The Protein Threading Problem With Sequence Amino Acid Interaction Preferences Is NPComplete

1
The Protein Threading Problem With Sequence Amino
Acid Interaction Preferences Is NP-Complete

• Richard H. Lathrop
• Artificial Intelligence Laboratory, MIT
• Presenter Chengbang Huang
• Oct. 26 2004

2
Introduction

• Protein consists of amino acids
• Amino acid interaction decides protein structure
• Predict protein structure using amino acid
  interaction preferences

3
Result

• The Protein Threading Decision Problem----does
  there exist a threading with a score less than K,
  is NP-complete, under two following assumptions
• Variable-length gaps are admitted into the
  alignment
• Interactions between amino acids from the
  sequence are admitted into the score function

4
Difficulties of Direct Prediction

• Direct approach---find the folded conformation
  with minimum energy
• Delicate energetic balance of powerful atomic
  forces
• Vast number of possible conformations
• Forces involved poorly understood or difficult to
  model accurately
• Summation over a large number of atoms

5
Alternative

• Use the known protein structures as spatial
  folding templates
• Only around 1,000 different protein structural
  families (Chothia, 1992)
• Each known protein structure recognizes protein
  sequences likely to fold into a similar structure.

6
Implementation

• The known structure provides a set of positions
  in 3-dimensional space, represented by an
  adjacency graph.
• These will be filled by amino acids from a
  sequence of known structure
• Different candidate threadings arise
• A score function can distinguish good from bad
  threadings

7
2 Assumptions

• Variable-length gaps are admitted into the
  alignment
• Interactions between amino acids from the
  sequence are admitted into the score function

8
Approaches w/o 2 Assumptions

• Fixed-length moving window, Crippen 1990
• Pro focus closely on the score function, which
  can be devised to identify correct match
• Con ignore variable-length gap, structure and
  sequence could be out of registration
• Ignore interactions between neighboring amino
  acids, Bowie et al. 1991
• Pro Simpler, sometimes perform well
• Con Give up structure information
• Both are accomplished in polynomial time.

9
To Prove NP-Completeness

• Problem is in NP
• Transform a known NP-complete problem to the
  problem studied. Encoding and decoding take
  polynomial time.

10
Transform to 1-in-3 3SAT problem

• SATisfiability a set of Boolean variables, plus
  a set of Boolean clauses. Does there exist any
  setting of variables that makes all the clauses
  true simultaneously?
• 3SAT clauses contain exactly 3 literals
• 1-in-3 3SAT each of the clauses can be made true
  by exactly one of the three literals.

11
Sketch of Proof

• Threading with a score of zero encode solutions
  of the original 1-in-3 3SAT problem
• Threadings with positive scores encode failures.

12
More Details

• True---Threonine, False---Phenalanine
• P (proline) first literal Q (glutamine)
  second R (arginine) third
• The sequence a to be threaded is
• aPQRPQRPQRPQRTFTFTF
• one PQR for each clause, one TF for each
  Boolean Variable.

13
Discussion

• Any protein threading algorithm must adopt one of
  the following choices
• Fail to admit variable-length gaps
• Fail to admit interaction preferences
• Fail to find the optimal threading
• Require an exponential amount of time

14
(No Transcript)