Roles of mutation and recombination in the evolution of protein thermodynamics

Genome-wide identification and expression analysis of the SET domain-containing gene family in potato (Solanum tuberosum L.)

Genes containing the SET domain can catalyse histone lysine methylation, which in turn has the potential to cause changes to chromatin structure and regulation of the transcription of genes involved in diverse physiological and developmental processes. However, the functions of SET domain-containing (StSET) genes in potato still need to be studied. The objectives of our study can be summarized as in silico analysis to (i) identify StSET genes in the potato genome, (ii) systematically analyse gene structure, chromosomal distribution, gene duplication events, promoter sequences, and protein domains, (iii) perform phylogenetic analyses, (iv) compare the SET domain-containing genes of potato with other plant species with respect to protein domains and orthologous relationships, (v) analyse tissue-specific expression, and (vi) study the expression of StSET genes in response to drought and heat stresses. In this study, we identified 57 StSET genes in the potato genome, and the genes were physically mapped onto eleven chromosomes. The phylogenetic analysis grouped these StSET genes into six clades. We found that tandem duplication through sub-functionalisation has contributed only marginally to the expansion of the StSET gene family. The protein domain TDBD (PFAM ID: PF16135) was detected in StSET genes of potato while it was absent in all other previously studied species. This study described three pollen-specific StSET genes in the potato genome. Expression analysis of four StSET genes under heat and drought in three potato clones revealed that these genes might have non-overlapping roles under different abiotic stress conditions and durations. The present study provides a comprehensive analysis of StSET genes in potatoes, and it serves as a basis for further functional characterisation of StSET genes towards understanding their underpinning biological mechanisms in conferring stress tolerance.

Consequences of Genetic Recombination on Protein Folding Stability

Genetic recombination is a common evolutionary mechanism that produces molecular diversity. However, its consequences on protein folding stability have not attracted the same attention as in the case of point mutations. Here, we studied the effects of homologous recombination on the computationally predicted protein folding stability for several protein families, finding less detrimental effects than we previously expected. Although recombination can affect multiple protein sites, we found that the fraction of recombined proteins that are eliminated by negative selection because of insufficient stability is not significantly larger than the corresponding fraction of proteins produced by mutation events. Indeed, although recombination disrupts epistatic interactions, the mean stability of recombinant proteins is not lower than that of their parents. On the other hand, the difference of stability between recombined proteins is amplified with respect to the parents, promoting phenotypic diversity. As a result, at least one third of recombined proteins present stability between those of their parents, and a substantial fraction have higher or lower stability than those of both parents. As expected, we found that parents with similar sequences tend to produce recombined proteins with stability close to that of the parents. Finally, the simulation of protein evolution along the ancestral recombination graph with empirical substitution models commonly used in phylogenetics, which ignore constraints on protein folding stability, showed that recombination favors the decrease of folding stability, supporting the convenience of adopting structurally constrained models when possible for inferences of protein evolutionary histories with recombination.

Conflicting effects of recombination on the evolvability and robustness in neutrally evolving populations

Understanding the benefits and costs of recombination under different scenarios of evolutionary adaptation remains an open problem for theoretical and experimental research. In this study, we focus on finite populations evolving on neutral networks comprising viable and unfit genotypes. We provide a comprehensive overview of the effects of recombination by jointly considering different measures of evolvability and mutational robustness over a broad parameter range, such that many evolutionary regimes are covered. We find that several of these measures vary non-monotonically with the rates of mutation and recombination. Moreover, the presence of unfit genotypes that introduce inhomogeneities in the network of viable states qualitatively alters the effects of recombination. We conclude that conflicting trends induced by recombination can be explained by an emerging trade-off between evolvability on the one hand, and mutational robustness on the other. Finally, we discuss how different implementations of the recombination scheme in theoretical models can affect the observed dependence on recombination rate through a coupling between recombination and genetic drift.

Physics of biomolecular recognition and conformational dynamics

Biomolecular recognition usually leads to the formation of binding complexes, often accompanied by large-scale conformational changes. This process is fundamental to biological functions at the molecular and cellular levels. Uncovering the physical mechanisms of biomolecular recognition and quantifying the key biomolecular interactions are vital to understand these functions. The recently developed energy landscape theory has been successful in quantifying recognition processes and revealing the underlying mechanisms. Recent studies have shown that in addition to affinity, specificity is also crucial for biomolecular recognition. The proposed physical concept of intrinsic specificity based on the underlying energy landscape theory provides a practical way to quantify the specificity. Optimization of affinity and specificity can be adopted as a principle to guide the evolution and design of molecular recognition. This approach can also be used in practice for drug discovery using multidimensional screening to identify lead compounds. The energy landscape topography of molecular recognition is important for revealing the underlying flexible binding or binding-folding mechanisms. In this review, we first introduce the energy landscape theory for molecular recognition and then address four critical issues related to biomolecular recognition and conformational dynamics: (1) specificity quantification of molecular recognition; (2) evolution and design in molecular recognition; (3) flexible molecular recognition; (4) chromosome structural dynamics. The results described here and the discussions of the insights gained from the energy landscape topography can provide valuable guidance for further computational and experimental investigations of biomolecular recognition and conformational dynamics.

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.

Quantifying the Mutational Robustness of Protein-Coding Genes

We use large-scale mutagenesis data and computer simulations to quantify the mutational robustness of protein-coding genes by taking into account constraints arising from protein function and the genetic code. Analyses of the distribution of amino acid substitutions from 18 mutagenesis studies revealed an average of 45% of neutral variants; while mutagenesis data of 12 proteins artificially designed under no other constraints but stability, reach an average of 60%. Simulations using a lattice protein model allow us to contrast these estimates to the expected mutational robustness of protein families by generating unbiased samples of foldable sequences, which we find to have 30% of neutral variants. In agreement with mutagenesis data of designed proteins, the model shows that maximally robust protein families might access up to twice the amount of neutral variants observed in the unbiased samples (i.e. 60%). A biophysical model of protein-ligand binding suggests that constraints associated to molecular function have only a moderate impact on robustness of approximately 5 to 10% of neutral variants; and that the direction of this effect depends on the relation between functional performance and thermodynamic stability. Although the genetic code constraints the access of a gene's nucleotide sequence to only 30% of the full distribution of amino acid mutations, it provides an extra 15 to 20% of neutral variants to the estimations above, such that the expected, observed, and maximal robustness of protein-coding genes are approximately 50, 65, and 75%, respectively. We discuss our results in the light of three main hypothesis put forward to explain the existence of mutationally robust genes.

Funneled energy landscape unifies principles of protein binding and evolution

Most proteins have evolved to spontaneously fold into native structure and specifically bind with their partners for the purpose of fulfilling biological functions. According to Darwin, protein sequences evolve through random mutations, and only the fittest survives. The understanding of how the evolutionary selection sculpts the interaction patterns for both biomolecular folding and binding is still challenging. In this study, we incorporated the constraint of functional binding into the selection fitness based on the principle of minimal frustration for the underlying biomolecular interactions. Thermodynamic stability and kinetic accessibility were derived and quantified from a global funneled energy landscape that satisfies the requirements of both the folding into the stable structure and binding with the specific partner. The evolution proceeds via a bowl-like evolution energy landscape in the sequence space with a closed-ring attractor at the bottom. The sequence space is increasingly reduced until this ring attractor is reached. The molecular-interaction patterns responsible for folding and binding are identified from the evolved sequences, respectively. The residual positions participating in the interactions responsible for folding are highly conserved and maintain the hydrophobic core under additional evolutionary constraints of functional binding. The positions responsible for binding constitute a distributed network via coupling conservations that determine the specificity of binding with the partner. This work unifies the principles of protein binding and evolution under minimal frustration and sheds light on the evolutionary design of proteins for functions.

Recombination and mutational robustness in neutral fitness landscapes

Mutational robustness quantifies the effect of random mutations on fitness. When mutational robustness is high, most mutations do not change fitness or have only a minor effect on it. From the point of view of fitness landscapes, robust genotypes form neutral networks of almost equal fitness. Using deterministic population models it has been shown that selection favors genotypes inside such networks, which results in increased mutational robustness. Here we demonstrate that this effect is massively enhanced by recombination. Our results are based on a detailed analysis of mesa-shaped fitness landscapes, where we derive precise expressions for the dependence of the robustness on the landscape parameters for recombining and non-recombining populations. In addition, we carry out numerical simulations on different types of random holey landscapes as well as on an empirical fitness landscape. We show that the mutational robustness of a genotype generally correlates with its recombination weight, a new measure that quantifies the likelihood for the genotype to arise from recombination. We argue that the favorable effect of recombination on mutational robustness is a highly universal feature that may have played an important role in the emergence and maintenance of mechanisms of genetic exchange.

Superfunneled Energy Landscape of Protein Evolution Unifies the Principles of Protein Evolution, Folding, and Design

Evolution is essential for shaping the biological functions. Darwin proposed the selection as the driving force for evolution upon mutations. While mutations are clear, the quantification of the selection force is still challenging. In this study, we identified and quantified both thermodynamic stability and kinetic accessibility as the selection forces for protein evolution. The protein evolution can be viewed and quantified as a trajectory moving along a superfunneled energy landscape with a line attractor at the bottom. The resulting evolved sequences and structures show strong protein characteristics including the hydrophobic core, high designability, and fast folding. The evolution principle uncovered here is validated on real proteins and sheds light on the protein design.

Biophysics of protein evolution and evolutionary protein biophysics

The study of molecular evolution at the level of protein-coding genes often entails comparing large datasets of sequences to infer their evolutionary relationships. Despite the importance of a protein's structure and conformational dynamics to its function and thus its fitness, common phylogenetic methods embody minimal biophysical knowledge of proteins. To underscore the biophysical constraints on natural selection, we survey effects of protein mutations, highlighting the physical basis for marginal stability of natural globular proteins and how requirement for kinetic stability and avoidance of misfolding and misinteractions might have affected protein evolution. The biophysical underpinnings of these effects have been addressed by models with an explicit coarse-grained spatial representation of the polypeptide chain. Sequence-structure mappings based on such models are powerful conceptual tools that rationalize mutational robustness, evolvability, epistasis, promiscuous function performed by 'hidden' conformational states, resolution of adaptive conflicts and conformational switches in the evolution from one protein fold to another. Recently, protein biophysics has been applied to derive more accurate evolutionary accounts of sequence data. Methods have also been developed to exploit sequence-based evolutionary information to predict biophysical behaviours of proteins. The success of these approaches demonstrates a deep synergy between the fields of protein biophysics and protein evolution.

The effects of recombination on phenotypic exploration and robustness in evolution

Recombination is a commonly used genetic operator in artificial and computational evolutionary systems. It has been empirically shown to be essential for evolutionary processes. However, little has been done to analyze the effects of recombination on quantitative genotypic and phenotypic properties. The majority of studies only consider mutation, mainly due to the more serious consequences of recombination in reorganizing entire genomes. Here we adopt methods from evolutionary biology to analyze a simple, yet representative, genetic programming method, linear genetic programming. We demonstrate that recombination has less disruptive effects on phenotype than mutation, that it accelerates novel phenotypic exploration, and that it particularly promotes robust phenotypes and evolves genotypic robustness and synergistic epistasis. Our results corroborate an explanation for the prevalence of recombination in complex living organisms, and helps elucidate a better understanding of the evolutionary mechanisms involved in the design of complex artificial evolutionary systems and intelligent algorithms.

A nonadaptive origin of a beneficial trait: in silico selection for free energy of folding leads to the neutral emergence of mutational robustness in single domain proteins

Proteins are regarded as being robust to the deleterious effects of mutations. Here, the neutral emergence of mutational robustness in a population of single domain proteins is explored using computer simulations. A pairwise contact model was used to calculate the ΔG of folding (ΔG folding) using the three dimensional protein structure of leech eglin C. A random amino acid sequence with low mutational robustness, defined as the average ΔΔG resulting from a point mutation (ΔΔG average), was threaded onto the structure. A population of 1,000 threaded sequences was evolved under selection for stability, using an upper and lower energy threshold. Under these conditions, mutational robustness increased over time in the most common sequence in the population. In contrast, when the wild type sequence was used it did not show an increase in robustness. This implies that the emergence of mutational robustness is sequence specific and that wild type sequences may be close to maximal robustness. In addition, an inverse relationship between ∆∆G average and protein stability is shown, resulting partly from a larger average effect of point mutations in more stable proteins. The emergence of mutational robustness was also observed in the Escherichia coli colE1 Rop and human CD59 proteins, implying that the property may be common in single domain proteins under certain simulation conditions. The results indicate that at least a portion of mutational robustness in small globular proteins might have arisen by a process of neutral emergence, and could be an example of a beneficial trait that has not been directly selected for, termed a "pseudaptation."

Applying physics-based scoring to calculate free energies of binding for single amino acid mutations in protein-protein complexes

Predicting changes in protein binding affinity due to single amino acid mutations helps us better understand the driving forces underlying protein-protein interactions and design improved biotherapeutics. Here, we use the MM-GBSA approach with the OPLS2005 force field and the VSGB2.0 solvent model to calculate differences in binding free energy between wild type and mutant proteins. Crucially, we made no changes to the scoring model as part of this work on protein-protein binding affinity--the energy model has been developed for structure prediction and has previously been validated only for calculating the energetics of small molecule binding. Here, we compare predictions to experimental data for a set of 418 single residue mutations in 21 targets and find that the MM-GBSA model, on average, performs well at scoring these single protein residue mutations. Correlation between the predicted and experimental change in binding affinity is statistically significant and the model performs well at picking "hotspots," or mutations that change binding affinity by more than 1 kcal/mol. The promising performance of this physics-based method with no tuned parameters for predicting binding energies suggests that it can be transferred to other protein engineering problems.

Dynamic landscapes: a model of context and contingency in evolution

Although the basic mechanics of evolution have been understood since Darwin, debate continues over whether macroevolutionary phenomena are driven by the fitness structure of genotype space or by ecological interaction. In this paper we propose a simple model capturing key features of fitness-landscape and ecological models of evolution. Our model describes evolutionary dynamics in a high-dimensional, structured genotype space with interspecies interaction. We find promising qualitative similarity with the empirical facts about macroevolution, including broadly distributed extinction sizes and realistic exploration of the genotype space. The abstraction of our model permits numerous applications beyond macroevolution, including protein and RNA evolution.

Evolutionary dynamics on protein bi-stability landscapes can potentially resolve adaptive conflicts

Experimental studies have shown that some proteins exist in two alternative native-state conformations. It has been proposed that such bi-stable proteins can potentially function as evolutionary bridges at the interface between two neutral networks of protein sequences that fold uniquely into the two different native conformations. Under adaptive conflict scenarios, bi-stable proteins may be of particular advantage if they simultaneously provide two beneficial biological functions. However, computational models that simulate protein structure evolution do not yet recognize the importance of bi-stability. Here we use a biophysical model to analyze sequence space to identify bi-stable or multi-stable proteins with two or more equally stable native-state structures. The inclusion of such proteins enhances phenotype connectivity between neutral networks in sequence space. Consideration of the sequence space neighborhood of bridge proteins revealed that bi-stability decreases gradually with each mutation that takes the sequence further away from an exactly bi-stable protein. With relaxed selection pressures, we found that bi-stable proteins in our model are highly successful under simulated adaptive conflict. Inspired by these model predictions, we developed a method to identify real proteins in the PDB with bridge-like properties, and have verified a clear bi-stability gradient for a series of mutants studied by Alexander et al. (Proc Nat Acad Sci USA 2009, 106:21149–21154) that connect two sequences that fold uniquely into two different native structures via a bridge-like intermediate mutant sequence. Based on these findings, new testable predictions for future studies on protein bi-stability and evolution are discussed.

Proteins are essential molecules for performing a majority of functions in all biological systems. These functions often depend on the three-dimensional structures of proteins. Here, we investigate a fundamental question in molecular evolution: how can proteins acquire new advantageous structures via mutations while not sacrificing their existing structures that are still needed? Some authors have suggested that the same protein may adopt two or more alternative structures, switch between them and thus perform different functions with each of the alternative structures. Intuitively, such a protein could provide an evolutionary compromise between conflicting demands for existing and new protein structures. Yet no theoretical study has systematically tackled the biophysical basis of such compromises during evolutionary processes. Here we devise a model of evolution that specifically recognizes protein molecules that can exist in several different stable structures. Our model demonstrates that proteins can indeed utilize multiple structures to satisfy conflicting evolutionary requirements. In light of these results, we identify data from known protein structures that are consistent with our predictions and suggest novel directions for future investigation.

Quantifying protein modularity and evolvability: a comparison of different techniques

Modularity increases evolvability by reducing constraints on adaptation and by allowing preexisting parts to function in new contexts for novel uses. Protein evolution provides an excellent context to study the causes and consequences of biological modularity. In order to address such questions, however, an index for protein modularity is necessary. This paper proposes a simple index for protein modularity-"module density"-which is the number of evolutionarily independent modules that compose a protein divided by the number of amino acids in the protein. The decomposition of proteins into constituent modules can be accomplished by either of two classes of methods. The first class of methods relies on "suppositional" criteria to assign amino acids to modules, whereas the second class of methods relies on "coevolutionary" criteria for this task. One simple and practical method from the first class consists of approximating the number of modules in a protein as the number of regular secondary structure elements (i.e., helices and sheets). Methods based on coevolutionary criteria require more elaborate data, but they have the advantage of being able to specify modules without prior assumptions about why they exist. Given the increasing availability of datasets sampling protein mutational spectra (e.g., from comparative genomics, experimental evolution, and computational prediction), methods based on coevolutionary criteria will likely become more promising in the near future. The ability to meaningfully quantify protein modularity via simple indices has the potential to aid future efforts to understand protein evolutionary rate determinants, improve molecular evolution models and engineer novel proteins.

Comparative modeling and protein-like features of hydrophobic-polar models on a two-dimensional lattice

Lattice models of proteins have been extensively used to study protein thermodynamics, folding dynamics, and evolution. Our study considers two different hydrophobic-polar (HP) models on the 2D square lattice: the purely HP model and a model where a compactness-favoring term is added. We exhaustively enumerate all the possible structures in our models and perform the study of their corresponding folds, HP arrangements in space and shapes. The two models considered differ greatly in their numbers of structures, folds, arrangements, and shapes. Despite their differences, both lattice models have distinctive protein-like features: (1) Shapes are compact in both models, especially when a compactness-favoring energy term is added. (2) The residue composition is independent of the chain length and is very close to 50% hydrophobic in both models, as we observe in real proteins. (3) Comparative modeling works well in both models, particularly in the more compact one. The fact that our models show protein-like features suggests that lattice models incorporate the fundamental physical principles of proteins. Our study supports the use of lattice models to study questions about proteins that require exactness and extensive calculations, such as protein design and evolution, which are often too complex and computationally demanding to be addressed with more detailed models.

Stability of domain structures in multi-domain proteins

Multi-domain proteins have many advantages with respect to stability and folding inside cells. Here we attempt to understand the intricate relationship between the domain-domain interactions and the stability of domains in isolation. We provide quantitative treatment and proof for prevailing intuitive ideas on the strategies employed by nature to stabilize otherwise unstable domains. We find that domains incapable of independent stability are stabilized by favourable interactions with tethered domains in the multi-domain context. Stability of such folds to exist independently is optimized by evolution. Specific residue mutations in the sites equivalent to inter-domain interface enhance the overall solvation, thereby stabilizing these domain folds independently. A few naturally occurring variants at these sites alter communication between domains and affect stability leading to disease manifestation. Our analysis provides safe guidelines for mutagenesis which have attractive applications in obtaining stable fragments and domain constructs essential for structural studies by crystallography and NMR.

The low cost of recombination in creating novel phenotypes: Recombination can create new phenotypes while disrupting well-adapted phenotypes much less than mutation

Recombination is often considered a disruptive force for well-adapted phenotypes, but recent evidence suggests that this cost of recombination can be small. A key benefit of recombination is that it can help create proteins and regulatory circuits with novel and useful phenotypes more efficiently than point mutation. Its effectiveness stems from the large-scale reorganization of genotypes that it causes, which can help explore far-flung regions in genotype space. Recent work on complex phenotypes in model gene regulatory circuits and proteins shows that the disruptive effects of recombination can be very mild compared to the effects of mutation. Recombination thus can have great benefits at a modest cost, but we do not understand the reasons well. A better understanding might shed light on the evolution of recombination and help improve evolutionary strategies in biochemical engineering.

Protein structural modularity and robustness are associated with evolvability

Theory suggests that biological modularity and robustness allow for maintenance of fitness under mutational change, and when this change is adaptive, for evolvability. Empirical demonstrations that these traits promote evolvability in nature remain scant however. This is in part because modularity, robustness, and evolvability are difficult to define and measure in real biological systems. Here, we address whether structural modularity and/or robustness confer evolvability at the level of proteins by looking for associations between indices of protein structural modularity, structural robustness, and evolvability. We propose a novel index for protein structural modularity: the number of regular secondary structure elements (helices and strands) divided by the number of residues in the structure. We index protein evolvability as the proportion of sites with evidence of being under positive selection multiplied by the average rate of adaptive evolution at these sites, and we measure this as an average over a phylogeny of 25 mammalian species. We use contact density as an index of protein designability, and thus, structural robustness. We find that protein evolvability is positively associated with structural modularity as well as structural robustness and that the effect of structural modularity on evolvability is independent of the structural robustness index. We interpret these associations to be the result of reduced constraints on amino acid substitutions in highly modular and robust protein structures, which results in faster adaptation through natural selection.

Neutrality and evolvability of designed protein sequences

The effect of foldability on protein's evolvability is analyzed by a two-prong approach consisting of a self-consistent mean-field theory and Monte Carlo simulations. Theory and simulation models representing protein sequences with binary patterning of amino acid residues compatible with a particular foldability criteria are used. This generalized foldability criterion is derived using the high temperature cumulant expansion approximating the free energy of folding. The effect of cumulative point mutations on these designed proteins is studied under neutral condition. The robustness, protein's ability to tolerate random point mutations is determined with a selective pressure of stability (ΔΔG) for the theory designed sequences, which are found to be more robust than that of Monte Carlo and mean-field-biased Monte Carlo generated sequences. The results show that this foldability criterion selects viable protein sequences more effectively compared to the Monte Carlo method, which has a marked effect on how the selective pressure shapes the evolutionary sequence space. These observations may impact de novo sequence design and its applications in protein engineering.

Evolvability and single-genotype fluctuation in phenotypic properties: a simple heteropolymer model

Experiment showed that the response of a genotype to mutation, i.e., the magnitude of mutational change in a phenotypic property, can be correlated with the extent of phenotypic fluctuation among genetic clones. To address a possible statistical mechanical basis for such phenomena at the protein level, we consider a simple hydrophobic-polar lattice protein-chain model with an exhaustive mapping between sequence (genotype) and conformational (phenotype) spaces. Using squared end-to-end distance, R(N)(2), as an example conformational property, we study how the thermal fluctuation of a sequence's R(N)(2) may be predictive of the changes in the Boltzmann average R(N)(2) caused by single-point mutations on that sequence. We found that sequences with the same ground-state (R(N)(2))(0) exhibit a funnel-like organization under conditions favorable to chain collapse or folding: fluctuation (standard deviation sigma) of R(N)(2) tends to increase with mutational distance from a prototype sequence whose R(N)(2) deviates little from its (R(N)(2))(0). In general, large mutational decreases in R(N)(2) or in sigma are only possible for some, though not all, sequences with large sigma values. This finding suggests that single-genotype phenotypic fluctuation is a necessary, though not sufficient, indicator of evolvability toward genotypes with less phenotypic fluctuations.

Evolutionary plasticity and innovations in complex metabolic reaction networks

Genome-scale metabolic networks are highly robust to the elimination of enzyme-coding genes. Their structure can evolve rapidly through mutations that eliminate such genes and through horizontal gene transfer that adds new enzyme-coding genes. Using flux balance analysis we study a vast space of metabolic network genotypes and their relationship to metabolic phenotypes, the ability to sustain life in an environment defined by an available spectrum of carbon sources. Two such networks typically differ in most of their reactions and have few essential reactions in common. Our observations suggest that the robustness of the Escherichia coli metabolic network to mutations is typical of networks with the same phenotype. We also demonstrate that networks with the same phenotype form large sets that can be traversed through single mutations, and that single mutations of different genotypes with the same phenotype can yield very different novel phenotypes. This means that the evolutionary plasticity and robustness of metabolic networks facilitates the evolution of new metabolic abilities. Our approach has broad implications for the evolution of metabolic networks, for our understanding of mutational robustness, for the design of antimetabolic drugs, and for metabolic engineering.

Understanding the fundamental processes that shape the evolution of bacterial organisms is of general interest to biology and may have important applications in medicine. We address the questions of how bacterial organisms acquire innovations, including drug resistance, allowing them to survive in new environments. We simulate the evolution of the metabolic network, the network of reactions that can occur inside a living organism. The metabolic network of an organism depends on the genes contained in its genome and can change by gaining genes from other organisms through horizontal gene transfer or loss of gene activity through mutations. Our observations suggest that the robustness to gene loss in Escherichia coli is typical of random viable metabolic networks of the same size. We also find that metabolic networks can change significantly without causing the loss of an organism's ability to survive in a given environment. This property allows organisms to explore a wide range of novel metabolic abilities and is the source of their ability to innovate. Finally we present a method to find reactions that are essential across all organisms. Drugs targeting such a reaction may avoid drug resistance mutations that bypass the reaction.

Neutral evolution of proteins: The superfunnel in sequence space and its relation to mutational robustness

Following Kimura's neutral theory of molecular evolution [M. Kimura, The Neutral Theory of Molecular Evolution (Cambridge University Press, Cambridge, 1983) (reprinted in 1986)], it has become common to assume that the vast majority of viable mutations of a gene confer little or no functional advantage. Yet, in silico models of protein evolution have shown that mutational robustness of sequences could be selected for, even in the context of neutral evolution. The evolution of a biological population can be seen as a diffusion on the network of viable sequences. This network is called a "neutral network." Depending on the mutation rate mu and the population size N, the biological population can evolve purely randomly (muN<<1) or it can evolve in such a way as to select for sequences of higher mutational robustness (muN>>1). The stringency of the selection depends not only on the product muN but also on the exact topology of the neutral network, the special arrangement of which was named "superfunnel." Even though the relation between mutation rate, population size, and selection was thoroughly investigated, a study of the salient topological features of the superfunnel that could affect the strength of the selection was wanting. This question is addressed in this study. We use two different models of proteins: on lattice and off lattice. We compare neutral networks computed using these models to random networks. From this, we identify two important factors of the topology that determine the stringency of the selection for mutationally robust sequences. First, the presence of highly connected nodes ("hubs") in the network increases the selection for mutationally robust sequences. Second, the stringency of the selection increases when the correlation between a sequence's mutational robustness and its neighbors' increases. The latter finding relates a global characteristic of the neutral network to a local one, which is attainable through experiments or molecular modeling.

Neutralism and selectionism: a network-based reconciliation

Neutralism and selectionism are extremes of an explanatory spectrum for understanding patterns of molecular evolution and the emergence of evolutionary innovation. Although recent genome-scale data from protein-coding genes argue against neutralism, molecular engineering and protein evolution data argue that neutral mutations and mutational robustness are important for evolutionary innovation. Here I propose a reconciliation in which neutral mutations prepare the ground for later evolutionary adaptation. Key to this perspective is an explicit understanding of molecular phenotypes that has only become accessible in recent years.

The effect of sequence on the conformational stability of a model heteropolymer in explicit water

We investigate the properties of a two-dimensional lattice heteropolymer model for a protein in which water is explicitly represented. The model protein distinguishes between hydrophobic and polar monomers through the effect of the hydrophobic monomers on the entropy and enthalpy of the hydrogen bonding of solvation shell water molecules. As experimentally observed, model heteropolymer sequences fold into stable native states characterized by a hydrophobic core to avoid unfavorable interactions with the solvent. These native states undergo cold, pressure, and thermal denaturation into distinct configurations for each type of unfolding transition. However, the heteropolymer sequence is an important element, since not all sequences will fold into stable native states at positive pressures. Simulation of a large collection of sequences indicates that these fall into two general groups, those exhibiting highly stable native structures and those that do not. Statistical analysis of important patterns in sequences shows a strong tendency for observing long blocks of hydrophobic or polar monomers in the most stable sequences. Statistical analysis also shows that alternation of hydrophobic and polar monomers appears infrequently among the most stable sequences. These observations are not absolute design rules and, in practice, these are not sufficient to rationally design very stable heteropolymers. We also study the effect of mutations on improving the stability of the model proteins, and demonstrate that it is possible to obtain a very stable heteropolymer from directed evolution of an initially unstable heteropolymer.

Mutagenic evidence for the optimal control of evolutionary dynamics

Elucidating the fitness measures optimized during the evolution of complex biological systems is a major challenge in evolutionary theory. We present experimental evidence and an analytical framework demonstrating how biochemical networks exploit optimal control strategies in their evolutionary dynamics. Optimal control theory explains a striking pattern of extremization in the redox potentials of electron transport proteins, assuming only that their fitness measure is a control objective functional with bounded controls.

Neutral evolution of protein-protein interactions: a computational study using simple models

Background

Protein-protein interactions are central to cellular organization, and must have appeared at an early stage of evolution. To understand better their role, we consider a simple model of protein evolution and determine the effect of an explicit selection for Protein-protein interactions.

Results

In the model, viable sequences all have the same fitness, following the neutral evolution theory. A very simple, two-dimensional lattice representation of the protein structures is used, and the model only considers two kinds of amino acids: hydrophobic and polar. With these approximations, exact calculations are performed. The results do not depend too strongly on these assumptions, since a model using a 3D, off-lattice representation of the proteins gives results in qualitative agreement with the 2D one. With both models, the evolutionary dynamics lead to a steady state population that is enriched in sequences that dimerize with a high affinity, well beyond the minimal level needed to survive. Correspondingly, sequences close to the viability threshold are less abundant in the steady state, being subject to a larger proportion of lethal mutations. The set of viable sequences has a "funnel" shape, consistent with earlier studies: sequences that are highly populated in the steady state are "close" to each other (with proximity being measured by the number of amino acids that differ).

Conclusion

This bias in the the steady state sequences should lead to an increased resistance of the population to environmental change and an increased ability to evolve.

Population dynamics simulations of functional model proteins

In order to probe the fundamental principles that govern protein evolution, we use a minimalist model of proteins to provide a mapping from genotype to phenotype. The model is based on physically realistic forces of protein folding and includes an explicit definition of protein function. Thus, we can find the fitness of a sequence from its ability to fold to a stable structure and perform a function. We study the fitness landscapes of these functional model proteins, that is, the set of all sequences mapped on to their corresponding fitnesses and connected to their one mutant neighbors. Through population dynamics simulations we directly study the influence of the nature of the fitness landscape on evolution. Populations are observed to move to a steady state, the distribution of which can often be predicted prior to the population dynamics simulations from the nature of the fitness landscape and a quantity analogous to a partition function. In this paper, we develop a scheme for predicting the steady-state population on a fitness landscape, based on the nature of the fitness landscape, thereby obviating the need for explicit population dynamics simulations and providing some insight into the impact on molecular evolution of the nature of fitness landscapes. Poor predictions are indicative of fitness landscapes that consist of a series of weakly connected sublandscapes.

Developing a move-set for protein model refinement

MOTIVATION

A wide variety of methods for the construction of an atomic model for a given amino acid sequence are known, the more accurate being those that use experimentally determined structures as templates. However, far fewer methods are aimed at refining these models. The approach presented here carefully blends models created by several different means, in an attempt to combine the good quality regions from each into a final, more refined, model.

RESULTS

We describe here a number of refinement operators (collectively, 'move-set') that enable a relatively large region of conformational space to be searched. This is used within a genetic algorithm that reshuffles and repacks structural components. The utility of the move-set is demonstrated by introducing a cost function, containing both physical and other components guiding the input structures towards the target structure. We show that our move-set has the potential to improve the conformation of models and that this improvement can be beyond even the best template for some comparative modelling targets.

AVAILABILITY

The populus software package and the source code are available at http://bmm.cancerresearchuk.org/~offman01/populus.html.

Evolution of Structural Shape in Bacterial Globin-Related Proteins

The globin family of proteins has a characteristic structural pattern of helix interactions that nonetheless exhibits some variation. A simplified model for globin structural evolution was developed in which protein shape evolved by random change of contacts between helices. A conserved globin domain of 15 bacterial proteins representing four structural families was studied. Using a parsimony approach ancestral structural states could be reconstructed. The distribution of number of contact changes per site for a fixed topology tree fit a gamma distribution. Homoplasy was high, with multiple changes per site and no support for an invariant class of residue-residue contacts. Contacts changed more slowly than sequence. A phylogenetic reconstruction using a distance measure based on the proportion of shared contacts was generally consistent with a sequence-based phylogeny but not highly resolved. Contact pattern convergence between members of different globin family proteins could not be detected. Simulation studies indicated the convergence test was sensitive enough to have detected convergence involving only 10% of the contacts, suggesting a limit on the extent of selection for a specific contact pattern. Contact site methods may provide additional approaches to study the relationship between protein structure and sequence evolution.

Physical origins of protein superfamilies

In this work, we discovered a fundamental connection between selection for protein stability and emergence of preferred structures of proteins. Using a standard exact three-dimensional lattice model we evolve sequences starting from random ones and determine the exact native structure after each mutation. Acceptance of mutations is biased to select for stable proteins. We found that certain structures, "wonderfolds", are independently discovered numerous times as native states of stable proteins in many unrelated runs of selection. The strong dependence of lattice fold usage on the structural determinant of designability quantitatively reproduces uneven fold usage in natural proteins. Diversity of sequences that fold into wonderfold structures gives rise to superfamilies, i.e. sets of dissimilar sequences that fold into the same or very similar structures. The present work establishes a model of pre-biotic structure selection, which identifies dominant structural patterns emerging upon optimization of proteins for survival in a hot environment. Convergently discovered pre-biotic initial superfamilies with wonderfold structures could have served as a seed for subsequent biological evolution involving gene duplications and divergence.

SELECTIVE ADVANTAGE OF RECOMBINATION IN EVOLVING PROTEIN POPULATIONS: A LATTICE MODEL STUDY

Recent research has attempted to clarify the contributions of several mutational processes, such as substitutions or homologous recombination. Simplistic, tractable protein models, which determine the compact native structure phenotype from the sequence genotype, are well-suited to such studies. In this paper, we use a lattice-protein model to examine the effects of point mutation and homologous recombination on evolving populations of proteins. We find that while the majority of mutation and recombination events are neutral or deleterious, recombination is far more likely to be beneficial. This results in a faster increase in fitness during evolution, although the final fitness level is not significantly changed. This transient advantage provides an evolutionary advantage to subpopulations that undergo recombination, allowing fixation of recombination to occur in the population.

Simulating protein evolution in sequence and structure space

Naturally occurring proteins comprise a special subset of all plausible sequences and structures selected through evolution. Simulating protein evolution with simplified and all-atom models has shed light on the evolutionary dynamics of protein populations, the nature of evolved sequences and structures, and the extent to which today's proteins are shaped by selection pressures on folding, structure and function. Extensive mapping of the native structure, stability and folding rate in sequence space using lattice proteins has revealed organizational principles of the sequence/structure map important for evolutionary dynamics. Evolutionary simulations with lattice proteins have highlighted the importance of fitness landscapes, evolutionary mechanisms, population dynamics and sequence space entropy in shaping the generic properties of proteins. Finally, evolutionary-like simulations with all-atom models, in particular computational protein design, have helped identify the dominant selection pressures on naturally occurring protein sequences and structures.

Comparing folding codes in simple heteropolymer models of protein evolutionary landscape: robustness of the superfunnel paradigm

Understanding the evolution of biopolymers is a key element in rationalizing their structures and functions. Simple exact models (SEMs) are well-positioned to address general principles of evolution as they permit the exhaustive enumeration of both sequence and structure (conformational) spaces. The physics-based models of the complete mapping between genotypes and phenotypes afforded by SEMs have proven valuable for gaining insight into how adaptation and selection operate among large collections of sequences and structures. This study compares the properties of evolutionary landscapes of a variety of SEMs to delineate robust predictions and possible model-specific artifacts. Among the models studied, the ruggedness of evolutionary landscape is significantly model-dependent; those derived from more protein-like models appear to be smoother. We found that a common practice of restricting protein structure space to maximally compact lattice conformations results in (i.e., "designs in") many encodable (designable) structures that are not otherwise encodable in the corresponding unrestrained structure space. This discrepancy is especially severe for model potentials that seek to mimic the major role of hydrophobic interactions in protein folding. In general, restricting conformations to be maximally compact leads to larger changes in the model genotype-phenotype mapping than a moderate shifting of reference state energy of the model potential function to allow for more specific encoding via the "designing out" effects of repulsive interactions. Despite these variations, the superfunnel paradigm applies to all SEMs we have tested: For a majority of neutral nets across different models, there exists a funnel-like organization of native stabilities for the sequences in a neutral net encoding for the same structure, and the thermodynamically most stable sequence is also the most robust against mutation.

Finite size effects on thermal denaturation of globular proteins

Finite size effects on the cooperative thermal denaturation of proteins are considered. A dimensionless measure of cooperativity, Omegac, scales as Nzeta, where N is the number of amino acids. Surprisingly, we find that zeta is universal with zeta=1+gamma, where the exponent gamma characterizes the divergence of the susceptibility for a self-avoiding walk. Our lattice model simulations and experimental data are consistent with the theory. Our finding rationalizes the marginal stability of proteins and substantiates the earlier predictions that the efficient folding of two-state proteins requires TF approximately Ttheta, where Ttheta and TF are the collapse and folding transition temperatures, respectively.

Stability and the evolvability of function in a model protein

Functional proteins must fold with some minimal stability to a structure that can perform a biochemical task. Here we use a simple model to investigate the relationship between the stability requirement and the capacity of a protein to evolve the function of binding to a ligand. Although our model contains no built-in tradeoff between stability and function, proteins evolved function more efficiently when the stability requirement was relaxed. Proteins with both high stability and high function evolved more efficiently when the stability requirement was gradually increased than when there was constant selection for high stability. These results show that in our model, the evolution of function is enhanced by allowing proteins to explore sequences corresponding to marginally stable structures, and that it is easier to improve stability while maintaining high function than to improve function while maintaining high stability. Our model also demonstrates that even in the absence of a fundamental biophysical tradeoff between stability and function, the speed with which function can evolve is limited by the stability requirement imposed on the protein.

Funnel-like organization in sequence space determines the distributions of protein stability and folding rate preferred by evolution

To understand the physical and evolutionary determinants of protein folding, we map out the complete organization of thermodynamic and kinetic properties for protein sequences that share the same fold. The exhaustive nature of our study necessitates using simplified models of protein folding. We obtain a stability map and a folding rate map in sequence space. Comparison of the two maps reveals a common organizational principle: optimality decreases more or less uniformly with distance from the optimal sequence in the sequence space. This gives a funnel-shaped optimality surface. Evolutionary dynamics of a sequence population on these two maps reveal how the simple organization of sequence space affects the distributions of stability and folding rate preferred by evolution.

Imprint of evolution on protein structures

We attempt to understand the evolutionary origin of protein folds by simulating their divergent evolution with a three-dimensional lattice model. Starting from an initial seed lattice structure, evolution of model proteins progresses by sequence duplication and subsequent point mutations. A new gene's ability to fold into a stable and unique structure is tested each time through direct kinetic folding simulations. Where possible, the algorithm accepts the new sequence and structure and thus a "new protein structure" is born. During the course of each run, this model evolutionary algorithm provides several thousand new proteins with diverse structures. Analysis of evolved structures shows that later evolved structures are more designable than seed structures as judged by recently developed structural determinant of protein designability, as well as direct estimate of designability for selected structures by thermodynamic sampling of their sequence space. We test the significance of this trend predicted on lattice models on real proteins and show that protein domains that are found in eukaryotic organisms only feature statistically significant higher designability than their prokaryotic counterparts. These results present a fundamental view on protein evolution highlighting the relative roles of structural selection and evolutionary dynamics on genesis of modern proteins.

What is the protein design alphabet?

Selecting a protein sequence that corresponds to a specific three-dimensional protein structure is known as the protein design problem. One principal bottleneck in solving this problem is our lack of knowledge of precise atomic interactions. Using a simple model of amino acid interactions, we determine three crucial factors that are important for solving the protein design problem. Among these factors is the protein alphabet-a set of sequence elements that encodes protein structure. Our model predicts that alphabet size is independent of protein length, suggesting the possibility of designing a protein of arbitrary length with the natural protein alphabet. We also find that protein alphabet size is governed by protein structural properties and the energetic properties of the protein alphabet units. We discover that the usage of average types of amino acid in proteins is less than expected if amino acids were chosen randomly with naturally occurring frequencies. We propose three possible scenarios that account for amino acid underusage in proteins. These scenarios suggest the possibility that amino acids themselves might not constitute the alphabet of natural proteins.

Novel use of a genetic algorithm for protein structure prediction: Searching template and sequence alignment space

A novel genetic algorithm was applied to all CASP5 targets. The algorithm simultaneously searches template and alignment space. Results show that the current implementation of the method is perhaps most useful in recognizing and refining remote homology targets. This new method is briefly described and results are analyzed. Strengths and weaknesses of the current implementation of the algorithm are discussed.