Pocket Detection in Protein Molecules via Quadrics

1. Pocket Detection in Protein Molecules via Quadrics Brian Byrne

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

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

4. Pockets • It has been shown that there exists a high correlation between protein pocket sizes and ligand binding activity1. • 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.

5. Example

6. Example

7. Quadrics • Quadratic surface in 3 variables • General form: • Ax2 + By2 + Cz2 + 2Dxy + 2Exz + 2Fyz + 2Gx + 2Hy + 2Iz + J = 0 http://www.rit.edu/~mkbsma/calculus/calculus305/quadraticsurfaces/quadsurfaces.html

8. Quadratics • Set z direction to surface normal • Bivariate Quadratic Function • f(x, y) = Ax2 + By2 + Cxy + Dx + Ey + F • For a point on the mesh surface, find normal direction and choose two orthogonal axes x, y. • Sample points along axes, solve for coefficients.

9. Applied Trough Saddle Peak

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

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

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