A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces

The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation of the surface and standard Cartesian grid methods in the embedding space. Recently, a closest point method with explicit time-stepping was proposed that uses finite differences derived from radial basis functions (RBF-FD). Here, we propose a least-squares implicit formulation of the closest point method to impose the constant-along-normal extension of the solution on the surface into the embedding space. Our proposed method is particularly flexible with respect to the choice of the computational grid in the embedding space. In particular, we may compute over a computational tube that contains problematic nodes. This fact enables us to combine the proposed method with the grid based particle method (Leung and Zhao, J. Comput. Phys. 228(8):2993-3024, [2009]) to obtain a numerical method for approximating PDEs on moving surfaces. We present a number of examples to illustrate the numerical convergence properties of our proposed method. Experiments for advection-diffusion equations and Cahn-Hilliard equations that are strongly coupled to the velocity of the surface are also presented

PROTCOM: searchable database of protein complexes enhanced with domain–domain structures

The database of protein complexes (PROTCOM) is a compilation of known 3D structures of protein–protein complexes enriched with artificially created domain–domain structures using the available entries in the Protein Data Bank. The domain–domain structures are generated by parsing single chain structures into loosely connected domains and are important features of the database. The database () could be used for benchmarking purposes of the docking and other algorithms for predicting 3D structures of protein–protein complexes. The database can be utilized as a template database in the homology or threading methods for modeling the 3D structures of unknown protein–protein complexes. PROTCOM provides the scientific community with an integrated set of tools for browsing, searching, visualizing and downloading a pool of protein complexes. The user is given the option to select a subset of entries using a combination of up to 10 different criteria. As on July 2006 the database contains 1770 entries, each of which consists of the known 3D structures and additional relevant information that can be displayed either in text-only or in visual mode

Electrostatic Properties of Protein-Protein Complexes

Statistical electrostatic analysis of 37 protein-protein complexes extracted from the previously developed database of protein complexes (ProtCom, http://www.ces.clemson.edu/compbio/protcom) is presented. It is shown that small interfaces have a higher content of charged and polar groups compared to large interfaces. In a vast majority of the cases the average pKa shifts for acidic residues induced by the complex formation are negative, indicating that complex formation stabilizes their ionizable states, whereas the histidines are predicted to destabilize the complex. The individual pKa shifts show the same tendency since 80% of the interfacial acidic groups were found to lower their pKas, whereas only 25% of histidines raise their pKa upon the complex formation. The interfacial groups have been divided into three sets according to the mechanism of their pKa shift, and statistical analysis of each set was performed. It was shown that the optimum pH values (pH of maximal stability) of the complex tend to be the same as the optimum pH values of the complex components. This finding can be used in the homology-based prediction of the 3D structures of protein complexes, especially when one needs to evaluate and rank putative models. It is more likely for a model to be correct if both components of the model complex and the entire complex have the same or at least similar values of the optimum pH

Blind Prediction of Interfacial Water Positions in CAPRI

We report the first assessment of blind predictions of water positions at protein-protein interfaces, performed as part of the CAPRI (Critical Assessment of Predicted Interactions) community-wide experiment. Groups submitting docking predictions for the complex of the DNase domain of colicin E2 and Im2 immunity protein (CAPRI target 47), were invited to predict the positions of interfacial water molecules using the method of their choice. The predictions – 20 groups submitted a total of 195 models – were assessed by measuring the recall fraction of water-mediated protein contacts. Of the 176 high or medium quality docking models – a very good docking performance per se – only 44% had a recall fraction above 0.3, and a mere 6% above 0.5. The actual water positions were in general predicted to an accuracy level no better than 1.5 Å, and even in good models about half of the contacts represented false positives. This notwithstanding, three hotspot interface water positions were quite well predicted, and so was one of the water positions that is believed to stabilize the loop that confers specificity in these complexes. Overall the best interface water predictions was achieved by groups that also produced high quality docking models, indicating that accurate modelling of the protein portion is a determinant factor. The use of established molecular mechanics force fields, coupled to sampling and optimization procedures also seemed to confer an advantage. Insights gained from this analysis should help improve the prediction of protein-water interactions and their role in stabilizing protein complexes

Docking by structural similarity at protein-protein interfaces

Rapid accumulation of experimental data on protein-protein complexes drives the paradigm shift in protein docking from ‘traditional,’ template free approaches to template based techniques. Homology docking algorithms based on sequence similarity between target and template complexes can account for up to 20% of known protein-protein interactions. When highly homologous templates for the target complex are not available, but the structure of the target monomers is known, docking by local structural alignment may provide an adequate solution. Such an algorithm was developed based on the structural comparison of monomers to co-crystallized interfaces. A library of the interfaces was generated from co-crystallized protein-protein complexes in PDB. The partial structure alignment algorithm was validated on the Dockground benchmark sets. The optimal performance of the partial (interface) structure alignment was achieved with the interface residues defined by 12Å distance across the interface. Overall, the partial structural alignment yielded more accurate models than the full structure alignment. Most templates identified by the partial structural alignment had low sequence identity to the target, which makes them hard to detect by sequence-based methods. The results indicate that the structure alignment techniques provide a much needed addition to the docking arsenal, with the combined structural alignment and template free docking success rate significantly surpassing that of the free docking alone