Doshisha Univ. JapanGECCO2002 Energy Minimization of Protein Tertiary Structure by Parallel Simulated Annealing using Genetic Crossover Takeshi YoshidaTomoyuki

Doshisha Univ. JapanGECCO2002

Energy Minimization of Protein Tertiary Structureby Parallel Simulated Annealing

using Genetic Crossover

Takeshi Yoshida Tomoyuki HiroyasuMitsunori Miki Maki Ogura

Doshisha University, Kyoto, Japan

Yuko OkamotoInstitute for Molecular Science, Aichi, Japan

Doshisha Univ. JapanDoshisha Univ. JapanGECCO2002GECCO2002


BackgroundProtein 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.


Protein Tertiary Structure

Energy function of protein

Folding protein to stable state

Tertiary StructureAmino acid array

Analyzing structureas 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


Simulated Annealing

High temperature

Local minimum

Global minimum

Low temperatureBy the parameters, SA’s searching point moves to worse a state in a certain probability.

T : Temperature of current step

Probability; P = － (Enext－ Ecurrent)

Texp

SA is often applied to prediction of Protein tertiary structure.

SA has parameters, those are a temperature and a step.


Energy function of Protein

Minimum in local areaMinimum in local area

Energy function of Protein has many minima in local areaAnd a few minima in global area.

Minimum in global areaMinimum in global area

No success result has ever prediction of protein using SA


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.


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


PSA/GAcPSA/GAc is based on Parallel SA.

SA

SA

SA

crossover

1 2 3

1 2 3

1 2 3

1 2 3

1 2 3

1 2 3

1 2 3

1 2 3

SA

cross

over

cross

over

en

d

temperaturetemperaturehighhigh lowlow

n n nn : crossover interval

Searching points : individuals Total number of SA : Population size

Genetic Crossover is used to exchange the information of individuals.

n


PSA/GAc

Genetic Crossover is performed as follows. e.q continuous optimization problem(3 dimensions)

1 2 3parent1

1 2 3parent2

crossover

1 2 3

1 2 3

child1

child2

cross point

-1.3

-1.8

-1.1

-2.0

energy

1 2 3

1 2 3

Nextsearching points


PSA/GAcPSA/GAc is based on Parallel SA.

SA

SA

SA

crossover

1 2 3

1 2 3

1 2 3

1 2 3

1 2 3

1 2 3

1 2 3

1 2 3

SA

cross

over

cross

over

en

d

temperaturetemperaturehighhigh lowlow

n n nn : crossover interval

Searching points : individuals Total number of SA : Population size

Each process reduce temperature from high to low as parameter of SA.

n


Target Protein Structures

C-peptide ; 13 amino acidsIn 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


Num of Processors

Parameters

Parameter

Population sizeInitial temperature

Crossover intervalRange 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.


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


Result : Protein structure

Simulation1: -46.7kcal/mol

• To derive a good solution , PSA/GAc with long MCsweep annealing is more effective than small Mcsweep annealing.

Simulation2: -57.8kcal/mol

• PSA/GAc has high searching ability in the prediction of protein tertiary structure.


Conclusion

This study show a new hybrid method, Parallel SimulatedAnnealing using Genetic Crossover(PSA/GAc).

We apply PSA/GAc to energy function of protein, this result shows that PSA/GAc has good searching abilityfor 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.

Documents

Doshisha Univ. JapanGECCO2002 Energy Minimization of Protein Tertiary Structure by Parallel Simulated Annealing using Genetic Crossover Takeshi YoshidaTomoyuki