arXiv subjects

Eugene I. Shakhnovich

Publications and source records attributed to Eugene I. Shakhnovich.

At least 37 records · Page 2Linked to original sources

arXiv2011

Sequence correlations shape protein promiscuity

We predict analytically that diagonal correlations of amino acid positions within protein sequences statistically enhance protein propensity for nonspecific binding. We use the term 'promiscuity' to describe such nonspecific binding. Diagonal correlations represent statistically significant repeats of sequence patterns where amino acids of the same type are clustered together. The predicted effect is qualitatively robust with respect to the form of the microscopic interaction potentials and the average amino acid composition. Our analytical results provide an explanation for the enhanced diagonal correlations observed in hubs of eukaryotic organismal proteomes [J. Mol. Biol. 409, 439 (2011)]. We suggest experiments that will allow direct testing of the predicted effect.

q-bio.BM↗

arXiv2011

Multi-scale sequence correlations increase proteome structural disorder and promiscuity

Numerous experiments demonstrate a high level of promiscuity and structural disorder in organismal proteomes. Here we ask the question what makes a protein promiscuous, i.e., prone to non-specific interactions, and structurally disordered. We predict that multi-scale correlations of amino acid positions within protein sequences statistically enhance the propensity for promiscuous intra- and inter-protein binding. We show that sequence correlations between amino acids of the same type are statistically enhanced in structurally disordered proteins and in hubs of organismal proteomes. We also show that structurally disordered proteins possess a significantly higher degree of sequence order than structurally ordered proteins. We develop an analytical theory for this effect and predict the robustness of our conclusions with respect to the amino acid composition and the form of the microscopic potential between the interacting sequences. Our findings have implications for understanding molecular mechanisms of protein aggregation diseases induced by the extension of sequence repeats.

q-bio.BM↗

arXiv2010

Protein abundances and interactions coevolve to promote functional complexes while suppressing non-specific binding

How do living cells achieve sufficient abundances of functional protein complexes while minimizing promiscuous non-functional interactions? Here we study this problem using a first-principle model of the cell whose phenotypic traits are directly determined from its genome through biophysical properties of protein structures and binding interactions in crowded cellular environment. The model cell includes three independent prototypical pathways, whose topologies of Protein-Protein Interaction (PPI) sub-networks are different, but whose contributions to the cell fitness are equal. Model cells evolve through genotypic mutations and phenotypic protein copy number variations. We found a strong relationship between evolved physical-chemical properties of protein interactions and their abundances due to a "frustration" effect: strengthening of functional interactions brings about hydrophobic interfaces, which make proteins prone to promiscuous binding. The balancing act is achieved by lowering concentrations of hub proteins while raising solubilities and abundances of functional monomers. Based on these principles we generated and analyzed a possible realization of the proteome-wide PPI network in yeast. In this simulation we found that high-throughput affinity capture - mass spectroscopy experiments can detect functional interactions with high fidelity only for high abundance proteins while missing most interactions for low abundance proteins.

q-bio.BM↗

arXiv2010

Optimality of mutation and selection in germinal centers

The population dynamics theory of B cells in a typical germinal center could play an important role in revealing how affinity maturation is achieved. However, the existing models encountered some conflicts with experiments. To resolve these conflicts, we present a coarse-grained model to calculate the B cell population development in affinity maturation, which allows a comprehensive analysis of its parameter space to look for optimal values of mutation rate, selection strength, and initial antibody-antigen binding level that maximize the affinity improvement. With these optimized parameters, the model is compatible with the experimental observations such as the ~100-fold affinity improvements, the number of mutations, the hypermutation rate, and the "all or none" phenomenon. Moreover, we study the reasons behind the optimal parameters. The optimal mutation rate, in agreement with the hypermutation rate in vivo, results from a tradeoff between accumulating enough beneficial mutations and avoiding too many deleterious or lethal mutations. The optimal selection strength evolves as a balance between the need for affinity improvement and the requirement to pass the population bottleneck. These findings point to the conclusion that germinal centers have been optimized by evolution to generate strong affinity antibodies effectively and rapidly. In addition, we study the enhancement of affinity improvement due to B cell migration between germinal centers. These results could enhance our understandings to the functions of germinal centers.

q-bio.PE↗

arXiv2009

Thymic selection of T-cell receptors as an extreme value problem

T lymphocytes (T cells) orchestrate adaptive immune responses upon activation. T cell activation requires sufficiently strong binding of T cell receptors (TCRs) on their surface to short peptides (p) derived from foreign proteins, which are bound to major histocompatibility (MHC) gene products (displayed on antigen presenting cells). A diverse and self-tolerant T cell repertoire is selected in the thymus. We map thymic selection processes to an extreme value problem and provide an analytic expression for the amino acid compositions of selected TCRs (which enable its recognition functions).

physics.bio-ph↗

arXiv2009

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.

q-bio.BM↗

arXiv2009

Slowly replicating lytic viruses: pseudolysogenic persistence and within-host competition

We study the population dynamics of lytic viruses which replicate slowly in dividing host cells within an organism or cell culture, and find a range of viral replication rates that allows viruses to persist, avoiding extinction of host cells or dilution of viruses at too rapid or too slow viral replication. For the within-host competition between multiple viral strains, a strain with a "stable" replication rate could outcompete another strain with a higher or lower replication rate, therefore natural selection of viruses stabilizes the viral persistence. However, when strains with higher and lower than the "stable" value replication rates are both present, competition between strains does not result in dominance of one strain, but in their coexistence.

q-bio.PE↗

arXiv2009

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.

q-bio.BM↗

arXiv2008

Emergence of species in evolutionary simulated annealing

Which factors govern the evolution of mutation rates and emergence of species? Here, we address this question using a first principles model of life where population dynamics of asexual organisms is coupled to molecular properties and interactions of proteins encoded in their genomes. Simulating evolution of populations, we found that fitness increases in punctuated steps via epistatic events, leading to formation of stable and functionally interacting proteins. At low mutation rates, species - populations of organisms with identical genotypes - form, while at higher mutation rates, species are lost through delocalization in sequence space without an apparent loss of fitness. However, when mutation rate was a selectable trait, the population initially maintained high mutation rate until a high fitness level is reached, after which organisms with low mutation rates are gradually selected, with the population eventually reaching mutation rates comparable to those of modern DNA-based organisms. These results provide microscopic insights into the dynamic fitness landscape of asexual populations of unicellular organisms.

q-bio.PE↗

arXiv2008

Sensitivity dependent model of protein-protein interaction networks

The scale free structure p(k)~k^{-gamma} of protein-protein interaction networks can be reproduced by a static physical model in simulation. We inspect the model theoretically, and find the key reason for the model to generate apparent scale free degree distributions. This explanation provides a generic mechanism of "scale free" networks. Moreover, we predict the dependence of gamma on experimental protein concentrations or other sensitivity factors in detecting interactions, and find experimental evidence to support the prediction.

q-bio.MN↗

arXiv2008

Emergence of mutationally robust proteins in a microscopic model of evolution

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.

q-bio.BM↗

arXiv2008

Diversity against adversity: How adaptive immunity evolves potent antibodies

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.

q-bio.CB↗

arXiv2007

Emergence of clonal selection and affinity maturation in an ab initio microscopic model of immunity

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.

q-bio.BM↗

arXiv2007

DNA unzipping phase diagram calculated via replica theory

We show how single-molecule unzipping experiments can provide strong evidence that the zero-force melting transition of long molecules of natural dsDNA should be classified as a phase transition of the higher-order type (continuous). We study a model for a long molecule of dsDNA, and compute the equilibrium phase diagram for the experiment in which the molecule is unzipped under force. We consider a perfect-matching dsDNA model, in which the loops are volume-excluding chains with arbitrary loop exponent c. We include stacking interactions, hydrogen bonds, and main-chain entropy, including sequence heterogeneity at the level of random sequences. We use the replica method to calculate the equilibrium properties of the system. As a function of temperature, we obtain the minimal force at which the molecule separates completely. This critical force curve is a line in the temperature-force phase diagram that marks the regions where the molecule exists primarily as a helix, versus the region where the molecule exists as two separate strands. Near melting, the critical force curve of our random-sequence model is very different from that of the homogeneous version of our model. For both sequence models, the critical force falls to zero at the melting temperature with a power law having exponent alpha. For the homogeneous model, alpha is 1/2 almost exactly, while for the random model, alpha is about 0.9. The shape of the critical force determines how the helix fraction falls to zero at melting, and thus classifies the melting transition as a type of phase transition.

cond-mat.soft↗

arXiv2007

Positive and negative design in stability and thermal adaptation of natural proteins

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.

q-bio.BM↗

arXiv2007

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.

q-bio.PE↗

arXiv2006

All-atom ab initio folding of a diverse set of proteins

Natural proteins fold to a unique, thermodynamically dominant state. Modeling of the folding process and prediction of the native fold of proteins are two major unsolved problems in biophysics. Here, we show successful all-atom ab initio folding of a representative diverse set of proteins, using a minimalist transferable energy model that consists of two-body atom-atom interactions, hydrogen-bonding, and a local sequence energy term that models sequence-specific chain stiffness. Starting from a random coil, the native-like structure was observed during replica exchange Monte Carlo (REMC) simulation for most proteins regardless of their structural classes; the lowest energy structure was close to native- in the range of 2-6 A root-mean-square deviation (RMSD). Our results demonstrate that the successful all-atom folding of a protein chain to its native state is governed by only a few crucial energetic terms.

q-bio.BM↗

arXiv2006

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.

q-bio.BM↗