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

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

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

Composite structural motifs of binding sites for delineating biological functions of proteins

Most biological processes are described as a series of interactions between proteins and other molecules, and interactions are in turn described in terms of atomic structures. To annotate protein functions as sets of interaction states at atomic resolution, and thereby to better understand the relation between protein interactions and biological functions, we conducted exhaustive all-against-all atomic structure comparisons of all known binding sites for ligands including small molecules, proteins and nucleic acids, and identified recurring elementary motifs. By integrating the elementary motifs associated with each subunit, we defined composite motifs which represent context-dependent combinations of elementary motifs. It is demonstrated that function similarity can be better inferred from composite motif similarity compared to the similarity of protein sequences or of individual binding sites. By integrating the composite motifs associated with each protein function, we define meta-composite motifs each of which is regarded as a time-independent diagrammatic representation of a biological process. It is shown that meta-composite motifs provide richer annotations of biological processes than sequence clusters. The present results serve as a basis for bridging atomic structures to higher-order biological phenomena by classification and integration of binding site structures.Comment: 34 pages, 7 figure

Inverse analysis of critical current density in a bulk high-temperature superconducting undulator

In order to optimise the design of undulators using high-temperature superconductor (HTS) bulks we have developed a method to estimate the critical current density (Jc) of each bulk from the overall measured magnetic field of an undulator. The vertical magnetic field was measured along the electron-beam axis in a HTS bulk-based undulator consisting of twenty Gd-Ba-Cu-O (GdBCO) bulks inserted in a 12-T solenoid. The Jc values of the bulks were estimated by an inverse analysis approach in which the magnetic field was calculated by the forward simulation of the shielding currents in each HTS bulk with a given Jc. Subsequently the Jc values were iteratively updated using the pre-calculated response matrix of the undulator magnetic field to Jc. We demonstrate that it is possible to determine the Jc of each HTS bulk with sufficient accuracy for practical application within around 10 iterations. The pre-calculated response matrix, created in advance, enables the inverse analysis to be performed within a practically short time, on the order of several hours. The measurement error, which destroys the uniqueness of the solution, was investigated and the points to be noted for future magnetic field measurements were clarified. The results show that this inverse-analysis method allows the estimation of the Jc of each bulk comprising an HTS bulk undulator.CHART (Swiss Accelerator Research and Technology Collaboration); EPSRC Early Career Fellowship, EP/P020313/