Sidechain Placement and Protein Design

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Sidechain Placement and Protein Design

• GCMB07, 2 May

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Protein design

• Sequence ? Structure ? FunctionKDTIALVVST
  Ribose YPVDLKLVVKQ binding protein
• Modify sequence TNTto change structure
  bindingand function Looger03
• or behavior Ambroggio06 folding order

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Protein Design or Redesign

• Create an amino acid sequence that folds to a
  stable protein and performs a desired function
• Avoid
• Sampling all sequences
• Solving protein folding
• Relying on molecular dynamics
• A successful design strategy build on an
  existing structure
• Scaffold backbone from a known folded structure
• Redesign 20 residues
• Find side chains that fit

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Outline

• Sidechain Rotamers Rotamer Libraries
• Algorithms for Sidechain Placement
• Brute Force
• Dead End Elimination
• Simulated Annealing
• Stochastic Mean Field
• Dynamic Programming
• A Biased View of Protein Structure Design
• How is design done?
• Why is it successful?

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Protein Structure

• Chemical
• 1-Dimensional Sequence of amino acids
• Two components for each amino acid
• Backbone (NCaCO)
• Side chain (residue)
• Placed residue a position in an amino acid
  sequence

S
OH
N
N
H2N
MSS
MSW
O
O
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Side chain geometry

• Conformation flexibility from dihedral angles
• Side chain internal geometry
• Bond angles and bond lengths fixed
• Dihedrals c1, c2, may rotate
• Rotamers rotational isomers
• Side chains have preferred conformations
• Prefer dihedrals around 60o, 180o and -60o
• Rotamer Library set of dihedral angles
  Ponder87, Dunbrack93, Lovel2000

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Side chain conformation
side chains differ in size ( of atoms) and
degrees of freedom ( of c angles)
N
N
?2
?1
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Serine c1 distribution
a chosen combination of side chain torsion
angles c1, c2, etc. for a residue is known
as a rotamer.
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Side chain conformations--canonical staggered
forms
Newman projections for c1 of glutamate
glutamate
ttrans, ggauche
name of conformation
Side chain angles are defined moving outward from
the backbone, starting with the N atom so the c1
angle is NCaCbCg, the c2 angle is CaCbCg Cd
...
IUPAC nomenclature http//www.chem.qmw.ac.uk/iupa
c/misc/biop.html
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Backbone independent rotamer library

• Dunbrack Cohen, 1997

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What do rotamer libraries provide? J. Meiler07

• Rotamer libraries significantly reduce the number
  of conformations that need to be evaluated during
  the search.
• This is done with almost no risk of missing the
  real conformations.
• Even small libraries of about 100-150 rotamers
  cover about 96-97 of the conformations actually
  found in protein structures.
• The probabilities of each rotamer in the library
  provide estimates of the potential energy due to
  interactions within the side chain and with the
  local backbone atoms, using the Boltzmann
  distribution E ? ln(P)

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Side chain geometry

• Conformation flexibility from dihedral angles
• Side chain internal geometry
• Bond angles and bond lengths fixed
• Dihedrals c1, c2, may rotate
• Rotamers rotational isomers
• Side chains have preferred conformations
• Prefer dihedrals around 60o, 180o and -60o
• Rotamer Library set of dihedral angles
  Ponder87, Dunbrack93, Lovel2000
• http//dunbrack.fccc.edu/bbdep/bbdepdownload.php
  (Backbone dependent and independent libraries)
• http//kinemage.biochem.duke.edu/databases/rotamer
  .html (Backbone independent library)

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Rotemers in crystallographic refinement
Fit structure to electron density from x-ray
diffraction

• Red indicate clashes w/ added hydrogen atoms

better choice of side chain
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Outline

• Sidechain Rotamers Rotamer Libraries
• Algorithms for Sidechain Placement
• Brute Force Search
• Dead End Elimination
• Simulated Annealing
• Stochastic Mean Field
• Dynamic Programming

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Side Chain Placement Problem

• Given
• A fixed protein backbone
• A set of fixed (background) residues
• A set of changing (molten) residues
• A list of allowed amino acids for each molten
  residue
• A rotamer library
• A pairwise decomposable energy function
• Find the assignment of rotamers to the molten
  residues, S, that minimizes the energy function

Kinemage rotamers for Ubiquitin surface residues
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Energy Functions

• f Protein Structure ? ?
• Lennard-Jones
• van der Waals attractive energies
• atom overlap repulsive overlap
• Electrostatics
• Solvent Effects
• Hydrogen bonds
• Often pairwise decomposable
• sum of atom-pair or rotamer-pair interaction
  energies

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Side Chain Placement Problem

• Find the assignment of rotamers to the molten
  residues, S, that minimizes the energy function
• Functions stated in terms of rotamer energies
• rotamer / background energy
• rotamer pair energies

Esingle
Epair
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Side Chain Placement Problem

• NP-Complete
• Reduction from SAT Pierce2002
• Techniques
• Optimality Guarantee
• Dead-End Elimination Desmet92, Goldstein94,
  Looger2001
• Integer Linear Programming Erickson2001
• Branch and Bound Gordon99, Canutescu2003
• Dynamic Programming Leaver-Fay2005
• No Optimality Guarantee
• Genetic Algorithms Jones94
• Simulated Annealing Holm92,Hellinga94,Kuhlman03
• Self-Consistent Mean Field Koehl96

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Dead End Elimination (DEE)

• Reduce the search space without losing the Global
  Minimum Energy Conformation (GMEC).
• Eliminates rotamers which cannot be in the GMEC,
  using more accurate (and more computationally
  expensive) upper and lower bounds.
• Uses brute force search on rotamers remaining.
• Typically assumes that the scoring function can
  be expressed as a sum of pair-wise interactions

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A first, simple condition for elimination

• A rotamer can be eliminated for a residue when
  the minimum (best) energy it obtains by
  interaction with other rotamers is still
  higher (worse) than the maximum energy of some
  other rotamer

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The Goldstein improvement

• A rotamer can be safely eliminated when there
  exists a rotamer that has lower (better) energy
  for each given environment.
• This criteria is more powerful, and typically
  requires though more computational time.

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Even more powerful criteria can be obtained with
even more computation

• A rotamer can be safely eliminated when, for each
  environment, there exists some rotamer that has
  lower (better) energy.

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Dynamic Programming via an Interaction Graph

• Surface residues on Ubiquitins b-sheet

Interaction Graph defined by Rosettas
energy function
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Interaction Graph

• G V, E, a multi-hypergraph
• vertices ? molten residues v
• state space ? rotamers for a residue S(v)
• edge ? possibility of residue interaction e ?V
• scoring function ? interaction energy fe ?S(v)
  ? ?

v?e
Hypergraph
Graph
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Interaction Graph Evaluation (Pairwise case)

• For G V, E, min
• Each vertex, v, has a function to capture
  interactions with the background fv S(v) ? R
• Each pair of interacting vertices, u, v,
  defines an edge with a function to capture pair
  interactions fu,v S(u) x S(v) ? R
• Given an interaction graph, GV,E, find the
  state assignment S that minimizes Sw?V?E fw

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Bottom Up Dynamic Programming

• Eliminate node v
• Let Ev be the edges incident upon v
• Let Nv be the neighbors of v
• For each edge e ? Ev with scoring function fe,
  let fe,vs be edge e s scoring function with
  vertex v fixed in state s
• Create a new hyperedge incident upon Nv.
• Compute fNv min s ? S(v) ? e ? Ev fe,vs
• Remove v from graph

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Scoring Function Representation Tables
u
Edge e u,v
S(v)
S(u)
v
f
g
h
i
j
a
b
c
d
e
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Scoring Function Representation Tables
w
Edge e u,v,w
v
u
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Experiments and Results

• Rotamer Relaxation Task
• Sequence fixed choose new rotamers for each
  residue
• Redesign Task
• Search of conformation and sequence spaces.
• Ubiquitins 15 surface residues
• Large rotamer library
• Relaxation, 32 states per vertex, tw-4
  interaction graph
• Redesign, 680 states per vertex, tw-3 interaction
  graph (drop one edge)

Running Time Memory
Relaxation 200 ms (small)
Redesign 15.99 hrs 3.7 GB
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Dynamic Programming for Hydrogen Placement

• Dynamic programming (DP) limited by treewidth of
  graph instances
• Treewidths from graphs in protein design too
  large for DP to be practical
• Adding hydrogen atoms to PDB
• Hydrogen placement via combinatorial
  optimization REDUCE Word99
• Non-pairwise decomposable energy function
• Previously used brute force
• Replaced with dynamic programming
• Interaction graphs have low treewidth
• Effective in practice minutes to ms.
• REDUCE v3.02 in Molprobity suite, and distributed
  from http//kinemage.biochem.duke.edu/software/red
  uce.php

H
O
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Simulated Annealing

• Stochastic optimization technique
• Monte Carlo
• Make a random change, determine ?E
• Metropolis criterion Metropolis57
• accept with probability
• Gradually lower temperature T
• In Side Chain Placement
• Assign each residue a rotamer
• Repeat
• Select a random residue, and a random alternate
  rotamer
• Find ?E induced by substituting the alternate
  rotamer
• Accept/Reject substitution according to
  Metropolis criterion

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Self-consistent mean field

• I planned to cull a description from Patrices
  BioEbook sections
• http//nook.cs.ucdavis.edu8080/koehl/BioEbook/de
  sign_scmf.html
• http//nook.cs.ucdavis.edu8080/koehl/BioEbook/sc
  mf.html
• but didnt have time in class.

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The practical problem of side chain modeling M07

• The way we deal today with the problem of protein
  structure prediction is very different from the
  way nature deals with it.
• Due to technical issues such as computation time
  we are usually forced to accept a fixed backbone
  and only then put the side chains on it.
• The quality of the side chain modeling is
  therefore heavily dependent on the position of
  the backbone. If the initial backbone
  conformation is wrong, the side chain modeling
  quality will be accordingly bad.
• What is really needed is a combined algorithm
  that optimizes backbone conformation
  simultaneously with side chain modeling.

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Protein Design or Redesign

• Create an amino acid sequence that folds to a
  stable protein and performs a desired function
• Avoid
• Sampling all sequences
• Solving protein folding
• Relying on molecular dynamics
• A successful design strategy build on an
  existing structure
• Scaffold backbone from a known folded structure
• Redesign 20 residues
• Find side chains that fit

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Why Design Proteins?

• Nature uses proteins
• to signal events
• to catalyze reactions
• to move cells (motors)
• to bear weight (I-beams)
• Design is an experiment to help understand
  folding/binding
• Industrial biosynthesis
• Proteins are both efficient and specific
• Cure disease
• Antibodies
• Inhibition peptides as drugs
• Perturb cell signaling pathways

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Why do RosettaDesign, Dezymer, work?

• Geometric approximations (3d jigsaw puzzles) are
  surprisingly effective in design.
• They mine PDB structures for behaviors of native
  proteins and fragments.
• They precompute energies for pairwise
  interactions.
• They use many fast computers to allow detailed
  sampling of discrete conformations.
• Fast optimization algorithms
• Competition

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How do RosettaDesign, Dezymer, fail?

• Computationally difficult to achieve good packing
  and hydrogen bond satisfaction in protein core
• Scores for packing, solvation and hydrogen bond
  satisfaction cannot be pairwise additive.
• Scores often used as filters wed prefer to
  optimize.
• Stability of designed proteins
• Multistate or negative design

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Protein Stability

• A naturally occurring protein adopts a compact
  geometry when placed in water
• Stability is difference in free energies of the
  folded and unfolded states

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Protein Stability

• A naturally occurring protein adopts a compact
  geometry when placed in water
• Different proteins have different free energies
  in their unfolded states

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Challenges in Protein Design

• Side chain placement is hard
• The complexities of individual instances of SCPP
  are related to the treewidth of their interaction
  graphs.
• Tight, collision-free packing is often impossible
  on the input scaffold
• The interaction graph to allow simultaneous
  optimization of side chain and backbone
  structures
• Protein stability is not well captured by
  pairwise decomposable energy functions
• The interaction graph supports using non-pairwise
  decomposable energy functions during side chain
  placement