Computational Tools for Analyzing Macromolecular Interactions

1
Computational Tools for Analyzing Macromolecular
Interactions

• Julie C. Mitchell
• Departments of Mathematics and Biochemistry
• University of Wisconsin - Madison

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Protein-Ligand Binding

• Proteins perform their functions by binding
• Proteins, DNA, small ligands and ions bind
• Chemistry happens at the interface
• Molecules fit together like puzzle pieces
• Complementary shape
• Complementary charge
• Flexibility is problematic

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Atomic Density Methods
JC Mitchell, R Kerr and LF Ten Eyck (2001 ) Rapid
atomic density measures for molecular shape
characterization. J. Mol. Graph. Model., 19(3)
324-329.

• Atomic density methods deduce local shape based
  on the distribution of atomic neighbors.
• The atomic density exponent, l, is higher in a
  crevice than near a protrusion.
• The Fast Atomic Density Evaluation
  (FADE) and Pairwise Atomic
  Density
  Reverse Engineering (PADRE) methods
  compute atomic density
  differently.

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Shape Complementarity

• A local shape complementarity score is given by
• where l1 and l2 are taken relative to each of
  the molecules, and l0 represents a median
  exponent.
• The value of Ci is less than or
• greater than zero for a shape
• match or mismatch.
• Total and average scores for
• complementarity across an
• interface are defined.

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FADE Complementarity Statistics
JC Mitchell, S Shahbaz and LF Ten Eyck, (2003)
Interfaces in Molecular Docking. Molecular
Simulation. In press.

• Average complementarity scores in a narrow range
  for 184 protein-protein and protein-DNA systems
• FADE highlighted systems known to have strong
  shape match (Trypsin-BPTI, PKA-PKI,
  Fasciculin-AChE)

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Critical Residues in ACHE-FAS
JC Mitchell, S Shahbaz and LF Ten Eyck, (2003)
Interfaces in Molecular Docking. Molecular
Simulation. In press.

• Five interface regions have strong
  complementarity
• Four complementarity markers correspond to
  fasciculin residues known to affect binding
  affinity.
• Whether mutation was favorable seemed to depend
  on flexibility.

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KcsA Potassium Channel Protein

• Potassium Channel exists as a tetramer.
• The most complementary region of the
  monomer-monomer interface is near the signature
  sequence, with numerous markers near TYR78.

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CAPRI Antibody-Antigen Interface
DS Law, LF Ten Eyck, O Katzenelson, I Tsigelny,
VA Roberts, ME Pique and JC Mitchell (2003)
Finding needles in haystacks Re-ranking DOT
results using shape complementarity, Prot.
Struct. Fun. Gen. 53 33-40.

• Can you tell which is the crystal structure and
  which we predicted?

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CAPRI System 6
DS Law, LF Ten Eyck, O Katzenelson, I Tsigelny,
VA Roberts, ME Pique and JC Mitchell (2003)
Finding needles in haystacks Re-ranking DOT
results using shape complementarity, Prot.
Struct. Fun. Gen. 53 33-40.

• Top graphs Histograms for top 1500 DOT
  solutions show the distribution of DOT energies,
  number of FADE interface points, and the FADE
  total and avg complementarity scores.
• Bottom graphs The above quantities (x-axes)
  plotted against the percentage of correct
  contacts (y-axes) for the top 1500 DOT solutions.
  The large dots show our predictions, and the
  vertical line gives the FADE data for the crystal
  structure.

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The Docking Mesh Evaluator (DoME)

• Docking Mesh Evaluator (DoME) uses adaptive
  Poisson-Boltzmann electrostatics
• Funded by a DOE Genomes to Life grant.
• A complete parallel version of DoME is finished.
• New global optimization methods are undergoing
  testing.

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Poisson-Boltzmann Equation
NA Baker, D Sept, S Joseph, MJ Holst, J A
McCammon. (2001) Electrostatics of nanosystems
Application to microtubules and the ribosome.
Proc. Natl. Acad. Sci. USA 98 10037-10041.

• The Poisson-Boltzmann Equation describes an
  implicit solvent model for electrostatics.
• The nonlinear equation can be solved using
  adaptive finite element methods.

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Lennard-Jones Potentials

• The van der Waals interaction is a subtle
  atom-atom attraction that can contribute
  significantly to the binding energy of a large
  interface.
• When atoms get too close, repulsion occurs.
• The Lennard-Jones 6-12
• potential has the form
• P(d) A/d12 - B/d6
• and models both repulsion
• and van der Waals forces.

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Parallel Timing

• DoME runs on traditional parallel machines,
  workstations and grid computing clusters.
• For a fixed platform, energy evaluation and
  optimization scale linearly according to the
  number of configurations.
• For a fixed problem, typical compute times are
  approximately linear in the number of processors

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Optimization
JC Mitchell, AT Phillips, JB Rosen, and LF Ten
Eyck, (1999) Coupled optimization in protein
docking, Proceedings of the Third Annual
International Conference on Computational
Molecular Biology (RECOMB99). ACM Press, New
York.

• Protein docking is a calculus of variations
  problem.
• The correct solution is the global min of an
  energy.
• Rugged landscape prevents finding the global min
  (of model energies) easily.
• Local opt does not give a global min.
• Global opt with improved Convex
  Global Underestimation
  (CGU).

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CAPRI System 8

• DoMEs local optimization increases the size of
  the macromolecular interface.

900 top results from 1.95M scan
1600 top results from 9.6M scan
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Prediction Accuracy for CAPRI System 4

• For CAPRI 4, we know the solution and can look at
  the effect of optimizing DoME results.
• Optimization improves the percentage of correct
  contacts and brings the best solutions near the
  30 target for useful predictions.

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Rotamer Search
RL Dunbrack, Jr. and M Karplus (1993)
Backbone-dependent Rotamer Library for
Proteins Application to Side-chain prediction.
J. Mol. Biol., 230 543-574.

• The docking parameter space is infinite. With no
  chemical restrictions, the size of the parameter
  space is 3 (R L), where R is the number of
  atoms in the receptor and L is the number in
  the ligand.
• By assuming an internally rigid chemical
  structure for both molecules, our problem has six
  free variables.
• Using rotamers, the search space can be made
  essentially finite (but large).
• Smart pre-filters and a backbone
  dependent library help efficiency.
• Flexibility can be introduced at a
  very small cost.

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Concluding Remarks

• Shape complementarity analysis highlights regions
  important to binding.
• Shape alone cannot be used for docking
  prediction. Detailed electrostatic models are
  important.
• Flexible protein docking with a backbone
  dependent rotamer library is in progress.
• Can we replace Lennard-Jones with a softer yet
  more precise geometric matching potential?

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Acknowledgements

• Lynn F. Ten Eyck, Scientist, San Diego
  Supercomputer Center
• Sharokina Shahbaz, Undergraduate, UCSD Chemical
  Engineering
• Rex Kerr, Postdoc, UCSD Biology
• Michael J. Holst, Assoc. Professor, UCSD
  Mathematics
• J. Ben Rosen, Professor, UCSD Computer Science
  and Engineering
• J. Andrew McCammon, Professor, UCSD Chemistry and
  Biochemistry, UCSD Pharmacology
• Victoria A. Roberts, Assoc. Professor, The
  Scripps Research Institute - Molecular Biology
• Susan D. Lindsey, Parallel Software Engineer, San
  Diego Supercomputer Center
• Roummel Marcia, Postdoc, San Diego Supercomputer
  Center
• US Dept. of Energy
• National Science Foundation
• Burroughs-Wellcome Fund

Molecular Docking and Shape Analysis (MDSA)
group http//biology.sdsc.edu/MDSA wisc.edu
website coming soon