Pocket Detection in Protein Molecules via QuadricsBrian Byrne

MotivationBiologists 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.

Molecular RecognitionCan be achieved through classifying basic aspects of ligand-protein interactions.

A proteins ligand (small molecule) binding sites provide information to its function.

PocketsIt 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.

Example

Example

QuadricsQuadratic surface in 3 variablesGeneral form:

Ax2 + By2 + Cz2 + 2Dxy + 2Exz + 2Fyz + 2Gx + 2Hy + 2Iz + J = 0http://www.rit.edu/~mkbsma/calculus/calculus305/quadraticsurfaces/quadsurfaces.html

QuadraticsSet z direction to surface normalBivariate Quadratic Function

f(x, y) = Ax2 + By2 + Cxy + Dx + Ey + FFor a point on the mesh surface, find normal direction and choose two orthogonal axes x, y.Sample points along axes, solve for coefficients.

Applied

PeakTroughSaddle

MethodFor 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.

To Be DoneMulti-scale application by selectively choosing

sample point locality.

Different weighting

and emphasisbased on curvaturelevels.

Empirical analysis against

other popular methods.

Peak

Plane

Trough

Future DirectionsImplement higher order approximating splines.

Smarter pocket selection.