Free energy calculations in rational drug design 2001 reddy erion

Chapter Historical Overview and Future Challenges J Andrew McCammon Howard Hughes Medical Institute, Department of Chemistry and Biochemistry, and Department of Pharmacology, University of California, San Diego, LaJoIIa, CA 92093 I INTRODUCTION The selective binding of molecules to form productive complexes is of central importance to pharmacology and medicinal chemistry Although kinetic factors can influence the yields of different molecular complexes in cellular and other non-equilibrium environments,1 the primary factors that one must consider in the analysis of molecular recognition are thermodynamic In particular, the equilibrium constant for the binding of molecules A and B to form the complex AB depends exponentially on the standard free energy change associated with complexation It has long been recognized that if one could compute the standard free energy change of complexation of biologically active molecules, it would be possible both to gain a deeper understanding of the origins of molecular recognition in biology, and to contemplate the "first principles" design of Pharmaceuticals and other compounds Such calculations were attempted, for example, by the Scheraga group as early as 1972,2 although limitations in computer power did not allow inclusion of solvation or entropic effects in this work In 1986, Wong and McCammon3 combined the statistical mechanical theory of free energy with atomistic simulations of solvent and solutes to calculate the relative standard free energy of binding of different small inhibitor molecules to an enzyme The necessary statistical mechanical theory had been available for many years Two new elements were required to make the calculation possible One was the increased power of computers, which allowed molecular dynamics simulation of the enzyme trypsin in a bath of explicitly represented water molecules The other was the concept of using thermodynamic cycles to relate the desired relative free energy to that of two nonphysical processes: computational "alchemical" transformations of one inhibitor into another one, in solution and in the binding site.4 Subsequent work has shown that free energy calculations that involve systems as large as proteins or other macromolecules can provide usefully accurate results in favorable cases But, in general, there are difficulties in achieving precise and accurate results with reasonable amounts of computer time, even using current state-of-the-art machines These difficulties arise primarily from the incomplete sampling of the rough, many-dimensional potential energy surfaces of such systems Below, I mention several lines of work that hold promise for making free energy calculations faster and more accurate for biomolecular systems The subsequent chapters in this volume describe some of these lines of work in more detail Excellent reviews of this work can also be found elsewhere.5"9 THEORY AND METHODS For calculations of relative free energies of binding, the theoretical framework outlined by Tembe and McCammon4 has been used essentially without change This framework recognizes that brute force calculations of standard free energies of binding will encounter convergence problems related to the dramatic changes in solvation of the binding partners, conformational changes that require physical times longer that those that can be explored by simulation, etc Tembe and McCammon4 introduced the use of thermodynamic cycle analyses that allow the desired relative free energies to be computed in terms of "alchemical" transformations, as described above The advantage is that only relatively localized changes occur in the simulated system, at least in favorable cases Calculation of the standard free energy of binding itself can be viewed as a special case of the above, in which one of the pair of ligands contains no atoms.10 Some care is required to be sure that such calculations yield answers that actually correspond to the desired standard state.11'12 Unfortunately, many calculations of free energies of binding have not made appropriate contact with a standard state, so that results in the literature must be interpreted with caution It has been mentioned that perhaps the greatest limitation to the precision of free energy calculations to date has been the ofteninadequate sampling of a representative set of configurations of the system Increases in computer power of course increase the "radius of convergence" of such calculations Such increases come not only from the "Moore's Law" improvements in hardware, but also from algorithmic advances for parallelization and for increasing time steps in molecular dynamics.13 New methods on the physical/theoretical side have also been developed to speed convergence One such method is the use of softcore solute models, so that one simulation can generate an adequate reference ensemble for a family of alchemical changes.14'15 The "lambda dynamics" method of Kong and Brooks16 increases the efficiency of free energy calculations by treating the coupling parameter as a dynamic variable More rapid convergence of free energy calculations can also be obtained by replacing part of the system with a simpler model, such as a continuum model for the solvent This has the advantage of obviating the need for sampling the configurations of this part of the system, and it also reduces the computation time so that longer simulations are possible for the rest of the system Reasonable agreement has sometimes been obtained with fully atomistic simulations when solvent regions near binding sites have been replaced by continuum.17' 18 But in view of the important role that specific hydrogen bonds may play, the combination of fully atomistic simulations with subsequent continuum analyses is probably a more reliable procedure.19 The Kollman group has demonstrated impressive success with this approach to calculations of free energies of binding.20 Calculations of relative free energies of binding often involve the alteration of bond lengths in the course of an alchemical simulation When the bond lengths are subject to constraints, a correction is needed for variation of the Jacobian factor in the expression for the free energy Although a number of expressions for the correction formula have been described in the literature, the correct expressions are those presented by Boresch and Karplus.21 OUTSTANDING PROBLEMS It was noted above that a continuum treatment of the solvent can be helpful, although representing certain solvent molecules explicitly may be necessary The expressions for handling the free energy contributions in such hybrid models have been derived by Gilson et al.11 Two remaining problems relating to the treatment of solvation include the slowness of Poisson-Boltzmann calculations, when these are used to treat electrostatic effects, and the difficulty of keeping buried, explicit solvent in equilibrium with the external solvent when, e.g., there are changes in nearby solute groups in an alchemical simulation Faster methods for solving the Poisson-Boltzmann equation by means of parallel finite element techniques are becoming available, however.22"24 For buried solvent molecules, open ensemble methods should be helpful, although extension of the existing methods to allow for solute flexibility is needed.18 It is not uncommon for protons to be taken up or released upon formation of a biomolecular complex Experimental data on such processes can be compared to computational results based on, for example, Poisson-Boltzmann calculations.25 There is a need for methods that automatically probe for the correct protonation state in free energy calculations This problem is complicated by the fact that proteins adapt to and stabilize whatever protonation state is assigned to them during the course of a molecular dynamics simulation.19 When the change in protonation state is known, equations are available to account for the addition or removal of protons from the solvent in the overall calculation of the free energy change.11 PROSPECTS Although challenges remain, and provide fruitful grounds for basic research, it is clear that computational methods for free energy calculations are becoming increasingly useful Computations are already of sufficient reliability for medium sized molecules such as synthetic host-guest systems, that they are an important tool for interpreting and even correcting experimental data in this area.7 Recent years have seen growing interest in these methods for protein-small molecule systems, as shown in the following chapters Acknowledgments Work in the author's laboratory is supported in parts by the NSF, NIH, the W M Keck Foundation, and the Howard Hughes Medical Institute REFERENCES J A McCammon, Theory of biomolecular recognition, Curr Op Struct Biol 8:245 (1998) K E B Platzer, F A Momany, and H A Scheraga, Conformational energy calculations of enzyme-substrate interactions II Computation of the binding energy for substrates in the active site of alpha-chymotrypsin, Int J Peptide Protein Res 4:201 (1972) C F Wong and J A McCammon, Dynamics and design of enzymes and inhibitors, J Am Chem Soc 108:3830 (1986) B L Tembe and J A McCammon, Ligand-receptor interactions, Comput Chem 8:281 (1984) 10 11 12 13 14 15 16 17 18 19 20 21 22 T P Straatsma, Free energy by molecular simulation, in: Reviews in Computational Chemistry, vol 9, K B Lipkowitz and D B Boyd, eds., VCH Publishers Inc., New York (1996), pp 217-309 P A Kollman, Advances and continuing challenges in achieving realistic and predictive simulations of the properties of organic and biological molecules, Ace Chem Res 29:461 (1996) M L Lamb and W L Jorgensen, Computational approaches to molecular recognition, Curr Opin Chem Biol 1:449 (1997) D A Pearlman and B G Rao, Free energy calculations: Methods and applications, in: Encyclopedia of Computational Chemistry, P v R Schleyer, ed., Wiley, New York (1999), pp 1036-1061 M R Reddy, M D Erion, and A Agarwal, Free energy calculations: use and limitations in predicting ligand binding affinities, in: Reviews in Computational Chemistry, vol 16, K B Lipkowitz and D B Boyd, eds., Wiley-VCH Inc., New York (2000), pp 217-304 W L Jorgensen, J K Buckner, S Boudon, and J Tirado-Rives, Efficient computation of absolute free energies of binding by computer simulations Application to methane dimer in water, J Chem Phys 89:3742 (1988) M K Gilson, J A Given, B L Bush, and J A McCammon, The statisticalthermodynamic basis for computation of binding affinities: A critical review, Biophys.J.72:1047(1997) J Hermans and L Wang, Inclusion of loss of translational and rotational freedom in theoretical estimates of free energies of binding Application to a complex of benzene and mutant T4-lysozyme, J Am Chem Soc 119:2707 (1997) T Schlick, R D Skeel, A T Brunger, L V Kale, J A Board, J Hermans, and K Schulten, Algorithmic challenges in computational molecular biophysics, J Comp Phys 151:9 (1999) H Liu, A E Mark, and W F van Gunsteren, On estimating the relative free energy of different molecular states with respect to a single reference state, J Phys Chem 100:9485 (1996) T Z Mordasini and J A McCammon, Calculations of relative hydration free energies: a comparative study using thermodynamic integration and an extrapolation method based on a single reference state, J Phys Chem B 104:360 (2000) X Kong and C L Brooks, Lambda-dynamics: a new approach to free energy calculations, J Chem Phys 105:2414 (1996) S T Wlodek, J Antosiewicz, J A McCammon, T P Straatsma, M K Gilson, J M Briggs, C Humblet, and J L Sussman, Binding of tacrine and 6chlorotacrine by acetylcholinesterase, Biopolymers 38:109 (1996) H Resat, T J Marrone, and J A McCammon, Enzyme-inhibitor association thermodynamics: Explicit and continuum solvent studies, Biophys J 72:522 (1997) S T Wlodek, J Antosiewicz, and J A McCammon, Prediction of titration properties of structures of a protein derived from molecular dynamics trajectories, Protein Sci 6:373 (1997) I Massova and P A Kollman, Combined molecular mechanical and continuum solvent approach (MM-PBSA/GBSA) to predict ligand binding, Perspect Drug Discov 18:113(2000) S Boresch and M Karplus, The Jacobian factor in free energy simulations, J Chem Phys 105:5145(1996) M Hoist, N Baker, and F Wang, Adaptive multilevel finite element solution of the Poisson-Boltzmann equation I: algorithms and examples, J Comp Chem 21:1319 (2000) 23 N Baker, M Hoist, and F Wang, Adaptive multilevel finite element solution of the Poisson-Boltzmann equation II: Refinement schemes based on solvent accessible surfaces, J Comp Chem 21:1343 (2000) 24 N Baker, D Sept, M Hoist, and J A McCammon, The adaptive multilevel finite element solution of the Poisson-Boltzmann equation on massively parallel computers, IBM J Res Dev in press (2001) 25 K A Xavier, S M McDonald, J A McCammon, and R C Willson, Association and dissociation kinetics of bobwhite quail lysozyme with monoclonal antibody HyHEL-5, Prot Eng 12:79 (1999) Section One Theory Chapter Free Energy Calculations: Methods for Estimating Ligand Binding Affinities David A Pearlman Vertex Pharmaceuticals, Incorporated, Cambridge, MA 02139-4242 INTRODUCTION Nearly two decades have now passed since the first macromolecular free energy calculations were published.1"3 These calculations drew on a statistical framework that was first described by Zwanzig years earlier4, but which until the advent of fast computers, molecular sampling techniques applicable to complex macromolecular systems, and reliable force fields could not be put into practice Groundbreaking work in the late 1970s demonstrated that a molecular dynamics (MD) approach could be used to perform configurational sampling for complex systems,5 and by the early 1980s, computers had become fast and cheap enough that such calculations were within the grasp of most well-funded research groups Extension of MD (or Monte Carlo [MC])6 sampling to the calculation of free energy differences as per Zwanzig was a natural one By the mid 1980s, a series of promising and exciting results reported in early free energy studies had sparked a flurry of research in the area.7'8 It is not hard to understand the interest Free energy is the property that dictates almost every physical process Understand the free energy behavior for any molecular system, and you can reliably predict how that system will behave Solvation, diffusion, binding, folding, and many other properties that are of critical interest to scientists can all be understood and (more importantly) predicted if we know the underlying free energy profiles It is not an exaggeration to say that an ability to reliably and rapidly predict these properties in the general case would revolutionize such endeavors as drug design Given the general feelings of euphoria that followed the early, promising papers in this field, one can ask what happened to the revolution? The answer, simply, is that free energy prediction turned out to be significantly more difficult than first thought While the statistical mechanics foundation is straightforward, as is integration with MD or MC sampling, issues related to sufficient sampling and to the adequacy of the force field quickly emerge when performing these calculations.9"17 With regard to sampling, we know what we need to do, but, outside of select amenable systems, current computer systems (which are many times faster than those used in the early free energy studies) are still orders of magnitude too slow to allow the kind of full conformational space exploration required to perform enough sampling to reliably predict free energy in the general case We thus confine ourselves to questions that fall within the class of systems for which we can hope to perform the requisite sampling While this is sub-optimal, there are still many questions of interest that can be addressed Much of the development in the free energy field over the past couple of decades has been in areas that attempt to better characterize the convergence characteristics of these calculations, and how to best carry them out to optimize the convergence.18"25 Major improvements have also been made in various procedural areas that make the models and equations used more correct.9'14'26'31 The tremendously promising results of early calculations in the field have, with hindsight, turned out to have been largely fortuitous We now know that those calculations, often performed with 10-40 ps of sampling, cannot possibly have yielded the kind of predictability they appeared to offer.9'17 The good news is that, after two decades of development and nearly unbelievable increases in available computer resources, we can now— for judiciously chosen questions—obtain predictions with quality that is truly as good as suggested by those first publications In this chapter, we shall review the various methods and protocols now available to perform free energy calculations EXACT FREE ENERGY CALCULATIONS There now exist several methods for predicting the free energy associated with a compositional or conformational change.7 These can be crudely classified into two types: "exact" and "approximate" free energy calculations The former type, which we shall discuss in the following sections, is based directly on rigorous equations from classical statistical mechanics The latter type, to be discussed later in this chapter, starts with statistical mechanics, but then combines these equations with assumptions and approximations to allow simulations to be carried out more rapidly 381 Index terms Links CHELPG 230 Chemical coordinate 197 Chemical Monte Carlo/Molecular Dynamics (CMC/MD) 195 Chemical potential 156 Cimetidine 126 CMIP procedure 303 Collagenase 97 Collective-solvent-coordinate model 80 Conductor-like screening model (COSMO) 325 244 64 α-Chymotrypsin Combinatorial libraries 288 319 81 Conformational sampling 189 Conformational variables 17 Continuum solvent models 64 80 solvation free energies 86 244 generalized Born/surface area (GB/SA) 98 86 217 Convergence profile simulation length 100 101 RMS deviation 290 326 328 Coordinate coupling dihydrofolate reductase 253 solvation free energies 113 theory 261 Coulomb's law 48 Coupling parameter 197 Covalent hydration adenosine deaminase 365 carbonyl compounds 368 free energy calculations 368 inhibitor design 366 heteroaromatic bases 369 pteridine analogues 370 369 371 This page has been reformatted by Knovel to provide easier navigation 373 382 Index terms Links Covalent hydration(Continued) purine riboside 366 369 373 COX, see Cyclooxygenase Cyclooxygenase (COX) binding free energies MC-FEP 304 mutant COX 305 Celecoxib 304 Cytochrome c peroxidase 217 Cytochrome P450-camphor 183 Cytosine 111 D Daunomycin 155 Deaza AMP analogues 232 Dehydroxystatine 150 DELPHI 245 Density functional theory 38 2'-Deoxycoformycin 365 2'-Deoxycytidine 5'-monophosphate 337 2'-Deoxyuridine 5'-monophosphate 337 Desolvation penalty 330 Diabetes 229 Dielectric constant 47 Dielectric descreening 81 7,8-Dihydrofolate tautomeric equilibrium 254 285 255 255 Dihydrofolate reductase (DHFR) binding free energy calculations 149 197 337 367 catalytic mechanism 254 276 dipole moment effects 265 290 359 This page has been reformatted by Knovel to provide easier navigation 301 329 383 Index terms Links Dihydrofolate reductase (DHFR) (Continued) hydride transfer free energy profile 270 protein interactions 272 hydrophobic hydration 355 inhibitors 343 linear interaction energy calculations 180 linear response approximation 354 mechanism-based substrates 344 346 proton transfer free energy profile 264 substrate interactions 268 QM/MM 259 solvent role 356 8-substituted deazapterins 344 346 355 8-substituted-pterin substrates 344 346 355 transition state 254 258 266 Dipole moment 48 51 265 Dipole-dipole interactions 47 Dispersion 83 163 164 Dissociation constants 231 Distamycin 155 DOCKing 248 Double topology 98 Double-wide sampling 20 321 DNA-ligand complex acridine 155 anthracycline antibiotics 155 DAPI 155 daunomycin 155 distamycin 155 ethidium 155 free energy calculations 158 163 This page has been reformatted by Knovel to provide easier navigation 271 165 384 Index terms Links DNA-ligand complex (Continued) Hoechst 33258 155 netropsin 159 DNA minor groove 155 162 Drug resistance 161 162 310 Dynamically Modified Windows (DMW) 22 E Electrostatics coefficients 175 179 180 decoupling 24 106 261 free energy 262 Poisson-Boltzmann equation 30 Empirical scoring methods 172 Endothiapepsin 143 inhibitors 28 Energy distribution method 175 14 Enthalpy calculation of 16 74 30 200 202 246 248 307 Entropy calculation of conformational 249 translational 248 rotational 248 vibrational 248 Equilibrium modeling 79 Error estimation 328 ESP fitted atomic partial charges 107 Ewald summation 124 Exchange repulsion 83 This page has been reformatted by Knovel to provide easier navigation 213 244 385 Index terms Explicit Solvent Models Links 97 TIP3P 98 SPC/E 98 F Fatty acid binding protein 181 FKBP 303 Floating independent reference frame (FIRF) 201 Fluorine scanning 202 5-Fluoro-2'deoxyuridylate monophosphate (FdUMP) 336 Force fields, Molecular Mechanics AMBER 41 CFF 41 CHARMM 41 GALAXY 259 GROMOS 175 MM3 41 MMFF 41 OPLS 41 Formycin A monophosphate 295 10-Formyl-5,8-dideazafolic acid (FDDF) 336 245 259 109 300 Free energy calculations, see also covalent hydration; linear interaction energy; lambda dynamics; ligand scanning; MM/PBSA; adenosine deaminase 373 cyclooxygenase 304 dihydrofolate reductase 258 DNA complexes 159 fructose 1,6-bisphosphatase 291 high throughput methods 172 HIV-1 protease 324 HIV reverse transcriptase 308 overview 345 200 226 10 This page has been reformatted by Knovel to provide easier navigation 243 386 Index terms Links Free energy calculations (Continued) pepsin 150 solvation 86 SRC SH2 domain 306 tautomerisation 122 thermolysin 144 thrombin 312 thymidylate synthase 338 Free energy decoupling 261 Free energy grid 100 29 Free energy perturbation (FEP), convergence 14 19 error estimation 19 329 historical overview method 13 outstanding problems theory 10 validation 197 319 322 Free energy profile 259 Fructose 1,6-bisphosphatase 285 289 AMP mimetic design 229 291 binding free energies 231 236 ligand scanning 228 287 G GALAXY program 259 Generalized Born/Surface Area (GB/SA) 98 Generalized Born model 81 Debye-Hückel modification 214 82 Ghost forces 210 Gluconeogenesis 285 GROMOS program 175 Guanine 111 128 This page has been reformatted by Knovel to provide easier navigation 290 292 387 Index terms Links H H2 receptor 126 Hellmann-Feynman theorem 83 Henry's law 69 Heteroaromatic hydration 369 Histamine 126 HIV-1 protease 146 175 317 drug design 317 324 330 free energy calculations 319 324 327 330 inhibitors 321 322 324 328 244 299 308 HIV reverse transcriptase drug resistance 310 HEPT 308 mutants 310 non-nucleoside inhibitors 308 TIBO analogues 218 Holonomic constraints Homology models Hook's law 329 309 308 310 311 227 229 232 229 234 238 18 143 42 Hydration free energy 123 see also covalent hydration Hydrogen bond 226 234 Acceptor 233 donor 232 strength 226 Hydrophobic free energy 175 Hydrophobic hydration 355 2-(4'-Hydroxyazobenzene) benzoic acid (HABA) 246 Hydroxyethylamine (Hea)-based inhibitor 144 Hypertension 146 323 This page has been reformatted by Knovel to provide easier navigation 233 388 Index terms Links I Ideal mixtures 66 Ideal solution 72 2-Imidazole distamycin 157 IMPACT program 108 Ionisation 123 weak acids and bases 304 131 J Jacobian factor Jean's equation 47 JG365 323 K K+-18-crown-6 complex 176 Knowledge-based scoring approaches 172 L Lambda dynamics continuum solvent 214 cytochrome c peroxidase 217 HIV reverse transcriptase 218 multiple ligand screening 195 multiple topology model 209 non-linear lambda scaling 26 pathway 216 sampling 205 theory 203 trypsin 217 Ligand interaction map 227 200 203 237 Ligand scanning AMP analogues 232 This page has been reformatted by Knovel to provide easier navigation 205 389 Index terms Links Ligand scanning (Continued) computational details 230 drug design 238 fructose 1,6-bisphosphatase 229 relative binding affinity 231 Ligand screening lambda dynamics 203 ligand interaction energies 238 ligand interaction scanning 225 239 (LIA) 182 200 continuum solvent 202 Linear Interaction Approximation Linear Interaction Energy (LIE) 28 accessible surface area 201 COX inhibitors 304 18-crown-6 176 DHFR inhibitors 180 endothiapepsin 175 FKBP12 183 free energies of hydration 302 HIV protease 182 HIV reverse transcriptase 308 mutants 173 243 310 LIE/SA 175 302 303 linear response approximation 173 182 354 Monte Carlo simulations 303 retinol binding protein 181 scoring 171 177 189 SRC SH2 domain 306 theory 173 thrombin 184 trypsin 175 312 This page has been reformatted by Knovel to provide easier navigation 302 390 Index terms Links Local density function (LDF) approach 254 Lysine binding protein 181 Lysozyme 182 M Matador 304 Matrix metalloproteinase (MMP) 244 MCPRO program 301 Methotrexate (MTX) 130 181 9-Methylpurine 372 375 MM3 program 41 51 Model validation 289 Molecular electrostatic potential (MEP) 347 253 Molecular mechanics, see also Force fields, angle bending 43 bond polarization 48 bond stretching 42 cross term function 48 dipole terms 47 electrostatic 47 hydrogen-bonding interactions 46 Lennard-Jones 6-12 potential 45 London dispersion forces 45 non-bonded interactions 44 overview 39 parameterization 50 torsion 46 288 Molecular-mechanics with Possion-Boltzmann/surface area approach (MM/PBSA) 202 avidin-biotin complexes 249 cathepsin D inhibitors 246 244 This page has been reformatted by Knovel to provide easier navigation 335 343 391 Index terms Links Molecular-mechanics with Possion-Boltzmann/surface area approach (MM/PBSA) (Continued) HIV RT inhibitors 248 MMP inhibitors 246 theory 244 Monte Carlo ensemble average sampling Multiple ligand screening methods 105 299 112 300 301 205 see also Chemical Monte Carlo/molecular dynamics; Lambda dynamics Multiple topology method Multipole expansion 209 82 N Netropsin, see DNA-ligand complex Neuraminidase 190 Nevirapine 309 Nicotinic acid 135 Non-additivity 338 Nonequilibrium solvation effects 87 Nonequilibrium properties 87 Nonideal solution 68 Non-linear Poisson-Boltzmann model Non-linear λ scaling 156 26 Non-steroidal anti-inflammatory drugs (NSAIDs) 304 Nucleic acid bases 111 P Parallelization PARSE radii 245 Particle insertion method Pepsin, Rhizopus free energy calculations 14 143 146 150 This page has been reformatted by Knovel to provide easier navigation 392 Index terms Links Pepsin, Rhizopus (Continued) inhibitors 149 mutation 147 Pepstatin 149 Phosphoramidate 144 Pictorial Representation of Free Energy Components (PROFEC) 201 339 30 Polarizable continuum model (PCM) 82 136 Potential energy surfaces 40 Potential of Mean Forces (PMF) 17 Poisson-Boltzmann equation 10-Propargyl-5,8-dideazafolic acid (PDDF) 336 Pteridine 370 Purine nucleoside phosphorylase 227 Purine riboside hydration 369 82 371 Q Quantum Mechanics ab initio 38 55 Hartree-Fock theory 52 245 Moller-Plesset corrections 52 368 255 259 Quantum Mechanics/Molecular Mechanics (QM/MM) dihydrofolate reductase 254 coordinate coupling 261 Quasi-harmonic analysis 248 QUEST program 147 368 R Rapamycin 184 Reaction field methods 80 Regression methods 319 Relative inhibitory potency 373 Renin 143 88 This page has been reformatted by Knovel to provide easier navigation 393 Index terms Links Residue-based cutoff radii 347 Resonance energy 376 Restrained electrostatic potential (RESP) 245 Retinol binding protein 181 335 Rhizopus Pepsin, see Pepsin S Sampling Schrodinger equation Screening virtual libraries Self-consistent reaction field 38 172 81 Semi-empirical quantum mechanics AM1 38 MNDO 38 PM3 38 Single topology 349 320 Slow growth method 13 Solubility 77 159 Solvation, absolute free energy convergence 98 108 112 99 369 100 explicit solvent models nucleic acid 98 111 relative free energy simulation length theory 97 100 74 Solvent accessible surface area 244 Solvent descriptors 84 Solvent/solute partitioning models 85 SRC SH2 domain 306 This page has been reformatted by Knovel to provide easier navigation 394 Index terms Statistical mechanics Links 64 free energy 79 models 64 theory Streptavidin-biotin 156 Structure-function studies 225 Subtilisin 225 Surface curvature Sustiva 84 308 T Tautomerism DNA bases 128 formycin A 129 free energy calculations 121 long range forces 134 sampling 135 solvent 138 guanine 119 heterocycles 126 histamine 126 134 imidazole 126 132 nicotinic acid 128 135 2-oxopyrimidine 129 triazole 127 Tethered water (TW) model 357 Tetraazanaphthalene 370 Thermodynamic integration method Thermolysin 128 133 134 12 143 binding free energy 145 Thread methodology 98 290 321 This page has been reformatted by Knovel to provide easier navigation 372 395 Index terms Thrombin Links 184 299 binding pocket 312 LIE analysis 183 312 130 335 binding free energy calculations 336 337 inhibitor design 340 non-additivity 338 TIBO analogues 247 308 Transition state 257 366 Trapezoidal rule 13 Thymidylate synthase Trimethoprim 350 Trypsin 175 217 Umbrella sampling 18 198 United-atom Hartree-Fock model (UHF) 83 312 339 U V Virtual bonds 374 W Weighted histogram analysis methods (WHAM) Window statistics 14 199 328 X XchemEdit program 303 Z Zinc ion constraints 374 ZMP 289 This page has been reformatted by Knovel to provide easier navigation 340 ... York (1999), pp 1036-1061 M R Reddy, M D Erion, and A Agarwal, Free energy calculations: use and limitations in predicting ligand binding affinities, in: Reviews in Computational Chemistry, vol... group) In essence, at each point, we are calculating the free energy for going from nothing at the grid point to having a probe atom at that grid point Since the reference state for each grid point... modern drug design in the industrial setting starts with high-throughput methods that require scoring methods faster than precise free energy calculations can hope to be (Precise free energy calculations