Conformational catalysis of cataract-associated aggregation by interacting intermediates in a human eye lens crystallin

Most known proteins in nature consist of multiple domains. Interactions between domains may lead to unexpected folding and misfolding phenomena. This study of human {\gamma}D-crystallin, a two-domain protein in the eye lens, revealed one such surprise: conformational catalysis of misfolding via intermolecular domain interface ''stealing''. An intermolecular interface between the more stable domains outcompetes the native intramolecular domain interface. Loss of the native interface in turn promotes misfolding and subsequent aggregation, especially in cataract-related {\gamma}D-crystallin variants. This phenomenon is likely a contributing factor in the development of cataract disease, the leading worldwide cause of blindness. However, interface stealing likely occurs in many proteins composed of two or more interacting domains.Comment: 26 pages, 6 figures+Supplementar

Lethal Mutagenesis in Viruses and Bacteria

Here we study how mutations which change physical properties of cell proteins (stability) impact population survival and growth. In our model the genotype is presented as a set of N numbers, folding free energies of cells N proteins. Mutations occur upon replications so that stabilities of some proteins in daughter cells differ from those in parent cell by random amounts drawn from experimental distribution of mutational effects on protein stability. The genotype-phenotype relationship posits that unstable proteins confer lethal phenotype to a cell and in addition the cells fitness (duplication rate) is proportional to the concentration of its folded proteins. Simulations reveal that lethal mutagenesis occurs at mutation rates close to 7 mutations per genome per replications for RNA viruses and about half of that for DNA based organisms, in accord with earlier predictions from analytical theory and experiment. This number appears somewhat dependent on the number of genes in the organisms and natural death rate. Further, our model reproduces the distribution of stabilities of natural proteins in excellent agreement with experiment. Our model predicts that species with high mutation rates, tend to have less stable proteins compared to species with low mutation rate

Growth tradeoffs produce complex microbial communities on a single limiting resource

The relationship between the dynamics of a community and its constituent pairwise interactions is a fundamental problem in ecology. Higher-order ecological effects beyond pairwise interactions may be key to complex ecosystems, but mechanisms to produce these effects remain poorly understood. Here we show that higher-order effects can arise from variation in multiple microbial growth traits, such as lag times and growth rates, on a single limiting resource with no other interactions. These effects produce a range of ecological phenomena: an unlimited number of strains can exhibit multistability and neutral coexistence, potentially with a single keystone strain; strains that coexist in pairs do not coexist all together; and the champion of all pairwise competitions may not dominate in a mixed community. Since variation in multiple growth traits is ubiquitous in microbial populations due to pleiotropy and non-genetic variation, our results indicate these higher-order effects may also be widespread, especially in laboratory ecology and evolution experiments

Emergence of the protein universe in organismal evolution

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 dynamic

Thermal Adaptation in Viruses and Bacteria

A previously established multiscale population genetics model states that fitness can be inferred from the physical properties of proteins under the physiological assumption that a loss of stability by any protein confers the lethal phenotype to an organism. Here we develop this model further by positing that replication rate (fitness) of a bacterial or viral strain directly depends on the copy number of folded proteins which determine its replication rate. Using this model, and both numerical and analytical approaches, we studied the adaptation process of bacteria and viruses at varied environmental temperatures. We found that a broad distribution of protein stabilities observed in the model and in experiment is the key determinant of thermal response for viruses and bacteria. Our results explain most of the earlier experimental observations: striking asymmetry of thermal response curves, the absence of evolutionary trade-off which was expected but not found in experiments, correlation between denaturation temperature for several protein families and the Optimal Growth Temperature (OGT) of their host organisms, and proximity of bacterial or viral OGTs to their evolutionary temperatures. Our theory quantitatively and with high accuracy described thermal response curves for 35 bacterial species using, for each species, only two adjustable parameters, the number of replication rate determining genes and energy barrier for metabolic reactions

Mode-coupling theory for heteropolymers

We study the Langevin dynamics of a heteropolymer by means of a mode-coupling approximation scheme, giving rise to a set of coupled integro-differential equations relating the response and correlation functions. The analysis shows that there is a regime at low temperature characterized by out-of-equilibrium dynamics, with violation of time-translational invariance and of the fluctuation-dissipation theorem. The onset of ageing dynamics at low temperatures gives new insight into the nature of the slow dynamics of a disordered polymer. We also introduce a renormalization-group treatment of our mode-coupling equations, which supports our analysis, and might be applicable to other systems.Comment: 23 page

Mutation rate variability as a driving force in adaptive evolution

Mutation rate is a key determinant of the pace as well as outcome of evolution, and variability in this rate has been shown in different scenarios to play a key role in evolutionary adaptation and resistance evolution under stress caused by selective pressure. Here we investigate the dynamics of resistance fixation in a bacterial population with variable mutation rates and show that evolutionary outcomes are most sensitive to mutation rate variations when the population is subject to environmental and demographic conditions that suppress the evolutionary advantage of high-fitness subpopulations. By directly mapping a biophysical fitness function to the system-level dynamics of the population we show that both low and very high, but not intermediate, levels of stress in the form of an antibiotic result in a disproportionate effect of hypermutation on resistance fixation. We demonstrate how this behavior is directly tied to the extent of genetic hitchhiking in the system, the propagation of high-mutation rate cells through association with high-fitness mutations. Our results indicate a substantial role for mutation rate flexibility in the evolution of antibiotic resistance under conditions that present a weak advantage over wildtype to resistant cells

Thermodynamics of the Hairpin Ribozyme from All-Atom Simulations

The structure of the self-cleaving hairpin ribozyme is well characterized, and its folding has been examined in bulk and by single-molecule fluorescence, establishing the importance of cations, especially magnesium in the stability of the native fold. Here we describe the first all-atom folding simulations of the hairpin ribozyme, using a version of a Go potential with separate secondary and tertiary structure energetic contributions. The ratio of tertiary/secondary interaction energies serves as a proxy for non-specific cation binding: a high ratio corresponds to a high concentration, while a low one mimics low concentration. By studying the unfolding behavior of the RNA over a range of temperature and tertiary/secondary energies, a three-state phase diagram emerges, with folded, unfolded (coil) and transient folding/unfolding tertiary structure species. The thermodynamics were verified by paired folding simulations in each region of the phase diagram. The three phase behaviors correspond with experimentally observed states, so this simple model captures the essential aspect of thermodynamics in RNA folding

Understanding hierarchical protein evolution from first principles

We propose a model that explains the hierarchical organization of proteins in fold families. The model, which is based on the evolutionary selection of proteins by their native state stability, reproduces patterns of amino acids conserved across protein families. Due to its dynamic nature, the model sheds light on the evolutionary time scales. By studying the relaxation of the correlation function between consecutive mutations at a given position in proteins, we observe separation of the evolutionary time scales: at the short time intervals families of proteins with similar sequences and structures are formed, while at long time intervals the families of structurally similar proteins that have low sequence similarity are formed. We discuss the evolutionary implications of our model. We provide a ``profile'' solution to our model and find agreement between predicted patterns of conserved amino acids and those actually observed in nature.Comment: 25 pages, 17 figure

Geometric and physical considerations for realistic protein models

Protein structure is generally conceptualized as the global arrangement or of smaller, local motifs of helices, sheets, and loops. These regular, recurring secondary structural elements have well-understood and standardized definitions in terms of amino acid backbone geometry and the manner in which hydrogen bonding requirements are satisfied. Recently, "tube" models have been proposed to explain protein secondary structure in terms of the geometrically optimal packing of a featureless cylinder. However, atomically detailed simulations demonstrate that such packing considerations alone are insufficient for defining secondary structure; both excluded volume and hydrogen bonding must be explicitly modeled for helix formation. These results have fundamental implications for the construction and interpretation of realistic and meaningful biomacromolecular models