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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. Grand challenge applications in nano-science

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First french japanese workshop petascale applications algorithms and programming paap

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


First french japanese workshop petascale applications algorithms and programming paap

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


First french japanese workshop petascale applications algorithms and programming paap

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


First french japanese workshop petascale applications algorithms and programming paap

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”


Cellulose ethanol enzymatic reaction the most efficeint way of decomposing cellulose

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.


First french japanese workshop petascale applications algorithms and programming paap

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


First french japanese workshop petascale applications algorithms and programming paap

  • 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”


First french japanese workshop petascale applications algorithms and programming paap

RISM-SCF theory predicts chemical reactions in solutions

Menshutkin reaction

H3N + CH3Cl H3N+–CH3 + Cl–

Solvent effect


First french japanese workshop petascale applications algorithms and programming paap

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


First french japanese workshop petascale applications algorithms and programming paap

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


First french japanese workshop petascale applications algorithms and programming paap

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?


First french japanese workshop petascale applications algorithms and programming paap

Ion channel ?

Extracellular

Intracellular

Water channel


First french japanese workshop petascale applications algorithms and programming paap

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.”


First french japanese workshop petascale applications algorithms and programming paap

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”


3d rism theory

3D-RISM Theory

3D-RISM equation

HNC Closure

Convolution integral

Just a multiplication

in the Fourier space

3D-DF

Solute-solvent interaction potential


Flow chart

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


Electronic structure in solution 3d rism fmo

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!”


Fluctuation of protein in soultion 3d rism md

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


3d rism md

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.


First french japanese workshop petascale applications algorithms and programming paap

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.


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