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1122 Journal of Chemical Education • Vol. 79 No. 9 September 2002 • JChemEd.chem.wisc.edu

This article describes a summer project designed for theREU (Research Experiences for Undergraduates) program atthe San Diego Supercomputer Center funded by the NationalScience Foundation. The goal is to give an undergraduate hands-on experience in using several modern tools of molecularmodeling for computer-aided drug design. These tools includequantum-mechanical calculation techniques, molecularmodeling and visualization software, a modern Poissonequation solver, and parallel computers. During the six-weekproject, the undergraduate was introduced to recent effortson estimating the binding affinity between proteins andinhibitors, as a guide to the development of new inhibitorsbased on existing drug leads. A common assumption aboutestimating the entropy loss of rotatable bonds of inhibitorsupon their binding to their receptors was pointed out, andthe student was encouraged to evaluate this assumption andprovide quantitative estimates for the entropy loss. Theimportance of hydration effects was emphasized and treatedwith a continuum electrostatics model. The student alsolearned to use statistical mechanical principles to relatemolecular properties to thermodynamic functions. The approachpresented here can be used to study other protein–ligandsystems as new undergraduate projects.

Background

Protein kinases (PK) play important roles in cell signalingand are important targets for pharmaceutical design. Forexample, an approach to treat cancer by blocking blood supplyto cancer cells may be realized by developing drugs that inhibitproangiogenic protein kinases. These protein kinases includethe receptors for the vascular endothelial growth factor (1),the basic fibroblast growth factor (2), the platelet-derivedgrowth factor (3), angiopoietin-1 (4 ), and epidermal growthfactor (5). Several drug candidates designed upon this prin-ciple are currently undergoing clinical trials.

Protein kinase A (PKA) is the first protein kinase forwhich a crystal structure has been determined (6 ). Subse-quently, a co-crystal structure of PKA with balanol, a highlypotent PKA inhibitor derived from the fungus Verticilliumbalanoides, was also determined (7 ). These structures pro-vide a firm structural basis for designing protein kinase in-hibitors. For example, they offer a good starting point forsetting up quantitative calculations to rank the binding af-finity of a drug lead and its derivatives to one or more pro-

tein kinases, to guide the design of novel selective inhibitorsfor synthesis.

This short project touches on one specific aspect of com-putationally estimating the binding affinity of small moleculesto biological targets: predicting the entropy loss of rotatablebonds of inhibitors upon target binding. This entropy lossis sometimes ignored or is modeled by assuming each sp3

hybridized rotatable bond to lose a constant value (e.g., T∆S ≈0.3 kcal/mol [8, 9]) upon binding. In this work, we use thebinding between PKA and balanol as an example to examinewhether hydroxyl groups attached to phenyl rings experiencenon-negligible entropy loss upon protein–ligand complex-ation and provide quantitative estimates for the entropy loss.

We first carried out semiempirical quantum mechanicalcalculations to obtain the potential energy curves of the fourhydroxyl groups of balanol in vacuum. These calculationswere carried out with GAMESS (10), which is freely available.We then illustrated how hydration effects could significantlyalter these curves by carrying out continuum electrostaticscalculations. The potential energy curves for the rotation ofhydroxyl groups in the protein PKA were also estimated.These curves were then used to estimate the entropy loss uponprotein–ligand binding using basic relations derived fromstatistical mechanics.

Methods

The gas-phase potential energy curves were calculatedwith a computationally less demanding semiempirical AM1model, because this project was designed to last for only 4–6weeks. However, the student was given the opportunity totry out a few ab initio calculations using a small 3-21G basisset to gain some insights into the computational resourcesrequired for doing an ab initio versus a semiempirical calcu-lation. The student also ran the ab initio calculations usingdifferent numbers of processors in a Beowulf Linux clusterto appreciate how parallel computing technology can helpsolve complex computational problems. The calculations onbalanol presented problems of SCF convergence when startedwith Hückel guess wave functions, owing to the presence ofsmall HOMO–LUMO gaps. The student learned one trickto solve this problem by using a level-shift parameter toartificially increase the HOMO–LUMO gap to prevent per-sistent swapping between the occupied and virtual orbitalsat the early part of an SCF calculation.

Entropy Loss of Hydroxyl Groups of Balanolupon Binding to Protein Kinase AGergely GidofalviDepartment of Chemistry, San Diego State University, San Diego, CA

Chung F. Wong*Department of Pharmacology and the Howard Hughes Medical Institute, University of California at San Diego,La Jolla, CA 92093-0365

J. Andrew McCammonDepartment of Chemistry and Biochemistry, Department of Pharmacology, and the Howard Hughes Medical Institute,University of California at San Diego, La Jolla, CA

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An energy-refined crystal structure of the PKA–balanolcomplex provided the starting point for the potential energycalculations. Starting from the PKA–balanol crystal structure(7), polar hydrogens were added using CHARMm22 (11).For neutral histidines, the hydrogen was added either at theδ or ε position, depending on which site was more likely toact as a hydrogen-bond donor. The protein–ligand complexwas allowed to relax by 100 steps of conjugate gradientenergy minimization using the CHARMm22 force field (11)and a distance-dependent dielectric of ε = 5R, where R isan interatomic distance. The ligand was then subjected toextensive conjugate gradient energy minimization with theprotein held fixed using the same distance dependent dielectricuntil a gradient norm < 0.001 kcal/mol/ Å was achieved. TheCHARMm22 force field(11) was used for PKA. For balanol,we used the same potential parameters as in the work ofHünenberger et al. (12). For calculating the rotational po-tential energy curves of the hydroxyl groups in vacuum, eachC–O–H group was rotated about the C–O bond in 15°increments. The rotation was done with the QUANTA98software (13) on an SGI workstation to let the student becomefamiliar with a popular commercial modeling softwarepackage. If such software or such a workstation is not available,one can simply use internal coordinates in the input file toGAMESS (10) to specify the proper dihedral angle to use ina calculation.

Continuum electrostatics calculations were carried outusing the UHBD program (14, 15), which calculates the elec-trostatic potential at different points in space by solving thePoisson equation (16 ):

∇ε∇φ = ρ (1)

where ε is the dielectric function, φ is the electrostatic po-tential, and ρ is the charge density. The detailed shape of themolecule was taken into account. The interior and exteriorof the molecule were assigned dielectric constants of 1 and78, respectively. The Poisson equation was solved numeri-cally by a finite-difference scheme using a grid of dimension100 × 100 × 100 and a grid spacing of 0.3 Å. The van derWaals radii used to define the shape of the molecule weretaken from the CHARMm22 force field (11). The atomiccharges of balanol were taken from Hünenberger et al. (12).Once the electrostatic potential is calculated, it can be usedto calculate the hydration energy by

∫ρφdV (2)

where the integral is computed over the grid.The contribution of hydrophobic effects to solvation was

estimated by assuming the hydrophobic energy to be pro-portional to the accessible surface area of the molecule by aconstant of 6 cal/mol/Å2. This constant was estimated fromthe transfer energy of aliphatic hydrocarbons of various sizesfrom the vapor to the aqueous phase (17, 18). The accessiblesurface area was determined by rolling a sphere of 1.4 Å,roughly the radius of a water molecule, over the ligand.

For calculating the potential energy curves of the rotationof the hydroxyl groups of balanol in the protein, models werebuilt in such a way that the ligand was surrounded by proteinatoms lying within 6.5 Å of the hydroxyl group of interest.Solvation effects were ignored in this part of the calculationsfor two major reasons. First, these calculations require more

computational time and are less suitable for a short projectlasting for only a few weeks. Second, it is a reasonable approxi-mation because the ligand, balanol, is buried inside the proteinso that the solvent is largely excluded.

Since only a part of the protein was included in each cal-culation, some peptide linkages needed to be split. The result-ing polypeptide segments were terminated by a (CO)(NH)CH3group at the N terminus and by a CH3(CO)(NH) group atthe C terminus. Amino acid side chains were also reduced toshort aliphatic hydrocarbons whenever the side chains ex-tended beyond 6.5 Å from the hydroxyl group of interest.

Once the potential energy curves were obtained, theywere used to calculate the entropy of the hydroxyl groupsusing the statistical mechanics formula(19):

S = R ln Q +∂ln Q

∂T(3)

where R is the gas constant and T is absolute temperature.The classical partition function Q is used here for simplicity,and is given by

Q = C ∫ e�β� dp dq = C ∫ ∫ e�β KE+PE dp dq =

C ∫ e�βKE dp ∫ e�βPE dq(4)

where � is the classical Hamiltonian, KE is the kinetic energy,PE is the potential energy, and q and p denote, respectively, theatomic coordinates and their conjugate momenta. C = (1/h)N,where h is the Planck’s constant and N is the number of degreesof freedom. The entropy loss of each hydroxyl group uponbinding is given by

∆S = Sbound – S free =

R lnQbound

Q free

+ RT∂ln Qbound

∂T– RT

∂ln Q free

∂T

(5)

where Qbound is the partition function for the ligand in theprotein (bound state) and Qfree is the partition function for theligand in aqueous solution (free state). The integral involvingthe kinetic energy is characteristic of the temperature so thatthe associated terms on both side of the equilibrium

PKA:balanol = PKA + balanol (6)

cancel out in calculating entropy changes. Therefore, for areaction at a constant temperature, the entropy change dependsonly on the terms involving the potential energy, and thekinetic energy terms can be removed. Carrying out the partialdifferentiation and approximating the integral by a sumresults in the following equation:

∆S = R ln

exp �Vibound/RTΣ

i∆θ

exp �Vi free/RTΣ

i∆θ

+

Viboundexp �Vibound

/RT ∆θΣi

T exp Vibound/RTΣ

i

–Vi free

exp �Vi free/RT ∆θΣ

i

T exp Vi free/RTΣ

i

(7)

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In deriving the above formula, we assumed the rotationof a hydroxyl group to be uncoupled to the other degrees offreedom. Therefore, the four hydroxyl groups rotated inde-pendently of each other so that their total entropy loss uponbinding could be approximated as a sum of contributionsfrom each hydroxyl group:

∆Sbinding = ∆SbindingH1 + ∆SbindingH4

+ ∆SbindingH5 + ∆SbindingH6

(8)

Results and Discussion

Figure 1 shows the structure of balanol with atoms labeledaccording to the Protein Data Bank entry 1BX6 (http://www.rcsb.org/pdb/). Figure 2 depicts the potential energy curves forrotating about the dihedral angle C4′–C5′–O5′–H1 for theligand in the gas phase, in aqueous solution, and in the protein.The results for the gas phase indicate that there are two localminima with similar energies and two barriers with similarheights. The two minima occur when the hydroxyl group liesin the same plane as the aromatic ring. Including hydrationeffects does not change the potential energy curve significantly.On the other hand, putting balanol in its binding pocket inPKA removes the degeneracy of the two low-energy con-figurations so that one is more stable than the other. The morestable configuration is possibly stabilized by the formation ofhydrogen bonds between the hydroxyl group and the nearbyprotein backbone in the linker region between the N-terminaland C-terminal lobes of the catalytic domain of PKA, asrevealed by graphical examination of the crystal structure.The energy barriers for conformational transition are also muchhigher in the protein than in vacuum or in aqueous solution.In the protein, this hydroxyl group largely populates onepotential energy well. One would therefore expect a loss inrotational entropy upon binding as the hydroxyl groupchanges from populating two wells to one well. Table 1 showsthat the entropy loss could contribute 0.49–0.60 kcal/molto the binding free energy, depending upon whether thehydration contribution is included in calculating the rota-tional entropy of the unbound ligand.

Figure 3 gives the results for rotation about the C3′′–C4′′–O4′′–H4 dihedral angle. In the gas phase, this hydroxyl grouptakes on one major configuration near 155o. This largely resultsfrom the favorable interaction between the hydroxyl hydrogenwith the nearby carbonyl oxygen O8′′ and possibly with thefurther-away charged carboxylate. However, hydrationchanges this pattern significantly because the high dielectricconstant of water screens the favorable electrostatic interactionand stabilizes the separated polar/charged groups. As a result,the most probable gas-phase configuration becomes less stablethan the configuration with the hydroxyl group lying in thesame plane as the aromatic ring to which it is attached. Anextra shallow potential well also appears at ~230°. Therefore,hydration significantly increases the rotational entropy of thishydroxyl group in aqueous solution. In the protein, the ligandis protected from the solvent and the rotational energy profileresembles that in the gas phase. Therefore, the entropy lossupon binding would be very small if there were no hydrationeffect (see Table 1). However, hydration effects increase thecontribution of the entropy loss to the binding free energyby as much as 0.64 kcal/mol.

Figure 2. Rotational potential energy curves for O5′–H1 in the gasphase, in aqueous solution, and in the protein PKA.

Ligand (g)Ligand (aq)Complex (g)

Angle / deg

Ene

rgy

/ (kc

al/m

ol)

0 100 200 300

0

5

10

15

20

25

Figure 3. Rotational potential energy curves for O4′′–H4 in the gasphase, in aqueous solution, and in the protein PKA.

Angle / deg

Ene

rgy

/ (kc

al/m

ol)

Ligand (g)Ligand (aq)Complex (g)

0 100 200 300

16

14

12

10

8

6

4

2

0

Figure 1. Labeling of atoms, as in the PDB entry 1BX6 (http://www.rcsb.org/pdb/ ), for balanol.

O

O

HO

H

O O

O

O

N

H

H

H

O

O

H

2O15 2O16

2O1A

2O1B

2C15

2C14

2C13

2C12

2C11

2O102C10

C9 C8C5''

C6'' C2''C1''

C2C3C4

C5C6 C7

C7''

C5C4

C3'

C2'C7'

C6'

C1'

O1'

O6'

H5H6

N1'

O4''

O5'

C4C3

H4

H1

HN

+

O−

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JChemEd.chem.wisc.edu • Vol. 79 No. 9 September 2002 • Journal of Chemical Education 1125

Figure 4 illustrates the energy profile for changing theC5′′–C6′′–O6′′–H5 dihedral angle. In the gas phase, a singlewell occurs around 50°. This configuration seems stabilizedby the interaction between the hydroxyl group and theproximal charged carboxylate. Hydration destabilizes thisconfiguration, and the one near 180° in which the hydroxylgroup is nearly coplanar with the aromatic ring becomes morestable. In the protein, the configuration near 200° dominatesthe rotational distribution. Since the free form is also largelydominated by one configuration, the entropy loss of thishydroxyl group upon binding is much smaller than that ofthe two hydroxyl groups previously discussed (Table 1).

The energy profile for rotating about the C9′′–2C10–2O10–H6 dihedral angle is presented in Figure 5. In the gasphase, the lowest energy configuration occurs near 40° and isprobably stabilized by its interaction with the nearby carbonyloxygen O8′′ . There is also a shallow well near 180°, lying onlyabout 2 kcal/mol higher in energy. Adding the hydrationcontribution reverses the relative stability of these configurationsbut the energy profile is relatively flat, varying within a range

Figure 4. Rotational potential energy curves for O6′′–H5 in the gasphase, in aqueous solution, and in the protein PKA.

Ligand (g)Ligand (aq)Complex (g)

Angle / deg

Ene

rgy

/ (kc

al/m

ol)

0 100 200 300

0

2

4

6

8

10

of 4 kcal/mol. One would therefore expect high entropy forthis hydroxyl group in the free form. On the other hand, thishydroxyl group is kept at about 210° upon binding to theprotein. Therefore, a large entropy loss results upon binding,as confirmed by quantitative entropy calculations (Table 1).

Overall, these results indicate that neglecting the rota-tional entropy loss of hydroxyl groups attached to aromaticrings of potential drugs may significantly underestimate theirunfavorable effects on binding affinity. For the balanol ex-ample, the entropy loss of the four hydroxyl groups of balanolcould contribute ~2 kcal/mol to the binding affinity. It is alsonot a good approximation to use a single constant value toestimate the entropy loss of apparently similar functionalgroups as their environment can significantly influence theentropy change. In the PKA–balanol example, the entropyloss from restraining the rotation of different hydroxyl groupscould contribute from almost nothing to ~0.6 kcal/mol tothe binding free energy.

Variations of this project can be incorporated into anundergraduate research program to teach students a numberof computational and theoretical tools for estimating thebinding affinity between potential drugs and their receptors.This project demonstrates the influence of hydration effectson the conformational distribution of molecules, a conceptnot usually covered in undergraduate curricula. This programalso stimulates a student to think seriously about differentapproximations employed in a computational model and de-velops skills in generating good models for solving computer-aided drug-design problems. The approach can also be appliedto study other drug targets and classes of inhibitors. For example,many protein kinases are important drug targets, and pharma-ceutical companies have already identified a number of usefuldrug leads for protein kinases. To adapt this project as a stand-alone laboratory exercise, one may look at just one rather thanfour hydroxyl groups so that the work can be completed inone or two laboratory sessions.

It is notable that all calculations were carried out withinexpensive Pentium II and Pentium III personal computers,except for the generation of different configurations of thehydroxyl groups using QUANTA (13) (which can be avoidedby, for example, using internal coordinates as input toGAMESS [10]). Even the illustration of parallel computingwas achieved by using a homemade cluster constructed fromcommodity computers connected by an inexpensive networkswitch. Therefore, we expect that similar projects can be easilycarried out in many colleges and universities.

Figure 5. Rotational potential energy curves for 2O10–H6 in thegas phase, in aqueous solution, and in the protein PKA.

Angle / deg

Ene

rgy

/ (kc

al/m

ol)

0 100 200 300

0

2

4

6

8

10

12

Ligand (g)Ligand (aq)Complex (g)

NOTE: Using eq 7, at 300 K.

ssoLyportnEdetciderP.1elbaT

negordyHT∆S )lom/lack(/

noitardyHhtiW noitardyHtuohtiW1H � 75.0 � 86.0

4H � 46.0 � 420.0

5H � 53.0 � 61.0

6H � 25.0 � 74.0

latoT � 00.2 � 52.1

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1126 Journal of Chemical Education • Vol. 79 No. 9 September 2002 • JChemEd.chem.wisc.edu

Acknowledgments

This work was supported in part by the NSF, the NIH,and Accelrys Inc. Gergely Gidofalvi is an undergraduate fromSan Diego State University who spent six weeks in the REU(Research Experiences for Undergraduates) program spon-sored by the NSF in the San Diego Supercomputer Centerat the University of California, San Diego.

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