Computational Tools to Study Protein Motion

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Computational Tools to Study Protein Motion

• Peggy Yao
• Prof. Latombes Group
• Stanford University

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Secret of Life
http//frank.itlab.us/spider_2002/dna_protein.gif
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Protein

• They perform many vital functions, e.g.
• Catalysis of reactions
• Transport of molecules
• Building blocks of muscles
• Storage of energy
• Defense against intruders
• They are large moleculescontaining 100s to 1000s
  atoms.
• They are made of amino acids.
• There are 20 different types of amino acids.

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Protein Structure
Amino acid

• A protein has one or a few chains of amino acids.
• A chain of amino acids folds into a 3D structure.
• Some substructures are regular helix shape (alpha
  helix), or instant noodle shape (beta sheet).
• The rest are irregular shape, called loops.
• Chains aggregate together into a bigger 3D
  structure.

loop
http//academic.brooklyn.cuny.edu/biology/bio4fv/p
age/3d_prot.htm.
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Structure Function

• Protein function is closely related to its 3D
  structure.
• E.g., mad-cow disease is due to PrP misfolding.
• E.g., calcium atoms bind to good-shape-loops.

calcium
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Structural Flexibility

• Protein structure is not static.
• Structural flexibility is important to protein
  function.
• In order to study protein functions, wed like to
  know various conformations a protein can take.

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Experimental Protein Structure Determination
Methods

• X-ray crystallography
• Requires protein crystals, which are hard to
  obtain.
• Returns a single static conformation.
• Nuclear magnetic resonance (NMR)
• Can obtain multiple conformations.
• However, it is only limited to small proteins.

Need computational methods to predict various
conformations! -- Conformation sampling.
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Starting from Loops

• Why I started the study from loops only?
• Loops are relatively more flexible than other
  substructures (alpha helices and beta sheets).
• Loops are sometimes binding sites.
• Loops are short, thus have less degrees of
  freedom.

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Sample Loop Conformations

• Valid loop conformations
• Closed
• Two ends of the loops overlap with the
• two anchors of the loop in correct orientation.
• Collision-free
• No atom on the loop collides with any other atom
  on the loop or any atom from the rest of the
  protein.
• Sample loop conformations
• Generate loop conformations broadly across the
  valid conformation space.

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Loop Model
Amino Acid (i-1)
Amino Acid i
Amino Acid (i1)
O
O
Cß

C
f
Ca
N
C
?
N

f
?
?
f
Ca
C
N
Ca
Cß
O
Cß

• A long kinematic chain with 2n DoFs if there are
  n amino acids in the loop.
• Each DoF is a dihedral angle.

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Challenges

• High dimensionality
• If 10 amino acids in the loop, we are studying a
  20-dimensional space.
• If only 4 values for each DoF,
• there are 1099511627776
• possible conformations!
• Need to satisfy two constraints
• simultaneously.
• Closed collision-free
• The valid conformation space
• is only a tiny subspace of the
• entire space.

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To Satisfy Each Constraint

• To close a loop
• Use exact inverse kinematics
• To detect collision
• Grid method
• Build a grid around a protein.
• An atom can only collide with atoms from the same
  grid cell, or from neighboring grid cells.

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Naïve Method

• Algorithm
• Sample all DoFs randomly.

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Naïve Method

• Algorithm
• Sample all DoFs randomly.
• Close the loop using exact inverse kinematics.

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Naïve Method

• Algorithm
• Sample all DoFs randomly.
• Close the loop using exact inverse kinematics.
• Check whether the resulting conformation is
  collision-free.
• If not, reject it and start another iteration
  until getting a closed, collision-free
  conformation.

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Naïve Method

• Algorithm
• Sample all DoFs randomly.
• Close the loop using exact inverse kinematics.
• Check whether the resulting conformation is
  collision-free.
• If not, reject it and start another iteration
  until getting a closed, collision-free
  conformation.
• Drawback
• Takes a long time to get a valid conformation due
  to high rejection rate.

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Our MethodPrioritized Constraint Satisfaction
Approach

• Intuition
• The two ends of the loop are more likely to get
  into collision.
• Prioritized constraint satisfaction
• Divide the loop into 3 fragments.
• Make sure the two ends are
• collision-free first.
• Dont care the closed constraint at this stage.
• Use the middle fragment to close the loop.

Middle fragment
Back end
Front end
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Our Method (1)

• Construct collision-free ends
• Each time, add one DoF and all atoms determined
  by that DoF such that they are all collision-free.

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Our Method (2)

• Use naïve method to fill the middle fragment.
• Randomly assign its DoF values.
• Close it to the back end using exact IK, assuming
  it is attached to the front end.
• Accept if it is collision-free.

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Our Method (2)

• Use naïve method to fill the middle fragment.
• Randomly assign its DoF values.
• Close it to the back end using exact IK, assuming
  it is attached to the front end.
• Accept if it is collision-free.

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Experimental Results (1)
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Experimental Results (2)

• Much more efficient than the naïve method.

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Protein Loop Kinematics Toolkit

• Protein structure manipulation
• https//simtk.org/home/looptk