Techniques from graph theory are applied to analyze the bond networks in proteins and identify the flexible and rigid regions. The bond network consists of distance constraints defined by the covalent and hydrogen bonds and salt bridges in the protein, identified by geometric and energetic criteria. We use an algorithm that counts the degrees of freedom within this constraint network and that identifies all the rigid and flexible substructures in the protein, including overconstrained regions (with more crosslinking bonds than are needed to rigidify the region) and underconstrained or flexible regions, in which dihedral bond rotations can occur. The number of extra constraints or remaining degrees of bond-rotational freedom within a substructure quantifies its relative rigidity/flexibility and provides a flexibility index for each bond in the structure. This novel computational procedure, first used in the analysis of glassy materials, is approximately a million times faster than molecular dynamics simulations and captures the essential conformational flexibility of the protein main and side-chains from analysis of a single, static three-dimensional structure. This approach is demonstrated by comparison with experimental measures of flexibility for three proteins in which hinge and loop motion are essential for biological function: HIV protease, adenylate kinase, and dihydrofolate reductase.

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BackgroundRelatively little is known about the genomic basis and evolution of wood-feeding in beetles. We undertook genome sequencing and annotation, gene expression assays, studies of plant cell wall degrading enzymes, and other functional and comparative studies of the Asian longhorned beetle, Anoplophora glabripennis, a globally significant invasive species capable of inflicting severe feeding damage on many important tree species. Complementary studies of genes encoding enzymes involved in digestion of woody plant tissues or detoxification of plant allelochemicals were undertaken with the genomes of 14 additional insects, including the newly sequenced emerald ash borer and bull-headed dung beetle.ResultsThe Asian longhorned beetle genome encodes a uniquely diverse arsenal of enzymes that can degrade the main polysaccharide networks in plant cell walls, detoxify plant allelochemicals, and otherwise facilitate feeding on woody plants. It has the metabolic plasticity needed to feed on diverse plant species, contributing to its highly invasive nature. Large expansions of chemosensory genes involved in the reception of pheromones and plant kairomones are consistent with the complexity of chemical cues it uses to find host plants and mates.ConclusionsAmplification and functional divergence of genes associated with specialized feeding on plants, including genes originally obtained via horizontal gene transfer from fungi and bacteria, contributed to the addition, expansion, and enhancement of the metabolic repertoire of the Asian longhorned beetle, certain other phytophagous beetles, and to a lesser degree, other phytophagous insects. Our results thus begin to establish a genomic basis for the evolutionary success of beetles on plants.Electronic supplementary materialThe online version of this article (doi:10.1186/s13059-016-1088-8) contains supplementary material, which is available to authorized users.

We relate the unfolding of a protein to its loss of structural stability or rigidity. Rigidity and flexibility are well defined concepts in mathematics and physics, with a body of theorems and algorithms that have been applied successfully to materials, allowing the constraints in a network to be related to its deformability. Here we simulate the weakening or dilution of the noncovalent bonds during protein unfolding, and identify the emergence of flexible regions as unfolding proceeds. The transition state is determined from the inflection point in the change in the number of independent bond-rotational degrees of freedom (floppy modes) of the protein as its mean atomic coordination decreases. The first derivative of the fraction of floppy modes as a function of mean coordination is similar to the fraction-folded curve for a protein as a function of denaturant concentration or temperature. The second derivative, a specific heat-like quantity, shows a peak around a mean coordination of ͗r͘ ‫؍‬ 2.41 for the 26 diverse proteins we have studied. As the protein denatures, it loses rigidity at the transition state, proceeds to a state where just the initial folding core remains stable, then becomes entirely denatured or flexible. This universal behavior for proteins of diverse architecture, including monomers and oligomers, is analogous to the rigid to floppy phase transition in network glasses. This approach provides a unifying view of the phase transitions of proteins and glasses, and identifies the mean coordination as the relevant structural variable, or reaction coordinate, along the unfolding pathway. Much interest is currently focused on the rapid and faithful folding of proteins from a one-dimensional sequence of amino acids in a random coil, to a three-dimensional biologically functional structure in the native state (1-4). Chemical and thermal denaturation of proteins are standard techniques in protein biochemistry to determine protein folding and unfolding equilibria and kinetics (3,5,6).A general view of protein folding is that it begins with hydrophobic collapse, in which the random coil changes to a compact state, with the hydrophobic groups in the interior region and polar groups at the surface interacting with the surrounding water. The packing is not yet optimal, with hydrophobic groups somewhat free to slide about in the interior of the globule, until residues are locked in place by the formation of specific hydrogen bonds. These hydrogen bonds can be regarded as a sort of Velcro that locks the various structural elements in the folded protein together. Once these interactions are optimized, the native state is predominantly rigid with flexible hinges or loops at the surface-the number and distribution of these depending on the particular protein.There have been many significant theoretical advances in understanding protein folding in recent years-including the concept of a funnel-shaped free-energy landscape (1, 7-9), simplified lattice models that are more tractable for simulations of folding (8, ...