Folding Proteins with Boltzmann Learning Rule

1
Folding Proteins with Boltzmann Learning Rule

• Alexei PodtelezhnikovDavid Wild_at_ SPAM

2
Machine Learning Ideas

• NOT a traditional ab initio approach
• First, maximize the probability of known several
  native folds by tweaking potentials
• Then, use the found potential for future folding

3
Boltzmann Learning Rule
Ole Winter Anders Krogh 2003
The probability of nativei fold given sequencei
and the model parameters ?
The updating of the model parameters with the
rate ?
4
Sampling Techniques

• Available methods - Molecular Dynamics slow in
  folding - Monte Carlo complex
• Internal instead of Cartesian coordinates -
  0.5N instead of 3N6 degrees of freedom - fewer
  adjustable model parameters ?
• Complexity - a tiny angle change affects global
  conformation - special moves (e.g. re-bridging)

5
Model Peptide Chain

• Perfectly planar, rigid peptide bonds
• Single-pseudoatom simplified side chains R
• Parallel CaC and NCa

6
Local Moves I

• Opposite changes in ?i and ?i1 result in a shift
  with no rotation
• An introduced random shift can be balanced out by
  the shifts in 3 consequent peptide bonds
• Numerical solution

7
Local Moves II

• Flexible tetrahedron at Ca
• Crankshaft rotations
• Random rotations at the termini
• Straightforward implementation

8
Demo

• Polyalanine alpha helix 2 sec on 1 GHz Athlon

9
Potentials

• Lennard-Jones between atoms X and Y
• Hydrogen bonds
• Other interactions

Total of more than 1000 model parameters to learn