2D-PME method and REX-MS method - Application of computational chemistry -

1. 2D-PME method and REX-MS method- Application of computational chemistry - Masaaki Kawata Grid Technology Research Center, AIST, JAPAN m.kawata@aist.go.jp

2. Outline • Introduction • What is 2D-PME method ? - how fast 2D-PME method is ! - • What is REX-MS method ? - how efficient REX-MS method is ! - • Perspective - combination of two methods -

3. Introduction • Task parallel calculation ex. Parallel molecular dynamics or Monte Carlo simulations. • Data parallel calculation ex. optimum-pairing-search of drug compounds (parameter survey)

4. Introduction(2) • Task parallel calculation Given a conformation of target compound, accurate estimation of physical quantities, whose accuracy are comparable to experiment, requires large amount of computational resources. ⇒parallel algorithm of molecular simulation → Parallel calculation of Coulomb interaction 　＝2D-PME method

5. Introduction(3) • Data parallel calculation Statistical interpretation should be included in molecular simulation. But now we can’t do statistical operation due to limited computational resources. Statistical operation requires extensive survey of parameters space. ⇒New strategy dealing with statistical ensemble 　　　 → REX-MS method

6. z y x What is 2D-PME method ? • 2D-PME method stands for Two-Dimensional Particle Mesh Ewald method. • Fast and accurate method to calculate Coulomb interaction in three-dimensional systems with two-dimensional periodicity (quasi-2D systems).

7. Why quasi-2D systems ? • Nano application ⇒surface of nano-structures • Bio application ⇒ membrane proteinfor drug design should be treated as Quasi-2D system

8. What is quasi-2D system H2O H2O Au CH3(CH2)nS (Left) Quasi two-dimensional simulation box, i.e., three-dimensional box with two-dimensional periodicity in the (x, y) directions and with non-periodicity in the z direction. Original particles are contained in the central box with lengths of the sides, Lx, Ly, and Lz in the x, y, and z directions, respectively. (Right) Self-assembled monlayer membrane system. Images of the simulation box are repeated in the (x,y) directions.

9. 7 6 5 kcal/mol 4 3 2 1 0 100 200 300 400 500 Angstrom Coulomb interaction Coulomb interaction has longer tail more than size of simulation box →Ewald method More than 90 % of CPU time is consumed for calculation of Coulombinteractions →fast Ewald method Acceleration of molecular simulations 　　⇒　Acceleration of Ewald method

10. 2D Ewald method

11. 2D-PME method Acceleration Charge q Contribution from each grid point: Ｑ(k1,k2,k3) FFT

12. Results(1) System 1 System 2 System 3

13. Results(2) CPU timea for a single-step MD calculation for a given accuracy, by using the original method and the 2D-PME method. CPU time on Compaq Alpha Station XP1000 (Alpha21264 667MHz).

14. Flow chart of parallel MD calculations with the 2D-PME method. Update and redistribute and Calculate bonded interactions Calculate and together with van der Waals interactions Calculate and Construct from Construct and their derivatives Set backward forward Data transform as illustrated (forward) 2D FFT and 1D Fourier integral Calculate Calculate 2D FFT and 1D Fourier integral Data transform as illustrated (backward) Calculate Sum of all interactions

15. Results (3) Speedup factor of the parallel MD calculations for the quasi-2D systems by using the 2D-PME method. The solid line is for calculations with an SP switch (300MB/sec BI-Direction) with user space protocol, and the dashed line is for calculations with internet protocol. The dotted line is the ideal speedup factor, assuming an infinitely fast network connecting the nodes.

16. What is REX-MS method? • REX-MS stands for Replica Exchange Molecular Simulation method. • Computationally efficient sampling method in the phase space. 　⇒ global optimization problem suitable for grid environment

17. In REX-MS method Replica１ • Run N independent simulation (N replicas) with N different parameters, respectively. • Exchange information among replicas during the simulation. • Search optimum solution among N simulations. Replica２ ReplicaN Extended statistical ensemble Sampling by using REX strategy is more efficient than that by the sum of N independent simulations (not REX).

18. Two type of REX-MS methods • REX-MC method (by t.ikegami & h.takemiya) Replica exchange Monte Carlo calculation • REX-MD method (by m.ito) Replica exchange Molecular Dynamics toolkit

19. REX-MC (by t.ikegami) • Potential energy survey of molecules using direct method (Combination of REX-MC with ab-initio MO calculation） ⇒Superior to random walk survey of complicated potential surface

20. Gridifying the program • Two levels of parallelization • Coarse grained: parallel monte-carlo sampling • Fine grained: parallel ab-initio energy calculation • Dynamic task scheduling, machine reconfiguration • Task scheduling for balancing load on a heterogeneous computing resources • Machine scheduling for reconfiguring machine sets on the fly Bookkeeper Reconfiguration request Dynamic scheduling REXMC client Task allocation Monitoring Reconfiguration Servers meta-computing test bed 10 institutes/20 Supercomputers ab initio calculation

21. AIST REXMC Client For C20 triplet REXMC Client For C20 singlet Bookkeeper HPC Challenge in SC2002 Metacomputing Test-bed • 10 institutions (3 continentals) / 20 parallel computer (7 types) • High Performance Computing Center Stuttgart (HLRS), • Sandia National Laboratories (SNL), • Pittsburgh Supercomputing Center (PSC), • Grid Technology Research Center (AIST), • Manchester Computing Centre (MCC), • National Center for High Performance Computing (NCHC), • Japan Atomic Energy Research Institute (JAERI), • Korea Institute of Science and Technology Information (KISTI), • European Center of Parallelism in Barcelona (CEPBA/CIRI), • Finnish IT center for Science (CSC).

22. Potential Survey on the Metacomputingtestbed • Parallel execution of 1６（３２） MC samples • Running over 150 hours with changing machine configurations • Calculating 145 MC samples/hour using 860 CPU’s (at maximum) • Potential survey for C20 might be completed in a month • (cf. > ~30 years on a single CPU) • Negligible Communication cost • < 1% of total time • Dynamic scheduling/configuration mechanism is useful for • long time simulation • Simulation on the unstable environment

23. REMD toolkit (by m.ito) • A toolkit was developed to build a replica-exchange method program suitable for solving the multiple-minima problem. • It is designed as an object-oriented framework to generate variants of simulation programs by assembling the toolkit components and force field programs. • The toolkit components provides the parallelization mechanisms for various computational environments and the sampling methods. • An arbitrary force field implementation can be plugged into the toolkit to generate an executable program. REMD toolkit Serial MPI Grid ＭＤ ＭＣ Ｎｅｗ　Ｍｏｄｅｌ Mindy(NAMD)

24. Why do we need a software framework for REM/REMD simulations? • Estimation of thermal distributions for molecular structures is essential for elucidating biological functionalities, e.g. a ligand-receptor binding. • Such estimation, however, is notoriously difficult at low temperature because of a multiple-minima problem. • Replica exchange method (REM) and replica-exchange molecular dynamics method (REMD) can overcome the difficulty. • Each component of an REM/REMD algorithm, a statistical ensemble, conformational sampling method, and potential energy function has to be customized to suit a particular biomolecular system. • Simulation programs are likely to adjust to various parallelization environments. • An object-oriented framework can facilitate to generate a variants of REM/REMD programs suitable for various molecular systems and different computational environments such as PC clusters and Grid. • Component-based software development PotentialEnergy 構造座標

25. Efficiency of the REMD toolkit • The efficiency of the generated program (toolkit + Mindy(NAMD)) was examined by estimzating the heat capacity. • The error was found to decay naturally according to the central limit theorem.

26. Perspective • Combination of 2D-PME method and REX-MS method leads to fast, accurate and extensive survey of the screening. ⇒higherthroughput in drug design and in material design of nano-structure. • Implementation of those methods on grid environment brings new stage of the design processes. ⇒a promisingapplication of grid technology.

27. Reference Formore details about: 2D-PME, ask me or m.kawata@aist.go.jp REX-MC, ask h.takemiya (here) or mail to t-ikegami@aist.go.jp REMD toolkit, mail to masakatsu-ito@aist.go.jp