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Significant progress has been made in recent years in a variety of seemingly unrelated fields such as sequencing, protein structure prediction, and high-throughput transcriptomics and metabolomics. At the same time, new microscopic models have been developed that made it possible to analyze the evolution of genes and genomes from first principles. The results from these efforts enable, for the first time, a comprehensive insight into the evolution of complex systems and organisms on all scales--from sequences to organisms and populations. Every newly sequenced genome uncovers new genes, families, and folds. Where do these new genes come from? How do gene duplication and subsequent divergence of sequence and structure affect the fitness of the organism? What role does regulation play in the evolution of proteins and folds? Emerging synergism between data and modeling provides first robust answers to these questions.

Although rigorous measures of similarity for sequence and structure are now well established, the problem of defining functional relationships has been particularly daunting. Here, we present several manifold embedding techniques to compute distances between Gene Ontology (GO) functional annotations and consequently estimate functional distances between protein domains. To evaluate accuracy, we correlate the functional distance to the well established measures of sequence, structural, and phylogenetic similarities. Finally, we show that manual classification of structures into folds and superfamilies is mirrored by proximity in the newly defined function space. We show how functional distances place structure–function relationships in biological context resulting in insight into divergent and convergent evolution. The methods and results in this paper can be readily generalized and applied to a wide array of biologically relevant investigations, such as accuracy of annotation transference, the relationship between sequence, structure, and function, or coherence of expression modules.

Understanding the observed variability in the number of homologs of a gene is a very important unsolved problem that has broad implications for research into coevolution of structure and function, gene duplication, pseudogene formation, and possibly for emerging diseases. Here, we attempt to define and elucidate some possible causes behind the observed irregularity in sequence space. We present evidence that sequence variability and functional diversity of a gene or fold family is influenced by quantifiable characteristics of the protein structure. These characteristics reflect the structural potential for sequence plasticity, i.e., the ability to accept mutation without losing thermodynamic stability. We identify a structural feature of a protein domain—contact density—that serves as a determinant of entropy in sequence space, i.e., the ability of a protein to accept mutations without destroying the fold (also known as fold designability). We show that (log) of average gene family size exhibits statistical correlation (R2 > 0.9.) with contact density of its three-dimensional structure. We present evidence that the size of individual gene families are influenced not only by the designability of the structure, but also by evolutionary history, e.g., the amount of time the gene family was in existence. We further show that our observed statistical correlation between gene family size and contact density of the structure is valid on many levels of evolutionary divergence, i.e., not only for closely related sequence, but also for less-related fold and superfamily levels of homology.

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.

An open question of great interest in biophysics is whether variations in structure cause protein folds to differ in the number of amino acid sequences that can fold to them stably, i.e., in their designability. Recently, we have shown that a novel quantitative measure of a fold's tertiary topology, called its contact trace, strongly correlates with the fold's designability. Here, we investigate the relationship between a fold's contact trace and its relative frequency of usage in mesophilic vs. thermophilic eubacteria. We observe that thermophilic organisms exhibit a bias toward using folds of higher contact trace when compared with mesophiles. We establish this difference both for the distributions of folds at the whole-proteome level and also through more focused structural comparisons of orthologous proteins. Our findings suggest that thermophilic adaptation in bacterial genomes occurs in part through natural selection of more designable folds, pointing to designability as a key component of protein fitness.

Using structural similarity clustering of protein domains: protein domain universe graph (PDUG), and a hierarchical functional annotation: gene ontology (GO) as two evolutionary lenses, we find that each structural cluster (domain fold) exhibits a distribution of functions that is unique to it. These functional distributions are functional fingerprints that are specific to characteristic structural clusters and vary from cluster to cluster. Furthermore, as structural similarity threshold for domain clustering in the PDUG is relaxed we observe an influx of earlier-diverged domains into clusters. These domains join clusters without destroying the functional fingerprint. These results can be understood in light of a divergent evolution scenario that posits correlated divergence of structural and functional traits in protein domains from one or few progenitors.

In this work we develop a microscopic physical model of early evolution, where phenotype,organism life expectancy, is directly related to genotype, the stability of its proteins in their native conformations which can be determined exactly in the model. Simulating the model on a computer, we consistently observe the Big Bang scenario whereby exponential population growth ensues as soon as favorable sequence-structure combinations (precursors of stable proteins) are discovered. Upon that, random diversity of the structural space abruptly collapses into a small set of preferred proteins. We observe that protein folds remain stable and abundant in the population at time scales much greater than mutation or organism lifetime, and the distribution of the lifetimes of dominant folds in a population approximately follows a power law. The separation of evolutionary time scales between discovery of new folds and generation of new sequences gives rise to emergence of protein families and superfamilies whose sizes are power-law distributed, closely matching the same distributions for real proteins. On the population level we observe emergence of species, subpopulations which carry similar genomes. Further we present a simple theory that relates stability of evolving proteins to the sizes of emerging genomes. Together, these results provide a microscopic first principles picture of how first gene families developed in the course of early evolution, Comment: In press, PLoS Computational Biology

We study statistical properties of interacting protein-like surfaces and predict two strong, related effects: (i) statistically enhanced self-attraction of proteins; (ii) statistically enhanced attraction of proteins with similar structures. The effects originate in the fact that the probability to find a pattern self-match between two identical, even randomly organized interacting protein surfaces is always higher compared with the probability for a pattern match between two different, promiscuous protein surfaces. This theoretical finding explains statistical prevalence of homodimers in protein-protein interaction networks reported earlier. Further, our findings are confirmed by the analysis of curated database of protein complexes that showed highly statistically significant overrepresentation of dimers formed by structurally similar proteins with highly divergent sequences ("superfamily heterodimers"). We suggest that promiscuous homodimeric interactions pose strong competitive interactions for heterodimers evolved from homodimers. Such evolutionary bottleneck is overcome using the negative design evolutionary pressure applied against promiscuous homodimer formation. This is achieved through the formation of highly specific contacts formed by charged residues as demonstrated both in model and real superfamily heterodimers.

ELISA (http://romi.bu.edu/elisa/) is a database that was designed for flexibility in defining interesting queries about protein domain evolution. We have defined and included both the inherent characteristics of the domains such as structure and function and comparisons of these characteristics between domains. Thus, the database is useful in defining structural and functional links between related protein domains and by extension sequences that encode them. In this database we introduce and employ a novel method of functional annotation and comparison. For each protein domain we create a probabilistic functional annotation tree using GO. We have designed an algorithm that accurately compares these trees and thus provides a measure of "functional distance" between two protein domains. Along with functional annotation, we have also included structural comparison between protein domains and best sequence comparisons to all known genomes. The latter enables researchers to dynamically do searches for domains sharing similar phylogenetic profiles. This combination of data and tools enables the researcher to design complex queries to carry out research in the areas of protein domain evolution, structure prediction and functional annotation of novel sequences.

The bottom-up approach to understanding the evolution of organisms is by studying molecular evolution. With the large number of protein structures identified in the past decades, we have discovered peculiar patterns that nature imprints on protein structural space in the course of evolution. In particular, we have discovered that the universe of protein structures is organized hierarchically into a scale-free network. By understanding the cause of these patterns, we attempt to glance at the very origin of life.