Investigation of solvent effects for the Claisen rearrangement of chorismate to prephenate: mechanistic interpretation via near attack conformations

Solvent effects on the rate of the Claisen rearrangement of chorismate to prephenate have been examined in water and methanol. The preequilibrium free-energy differences between diaxial and diequatorial conformers of chorismate, which had previously been implicated as the sole basis for the observed 100-fold rate increase in water over methanol, have been reframed using the near attack conformation (NAC) concept of Bruice and co-workers. Using a combined QM/MM Monte Carlo/free-energy perturbation (MC/FEP) method, 82%, 57%, and 1% of chorismate conformers were found to be NAC structures (NACs) in water, methanol, and the gas phase, respectively. As a consequence, the conversion of non-NACs to NACs provides no free-energy contributions to the overall relative reaction rates in water versus methanol. Free-energy perturbation calculations yielded differences in free energies of activation for the two polar protic solvents and the gas phase. The rate enhancement in water over the gas phase arises from preferential hydration of the transition state (TS) relative to the reactants via increased hydrogen bonding and long-range electrostatic interactions, which accompany bringing the two negatively charged carboxylates into closer proximity. More specifically, there is an increase of 1.3 and 0.6 hydrogen bonds to the carboxylate groups and the ether oxygen, respectively, in going from the reactant to the TS in water. In methanol, the corresponding changes in hydrogen bonding with first shell solvent molecules are small; the rate enhancement arises primarily from the enhanced long-range interactions with solvent molecules. Thus, the reaction occurs faster in water than in methanol due to greater stabilization of the TS in water by specific interactions with first shell solvent molecules.     

Enzymes do what is expected (chalcone isomerase versus chorismate mutase)

Madicago sativa chalcone isomerase (CI) catalyzes the isomerization of chalcone to flavanone, whereas E. coli chorismate mutase (CM) catalyzes the pericyclic rearrangement of chorismate to prephenate. Covalent intermediates are not formed in either of the enzyme-catalyzed reactions, K(M) and k(cat) are virtually the same for both enzymes, and the rate constants (k(o)) for the noncatalyzed reactions in water are also the same. This kinetic identity of both the enzymatic and the nonenzymatic reactions is not shared by a similarity in driving forces. The efficiency (DeltaG(o)() - DeltaG(cat)()) for the CI mechanism involves transition-state stabilization through general-acid catalysis and freeing of three water molecules trapped in the E.S species. The contribution to lowering DeltaG(cat)() by an increase in near attack conformer (NAC) formation in E.S as compared to S in water is not so important. In the CM reaction, the standard free energy for NAC formation in water is 8.4 kcal/mol as compared to 0.6 kcal/mol in E.S. Because the value of (DeltaG(o)() - DeltaG(cat)()) is 9 kcal/mol, the greater percentage of NACs accounts for approximately 90% of the kinetic advantage of the CM reaction. There is no discernible transition-state stabilization in the CM reaction. These results are discussed. In anthropomorphic terms, each enzyme has had to do what it must to have a biologically relevant rate of reaction.     

Just a near attack conformer for catalysis (chorismate to prephenate rearrangements in water,antibody, enzymes,and their mutants)

Standard free energies for formation of ground-state reactive conformers (DeltaGN degrees ) and transition states (DeltaG) in the conversion of chorismate to prephenate in water, B. subtilis mutase, E. coli mutase, and their mutants, as well as a catalytic antibody, are related by DeltaG = DeltaGN degrees + 16 kcal/mol. Thus, the differences in the rate constants for the water reaction and catalysts reactions reside in the mole fraction of substrate present as reactive conformers (NACs). These results, and knowledge of the importance of transition state stabilization in other cases, suggest a proposal that enzymes utilize both NAC and transition state stabilization in the mix required for the most efficient catalysis.     

Theoretical insights in enzyme catalysis

In this tutorial review we show how the methods and techniques of computational chemistry have been applied to the understanding of the physical basis of the rate enhancement of chemical reactions by enzymes. This is to answer the question: Why is the activation free energy in enzyme catalysed reactions smaller than the activation free energy observed in solution? Two important points of view are presented: Transition State (TS) theories and Michaelis Complex (MC) theories. After reviewing some of the most popular computational methods employed, we analyse two particular enzymatic reactions: the conversion of chorismate to prephenate catalysed by Bacillus subtilis chorismate mutase, and a methyl transfer from S-adenosylmethionine to catecholate catalysed by catechol O-methyltransferase. The results and conclusions obtained by different authors on these two systems, supporting either TS stabilisation or substrate preorganization, are presented and compared. Finally we try to give a unified view, where a preorganized enzyme active site, prepared to stabilise the TS, also favours those reactive conformations geometrically closer to the TS.     

Solvation free energies calculated using the GB/SA model: Sensitivity of results on charge sets,protocols, and force fields

The sensitivity of aqueous solvation free energies (SFEs), estimated using the GB/SA continuum solvent model, on charge sets, protocols, and force fields, was studied. Simple energy calculations using the GB/SA solvent model were performed on 11 monofunctional organic compounds. Results indicate that calculated SFEs are strongly dependent on the charge sets. Charges derived from electrostatic potential fitting to high level ab initio wave functions using the CHELPG procedure and “class IV” charges from AM1/CM1a or PM3/CM1p calculations yielded better results than the corresponding Mulliken charges. Calculated SFEs were similar to MC/FEP energies obtained in the presence of explicit TIP4P water. Further improvements were obtained by using GVB/6-31G** and MP2/6-31+G** (CHELPG) charge sets that included correlation effects. SFEs calculated using charge sets assigned by the OPLSA* force field gave the best results of all standard force fields (MM2*, MM3*, MMFF, AMBER*, and OPLSA*) implemented in MacroModel. Comparison of relative and absolute SFEs computed using either the GB/SA continuum model or MC/FEP calculations in the presence of explicit TIP4P water showed that, in general, relative SFEs can be estimated with greater accuracy. A second set of 20 mono- and difunctional molecules was also studied and relative SFEs estimated using energy minimization and thermodynamic cycle perturbation (TCP) protocols. SFEs calculated from TCP calculations using the GB/SA model were sensitive to bond lengths of dummy bonds (i.e., bonds involving dummy atoms). In such cases, keeping the bond lengths of dummy bonds close to the corresponding bond lengths of the starting structures improved the agreement of TCP-calculated SFEs with energy minimization results. Overall, these results indicate that GB/SA solvation free energy estimates from simple energy minimization calculations are of similar accuracy and value to those obtained using more elaborate TCP protocols. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 769–780, 1998     

Molecular dynamics and free energy perturbation study of hydride-ion transfer step in dihydrofolate reductase using combined quantum and molecular mechanical model

We used molecular dynamics simulation and free energy perturbation (FEP) methods to investigate the hydride-ion transfer step in the mechanism for the nicotinamide adenine dinucleotide phosphate (NADPH)-dependent reduction of a novel substrate by the enzyme dihydrofolate reductase (DHFR). The system is represented by a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1 semiempirical molecular orbital method for the reacting substrate and NADPH cofactor fragments, the AMBER force field for DHFR, and the TIP3P model for solvent water. The FEP calculations were performed for a number of choices for the QM system. The substrate, 8-methylpterin, was treated quantum mechanically in all the calculations, while the larger cofactor molecule was partitioned into various QM and MM regions with the addition of “link” atoms (F, CH₃, and H). Calculations were also carried out with the entire NADPH molecule treated by QM. The free energies of reaction and the net charges on the NADPH fragments were used to determine the most appropriate QM/MM model. The hydride-ion transfer was also carried out over several FEP pathways, and the QM and QM/MM component free energies thus calculated were found to be state functions (i.e., independent of pathway). A ca. 10 kcal/mol increase in free energy for the hydride-ion transfer with an activation barrier of ca. 30 kcal/mol was calculated. The increase in free energy on the hydride-ion transfer arose largely from the QM/MM component. Analysis of the QM/MM energy components suggests that, although a number of charged residues may contribute to the free energy change through long-range electrostatic interactions, the only interaction that can account for the 10 kcal/mol increase in free energy is the hydrogen bond between the carboxylate side chain of Glu30 (avian DHFR) and the activated (protonated) substrate. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 977–988, 1998     

Apparent NAC effect in chorismate mutase reflects electrostatic transition state stabilization

The catalytic reaction of chorismate mutase (CM) has been the subject of major current attention. Nevertheless, the origin of the catalytic power of CM remains an open question. In particular, it has not been clear whether the enzyme works by providing electrostatic transition state stabilization (TSS), by applying steric strain, or by populating near attack conformation (NAC). The present work explores this issue by a systematic quantitative analysis. The overall catalytic effect is reproduced by the empirical valence bond (EVB) method. In addition, the binding free energy of the ground state and the transition state is evaluated, demonstrating that the enzyme works by TSS. Furthermore, the evaluation of the electrostatic contribution to the reduction of the activation energy establishes that the TSS results from electrostatic effects. It is also found that the apparent NAC effect is not the reason for the catalytic effect but the result of the TSS. It is concluded that in CM as in other enzymes the key catalytic effect is electrostatic TSS. However, since the charge distribution of the transition state and the reactant state is similar, the stabilization of the transition state leads to reduction in the distance between the reacting atoms in the reactant state.     

Cope elimination: elucidation of solvent effects from QM/MM simulations

The Cope elimination reactions for threo- and erythro-N,N-dimethyl-3-phenyl-2-butylamine oxide have been investigated using QM/MM calculations in water, THF, and DMSO. The aprotic solvents provide up to million-fold rate accelerations. The effects of solvation on the reactants, transition structures, and rates of reaction are elucidated here using two-dimensional potentials of mean force (PMF) derived from free-energy perturbation calculations in Monte Carlo simulations (MC/FEP). The resultant free energies of activation in solution are in close agreement with experiment. Ab initio calculations at the MP2/6-311+G-(2d,p) level using the PCM continuum solvent model were also carried out; however, only the QM/MM methodology was able to reproduce the large rate increases in proceeding from water to the dipolar aprotic solvents. Solute-solvent interaction energies and radial distribution functions are also analyzed and show that poorer solvation of the reactant in the aprotic solvents is primarily responsible for the observed rate enhancements. It is found that the amine oxide oxygen is the acceptor of three hydrogen bonds from water molecules for the reactant but only one to two weaker ones at the transition state. The overall quantitative success of the computations supports the present QM/MM/MC approach, featuring PDDG/PM3 as the QM method.     

Comparison of formation of reactive conformers (NACs) for the Claisen rearrangement of chorismate to prephenate in water and in the E. coli mutase: the efficiency of the enzyme catalysis

The Claisen rearrangements of chorismate (CHOR) in water and at the active site of E. coli chorismate mutase (EcCM) have been compared. From a total of 33 ns molecular dynamics simulation of chorismate in water solvent, seven diaxial conformers I-VII were identified. Most of the time (approximately 99%), the side chain carboxylate of the chorismate is positioned away from the ring due to the electrostatic repulsion from the carboxylate in the ring. Proximity of the two carboxylates, as seen in conformer I, is a requirement for the formation of a near attack conformer (NAC) that can proceed to the transition state (TS). In the EcCM.CHOR complex, the two carboxylates of CHOR are tightly held by Arg28 of one subunit and Arg11* of the other subunit, resulting in the side chain C16 being positioned adjacent to C5 with their motions restricted by van der Waals contacts with methyl groups of Val35 and Ile81. With the definition of NAC as the C5...C16 distance < or =3.7 A and the attack angle < or =30 degrees, it was estimated from our MD trajectories that the free energy of NAC formation is approximately 8.4 kcal/mol above the total ground state in water, whereas in the enzyme it is only 0.6 kcal/mol above the average of the Michaelis complex EcCM.CHOR. The experimentally measured difference in the activation free energies of the water and enzymatic reactions (Delta Delta G(++)) is 9 kcal/mol. It follows that the efficiency of formation of NAC (7.8 kcal/mol) at the active site provides approximately 90% of the kinetic advantage of the enzymatic reaction as compared to the water reaction. Comparison of the EcCM.TSA (transition state analogue) and EcCM.NAC simulations suggests that the experimentally measured 100 fold tighter binding of TSA compared to CHOR does not originate from the difference between NAC and the TS binding affinities, but might be due to the free energy cost to bring the two carboxylates of CHOR together to interact with Arg28 and Arg11* at the active site. The two carboxylates of TSA are fixed by a bicyclic structure. The remaining approximately 10% of Delta Delta G(++) may be attributed to a preferential interaction of Lys39-NH(3)(+) with O13 ether oxygen in the TS.     

Effects of Water Placement on Predictions of Binding Affinities for p38α MAP Kinase Inhibitors

Monte Carlo free energy perturbation (MC/FEP) calculations have been applied to compute the relative binding affinities of 17 congeneric pyridazo-pyrimidinone inhibitors of the protein p38α MAP kinase. Overall correlation with experiment was found to be modest when the complexes were hydrated using a traditional procedure with a stored solvent box. Significant improvements in accuracy were obtained when the MC/FEP calculations were repeated using initial solvent distributions optimized by the water placement algorithm JAWS. The results underscore the importance of accurate placement of water molecules in a ligand binding site for the reliable prediction of relative free energies of binding.     

Use of a QM/MM-based FEP method to evaluate the anomalous hydration behavior of simple alkyl amines and amides: application to the design of FBPase inhibitors for the treatment of type-2 diabetes

Standard molecular mechanics (MM) force fields predict a nearly linear decrease in hydration free energy with each successive addition of a methyl group to ammonia or acetamide, whereas a nonadditive relationship is observed experimentally. In contrast, the non-additive hydration behavior is reproduced directly using a quantum mechanics (QM)/MM-based free-energy perturbation (FEP) method wherein the solute partial atomic charges are updated at every window. Decomposing the free energies into electrostatic and van der Waals contributions and comparing the results with the corresponding free energies obtained using a conventional FEP method and a QM/MM method wherein the charges are not updated suggests that inaccuracies in the electrostatic free energies are the primary reason for the inability of the conventional FEP method to predict the experimental findings. The QM/MM-based FEP method was subsequently used to evaluate inhibitors of the diabetes drug target fructose-1,6-bisphosphatase adenosine 5'-monophosphate and 6-methylamino purine riboside 5'-monophosphate. The predicted relative binding free energy was consistent with the experimental findings, whereas the relative binding free energy predicted using the conventional FEP method differed from the experimental finding by an amount consistent with the overestimated relative solvation free energies calculated for alkylamines. Accordingly, the QM/MM-based FEP method offers potential advantages over conventional FEP methods, including greater accuracy and reduced user input. Moreover, since drug candidates often contain either functionality that is inadequately treated by MM (e.g., simple alkylamines and alkylamides) or new molecular scaffolds that require time-consuming development of MM parameters, these advantages could enable future automation of FEP calculations as well as greatly increase the use and impact of FEP calculations in drug discovery.     

Computer simulation of the chemical catalysis of DNA polymerases: discriminating between alternative nucleotide insertion mechanisms for T7 DNA polymerase

Understanding the chemical step in the catalytic reaction of DNA polymerases is essential for elucidating the molecular basis of the fidelity of DNA replication. The present work evaluates the free energy surface for the nucleotide transfer reaction of T7 polymerase by free energy perturbation/empirical valence bond (FEP/EVB) calculations. A key aspect of the enzyme simulation is a comparison of enzymatic free energy profiles with the corresponding reference reactions in water using the same computational methodology, thereby enabling a quantitative estimate for the free energy of the nucleotide insertion reaction. The reaction is driven by the FEP/EVB methodology between valence bond structures representing the reactant, pentacovalent intermediate, and the product states. This pathway corresponds to three microscopic chemical steps, deprotonation of the attacking group, a nucleophilic attack on the P(alpha) atom of the dNTP substrate, and departure of the leaving group. Three different mechanisms for the first microscopic step, the generation of the RO(-) nucleophile from the 3'-OH hydroxyl of the primer, are examined: (i) proton transfer to the bulk solvent, (ii) proton transfer to one of the ionic oxygens of the P(alpha) phosphate group, and (iii) proton transfer to the ionized Asp654 residue. The most favorable reaction mechanism in T7 pol is predicted to involve the proton transfer to Asp654. This finding sheds light on the long standing issue of the actual role of conserved aspartates. The structural preorganization that helps to catalyze the reaction is also considered and analyzed. The overall calculated mechanism consists of three subsequent steps with a similar activation free energy of about 12 kcal/mol. The similarity of the activation barriers of the three microscopic chemical steps indicates that the T7 polymerase may select against the incorrect dNTP substrate by raising any of these barriers. The relative height of these barriers comparing right and wrong dNTP substrates should therefore be a primary focus of future computational studies of the fidelity of DNA polymerases.     

Charge optimization increases the potency and selectivity of a chorismate mutase inhibitor

The highest affinity inhibitor for chorismate mutases, a conformationally constrained oxabicyclic dicarboxylate transition state analogue, was modified as suggested by computational charge optimization methods. As predicted, replacement of the C10 carboxylate in this molecule with a nitro group yields an even more potent inhibitor of a chorismate mutase from Bacillus subtilis (BsCM), but the magnitude of the improvement (roughly 3-fold, corresponding to a DeltaDeltaG of -0.7 kcal/mol) is substantially lower than the gain of 2-3 kcal/mol binding free energy anticipated for the reduced desolvation penalty upon binding. Experiments with a truncated version of the enzyme show that the flexible C terminus, which was only partially resolved in the crystal structure and hence omitted from the calculations, provides favorable interactions with the C10 group that partially compensate for its desolvation. Although truncation diminishes the affinity of the enzyme for both inhibitors, the nitro derivative binds 1.7 kcal/mol more tightly than the dicarboxylate, in reasonable agreement with the calculations. Significantly, substitution of the C10 carboxylate with a nitro group also enhances the selectivity of inhibition of BsCM relative to a chorismate mutase from Escherichia coli (EcCM), which has a completely different fold and binding pocket, by 10-fold. These results experimentally verify the utility of charge optimization methods for improving interactions between proteins and low-molecular weight ligands.     

A hybrid potential reaction path and free energy study of the chorismate mutase reaction.

We present a combination of two techniques--QM/MM statistical simulation methods and QM/MM internal energy minimizations--to get a deeper insight into the reaction catalyzed by the enzyme chorismate mutase. Structures, internal energies and free energies, taken from the paths of the reaction in solution and in the enzyme have been analyzed in order to estimate the relative importance of the reorganization and preorganization effects. The results we obtain for this reaction are in good agreement with experiment and show that chorismate mutase achieves its catalytic efficiency in two ways; first, it preferentially binds the active conformer of the substrate and, second, it reduces the free energy of activation for the reaction relative to that in solution by providing an environment which stabilizes the transition state.     

Free energy perturbation (FEP) simulation on the transition states of cocaine hydrolysis catalyzed by human butyrylcholinesterase and its mutants

A novel computational protocol based on free energy perturbation (FEP) simulations on both the free enzyme and transition state structures has been developed and tested to predict the mutation-caused shift of the free energy change from the free enzyme to the rate-determining transition state for human butyrylcholinesterase (BChE)-catalyzed hydrolysis of (-)-cocaine. The calculated shift, denoted by DeltaDeltaG(1 --> 2), of such kind of free energy change determines the catalytic efficiency (kcat/KM) change caused by the simulated mutation transforming enzyme 1 to enzyme 2. By using the FEP-based computational protocol, the DeltaDeltaG(1 --> 2) values for the mutations A328W/Y332A --> A328W/Y332G and A328W/Y332G --> A328W/Y332G/A199S were calculated to be -0.22 and -1.94 kcal/mol, respectively. The calculated DeltaDeltaG(1 --> 2) values predict that the change from the A328W/Y332A mutant to the A328W/Y332G mutant should slightly improve the catalytic efficiency and that the change from the A328W/Y332G mutant to the A328W/Y332G/A199S mutant should significantly improve the catalytic efficiency of the enzyme for the (-)-cocaine hydrolysis. The predicted catalytic efficiency increases are supported by the experimental data showing that kcat/KM = 8.5 x 10(6), 1.4 x 10(7), and 7.2 x 10(7) min(-1) M(-1) for the A328W/Y332A, A328W/Y332G, and A328W/Y332G/A199S mutants, respectively. The qualitative agreement between the computational and experimental data suggests that the FEP simulations may provide a promising protocol for rational design of high-activity mutants of an enzyme. The general computational strategy of the FEP simulation on a transition state can be used to study the effects of a mutation on the activation free energy for any enzymatic reaction.     

Influence of inter- and intramolecular hydrogen bonding on kemp decarboxylations from QM/MM simulations

The Kemp decarboxylation reaction for benzisoxazole-3-carboxylic acid derivatives has been investigated using QM/MM calculations in protic and dipolar aprotic solvents. Aprotic solvents have been shown to accelerate the rates of reaction by 7-8 orders of magnitude over water; however, the inclusion of an internal hydrogen bond effectively inhibits the reaction with near solvent independence. The effects of solvation and intramolecular hydrogen bonding on the reactants, transition structures, and the rate of reaction are elucidated using two-dimensional potentials of mean force (PMF) derived from free energy perturbation calculations in Monte Carlo simulations (MC/FEP). Free energies of activation in six solvents have been computed to be in close agreement with experiment. Solute-solvent interaction energies show that poorer solvation of the reactant anion in the dipolar aprotic solvents is primarily responsible for the observed rate enhancements over protic media. In addition, a discrepancy for the experimental rate in chloroform has been studied in detail with the conclusion that ion-pairing between the reactant anion and tetramethylguanidinium counterion is responsible for the anomalously slow reaction rate. The overall quantitative success of the computations supports the present QM/MM/MC approach, which features PDDG/PM3 as the QM method.     

Preorganization and reorganization as related factors in enzyme catalysis: the chorismate mutase case

In this paper a deeper insight into the chorismate-to prephenate-rearrangement, catalyzed by Bacillus subtilis chorismate mutase, is provided by means of a combination of statistical quantum mechanics/molecular mechanics simulation methods and hybrid potential energy surface exploration techniques. The main aim of this work is to present an estimation of the preorganization and reorganization terms of the enzyme catalytic rate enhancement. To analyze the first of these, we have studied different conformational equilibria of chorismate in aqueous solution and in the enzyme active site. Our conclusion is that chorismate mutase preferentially binds the reactive conformer of the substrate--that presenting a structure similar to the transition state of the reaction to be catalyzed--with shorter distances between the carbon atoms to be bonded and more diaxial character. With respect to the reorganization effect, an energy decomposition analysis of the potential energies of the reactive reactant and of the reaction transition state in aqueous solution and in the enzyme shows that the enzyme structure is better adapted to the transition structure. This means not only a more negative electrostatic interaction energy with the transition state but also a low enzyme deformation contribution to the energy barrier. Our calculations reveal that the structure of the enzyme is responsible for stabilizing the transition state structure of the reaction, with concomitant selection of the reactive form of the reactants. This is, the same enzymatic pattern that stabilizes the transition structure also promotes those reactant structures closer to the transition structure (i.e., the reactive reactants). In fact, both reorganization and preorganization effects have to be considered as the two faces of the same coin, having a common origin in the effect of the enzyme structure on the energy surface of the substrate.     

Computing Alchemical Free Energy Differences with Hamiltonian Replica Exchange Molecular Dynamics (H-REMD) Simulations

Alchemical free energy calculations play a very important role in the field of molecular modeling. Efforts have been made to improve the accuracy and precision of those calculations. One of the efforts is to employ a Hamiltonian replica exchange molecular dynamics (H-REMD) method to enhance conformational sampling. In this paper, we demonstrated that HREMD method not only improves convergence in alchemical free energy calculations but also can be used to compute free energy differences directly via the Free Energy Perturbation (FEP)algorithm. We show a direct mapping between the H-REMD and the usual FEP equations, which are then used directly to compute free energies. The H-REMD alchemical free energy calculation (Replica exchange Free Energy Perturbation, REFEP) was tested on predicting the pK(a) value of the buried Asp26 in thioredoxin. We compare the results of REFEP with TI and regular FEP simulations. REFEP calculations converged faster than those from TI and regular FEP simulations. The final predicted pK(a) value from the H-REMD simulation was also very accurate, only 0.4 pK(a) unit above the experimental value. Utilizing the REFEP algorithm significantly improves conformational sampling, and this in turn improves the convergence of alchemical free energy simulations.     

Alternative approaches to potential of mean force calculations: Free energy perturbation versus thermodynamic integration. Case study of some representative nonpolar interactions

We investigated the convergence behavior of potential of mean force (PMF) calculations using free energy perturbation (FEP), thermodynamic integration (TI), and “slow growth” (SG) techniques. The critical comparison of these alternative approaches is illustrated by the study of three different systems: two tagged argon atoms in a periodic box of argon, two methane molecules, and two benzene molecules maintained in a “T-shaped” conformation, both dimers embedded in a periodic box of water. The complete PMF simulations were carried out considering several protocols, in which the number of intermediate “λ” states, together with the amount of sampling per individual state, were varied. In most cases, as much as 1 ns of molecular dynamics (MD) sampling was used to derive each free energy profile. For the different systems examined, we find that FEP and TI unquestionably constitute robust computational methods leading to results of comparable accuracy. We also show that proper convergence of the free energy calculations, and further quantitative interpretation of the PMFs, requires total simulation times much higher than has been hitherto estimated. In some circumstances, the free energy profiles derived from FEP calculations tend to be slightly poorer than those obtained with TI, as a probable consequence of the greater sensitivity of FEP to the window spacing δλ. In the context of TI, and to a lesser extent FEP, simulations, it appears preferable to employ a limited number of “λ” points of the integrand involving extensive sampling, rather than numerous points with fewer samplings. Finally, we note that, at least in the case of nonpolar interactions, PMFs of reasonable quality can be generated using SG, and at a substantially lower cost than with either FEP or TI. © 1996 by John Wiley & Sons, Inc.     

Calculation of relative binding free energy differences for fructose 1,6-bisphosphatase inhibitors using the thermodynamic cycle perturbation approach.

An iterative, computer-assisted, drug design strategy that combines molecular design, molecular mechanics, molecular dynamics (MD), and free energy perturbation (FEP) calculations with compound synthesis, biochemical testing of inhibitors, and crystallographic structure determination of protein-inhibitor complexes was successfully used to predict the rank order of a series of nucleoside monophosphate analogues as fructose 1,6-bisphosphatase (FBPase) inhibitors. The X-ray structure of FBPase complexed with 5-aminoimidazole-4-carboxamide-1-beta-D-ribofuranosyl 5'-monophosphate (ZMP) provided structural information used for subsequent analogue design and free energy calculations. The FEP protocol was validated by calculating the free energy differences for the mutation of ZMP (1) to AMP (2). The calculated results showed a net gain of 1.7 kcal/mol, which agreed with the experimental result of 1.3 kcal/mol. FEP calculations were performed for 18 other AMP analogues. Inhibition constants were determined for over half of these analogues, usually after completion of the calculation, and were consistent with the predictions. Solvation free energy differences between AMP and various AMP analogues proved to be an important factor in binding free energies, suggesting that increased desolvation costs associated with the addition of polar groups to an inhibitor must be overcome by stronger ligand-protein interactions if the structural modification is to enhance inhibitor potency. The results indicate that FEP calculations predict relative binding affinities with high accuracy and provide valuable insight into the factors that influence inhibitor binding and therefore should greatly aid efforts to optimize initial lead compounds and reduce the time required for the discovery of new drug candidates.