Model Of Protein Evolution Research Articles

What's in a Likelihood? Simple Models of Protein Evolution and the Contribution of Structurally Viable Reconstructions to the Likelihood

Most phylogenetic models of protein evolution assume that sites are independent and identically distributed. Interactions between sites are ignored, and the likelihood can be conveniently calculated as the product of the individual site likelihoods. The calculation considers all possible transition paths (also called substitution histories or mappings) that are consistent with the observed states at the terminals, and the probability density of any particular reconstruction depends on the substitution model. The likelihood is the integral of the probability density of each substitution history taken over all possible histories that are consistent with the observed data. We investigated the extent to which transition paths that are incompatible with a protein's three-dimensional structure contribute to the likelihood. Several empirical amino acid models were tested for sequence pairs of different degrees of divergence. When simulating substitutional histories starting from a real sequence, the structural integrity of the simulated sequences quickly disintegrated. This result indicates that simple models are clearly unable to capture the constraints on sequence evolution. However, when we sampled transition paths between real sequences from the posterior probability distribution according to these same models, we found that the sampled histories were largely consistent with the tertiary structure. This suggests that simple empirical substitution models may be adequate for interpolating changes between observed sequences during phylogenetic inference despite the fact that the models cannot predict the effects of structural constraints from first principles. This study is significant because it provides a quantitative assessment of the biological realism of substitution models from the perspective of protein structure, and it provides insight on the prospects for improving models of protein sequence evolution.

Estudio computacional de las relaciones evolutivas de los receptores ionotrópicos NMDA, AMPA y kainato en cuatro especies de primates

<p><strong></strong><strong>Objective.</strong> To identify the influence of changes on the secondary structure and evolutionary relationship of NMDA, AMPA and kainate receptors in <em>Homo sapiens</em>,<em> Pan troglodytes</em>, <em>Pongo pygmaeus</em> and <em>Macaca mulatta</em>. <strong>Materials and methods.</strong> We identified 91 sequences for NMDA, AMPA and kainate receptors and analyzed with software for predicting secondary structure, phosphorylation sites, multiple alignments, selection of protein evolution models and phylogenetic prediction. <strong>Results.</strong> We found that subunits GLUR5, NR2A, NR2C and NR3A showed structural changes in the C-terminal region and formation or loss of phosphorylation sites in this zone. Additionally the phylogenetic prediction suggests that the NMDA NR2 subunits are the closest to the ancestral node that gives rise to the other subunits. <strong>Conclusions.</strong> Changes in structure and phosphorylation sites in GLUR5, NR2A, NR2C and NR3A subunits suggest variations in the interaction of the C-terminal region with kinase proteins and with proteins with PDZ domains, which could affect the trafficking and anchoring of the subunits. On the other hand, the phylogenetic prediction suggests that the changes that occurred in the NR2 subunits gave rise to the other subunits of glutamate ionotropic receptors, primarily because the NMDA and particularly the NR2D subunits are the most closely related to the ancestral node that possibly gave rise to the iGluRs.</p> <p><strong>Key words: </strong>glutamate ionotropic receptors, iGluRs, NMDA, NR1, NR2A, NR2C, NR3A, AMPA, GluR5.</p><br />

Comparing Models of Evolution for Ordered and Disordered Proteins

Most models of protein evolution are based upon proteins that form relatively rigid 3D structures. A significant fraction of proteins, the so-called disordered proteins, do not form rigid 3D structures and sample a broad conformational ensemble. Disordered proteins do not typically maintain long-range interactions, so the constraints on their evolution should be different than ordered proteins. To test this hypothesis, we developed and compared models of evolution for disordered and ordered proteins. Substitution matrices were constructed using the sequences of putative homologs for sets of experimentally characterized disordered and ordered proteins. Separate matrices, at three levels of sequence similarity (>85%, 85–60%, and 60–40%), were inferred for each type of protein structure. The substitution matrices for disordered and ordered proteins differed significantly at each level of sequence similarity. The disordered matrices reflected a greater likelihood of evolutionary changes, relative to the ordered matrices, and these changes involved nonconservative substitutions. Glutamic acid and asparagine were interesting exceptions to this result. Important differences between the substitutions that are accepted in disordered proteins relative to ordered proteins were also identified. In general, disordered proteins have fewer evolutionary constraints than ordered proteins. However, some residues like tryptophan and tyrosine are highly conserved in disordered proteins. This is due to their important role in forming protein–protein interfaces. Finally, the amino acid frequencies for disordered proteins, computed during the development of the matrices, were compared with amino acid frequencies for different categories of secondary structure in ordered proteins. The highest correlations were observed between the amino acid frequencies in disordered proteins and the solvent-exposed loops and turns of ordered proteins, supporting an emerging structural model for disordered proteins.

Pairwise and higher-order correlations among drug-resistance mutations in HIV-1 subtype B protease

BackgroundThe reaction of HIV protease to inhibitor therapy is characterized by the emergence of complex mutational patterns which confer drug resistance. The response of HIV protease to drugs often involves both primary mutations that directly inhibit the action of the drug, and a host of accessory resistance mutations that may occur far from the active site but may contribute to restoring the fitness or stability of the enzyme. Here we develop a probabilistic approach based on connected information that allows us to study residue, pair level and higher-order correlations within the same framework.ResultsWe apply our methodology to a database of approximately 13,000 sequences which have been annotated by the treatment history of the patients from which the samples were obtained. We show that including pair interactions is essential for agreement with the mutational data, since neglect of these interactions results in order-of-magnitude errors in the probabilities of the simultaneous occurence of many mutations. The magnitude of these pair correlations changes dramatically between sequences obtained from patients that were or were not exposed to drugs. Higher-order effects make a contribution of as much as 10% for residues taken three at a time, but increase to more than twice that for 10 to 15-residue groups. The sequence data is insufficient to determine the higher-order effects for larger groups. We find that higher-order interactions have a significant effect on the predicted frequencies of sequences with large numbers of mutations. While relatively rare, such sequences are more prevalent after multi-drug therapy. The relative importance of these higher-order interactions increases with the number of drugs the patient had been exposed to.ConclusionCorrelations are critical for the understanding of mutation patterns in HIV protease. Pair interactions have substantial qualitative effects, while higher-order interactions are individually smaller but may have a collective effect. Together they lead to correlations which could have an important impact on the dynamics of the evolution of cross-resistance, by allowing the virus to pass through otherwise unlikely mutational states. These findings also indicate that pairwise and possibly higher-order effects should be included in the models of protein evolution, instead of assuming that all residues mutate independently of one another.

PROCOV: maximum likelihood estimation of protein phylogeny under covarion models and site-specific covarion pattern analysis

BackgroundThe covarion hypothesis of molecular evolution holds that selective pressures on a given amino acid or nucleotide site are dependent on the identity of other sites in the molecule that change throughout time, resulting in changes of evolutionary rates of sites along the branches of a phylogenetic tree. At the sequence level, covarion-like evolution at a site manifests as conservation of nucleotide or amino acid states among some homologs where the states are not conserved in other homologs (or groups of homologs). Covarion-like evolution has been shown to relate to changes in functions at sites in different clades, and, if ignored, can adversely affect the accuracy of phylogenetic inference.ResultsPROCOV (protein covarion analysis) is a software tool that implements a number of previously proposed covarion models of protein evolution for phylogenetic inference in a maximum likelihood framework. Several algorithmic and implementation improvements in this tool over previous versions make computationally expensive tree searches with covarion models more efficient and analyses of large phylogenomic data sets tractable. PROCOV can be used to identify covarion sites by comparing the site likelihoods under the covarion process to the corresponding site likelihoods under a rates-across-sites (RAS) process. Those sites with the greatest log-likelihood difference between a 'covarion' and an RAS process were found to be of functional or structural significance in a dataset of bacterial and eukaryotic elongation factors.ConclusionCovarion models implemented in PROCOV may be especially useful for phylogenetic estimation when ancient divergences between sequences have occurred and rates of evolution at sites are likely to have changed over the tree. It can also be used to study lineage-specific functional shifts in protein families that result in changes in the patterns of site variability among subtrees.

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.

The Universal Trend of Amino Acid Gain–Loss is Caused by CpG Hypermutability

Understanding the cause of the changes in the amino acid composition of proteins is essential for understanding the evolution of protein functions. Since the early 1970s, it has been known that the frequency of some amino acids in protein sequences is increasing and that of others is decreasing. Recently, it was found that the trends of amino acid changes were similar in 15 taxa representing Bacteria, Archaea, and Eukaryota. However, the cause of this similarity in the trend of the gains and losses of amino acids continued to be debated. Here, we show that this trend of the gain and loss of amino acids can be simply explained by CpG hypermutability. We found that the frequency of amino acids coded by codons with TpG dinucleotides and those with CpA dinucleotides is increasing, while that of amino acids coded by codons with CpG dinucleotides is decreasing. We also found that organisms that lack DNA methyltransferase show different trends of the gain and loss of amino acids. DNA methyltransferase methylates CpG dinucleotides and induces CpG hypermutability. The incorporation of CpG hypermutability into models of protein evolution will improve studies on protein evolution in different organisms.

Frequent and Widespread Parallel Evolution of Protein Sequences

Understanding the patterns and causes of protein sequence evolution is a major challenge in evolutionary biology. One of the critical unresolved issues is the relative contribution of selection and genetic drift to the fixation of amino acid sequence differences between species. Molecular homoplasy, the independent evolution of the same amino acids at orthologous sites in different taxa, is one potential signature of selection; however, relatively little is known about its prevalence in eukaryotic proteomes. To quantify the extent and type of homoplasy among evolving proteins, we used phylogenetic methodology to analyze 8 genome-scale data matrices from clades of different evolutionary depths that span the eukaryotic tree of life. We found that the frequency of homoplastic amino acid substitutions in eukaryotic proteins was more than 2-fold higher than expected under neutral models of protein evolution. The overwhelming majority of homoplastic substitutions were parallelisms that involved the most frequently exchanged amino acids with similar physicochemical properties and that could be reached by a single-mutational step. We conclude that the role of homoplasy in shaping the protein record is much larger than generally assumed, and we suggest that its high frequency can be explained by both weak positive selection for certain substitutions and purifying selection that constrains substitutions to a small number of functionally equivalent amino acids.

Effective connectivity profile: A structural representation that evidences the relationship between protein structures and sequences

The complexity of protein structures calls for simplified representations of their topology. The simplest possible mathematical description of a protein structure is a one-dimensional profile representing, for instance, buriedness or secondary structure. This kind of representation has been introduced for studying the sequence to structure relationship, with applications to fold recognition. Here we define the effective connectivity profile (EC), a network theoretical profile that self-consistently represents the network structure of the protein contact matrix. The EC profile makes mathematically explicit the relationship between protein structure and protein sequence, because it allows predicting the average hydrophobicity profile (HP) and the distributions of amino acids at each site for families of homologous proteins sharing the same structure. In this sense, the EC provides an analytic solution to the statistical inverse folding problem, which consists in finding the statistical properties of the set of sequences compatible with a given structure. We tested these predictions with simulations of the structurally constrained neutral (SCN) model of protein evolution with structure conservation, for single- and multi-domain proteins, and for a wide range of mutation processes, the latter producing sequences with very different hydrophobicity profiles, finding that the EC-based predictions are accurate even when only one sequence of the family is known. The EC profile is very significantly correlated with the HP for sequence-structure pairs in the PDB as well. The EC profile generalizes the properties of previously introduced structural profiles to modular proteins such as multidomain chains, and its correlation with the sequence profile is substantially improved with respect to the previously defined profiles, particularly for long proteins. Furthermore, the EC profile has a dynamic interpretation, since the EC components are strongly inversely related with the temperature factors measured in X-ray experiments, meaning that positions with large EC component are more strongly constrained in their equilibrium dynamics. Last, the EC profile allows to define a natural measure of modularity that correlates with the number of domains composing the protein, suggesting its application for domain decomposition. Finally, we show that structurally similar proteins have similar EC profiles, so that the similarity between aligned EC profiles can be used as a structure similarity measure, a property that we have recently applied for protein structure alignment. The code for computing the EC profile is available upon request writing to ubastolla@cbm.uam.es, and the structural profiles discussed in this article can be downloaded from the SLOTH webserver http://www.fkp.tu-darmstadt.de/SLOTH/.

A Test of the Markov Model of Evolution in Proteins

INTRODUCTIONThe percent accepted mutation (PAM) scoring matrix is based on the Dayhoff model of protein evolution, which is a Markov process. In the Markov model of amino acid change, the probability of mutation at each site is independent of the previous history of mutations. Use of this model makes it possible to extrapolate amino acid substitutions observed over a relatively short period of evolutionary time to longer periods of evolutionary time. One criticism of the PAM scoring matrix is that the frequency of amino acid changes that require two nucleotide changes is higher than would be expected by chance. This article describes a test of the Markov model of protein evolution, which shows that the model can be valid if certain changes are made in the way that PAM matrices are calculated.

Protein Interaction Network. Double Exponential Model

proper theoretical description of the distribution of the node degree for yeast protein-protein interaction network was investigated to deal with the observed discrepancy between usually proposed models and the existing data. power law or the generalized power law with exponential cut-off were shown to be inaccurate within a wide range of degree values. Proposed linear-combination-of-exponentialdecays- method exactly characterizing the distribution by the spectrum of decay constants revealed two separate parameter domains. A consequent hypothesis that the node degree distribution could follow the universal double exponential law was successfully verified by selected model comparison using the AIC criterion. BIND and DIP data for H. pylori, E. coli, S. cerevisiae, D. melanogaster, C. elegans and A. thaliana were used for this purpose. A linear change in the magnitude of the distribution components with proteome size was observed, manifesting the evolutional stability of the process of developing the protein interaction network. Proposed kinetic model of protein evolution, considering the two hypothetical protein classes, first, with a relatively rapid emerging rate and a short characteristic residence time, and the second one, with the opposite properties, analytically described the nature of bi-exponential pattern. model presents a situation in which evolutionary conserved proteins increase their interactions due to specific kinetic conditions. Thus, we oppose the opinion that the majority of such interactions are biologically significant, and, therefore the older parts of interactome are more complex. We believe that our interactome results support the hypothesis of Stuart Kaufman, presented in his book The Origin of Order, that random mutations and natural selection constitute the origin of order and complexity.

The look-ahead effect of phenotypic mutations

BackgroundThe evolution of complex molecular traits such as disulphide bridges often requires multiple mutations. The intermediate steps in such evolutionary trajectories are likely to be selectively neutral or deleterious. Therefore, large populations and long times may be required to evolve such traits.ResultsWe propose that errors in transcription and translation may allow selection for the intermediate mutations, if the final trait provides a large enough selective advantage. We test this hypothesis using a population based model of protein evolution.ConclusionIf an individual acquires one of two mutations needed for a novel trait, the second mutation can be introduced into the phenotype due to transcription and translation errors. If the novel trait is advantageous enough, the allele with only one mutation will spread through the population, even though the gene sequence does not yet code for the complettrait. Thus, errors allow protein sequences to "look-ahead" for a more direct path to a complex trait.ReviewersThis article was reviewed by Eugene Koonin, Subhajyoti De (nomimated by Madan Babu), and David Krakauer.

Evolutionary framework for protein sequence evolution and gene pleiotropy.

In this article, we develop an evolutionary model for protein sequence evolution. Gene pleiotropy is characterized by K distinct but correlated components (molecular phenotypes) that affect the organismal fitness. These K molecular phenotypes are under stabilizing selection with microadaptation (SM) due to random optima shifts, the SM model. Random coding mutations generate a correlated distribution of K molecular phenotypes. Under this SM model, we further develop a statistical method to estimate the "effective" number of molecular phenotypes (K(e)) of the gene. Therefore, for the first time we can empirically evaluate gene pleiotropy from the protein sequence analysis. Case studies of vertebrate proteins indicate that K(e) is typically approximately 6-9. We demonstrate that the newly developed SM model of protein evolution may provide a basis for exploring genomic evolution and correlations.

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

BackgroundProtein-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.ResultsIn 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).ConclusionThis 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.

Neighboring-site effects of amino acid mutation

Although the context dependence of nucleotide mutation has been supported by accumulating theoretical and experimental evidence, whether this effect can be extended to amino acid mutation remains obscure. As the amino acid doublets (20 × 20) are much more diverse than their nucleotide counterparts (4 × 4), any attempt to address the neighboring-site effects of amino acid mutation was frustrated by deficient amino acid mutation data. Based on the recently revealed 599,745 mutation sites in 45,137 orthologous proteins, we provide solid evidence for the first time to support the existence of neighboring-site effects in amino acid mutation, which is significantly important to improving the prevalent protein-evolution models.

Quaternary Structure Constraints on Evolutionary Sequence Divergence

The structurally constrained protein evolution (SCPE) model simulates protein divergence considering protein structure explicitly. The model is based on the observation that protein structure is more conserved during evolution than the sequences encoding for that structure. In the previous work, the SCPE model considered only the tertiary structure. Here we show that the performance of the model is enhanced when the oligomeric structure is taken into account. Our results agree with recent evolutionary studies of oligomeric proteins, which show that conservation of the quaternary structure imposes additional constraints on sequence divergence. The incorporation of protein-protein interactions into protein evolution models may be important in the study of quaternary protein structures and complex protein assemblies.

Assessing Site-Interdependent Phylogenetic Models of Sequence Evolution

In recent works, methods have been proposed for applying phylogenetic models that allow for a general interdependence between the amino acid positions of a protein. As of yet, such models have focused on site interdependencies resulting from sequence-structure compatibility constraints, using simplified structural representations in combination with a set of statistical potentials. This structural compatibility criterion is meant as a proxy for sequence fitness, and the methods developed thus far can incorporate different site-interdependent fitness proxies based on other measurements. However, no methods have been proposed for comparing and evaluating the adequacy of alternative fitness proxies in this context, or for more general comparisons with canonical models of protein evolution. In the present work, we apply Bayesian methods of model selection-based on numerical calculations of marginal likelihoods and posterior predictive checks-to evaluate models encompassing the site-interdependent framework. Our application of these methods indicates that considering site-interdependencies, as done here, leads to an improved model fit for all data sets studied. Yet, we find that the use of pairwise contact potentials alone does not suitably account for across-site rate heterogeneity or amino acid exchange propensities; for such complexities, site-independent treatments are still called for. The most favored models combine the use of statistical potentials with a suitably rich site-independent model. Altogether, the methodology employed here should allow for a more rigorous and systematic exploration of different ways of modeling explicit structural constraints, or any other site-interdependent criterion, while best exploiting the richness of previously proposed models.

Testing for Spatial Clustering of Amino Acid Replacements Within Protein Tertiary Structure

Widely used models of protein evolution ignore protein structure. Therefore, these models do not predict spatial clustering of amino acid replacements with respect to tertiary structure. One formal and biologically implausible possibility is that there is no tendency for amino acid replacements to be spatially clustered during evolution. An alternative to this is that amino acid replacements are spatially clustered and this spatial clustering can be fully explained by a tendency for similar rates of amino acid replacement at sites that are nearby in protein tertiary structure. A third possibility is that the amount of clustering exceeds that which can be explained solely on the basis of independently evolving protein sites with spatially clustered replacement rates. We introduce two simple and not very parametric hypothesis tests that help distinguish these three possibilities. We then apply these tests to 273 homologous protein families. The null hypothesis of no spatial clustering is rejected for 102 of 273 families. The explanation of spatially clustered rates but independent change among sites is rejected for 43 families. These findings need to be reconciled with the common practice of basing evolutionary inferences on models that assume independent change among sites.

Molecular Evolution of the Plant Virus Family Bromoviridae Based on RNA3-Encoded Proteins

We have carried out an evolutionary study of the two proteins encoded by the RNA 3 from members of the plant virus family Bromoviridae. Using maximum likelihood methods, we have inferred the patterns of amino acid substitution that better explain the diversification of this viral family. The results indicate that the molecular evolution of this family was rather complex, with each protein evolving at different rates and according to different patterns of amino acid substitution. These differences include different amino acid equilibrium frequencies, heterogeneity in substitution rates among sites, and covariation among sites. Despite these differences, the model of protein evolution that better fits both proteins is one specifically proposed for the evolution of globular proteins. We also found evidence for coevolution between domains of these two proteins. Finally, our analyses suggest that the molecular clock hypothesis does not hold, since different lineages evolved at different rates. The implications of these results for the taxonomy of this important family of plant viruses are discussed.

Glassy dynamics in the adaptive immune response prevents autoimmune disease.

The immune system normally protects the human host against death by infection. However, when an immune response is mistakenly directed at self-antigens, autoimmune disease can occur. We describe a model of protein evolution to simulate the dynamics of the adaptive immune response to antigens. Computer simulations of the dynamics of antibody evolution show that different evolutionary mechanisms, namely, gene segment swapping and point mutation, lead to different evolved antibody binding affinities. Although a combination of gene segment swapping and point mutation can yield a greater affinity to a specific antigen than point mutation alone, the antibodies so evolved are highly cross reactive and would cause autoimmune disease, and this is not the chosen dynamics of the immune system. We suggest that in the immune system's search for antibodies, a balance has evolved between binding affinity and specificity.