Advances in Binding Free Energies Calculations

7 downloads 0 Views 697KB Size Report
identification and prioritization of potential target molecules prior to synthesis and ...... that molecules having amine groups exhibit following rank order for solvation energies -. (NH2CH3 < NH3 ≈ NH(CH3)2 < N(CH3)3) which is different than.
Send Orders of Reprints at [email protected] 4674

Current Pharmaceutical Design, 2013, 19, 4674-4686

Advances in Binding Free Energies Calculations: QM/MM-Based Free Energy Perturbation Method for Drug Design R.S. Rathore1,2,*, M. Sumakanth1,3, M. Siva Reddy1, P. Reddanna4, Allam Appa Rao5, Mark D. Erion6 and M.R. Reddy1,* 1 Rational Labs Pvt Ltd, Plot # 177, IDA Mallapur, Hyderabad-500 076, India; 2Bioinformatics Infrastructure Facility, School of Life Sciences, University of Hyderabad, Hyderabad 500 046, India; 3RBVRR Womens College of Pharmacy, 3-4-343, Barkatpura, Hyderabad-500 027, India; 4National Institute of Animal Biotechnology, University of Hyderabad Campus, Hyderabad 500 046, India; 5 C.R.Rao Advanced Institute of Mathematics, Statistics and Computer Science, Hyderabad; 6Merck & Co, Inc, 126 E. Lincoln Ave., Rahway, NJ 07065

Abstract: Multiple approaches have been devised and evaluated to computationally estimate binding free energies. Results using a recently developed Quantum Mechanics (QM)/Molecular Mechanics (MM) based Free Energy Perturbation (FEP) method suggest that this method has the potential to provide the most accurate estimation of binding affinities to date. The method treats ligands/inhibitors using QM while using MM for the rest of the system. The method has been applied and validated for a structurally diverse set of fructose 1,6bisphosphatase (FBPase) inhibitors suggesting that the approach has the potential to be used as an integral part of drug discovery for both lead identification lead optimization, where there is a structure available. In addition, this QM/MM-based FEP method was shown to accurately replicate the anomalous hydration behavior exhibited by simple amines and amides suggesting that the method may also prove useful in predicting physical properties of molecules. While the method is about 5-fold more computationally demanding than conventional FEP, it has the potential to be less demanding on the end user since it avoids development of MM force field parameters for novel ligands and thereby eliminates this time-consuming step that often contributes significantly to the inaccuracy of binding affinity predictions using conventional FEP methods. The QM/MM-based FEP method has been extensively tested with respect to important considerations such as the length of the simulation required to obtain satisfactory convergence in the calculated relative solvation and binding free energies for both small and large structural changes between ligands. Future automation of the method and parallelization of the code is expected to enhance the speed and increase its use for drug design and lead optimization.

Keywords: Quantum mechanics, molecular mechanics, free energy perturbation, fructose 1,6-bisphosphatase (FBPase), QM/MM based FEP method. 1. COMPUTER-AIDED DRUG DESIGN (CADD) METHODS 1.1. Computational Approaches for Estimation of Binding Affinity Computer-aided Drug Design (CADD) methodologies aid the identification and prioritization of potential target molecules prior to synthesis and biological testing. The success of computational methods lies in their ability to accurately predict ligand binding affinities to a given receptor. During the last five decades, many CADD approaches have been proposed [1,2] that were intended to qualitatively or quantitatively estimate relative binding affinities [3]. Despite several advances in computational chemistry, accurate prediction of binding affinities between inhibitors to a given drug target remains a formidable challenge. A variety of computational methods were proposed such as molecular docking, molecular mechanics, QSAR (quantitative structure activity relationships) as well as methods of free energy calculations for lead identification and optimization, Table 1. Molecular docking is one of the most commonly employed methods and involves sampling of the ligand and the receptor atoms in the vicinity of the active site [4,5]. These methods attempt to identify prospective hit/lead candidates by using force field-based, empirical and knowledge-based scoring schemes [4]. These methods are quick and allow virtual screening of thousands of small molecules in a reasonable time scale. Unfortunately, apart from insufficient sampling, most of the molecular docking methodologies ignore many inherent factors underlying ligand-receptor interactions such as solvation. Moreover these methods are often inadequate in their treatment of binding site water molecules, entropy, *Address correspondence to these authors at the Rational Labs Pvt Ltd, Plot # 177, IDA Mallapur, Hyderabad-500 076, India; Tel: 91-9849365114; Fax: 91-40-2715458; E-mails: [email protected]; [email protected]; [email protected] 1873-4286/13 $58.00+.00

binding kinetics and induced-fit changes within the receptor and hence provide only an approximate assessment of binding affinities. In recent years, attempts were made to include some of these factors and enhance the accuracy of docking predictions [3,6-10]. Though molecular mechanics methods would be expected to enhance the accuracy of binding affinity predictions, results from a variety of studies have shown only modest success [11], which has been attributed to the large approximations involved in the analysis (e.g. solvent model used, lack of entropic terms, etc.). Over the past years, some improvements have been realized through inclusion of an analysis of the binding conformations of new analogs by Monte Carlo (MC)/Energy Minimization (EM) methodology, and qualitative prediction of relative binding affinities using molecular mechanics calculations to evaluate interaction energies and ligand strain. For example, purine nucleoside phosphorylase (PNP) inhibitors [12-14] were designed and evaluated prior to synthesis using MC/EM techniques to derive the binding conformations and interaction energies that were used in predictions of relative binding affinities. The energy differences between inhibitors were thought to reflect relative binding affinities, since the structures were not highly dissimilar and contained few rotatable bonds, both of which suggested that differences in solvation and entropy would contribute minimally to binding affinity. Although the binding conformation were accurately predicted in this study, interaction energies for some inhibitors proved to be less informative, presumably because of unaccounted factors such as desolvation and entropy. Another example using these techniques [15] was reported for the design of HIV 1 protease inhibitors, which gave qualitative agreement with the experimental results. Ligand-based approaches such as QSAR methods are another class of methods [16-18]. These methods require no knowledge of receptor structure. They are semi-automated, which require manual

© 2013 Bentham Science Publishers

Current Pharmaceutical Design, 2013, Vol. 19, No. 26

Advances in Binding Free Energies Calculations

Table 1.

History of CADD Methods and their Accuracy

Accuracy*

Method

Time period

50 - 55%

Ball & Stick models

1960 - 1980

55 - 65%

Semi-empirical Calculations

1970 - current

65 - 75%

Docking, MM, QSAR

1980 - current

75 - 90%

MM/MM FEP Calculations

1990 - current

90 - 95%

QM/MM FEP Calculations

2004 - current

> 95%

QM FEP Calculations

Future prospects

* an approximate estimate of overall accuracy of the result.

data processing and hence require relatively more physical time. In addition, a host of computational and chemoinformatics methods are also employed that qualitatively assist in identification and optimization of lead compounds [2,19-21]. (Fig. 1) qualitatively illustrates an overall picture of different computational methods with respective accuracy of results and amount of time required 1.2. Approximations Involved in CADD Methods and their Limitations Virtual screening of large compound libraries using these automated methods [26-30] is used to provide potential starting points for lead generation. Most of these methods use algorithms that rely on a multitude of approximations through a simplified treatment of entropy and solvent interactions using molecular mechanics force fields. These approximations are intended to drive calculation speed and compound throughput. There are approximations in theory as well as in the computational methods. The approximation and consequent limitations are readily evident by examination of the equations of thermodynamics used in these calculations [31] Gbind = Hbind – T Sbind = -KBTln(K2/K1) …(1) Hbind = Ebind + P Vbind …(2) Ebind = Ecom – Eaq ...(3) Gbind  Ecom  -KBTln(K2/K1) …(4) where Gbind , Hbind , Sbind , Ebind and Vbind are relative free energy, enthalpy, entropy, energy and volume of bindings between two inhibitors/ligands to a given target, respectively, whereas Ecom and Eaq are the relative energy of complex and solvation. When we ignore the second term (T Sbind) on the right hand side of equation (1), the calculated Gbind , for molecules having rotatable bond(s) would not give accurate predictions. Similarly, for large vs small molecules as well as polar and nonpolar molecules, a method that ignores the second terms (P Vbind , Eaq, respectively), in right hand side of equations (2 & 3) would not produce accurate results. It turns out that while such methods are quite appealing and convenient to apply, all too often these semi-quantitative calculations lead to erroneous conclusions giving rise to compounds that lack the desired potency. Accordingly, there has been significant interest in the development of new methodologies that depend on fewer approximations and thereby could provide a more accurate estimation of binding affinity. 1.3. Towards Accurate Binding-affinity Measurements: Freeenergy Calculations Over the years, methods of free-energy calculations have emerged as a promising strategy [23,25,32-36]. Free energy methods, in principle, do not require major approximations, and are generally considered to be the superior CADD method for predicting

4675

binding affinity. Relative to the methods described earlier, binding affinity calculations using Free Energy Perturbation (FEP) based methods have lower throughput, but the accuracy is higher. Several calculations on relative differences in lipophilicity, ionization, covalent hydration and solvation have demonstrated the power of the FEP-method to replicate experimental findings [32,37,38]. Further, the approach has also shown good accuracy in predicting relative binding free energies for inhibitors of numerous enzymes, including those considered as potential drug targets [23,34,39]. Despite these impressive results, FEP methods are rarely used in the pharmaceutical industry due to several limitations. First, FEP calculations are computationally intensive and these methods are low in throughput. Second, real-life drug design problems involve the calculation of relative binding affinities for inhibitors with a greater degree of structural dissimilarity. Large structural differences result in poor convergence of the calculated results. Third, FEP calculations are limited by the need to develop molecular mechanics force field parameters. Drug candidates often contain new scaffolds that are inadequately represented by these default set of generalized force field parameters. This requires the user to develop and then input parameters into the MM force field prior to FEP calculations. Parameter development is a time-consuming process and often limited by the absence of relevant experimental data. Further, the process is difficult to automate and requires considerable user expertise and judgment. One strategy that eliminates the need of force field parameter development and may enable automation of FEP calculations is to use quantum mechanics to describe the ligand, and molecular mechanics to describe the surrounding environment containing standard structures like protein and water, for which the standard parameters are already available [24,25,35]. The QM/MM- approach has been successfully applied to determine activation free energies and free energy profiles of enzymatic reactions [40,41]. Over the years, we have developed a novel QM/MM method to predict relative solvation and binding free energies [24,25,35,42]. of inhibitors to a given drug target The success of this QM/MM-based FEP method for calculation of relative solvation and binding free energies of a large set of fructose-1,6-bisphosphatase inhibitors indeed demonstrate the potential use of the method for prediction [25,42]. This review covers advances in QM/MM-based free energy methods and the application of these methods for predicting relative binding affinities of inhibitors for Fructose 1,6-bisphosphsatase. 2. APPROACHES OF FREE ENERGY CALCULATIONS Several approaches for free energy calculations have been proposed in the past [23,25,32,33,35,36]. In general, they could be classified into two distinct categories. One approach is based on thermodynamic pathways and includes Free Energy Perturbation (FEP) [23,25,32,33,35], Thermodynamic Integration (TI) [43,44] and Slow Growth (SG) methods [45]. These methods are highly accurate but computationally demanding. The second approach is less rigorous end-point (two-points) methods such as Linear Interaction Energy (LIE) [46-48], Molecular Mechanics-Poisson Boltzmann Surface Area (MM-PBSA)/ Generalized Born Surface Area (MM-GBSA) [49,50] and -dynamics [51]. In contrast to the rigorous FEP and TI approaches, these methods attempt to balance speed and accuracy in order to increase throughput and to calculate free energy differences for a more structurally diverse set of compounds. This review will focus on the FEP method and its potential application to drug discovery, 2.1. The Free Energy Perturbation (FEP): Theoretical Background The statistical perturbation theory arising from the classical work of Zwanzig [52] and its detailed implementation in a molecular dynamics program to compute the free energy is well described

4676 Current Pharmaceutical Design, 2013, Vol. 19, No. 26

Rathore et al.

Docking

MM

QSAR

Conventional FEP

QM/MM FEP

MM1

MM

MM

Classical

QM

Implicit

Yes

Implicit

Yes

Yes

Yes

Yes

Yes

No

Beyond reach

Hours

Hours

Hours

Days

Weeks

Low to medium

Low to medium

Medium

High

Very high

Programs

Glide,Gold, Autodock, Dock, SurflexDoc, FlexX,

Accelrys, Schrodinger, Tripos and several academic &commercial programs

Sybyl/Topomer (COMFA/COMSIA), Phase/FQSAR and Several academic &commercial packages

Amber, Desmond, Gromacs, Amsol MacroModel

Galaxy

References

[4]

[2,22]

[18]

[23]

[24-25]

Ligand Treatment Inclusion of factors Imp for Ligand-receptor binding (e.g. solvation, entropy, etc.) Applicability for Virtual Screening CPU Time (order) Reliability/Quality of results

MM= Molecular Mechanics; QM= Quantum Mechanics

Fig. (1). Representative CADD methods commonly employed in drug discovery (a) on left: graphical illustration, qualitatively comparing various CADD methods with respect to accuracy and time (b) bottom: relative comparison of CADD methods and their capabilities *time refers to CPU and manual data collection and processing

in the literature [23,34,52-54]. For completeness, a very brief description of the FEP method is given here.

coupled Hamiltonian of the system at a given ( 0    1). For a simple linear coupling, H() can be written as,

The total Hamiltonian (H) of a system may be written as the sum of the Hamiltonian of the unperturbed (H0) and the perturbed (H1) systems: H = H 0 + H1 … (5)

H ( ) =  H A + (1  ) H B

The free energy contribution due to the perturbation could be described as,

G1 = 

1 exp( H 1 ) 0 

…(6) where  = 1/kT, k is the Boltzmann constant and T is the absolute temperature. The mean of exp (-H1) is computed over the unperturbed ensemble of the system. To compute G, the difference in free energy between the two solute states, the Hamiltonian for states A and B can be linked by the coupling parameter , either in a linear or non-linear manner such that, H() represents hypothetical

…(7)

In the above equation, HA is the Hamiltonian for the system at state A, and HB is that for state B. For both simple linear and nonlinear coupling of two solute states, when  = 0, H() = HB i.e,, the system is purely in state B and when  = 1, H() = HA at which point the system is purely in state A. During intermediate value of , the solute is a mixture of A and B. This type of coupling ensures a very smooth conversion of two solutes A and B, allowing the system to read just its configuration smoothly as a function of the state. If we divide  into N windows, then at each window i, the solute state is perturbed between i+1 and i-1 states by taking the reference state as H(i). The free energy difference between the two solute states A and B is a simple summation over all windows of [G1(i)] as given by,

Current Pharmaceutical Design, 2013, Vol. 19, No. 26

Advances in Binding Free Energies Calculations N

G = G1 ( i )

…(8)

ri = ri A + (1   )ri B

…(12)

 i =  iA + (1   ) iB

…(13)

i=1

The evaluation of G1 at i+1 and i-1 is a check for possible hysteresis in the calculation and is a measure of the statistical error for the free energy change. 2.2. Free Energy Decoupling Even though the free energy difference is a path independent quantity, it is observed that certain sampling difficulties arise when a polar solute is transferred to a non polar solute accompanied by a large change in molecular volume. Under this circumstance, if one attempts to mutate both the partial charges and the non bonded parameters simultaneously, the solute-solvent energy increases enormously as a consequence of very close approach of some of the solvent molecules. This artificial limitation can be avoided by decoupling the total free energy as a sum of electrostatic and van der Waals contributions. If we denote the energy due to bond, angle and dihedral as Ebad, the electrostatic energy as Eele and the van der Waals interaction energy as Evdw, the total energy of the system can be written as:

Etot = Ebad + Eele + Evdw

…(9) The conversion of state A to B is achieved through an intermediate stage A' such that AA'  B and the corresponding net free energy change is:

G AB = G AA' + G A' B

…(10) Here, the state A' has the charge distribution of B, but maintains the molecular geometry and van der Waals parameters of A. Hence GAA' corresponds to the electrostatic contribution to the free energy difference. The conversion of A to A' is achieved smoothly since the van der Waals parameters are the same for these two states. GA'B is the van der Waals contribution to the free energy, which includes the bond, angle and dihedral contributions as well as the non-bonded interactions. 2.3. QM/MM-based FEP Method The idea of QM/MM was founded in order to provide a partial solution towards eliminating force field parameterization problem [55,56]. QM/MM combines the strength of QM (for accuracy) and MM (for speed). The QM/MM based free energy perturbation method uses the molecular mechanics force field for treating the protein and solvent, quantum mechanics for treating the ligands, and the FEP method for computing free energy differences. The conventional FEP calculation entails coupling the MM parameters according to  and calculating the corresponding MM energies and forces at each . In contrast, the QM-based FEP method uses QM methods to calculate the energies and forces for the solute (ligands) in the system and MM to describe the solvent and macromolecule as well as interactions between solvent/macromolecule and solute. To calculate the QM energy and forces, we implemented a procedure that separated the threaded molecule into two molecules (A and B) at each dynamic step [24,25,35,42,57]. The quantum mechanical energies and forces were then computed and the combined energies and forces recomputed using the -coupling method. The interaction energy between the perturbing system and the surroundings at any value of  is calculated by coupling the charges, radius and well depth of the perturbing system as follows: The partial charge on atom i at any value of  is given by;

qi = qiA + (1   )qiB

…(11)

The radius and well depth of atom i at a given value of  is given by;

4677

On the other hand, the QM forces and energies are calculated for each molecule, A and B, separately and then coupled based on  using eqs. (14) and (15),

f i = f Ai + (1   ) f Bi E

= E

QM 

QM A

+ (1   ) E

…(14)

QM B

…(15) Accordingly, the QM energy and force will correspond to molecule B when  = 0 and to molecule A when  = 1. It should be noted that the energies and forces are calculated at a given  and thus enters into the eqs. (14) and (15) as constant. The total energy for the system is determined using eq. (16), where the term EQM/MM represents the interaction energy involving the MM and QM part of the system. The free energy change [eq. (17)] is decomposed into the free energy contribution from the subsystem treated by QM and the free energy contribution from the surroundings, i.e. the subsystem not treated by QM (non-QM or NQM). Etot = EQM + E MM + EQM / MM ...(16) Gtot = GQM + GNQM …(17) 2.4. Thermodynamic Cycle Perturbation (TCP) Approach Even though the perturbation theory was formulated over five decades ago [52], however, it was not possible to computationally calculate free energy, untill McCammon and coworkers around 1980s applied the concept, commonly known as computer alchemy [53] to computationally measure ligand-binding affinities. The basic strategy is to compute free energy changes by non-physical transformations, which involves transformation of one ligand to a structurally different ligand. This procedure is now routinely employed for obtaining relative binding free energies. As free energy is a state function the free energy difference for the physically traversed path is same as along non-physical path, provided the endpoints match. This forms the foundation of Thermodynamic-Cycle Perturbation (TCP) approach. A schematic diagram of a typical TCP for enzyme-ligand interaction is shown in (Fig. 2). To measure the relative free energy of binding of two substrates to the enzyme, one can estimate it by measuring the free energy G1 and G2, associated with the physical processes, as described via horizontal lines (Fig. 2). However, conducting simulation on such physically relevant pathways is difficult, which involves defining reaction coordinates. The free energy along such coordinates may be slow to converge. QM

Agas ΔGgas

ΔG1

QM

Aaq + FBPaseaq ΔGaq

Solvation (ΔΔGsol)

QM

Bgas

ΔG2

QM

ΔG3

Binding(ΔΔGbind)

Baq + FBPaseaq

ΔG4

QM

Aaq :FBPaseaq ΔGcom

QM

Baq :FBPaseaq

Fig. (2). Thermodynamic cycle for computing solvation and binding free energy differences between FBPase inhibitors. A, B and FBPase stands for ligands and enzyme, respectively.

As the free energy is a state variable, the difference can as calculated as well along the non-physical path (represented by the vertical lines). This calculation is comparatively easier to perform and also tends to converge with much less simulation. In the non-

4678 Current Pharmaceutical Design, 2013, Vol. 19, No. 26

physical process, the molecule A is transformed to B as described earlier, both in solution and within the binding site of an enzyme. The Gaq is the result of making changes A B in solution, while Gcom is the outcome of the same transformation within the active site. Thus the relative free energy of ligand binding can be calculated by either of the pathways. Gbind = G4 - G3 = G com - Gaq … .(18) TCP approach therefore enables calculation of the relative change in binding free energy difference (Gbind) between the two related compounds, by computationally simulating the 'mutation' of one to the other. Similarly, the relative solvation free energy change (Gsol) for two compounds can be computed with the help of the first cycle, shown in (Fig. 2). Gsol = G2 - G1 = Gaq - Ggas … (19) 3. APPLICATION OF QM/MM-BASED FEP METHOD FOR FBPASE INHIBITORS Both conventional and QM/MM-based FEP methods have been applied for prediction of protein-ligand binding affinity for some of the important drug targets, namely, FBPase, HIV Protease and Cox2 [23,58]. Here we discuss the application of QM/MM -based FEP method for FBPase Inhibitors. 3.1. Fructose 1,6-bisphosphatase (FBPase) FBPase (FBPase; EC: 3.1.3.11) is a key regulatory enzyme in the gluconeogenesis pathway, which catalyzes the hydrolysis of fructose 1,6-bisphosphate to fructose 6-phosphate (F6P) and inorganic phosphate [59]. This pathway is shown to be associated with the excessive production of hepatic glucose in patients suffering from diabetes mellitus. Despite several efforts, the discovery of potent FBPase inhibitors proved elusive for over three decades due to hydrophilic nature of both the substrate binding and the allosteric regulatory sites. The latter site binds adenosine monophosphate (AMP), which induces a protein conformational change that results in decreased enzymatic activity. Recently, we have reported a structure-guided drug design strategy that led to the first potent inhibitors of FBPase and demonstrated that these inhibitors result in robust glucose lowering activity in animals of type 2 diabetes [60,61]. 3.2. Crystal structure of Fructose 1,6-bisphosphatase Several crystal structures of FBPase complexes with AMP and its analogs have been determined (http://www.rcsb.org/). The threedimensional structure of the human FBPase-14 complex, solved to 2.0 Å resolution was used for calculating relative binding free energies between all the inhibitors. (for molecular surface representation of the FBPase:14 complex, see (Figs. 4 & 5) in [42]) . 3.3. Applicability of QM/MM-based FEP for Structurally Diverse Inhibitors FEP methods are generally employed for structurally similar compounds. Large mutations often lead to non-convergence of results, which has limited the scope of the method for lead optimizations. With a purpose to enhance the scope of FEP for in silico virtual screening, QM/MM-based FEP method was used for predicting binding affinities of a set of diverse FBPase inhibitors [42]. This validation set consisted of several important mutations (Fig. 3), involving large structural changes as well as polar and non-polar substitutions with high conformational degree of freedom. To our knowledge, this was the first FEP study that reported largest possible mutations with greater degree of conformational freedom. Relative binding free energies were calculated using QM/MM-based FEP, employing AM1 for the gradients and energies (at each MD step) of inhibitors and the HF/6-31G*/ ESP for partial atomic charges of the inhibitors in the beginning of the simulation, and solvent and protein atoms were treated using MM force field. Conventional FEP method was also used (with HF/6-31G*/ESP partial

Rathore et al.

atomic charges) to calculate energy values. The results are shown in Table 2. The calculated relative binding free energies for these analogs using QM/MM-based FEP method suggested that R9-group substitution such as cyclo-hexylethyl group leads to favorable binding affinity due to gain in desolvation penalty and favorable hydrophobic interactions of cyclo-hexylethyl with the hydrophobic residues surrounding the R9-position as compared to other substitutions (Fig. 3, Table 2). These results are consistent with the experimentally measured values. The relative binding free energies were further used to assess the optimal spacer (2 to 4 atoms) using different substitutions at C8 position (Fig. 3). Quite appealing, the QM/MM method was able to reproduce experimental results within ±0.1 kcal.. Consistent with experimental results, the method suggested that 3-atom linker is the best spacer. Entropic changes associated with the ring spacer as well as favorable electrostatic interactions in the binding site give rise to 2,5-furanyl spacer as the most suitable linker. As expected, the non-polar substitutions reduced the desolvation penalty and gained hydrophobic interactions with protein residues leading to favorable binding energy. In this study, simultaneous substitutions were also tested. The combined substitutions of 2,5-furnyl and neoPentyl give rise to much better analog with Gbind of -4.4 kcal/mol (exp. -4.0 kcal/mol). Simultaneous substitution at all the three places namely, pyrimidine ring, R9-position and C8-spacer were performed (mutations 21/22). The calculated results for mutation 22 (Spacer2,5-furanyl ;Pyrimidine X = NC-F; X' = NC-Et; R9 cyclo-hexylethyl) suggested that compound 14 is the best lead compound, in agreement with the experimental data. In this validation study, the QM/MM-based FEP method was shown to reproduce the experimental binding affinities within ±0.5 kcal/mol. A comparison of these results with results generated using conventional FEP suggested that this method might be more accurate. The study also showed that relative to conventional FEP, the computational time was approximately five fold longer. 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. 4. DEPENDENCE OF RESULTS ON MD SIMULATION LENGTH In free energy calculations, the convergence of the results often requires lengthy simulations (especially for large perturbations) and therefore represents another factor that can limit calculation accuracy [62-64]. Several FEP investigations have been carried out in the past using only short MD simulations, typically varying in 50200 ps ranges [34,65-68]. Hence, in drug design efforts, employing FEP methodologies, the establishment of quantitative criteria of simulation length would serve a useful benchmark, to draw a meaningful and unequivocal conclusion. Early on, McCammon and Kollman’s work indicated that such short simulations would yield grossly underestimated values giving rise to unreliable results [69,70]. Further investigations [62,63] on convergence of relative solvation free energies using both conventional- and QM/MM-based FEP methods conclusively established that simulation time, significantly longer than those typically used for FEP calculations are indeed required to attain sufficient accuracy of results. The study suggested that for transformations involving small structural changes, a simulation length of about 1 ns is sufficient to obtain satisfactory convergence. This study also made it clear that a single simulation of longer length generally yields much more consistent result rather than using the average result of two or three simulations. Subsequently, a systematic investigation on the convergence was carried out to quantify the optimal simulation length for binding free energies [64]. Using QM/MM-based

Current Pharmaceutical Design, 2013, Vol. 19, No. 26

Advances in Binding Free Energies Calculations

4679

NH2 O

N

X

[Spacer] X'

N

P OO-

R Compound #

C8-Spacer

Pyrimidine X

X'

R9

IC50 (μM)

1

N(H)CH2

N

N

Ribose

>1000 a

2

N(H)CH2CH 2

N

N

Ribose

118 ± 9

3

N(H)CH2CH 2CH2

N

N

Ribose

>1000 b

4

N(H)CH2CH 2

N

N

H

500 ± 10

5

N(H)CH2

N

N

chexylethyl

~1000

6

N(H)CH2CH 2

N

N

chexylethyl

97 ± 20

7

CH2CH2 CH2

N

N

chexylethyl

26 ± 1

8

CH2OCH2

N

N

chexylethyl

15 ± 3

9

2,5-furanyl

N

N

phenethyl

5±0

10

2,5-furanyl

N

N

chexylethyl

1.2 ± 0.9

11

2,5-furanyl

N

N

iBu

2.2 ± 0.2

12

2,5-furanyl

N

N

neoPentyl

1.1 ± 0.2

13

2,5-furanyl

CH

CH

iBu

1.6 ± 0.1

14

2,5-furanyl

CF

C-Et

iBu

0.09 ± 0.1

a

27% inhibition at 1 mM; b33% inhibition at 1 mM. Abbreviations: chexylethyl, cyclo-hexylethyl, iBu, iso-Butyl, C-Et, C-Ethyl. Reproduced with permission from Springer.

Fig. (3). Structurally diverse FBPase inhibitors considered for FEP calculations and their IC50 values [42].

Table 2.

Relative Binding Free Energies (kcal/mol) of FBPase Inhibitors for Structurally Diverse Mutations [42]

No

G(QM/AM1/MM)a

G(MM)b

Gbind(exp)c

1.3±0.9

1.4±0.9

0.9

Hcyclo-hexylethyl

-1.4±0.9

-1.6±0.9

-1.0

Transformation (S1S2)

1

24d

2

46

d

3

910d

RiboseH

Phenethylcyclo-hexylethyl

-1.1±0.8

-1.4±0.8

-0.8

12

d

N(H)CH2N(H)CH2 CH2

-1.7±0.6

-2.0±0.7

1.3

6

56d

N(H)CH2N(H)CH2 CH2

-1.5±0.6

-1.7±0.6

-1.4

7

57d

N(H)CH2CH2CH 2CH 2

-2.5±0.6

-2.6±0.6

-2.2

8

58

d

N(H)CH2CH2OCH 2

-2.7±0.6

-3.0±0.6

-2.5

9

510d

N(H)CH22,5-furanyl

-4.3±0.7

-4.7±0.7

-4.0

10

67e

N(H)CH2CH 2CH 2CH 2CH2

-1.1±0.5

-1.3±0.5

-0.80

11

e

CH2CH2 CH2CH2OCH2

-0.7±0.5

-0.8±0.6

-0.40

4

78

4680 Current Pharmaceutical Design, 2013, Vol. 19, No. 26

Rathore et al.

(Table 2) Contd…. No

Transformation (S1S2)

G(QM/AM1/MM)a

G(MM)b

Gbind(exp)c

12

810d

CH2OCH2 2,5-furanyl

-1.8±0.7

-1.9±0.7

-1.5

13

1113e

X,X' = NCH

-0.5±0.4

-0.7±0.5

-0.2

14

1114

d

X = NC-F; X' = NC-Et

-2.2±0.6

-2.4±0.6

-1.9

15

1314

d

X = CHC-F; X' = CHC-Et

-2.0±0.6

-2.1±0.6

-1.7

16

17d

N(H)CH2CH 2 CH2CH 2 ; Ribosecyclo-hexylethyl

-2.6±0.9

-2.8±0.9

19.0

6.7

(b) Relative Binding Free Energies between AMP Analogs (kJ/mol) for Simulation Started with Completely Different Configurations [64] System

Length of MD run (ps)a

G(Calc)b

G(Calc)c

G(Exp)d

AMP  1

1248 (run1)

11.9 ± 2.0

12.5 ± 1.9

13.8

1248 (run2)

12.1 ± 2.2

12.8 ± 2.0

1248 (run3)

11.7 ± 2.1

12.9 ± 2.1

1248 (run1)

9.9 ± 2.2

10.4 ± 2.1

1248 (run2)

9.5 ± 2.1

10.7 ± 2.3

1248 (run3)

9.7 ± 2.3

10.3 ± 2.0

1248 (run1)

5.1 ± 2.2

5.5 ± 2.2

1248 (run2)

5.3 ± 2.2

5.6 ± 2.3

1248 (run3)

5.2 ± 2.3

5.4 ± 2.2

AMP  2

AMP  3

11.3

5.9

4682 Current Pharmaceutical Design, 2013, Vol. 19, No. 26

Rathore et al.

(Table 3) Contd…. System

Length of MD run (ps)a

G(Calc)b

G(Calc)c

G(Exp)d

AMP  4

1248 (run1)

16.9 ± 2.0

20.4 ± 2.1

>19.0

1248 (run2)

17.2 ± 2.1

20.1 ± 2.2

1248 (run3)

16.7 ± 2.2

19.9 ± 2.0

1248 (run1)

7.3 ± 2.6

6.5 ± 2.5

1248 (run2)

7.4 ± 2.5

6.6 ± 2.7

1248 (run3)

7.6 ± 2.7

6.3 ± 2.5

AMP  5

6.7

Each simulation started from the same well-equilibrated configurations; the initial configuration for run1 corresponds to calculations reported in Table 3(a); bcalculated using a conventional FEP method and HF/6-31G*/ESP for partial atomic charges; ccalculated using AM1 for gradients and ab initio HF/6-31G*/ESP for partial atomic charges ; dvalues obtained from the experimental data reported in the literature [64]. a

Table 4.

Relative Solvation Free Energies of Simple Amines (kcal/mol) [35] Transformationsa

G(QM)b

G(MM)c

G(E)d

NH3NH2 Me

-0.20 ± 0.4

0.50 ± 0.4

-0.26\

NH2MeNHMe2

0.60 ± 0.4

1.50 ± 0.5

0.27

NHMe2NMe3

1.40 ± 0.5

2.10 ± 0.6

1.06

NH3 NHMe2

0.35 ± 0.6

1.90 ± 0.6

0.01

1.60 ± 0.7

3.60 ± 0.8

1.07

NH3 NMe3 a

b

abbreviations: Me, methyl; calculated using ab initio QM/MM-based FEP method and HF/6-31G**/ESP derived partial atomic charges updated at every window. ccalculated using a conventional FEP method and HF/6-31G**/ESP derived partial atomic charges. dvalues obtained from experimental data [71-74].

Like amines, simple alkyl amides also exhibit a similar anomalous behavior [71-74]. Using ab intio QM/MM based FEP method, the relative hydration free energies for different combinations of simple alkyl amides were also calculated Table 5.

Table 5. Relative Solvation Free Energies of Simple Amides (kcal/mol) [35] Transformationsa

G(QM)b

G(MM)c

G(E)d

AC MAC

-0.25 ± 0.4

1.70 ± 0.4

-0.40

MAC DMAC

1.35 ± 0.4

1.10 ± 0.5

1.53

AC DMAC

1.25 ± 0.6

2.60 ± 0.7

1.13

t-MACc-MAC

-0.30 ± 0.3

-0.60 ± 0.3

~0.0

a abbreviations: AC, acetamide; MAC, N-methylacetamide; DMAC,N,Ndimethylacetamide. bcalculated using ab initio QM/MM-based FEP method and HF/631G**/ESP derived partial atomic charges updated at every window. ccalculated using a conventional FEP method and HF/6-31G**/ESP derived partial atomic charges. d values obtained from expt. data [71-74].

Fig. (5). Relative Solvation Free Energies between Simple Alkyl Amine Analogs

For alkyl amide case, (Table 5 & Fig. 6), the QM/MM-based FEP method was also able to reproduce the experimental results, whereas conventional FEP failed as previously reported by others [68,77]. Closer agreement with experimental findings was also obtained Table 6 with this method for two isomers, trans- and cisN-methylacetamide that surprisingly exhibited similar hydration free energies despite large differences in their permanent dipole

Fig. (6). Relative Solvation Free Energies Between Simple Alkyl Amide Analogs [35].

Current Pharmaceutical Design, 2013, Vol. 19, No. 26

Advances in Binding Free Energies Calculations

moments [71-73]. Additional evidence for the robustness of this method was derived from the good agreement between the calculated and the experimental data for the absolute free energies for NH3 and NH2Me Table 6. Table 6. Solvation Free Energies of Ammonia, Methylamine and Water (kcal/mol) [35] Transformationsa

G(QM)b

G(MM)c

G(E)d

NH3Nothing

-4.10 ± 0.6

-4.05 ± 0.6

-4.30

NH2MeNothing

-4.35 ± 0.7

-3.65 ± 0.7

-4.60

-6.40 ± 0.6

-6.15 ± 0.6

-6.30

H2ONothing a

4683

using QM/MM method [39,64]. The relative binding affinity predicted using conventional FEP method [60,80] failed to agree with the experimental results because the desolvation free energy (2.0 ± 0.5 kcal/mole) was overestimated in conventional method which is consistent with the calculated relative solvation free energies of alkyl amine analogs. Therefore, these results indicate that only the QM/MM-based FEP method is able to predict relative solvation and binding affinities of AMP (I) and methyl substituted 6-NH2 analog (II) very accurately. The method should assist in drug candidates that contain amines and amides, structural moieties that are commonly found in many potential drug candidates.

b

abbreviations: Me, methyl; calculated using ab initio QM/MM-based FEP method and HF/6-31G**/ESP derived partial atomic charges updated at every window. ccalculated using a conventional FEP method and HF/6-31G**/ESP derived partial atomic charges. dvalues obtained from experimental data [71-74].

The ability of the QM/MM-based FEP method to reproduce the anomalous hydration behavior led to further investigations on dependencies of results on partial charges. The conventional FEP method (G(MM)) was compared with the QM/MM-based FEP method wherein the partial atomic charges were either kept the same (G(QM')) which is consistent with the reported conventional FEP results [35] or updated after every window (G(QM)). Separation of the electrostatic and van der Waals contributions provided additional insight. Results for the NH3NH2CH3 transformation were as follows: G(MM) = 0.5 kcal/mol (0.3(ele) + 0.2(vdw)); G(QM') = 0.35 kcal/mol (0.2(ele) + 0.15(vdw)); G(QM) = -0.2 kcal/mol (-0.3(ele) + 0.1(vdw)), and for the NH3N(CH3)3 transformation are: G(MM) = 3.6 kcal/mol (1.0(ele) + 2.6vdw)); G(QM') = 2.65 kcal/mol (0.85(ele) + 1.80(vdw)); G(QM) = 1.60 kcal/mol (0.1(ele) + 1.50(vdw)). In both cases the results calculated using G(QM) gave an excellent agreement with the experimental results (-0.2 vs. -0.26 kcal/mol and 1.6 vs. 1.07 kcal/mol), which suggested that the greater accuracy realized by G(QM) could largely be attributed to differences in the handling of the partial atomic charges and the inaccuracies introduced primarily into the electrostatic contribution to the free energy when the partial atomic charges of the solute are not updated throughout the transformation. Similar trends were observed in calculations involving transformations of simple amides.

The predicted relative binding free energy results (0.7 ± 0.6 kcal/mol) using conventional FEP method indicated that replacing one of the hydrogens participating in hydrogen bonding (Fig. 7) in 6-NH2 of AMP by methyl group is not going to be significantly affected the binding affinity of II to FBPase but the experimental data (1.5 kcal/mol) showed significant change in the binding affinity between these analogs. Instead QM/MM based FEP method predicted that replacing one of the hydrogens in 6-NH2 of AMP by methyl group will results in a weaker inhibitor (1.7± 0.6 kcal/mole), which is consistent with the experiment data (1.5 kcal/mole). A clear understanding of the molecular basis for this loss in inhibitory potency can provide valuable information for the design of the next inhibitor and the optimization of the series [81].

5.1. Relative Solvation and Binding Free Energies of FBPase Inhibitors Once amine and amide related problem is resolved using QM/MM-based FEP method, it was relevant to examine binding free energies for inhibitors involving such groups. Relative solvation and binding free energies between adenosine monophosphate (AMP(I)) and 6-(methylamino) purine riboside monophosphate (II) complexed with FBPase using both conventional [60,80] and QM/MM-based FEP methods [39,64] were computed. In the QM/MM-based FEP method, inhibitors gradients and energies at every MD step were calculated using AM1 and partial atomic charges were calculated [39,64] using HF/6-31G**/ESP method and updated at every window and rest of the system (Solvent + Protein) was treated using MM force field [57]. In the conventional FEP method, inhibitors partial atomic charges were calculated using HF/6-31G**/ESP method [39,64] only in the beginning of the MD simulations and all the system (Solvent+Inhibitor+Protein) was treated using MM force field [57]. The calculated relative solvation and binding free energies between AMP and II using conventional and QM/MM based FEP methods [39,60,64,80] were: 2.0 ± 0.5 kcal/mole, 0.6 ± 0.5 kcal/mol, 0.7± 0.6 kcal/mol and 1.7 ± 0.6 kcal/mol, respectively, and the experimental value is 1.5 kcal/mol, which is consistent only with the relative binding affinity calculated

6. CONCLUSION The key to successful lead optimization in CADD lies in the ability of CADD to accurately predict binding affinity. A novel QM/MM-based FEP method represents the most accurate computational method reported to date. The method has been validated for a diverse set of FBPase (a target for type-2 diabetes). As the results obtained from FEP methods are very sensitive to factors like structural diversity in mutations and simulation time, the method was also extensively tested to assess its applicability. Various calculation criteria such as the minimal simulation time length to obtain satisfactory convergence were established. Amines and amides represent functionality commonly found in drug candidates. Accordingly, the failure of earlier efforts to accurately calculate absolute and relative hydration free energies of simple alkyl amines and amides, raises concerns regarding possible inherent inaccuracies associated with these methods that could limit their ability to computationally discriminate between drug candidates. Standard molecular mechanics force fields predict a near linear decrease in hydration free energy with each successive addition of methyl groups to ammonia or acetamide, whereas a nonadditive relationship is observed experimentally. The anomalous hydration behavior exhibited by simple amines and amides was successfully reproduced using a QM/MM-based free energy pertur-

I

II

Fig. (7). FBPase inhibitors considered for FEP calculations: a) 6-amino purine riboside monophosphate (I), and b) 6-(methylamino) purine riboside monophosphate (II). And also shown are two good hydrogen bonds between 6-amino group of AMP and Thr31 and Val 17 residues of FBPase.

4684 Current Pharmaceutical Design, 2013, Vol. 19, No. 26

bation method. In addition, this method was also tested for predicting relative solvation and binding free energies of 6-amino purine riboside monophosphate and 6-(methylamino) purine riboside monophosphate to FBPase. The method yielded consistent results with the experimental data, which otherwise is not possible using conventional FEP methods. The results suggest that the QM/MM-based FEP method offers several potential advantages over conventional FEP, including greater accuracy and reduced user input. Moreover, since drug candidates often contain functional groups inadequately treated by MM (e.g. simple alkyl amines and amides) or contain new molecular scaffolds that require time-consuming development of MM parameters. The ability of QM/MM-FEP to avoid development of MM parameters could enable future automation of FEP calculations and as a consequence greatly increase the use and impact of FEP calculations in drug discovery It should be noted that although QM/MM-FEP in particular and FEP in general are a superior technique to other less time consuming methods of computational drug design such as docking, MM & QSAR, their low applicability for lead design due to very high CPU requirements remain as potential hurdles for these calculations. In the future, however, these limitations may be addressed by emerging technologies such as cloud computing and/or by parallelization/automation, which would be expected to greatly enhance the use and impact of FEP calculations in drug discovery.

Rathore et al. [12]

[13]

[14]

[15]

[16]

[17] [18]

CONFLICT OF INTEREST The authors confirm that this article content has no conflicts of interest.

[19] [20]

ACKNOWLEDGEMENTS Declared none.

[21]

REFERENCES

[22] [23]

[1]

[2] [3] [4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

Parrill AL, Rami Reddy M, Eds. Rational drug design: novel methodology and practical applications (ACS Symposium) American Chemical Society, 1999. Merz KM, Ringe D, Reynolds CH. Drug design: structure- and ligand-based approaches, Cambridge, University Press, UK 2010. Gilson MK, Zhou HX, Calculation of protein-ligand binding affinities. Ann Rev Biophys Biomol Struct 2007; 36: 21-42. Moitessier N, Englebienne P, Lee D, Lawandi J, Corbeil CR. Towards the development of universal, fast and highly accurate docking/scoring methods: a long way to go. British J Pharmacol 2008; 153: S7–S26. Mobley DL, Dill KA. Binding of small-molecule ligands to proteins: "what you see" is not always "what you get". Structure 2009; 17: 489-98. Sherman W, Day T, Jacobson MP, Friesner RA, Farid R. Novel procedure for modeling ligand/receptor induced fit effects. J Med Chem 2006; 49: 534-54. Friesner RA, Murphy RB, Repasky MP, Frye LL, Greenwood JR, Halgren TA, Sanschagrin PC, Mainz DT. Extra precision glide: docking and scoring incorporating a model of hydrophobic enclosure for proteinligand complexes. J Med Chem 2006; 49: 6177– 96. Huang SY, Zou X. Inclusion of solvation and entropy in the knowledge-based scoring function for proteinligand interactions. J Chem Inf Model 2010; 50: 262-73. Shah F, Gut J, Legac J, Shivakumar D, Sherman W, Rosenthal PJ, Avery MA, Computer-aided drug design of falcipain inhibitors: virtual screening, structure–activity relationships, hydration site thermodynamics, and reactivity analysis. J Chem Inf Model 2012; 52: 696-710. Beuming T, Che Y, Abel R, Kim B, Shanmugasundaram V, Sherman W. Thermodynamic analysis of water molecules at the surface of proteins and applications to binding site prediction and characterization. Proteins 2012; 80: 871-83. Sansom CE, Wu J, Weber IT, Molecular mechanics analysis of inhibitor binding to HIV-1 protease. Protein Engg 1992; 5: 659-67.

[24]

[25]

[26]

[27] [28]

[29]

[30]

[31]

[32]

[33] [34]

[35]

Montgomery JA, Niwas S, Rose JD, Secrist JA, Babu SY, Bugg CE, Erion MD, Guida WC, Ealick SE Structure-based design of inhibitors of purine nucleoside phosphorylase. 1. 9-(Arylmethyl) derivatives of 9-deazaguanine. J Med Chem 1993; 36: 55–69. Erion MD, Niwas S, Rose JD, Ananthan S, Allen M, Secrist JA, Babu YS, Bugg CE, Guida WC, Structure-based design of inhibitors of purine nucleoside phosphorylase. 3. 9-Arylmethyl derivatives of 9-deazaguanine substituted on the arylmethyl group. J Med Chem1993; 36: 3771-3783. Secrist JA, Niwas S, Rose JD, Babu, SY, Bugg, CE, Erion MD, Guida WC, Ealick SE, Montgomery JA, Structure-based design of inhibitors of purine nucleoside phosphorylase. 2. 9-Alicyclic and 9heteroalicyclic derivatives of 9-deazaguanine. J Med Chem 1993; 36: 1847-54. ViswanadhanVN, Rami Redy M, Wlodawer A, Varney MD, Weinstein JN. An approach to rapid estimation of relative binding affinities of enzyme inhibitors: application to peptidomimetic inhibitors of the human immunodeficiency virus type 1 protease. J Med Chem 1996; 39: 705-712. Dudek AZ, Arodz T, Gálvez J. Computational methods in developing quantitative structure-activity relationships (QSAR): a review. Combinatorial Chemistry & High Throughput Screening, 2006; 9: 213-228. Verma J, Khedkar VM, Coutinho EC. 3D-QSAR in drug design-a review. Curr Top Med Chem 2010; 10: 95-115. Kubinyi H, Folkers G, Martin YC. 3D QSAR in drug design. Volume 2, Kluwer Academic Publishers, New York 1998. Gasteiger J, Engel T, Eds. Chemoinformatics, Wiley-VCH, 2010. Khedkar SA, Malde AK, Coutinho EC, Srivastava S. Pharmacophore modeling in drug discovery and development: an overview. Med Chem 2007; 3: 187-97. Yang SY, Pharmacophore modeling and applications in drug discovery: challenges and recent advances. Drug Discov Today 2010; 15: 444-450. Schrodinger Inc. (2012). http://www.schrodinger.com/ Reddy MR, Erion MD, Eds. Free energy calculations in rational drug design; Plenum Press: New York, 2001. Reddy MR, Singh UC, Erion MD. Development of a quantum mechanics-based free-energy perturbation method: use in the calculation of relative solvation free energies. J Am Chem Soc 2004; 126: 6224-25. Reddy MR, Singh UC, Erion MD. Ab initio quantum mechanicsbased free energy perturbation method for calculating relative solvation free energies. J Comput Chem, 2007; 28: 491-94. Shaikh SA, Jain T, Sandhu G, Latha N, Jayaram B. From drug target to leads-sketching a physicochemical pathway for lead molecule design in silico. Curr Pharm Des 2007; 13: 3454–70. Alvarej J, Shoichet B. Virtual screening in drug discovery. CRC press, Taylor & Francis, Boca Raton, FL, 2005. Tropsha A, Golbraikh A. Predictive QSAR modeling workflow, model applicability domains, and virtual screening. Curr Pharm Des 2007; 13: 3494-3504. Cheng T, Li Q, Zhou Z, Wang Y, Bryant SH. Structure-based virtual screening for drug discovery: a problem-centric review. AAPS J. 2012; 14: 133-141. Sukumar N, Das S. Current trends in virtual high throughput screening using ligand-based and structure-based methods. Comb Chem High Throughput Screen 2011; 14: 872-88. Reddy MR, Viswanandhan VN, Erion MD. Rapid estimation of relative binding affinities of enzyme inhibitors. In: Kubinyi H, Folkers G, Martin YC, Eds. Perspectives in Drug Discovery and Design, Vol 9-11. Kluwer publishers, New York, 1998; pp 85–98. Jorgensen WL, Briggs JM, Gao J, A priori calculations of pKa's for organic compounds in water. The pKa of ethane. J Am Chem Soc 1987; 109: 6857–58. Kollman P. Free energy calculations: applications to chemical and biochemical phenomena. Chem Rev 1993; 93: 2395-2417. Reddy MR, Erion MD, Agarwal A. Free energy calculations: use and limitations in predicting ligand binding affinities. In: Lipkowitz KB, Boyd DB, Eds. Reviews in computational chemistry, vol 16. Wiley-VCH Inc., New York, 2000, pp 217–304. Reddy MR, Singh UC, Erion MD. Use of a QM/MM-based FEP method to evaluate the anomalous hydration behavior of simple al-

Current Pharmaceutical Design, 2013, Vol. 19, No. 26

Advances in Binding Free Energies Calculations

[36]

[37]

[38]

[39]

[40]

[41]

[42]

[43]

[44]

[45]

[46]

[47] [48]

[49]

[50]

[51] [52] [53] [54]

[55]

[56] [57] [58]

kyl amines and amides: application to the design of FBPase inhibitors for the treatment of type-2 diabetes. J Am Chem Soc 2011; 133: 8059–61. Chipot C, Pohorille A. Free energy calculations: theory and applications in chemistry and biology (Springer Series in Chemical Physics) 2007. Jorgensen WL, Briggs JM, Contreras ML. Relative partition coefficients for organic solutes from fluid simulations. J Phys Chem 1990; 94: 1683–86. Erion MD, Reddy MR, Calculation of relative hydration free energy differences for heteroaromatic compounds: use in the design of adenosine deaminase and cytidine deaminase inhibitors. J Am Chem Soc, 1998; 120: 3295–3304. Reddy MR, Erion MD. Relative binding affinities of fructose-1,6bisphosphatase inhibitors calculated using a quantum mechanicsbased free energy perturbation method. J Am Chem Soc, 2007; 129: 9296-97. Klähn M, Braun-Sand S, Rosta E, Warshel A. On possible pitfalls in ab initio quantum mechanics/molecular mechanics minimization approaches for studies of enzymatic reactions. J Phys Chem B 2005; 109: 15645-50. Rosta E, Klähn M, Warshel A. Towards accurate ab initio qm/mm calculations of free-energy profiles of enzymatic reactions. J Phys Chem B. 2006; 110: 2934-41. Rathore RS, Reddy RN, Kondapi AK, Reddanna P, Rami Reddy M. Use of quantum mechanics/molecular mechanics-based FEP method for calculating relative binding affinities of FBPase inhibitors for type-2 diabetes. Theo Chem Acc, 2012; 131:1096. Beveridge DL, DiCapua, FM. Free energy via molecular simulation: applications to chemical and biomolecular systems. Ann Rev Biophys Biophysical Chem 1989; 18: 431-92. Pearlman DA, Rao BG. Free energy calculations: methods and developments. In: P. von Raque Schleyer, Ed. Encyclopedia in computational chemistry. Wiley Inter Science, 1998, pp 1036-61. Hu H, Yun RH, Hermans J. Reversibility of free energy simulations: slow growth may have a unique advantage. (with a note on use of Ewald summation). Mol. Simulation, 2002; 28: 67-80. Åqvist J, Medina C, Samuelsson JE. A new method for predicting binding affinity in computer-aided drug design. Protein Engg Des. Selection, 1994; 7: 385-91. Åqvist J, Luzhkov VB, Brandsdal BO. Ligand binding affinities from MD simulations. Acc Chem Res, 2002; 35: 358-65. Hansson T, Åqvist J. Estimation of binding free energies for HIV proteinase inhibitors by molecular dynamics simulations. Protein Engg. Des. Selection, 1995, 8: 1137-44. Srinivasan J, Cheatham TE, III, Cieplak P, Kollman PA, Case DA. Continuum solvent studies of the stability of DNA, RNA, and phosphoramidateDNA helices. J Am Chem Soc 1998; 120: 9401-09. Kollman PA, Massova I, Reyes C, Kuhn B, Huo S, Chong L, Lee M, Lee T, Duan Y, Wang W, Donini O, Cieplak P, Srinivasan J, Case DA, Cheatham TE, 3rd. Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models. Acc Chem Res, 2000, 33: 889-97. Knight JL, Brooks III, CL. -Dynamics free energy simulation methods. J Comput Chem, 2009; 30: 1692–1700. Zwanzig RW. High temperature equation of state by a perturbation method. I. Nonpolar gases. J Chem Phys, 1954; 22: 1420-26. Tembe BL, McCammon JA, Ligand-receptor interactions. Comput Chem, 1984; 8: 281–83. Pearlman D. Free Energy Calculations: Methods for Estimating Ligand Binding Affinities. In: Reddy MR, Erion, MD, Eds. Free Energy Calculations in Rational Drug Design. New York, Kluwer Academic/Plenum. 2001; pp. 9-35. Warshel A, Levitt M. Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. J Mol Biol 1976; 103: 227-249. Senn HM, Thiel W. QM/MM methods for biomolecular systems. Angew Chemie Int Edition 2009; 48: 1198-1229. Galaxy Molecular Modeling Software and AM2000 Macromolecular Simulation package, AM Technologies, San Antonio, TX, 1995. Reddy MR, Erion MD, Nageswara Reddy R, Aparoy P, Rathore RS, Reddanna P. Free energy calculations to estimate ligand-

[59] [60]

[61]

[62]

[63]

[64]

[65]

[66]

[67]

[68] [69]

[70]

[71]

[72] [73]

[74] [75]

[76]

[77]

[78]

[79]

4685

binding affinities in structure-based drug design. In: G. Toth Computational Structure Based Drug Discovery (edited by G. Toth) John Wiley & Sons, NJ, USA, ISBN: 978-0-470-55647-4, pp. 1-51 (Chapter 21), in press, (2013). Granner D, Pilkis S, The genes of hepatic glucose metabolism. J Biol Chem, 1990; 265: 10173-176. Erion MD, Dang Q, Reddy MR, Kasibhatla SR, Huang J, Lipscomb WN, van Poelje, PD, Structure-guided design of AMP mimics that inhibit fructose-1,6-bisphosphatase with high affinity and specificity. J Am Chem Soc 2007, 129: 15480-90. Dang Q, Kasibhatla, S.R., Reddy, K.R., Jiang, T., Reddy, M.R., Potter, S.C., Fujitaki, J.M., van Poelje, P.D., Huang, J., Lipscomb, W.N., Erion, M.D. J. Am. Chem. Soc., 2007, 129: 15491-15502. Discovery of potent and specific fructose-1,6-bisphosphatase inhibitors and a series of orally-bioavailable phosphoramidasesensitive prodrugs for the treatment of type 2 diabetes. Reddy MR, Erion MD. Calculation of relative solvation free energy differences by thermodynamic perturbation method: Dependence of free energy results on simulation length. J Comput Chem 1999; 20: 1018-27. Reddy MR, Erion MD. Relative solvation free energies calculated using an ab initio QM/MM-based free energy perturbation method: dependence of results on simulation length. J Comput Aided Mol Des 2009; 23: 837-43. Rathore RS, Aparoy P, Reddanna P, Kondapi AK, Reddy MR. 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. J Comput Chem 2011; 32: 2097–2103. Jorgensen WL, Ravimohan C. Monte Carlo simulation of differences in free energies of hydration. J Chem Phys 1985; 83: 305054. Bash PA, Singh UC, Brown FK, Langridge R, Kollman PA. Calculation of the relative change in binding free energy of a proteininhibitor complex. Science 1987; 235, 574-6. Reddy MR, Viswanadhan VN, Weinstein JN. Relative differences in the binding free energies of human immunodeficiency virus 1 protease inhibitors: a thermodynamic cycle-perturbation approach. Proc Natl Acad Sci USA 1991; 88: 10287-10291. Rao BG, Singh UC. Hydrophobic hydration: a free energy perturbation study. J Am Chem Soc 1989; 111: 3125-33. Mitchell MJ, McCammon JA. Free energy difference calculations by thermodynamic integration: Difficulties in obtaining a precise value. J Comput Chem 1991; 12: 271-75. Pearlman DA, Kollman PA. The overlooked bond-stretching contribution in free energy perturbation calculations. J Chem Phys 1991; 94: 4532. Jones FM, Arnett EM. Thermodynamics of ionization and solution of aliphatic amines in water. Prog Phys. Org Chem 1974; 11: 263322. Wolfenden R. Interaction of the peptide bond with solvent water: a vapor phase analysis Biochem 1978; 17: 201-4. Radzicka A, Pedersen L, Wolfenden R. Influences of solvent water on protein folding: free energies of solvation of cis and trans peptides are nearly identical. Biochemistry 1988; 27: 4538-41. Ben-Naim A, Marcus Y. Solvation thermodynamics of nonionic solutes. J Chem Phys 1984; 81: 2016-27. Cramer CJ, Truhlar DG. Continuum Solvation Models: Classical and Quantum Mechanical Implementations. Rev Comput Chem 1995; 6: 1-72. Marten B, Kim K, Cortis RA, Friesner R, et al.. New model for calculation of solvation free energies: correction of self-consistent reaction field continuum dielectric theory for short-range hydrogenbonding effects. J Phys Chem 1996; 100: 11775-778. Morgantini PY, Kollman PA. Solvation free energies of amides and amines: disagreement between free energy calculations and experiment. J Am Chem Soc 1995; 117: 6057-63. Rizzo RC, Jorgensen WL. OPLS all-atom model for amines: resolution of the amine hydration problem. J Am Chem Soc 1999; 121: 4827-36. Oostenbrink C, Juchli D, van Gunsteren WF. Amine hydration: a united-atom force-field solution. ChemPhysChem 2005; 6: 1800-4.

4686 Current Pharmaceutical Design, 2013, Vol. 19, No. 26 [80]

Reddy MR, Erion MD. Calculation of relative binding free energy differences for fructose 1,6-bisphosphatase inhibitors using the thermodynamic cycle perturbation approach. J Am Chem Soc 2001; 123: 6246-52.

Received: October 22, 2012

Accepted: December 17, 2012

Rathore et al. [81]

Erion MD, van Poelje PD, Dang Q, Kasibhatla SR, Potter SC, Reddy MR, Reddy KR, Jiang T, Lipscomb WN. MB06322 (CS917): A potent and selective inhibitor of fructose 1,6-bisphosphatase for controlling gluconeogenesis in type 2 diabetes. Proc Natl Acad Sci USA 2005; 102: 7970-75.