Protein Design

1
Protein Design
Crystal structure of top7 A novel protein
structure created with RosettaDesign.
CS273 Final Project Charles Kou charlesk_at_stanford
.edu
http//rosettadesign.med.unc.edu/
2
What is Protein Design

• Opposite of structure prediction determine low
  energy sequence that yield given structure.
• Computationally difficult
• Search space of 20n where n sequence length
  (20 amino acids)
• Major algorithms Dead-end elimination, genetic
  algorithms, Monte Carlo, Branch Bound.

http//www.stanford.edu/class/cs273/project/projec
t.html
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Major Algorithms

• Trade off between thoroughness and computational
  speed.
• Monte Carlo / Genetic Algorithm
• Can sample space with infinite number of
  solutions
• Sidechain identity, side chain orientation and
  backbone structure can be varied continuously.
• No guarantee of reaching global energy minimum.
• Dead-End Elimination
• Allows only discrete conformations.
• Rejection criteria is used to prune the search
  space.

Desjarlais JR, Clarke ND. Computer search
algorithms in protein modification and design.
Curr Opin Struct Biol. 1998 Aug8(4)471-5.
PubMed
4
Review Energy Landscape
JC Lantombe, Energy2.ppt
5
Review Example Energy Function

• E S bonded terms S non-bonded terms
  S solvation terms
• E (ES EQ ES-B ETor) (EvdW Edipole)
• Bonded terms - Relatively few
• Non-bonded terms - Depend on distances between
  pairs of atoms - O(n2) ? Expensive to compute
• Solvation terms- May require computing molecular
  surface

JC Lantombe, Energy2.ppt
6
Review Monte Carlo Simulation (MCS)

• Random walk through conformation space
• At each cycle
• Perturb current conformation at random
• Accept step with probability
• (Metropolis acceptance criterion)
• The conformations generated by an arbitrarily
  long MCS are Boltzman distributed, i.e.,
  conformations in V

JC Lantombe, Energy2.ppt
7
Monte Carlo Simulation

• Tend to waste time in local min.
• May consist of millions of steps.
• Energy must be evaluated frequently
  (computationally expensive).
• Use ChainTree to improve performance.

Lotan, I., Schwarzer, F., Halperin, D., Latombe,
J.C. Efficient maintenance and self-collision
testing for kinematic chains. In Symposium on
Computational Geometry (2002) 4352
Koehl, P and Levitt, M. De novo protein design.
I. In search of stability and specificity.
Journal of Molecular Biology, 293, 1161-1181
(1999).
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Genetic Algorithm

• Starts with First generation pool.
• Iteratively apply genetic operators (selection,
  recombination, mutation).
• Evloves toward better solution (low energy
  function).

S. M. Larson, J. England, J. DesJarlais, and V.
S. Pande. Thoroughly sampling sequence space
large-scale protein design of structural
ensembles. Protein Science 11 2804-281 (2002).
Protein Science
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Selection

• Selection function takes into account the value
  of fitness function. This gives priority to the
  fit organism but also gives chance for less
  fit organisms.

http//en.wikipedia.org/wiki/Genetic_algorithm
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Selection Method

• Roulette Method probability of selection is
  proportional to the value of fitness function
• Tournament picks k individuals (tournament
  size), and choose the individual with probability
  p. Iterate with probability p(1-p), then
  p(p(1-p))
• Higher k less chance for weaker individual.

http//en.wikipedia.org/wiki/Roulette_wheel_select
ion
http//en.wikipedia.org/wiki/Tournament_selection
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Recombination, Mutation

• Recombination different segment of the structure
  which is optimized in parallel can be recombined
  into the same model. Recombination occurs with a
  set probability. Otherwise, the population is
  propogated to the next generation.
• Mutation avoids local minima by mutating the
  child with a set probability.
• Similar to MC there is no guarantee to converge
  into global minimum.

http//en.wikipedia.org/wiki/Genetic_operator
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Genome_at_home

• Genome_at_Home uses distributed computing and
  genetic algorithm.
• It also incorporates backbone flexibility using
  Monte Carlo (random perturbation with RMSDlt1.0a)
  which improves the result.

http//www.stanford.edu/group/pandegroup/genome/
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Dead-end Elimination

• Discrete conformational search.
• Functionally equivalent to exhustive search.
• It uses rejection criteria to prune the search
  space.
• The robustness depends on the discreteness and
  the rejection criteria used.
• Guaranteed convergence to global min.
• Initially used for sidechain placement. More
  difficult for protein design because of high
  degrees of freedom.

Looger LL, Hellinga HW. Generalized dead-end
elimination algorithms make large-scale protein
side-chain structure prediction tractable
implications for protein design and structural
genomics. J Mol Biol. 2001 Mar 16307(1)429-45.
PubMed
14
Energy of conformation

• Reformulation of sidechain placement problem
  Amino acid identity is used instead of rotamer.
• The general DEE allows residue up to 300.
• Energy of conformation is defined as sum of
  interaction among side chains and sum of
  interaction of sidechain and the backbone.
• Rejection criteria is used and iterated until no
  more rotamers can be eliminated. Convergence
  occurs, or reduces the problem sufficiently for
  exhaustive serach.

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DEE filter Rejection Criteria

• Simple Criterion If lowest energy struct that
  can be found using a given sidechain rotamer (low
  energy side chain conformation) is higer than the
  highest energy struct w/ different rotamer, the
  first rotamer is eliminated.

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DEE filter Rejection Criteria

• Goldstein Criteria if energy struct containing
  one rotamer is always lowered by changing to a
  second one, the first one is eliminated.

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DEE filter Rejection Criteria

• Generalized Criterion residues are added in
  group, eliminated clusters of rotamers in the
  groups maybe excluded from the minimum operator,
  in addition to those which form dead-end clusters
  with c.

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Mean Field Theory

• Reduce search space.
• Self-consistency is sought by placing amino acids
  at pre-selected positions in a given structure.
• Energy function is minimized by mean field.

Voigt CA, Mayo SL, Arnold FH, Wang ZG.
Computational method to reduce the search space
for directed protein evolution. Proc Natl Acad
Sci U S A. 2001 Mar 2798(7)3778-83. PNAS
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Review Branch Bound

• Set of solutions can be partitioned into subsets
  (branch)
• Upper limit on a subsets solution can be
  computed fast (bound)
• Branch Bound
• Select subset with best possible bound
• Subdivide it, and compute a bound for each subset

S.Batzoglou, Threading2.ppt
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Rosetta Design

• Initial backbone designed without regard to
  side-chain packing.
• Iterates between sequence design and backbone
  optimization using Monte Carlo.
• Perturbation in random change in the torsional
  angles of 1-5 random residue, or substitution of
  backbone torsonal angles of 1-3 consecutive
  residues with torsional angles from a structure
  in the PDB. Sidechain optimization. Accept/reject
  using Metropolis criterion.
• 1.17-a backbone atom RMSD between model and
  structure.

Crystal structure of top7 A novel protein
structure created with RosettaDesign.
http//rosettadesign.med.unc.edu/
Kuhlman B, Dantas G, Ireton GC, Varani G,
Stoddard BL, Baker D. Design of a novel globular
protein fold with atomic-level accuracy.
Science. 2003 Nov 21302(5649)1364-8. PubMed
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Using Rosetta Design

• Red PDB 1A1M Mhc Class I Molecule B5301
  Complexed With Peptide Typdinqml From Gag Protein
  Of Hiv2
• Blue Rosetta Stone Designed
• Visualized with Deep View / Swiss-PdbViewer.

http//us.expasy.org/spdbv/
http//www.rcsb.org/pdb/cgi/explore.cgi?pid195321
117535569pdbId1A1M
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b.e.a.n.s.

• A simple openGL based program was developed to
  test monte carol and genetic algorithms on
  designing chain of jelly beans.
• User is able to vary the initial structure of the
  beans and compare the efficiency of the
  algorithms via built-in timer.