Toward an accurate prediction of inter-residue distances in proteins using 2D recursive neural networks

BACKGROUND: Protein inter-residue contact maps provide a translation and rotation invariant topological representation of a protein. They can be used as an intermediary step in protein structure predictions. However, the prediction of contact maps represents an unbalanced problem as far fewer examples of contacts than non-contacts exist in a protein structure. In this study we explore the possibility of completely eliminating the unbalanced nature of the contact map prediction problem by predicting real-value distances between residues. Predicting full inter-residue distance maps and applying them in protein structure predictions has been relatively unexplored in the past. RESULTS: We initially demonstrate that the use of native-like distance maps is able to reproduce 3D structures almost identical to the targets, giving an average RMSD of 0.5Å. In addition, the corrupted physical maps with an introduced random error of ±6Å are able to reconstruct the targets within an average RMSD of 2Å. After demonstrating the reconstruction potential of distance maps, we develop two classes of predictors using two-dimensional recursive neural networks: an ab initio predictor that relies only on the protein sequence and evolutionary information, and a template-based predictor in which additional structural homology information is provided. We find that the ab initio predictor is able to reproduce distances with an RMSD of 6Å, regardless of the evolutionary content provided. Furthermore, we show that the template-based predictor exploits both sequence and structure information even in cases of dubious homology and outperforms the best template hit with a clear margin of up to 3.7Å. Lastly, we demonstrate the ability of the two predictors to reconstruct the CASP9 targets shorter than 200 residues producing the results similar to the state of the machine learning art approach implemented in the Distill server. CONCLUSIONS: The methodology presented here, if complemented by more complex reconstruction protocols, can represent a possible path to improve machine learning algorithms for 3D protein structure prediction. Moreover, it can be used as an intermediary step in protein structure predictions either on its own or complemented by NMR restraints

Preliminary calculations of flow in channel with triangular and rectangular obstacle

The paper presents the results of preliminary numerical calculations of a fluid flow in a channel with an obstacle. The flow problem was solved with an application of the finite elements method. Various geometries of obstacles were considered

RNAmap2D – calculation, visualization and analysis of contact and distance maps for RNA and protein-RNA complex structures

Abstract Background The structures of biological macromolecules provide a framework for studying their biological functions. Three-dimensional structures of proteins, nucleic acids, or their complexes, are difficult to visualize in detail on flat surfaces, and algorithms for their spatial superposition and comparison are computationally costly. Molecular structures, however, can be represented as 2D maps of interactions between the individual residues, which are easier to visualize and compare, and which can be reconverted to 3D structures with reasonable precision. There are many visualization tools for maps of protein structures, but few for nucleic acids. Results We developed RNAmap2D, a platform-independent software tool for calculation, visualization and analysis of contact and distance maps for nucleic acid molecules and their complexes with proteins or ligands. The program addresses the problem of paucity of bioinformatics tools dedicated to analyzing RNA 2D maps, given the growing number of experimentally solved RNA structures in the Protein Data Bank (PDB) repository, as well as the growing number of tools for RNA 2D and 3D structure prediction. RNAmap2D allows for calculation and analysis of contacts and distances between various classes of atoms in nucleic acid, protein, and small ligand molecules. It also discriminates between different types of base pairing and stacking. Conclusions RNAmap2D is an easy to use method to visualize, analyze and compare structures of nucleic acid molecules and their complexes with other molecules, such as proteins or ligands and metal ions. Its special features make it a very useful tool for analysis of tertiary structures of RNAs. RNAmap2D for Windows/Linux/MacOSX is freely available for academic users at http://iimcb.genesilico.pl/rnamap2d.html</p

Solvers for Systems of Nonlinear Algebraic Equations - Their Sensitivity to Starting Vectors

In this note we compare the sensitivity of six advanced solvers for systems of nonlinear algebraic equations to the choice of starting vectors. We will report on results of our experiments in which, for each test problem, the calculated solution was used as the center from which we have moved away in various directions and observed the behavior of each solver attempting to find the solution. We are particularly interested in determining the best global starting vectors. Experimental results are presented and discussed