Pocket Detection in Protein Molecules via Quadrics Brian Byrne

Motivation Biologists able to construct proteins with unknown function. Biologists able to construct proteins with unknown function. Wish to be able to estimate function without having to examine molecule in depth. Wish to be able to estimate function without having to examine molecule in depth. Drug companies interested in reducing search space for new medicines. Drug companies interested in reducing search space for new medicines.

Molecular Recognition Can be achieved through classifying basic aspects of ligand-protein interactions. Can be achieved through classifying basic aspects of ligand-protein interactions. A protein’s ligand (small molecule) binding sites provide information to its function. A protein’s ligand (small molecule) binding sites provide information to its function.

Pockets It has been shown that there exists a high correlation between protein pocket sizes and ligand binding activity 1. It has been shown that there exists a high correlation between protein pocket sizes and ligand binding activity 1. Goal: Find, detect, and classify all pockets efficiently and accurately. Goal: Find, detect, and classify all pockets efficiently and accurately. 1 Glaser, F. et al. A Method for Localizing Ligand Binding Pockets in Protein Structures.

Example

Example

Quadrics Quadratic surface in 3 variables Quadratic surface in 3 variables General form: General form: –Ax 2 + By 2 + Cz 2 + 2Dxy + 2Exz + 2Fyz + 2Gx + 2Hy + 2Iz + J = 0

Quadratics Set z direction to surface normal Set z direction to surface normal Bivariate Quadratic Function Bivariate Quadratic Function –f(x, y) = Ax 2 + By 2 + Cxy + Dx + Ey + F For a point on the mesh surface, find normal direction and choose two orthogonal axes x, y. For a point on the mesh surface, find normal direction and choose two orthogonal axes x, y. Sample points along axes, solve for coefficients. Sample points along axes, solve for coefficients.

Applied Peak Trough Saddle

Method For every step on the surface, compute approximating quadratic surface. For every step on the surface, compute approximating quadratic surface. Primarily interested in ‘bowls’ where surface normal points into parabola openness. Primarily interested in ‘bowls’ where surface normal points into parabola openness. Group points with above property into pocket neighborhoods via connected components. Group points with above property into pocket neighborhoods via connected components.

To Be Done Multi-scale application by selectively choosing Multi-scale application by selectively choosing sample point locality. Different weighting Different weighting and emphasis based on curvature levels. Empirical analysis against Empirical analysis against other popular methods. Peak Plane Trough

Future Directions Implement higher order approximating splines. Implement higher order approximating splines. Smarter pocket selection. Smarter pocket selection.