Chem. Rev. 1993, 93, 2395-2417
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Free Energy Calculations: Applications to Chemical and Biochemical Phenomena Peter Kollman Depattment of pharmaceutical Chemlstty, University of California, San Francisco, California 94 143 Received May 5, 1993 (Revlsed Manuscript Received August 24, 1993)
Contents I. Abstract 11. Introduction I I I. Methodological Issues
A. Basic Formulation of Free Energy Calculations B. A Sample Application: The Relative Solvation Free Energy of Methanol and Ethane C. Why is the Calculation of AG More Accurate Than the Calculation of AH and
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AS? D. Historical Perspective of Free Energy Calculations Applied to Chemistry/ Biochemistry E. Challenges in Free Energy Calculations on the Solvation of Ionic, Polar, and Nonpolar Molecules F. Single and Dual Topologies in Free Energy Calculations G. Limitations in’ the Implementationof Free Energy Methodology in AMBER3 and the Removal of These Limitations in AMBER4 H. Comparison of Statistical Perturbation Theory, Thermodynamic Integration, and Slow Growth I. Free Energies Can Be Calculated for Coordinate as Well as Topology Changes J. Dependence of Calculated Free Energies on Molecular Mechanical Model K. The Sampling Issue L. Combining Quantum and Molecular Mechanical Methods IV. Applications A. Solvation 1. Aqueous Solvation 2. Nonaqueous Solvents and Partition Coefficients 3. Free Energy as a Function of Conformation 4. Solvent Effects on Tautomerism, Reduction/Oxidation, AcMlty/Basicity, Excited States, and Reactions in Solution 5. Protein Solvation 6. Molecular Association 1. “Small” Organic Hosts 2. Absolute Free Energies of Association 3. Protein “Hosts” C. Sequence Dependence on Ligand Binding and Catalysis D. Sequence Dependent Stabilities
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E. Combining Quantum Mechanical 2412 Calculations with Free Energy Calculations V. Summary 2413
I . Absfracf I will review the applications of free energy calculations employing molecular dynamics or Monte Carlo methods to a variety of chemical and biochemical phenomena. The focus is on the applications of such calculations to molecular solvation, molecular association, macromolecular stability, and enzyme catalysis. The molecules discussed range from monovalent ions and small molecules to proteins and nucleic acids. I I . Infroductlon
Free energy is arguably the most important general concept in physical chemistry. The free energies of molecular systems describe their tendencies to associate and react. Thus, being able to predict this quantity using molecular theory in general would be an enormously important advance and is a seductive goal. Progress toward this goal has been made in recent years, and this review attempts to describe this progress as it applies to the use of molecular dynamics and Monte Carlo methods to carry out free energy calculations in the following areas: (1)solvation of small molecules, (2) ligand binding to organic hosts and to proteins and nucleic acids, (3) sequence-dependent stabilities of proteins and nucleic acids, and (4) environmental effects on reactions in solutions and in enzymes. I will review of the methodologies used in such free energy calculations. After presenting some of the basic equations, I present a detailed discussion of the first application of the methodology to the calculation of the relative solvation free energy of the organic molecules methanol and ethane. The agreement between the calculated and experimental free energy is impressive, as is the inherent statistical error of
