Höfinger, S.

Kranzlmüller, D.

Mahajan, R.

Volkert, J.

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John von Neumann Institute for ComputingLarge Scale Molecular Dynamics Simulationsfor the Derivation of Solvation Free Energies ofStrongly Hydrophobic MoleculesReema Mahajan, Dieter Kranzlmu¨ller, Jens Volkert,Siegfried Ho¨fingerpublished inNIC Workshop 2006,From Computational Biophysics to Systems Biology,Jan Meinke, Olav Zimmermann,Sandipan Mohanty, Ulrich H.E. Hansmann (Editors)John von Neumann Institute for Computing, Ju¨lich,NIC Series, Vol. 34, ISBN-10: 3-9810843-0-6,ISBN-13: 978-3-9810843-0-6, pp. 173-176 , 2006.c© 2006 by John von Neumann Institute for ComputingPermission to make digital or hard copies of portions of this work forpersonal or classroom use is granted provided that the copies are notmade or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwiserequires prior specific permission by the publisher mentioned above.http://www.fz-juelich.de/nic-series/volume34Large Scale Molecular Dynamics Simulations for theDerivation of Solvation Free Energies of StronglyHydrophobic MoleculesReema Mahajan1, Dieter Kranzlmu¨ller2, Jens Volkert2, and Siegfried Ho¨finger31 Indian Institute of Technology,Department of Chemical Engineering,Hauz Khas, New Delhi-16, IndiaE-mail: reema.mahajan@gmail.com2 Johannes Kepler University of Linz,Institute of Graphics and Parallel ProcessingAltenberger Straße 69, A-4040, Linz, AustriaE-mail: {kranzlmueller,volkert}@gup.uni-linz.ac.at3 Michigan Technological University,Department of Physics,1400 Townsend Drive, Houghton, MI 49931, USAE-mail: shoefing@mtu.eduLiquid water is believed to be of crucial biological importance when it comes to solvating hy-drophobic molecules. The so-called hydrophobic effect is a key-determinant in the proteinfolding problem and a deeper understanding of it would certainly be of great value to the bio-physics community. The process of solvating hydrophobic molecules in water may be studiedwith the help of computer simulations that establish an atomistic picture of the liquid state ofwater. A study has already been carried out in the past using Molecular Dynamics simulationsand a polarizable force field description for the water molecules. The focus of that study wason the temperature dependence of the free energy change observed for the onset and growthof a repulsive sphere that represented the hydrophobic species. The obtained data was in goodagreement to predictions from the Lum Chandler Weeks theory on the unit volume entropy.However, only small-sized hydrophobic solutes could be studied and the critical domain whereLCW theory claims a change in underlying physics could not be examined. Therefore an ex-tension of this previous study is currently underway using again a high level polarizable forcefield and a largely extended water box of dimension 60x60x60 A˚. The technical complexity ofsuch an approach is discussed and an outlook is given on the various implications of such aninvestigation.1 IntroductionAbout 50 years have passed by since Walter Kauzmann has published his extensive re-view on thermodynamic principles of protein unfolding1. One of his conclusions has beenthat the so-called “Hydrophobic Bonds” would constitute the major stabilizing factor forprotein assembly and protein stability. It is however till today that the actual kernel ofhydrophobicity must still be considered an unsolved problem. Among other theoreticalattempts Lum Chandler Weeks (LCW) theory of hydrophobicity has become fashionable.LCW theory divides small length scale hydrophobicity from large length scale hydropho-bicity formally (volume dependence versus surface area dependence) as well as in termsof underlying physics (entropy drop versus entropy gain). The switch between these two173domains is said to occur at dimensions of r=10 A˚ of spherical model solutes. Since an un-biased experimental verification of such a picture of hydrophobicity is extremely difficultit appears to be only natural to address the underlying physics behind LCW theory withcomputational approaches.2 MethodsSuitable computational techniques for this kind of problem are free energy calculations,which have been introduced and methodically refined to directly study ∆G trends for var-ious physico-chemical processes2. The obvious physical process to study here was the∆G corresponding to the introduction, onset and growth of an artificial repulsive spherelocated in the center of a simulation cell otherwise filled with water molecules. The spher-ical repulsive cavity would then represent a model hydrophobic solute and the associatedfree energy change was the energy necessary to embed this hydrophobic solute in water.Exactly the same type of ∆G has also become known as the cavitation free energy3.A previous study has already been carried out employing the high level polarizableAMOEBA force field4 for computer simulation of liquid water at seven individual tem-peratures in the range of 277K to 370K for calculating the free energy cost of creation ofsmall-sized cavities (work currently under review). Ewald summation had been appliedwithin the Molecular Dynamics simulations (MD) that form the basis of the Free EnergyPerturbation (FEP) calculations in the framework of the Overlapping Spheres Technique(OST)5. Our previous study could reconfirm the Chandler picture of the unit volume en-tropy ∆S for small-sized hydrophobic solutes (from the temperature profiles of ∆G). Thecomputational demand of this study was on the order of three CPU years (Itanium 1.4GHz). Volumes of up to r≈3 A˚ could be introduced, hence the small cavity regime couldbe examined.In extension to this previous study our present efforts focus on largely increased vol-umes of up to r=10 A˚ to probe the critical domain where the switch in physical exem-plification is thought to occur. We therefore need to increase our water box substantiallyand start out with a trial system of dimension 60A˚ x60A˚ x60A˚. The CPU requirementsof such an approach must be tremendous. In this current work we estimate the requiredcomputational resource allocation of such a large scale attempt and try to find a suitablecompromise in case the resource allocation turns out to be simply un-feasible.3 Results and ConclusionsThe estimated computational resource allocation for the case of a MD/FEP study basedon AMOEBA water boxes of dimension 60A˚ x60A˚ x60A˚ is summarized in Table 1 (mid-dle column). Compared to the previously required computing resources (see Table 1, leftcolumn) this is however far beyond any acceptable limit. We therefore shrinked the sizeof the water boxes layer by layer and estimated resulting overall resource allocations forvarious constellations. A cubic arrangement of about 1331 water molecules (see Table1,right column) was finally chosen for production runs because it represents a good compro-mise between intended problem size and acceptable resource allocation. Such large scalecomputations can be conveniently carried out on large GRID systems in reasonable timelines.174Previously Estimate Estimate(B <= 3 A˚) (B ≈ 10 A˚) (B ≈ 8 A˚)# WaterMolecules 216 8000 1331Box Size (18.6A˚)3 (60A˚)3 (34.2A˚)3Ewald, Cut-Off Radius 14 A˚ 14 A˚ 14 A˚Time Step 1 fs 1 fs 1 fs∆B in ± 25 x ± 25 x ± 25 xOST 0.0032 A˚ 0.0032 A˚ 0.0032 A˚# Intervals inOST per A˚ 12.5 12.5 12.5MaximumAllowedPerturbation 2 RT 2 RT 2 RTAnnealingPeriod 2 ps 2 ps 2 ps# TemperaturesConsidered 7 3 3IntendedMD/FEP Period 100 ps 100 ps 100 ps# Trajectoriesper Temperature 29 120 90Estimated CPUTime per Trajectory(Itanium 2, 1.4 Ghz) 5 days 5 years 2 months# Trajectories Total 203 360 270Estimated TotalCPU Time 2.78 years 1800 years 45 yearsTable 1. Experienced and estimated resource allocation for large scale MD/FEP simulations on cavitation freeenergy calculations in AMOEBA water. Previously consumed resources are shown in the column to the left, themiddle column gives an estimate for a huge water box aimed at studies of cavities of radii up to B≈ 10 A˚, and theright column shows estimates for a largely increased water box for cavitation studies of radii up to B ≈ 8 A˚. Thisfinal column to the right represents a good compromise between intended study size and feasible computationalthroughput.AcknowledgmentsThis work was supported in part by the National Institutes of Health Grant GM62838.References1. W. Kauzmann, Some factors in the interpretation of protein denaturation, Adv. Pro-tein Chem. 14, 1–63 (1959).1752. T. Simonson, G. Archontis, M. Karplus, Protein-Ligand Recognition: Free EnergySimulations Come of Age, Acc. Chem. Res. 35, 430–437 (2002).3. J. Tomasi, B. Mennucci, R. Cammi, Quantum Mechanical Continuum Solvation Mod-els, Chem. Rev. 105, 2999–3094 (2005).4. P. Ren, J. W. Ponder, Polarizable Atomic Multipole Water Model for Molecular Me-chanics Simulation, J. Phys. Chem. B 107, 5933–5947 (2003).5. P. M. Postma, H. J. C. Berendsen, J. R. Haak, Thermodynamics of cavity formation inwater, Farad. Symp. Chem. Soc. 17, 55–67 (1982).176

Large Scale Molecular Dynamics Simulations for the Derivation of Solvation Free Energies of Strongly Hydrophobic Molecules

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Large Scale Molecular Dynamics Simulations for the Derivation of Solvation Free Energies of Strongly Hydrophobic Molecules

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