http://vision.unipv.it/ ANALYSIS OF GEMOMETRICAL AND TOPOLOGICAL - PowerPoint PPT Presentation

http://vision.unipv.it/ ANALYSIS OF GEMOMETRICAL AND TOPOLOGICAL ATTITUDE FOR PROTEIN-PROTEIN INTERACTION VIRGINIO CANTONI, LUCE LOMBARDI, RICCARDO GATTI Dipartimento di Informatica e Sistemistica, Università di PAVIA, { virginio.cantoni, luca.lombardi, riccardo gatti } @unipv.it

Overview • Study the interaction between structures and other molecules (Protein Docking) – Molecular surface representation – Protein surface analysis – Geometric shape descriptors – Shape matching algorithms 2

Surface Modeling Van der Waals surface Convex hull Solvent-excluded surface Solvent accessibile surface September 13, 2011 PR PS BB 2011 3 3

Mathermatical morphology: Closing Operation Dilation Erosion The structural element is a sphere representing the solvent September 13, 2011 PR PS BB 2011 4 4

Docking Protein-Protein Interfaces The docking site is more planar rather than a cavity. 5

Convex Hull Note that straight lines (facet in 3D) are represented in a point in the EGI, and their „spike‟ can be easily eliminated, leaving only the true contour (surface) of the object (protein). 6

A CH of a molecule (1MK5) • The CH of a molecule is the smallest convex polyhedron that contains the molecule • A practical O(n log n) algorithm for general dimensions CH computing, is Quickhull (Barber, 1996) September 13, 2011 PR PS BB 2011 7 7

Propagation in concavity volume from CH September 13, 2011 PR PS BB 2011 8 8

Propagation in the concavitiy volume • The concavity volume is the region R between the CH and the SES • B CH is the set of the border voxels of CH • A is the increasing set of voxels contained in R; E is to the recruited near neighbors • d n + w n is the minimum distance in the near neighbors by the displacement w September 13, 2011 PR PS BB 2011 9 9

Propagation in the CV: 2D sketch L I h g F A E a D C C E D b B g L F I h A B g September 13, 2011 PR PS BB 2011 10 10

Back-propagation for pockets and tunnels search (1MK5) The vertical clusters not associated to any pockets are black, the ones representing pockets are colored 11

Pockets detected on the 1MK5 12

Protein Inspector – finding pockets 13

Protein Inspector: pockets refinement All pockets at once with TD constraint 14

Protein Inspector – pockets refinement Single pocket with TD and ligand box constraints 15

The main pocket September 13, 2011 PR PS BB 2011 16 16

The second main pocket September 13, 2011 PR PS BB 2011 17 17

The main pocket of 1MK5 • Adjacent atoms – green from CAST p – Red and green from PPS September 13, 2011 PR PS BB 2011 18 18

1MK5 Credits: SW by Riccardo Gatti September 13, 2011 PR PS BB 2011 19 19

Protein Inspector – finding protrusions Segmentation of protrusions for a 2D shape 20

Protein Inspector – finding protrusions 21

Protein inspector – user interface 22

2D sketch for searching protuberances 23

Active sites matching • Two data structures are proposed: – the Concavity Tree Arcelli C, Sanniti di Baja G (1978) “Polygonal covering and concavity tree of binary digital pictures”, Proceeding International Conference MECO ‟78, Athens, pp. 292– 297. – the Extended Gaussian Image Hu , Z., · Chung, R., · Fung K. S. M., (2010), “EC -EGI: enriched complex EGI for 3D shape registration”, Machine Vision and Applications, 2, 177 – 188. 24

Concavity Tree B331 B321 B33 D1 B311 B111 B31 B32 B3 B3 D B11 D2 B B1 B1 B2 A C A1 B12 B22 A2 C1 B2 B21 B211 25

Concavity Tree A B C D First level A1 D1 A2 C1 D2 Second level B1 B2 B3 B11 B12 B22 B21 Third level B31 B32 B33 Fourth level B111 B311 B321 B331 B211 26

Protein 1MK5 27

Protein 1MK5 concavity tree September 13, 2011 June 8, 2011 PR PS BB 2011 28 28

Concavity tree 29

CT: node content • Volume • Travel Depth • Surface to Volume • Top Five Peaks and Ratio Valleys • Skewness of Height • Summit Density Distribution • Mean Summit • Kurtosis of Height Curvatures Distribution • Interfacial Area Ratio • Mouth Aperture • Residue Conservation September 13, 2011 PR PS BB 2011 30 30

Protein-protein interaction 31

Protein-protein interaction

CAPRI: Critical Assessment of PRediction of Interactions • CAPRI (Critical Assessment of PRedicted Interaction) is an international effort, aimed at objectively assessing the performance of these methods by inviting developers to test their algorithms on the same protein targets and objectively evaluating the results. 33