Post on 29-May-2015
A new integer programming model for HP problem
N. Yanev 1, P. Milanov 2; 3, I. Trenchev 2
1 Faculty of Mathematics and Informatics, University of Sofia, Bulgaria.
2 South-West University “Neot Rilski", Blagoevgrad, Bulgaria.
3 Institute of Mathematics and Informatics, Bulgarian Academy of Sciences.
choby@math.bas.bg, peter milanov77@yahoo.com, trenchev@swu.bg
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Our goal is to put red and blue balls on the grid as:
- every two neighbours balls in the sequence must be adjacent in the grid;- in each cell can be placed only one ball.
Problem formulation
A self-avoiding walk is a path from one point to another which never intersects itself.
Such paths are usually considered to occur on lattices, so that steps are only allowed in
a discrete number of directions and of certain lengths.
Problem formulation
Goal: problem maximizes the number of blue, blue pairs of contacts
Amino acids sequence:SLDRSSCFTGSLDSIRAQSGLGCNSFRY
HP folding sequence : PHPPPPPHPPPHPPHPHPPPHPPPPHPP
In this research, we study the hydrophobic-hydrophilic (HP) model on two-dimensional (2D) square lattice, which is one of the most extensively studied lattice models. The HP model was first introduced by Dill (1985).
From Protein folding to HP model
Figure 3: Optimal fold of a protein of length36
Figure 2: A fold constructed by the Hart-Istrail algorithm
Optimal vs heuristics
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H H PP H P
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Conversion to Graph problem
Mathematical problem is to find a path in the graph from first column to the last with maximum green arcs
We used a 3D cubic lattice with dimension 6 .
The primary sequence of these two proteins is:
SLDRSSCFTGSLDSIRAQSGLGCNSFRY – orexin peptide;
FSGPPGLQGRLQRLLQASGNHAAGILTM – hypotensive hormone.
Figure 4. Graphical presentation for HP folding of 1ANP
Computational runs
Future trends:
• Improving of the model;
• Adaptation of CPLEX for special branch and bound for HP folding;
• Solving larger problems.
Thank you for attention.