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The ability to absorb mutations while retaining structure and function, or mutational robustness, is a remarkable property of natural proteins. In this Letter, we use a computational model of organismic evolution [Zeldovich et al, PLOS Comp Biol 3(7):e139 (2007)], which explicitly couples protein physics and population dynamics, to study mutational robustness of evolved model proteins. We find that dominant protein structures which evolved in the simulations are highly designable ones, in accord with some of the earlier observations. Next, we compare evolved sequences with the ones designed to fold into the same dominant structures and having the same thermodynamic stability, and find that evolved sequences are more robust against point mutations, being less likely to be destabilized upon them. These results point to sequence evolution as an important method of protein engineering if mutational robustness of the artificially developed proteins is desired. On the biological side, mutational robustness of proteins appears to be a natural consequence of the mutation-selection evolutionary process.

How does immune system evolve functional proteins - potent antibodies - in such a short time? We address this question using a microscopic, protein-level, sequence-based model of humoral immune response with explicitly defined interactions between Immunoglobulins, host and pathogen proteins. Potent Immunoglobulins are discovered in this model via clonal selection and affinity maturation. Possible outcomes of an infection (extinction of cells, survival with complete elimination of viruses, or persistent infection) crucially depend on mutation rates of viral and Immunoglobulin proteins. The model predicts that there is an optimal Somatic Hypermutation (SHM) rate close to experimentally observed 10-3 per nucleotide per replication. Further, we developed an analytical theory which explains the physical reason for an optimal SHM program as a compromise between deleterious effects of random mutations on nascent maturing Immunoglobulins (adversity) and the need to generate diverse pool of mutated antibodies from which highly potent ones can be drawn (diversity). The theory explains such effects as dependence of B cell fate on affinity for an incoming antigen, ceiling in affinity of mature antibodies, Germinal Center sizes and maturation times. The theory reveals the molecular factors which determine the efficiency of affinity maturation, providing insight into variability of immune response to cytopathic (direct response by germline antibodies) and poorly cytopathic viruses (crucial role of SHM in response). These results demonstrate the feasibility and promise of microscopic sequence-based models of immune system, where population dynamics of evolving Immunoglobulins is explicitly tied to their molecular properties.

Mechanisms of immunity, and of the host-pathogen interactions in general are among the most fundamental problems of medicine, ecology, and evolution studies. Here, we present a microscopic, protein-level, sequence-based model of immune system, with explicitly defined interactions between host and pathogen proteins.. Simulations of this model show that possible outcomes of the infection (extinction of cells, survival with complete elimination of viruses, or chronic infection with continuous coexistence of cells and viruses) crucially depend on mutation rates of the viral and immunoglobulin proteins. Infection is always lethal if the virus mutation rate exceeds a certain threshold. Potent immunoglobulins are discovered in this model via clonal selection and affinity maturation. Surviving cells acquire lasting immunity against subsequent infection by the same virus strain. As a second line of defense cells develop apoptosis-like behavior by reducing their lifetimes to eliminate viruses. These results demonstrate the feasibility of microscopic sequence-based models of immune system, where population dynamics of the evolving B-cells is explicitly tied to the molecular properties of their proteins.

An increasing number of proteins are being discovered with a remarkable and somewhat surprising feature, a knot in their native structures. How the polypeptide chain is able to knot itself during the folding process to form these highly intricate protein topologies is not known. Here, we perform a computational study on the 160-amino acid homodimeric protein YibK which, like other proteins in the SpoU family of MTases, contains a deep trefoil knot in its C-terminal region. In this study, we use a coarse-grained C-alpha-chain representation and Langevin dynamics to study folding kinetics. We find that specific, attractive nonnative interactions are critical for knot formation. In the absence of these interactions, i.e. in an energetics driven entirely by native interactions, knot formation is exceedingly unlikely. Further, we find, in concert with recent experimental data on YibK, two parallel folding pathways which we attribute to an early and a late formation of the trefoil knot, respectively. For both pathways, knot formation occurs before dimerization. A bioinformatics analysis of the SpoU family of proteins reveals further that the critical nonnative interactions may originate from evolutionary conserved hydrophobic segments around the knotted region.

Prokaryotes living at extreme environmental temperatures exhibit pronounced signatures in the amino acid composition of their proteins and nucleotide compositions of their genomes reflective of adaptation to their thermal environments. However, despite significant efforts, the definitive answer of what are the genomic and proteomic compositional determinants of Optimal Growth Temperature of prokaryotic organisms remained elusive. Here the authors performed a comprehensive analysis of amino acid and nucleotide compositional signatures of thermophylic adaptation by exhaustively evaluating all combinations of amino acids and nucleotides as possible determinants of Optimal Growth Temperature for all prokaryotic organisms with fully sequences genomes.. The authors discovered that total concentration of seven amino acids in proteomes, IVYWREL, serves as a universal proteomic predictor of Optimal Growth Temperature in prokaryotes. Resolving the old-standing controversy the authors determined that the variation in nucleotide composition (increase of purine load, or A+G content with temperature) is largely a consequence of thermal adaptation of proteins. However, the frequency with which A and G nucleotides appear as nearest neighbors in genome sequences is strongly and independently correlated with Optimal Growth Temperature. as a result of codon bias in corresponding genomes. Together these results provide a complete picture of proteomic and genomic determinants of thermophilic adaptation., Comment: in press PLoS Computational Biology; revised version

The aim of this work is to elucidate how physical principles of protein design are reflected in natural sequences that evolved in response to the thermal conditions of the environment. Using an exactly solvable lattice model, we design sequences with selected thermal properties. Compositional analysis of designed model sequences and natural proteomes reveals a specific trend in amino acid compositions in response to the requirement of stability at elevated environmental temperature, i.e. the increase of fractions of hydrophobic and charged amino acid residues at the expense of polar ones. We show that this from both ends of hydrophobicity scale trend is due to positive (to stabilize the native state) and negative (to destabilize misfolded states) components of protein design. Negative design strengthens specific repulsive nonnative interactions that appear in misfolded structures. A pressure to preserve specific repulsive interactions in non-native conformations may result in correlated mutations between amino acids which are far apart in the native state but may be in contact in misfolded conformations. Such correlated mutations are indeed found in TIM barrel and other proteins., Comment: PLoS Computational Biology, in press

In this work we propose a physical model of organismal evolution, where phenotype, organism life expectancy, is directly related to genotype i.e. the stability of its proteins 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 favorable sequence-structure combinations (precursors of stable proteins) are discovered. After that, random diversity of the structural space abruptly collapses into a small set of preferred structural motifs. 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. The network of structural similarities of the universe of evolved proteins has the same scale-free like character as the actual protein domain universe graph (PDUG). Further, the model predicts that ancient protein domains represent a highly connected and clustered subset of all protein domains, in complete agreement with reality. Together, these results provide a microscopic first principles picture of how protein structures and gene families evolved in the course of evolution., Comment: Replaced with revised version; power-law distributions are shown here to emerge from microscopic model evolutionary dynamics

In this work, we discovered a fundamental connection between selection for protein stability and emergence of preferred structures of proteins. Using standard exact 3-dimensional lattice model we evolve sequences starting from random ones and determining exact native structure after each mutation. Acceptance of mutations is biased to select for stable proteins. We found that certain structures, wonderfold, are independently discovered numerous times as native states of stable proteins in many unrelated runs of selection. 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. Wonderfolds appear to be the most designable structures out of complete set of compact lattice proteins. Furthermore, proteins having wondefolds as their native structure tend to be most thermostable among all evolved proteins. This effect is purely due to the favorable geometric properties of wonderfolds and, thus, dominates any dependence on sequences. The present work establishes a model of prebiotic structure selection, which identifies dominant structural patterns emerging upon optimization of proteins for survival in hot environment. Convergently discovered prebiotic initial superfamilies with wonderfold structures could have served as a seed for subsequent biological evolution involving gene duplications and divergence.