1. Doshisha Univ. JapanGECCO2002 Energy Minimization of Protein Tertiary Structure by Parallel Simulated Annealing using Genetic Crossover Takeshi YoshidaTomoyuki Hiroyasu Mitsunori MikiMaki Ogura Doshisha University, Kyoto, Japan Yuko Okamoto Institute for Molecular Science, Aichi, Japan Doshisha Univ. Japan GECCO2002

2. Doshisha Univ. Japan GECCO2002 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 Molecular simulation high searching ability need huge calculate time Apply Heuristic method to this problem.

3. Doshisha Univ. Japan GECCO2002 Protein Tertiary Structure Energy function of protein Folding protein to stable state Tertiary StructureAmino acid array Analyzing structure as Optimization problem Protein structure naturally exist with lowest energy Protein is composed of an array with 20 amino acids. Amino acid array is folding to the lowest energy

4. Doshisha Univ. Japan GECCO2002 Simulated Annealing High temperature Local minimum Global minimum Low temperature By the parameters, SA’s searching point moves to worse a state in a certain probability. T : Temperature of current step Probability; P = － (E next － E current ) T exp SA is often applied to prediction of Protein tertiary structure. SA has parameters, those are a temperature and a step.

5. Doshisha Univ. Japan GECCO2002 Energy function of Protein Minimum in local area Energy function of Protein has many minima in local area And a few minima in global area. Minimum in global area No success result has ever prediction of protein using SA

6. Doshisha Univ. Japan GECCO2002 Purpose of this study Parallel SA using Genetic Crossover(PSA/GAc) Genetic Algorithm(GA) is good at searching a solution in a wider area.(global search) Parallel SA GA operation + PSA/GAc is a hybrid method of SA with GA operation 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. Doshisha Univ. Japan GECCO2002 Modeling of Protein tertiary structure Design variable : dihedral angle between main chain and side chain. Minimize energy function of protein Protein is composed of an array with 20 amino acids. Changing dihedral angle dihedral angle

8. Doshisha Univ. Japan GECCO2002 PSA/GAc PSA/GAc is based on Parallel SA. SA crossover 123 123 123 123 123 123 123 123 SA crossover end temperaturehighlow nnn n : crossover interval Searching points : individualsTotal number of SA : Population size Genetic Crossover is used to exchange the information of individuals. n

9. Doshisha Univ. Japan GECCO2002 PSA/GAc Genetic Crossover is performed as follows. e.q continuous optimization problem(3 dimensions) 123 parent1 123 parent2 crossover 123 123 child1 child2 cross point -1.3 -1.8 -1.1 -2.0 energy 123123 Next searching points

10. Doshisha Univ. Japan GECCO2002 PSA/GAc PSA/GAc is based on Parallel SA. SA crossover 123 123 123 123 123 123 123 123 SA crossover end temperaturehighlow nnn n : crossover interval Searching points : individualsTotal number of SA : Population size Each process reduce temperature from high to low as parameter of SA. n

11. Doshisha Univ. Japan GECCO2002 Target Protein Structures C-peptide ; 13 amino acids In case of using ECEPP/2 program, Protein for numerical example Lowest-energy conformation E < - 42 kcal/mol [okamoto,1991] 64 dihedral angles Design variables There are 64 times annealing per 1MCsweep C-peptide structure

12. Doshisha Univ. Japan GECCO2002 Num of Processors Parameters Parameter Population size Initial temperature Crossover interval Range size Value 2.0(100k) 24 0.1(50K) 32 6 Last temperature 180(180 0.3) We tried two types of simulations. Simulation1 : 4164 MCsweeps and 10 trials. (100,000 MCsweeps totally) Simulation2 : 41646 MCsweeps and 7 trials.

13. Doshisha Univ. Japan GECCO2002 Optimum [Okamoto, 1991] Result : Energy PSA/GAc Simulation1 Energy (kcal/mol) - 46.7 To derive a good solution, PSA/GAc with long MCsweep annealing is more effective than small Mcsweep annealing. PSA/GAc Simulation2 - 57.8 - 42 Simulation Type PSA/GAc has high searching ability in predicting protein tertiary structure problem

14. Doshisha Univ. Japan GECCO2002 Result : Protein structure Simulation1: -46.7 kcal/mol To derive a good solution, PSA/GAc with long MCsweep annealing is more effective than small Mcsweep annealing. Simulation2: -57.8 kcal/mol PSA/GAc has high searching ability in the prediction of protein tertiary structure.

15. Doshisha Univ. Japan GECCO2002 Conclusion This study show a new hybrid method, Parallel Simulated Annealing using Genetic Crossover(PSA/GAc). 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. PSA/GAc has follow features use Genetic crossover to exchange the information between the individuals is good at searching not only locally but also globally. is based on Parallel SA, so calculate time is less than sequential SA.