238 Oliver S. Smartmov<strong>in</strong>g conformations and <strong>in</strong>termediates to represent a conformational change, <strong>in</strong>comparison to the Cartesian application where small atomic deviations producelarge <strong>in</strong>creases <strong>in</strong> bond energy. Secondly, the use of dihedral angle space allows thedescription of the conformation of a molecule with approximately one-eighth thenumber of <strong>in</strong>dependent variables. F<strong>in</strong>ally, the use of dihedral space would enablemore reasonable start<strong>in</strong>g conformations to be generated. Different start<strong>in</strong>g conformationscould be modelled by try<strong>in</strong>g alternative possibilities for dihedral angleswhich change markedly between the fixed end po<strong>in</strong>ts. Such a method has been usedby Ech-Cherif El-Kettani and Durup [42] to generate <strong>in</strong>itial routes, before apply<strong>in</strong>ga variant of the SPW procedure <strong>in</strong> Cartesian space. For the reasons set out, an applicationof the PEM method <strong>in</strong> dihedral angle space can be expected to be verymuch more efficient than the present application and should allow simulation of <strong>in</strong>terest<strong>in</strong>gconformational transitions of macromolecules.8.6 SummaryA new method for the generation of reaction coord<strong>in</strong>ates for conformational transitions<strong>in</strong> large <strong>molecular</strong> systems is presented. The path energy mimimization (PEM)technique optimizes the peak energy of a quasi-cont<strong>in</strong>uous route through conformationalspace between two given m<strong>in</strong>ima: locat<strong>in</strong>g the transition state and the optimalvector through this conformation. The method produces a series of conformationswhich effectively def<strong>in</strong>e a reaction coord<strong>in</strong>ate for the change. A transition <strong>in</strong>volv<strong>in</strong>ga pucker angle change for the sugar a-D-xylulofuranose is used to test the procedure.The results are compared with those obta<strong>in</strong>ed by both adiabatic mapp<strong>in</strong>g and theSelf Penalty Walk procedure developed by Elber and co-workers. The method is appliedto recalculate the energy barrier for a conformational rearrangement of thesubstrate <strong>in</strong> the active site of D-xylose isomerase, where it is shown to outperforman earlier adiabatic mapp<strong>in</strong>g study. Potential improvements to the method werediscussed.AcknowledgementsThis work was supported by the UK Science and Eng<strong>in</strong>eer<strong>in</strong>g Research Councilunder project grant GR/G49494 and the Molecular Recognition and ComputationalScience Initiatives. I thank Julia Goodfellow, Bonnie Wallace and David Blow forencouragement and many discussions. The ~-xylose isomerase coord<strong>in</strong>ates and reactionmechanism are the result of years of hard work by Charles Collyer, Kim Henrickand Jonathon Goldberg.
8 Path Energy M<strong>in</strong>imization 239ReferencesMonod, J., Wyman, J., Changeux, J. P., J. Mol. Biol. 1965, 12, 88-118.Perutz, M., Q. Rev. Biophys. 1989, 22, 138-236.Baldw<strong>in</strong>, J., Chothia, C., J. Mol. Biol. 1979, 129, 175-220.Stevens, R. C., Lipscomp, W. N., <strong>in</strong>: Molecular Structures <strong>in</strong> Biology, Diamond, R.,Toetzle, T. F., Prout, K., Richardson, J. A. (eds.), Oxford University Press, Oxford, 1993,pp. 223-259.Harvey, S. C., Nucl. Acids Res. 1983, 11, 4867-4878.Leroy, J. L., Kochoyan, M., Huynh-D<strong>in</strong>h, T., GuCron, M., J. Mol. Biol. 1988, 200,223 -238.Moe, J. G., Russu, I. M., Biochemistry 1992, 31, 8421-8428.Urry, D. W., Long, M. M., Jacobs, M., Harris, R. D., Ann. N. I: Acad. Sci. 1975, 264,203-220.Wallace, B. A., Biophys. .l 1984, 45, 114-116.Killian, J. A., de Kruijff, B., Biophys. .l 1988, 53, 111-117.Karplus, M., Evanseck, J. D., Joseph, D., Bash, P. A., Field, M. J., Faraday Discuss. R.SOC. Chem. 1992, 93, 239-248.Brooks, C. L. 111, Curr. Op<strong>in</strong>. Struct. Biol. 1993, 3, 92-98.Wade, R. C., Davis, M. E., Luty, B. A., Madura, J. D., McCammon, J. A., Biophys. J.1993, 64, 9-15.Eyr<strong>in</strong>g, H., J. Chem. Phys. 1935, 3, 107-115.Evans, M. G., Polanyi, M., Duns. Faraday SOC. 1935, 31, 875-894.Laidler, K. J., Chemical K<strong>in</strong>etics, Third edition, Harper & Row, New York, 1987.Northrup, S. H., Pear, M. R., Lee, C.-Y., McCammon, J. A., Karplus, M., Proc. Natl.Acad. Sci. USA 1982, 79, 4035-4039.McCammon, J. A., Harvey, S. C., Dynamics of Prote<strong>in</strong>s and Nucleic Acids, CambridgeUniversity Press, Cambridge, 1987.Elber, R., J. Chem. Phys. 1990, 93, 4312-4321.Verkhivker, G., Elber, R., Nowak, W., J. Chem. Phys. 1992, 97, 7838-7841.Elber, R., Karplus, M., Science 1987, 235, 318-321.McIver, J. W. Jr., Komornicki, A., J. Am. Chem. SOC. 1972, 94, 2625-2633.Popp<strong>in</strong>ger, D., Chem. Phys. Lett. 1975, 35, 550-554.Muller, K., Brown, L. D., Theor. Chim. Acta 1979, 53, 75-93.Cerjan, C. J., Miller, W. H., J. Chem. Phys. 1981, 75, 2800-2806.Simons, J., Jorgensen, P., Taylor, H., Ozment, J., J. Phys. Chem. 1983, 87, 2745-2753.Nguyen, D. T., Case, D. A., J. Phys. Chem. 1985, 89, 4020-4026.Bell, S., Crighton, J. S., J. Chem. Phys. 1984, 80, 2464-2475.[29] Gel<strong>in</strong>, B. R., Karplus, M., Proc. Natl. Acad. Sci. USA 1975, 72, 2002-2006.[30] Ha, S. N., Madsen, L. J., Brady, J. W., Biopolymers 1988, 27, 1927-1952.[31] French, A. D., Tran, V., Biopolymers 1990, 29, 1599-1611.[32] Smart, 0. S., Ak<strong>in</strong>s, J., Blow, D. M., Prote<strong>in</strong>s 1992, 13, 100-111.[33] Gabb, H. A., Harvey, S. C., J. Am. Chem. SOC. 1993, 115, 4218-4227.[34] Harvey, S. C., Gabb, H. A., Biopolymers 1993, 33, 1167-1172.[35] Miiller, K., Angew. Chem. Znt. Ed. Engl. 1980, 19, 1-78.[36] Smart, 0. S., Goodfellow, J. M., Mol. Simul. 1995, <strong>in</strong> press.[37] S<strong>in</strong>clair, J. E., Fletcher, R., J. Phys. C 1974, 7, 864-870.[38] Smart, 0. S., Ph. D. Thesis, University of London, 1991.
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Computer Modellingin Molecular Biol
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Professor Julia M. GoodfellowDepart
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ContentsColour Illustrations ......
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XContributorsBenoit RouxGroupe de R
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