Pocket Detection in Protein Molecules via Quadrics

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Pocket Detection in Protein Molecules via Quadrics

• Brian Byrne

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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.

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Molecular Recognition

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

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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.
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Example
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Example
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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/qu
adraticsurfaces/quadsurfaces.html
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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.

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Applied
Trough
Saddle
Peak
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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.

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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
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Future Directions

• Implement higher order approximating splines.
• Smarter pocket selection.