Geometric computing in protein design

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Geometric computing in protein design

• Jack Snoeyink
• UNC Computer Science

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Outline

• Introducing Computational Geometry Proteins
• Projects
• 3-d jigsaw puzzles of Protein design
• Precision requirements for exact geometric
  computation
• Classes
• COMP 281 Computational Geometry
• COMP 290-079 seminar/lab in Applied Optimization
  in Computational Biology
• Collaboration
• program in cellular and molecular biophysics
• program in bioinformatics

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Computational Geometry

• A branch of the theory of computer science that
  considers
• the design and analysis of algorithms and data
  structures
• for problems that are best stated in geometric
  form.
• Application areas include robotics, databases,
  GIS, computer graphics, mathematics, and
  molecular biology.

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Beautiful geometry (?)
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Diagramatic representations

• PXR with bound ligand
• ?Ball stick / van der Waals spheres
• ?Model diagram
• ?Solvent accessible surface

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Geometry on computers

• Where we can see structure, shape, connections,
  regions,
• The computer sees only coordinates
• For example, this PXR protein ligand is in the
  Protein Data Bank as

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REMARK Written by O version 7.0.0 REMARK Sun Jan
21 152451 2001 CRYST1 91.345 91.345
85.302 90.00 90.00 90.00 ORIGX1 1.000000
0.000000 0.000000 0.00000 ORIGX2
0.000000 1.000000 0.000000
0.00000 ORIGX3 0.000000 0.000000 1.000000
0.00000 SCALE1 0.010948 0.000000
0.000000 0.00000 SCALE2 0.000000
0.010948 0.000000 0.00000 SCALE3
0.000000 0.000000 0.011723 0.00000 ATOM
1 C GLY 142 -5.808 44.753 13.561
1.00 58.97 6 ATOM 2 O GLY 142
-5.723 45.523 14.515 1.00 59.54 8 ATOM
3 N GLY 142 -4.377 43.177 14.842
1.00 59.37 7 ATOM 4 CA GLY 142
-5.307 43.330 13.685 1.00 59.68 6 ATOM
5 N LEU 143 -6.324 45.108 12.387
1.00 58.87 7 ATOM 6 CA LEU 143
-6.839 46.455 12.152 1.00 58.50 6 ATOM
7 CB LEU 143 -6.483 46.907 10.736
1.00 57.90 6 ATOM 8 CG LEU 143
-5.849 48.290 10.555 1.00 57.77 6 ATOM
9 CD1 LEU 143 -4.599 48.411 11.407
1.00 56.51 6 ATOM 10 CD2 LEU 143
-5.505 48.492 9.090 1.00 56.92 6 ATOM
11 C LEU 143 -8.352 46.446 12.333
1.00 58.92 6 ATOM 12 O LEU 143
-9.046 45.640 11.714 1.00 59.85 8 ATOM
13 N THR 144 -8.862 47.341 13.174
1.00 58.88 7 ATOM 14 CA THR 144
-10.299 47.407 13.444 1.00 59.76 6
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Protein Design

• Goal CAD for protein design
• BioGeometry Project (NSF ITR)
• F. Brooks, C. Carter, A. Tropsha, Duke, Stanford,
  NC AT
• Enzyme design (DARPA seed funding)
• H. Hellinga, DJ Richardson (Duke), J. Snoeyink
  (UNC)

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Protein structure hierarchy

• Primary AA sequence
• Secondary helices/sheets
• Tertiary folding in 3D
• Quaternary conformation of two or more molecules

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Primary amino acid sequence

• 20 amino acids
• Backbone linked peptide units
• Side chains differ
• Geometry ?, ? angles at bonds with Ca carbon

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Primary amino acid sequence
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Protein synthesis

• Transcription and translation in protein
  synthesizing
• DNA and RNA have nucleotides that determine kind
  of protein
• 3 nucleotides 1 amino acid of a protein

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Secondary a-helices

• Stabilized by hydrogen bonds

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Secondary b-sheets

• Parallel and Anti-parallel
• Also stabilized by H-bonds

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Tertiary folding

• Critically important
• 3D Structure ? Function
• Protein Folding problem
• Given the sequence, determine the structure
• Decoy Discrimination problem
• Given several folds, determine the native

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Quatenary Structure

• GroEL is made of 28 protein units, in four
  7-member rings, that form a pair of cavities in
  which proteins can be unfolded.
• GroES subunits form another 7-membered ring that
  caps the GroEL ring

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Structure - Function
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Protein Design

• Goal CAD for protein design
• BioGeometry Project (NSF ITR)
• F. Brooks, C. Carter, A. Tropsha, Duke, Stanford,
  NC AT
• Enzyme design (DARPA seed funding)
• H. Hellinga, DJ Richardson (Duke), J. Snoeyink
  (UNC)

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NSF ITR Project Team
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Protein Design

• Goal CAD for protein design
• BioGeometry Project (NSF ITR)
• F. Brooks, C. Carter, A. Tropsha, Duke, Stanford,
  NC AT
• Enzyme design (DARPA seed funding)
• H. Hellinga, DJ Richardson (Duke), J. Snoeyink
  (UNC)

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Protein design

• Dezymer software
• H. Hellinga, L. Looger
• Input fixed backbone
• and ligand
• Output top-ranked
• receptor designs
• Example RBP (Ribose Binding Protein)
• Redesigned receptor site to bind TNT
• Generated different receptor designs with
  modified backbone

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Backbone modification

• Goal CAD for protein design
• Objective local backbone motion
• modify segment of backbone, leaving remainder of
  chain fixed
• develop a library of allowed motions
• Motivation
• crystallographic refinement
• receptor design

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Crystallographic refinement
fit structure to electron density from x-ray
diffraction
Crystal structure obtained without hydrogen
atoms Some clashes result after adding hydrogen
atoms Red spikes bad clashes Blue dots
favorable interactions
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Crystallographic refinement
fit structure to electron density from x-ray
diffraction
modified backbone resolves clashes
better choice of side chain
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Problems Approaches

• Problems from biology
• threading in electron density
• crystal packing
• motion libraries
• Robotics techniques
• exact inverse kinematics
• probabilistic roadmaps
• Geometric algorithms
• data representation
• code optimization

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Arithmetic precision as a computational resource

• Provably correct algorithms optimal in time,
  space, and arithmetic precision
• Examples
• line segment intersection (w/ Mantler)
• ray/polygon intersection
• 3d/4d Delaunay (w/ Liu, Mascarenhas)
• Geometric rounding on output

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Restricted tests imply...

• Restricted to double precision
• Cant test where an intersection is
• Cant sort on lines
• Cant sort by x

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spaghetti lines.

• Restricted to double precision
• Push segments as far right as possible
• Endpoints witness intersections

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3D RayPolygon test
If (pq)(pd) return MISS hitmiss MISS For
(i0 ipi1 pipi1qr0 return GRAZE // hit edge pi,pi1
Else if (pipi1qrtoggle hitmiss // pi,pi1 r separates q?
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Topology for visualization
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Teaching this semester

• Computational Geometry3 credit courseCOMP
  281TTh 200-315Sitterson 325
• blackboard site link

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Teaching this semester

• Applied Optimization in Computational Biology1
  credit seminar/working labCOMP 290-079Th
  400-500Beard 116 (Pharmacy)
• www.cs.unc.edu/snoeyink/comp290opt/syllabus

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Biophysics training program

• Interdisciplinary program lead by Barry Lentz
• www.hekto.med.unc.edu
• Module courses
• Research rotations

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Bioinformatics training program

• New initiative at UNC
• Biophysics, Biochemistry, SILS, Pharmacy, OR,
  Appl. Math, Comp. Sci.
• Faculty Wei Wang, Jan Prins, JS
• Students Luke Huan, Andrew Leaver-Fay
• Fits with CS PhD program
• 7 credits of module courses over 2 years
• Seminar/journal club 4pm Weds
• Optimization seminar/lab 4pm Thur, Beard 116
• Talk to me, Jan, Wei, or Todd Vision

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Puzzles

• What motivates the researcher is the conviction
  that, if only he (or she) is skilled enough, he
  (or she) will succeed in solving a puzzle that
  no-one before has solved or solved so well.
• The structure of scientific revolutions
• Thomas Kuhn

Jack Snoeyink snoeyink_at_cs.unc.edu Sitterson
333 Tonight 6-8pm Monday 9-12am