Off-lattice Hydrophobic Polar (HP) protein folding model   



Off-lattice protein models are similar to lattice protein models but they do not follow a given lattice topology. Instead, the 2d or 3d coordinate in the real axis define the positions of the residues. Among the off-lattice models with known lowest energy states is the AB model (Stillinger_et_al:1993) where A stands from hydrophobic and B from the polar residue. The distances between consecutive residues along the chain are held fixed to b=1, while non-consecutive residues interact through a modified Lennard-Jones potential. There is an additional energy contribution from each angle between successsive bonds.

In our representation, angles are represented as continuous values in [0, 2pi]. We look for the set of angles that defines an optimal off-lattice configuration. As instances, we consider Fibbonacci sequences defined recursively. The univariate Gaussian EDA implementation is described below. Other sequence configurations can be used instead. 


 %Gaussian UMDA for  the off-lattice HP Model continuous function 
 %For reference on the off-lattice HP model see (Hsu_and_Mehra_2003) 
 
 Fibbonacci_n = 7; % Fibbonacci_n: Value n for the construction of the Fibbonacci sequence. NumbVar = F(n)
 global InitConf;
 InitConf = CreateFibbInitConf(Fibbonacci_n); % HP Fibbonacci configuration 
 NumbVar = size(InitConf,2);
 PopSize = 1000; 
 F = 'EvaluateOffHPProtein';
 cache  = [0,0,0,0,0]; Card = [zeros(1,NumbVar);2*pi*ones(1,NumbVar)];
 edaparams{1} = {'learning_method','LearnGaussianUnivModel',{}};
 edaparams{2} = {'sampling_method','SampleGaussianUnivModel',{PopSize,3}};
 edaparams{3} = {'replacement_method','elitism',{1,'fitness_ordering'}};
 edaparams{4} = {'selection_method','prop_selection',{2}};
 edaparams{5} = {'repairing_method','SetInBounds_repairing',{}};
 [AllStat,Cache]=RunEDA(PopSize,NumbVar,F,Card,cache,edaparams) 
 % To draw the resulting solution use function OffPrintProtein(vector),
 % where vector is the best solution found.
 [AllStat,Cache]=RunEDA(PopSize,NumbVar,F,Card,cache,edaparams)




(Hsu_et_al:2003): H. P. Hsu, V. Mehra and P. Grassberger (2003) Structure optimization in an off-lattice protein model. Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 2):037703. Epub 2003 Sep 30.

(Stillinger_et_al:1993) F. H. Stillinger, T. Head-Gordon and C. Hirshfeld (1993). Toy model for protein folding. Physical Review E. (48):1469-1477

 
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