Constraint logic programming approach to protein structure prediction

1
Constraint logic programming approach to protein
structure prediction
A. Dal Palu, A. Dovier, and F. Fogolari BMC
Bioinformatics, 2004.

• Presented by
• Morshed Osmani

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INTRODUCTION

• The protein structure prediction problem is one
  of the most challenging problems in biological
  sciences.
• However, the protein structure prediction problem
  can be cast in the form of an optimization
  problem.
• Constraint Logic Programming which is a
  declarative programming paradigm can be used for
  solving this combinatorial optimization problem.
• Face-Centered Cube (FCC) lattice model is used
  here.

3
Background

• Faster method for protein structure prediction
  evolves along two lines
• Assembling the structure of a protein using
  structural fragments of similar sequences,
  available in the protein structure repository,
  and later screening the feasibility of the
  resulting structures, using energetic criteria
• Representing the protein chain by a highly
  simplified model which is, hopefully, treatable.
• This paper follows the second strategy.

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Background (Contd.)

• The simplified approach has several advantages
• Less no. of variables so linkage between
  kinetics, thermodynamics of protein folding
  process, and intramolecular interactions is more
  easily addressable
• Simplified model supports the idea that details
  of atomic interactions between amino-acid
  residues are less important than the overall
  character of these interactions
• Generation and evaluation of energy of a
  conformation is easy and less time consuming

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Constraint Logic Programming

• It is a declarative programming paradigm
  particularly well suited for encoding
  combinatorial minimization problems.
• CLP is the natural merger of the two declarative
  paradigms known as Constraint Solving and Logic
  programming.
• It is independent of the problem modeling and the
  search strategy.

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CLP (Contd.)

• It is a Constrain Generate technique in
  contrast to classical Generate Test technique
• First phase is a deterministic phase that
  produces a number of constraints
• In the second phase solutions space is generated
  non-deterministically following those
  constraints.
• Some languages has built-in support for CLP (for
  example, S1CStus Prolog)

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Lattice Models
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Lattice Models (cont.)

• Each side of the cube is 2 unit
• Points at Euclidean distance v2 are linked their
  distance is called lattice unit.
• For linked points i and j, it holds that xi-xj
  yi-yj zi-zj 2.
• A contact is defined between two non adjacent
  residues placed on two vertices of a side of a
  cube.

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Mathematical Formalization

• Given asequence S s1 ... sn, with each si being
  an amino acid residue, a fold of S is a function
  ? 1, ..., n ?FCC such that ?(i) - ?(i
  1)v2 and ?(i) - ?(j) 2 for i ? j.
• The protein folding problem can be reduced to the
  optimization problem of finding the fold ? of S
  such that the following energy is minimized
• E(w)
• where contact(?(i), ?(j)) is 1 if ?(i) - ?(j)
  2, 0 otherwise.

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Important Features

• Secondary structure (alpha helix, beta sheet )
  property is used.
• Simulated Annealing strategy is used.
• Globularity of the simulated protein is forced by
  a harmonic constraint on the radius of gyration.
• Size of solution space is 1.26N0.162(10.0364)N
• Imposing additional constraints can reduce this
  search space substantially

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Main Program Predicate

• fcc_pf( ID, Time, Compact)-
• initialization,
• protein(ID, Primary, Secondary),
• constrain(Primary, Secondary, Indexes, Tertiary,
  Energy, Matrix, Freq, Compact),
• writetime,
• solution_search(Time, Primary, Secondary,
  Indexes, Tertiary, Energy, Matrix, Freq),
• print results(ID,Time,Primary, Secondary,
  Tertiary,Compact).

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Constraint Example

• next(X1,Y1,Z1,X2,Y2,Z2),
• next_constraints(X2,Y2,Z2C).
• next_constraints(_,_,_).
• next(X1,Y1,Z1,X2,Y2,Z2)-
• domain(Dx,Dy,Dz,0,1),
• Dx abs(X1-X2),
• Dy abs(Y1-Y2),
• Dz abs(Z1-Z2),
• Dx Dy Dz 2.

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Protein Definition

• protein(1YPA, Primary, Secondary)-
• Primary m,k,t,e,w,p,e,l,v,g,k,a,v,a,a,a,k,k,v,i
  ,l,q,d,k,p,e,a,q,i,i,v,l,p,v,g,t,i,v,t,m,e,y,r,i,d
  ,r,v,r,l,f,v,d,k,l,d,n,i,a,q,v,p,r,v,
• Secondary helix(13,23), strand(28,33),
  strand(45,51), strand(61,63).

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Some more constraints
Distance_constraint ensures that two consecutive
lattice points are separated by more than one
lattice unit Compact_constraint ensures that for
every pair of aminoacids, the norm of the
projection of their distance on each x, y, z
coordinate, is smaller than CompactFactor N.
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Some more constraints (contd.)

• FCC allows angles 60, 90, 120, 180 however
  protein fold favors angles 90-150, so 60 and
  180 angles are removed from possibility
• Index stores torsional angles. Alpha helix
  assumes angle 300 and beta sheet 120. This angles
  are treated as constraints also.

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Results
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RELATED WORK

• This work is further extended by Dovier et al
  1.
• Similar works can be found in Backofens
  paper2.

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References

• Alessandro Dal Palù, Agostino Dovier, Enrico
  Pontelli Heuristics, optimizations, and
  parallelism for protein structure prediction in
  CLP(FD). PPDP 2005 230-241
• R. Backofen. The protein structure prediction
  problem A constraint optimization approach using
  a new lower bound.Constraints, 6(23)223255,
  2001.
• A. Dal Palu, A. Dovier, and F. Fogolari.
  Constraint logic programming approach to protein
  structure prediction. BMC Bioinformatics, 5(186),
  2004.