Artificial reaction coordinate “tunneling” in free-energy calculations: The catalytic reaction of RNase H

Authors

  • Edina Rosta,

    1. Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892-0520
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  • H. Lee Woodcock,

    1. Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Rockville, Maryland 20892-9314
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  • Bernard R. Brooks,

    1. Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Rockville, Maryland 20892-9314
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  • Gerhard Hummer

    Corresponding author
    1. Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892-0520
    • Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892-0520
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  • This article is a U.S. Government work, and as such, is in the public domain in the United States of America.

Abstract

We describe a method for the systematic improvement of reaction coordinates in quantum mechanical/molecular mechanical (QM/MM) calculations of reaction free-energy profiles. In umbrella-sampling free-energy calculations, a biasing potential acting on a chosen reaction coordinate is used to sample the system in reactant, product, and transition states. Sharp, nearly discontinuous changes along the resulting reaction path are used to identify coordinates that are relevant for the reaction but not properly sampled. These degrees of freedom are then included in an extended reaction coordinate. The general formalism is illustrated for the catalytic cleavage of the RNA backbone of an RNA/DNA hybrid duplex by the RNase H enzyme of Bacillus halodurans. We find that in the initial attack of the phosphate diester by water, the oxygen-phosphorus distances alone are not sufficient as reaction coordinates, resulting in substantial hysteresis in the proton degrees of freedom and a barrier that is too low (∼10 kcal/mol). If the proton degrees of freedom are included in an extended reaction coordinate, we obtain a barrier of 21.6 kcal/mol consistent with the experimental rates. As the barrier is approached, the attacking water molecule transfers one of its protons to the O1P oxygen of the phosphate group. At the barrier top, the resulting hydroxide ion forms a penta-coordinated phosphate intermediate. The method used to identify important degrees of freedom, and the procedure to optimize the reaction coordinate are general and should be useful both in classical and in QM/MM free-energy calculations. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009

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