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.     

Combining protein evolution and secondary structure

An evolutionary model that combines protein secondary structure and amino acid replacement is introduced. It allows likelihood analysis of aligned protein sequences and does not require the underlying secondary (or tertiary) structures of these sequences to be known. One component of the model describes the organization of secondary structure along a protein sequence and another specifies the evolutionary process for each category of secondary structure. A database of proteins with known secondary structures is used to estimate model parameters representing these two components. Phylogeny, the third component of the model, can be estimated from the data set of interest. As an example, we employ our model to analyze a set of sucrose synthase sequences. For the evolution of sucrose synthase, a parametric bootstrap approach indicates that our model is statistically preferable to one that ignores secondary structure.      

Modularity in the evolution of yeast protein interaction network

Protein interaction networks are known to exhibit remarkable structures: scale-free and small-world and modular structures. To explain the evolutionary processes of protein interaction networks possessing scale-free and small-world structures, preferential attachment and duplication-divergence models have been proposed as mathematical models. Protein interaction networks are also known to exhibit another remarkable structural characteristic, modular structure. How the protein interaction networks became to exhibit modularity in their evolution? Here, we propose a hypothesis of modularity in the evolution of yeast protein interaction network based on molecular evolutionary evidence. We assigned yeast proteins into six evolutionary ages by constructing a phylogenetic profile. We found that all the almost half of hub proteins are evolutionarily new. Examining the evolutionary processes of protein complexes, functional modules and topological modules, we also found that member proteins of these modules tend to appear in one or two evolutionary ages. Moreover, proteins in protein complexes and topological modules show significantly low evolutionary rates than those not in these modules. Our results suggest a hypothesis of modularity in the evolution of yeast protein interaction network as systems evolution.     

HIV-specific probabilistic models of protein evolution

Comparative sequence analyses, including such fundamental bioinformatics techniques as similarity searching, sequence alignment and phylogenetic inference, have become a mainstay for researchers studying type 1 Human Immunodeficiency Virus (HIV-1) genome structure and evolution. Implicit in comparative analyses is an underlying model of evolution, and the chosen model can significantly affect the results. In general, evolutionary models describe the probabilities of replacing one amino acid character with another over a period of time. Most widely used evolutionary models for protein sequences have been derived from curated alignments of hundreds of proteins, usually based on mammalian genomes. It is unclear to what extent these empirical models are generalizable to a very different organism, such as HIV-1-the most extensively sequenced organism in existence. We developed a maximum likelihood model fitting procedure to a collection of HIV-1 alignments sampled from different viral genes, and inferred two empirical substitution models, suitable for describing between-and within-host evolution. Our procedure pools the information from multiple sequence alignments, and provided software implementation can be run efficiently in parallel on a computer cluster. We describe how the inferred substitution models can be used to generate scoring matrices suitable for alignment and similarity searches. Our models had a consistently superior fit relative to the best existing models and to parameter-rich data-driven models when benchmarked on independent HIV-1 alignments, demonstrating evolutionary biases in amino-acid substitution that are unique to HIV, and that are not captured by the existing models. The scoring matrices derived from the models showed a marked difference from common amino-acid scoring matrices. The use of an appropriate evolutionary model recovered a known viral transmission history, whereas a poorly chosen model introduced phylogenetic error. We argue that our model derivation procedure is immediately applicable to other organisms with extensive sequence data available, such as Hepatitis C and Influenza A viruses.     

The interface of protein structure, protein biophysics, and molecular evolution

Abstract The interface of protein structural biology, protein biophysics, molecular evolution, and molecular population genetics forms the foundations for a mechanistic understanding of many aspects of protein biochemistry. Current efforts in interdisciplinary protein modeling are in their infancy and the state-of-the art of such models is described. Beyond the relationship between amino acid substitution and static protein structure, protein function, and corresponding organismal fitness, other considerations are also discussed. More complex mutational processes such as insertion and deletion and domain rearrangements and even circular permutations should be evaluated. The role of intrinsically disordered proteins is still controversial, but may be increasingly important to consider. Protein geometry and protein dynamics as a deviation from static considerations of protein structure are also important. Protein expression level is known to be a major determinant of evolutionary rate and several considerations including selection at the mRNA level and the role of interaction specificity are discussed. Lastly, the relationship between modeling and needed high-throughput experimental data as well as experimental examination of protein evolution using ancestral sequence resurrection and in vitro biochemistry are presented, towards an aim of ultimately generating better models for biological inference and prediction.     

Effects of point mutations on protein structure are nonexponentially distributed

Inspection of structure changes in proteins borne by altering their sequences brings understanding of physics, functioning and evolution of existing proteins, and helps engineer modified ones. On single amino acid substitutions, the most frequent mutation type, shifts in backbone conformation are typically small, raising doubts if and how such minor modifications could drive evolutionary divergence. Here, we report that the distribution of magnitudes of structure change on such substitutions is heavy-tailed--whereas protein structures are robust to most substitutions, changes much larger than average occur with raised odds compared to what would be expected for exponential distribution with the same mean. This nonexponential behavior allows for reconciling the apparent contradiction between the observed conservation of protein structures and the substantial evolutionary plasticity implied in their diversity. The presence of the heavy tail in the distribution promotes structure divergence, facilitating exploration of new functionality, and conformations within folds, as well as exploration of structure space for new folds.     

Basing population genetic inferences and models of molecular evolution upon desired stationary distributions of DNA or protein sequences

Models of molecular evolution tend to be overly simplistic caricatures of biology that are prone to assigning high probabilities to biologically implausible DNA or protein sequences. Here, we explore how to construct time-reversible evolutionary models that yield stationary distributions of sequences that match given target distributions. By adopting comparatively realistic target distributions,evolutionary models can be improved. Instead of focusing on estimating parameters, we concentrate on the population genetic implications of these models. Specifically, we obtain estimates of the product of effective population size and relative fitness difference of alleles. The approach is illustrated with two applications to protein-coding DNA. In the first, a codon-based evolutionary model yields a stationary distribution of sequences, which, when the sequences are translated,matches a variable-length Markov model trained on human proteins. In the second, we introduce an insertion-deletion model that describes selectively neutral evolutionary changes to DNA. We then show how to modify the neutral model so that its stationary distribution at the amino acid level can match a profile hidden Markov model, such as the one associated with the Pfam database.     

Combining inference from evolution and geometric probability in protein structure evaluation

Starting from the hypothesis that evolutionarily important residues form a spatially limited cluster in a protein's native fold, we discuss the possibility of detecting a non-native structure based on the absence of such clustering. The relevant residues are determined using the Evolutionary Trace method. We propose a quantity to measure clustering of the selected residues on the structure and show that the exact values for its average and variance over several ensembles of interest can be found. This enables us to study the behavior of the associated z-scores. Since our approach rests on an analytic result, it proves to be general, customizable, and computationally fast. We find that clustering is indeed detectable in a large representative protein set. Furthermore, we show that non-native structures tend to achieve lower residue-clustering z-scores than those attained by the native folds. The most important conclusion that we draw from this work is that consistency between structural and evolutionary information, manifested in clustering of key residues, imposes powerful constraints on the conformational space of a protein.     

Structural evolution of the protein kinase-like superfamily

The protein kinase family is large and important, but it is only one family in a larger superfamily of homologous kinases that phosphorylate a variety of substrates and play important roles in all three superkingdoms of life. We used a carefully constructed structural alignment of selected kinases as the basis for a study of the structural evolution of the protein kinase-like superfamily. The comparison of structures revealed a "universal core" domain consisting only of regions required for ATP binding and the phosphotransfer reaction. Remarkably, even within the universal core some kinase structures display notable changes, while still retaining essential activity. Hence, the protein kinase-like superfamily has undergone substantial structural and sequence revision over long evolutionary timescales. We constructed a phylogenetic tree for the superfamily using a novel approach that allowed for the combination of sequence and structure information into a unified quantitative analysis. When considered against the backdrop of species distribution and other metrics, our tree provides a compelling scenario for the development of the various kinase families from a shared common ancestor. We propose that most of the so-called "atypical kinases" are not intermittently derived from protein kinases, but rather diverged early in evolution to form a distinct phyletic group. Within the atypical kinases, the aminoglycoside and choline kinase families appear to share the closest relationship. These two families in turn appear to be the most closely related to the protein kinase family. In addition, our analysis suggests that the actin-fragmin kinase, an atypical protein kinase, is more closely related to the phosphoinositide-3 kinase family than to the protein kinase family. The two most divergent families, alpha-kinases and phosphatidylinositol phosphate kinases (PIPKs), appear to have distinct evolutionary histories. While the PIPKs probably have an evolutionary relationship with the rest of the kinase superfamily, the relationship appears to be very distant (and perhaps indirect). Conversely, the alpha-kinases appear to be an exception to the scenario of early divergence for the atypical kinases: they apparently arose relatively recently in eukaryotes. We present possible scenarios for the derivation of the alpha-kinases from an extant kinase fold.     

Pairwise alignment of protein interaction networks.

With an ever-increasing amount of available data on protein-protein interaction (PPI) networks and research revealing that these networks evolve at a modular level, discovery of conserved patterns in these networks becomes an important problem. Although available data on protein-protein interactions is currently limited, recently developed algorithms have been shown to convey novel biological insights through employment of elegant mathematical models. The main challenge in aligning PPI networks is to define a graph theoretical measure of similarity between graph structures that captures underlying biological phenomena accurately. In this respect, modeling of conservation and divergence of interactions, as well as the interpretation of resulting alignments, are important design parameters. In this paper, we develop a framework for comprehensive alignment of PPI networks, which is inspired by duplication/divergence models that focus on understanding the evolution of protein interactions. We propose a mathematical model that extends the concepts of match, mismatch, and gap in sequence alignment to that of match, mismatch, and duplication in network alignment and evaluates similarity between graph structures through a scoring function that accounts for evolutionary events. By relying on evolutionary models, the proposed framework facilitates interpretation of resulting alignments in terms of not only conservation but also divergence of modularity in PPI networks. Furthermore, as in the case of sequence alignment, our model allows flexibility in adjusting parameters to quantify underlying evolutionary relationships. Based on the proposed model, we formulate PPI network alignment as an optimization problem and present fast algorithms to solve this problem. Detailed experimental results from an implementation of the proposed framework show that our algorithm is able to discover conserved interaction patterns very effectively, in terms of both accuracies and computational cost.     

The relationship between relative solvent accessibility and evolutionary rate in protein evolution

Recent work with Saccharomyces cerevisiae shows a linear relationship between the evolutionary rate of sites and the relative solvent accessibility (RSA) of the corresponding residues in the folded protein. Here, we aim to develop a mathematical model that can reproduce this linear relationship. We first demonstrate that two models that both seem reasonable choices (a simple model in which selection strength correlates with RSA and a more complex model based on RSA-dependent amino acid distributions) fail to reproduce the observed relationship. We then develop a model on the basis of observed site-specific amino acid distributions and show that this model behaves appropriately. We conclude that evolutionary rates are directly linked to the distribution of amino acids at individual sites. Because of this link, any future insight into the biophysical mechanisms that determine amino acid distributions will improve our understanding of evolutionary rates.     

Understanding the evolution of restriction-modification systems: clues from sequence and structure comparisons

Restriction-modification (RM) systems comprise two opposing enzymatic activities: a restriction endonuclease, that targets specific DNA sequences and performs endonucleolytic cleavage, and a modification methyltransferase that renders these sequences resistant to cleavage. Studies on molecular genetics and biochemistry of RM systems have been carried out over the past four decades, laying foundations for modern molecular biology and providing important models for mechanisms of highly specific protein-DNA interactions. Although the number of known, relevant sequences 3D structures of RM proteins is growing steadily, we do not fully understand their functional diversities from an evolutionary perspective and we are not yet able to engineer new sequence specificities based on rational approaches. Recent findings on the evolution of RM systems and on their structures and mechanisms of action have led to a picture in which conserved modules with defined function are shared between different RM proteins and other enzymes involved in nucleic acid biochemistry. On the other hand, it has been realized that some of the modules have been replaced in the evolution by unrelated domains exerting similar function. The aim of this review is to give a survey on the recent progress in the field of structural phylogeny of RM enzymes with special emphasis on studies of sequence-structure-function relationships and emerging potential applications in biotechnology.     

GLASS: A tool to visualize protein structure prediction data in three dimensions and evaluate their consistency

When a protein sequence does not share any significant sequence similarity with a protein of known structure, homology modeling cannot be applied. However, many novel and interesting methods, such as secondary structure prediction, fold recognition, and prediction of long-range interactions, are being developed and have been shown to be reasonably successful in predicting protein structures from sequence data and evolutionary information. The a priori evaluation of the correctness of a prediction obtained by one of these methods is however often problematic. Consequently, it is important to use all available information provided by as many different methods as possible and all the available experimental data about the protein of interest, since the consistency of the results is indicative of the reliability of the prediction. Hence the need has arisen for suitable tools able to compare results provided by different methods and evaluate their consistency. We have therefore constructed GLASS, a general platform to read, visualize, compare, and evaluate prediction results from many different sources and to project these prediction results into three dimensions. In addition, GLASS allows the comparison of selected parameters calculated for a model with the distribution observed in real protein structures, thus providing an easy way to test new methods for evaluating the likelihood of different structural models. GLASS can be considered as a “workbench” for structural predictions useful to both experimentalists and theoreticians. Proteins 30:339–351, 1998. © 1998 Wiley-Liss, Inc.     

Comparative study of the evolution of nuclear ribosomal spacers incorporating secondary structure analyzes within Dodonaeoideae,Hippocastanoideae and Xanthoceroideae (Sapindaceae)

Ribosomal DNA internal transcribed spacers (ITS) and partial external transcribed spacers (ETSf) are popularly used to infer evolutionary hypotheses. However, there is generally little consideration given to the secondary structures of these small RNA molecules and their potential effects on sequence alignment and phylogenetic analyzes. Intergeneric relationships amongst three of the four major lineages in the Sapindaceae, the Dodonaeoideae, Hippcastanoideae and Xanthoceroideae were assessed by firstly, generating secondary structure predictions for ITS and partial ETSf sequences, and then these predictions were used to assist alignment of the sequences. Secondly, the alignment was analyzed using RNA specific models of sequence evolution that account for the variation in nucleotide evolution in the independent loops and covariating stems regions of the ribosomal spacers. These models and phylogeny drawn from these analyzes were compared with that from analyzes using ‘traditional’ 4-state models and previous plastid analyzes. These analyzes identified that paired-site models developed to deal specifically with stem structures in RNA encoding sequences more appropriately account for the evolutionary history of the sequences than traditional 4-state substitution models.     

The role of protein conformational fluctuations in allostery, function, and evolution

It is now well-known that proteins exist at equilibrium as ensembles of conformational states rather than as unique static structures. Here we review from an ensemble perspective important biological effects of such spontaneous fluctuations on protein allostery, function, and evolution. However, rather than present a thorough literature review on each subject, we focus instead on connecting these phenomena through the ensemble-based experimental, theoretical, and computational investigations from our laboratory over the past decade. Special emphasis is given to insights that run counter to some of the prevailing ideas that have emerged over the past 40 years of structural biology research. For instance, when proteins are viewed as conformational ensembles rather than as single structures, the commonly held notion of an allosteric pathway as an obligate series of individual structural distortions loses its meaning. Instead, allostery can result from energetic linkage between distal sites as one Boltzmann distribution of states transitions to another. Additionally, the emerging principles from this ensemble view of proteins have proven surprisingly useful in describing the role of intrinsic disorder in inter-domain communication, functional adaptation mediated by mutational control of fluctuations, and evolutionary conservation of the energetics of protein stability.     

A decade of CASP: progress, bottlenecks and prognosis in protein structure prediction

For the past ten years, CASP (Critical Assessment of Structure Prediction) has monitored the state of the art in modeling protein structure from sequence. During this period, there has been substantial progress in both comparative modeling of structure (using information from an evolutionarily related structural template) and template-free modeling. The quality of comparative models depends on the closeness of the evolutionary relationship on which they are based. Template-free modeling, although still very approximate, now produces topologically near correct models for some small proteins. Current major challenges are refining comparative models so that they match experimental accuracy, obtaining accurate sequence alignments for models based on remote evolutionary relationships, and extending template-free modeling methods so that they produce more accurate models, handle parts of comparative models not available from a template and deal with larger structures.     

Testing for covarion-like evolution in protein sequences

The covarion hypothesis of molecular evolution proposes that selective pressures on an amino acid or nucleotide site change through time, thus causing changes of evolutionary rate along the edges of a phylogenetic tree. Several kinds of Markov models for the covarion process have been proposed. One model, proposed by Huelsenbeck (2002), has 2 substitution rate classes: the substitution process at a site can switch between a single variable rate, drawn from a discrete gamma distribution, and a zero invariable rate. A second model, suggested by Galtier (2001), assumes rate switches among an arbitrary number of rate classes but switching to and from the invariable rate class is not allowed. The latter model allows for some sites that do not participate in the rate-switching process. Here we propose a general covarion model that combines features of both models, allowing evolutionary rates not only to switch between variable and invariable classes but also to switch among different rates when they are in a variable state. We have implemented all 3 covarion models in a maximum likelihood framework for amino acid sequences and tested them on 23 protein data sets. We found significant likelihood increases for all data sets for the 3 models, compared with a model that does not allow site-specific rate switches along the tree. Furthermore, we found that the general model fit the data better than the simpler covarion models in the majority of the cases, highlighting the complexity in modeling the covarion process. The general covarion model can be used for comparing tree topologies, molecular dating studies, and the investigation of protein adaptation.     

The emergence of scaling in sequence-based physical models of protein evolution

It has recently been discovered that many biological systems, when represented as graphs, exhibit a scale-free topology. One such system is the set of structural relationships among protein domains. The scale-free nature of this and other systems has previously been explained using network growth models that, although motivated by biological processes, do not explicitly consider the underlying physics or biology. In this work we explore a sequence-based model for the evolution protein structures and demonstrate that this model is able to recapitulate the scale-free nature observed in graphs of real protein structures. We find that this model also reproduces other statistical feature of the protein domain graph. This represents, to our knowledge, the first such microscopic, physics-based evolutionary model for a scale-free network of biological importance and as such has strong implications for our understanding of the evolution of protein structures and of other biological networks.