Sequence composition and environment effects on residue fluctuations in protein structures

The spectrum and scale of fluctuations in protein structures affect the range of cell phenomena, including stability of protein structures or their fragments, allosteric transitions and energy transfer. The study presents a statistical-thermodynamic analysis of relationship between the sequence composition and the distribution of residue fluctuations in protein-protein complexes. A one-node-per residue elastic network model accounting for the nonhomogeneous protein mass distribution and the inter-atomic interactions through the renormalized inter-residue potential is developed. Two factors, a protein mass distribution and a residue environment, were found to determine the scale of residue fluctuations. Surface residues undergo larger fluctuations than core residues, showing agreement with experimental observations. Ranking residues over the normalized scale of fluctuations yields a distinct classification of amino acids into three groups. The structural instability in proteins possibly relates to the high content of the highly fluctuating residues and a deficiency of the weakly fluctuating residues in irregular secondary structure elements (loops), chameleon sequences and disordered proteins. Strong correlation between residue fluctuations and the sequence composition of protein loops supports this hypothesis. Comparing fluctuations of binding site residues (interface residues) with other surface residues shows that, on average, the interface is more rigid than the rest of the protein surface and Gly, Ala, Ser, Cys, Leu and Trp have a propensity to form more stable docking patches on the interface. The findings have broad implications for understanding mechanisms of protein association and stability of protein structures.Comment: 8 pages, 4 figure

Side-chain conformational changes upon protein-protein association

Conformational changes upon protein-protein association are the key element of the binding mechanism. The study presents a systematic large-scale analysis of such conformational changes in the side chains. The results indicate that short and long side chains have different propensities for the conformational changes. Long side chains with three or more dihedral angles are often subject to large conformational transition. Shorter residues with one or two dihedral angles typically undergo local conformational changes not leading to a conformational transition. The relationship between the local readjustments and the equilibrium fluctuations of a side chain around its unbound conformation is suggested. Most of the side chains undergo larger changes in the dihedral angle most distant from the backbone. The amino acids with symmetric aromatic (Phe and Tyr) and charged (Asp and Glu) groups show the opposite trend where the near-backbone dihedral angles change the most. The frequencies of the core-to-surface interface transitions of six nonpolar residues and Tyr exceed the frequencies of the opposite, surface-to-core transitions. The binding increases both polar and nonpolar interface areas. However, the increase of the nonpolar area is larger for all considered classes of protein complexes. The results suggest that the protein association perturbs the unbound interfaces to increase the hydrophobic forces. The results facilitate better understanding of the conformational changes in proteins and suggest directions for efficient conformational sampling in docking protocols.Comment: 21 pages, 6 figure

Detecting heterozygosity in shotgun genome assemblies: Lessons from obligately outcrossing nematodes

The majority of nematodes are gonochoristic (dioecious) with distinct male and female sexes, but the best-studied species, Caenorhabditis elegans, is a self-fertile hermaphrodite. The sequencing of the genomes of C. elegans and a second hermaphrodite, C. briggsae, was facilitated in part by the low amount of natural heterozygosity, which typifies selfing species. Ongoing genome projects for gonochoristic Caenorhabditis species seek to approximate this condition by intense inbreeding prior to sequencing. Here we show that despite this inbreeding, the heterozygous fraction of the whole genome shotgun assemblies of three gonochoristic Caenorhabditis species, C. brenneri, C. remanei, and C. japonica, is considerable. We first demonstrate experimentally that independently assembled sequence variants in C. remanei and C. brenneri are allelic. We then present gene-based approaches for recognizing heterozygous regions of WGS assemblies. We also develop a simple method for quantifying heterozygosity that can be applied to assemblies lacking gene annotations. Consistently we find that ∼10% and 30% of the C. remanei and C. brenneri genomes, respectively, are represented by two alleles in the assemblies. Heterozygosity is restricted to autosomes and its retention is accompanied by substantial inbreeding depression, suggesting that it is caused by multiple recessive deleterious alleles and not merely by chance. Both the overall amount and chromosomal distribution of heterozygous DNA is highly variable between assemblies of close relatives produced by identical methodologies, and allele frequencies have continued to change after strains were sequenced. Our results highlight the impact of mating systems on genome sequencing projects

Square Patterns and Quasi-patterns in Weakly Damped Faraday Waves

Pattern formation in parametric surface waves is studied in the limit of weak viscous dissipation. A set of quasi-potential equations (QPEs) is introduced that admits a closed representation in terms of surface variables alone. A multiscale expansion of the QPEs reveals the importance of triad resonant interactions, and the saturating effect of the driving force leading to a gradient amplitude equation. Minimization of the associated Lyapunov function yields standing wave patterns of square symmetry for capillary waves, and hexagonal patterns and a sequence of quasi-patterns for mixed capillary-gravity waves. Numerical integration of the QPEs reveals a quasi-pattern of eight-fold symmetry in the range of parameters predicted by the multiscale expansion.Comment: RevTeX, 11 pages, 8 figure

Theory of weakly damped free-surface flows: a new formulation based on potential flow solutions

Several theories for weakly damped free-surface flows have been formulated. In this paper we use the linear approximation to the Navier-Stokes equations to derive a new set of equations for potential flow which include dissipation due to viscosity. A viscous correction is added not only to the irrotational pressure (Bernoulli's equation), but also to the kinematic boundary condition. The nonlinear Schr\"odinger (NLS) equation that one can derive from the new set of equations to describe the modulations of weakly nonlinear, weakly damped deep-water gravity waves turns out to be the classical damped version of the NLS equation that has been used by many authors without rigorous justification

Anatomical network analysis of the musculoskeletal system reveals integration loss and parcellation boost during the fins-to-limbs transition

Tetrapods evolved from within the lobe-finned fishes around 370 Ma. The evolution of limbs from lobe-fins entailed a major re-organization of the skeletal and muscular anatomy of appendages in early tetrapods. Concurrently, a degree of similarity between pectoral and pelvic appendages also evolved. Here, we compared the anatomy of appendages in extant lobe-finned fishes (Latimeria and Neoceratodus) and anatomically plesiomorphic amphibians (Ambystoma, Salamandra) and amniotes (Sphenodon) to trace and reconstruct the musculoskeletal changes that took place during the fins-to-limbs transition. We quantified the anatomy of appendages using network analysis. First, we built network models—in which nodes represent bones and muscles, and links represent their anatomical connections—and then we measured network parameters related to their anatomical integration, heterogeneity, and modularity. Our results reveal an evolutionary transition toward less integrated, more modular appendages. We interpret this transition as a diversification of muscle functions in tetrapods compared to lobe-finned fishes. Limbs and lobe-fins show also a greater similarity between their pectoral and pelvic appendages than ray-fins do. These findings on extant species provide a basis for future quantitative and comprehensive reconstructions of the anatomy of limbs in early tetrapod fossils, and a way to better understand the fins-to-limbs transition