Spicoli

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Spicoli

• A Surface Toolkit, dude.

2
Molecular Surfaces

• Visualization
• GRASP, others
• Quantification
• Surface area, PSA
• Physical Meaning
• Dielectric Boundary in PB

3
Surface As First Class Objects (FCO)

• Axiomatic definition Minimal requirements
• Associative properties
• Specific properties
• Subset, combine
• Generate other FCOs, generate from other FCOs
• Compare (Identity Distance)
• Read and Write
• Display

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What is a Surface?

• Separator of two volumes
• 2D manifold
• Visual envelope
• Mesh of polygons
• Personality type

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Spicoli Surfaces

• Made of triangles
• A triangle indexed to 3 vertices
• Each edge has at most two triangles
• Closed surface if ever edge has exactly two
• Vertices are consistently ordered
• Clockwise relative to triangle face direction
• Opposite ordering across every edge

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Minimum Spicoli Surface

• List of Vertex positions
• List of Triangle vertices

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Constructible Data

• Normals (vertex, triangle face)
• Edges (vertices, triangles)
• Vertex lists (triangles, edges, normals)
• Triangle lists (vertices, face normals, edges)

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Specific Data

• Connectivity
• Volumes, Areas
• Depth (convex hull)
• Curvature
• Accessibility to a sphere
• Cross- and Intra-Surface Distances

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Associative Data

• Electrostatic potential
• Any grid properties
• Distances to other objects
• Index to other objects

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Generate from FCOs

• Molecule
• Grids
• Geometrics (Ellipsoids)
• Bunch-of-lines
• (lines, sheets of points)

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Generate FCOs

• Line contours (2D-gt1D)
• Grids (2D-gt3D)
• Mathematical Abstractions

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Surface Connectivity

• Surface Floods

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Cropping / Subsetting
Subset
CLIQUE
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Surface As First Class Objects (FCO)?

• Axiomatic definition Minimal Surface YES
• Associative properties YES
• Specific properties YES
• Subset, Combine YES
• Generate other FCOs YES
• Generate from other FCOs YES
• Compare (Identity Distance)
• Read and Write YES
• Display YES

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Example Programs

• Size of largest protein hydrophobic patch
• Void Volumes
• FASP
• Partial PREPS
• Diskify
• Surface compression and comparison

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Simple Program

• Make a surface from a molecule
• Get the surface-to-atom correspondence array
• Use this to set a surface property
• Make a clique from this surface based on this
  property and a threshold
• Make this clique into a new surface
• Find the connectivity of the new surface (each
  becomes a new clique)
• Calculate the area of each connected clique
• Output the clique of largest area

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Void Volumes

• Take a protein and ligand complex
• Find space between a ligand and a protein
  (inaccessible to water)
• Find any spaces for trapped waters (cavities).
• Write report and surfaces/grids

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Void Volumes Process Void Surface

• Generate grids of
• protein
• ligand
• protein-ligand
• Calculate grid (4) (3)-(1)-(2)
• Calculate surface from (4)
• Report statistics (volume, area, ratio)
• Output surface surfaces

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Void Volumes Process Thickness

• Calculate surface from (4)
• Calculate distance from surface to protein, from
  surface to ligand.
• Store the larger of the two.

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Void Volumes Process Cavities

• Calculate surface from (4)
• Find surface connectivities
• See if any of them are water cavities (negative
  volume)
• Extract these surfaces, expand to water size
• Report
• Output them alone or merged with Void Volume

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FASP

• FRED docking function to generate shapes
  complementary to the surface
• Choose by
• size
• depth
• proximity residue, surface point, ligand
• Output
• Surfaces
• Pockets
• Blobs
• Grids
• ROCS query
• ROCS target

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FASP Process

• Make a grid of FRED potentials
• Make a surface at a given threshold
• Find all disconnected surfaces
• Select the biggest/deepest/closest-to
• Make a grid from that surface
• Convolute that grid with a sphere/Gaussian
• Make a surface at given threshold
• Output surfaces/grids etc.

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Kinase Active Sites
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What makes FASP unusual?

• Theres a manual.
• It can find active sites but doesnt care.

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Preps Polynomial Representations of
Electrostatic Potentials
1
5
2
4
3
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Partial Preps

• Enumerate distinct surfaces
• Make each into individual surfaces
• Make a grid from of each surface
• Construct a prep from each grid
• Append each prep to the molecule
• Invent Electrostatic Tversky

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The Phase Problem
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Automorphisms
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5
3
1
2
1
6
7
8
9
10
12
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13
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Canonicalization
1
13
1
13
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The Assignment Problem
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13
1
1
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Disk

• How to map a convoluted surface into a simple
  disk for
• Viewing an active site
• Showing the limitations of GBSA

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GBSA limitations

• GBSA has the form
• But A constant on the surface
• i.e. its essentially a radial function

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Convex/concave positioning of charges and local
errors from GBSA
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Flat and Saddle point
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The Next Logical Step
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Parametric Representations

• Compressible
• Regenerate surfaces
• Morph-able
• Comparable (with Metric properties)
• Reducible
• Embed properties

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Summary

• Spicoli makes the concept of a surface as a First
  Class Object real
• Itll do everything
• It will be available in C, C and Python by the
  summer ACS.
• Its probably the last thing Im going to write.