutionary value does not generally compensate for the twofold cost of males.

Parameters and determinants of responses to selection in antibody libraries.

The sequences of antibodies from a given repertoire are highly diverse at few sites located on the surface of a genome-encoded larger scaffold. The scaffold is often considered to play a lesser role than highly diverse, non-genome-encoded sites in controlling binding affinity and specificity. To gauge the impact of the scaffold, we carried out quantitative phage display experiments where we compare the response to selection for binding to four different targets of three different antibody libraries based on distinct scaffolds but harboring the same diversity at randomized sites. We first show that the response to selection of an antibody library may be captured by two measurable parameters. Second, we provide evidence that one of these parameters is determined by the degree of affinity maturation of the scaffold, affinity maturation being the process by which antibodies accumulate somatic mutations to evolve towards higher affinities during the natural immune response. In all cases, we find that libraries of antibodies built around maturated scaffolds have a lower response to selection to other arbitrary targets than libraries built around germline-based scaffolds. We thus propose that germline-encoded scaffolds have a higher selective potential than maturated ones as a consequence of a selection for this potential over the long-term evolution of germline antibody genes. Our results are a first step towards quantifying the evolutionary potential of biomolecules.

Geometry and Flexibility of Optimal Catalysts in a Minimal Elastic Model.

We have general knowledge of the principles by which catalysts accelerate the rate of chemical reactions but no precise understanding of the geometrical and physical constraints to which their design is subject. To analyze these constraints, we introduce a minimal model of catalysis based on elastic networks where the implications of the geometry and flexibility of a catalyst can be studied systematically. The model demonstrates the relevance and limitations of the principle of transition-state stabilization: optimal catalysts are found to have a geometry complementary to the transition state but a degree of flexibility that nontrivially depends on the parameters of the reaction as well as on external parameters such as the concentrations of reactants and products. The results illustrate how simple physical models can provide valuable insights into the design of catalysts.

Parsimonious evolutionary scenario for the origin of allostery and coevolution patterns in proteins.

Proteins display generic properties that are challenging to explain by direct selection, notably allostery, the capacity to be regulated through long-range effects, and evolvability, the capacity to adapt to new selective pressures. An evolutionary scenario is proposed where proteins acquire these two features indirectly as a by-product of their selection for a more fundamental property, exquisite discrimination, the capacity to bind discriminatively very similar ligands. Achieving this task is shown to typically require proteins to undergo a conformational change. We argue that physical and evolutionary constraints impel this change to be controlled by a group of sites extending from the binding site. Proteins can thus acquire a latent potential for allosteric regulation and evolutionary adaptation because of long-range effects that initially arise as evolutionary spandrels. This scenario accounts for the groups of conserved and coevolving residues observed in multiple sequence alignments. However, we propose that most pairs of coevolving and contacting residues inferred from such alignments have a different origin, related to thermal stability. A physical model is presented that illustrates this evolutionary scenario and its implications. The scenario can be implemented in experiments of protein evolution to directly test its predictions.

A Two-Enzyme Adaptive Unit within Bacterial Folate Metabolism.

Enzyme function and evolution are influenced by the larger context of a metabolic pathway. Deleterious mutations or perturbations in one enzyme can often be compensated by mutations to others. We used comparative genomics and experiments to examine evolutionary interactions with the essential metabolic enzyme dihydrofolate reductase (DHFR). Analyses of synteny and co-occurrence across bacterial species indicate that DHFR is coupled to thymidylate synthase (TYMS) but relatively independent from the rest of folate metabolism. Using quantitative growth rate measurements and forward evolution in Escherichia coli, we demonstrate that the two enzymes adapt as a relatively independent unit in response to antibiotic stress. Metabolomic profiling revealed that TYMS activity must not exceed DHFR activity to prevent the depletion of reduced folates and the accumulation of the intermediate dihydrofolate. Comparative genomics analyses identified >200 gene pairs with similar statistical signatures of modular co-evolution, suggesting that cellular pathways may be decomposable into small adaptive units.

Universal and idiosyncratic characteristic lengths in bacterial genomes.

In condensed matter physics, simplified descriptions are obtained by coarse-graining the features of a system at a certain characteristic length, defined as the typical length beyond which some properties are no longer correlated. From a physics standpoint, in vitro DNA has thus a characteristic length of 300 base pairs (bp), the Kuhn length of the molecule beyond which correlations in its orientations are typically lost. From a biology standpoint, in vivo DNA has a characteristic length of 1000 bp, the typical length of genes. Since bacteria live in very different physico-chemical conditions and since their genomes lack translational invariance, whether larger, universal characteristic lengths exist is a non-trivial question. Here, we examine this problem by leveraging the large number of fully sequenced genomes available in public databases. By analyzing GC content correlations and the evolutionary conservation of gene contexts (synteny) in hundreds of bacterial chromosomes, we conclude that a fundamental characteristic length around 10-20 kb can be defined. This characteristic length reflects elementary structures involved in the coordination of gene expression, which are present all along the genome of nearly all bacteria. Technically, reaching this conclusion required us to implement methods that are insensitive to the presence of large idiosyncratic genomic features, which may co-exist along these fundamental universal structures.

Transitions in optimal adaptive strategies for populations in fluctuating environments.

Biological populations are subject to fluctuating environmental conditions. Different adaptive strategies can allow them to cope with these fluctuations: specialization to one particular environmental condition, adoption of a generalist phenotype that compromises between conditions, or population-wise diversification (bet hedging). Which strategy provides the largest selective advantage in the long run depends on the range of accessible phenotypes and the statistics of the environmental fluctuations. Here, we analyze this problem in a simple mathematical model of population growth. First, we review and extend a graphical method to identify the nature of the optimal strategy when the environmental fluctuations are uncorrelated. Temporal correlations in environmental fluctuations open up new strategies that rely on memory but are mathematically challenging to study: We present analytical results to address this challenge. We illustrate our general approach by analyzing optimal adaptive strategies in the presence of trade-offs that constrain the range of accessible phenotypes. Our results extend several previous studies and have applications to a variety of biological phenomena, from antibiotic resistance in bacteria to immune responses in vertebrates.

Diversity of immune strategies explained by adaptation to pathogen statistics.

Biological organisms have evolved a wide range of immune mechanisms to defend themselves against pathogens. Beyond molecular details, these mechanisms differ in how protection is acquired, processed, and passed on to subsequent generations-differences that may be essential to long-term survival. Here, we introduce a mathematical framework to compare the long-term adaptation of populations as a function of the pathogen dynamics that they experience and of the immune strategy that they adopt. We find that the two key determinants of an optimal immune strategy are the frequency and the characteristic timescale of the pathogens. Depending on these two parameters, our framework identifies distinct modes of immunity, including adaptive, innate, bet-hedging, and CRISPR-like immunities, which recapitulate the diversity of natural immune systems.

Evolution-Based Functional Decomposition of Proteins.

The essential biological properties of proteins-folding, biochemical activities, and the capacity to adapt-arise from the global pattern of interactions between amino acid residues. The statistical coupling analysis (SCA) is an approach to defining this pattern that involves the study of amino acid coevolution in an ensemble of sequences comprising a protein family. This approach indicates a functional architecture within proteins in which the basic units are coupled networks of amino acids termed sectors. This evolution-based decomposition has potential for new understandings of the structural basis for protein function. To facilitate its usage, we present here the principles and practice of the SCA and introduce new methods for sector analysis in a python-based software package (pySCA). We show that the pattern of amino acid interactions within sectors is linked to the divergence of functional lineages in a multiple sequence alignment-a model for how sector properties might be differentially tuned in members of a protein family. This work provides new tools for studying proteins and for generally testing the concept of sectors as the principal units of function and adaptive variation.

Conserved Units of Co-Expression in Bacterial Genomes: An Evolutionary Insight into Transcriptional Regulation.

Genome-wide measurements of transcriptional activity in bacteria indicate that the transcription of successive genes is strongly correlated beyond the scale of operons. Here, we analyze hundreds of bacterial genomes to identify supra-operonic segments of genes that are proximal in a large number of genomes. We show that these synteny segments correspond to genomic units of strong transcriptional co-expression. Structurally, the segments contain operons with specific relative orientations (co-directional or divergent) and nucleoid-associated proteins are found to bind at their boundaries. Functionally, operons inside a same segment are highly co-expressed even in the apparent absence of regulatory factors at their promoter regions. Remote operons along DNA can also be co-expressed if their corresponding segments share a transcriptional or sigma factor, without requiring these factors to bind directly to the promoters of the operons. As evidence that these results apply across the bacterial kingdom, we demonstrate them both in the Gram-negative bacterium Escherichia coli and in the Gram-positive bacterium Bacillus subtilis. The underlying process that we propose involves only RNA-polymerases and DNA: it implies that the transcription of an operon mechanically enhances the transcription of adjacent operons. In support of a primary role of this regulation by facilitated co-transcription, we show that the transcription en bloc of successive operons as a result of transcriptional read-through is strongly and specifically enhanced in synteny segments. Finally, our analysis indicates that facilitated co-transcription may be evolutionary primitive and may apply beyond bacteria.