Similarity search for local protein structures at atomic resolution by exploiting a database management system

A method to search for local structural similarities in proteins at atomic resolution is presented. It is demonstrated that a huge amount of structural data can be handled within a reasonable CPU time by using a conventional relational database management system with appropriate indexing of geometric data. This method, which we call geometric indexing, can enumerate ligand binding sites that are structurally similar to sub-structures of a query protein among more than 160,000 possible candidates within a few hours of CPU time on an ordinary desktop computer. After detecting a set of high scoring ligand binding sites by the geometric indexing search, structural alignments at atomic resolution are constructed by iteratively applying the Hungarian algorithm, and the statistical significance of the final score is estimated from an empirical model based on a gamma distribution. Applications of this method to several protein structures clearly shows that significant similarities can be detected between local structures of non-homologous as well as homologous proteins.Comment: 29 pages, 8 figures, 3 table

CRNPRED: highly accurate prediction of one-dimensional protein structures by large-scale critical random networks

BACKGROUND: One-dimensional protein structures such as secondary structures or contact numbers are useful for three-dimensional structure prediction and helpful for intuitive understanding of the sequence-structure relationship. Accurate prediction methods will serve as a basis for these and other purposes. RESULTS: We implemented a program CRNPRED which predicts secondary structures, contact numbers and residue-wise contact orders. This program is based on a novel machine learning scheme called critical random networks. Unlike most conventional one-dimensional structure prediction methods which are based on local windows of an amino acid sequence, CRNPRED takes into account the whole sequence. CRNPRED achieves, on average per chain, Q(3 )= 81% for secondary structure prediction, and correlation coefficients of 0.75 and 0.61 for contact number and residue-wise contact order predictions, respectively. CONCLUSION: CRNPRED will be a useful tool for computational as well as experimental biologists who need accurate one-dimensional protein structure predictions

Computational Modelling of Plasticity-Led Evolution

Plasticity-led evolution is a form of evolution where a change in the environment induces novel traits via phenotypic plasticity, after which the novel traits are genetically accommodated over generations under the novel environment. This mode of evolution is expected to resolve the problem of gradualism (i.e., evolution by the slow accumulation of mutations that induce phenotypic variation) implied by the Modern Evolutionary Synthesis, in the face of a large environmental change. While experimental works are essential for validating that plasticity-led evolution indeed happened, we need computational models to gain insight into its underlying mechanisms and make qualitative predictions. Such computational models should include the developmental process and gene-environment interactions in addition to genetics and natural selection. We point out that gene regulatory network models can incorporate all the above notions. In this review, we highlight results from computational modelling of gene regulatory networks that consolidate the criteria of plasticity-led evolution. Since gene regulatory networks are mathematically equivalent to artificial recurrent neural networks, we also discuss their analogies and discrepancies, which may help further understand the mechanisms underlying plasticity-led evolution.Comment: 20 pages, 2 tables, 1 bo

On the optimal contact potential of proteins

We analytically derive the lower bound of the total conformational energy of a protein structure by assuming that the total conformational energy is well approximated by the sum of sequence-dependent pairwise contact energies. The condition for the native structure achieving the lower bound leads to the contact energy matrix that is a scalar multiple of the native contact matrix, i.e., the so-called Go potential. We also derive spectral relations between contact matrix and energy matrix, and approximations related to one-dimensional protein structures. Implications for protein structure prediction are discussed.Comment: 5 pages, text onl

Properties of contact matrices induced by pairwise interactions in proteins

The total conformational energy is assumed to consist of pairwise interaction energies between atoms or residues, each of which is expressed as a product of a conformation-dependent function (an element of a contact matrix, C-matrix) and a sequence-dependent energy parameter (an element of a contact energy matrix, E-matrix). Such pairwise interactions in proteins force native C-matrices to be in a relationship as if the interactions are a Go-like potential [N. Go, Annu. Rev. Biophys. Bioeng. 12. 183 (1983)] for the native C-matrix, because the lowest bound of the total energy function is equal to the total energy of the native conformation interacting in a Go-like pairwise potential. This relationship between C- and E-matrices corresponds to (a) a parallel relationship between the eigenvectors of the C- and E-matrices and a linear relationship between their eigenvalues, and (b) a parallel relationship between a contact number vector and the principal eigenvectors of the C- and E-matrices; the E-matrix is expanded in a series of eigenspaces with an additional constant term, which corresponds to a threshold of contact energy that approximately separates native contacts from non-native ones. These relationships are confirmed in 182 representatives from each family of the SCOP database by examining inner products between the principal eigenvector of the C-matrix, that of the E-matrix evaluated with a statistical contact potential, and a contact number vector. In addition, the spectral representation of C- and E-matrices reveals that pairwise residue-residue interactions, which depends only on the types of interacting amino acids but not on other residues in a protein, are insufficient and other interactions including residue connectivities and steric hindrance are needed to make native structures the unique lowest energy conformations.Comment: Errata in DOI:10.1103/PhysRevE.77.051910 has been corrected in the present versio