Pocket Detection in Pocket Detection in Protein Molecules via Protein Molecules via

QuadricsQuadrics

Brian ByrneBrian Byrne

MotivationMotivation

Biologists able to construct proteins Biologists able to construct proteins with unknown function.with unknown function.

Wish to be able to estimate function Wish to be able to estimate function without having to examine molecule in without having to examine molecule in depth.depth.

Drug companies interested in reducing Drug companies interested in reducing search space for new medicines.search space for new medicines.

Molecular RecognitionMolecular Recognition

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

A protein’s ligand (small molecule) A protein’s ligand (small molecule) binding sites provide information to binding sites provide information to its function.its function.

PocketsPockets

It has been shown that there exists a It has been shown that there exists a high correlation between protein high correlation between protein pocket sizes and ligand binding pocket sizes and ligand binding activityactivity11..

Goal: Find, detect, and classify all Goal: Find, detect, and classify all pockets efficiently and accurately.pockets efficiently and accurately.

1 Glaser, F. et al. A Method for Localizing Ligand Binding Pockets in Protein Structures.

ExampleExample

ExampleExample

QuadricsQuadrics

Quadratic surface in 3 variablesQuadratic surface in 3 variables General form:General form:

– AxAx22 + By + By22 + Cz + Cz22 + 2Dxy + 2Exz + 2Fyz + 2Gx + 2Hy + 2Iz + J + 2Dxy + 2Exz + 2Fyz + 2Gx + 2Hy + 2Iz + J = 0= 0

http://www.rit.edu/~mkbsma/calculus/calculus305/quadraticsurfaces/quadsurfaces.html

QuadraticsQuadratics

Set z direction to surface normalSet z direction to surface normal Bivariate Quadratic FunctionBivariate Quadratic Function

– f(x, y) = Axf(x, y) = Ax22 + By + By22 + Cxy + Dx + Ey + F + Cxy + Dx + Ey + F For a point on the mesh surface, find For a point on the mesh surface, find

normal direction and choose two normal direction and choose two orthogonal axes x, y.orthogonal axes x, y.

Sample points along axes, solve for Sample points along axes, solve for coefficients.coefficients.

AppliedApplied

Peak

Trough

Saddle

MethodMethod

For every step on the surface, For every step on the surface, compute approximating quadratic compute approximating quadratic surface.surface.

Primarily interested in ‘bowls’ where Primarily interested in ‘bowls’ where surface normal points into parabola surface normal points into parabola openness.openness.

Group points with above property Group points with above property into pocket neighborhoods via into pocket neighborhoods via connected components.connected components.

To Be DoneTo Be Done Multi-scale application by selectively Multi-scale application by selectively

choosingchoosingsample point locality.sample point locality.

Different weightingDifferent weightingand emphasisand emphasisbased on curvaturebased on curvaturelevels.levels.

Empirical analysis againstEmpirical analysis againstother popular methods.other popular methods.

Peak

Plane

Trough

Future DirectionsFuture Directions

Implement higher order Implement higher order approximating splines.approximating splines.

Smarter pocket selection.Smarter pocket selection.