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Takeshi Yoshida

Energy Minimization of Protein Tertiary Structure by Parallel Simulated Annealing using Genetic Crossover . GECCO2002. Doshisha Univ. Japan. GECCO2002. Doshisha Univ. Japan. Doshisha University, Kyoto, Japan. Takeshi Yoshida. Tomoyuki Hiroyasu. Mitsunori Miki. Maki Ogura.

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Takeshi Yoshida

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  1. Energy Minimization of Protein Tertiary Structureby Parallel Simulated Annealingusing Genetic Crossover GECCO2002 Doshisha Univ. Japan GECCO2002 Doshisha Univ. Japan Doshisha University, Kyoto, Japan Takeshi Yoshida Tomoyuki Hiroyasu Mitsunori Miki Maki Ogura Institute for Molecular Science, Aichi, Japan Yuko Okamoto

  2. Molecular simulation Apply Heuristic method to this problem. Background Protein tertiary structure is closely related with biological function. • lead to development new medicines. • lead to manifestation mechanism of pathology. Prediction of protein tertiary structure • high searching ability • need huge calculate time

  3. Protein Tertiary Structure • Protein is composed of an array with 20 amino acids. • Amino acid array is folding to the lowest energy • Protein structure naturally exist with lowest energy Energy function of protein Analyzing structure as Optimization problem Folding protein to stable state Amino acid array Tertiary Structure

  4. Low temperature －(Enext－Ecurrent) exp T Probability;P = Simulated Annealing SA is often applied to prediction of Protein tertiary structure. SA has parameters, those are a temperature and a step. High temperature By the parameters, SA’s searching point moves to worse a state in a certain probability. Local minimum Global minimum T: Temperature of current step

  5. Energy function of Protein Minimum in global area Minimum in local area Energy function of Protein has many minima in local area And a few minima in global area. No success result has ever prediction of protein using SA

  6. Parallel SA + GA operation Purpose of this study PSA/GAc is a hybrid method of SA with GA operation Parallel SA using Genetic Crossover(PSA/GAc) • Genetic Algorithm(GA) is good at searching a solution • in a wider area.(global search) • Simulated Annealing(SA) is good at searching a solution • in narrower area.(local search) PSA/GAc is good at searching not only locally but also globally. We apply PSA/GAc to Protein tertiary structure.

  7. Modeling of Protein tertiary structure Protein is composed of an array with 20 amino acids. dihedral angle Design variable : dihedral angle between main chain and side chain. Changing dihedral angle Minimize energy function of protein

  8. PSA/GAc PSA/GAc is based on Parallel SA. Searching points : individuals Total number of SA : Population size n : crossover interval n n n n crossover SA 1 2 3 1 2 3 SA 1 2 3 1 2 3 end crossover crossover SA 1 2 3 1 2 3 SA 1 2 3 1 2 3 high temperature low Genetic Crossover is used to exchange the information of individuals.

  9. 1 2 3 1 2 3 PSA/GAc Genetic Crossover is performed as follows. e.q continuous optimization problem(3 dimensions) energy cross point 1 2 3 parent1 -1.3 Next searching points 1 2 3 parent2 -1.8 crossover 1 2 3 child1 -1.1 1 2 3 child2 -2.0

  10. PSA/GAc PSA/GAc is based on Parallel SA. Searching points : individuals Total number of SA : Population size n : crossover interval n n n n crossover SA 1 2 3 1 2 3 SA 1 2 3 1 2 3 end crossover crossover SA 1 2 3 1 2 3 SA 1 2 3 1 2 3 high temperature low Each process reduce temperature from high to low as parameter of SA.

  11. Lowest-energy conformation [okamoto,1991] E < - 42kcal/mol • Design variables 64 dihedral angles Target Protein Structures Protein for numerical example C-peptide ; 13 amino acids In case of using ECEPP/2 program, • There are 64 times annealing per 1MCsweep C-peptide structure

  12. 180 (180 0.3) Parameters Parameter Value 24 Population size 2.0(100k) Initial temperature 0.1(50K) Last temperature 32 Crossover interval Range size Num of Processors 6 We tried two types of simulations. Simulation1 : 4164 MCsweeps and 10 trials. (100,000 MCsweeps totally) Simulation2: 41646 MCsweeps and 7 trials.

  13. Result : Energy Simulation Type Energy (kcal/mol) PSA/GAc Simulation1 - 46.7 PSA/GAc Simulation2 - 57.8 Optimum [Okamoto, 1991] - 42 • To derive a good solution , PSA/GAc with long MCsweep • annealing is more effective than small Mcsweep annealing. • PSA/GAc has high searching ability in predicting protein • tertiary structure problem

  14. Result : Protein structure Simulation1: -46.7kcal/mol Simulation2: -57.8kcal/mol • To derive a good solution , PSA/GAc with long MCsweep • annealing is more effective than small Mcsweep annealing. • PSA/GAc has high searching ability in the prediction of • protein tertiary structure.

  15. Conclusion This study show a new hybrid method, Parallel Simulated Annealing using Genetic Crossover(PSA/GAc). PSA/GAc has follow features • is based on Parallel SA, so calculate time is less than sequential SA. • use Genetic crossover to exchange the information between the individuals • is good at searching not only locally but also globally. We apply PSA/GAc to energy function of protein, this result shows that PSA/GAc has good searching ability for prediction of protein tertiary structure.

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