First French-Japanese Workshop Petascale Applications, Algorithms and Programming(PAAP)

1. First French-Japanese Workshop Petascale Applications, Algorithms and Programming(PAAP) A grand challenge application for the next-generation supercomputer in the soft nano-science Fumio Hirata Institute for Molecular Science

2. Grand challenge applications in nano-science (The next-generation Integrated Nanoscience Simulations) （１）Material science for the information technology 　　　（post-silico electronic devise) molecular switch, nano-wire, etc. （２）Material science for the biotechnology (medicine, pharmaceutical…) virus, cancer drug, drug delivery, etc. （3）Material science related to effective use of the solar energy (environment and energy shortage) solar cells, enzyme (cellulase), super capacitor, etc. These problems are “grand challenges” in dual senses. 1. important for the society (economy, medicine, environment…) 2. unsolved scientific problems

3. What is “nanoscience”? Why makes “nanoscience” so challenging? micro nanomacro (10-11〜10-8 M)(10-9〜10-6 M) (10-6〜 ) visible materials macromolecules molecular assembly electrons, atoms, molecules Statistical Mechanics Thermodynamics Hydrodynamics Electromagnetism Quantum mechanics Mechanics × ??? molecular device anticancer drug Enzymatic reactions etc. micro chip (IC, LSI) car design etc. Multi-scale & multi-physics

4. Molecular (microscopic) theories to be applied to nano-phenomena Hard nano-phenomena: (ex. electron conduction in molecular wire) Band theory, DFT, Hubbard model, ab-initio MD (Car-Parrinello), QED Soft nano-phenomena: (ex. Enzymatic reactions) Molecular simulation (MC, MD), Car-Parrinello method Generalized ensemble method (Replica exchange, etc.) Statistical mechanics of liquids (RISM, ….) Molecular orbital(MO) theory (FMO, DFT, ONIOM) “None of a single theory can explain an entire nano-phenomenon”

5. cellulose→ethanolenzymatic reaction(The most efficeint way of decomposing cellulose) Energy cycle cellulose As food enzyme cellulase Enzyme to decompose cellulose ・human being does not have ・exist in bacteria (yeast) Cellulose as Energy resorce sugar Fermentation with enzyme ethanol + Carbon dioxide Photo synthesis Celulase CELC We use the peta machine to design an enzyme to decompose Cellulose.

6. What is the enzimatic reaction? Why is it difficult to treat by theory? accelerate a reaction without enzyme catalysts：enhances reaction rate dramatically. (1000 to 1 million times） example: binap by Prof. Noyori enzyme（biocatalyst）：catalyses almost all chemical reactions occurring in our body with enzyme or catalyst reactant product recognition feature： 　（１）it works in water（theory of water is essential） 　（２）it should accommodate substrate molecules in the active-site（molecular recognition） reaction releasing The reaction to alcohol from cellulose （２ steps） （１）cellulosesugar (glucose） （２）sugaralcohol Enzymes concern both reactions, but the mechanism of the first step has not been well understood. cellulose enzymatic reaction β-glucose

7. Important factors in enzymatic reactions: • Intake and release of substrate molecules by enzyme (molecular recognition) • affinity (free energy) between protein and substrate • structural fluctuations of protein • methodology: • RISM/3D-RISM(statistical mechanics), • Gneralized Langevin Dynamics (statistical mechanics) • (2)Chemical reactions (hydrolysis, redox, etc.) in Protein • Change in the electronic structure • methodology: • 3D-RISM-FMO In any case, “water (solvent) plays essential role”

8. RISM-SCF theory predicts chemical reactions in solutions Menshutkin reaction H3N + CH3Cl H3N+–CH3 + Cl– Solvent effect

9. 3D-RISM theory 3D-RISM/HNC equations Input: oprotein structureprotein data bank(PDB) o the solute-solvent interactions, uuv(r) o the correlation functions of solvent, wvv(r), hvv(r) o temperature,b= 1/kBT;the density of solvent, r gO(r) > 2 Isosurface representation of the 3D-distribution function of water oxygen Output: The distribution function of solvent atoms normalized by solvent density gg(r) =hg(r) + 1 gg(r) = rg(r) / r

10. Results (1-1) Cavity 1: 3D distribution (Imai, Hiraoka, FH， JACS communcation, 2005) o Hydration structure in Cavity 1 determined by 3D-RISM is in excellent agreement with the X-ray structure gO(r) > 8 gH(r) > 8 = (a) 3D distribution functions of water (b) Hydration model reproduced from (a) (c) X-ray structure

11. Aquaporin (water channel) Works in our body to control water concentration (kidney, eye, etc.) Questions asked for aquaprins. What is the conduction mechanism of aquaporin? What is the gating mechanism of the channels? Why aquaporin does not permeate proton? Does aquaporin permeate Ions? How and what extent? What is the role of c-GMP in aquaporin as an ion Channel?

12. Ion channel ? Extracellular Intracellular Water channel

13. Enzymatic reaction to decompose cellulose into sugar “hydrolysis” reaction “Water is one of reacting species (substrate)” “The position of water molecule in the reaction Pocket is essential.”

14. The finding so far is a big step toward final solution, but not quite enough to predict entire enzymatic reaction. • Following problems have not been done yet. • To realize the free energy profile, the electronic structure • should be calculated along the reaction coordinate. • 3D-RISM/FMO • Dynamics of protein should be done in order to take into • account the protein fluctuation. • 3D-RISM/MD Huge amount of calculation should be made. Key words,“3D-FFT” and “Eigen-value-problem”

15. 3D-RISM Theory 3D-RISM equation HNC Closure Convolution integral Just a multiplication in the Fourier space 3D-DF Solute-solvent interaction potential

16. Flow chart 1.Potential parameter for solute and solvent molecules 2. Calculate the interaction potential energy 3. Initial value of  4. Convert  by 3D-FFT 5. Solve 3D-RISM in k-space 6. Inverse transform of c by 3D-FFT 7. Solve HNC eq. to get  8. Go back to 4 if  is not converged 9. Calculate 3D-distribution function from  and c • INPUT: • Potential Parameters of solute and solvent molecule • Structure of solute and solvent molecule Interaction Potential 3D-RISM equation inverse 3D-FFT 3D-FFT Closure equation • OUTPUT: • Distribution functions of solvent molecule • Solvation free energy

17. Electronic structure in solution3D-RISM-FMO • Combined 3D-RISM/FMO calculation • Solve solvent distribution and electronic structure self-consistently • Bottle neck • Solvated Fock and electro-static potential→ easy to parallelize • FMO • 3D-RISM → 3D-FFT • FMO and Solvated Fock（and potential) is most expensive, but those can be readily parallelized. fragment SCF UV potential 3D-RISM Solvated Fock Converge? Solvated Fock for fragment pair Fragment pair SCF “Fast eigen-value-problem solver Is essential!”

18. Fluctuation of protein in soultion3D-RISM/MD • Describe sovent with 3D-RISM, while move solute with MD. • Solvent is always equilibrium to the solute structure. • Bottle neck • ３Ｄ−ＲＩＳＭ → necessary to accelerate 3D-FFT • Gradient　→ redily parallelized MD(溶質) potential gradient 3D-RISM

19. 3D-RISM/MD • Simulation of protein in solvent • １０００ atoms (protein) • Solvent (water＋electrolytes, etc.) • グリッド：２５６３、0.5Å • If one use SR11000・・・ • 4node/64core(2Tflops) • 320sec/iteration(3D-RISM,62%: gradient,38%: others, 0%) • 1ns with time step 1fs, multi time step：3 years • If one use１０ＰＥＴＡ (２００００ times faster than SR11000), 1.5 hours If this became reality, the protein folding can be done.

20. We do not “simulate” the earth, but try to “save” it from the energy and environmental crisis. But, in order make it reality, we need 3D-FFT and eigen-value-problem solver well tuned for the next generation super-machine. Thank you for your attention.