Calculation of relative binding affinities of fructose 1,6-bisphosphatase mutants with adenosine monophosphate using free energy perturbation method

The free energy perturbation (FEP) methodology is the most accurate means of estimating relative binding affinities between inhibitors and protein variants. In this article, the importance of hydrophobic and hydrophilic residues to the binding of adenosine monophosphate (AMP) to the fructose 1,6-bisphosphatase (FBPase), a target enzyme for type-II diabetes, was examined by FEP method. Five mutations were made to the FBPase enzyme with AMP inhibitor bound: 113Tyr --> 113Phe, 31Thr --> 31Ala, 31Thr --> 31Ser, 177Met --> 177Ala, and 30Leu --> 30Phe. These mutations test the strength of hydrogen bonds and van der Waals interactions between the ligand and enzyme. The calculated relative free energies indicated that: 113Tyr and 31Thr play an important role, each via two hydrogen bonds affecting the binding affinity of inhibitor AMP to FBPase, and any changes in these hydrogen bonds due to mutations on the protein will have significant effect on the binding affinity of AMP to FBPase, consistent to experimental results. Also, the free energy calculations clearly show that the hydrophilic interactions are more important than the hydrophobic interactions of the binding pocket of FBPase.     

Use of quantum mechanics/molecular mechanics-based FEP method for calculating relative binding affinities of FBPase inhibitors for type-2 diabetes

A quantum mechanics (QM)/molecular mechanics (MM)-based free energy perturbation (FEP) method, developed recently, provides most accurate estimation of binding affinities. The validity of the method was evaluated for a large set of diverse inhibitors for fructose 1,6-bisphosphatase (FBPase), a target enzyme for type-II diabetes mellitus. The validation set comprises of 22 important structurally different mutations. The calculated relative binding free energies using the QM/MM-based FEP method reproduce the experimental values with exceptional precision of less than ±0.5 kcal/mol. The CPU requirements for QM/MM-based FEP are about fivefold greater than conventional FEP methods, but it is superior in accuracy of predictions. In addition, the QM/MM-based FEP method eliminates the need for time-consuming development of MM force field parameters, which are frequently required for novel inhibitors described by MM. Future automation of the method and parallelization of the code for 128/256/512 cluster computers is expected to enhance the speed and increase its use for drug design and lead optimization. The present application of QM/MM-based FEP method for structurally diverse set of analogs serves to enhance the scope of FEP method and demonstrate the utility of QM/MM-based FEP method for its potential in drug discovery.     

Minimum MD simulation length required to achieve reliable results in free energy perturbation calculations: Case study of relative binding free energies of fructose‐1,6‐bisphosphatase inhibitors

In an attempt to establish the criteria for the length of simulation to achieve the desired convergence of free energy calculations, two studies were carried out on chosen complexes of FBPase‐AMP mimics. Calculations were performed for varied length of simulations and for different starting configurations using both conventional‐ and QM/MM‐FEP methods. The results demonstrate that for small perturbations, 1248 ps simulation time could be regarded a reasonable yardstick to achieve convergence of the results. As the simulation time is extended, the errors associated with free energy calculations also gradually tapers off. Moreover, when starting the simulation from different initial configurations of the systems, the results are not changed significantly, when performed for 1248 ps. This study carried on FBPase‐AMP mimics corroborates well with our previous successful demonstration of requirement of simulation time for solvation studies, both by conventional and ab initio FEP. The establishment of aforementioned criteria of simulation length serves a useful benchmark in drug design efforts using FEP methodologies, to draw a meaningful and unequivocal conclusion. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Structure-guided design of AMP mimics that inhibit fructose-1,6-bisphosphatase with high affinity and specificity

AMP binding sites are commonly used by nature for allosteric regulation of enzymes controlling the production and metabolism of carbohydrates and lipids. Since many of these enzymes represent potential drug targets for metabolic diseases, efforts were initiated to discover AMP mimics that bind to AMP-binding sites with high affinity and high enzyme specificity. Herein we report the structure-guided design of potent fructose 1,6-bisphosphatase (FBPase) inhibitors that interact with the AMP binding site on FBPase despite their structural dissimilarity to AMP. Molecular modeling, free-energy perturbation calculations, X-ray crystallography, and enzyme kinetic data guided our redesign of AMP, which began by replacing the 5'-phosphate with a phosphonic acid attached to C8 of the adenine base via a 3-atom spacer. Additional binding affinity was gained by replacing the ribose with an alkyl group that formed van der Waals interactions with a hydrophobic region within the AMP binding site and by replacing the purine nitrogens N1 and N3 with carbons to minimize desolvation energy expenditures. The resulting benzimidazole phosphonic acid, 16, inhibited human FBPase (IC50 = 90 nM) 11-fold more potently than AMP and exhibited high specificity for the AMP binding site on FBPase. 16 also inhibited FBPase in primary rat hepatocytes and correspondingly resulted in concentration-dependent inhibition of the gluconeogenesis pathway. Accordingly, these results suggest that the AMP site of FBPase may represent a potential drug target for reducing the excessive glucose produced by the gluconeogenesis pathway in patients with type 2 diabetes.     

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.     

Comparison of 6-31G*-based MST/SCRF and FEP evaluations of the free energies of hydration for small neutral molecules

A comparison between Miertus–Scrocco–Tomasi (MST) SCRF and free energy perturbation (FEP) estimates of the free energy of hydration of eight small neutral molecules is presented. In both cases, the 6-31G* molecular electrostatic potential is used to describe the electrostatic properties of the molecules. The results demonstrate the ability of both methodologies to provide useful theoretical estimates of the total free energy of hydration; the average errors are only 1.5 kcal/mol (FEP) and 0.8 kcal/mol (MST/SCRF). The largest errors in the FEP and MST/SCRF results are less than 1.5 kcal/mol for all molecules except acetic acid, where the FEP method overestimates the free energy of hydration by 3.3 kcal/mol. © John Wiley & Sons, Inc.     

Computational insights into factor affecting the potency of diaryl sulfone analogs as Escherichia coli dihydropteroate synthase inhibitors

Dihydropteroate synthase (DHPS) is an alluring target for designing novel drug candidates to prevent infections caused by pathogenic Escherichia coli strains. Diaryl Sulfone (SO) compounds are found to inhibit DHPS competitively with respect to the substrate pABA (p-aminobenzoate). The extra aromatic ring of diaryl sulfone compounds found to stabilize them in highly flexible pABA binding loops. In this present study, a statistically significant 3D-QSAR model was developed using a data set of diaryl sulfone compounds. The favourable and unfavourable contributions of substitutions in sulfone compounds were illustrated by contour plot obtained from the developed 3D-QSAR model. Molecular docking calculations were performed to investigate the putative binding mode of diaryl sulfone compounds at the catalytic pocket. DFT calculations were carried out using SCF approach, B3LYP- 6-31 G (d) basis set to compute the HOMO, LUMO energies and their respective location at pABA binding pocket. Further, the developed model was validated by FEP (Free Energy Perturbation) calculations. The calculated relative free energy of binding between the highly potent and less potent sulfone compound was found to be −3.78 kcal/ mol which is comparable to the experimental value of −5.85 kcal/mol. A 10 ns molecular dynamics simulation of inhibitor and DHPS confirmed its stability at pABA catalytic site. Outcomes of the present work provide deeper insight in designing novel drug candidates for pathogenic Escherichia coli strains.     

Relative energies of binding for antibody-carbohydrate-antigen complexes computed from free-energy simulations

Free-energy perturbation (FEP) simulations have been applied to a series of analogues of the natural trisaccharide epitope of Salmonella serotype B bound to a fragment of the monoclonal anti-Salmonella antibody Se155-4. This system was selected in order to assess the ability of free-energy perturbation (FEP) simulations to predict carbohydrate-protein interaction energies. The ultimate goal is to use FEP simulations to aid in the design of synthetic high affinity ligands for carbohydrate-binding proteins. The molecular dynamics (MD) simulations were performed in the explicit presence of water molecules, at room temperature. The AMBER force field, with the GLYCAM parameter set for oligosaccharides, was employed. In contrast to many modeling protocols, FEP simulations are capable of including the effects of entropy, arising from differential ligand flexibilities and solvation properties. The experimental binding affinities are all close in value, resulting in small relative free energies of binding. Many of the DeltaDeltaG values are on the order of 0-1 kcal mol(-1), making their accurate calculation particularly challenging. The simulations were shown to reasonably reproduce the known geometries of the ligands and the ligand-protein complexes. A model for the conformational behavior of the unbound antigen is proposed that is consistent with the reported NMR data. The best agreement with experiment was obtained when histidine 97H was treated as fully protonated, for which the relative binding energies were predicted to well within 1 kcal mol(-1). To our knowledge this is the first report of FEP simulations applied to an oligosaccharide-protein complex.     

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     

Discovery of potent and specific fructose-1,6-bisphosphatase inhibitors and a series of orally-bioavailable phosphoramidase-sensitive prodrugs for the treatment of type 2 diabetes

Excessive glucose production by the liver coupled with decreased glucose uptake and metabolism by muscle, fat, and liver results in chronically elevated blood glucose levels in patients with type 2 diabetes. Efforts to treat diabetes by reducing glucose production have largely focused on the gluconeogenesis pathway and rate-limiting enzymes within this pathway such as fructose-1,6-bisphosphatase (FBPase). The first potent FBPase inhibitors were identified using a structure-guided drug design strategy (Erion, M. D.; et al. J. Am. Chem. Soc. 2007, 129, 15480-15490) but proved difficult to deliver orally. Herein, we report the synthesis and characterization of a series of orally bioavailable FBPase inhibitors identified following the combined discoveries of a low molecular weight inhibitor series with increased potency and a phosphonate prodrug class suitable for their oral delivery. The lead inhibitor, 10A, was designed with the aid of X-ray crystallography and molecular modeling to bind to the allosteric AMP binding site of FBPase. High potency (IC50 = 16 nM) and FBPase specificity were achieved by linking a 2-aminothiazole with a phosphonic acid. Free-energy perturbation calculations provided insight into the factors that contributed to the high binding affinity. 10A and standard phosphonate prodrugs of 10A exhibited poor oral bioavailability (0.2-11%). Improved oral bioavailability (22-47%) was achieved using phosphonate diamides that convert to the corresponding phosphonic acid by sequential action of an esterase and a phosphoramidase. Oral administration of the lead prodrug, MB06322 (30, CS-917), to Zucker Diabetic Fatty rats led to dose-dependent inhibition of gluconeogenesis and endogenous glucose production and consequently to significant blood glucose reduction.     

Properties of inhibitors of methane hydrate formation via molecular dynamics simulations

Within the framework of a proposed two-step mechanism for hydrate inhibition, the energy of binding of four inhibitor molecules (PEO, PVP, PVCap, and VIMA) to a hydrate surface is estimated with molecular dynamic simulations. One key feature of this proposed mechanism is that the binding of an inhibitor molecule to the surface of an ensuing hydrate crystal disrupts growth and therein crystallization. It is found through the molecular dynamic simulations that inhibitor molecules that experimentally exhibit better inhibition strength also have higher free energies of binding, an indirect confirmation of our proposed mechanism. Inhibitors increasing in effectiveness, PEO < PVP < PVCap < VIMA, have increasingly negative (exothermic) binding energies of -0.2 < -20.6 < -37.5 < -45.8 kcal/mol and binding free energies of increasing favorability (+0.4 approximately = +0.5 < -9.4 < -15.1 kcal/mol). Furthermore, the effect of an inhibitor molecule on the local liquid water structure under hydrate-forming conditions was examined and correlated to the experimental effectiveness of the inhibitors. Two molecular characteristics that lead to strongly binding inhibitors were found: (1) a charge distribution on the edge of the inhibitor that mimics the charge separation in the water molecules on the surface of the hydrate and (2) the congruence of the size of the inhibitor with respect to the available space at the hydrate-surface binding site. Equipped with this molecular-level understanding of the process of hydrate inhibition via low-dosage kinetic hydrate inhibitors we can design new, more effective inhibitor molecules.     

Relative binding affinities of alkali metal cations to

The binding affinity and selectivity of a new ionophore, [1(8)]starand (1), toward alkali metal cations in methanol were examined through NMR titration experiments and free energy perturbation (FEP) and molecular dynamics simulations. The preference was determined to be K(+) > Rb(+) > Cs(+) > Na(+) > Li(+) in both FEP simulations and NMR experiments. The FEP simulation results were able to predict the relative binding free energies with errors less than 0.13 kcal/mol, except for the case between Li(+) and Na(+). The cation selectivity was rationalized by analyzing the radial distribution functions of the M-O and M-C distances of free metal cations in methanol and those of metal-ionophore complexes in methanol.     

Toward quantitative estimates of binding affinities for protein–ligand systems involving large inhibitor compounds: A steered molecular dynamics simulation route

Understanding binding mechanisms between enzymes and potential inhibitors and quantifying protein – ligand affinities in terms of binding free energy is of primary importance in drug design studies. In this respect, several approaches based on molecular dynamics simulations, often combined with docking techniques, have been exploited to investigate the physicochemical properties of complexes of pharmaceutical interest. Even if the geometric properties of a modeled protein – ligand complex can be well predicted by computational methods, it is still challenging to rank with chemical accuracy a series of ligand analogues in a consistent way. In this article, we face this issue calculating relative binding free energies of a focal adhesion kinase, an important target for the development of anticancer drugs, with pyrrolopyrimidine‐based ligands having different inhibitory power. To this aim, we employ steered molecular dynamics simulations combined with nonequilibrium work theorems for free energy calculations. This technique proves very powerful when a series of ligand analogues is considered, allowing one to tackle estimation of protein – ligand relative binding free energies in a reasonable time. In our cases, the calculated binding affinities are comparable with those recovered from experiments by exploiting the Michaelis – Menten mechanism with a competitive inhibitor.     

Use of MM-PBSA in reproducing the binding free energies to HIV-1 RT of TIBO derivatives and predicting the binding mode to HIV-1 RT of efavirenz by docking and MM-PBSA.

In this work, a new ansatz is presented that combines molecular dynamics simulations with MM-PBSA (Molecular Mechanics Poisson-Boltzmann/surface area) to rank the binding affinities of 12 TIBO-like HIV-1 RT inhibitors. Encouraging results have been obtained not only for the relative binding free energies, but also for the absolute ones, which have a root-mean-square deviation of 1.0 kcal/mol (the maximum error is 1.89 kcal/mol). Since the root-mean-square error is rather small, this approach can be reliably applied in ranking the ligands from the databases for this important target. Encouraged by the results, we decided to apply MM-PBSA combined with molecular docking to determine the binding mode of efavirenz SUSTIVA(TM) another promising HIV-1 RT inhibitor for which no ligand-protein crystal structure had been published at the time of this work. To proceed, we define the following ansatz: Five hundred picosecond molecular dynamics simulations were first performed for the five binding modes suggested by DOCK 4.0, and then MM-PBSA was carried out for the collected snapshots. MM-PBSA successfully identified the correct binding mode, which has a binding free energy about 7 kcal/mol more favorable than the second best mode. Moreover, the calculated binding free energy (-13.2 kcal/mol) is in reasonable agreement with experiment (-11.6 kcal/mol). In addition, this procedure was also quite successful in modeling the complex and the structure of the last snapshot was quite close to that of the measured 2,3 A resolution crystal (structure the root-mean-square deviation of the 54 C(alpha) around the binding site and the inhibitor is 1.1 A). We want to point out that this result was achieved without prior knowledge of the structure of the efavirenz/RT complex. Therefore, molecular docking combined with MD simulations followed by MM-PBSA analysis is an attractive approach for modeling protein complexes a priori.     

Free energy perturbation calculations on models of active sites: Applications to adenosine deaminase inhibitors

Free energy perturbation calculations were performed to determine the free energy of binding associated with the presence of perhaps an unusual hydroxyl group in the transition state analog of nebularine, an inhibitor of the enzyme adenosine deaminase. The presence of a single hydroxyl group in this inhibitor has been found to contribute ?9.8 kcal/mol to the free energy of binding, with a 10⁸-fold increase in the binding affinity by the enzyme. In this work, we calculate the difference in solvation free energy for the 1,6-dihydropurine complex versus that of the 6-hydroxyl-1,6-dihydropurine complex to determine if this marked increase in binding affinity is attributed to an unusually hydrophobic hydroxyl group. The calculated ΔG associated for the solvation free energy is ?11.8 kcal/mol. This large change in the solvation free energy suggests that this hydroxyl is instead unusually hydrophilic and that the difference in free energy of interaction for the two inhibitors to the enzyme must be at least ca. 20 kcal/mol. Although the crystal structure for adenosine deaminase is currently not known, we attempt to mimic the nature of the active site by constructing models which simulate the enzyme-inhibitor complex. We present a first attempt at determining the change in free energy of binding for a system in which structural data for the enzyme is incomplete. To do this, we construct what we believe is a minimal model of the binding between adenosine deaminase and an inhibitor. The active site is simulated as a single charged carboxyl group which can form a hydrogen bond with the hydroxyl group of the analog. Two different carboxyl anion models are used. In the first model, the association is modeled between an acetic acid anion and the modified inhibitor. The second model consists of a hydrophobic amino acid pocket with an interior Glu residue in the active site. From these models we calculate the change in free energy of association and the overall change in free energy of binding. We calculate the free energies of interaction both in the absence and presence of water. We conclude from this that the presence of a single suitably placed-CO^?₂ group probably cannot explain the binding effect of the-OH group and that additional interactions will be found in the adenosine deaminase active site.     

Oversampling Free Energy Perturbation Simulation in Determination of the Ligand-Binding Free Energy

Determination of the ligand-binding affinity is an extremely interesting problem. Normally, the free energy perturbation (FEP) method provides an appropriate result. However, it is of great interest to improve the accuracy and precision of this method. In this context, temperature replica exchange molecular dynamics implementation of the FEP computational approach, which we call replica exchange free energy perturbation (REP) was proposed. In particular, during REP simulations, the system can easily escape from being trapped in local minima by exchanging configurations with high temperatures, resulting in significant improvement in the accuracy and precision of protein–ligand binding affinity calculations. The distribution of the decoupling free energy was enlarged, and its mean values were decreased. This results in changes in the magnitude of the calculated binding free energies as well as in alteration in the binding mechanism. Moreover, the REP correlation coefficient with respect to experiment ( R^REP = 0.85 ± 0.15 ) is significantly boosted in comparison with the FEP one ( R^FEP = 0.64 ± 0.30 ). Furthermore, the root-mean-square error (RMSE) of REP is also smaller than FEP, RMSE^REP = 4.28 ± 0.69 versus RMSE^FEP = 5.80 ± 1.11 kcal/mol, respectively. © 2019 Wiley Periodicals, Inc.     

葡萄糖苷酶抑制剂作用机理的分子动力学模拟和自由能计算

含有锍离子的葡萄糖苷酶抑制剂如kotalanol (SK)和它除去磺酸基团后的衍生物(DSK), 是潜在的毒副作用较小的治疗II 型糖尿病的候选药物. α-葡萄糖苷酶抑制活性实验显示, DSK活性比SK略高, 而将二者环上的S原子替换成NH后(分别称为DSN和SN), DSN的活性要比SN高1500倍左右. 本文用分子动力学模拟, 结合自由能计算和自由能分解的方法对上述四个抑制剂的作用机理进行了研究. 研究结果表明活性的巨大差异是由NH基团取代效应和磺酸基团立体效应共同作用的结果, 由于N―C键长比S―C键长短, NH基团取代导致烷基链的翻转, 同时, 磺酸基团限制了链的翻转, 因此改变了抑制剂的结合模式. 计算结果与实验基本一致.本文的研究结果有助于进一步理解含锍离子的葡萄糖苷酶抑制剂的结合机理, 并为设计更有潜力的葡萄糖苷酶抑制剂提供了有价值的信息.     

Design of new secreted phospholipase A<Subscript>2</Subscript> inhibitors based on docking calculations by modifying the pharmacophore segments of the FPL67047XX inhibitor

Docking calculations that allow the estimation of the binding energy of small ligands in the GIIA sPLA₂ active site were used in a structure-based design protocol. Four GIIA sPLA₂ inhibitors co-crystallised with the enzyme, were used for examining the enzyme active site and for testing the FlexX in SYBYL 6.8 molecular docking program to reproduce the crystallographic experimental data. The FPL67047XX inhibitor was chosen as a prototype structure for applying free energy perturbation (FEP) studies. Structural modifications of the initial structure of the FPL67047XX inhibitor (IC₅₀ 0.013 μM) were performed in an effort to optimise the interactions in the GIIA sPLA₂ active site. The structural modifications were based on: (1) the exploration of absolute configuration (i.e. comparison of the binding score of (R)- and (S)-enantiomers); (2) bioisosterism (i.e. replacement of the carboxylate group with the bioisosteric sulphonate and phosphonate groups); (3) insertion of substituents that fit better in the active site. The generated new structures exhibited higher binding energy. Such structures may spark off the interest of medicinal chemists for synthesizing potentially more active GIIA sPLA₂ inhibitors.     

New parameterization approaches of the LIE method to improve free energy calculations of PlmII‐Inhibitors complexes

The standard parameterization of the Linear Interaction Energy (LIE) method has been applied with quite good results to reproduce the experimental absolute binding free energies for several protein–ligand systems. However, we found that this parameterization failed to reproduce the experimental binding free energy of Plasmepsin II (PlmII) in complexes with inhibitors belonging to four dissimilar scaffolds. To overcome this fact, we developed three approaches of LIE, which combine systematic approaches to predict the inhibitor‐specific values of α, β, and γ parameters, to gauge their ability to calculate the absolute binding free energies for these PlmII‐Inhibitor complexes. Specifically: (i) we modified the linear relationship between the weighted nonpolar desolvation ratio (WNDR) and the α parameter, by introducing two models of the β parameter determined by the free energy perturbation (FEP) method in the absence of the constant term γ, and (ii) we developed a new parameterization model to investigate the linear correlation between WNDR and the correction term γ. Using these parameterizations, we were able to reproduce the experimental binding free energy from these systems with mean absolute errors lower than 1.5 kcal/mol. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

Free energy profiles for monomer capture in Grubbs- and SHOP-type olefin polymerization catalysts: a constraint ab initio molecular dynamics study

Density functional theory together with Car-Parrinello ab initio molecular dynamics simulation has been used to investigate the free energy profiles (FEP) of monomer capture in Grubbs- and SHOP-type olefin polymerization catalysts. The FEPs along the reaction coordinates at 300 K were determined directly by a point wise thermodynamic integration technique. Comparison between potential energy profile (PEP) and the FEP has been made. The results show that, for both catalysts, the PEP for the monomer ethylene uptake by the metal center is a typical Morse curve without energy barrier. However, a small barrier (1.8 kcal/mol for Grubbs catalyst and 2.4 kcal/mol for SHOP catalyst) exists on the FEP. The pi complexation energy on the FES at 300 K is higher by 10-12 kcal/mol over that on the PES. The differences between FES and PES are due to entropy contribution. Slow growth simulations on the ethylene capture process show that the ethylene attacks the metal center by an asynchronous mode. This indicates that the forming of the pi-bonding between the metal and ethylene is initiated by electrophilic attack of the metal to one of the ethylene carbons.