free energy perturbation and molecular dynamics calculations of copper binding to azurin

Free Energy Perturbation and Molecular DynamicsCalculations of Copper Binding to Azurin

MATTEO PAPPALARDO, DANILO MILARDI, DOMENICO M. GRASSO, CARMELO LA ROSADipartimento di Scienze Chimiche, Universita’ di Catania, V.le A. Doria 6, 95125 Catania, Italy

Received 13 July 2002; Accepted 3 September 2002

Abstract: Free energy perturbation/molecular dynamics simulations have been carried out on copper/azurin systemscalculating the binding affinities of copper (II) ion to azurin either in the native or in the unfolded state. In order to testthe validity of the strategy adopted for the calculations and to establish what force field is suitable for these kinds ofcalculations, three different force fields, AMBER, CVFF, and CFF, have been alternatively used for the calculations andthe results have been compared with experimental data obtained by spectroscopic titrations of copper (II)/azurinsolutions and denaturation experiments. Our findings have pointed out that only CFF gives satisfactory results, thusproviding a reliable tool for copper binding simulations in copper protein.

© 2003 Wiley Periodicals, Inc. J Comput Chem 24: 779–785, 2003

Key words: CFF; metallo-protein; metal binding; molecular dynamics; thermodynamics; free energy perturbation

Introduction

An important challenge in protein engineering is the creation ormodification of metal sites in proteins.1,2 Properties that one mightwish to manipulate range from metal binding strength and metalsite stability to redox potential, enzymatic activity, and thermody-namic stability. With reference to this last aspect the heat-induceddenaturation of proteins provides information about the drivingforce of the spontaneous folding of a protein into its native three-dimensional structure. In metallo-proteins, the understanding ofthe contribution of the metal ion to the thermodynamic stability ofthe protein is an additional requirement for elucidating all thefeatures of the folding/unfolding process. The commonly adoptedstrategy for these investigations is the comparison of the thermo-dynamic stability of the apo protein with respect to the holoform.3–7 In this strategy two factors can contribute to the observedchanges in protein stability: the effects of metal insertion/removalin the native (N) and in the unfolded (U), respectively. It is difficultto assess which of these two factors is dominant in stabilizing theprotein because they originate from different states, and experi-mental stability studies measure only relative free energy differ-ences between the N and U states.

In order to clear up this point it is necessary to measure thebinding energy of the metal to the protein, either in the N or in theU state. Sometimes this parameter is not experimentally accessi-ble, and, in these cases, it may be useful to use computer-assistedmolecular modeling. In the last few years the increased computa-tional resources and the improvements in the parameterization of

the simulation engines have allowed the build up of reliablecomputational methods to address with a reasonable accuracy theproblem of metal binding to proteins. The most frequent way ofestimating the energetics of this process involves the use of forcefield (FF) molecular dynamics (MD) simulations coupled with freeenergy perturbation (FEP) theory.8

The present work focuses on the metal binding properties of theblue copper protein azurin from Pseudomonas Aeruginosa, show-ing that computer-simulations of metal binding to protein can besuccessfully applied. In order to assess the influence of the differ-ent force fields on the validity of results, the binding free energy ofcopper to the N protein was calculated by means of three differentforce fields: AMBER, CVFF (consistent-valence force field), andCFF (consistent force field). In order to adequately compare the-oretical data with experimental data we also calculated the bindingfree energy of copper to the U state of the protein, and copperhydration energy, as discussed in the text.

It has been shown that only CFF gives results that are highlycomparable with experimental data. The calculated free energies ofbinding correlate well with the differences in experimental ther-modynamic stability relative to the unfolding process for holo andapo azurin.9

Correspondence to: C. La Rosa; e-mail: [email protected]

Contract/grant sponsor: MURST (Ministero dell’ Universita e dellaRicerca Scientifica e Tecnologica)

Contract/grant sponsor: Universita degli Studi di Catania

© 2003 Wiley Periodicals, Inc.

Computational Methods

Force Fields

Three different force fields, AMBER, CVFF, and CFF were alter-natively tested. CVFF and CFF are licensed by MSI-MolecularSimulations, Inc. All calculations were carried out by using themodule DISCOVER95 and DISCOVER3 in the INSIGHT II soft-ware environment (MSI-Molecular Simulations, Inc.) on an SGIOCTANE R12000 workstation.

The standard AMBER force field10,11 is parameterized to smallorganic constituents of proteins and nucleic acids. Only experi-mental data were used in parameterization.

CVFF force field is a generalized valence force field.12,14

Parameters are provided for amino acids, water, and a variety ofother functional groups. CVFF also has the ability to use automaticparameters (automatic assignment of values for missing parame-ters) when no explicit parameters are present.

In CFF intramolecular parameters are based on the energies andenergy derivatives computed by ab initio quantum mechanicalprocedures for a series of model compounds. CFF uses quantumcomputations in the Hartree-Fock approximation with the 6-31G*basis set to expand the wave functions.15,16 Energies, energy first

derivatives (gradients), and their second derivatives (Hessians)were computed for the equilibrium molecular structures, and for aset of distorted structures. The distorted molecular structures weregenerated by randomly deforming all the internal coordinates, aswell as by systematically rotating about individual bonds. Thesequantum observables were fitted to the energy expression to obtainthe class II parameters.17,18 Many of the atomic partial chargeswere also determined quantum mechanically.19 The remainingCFF force field intermolecular and nonbond parameters werecomputed by fitting to experimental crystal lattice constants andsublimation energies of crystals.13,14,20 The internal energy of themolecule was expressed in terms of internal coordinates such asbond lengths, bond angles, and dihedral angles. For class II forcefields this set of descriptors was greatly expanded by includingcross terms, that is, the interactions between bond lengths andangles, between pairs of angles, and so forth. CFF contains, in all,12 types of energy terms: bond stretching, valence angle bending,valence dihedral angles, out-of-plane deformation, and eight crossterms. The cross terms extend the accuracy and range of applica-tion of the force field by including the effect of neighboring atomicpositions on each of the bond lengths, valence angles, and dihedralangles. The general expression for the energy in CFF is reportedbelow:

ECFF � Sb �b

�K2�b � b0�2 � K3�b � b0�

3 � K4�b � b0�4��S� �

�

�H2�� 0�2 � H3�� 0�

3 � H4�� 0�4� � S� �

�

[V1�1 � cos�� 10��

� [V2[1 � cos�2� � �20� � �V3�1 � cos�3� � �3

0�� S� ��

K��2 � Sc ��b

�b1

Fbb1�b � b0��b1 � b0� � ��

��1

F��1�� 0��1 � �0�

� �b

��

Fb��b � b0��1 � �0� � �b

��

�b � b0��V1cos � � V2cos 2� � V3cos 3�� b1

��

�b1 � b0��V1cos � � V2cos 2� � V3cos 3��

� ��

��

��1 � �0��V1cos � � V2cos 2� � V3cos 3��

��

��1

K��1cos �(� � �0)(�1 � �0

1)� � �i�j

qiqj

�rij� �

i�j�Aij

rij9 �

Bij

rij6 � (1)

All the terms with 0 subscript represent a reference state withminimal energy. The terms b, �, and �, represent a bond length,a valence bond angle, and a dihedral or torsion angle, respectively.b and b� are neighboring bond pairs sharing a common atom orbond, � and �1 are adjacent valence angles sharing one or twocommon atoms, q represents the charge and � the dielectric con-stant, and A and B are van der Waals parameters. Terms Sc, Sb,S�, S�, are experimentally obtained corrective terms.21,22

In CFF, copper (II) is parametrized only for nonbonding forces.In order to achieve an optimal description of the copper bond withligand, an additional harmonic restraint was considered by thefollowing equation:

E � K�b � b0�2 (2)

where K represents the harmonic constant, and b and b0 representthe distance between the copper ion and residues. An averagevalue of 25 kcal/mol/Å2 was used for each copper/ligand bond onthe basis of experimental data from Raman measurements.23

FEP Calculations

The common features of the methods used to calculate the free energydifferences between two systems is that a path has to be defined thatconnects the two systems in the configurational space. In doing this acoupling parameter � is introduced that varies from 0 to 1 and slowlytransforms the initial system “0” to the final system “1.” Successfulresults in these calculations depend on the correct choice of themutation path in order to keep as low as possible (maximum 2 KBT)the energy differences between a state and the following one,24 inorder to avoid conformational modification in protein structure. In our

780 Pappalardo et al. • Vol. 24, No. 6 • Journal of Computational Chemistry

case, the mutation path from holo azurin (0) to the apo form (1) wasdefined by using the coupling parameter � � 0.015 (66 simulationwindows) to smoothly convert the potential energy of the holo forminto that of the apo form. Every mutation step consisted of 20 ps ofequilibration and 20 ps of sampling time. The energy in the transfor-mation path is found according to the equation proposed by Mezei andBeveridge:25

E�� 1 � ��kE0 � �kE1 (3)

where E0 and E1, respectively, represent the potential energies ofthe initial and final structures. The free energy calculation wasexecuted using the finite difference thermodynamic integrationMezei algorithm25 according to the following equation:

A � �i�1

n1

A��i, �i�1 � ��i

� RT ��0

1

ln�exp�E�� E��

RT ��

(4)

where the quantity in angle brackets is the statistical average overthe configurational space sampled by the MD simulation of thestage �. Strictly speaking, because all the simulations were per-formed in a NVT ensemble, only the Helmholtz free energydifferences (A) are accessible; however, because volumechanges are negligible, the Helmholtz free energy differences(A) can be approximated to the Gibbs free energy differences(G).

Computational Details

N State

The N protein system was prepared by using the X-ray structure at1.9 Å resolution26 (PDB code: 4AZU) as the starting configura-tion. The PDB file contains the coordinates of four azurin subunits,324 water molecules, and one NO3

ion. Of these, three proteinsubunits, water, and the nitrate ion were deleted in order to obtaina file containing only one protein molecule (975 atoms plus cop-per). Protons were added taking into account the ionization equi-libria of the residues at neutral pH at which each simulation wasperformed. N azurin was immersed in a water sphere consisting ofeight layers corresponding to 2000 molecules of solvent and wasneutralized by adding properly Na� and Cl counterions. The finalnumber of atoms was 7964. This model represents a system witha density of about 1.0 g/cm3.

In N azurin the copper ion is bound to the protein by means ofthree planar ligands (Fig. 1a; His46, His117, Cys112) and twoaxial ligands (Met121 and Gly45). Nonbonding interactions wereconsidered by applying an atom-based method with a cutoff of 9 Åfor van der Waals interactions and of 14 Å for Coulombic withelectrostatic forces. The integration timestep was 0.5 fs for all

calculations. The temperature was maintained constant at T � 298K by using the Nose-Hoover27–30 method for each simulation. Thissystem was firstly optimized by an “in vacuum” minimization step,using the Polak-Ribiere algorithm, aimed at the elimination ofhighly strained structures with overlapping atoms, until the energydifference between two successive simulation steps was less than10 kcal/mol. Subsequently, a 200 ps molecular dynamics simula-tion in water was performed to equilibrate the system using theVelocity Verlet algorithm.31

In order to establish to what extent the accuracy of the forcefield adopted affects the validity of the results, calculation on theN azurin only was performed using, alternatively, AMBER,CVFF, and CFF. The calculus was focused on the atoms within asphere centered in the copper ion with a radius of 8 Å (the activesite zone). All the atoms outside the active site zone were “frozen”in fixed positions. Increasing the size of the active site zone, inspite of a noticeable increase of the computational demand, did notmodify the results significantly (data not shown). After 200 ps ofequilibration time, the holo protein was gradually mutated to the apoform by turning off all the interactions of the ion with its environment.Firstly, the value of force constants K were smoothly decreasedstepwise from Kharmonic � 25 to 0 (kcal/mol � Å2), and, secondly, thecharge of copper was decreased from �2 to 0. Every stage consistedof 33 intermediate steps of 40 ps of simulation each.

All simulation was performed forward and backward, in orderto determine the statistical error of the method.

U State

In order to adequately represent the U state of azurin a shortpeptide of 12 amino acids (from 111th to 123rd of azurin sequence),according to a strategy already successfully adopted in a previousarticle,32,33 was adopted as a model (Fig. 1b). It is in fact knownthat upon azurin unfolding copper remains bound to the openpolypeptide chain in a trigonal arrangement by Cys112, His117,and Met 121.33 Similarly to the N state, harmonic restraints be-tween three residues and copper were applied, with the sameharmonic constant than in N state. Minimization and equilibrationsteps were performed as previously described for the N state. Thecalculations relative to the U state were performed as described forthe N one, but in this case the water solvent was explicitlyconsidered in all MD/FEP simulations due to the strong dipoleinteraction between the copper ion and solvent. No additionalrestraints were applied during FEP calculations.

Results and Discussion

In order to estimate the binding free energy of copper to azurin inaqueous solution it is important to specify accurately the modeladopted for calculations. In our description we transform the holointo apo-azurin by switching off both electrostatic and bondinginteractions between copper and its environment. Because at theend of this mutation the copper ion does not interact with anygroup, this mutation is equivalent to transferring the copper fromprotein to vacuum. Thus, if we want to compare the outcome of the

FEP and MD Calculations of Copper Binding to Azurin 781

theoretical calculations with the spectroscopic experiments wehave to take into account the free energy of hydration of copper bytransferring the ion from the vacuum to water. The calculation of

copper hydration free energy was performed by using the abovedefined parameters adopted for the other cases. Let us consider thefollowing chemical reaction:

Figure 1. (a) Azurin WT (PDB code 4AZU) active site. Bipyramidal trigonalgeometry of the metal complex is highlighted with gray lines. (b) The unfolded statemodel used in the calculations reported in the present article. The pictures wereobtained by using the VMD V.1.6 software package.37


Cu-Azu(aqueous)�� 7 Cu(vacuum)

��

� apo-Azu(aqueous)

Ga � 1)

Cu(vacuum)�� 7 Cu(aqueous)

�� Gb � 2)

Cu-Azu(aqueous)�� 7 Cu(aqueous)

��

� apo-Azu(aqueous)

Gbinding � Ga � Gb 3)

For N and U azurin, FEP/MD simulations give Ga � 2289 kJmol1 and Ga � 2253 kJ mol1, respectively. The hydration ofcopper (reaction 2) gives a value of Gb � 2162 kJ mol1.Thus, by subtracting reaction (2) from reaction (1) we obtain theGibbs free energy of binding of copper to protein of 127 � 1 kJmol1 and 91 � 1 kJ mol1 for N and U state, respectively.

In Table 1 we report the G of copper binding obtainedexperimentally9 and theoretically by FEP calculations for N and Uazurin. The uncertainty range in FEP simulations was determinedas the difference between the forward and reverse calculation, asexplained elsewhere.24 It can be noted that results obtained byAMBER and CVFF overestimate remarkably the experimentaldata, while CFF results are in good agreement with experiments.The reason for this is the more accurate parameterization of thenonbond interaction of the copper ion in CFF that it is lacking inboth CVFF and AMBER. For this reason only CFF was used forall other simulations. With reference to the N state, CFF underes-timates by 10 kJ mol1 the experimental value. This differencemight be ascribed to an internal proton rearrangement of the activesite when copper is removed. We have to remind the reader at thispoint that the free energies of stabilization for complex as forma-tion events in aqueous solution are difference of energies betweensolute-solute and solute-solvent ensembles. Given that the bindingfree energies are usually small differences between large absolutevalues, very accurate details are needed about these processes fora complete description of the phenomenon. In particular, the roleplayed by the solvent in the N and in the U state should beaccurately considered.

Unfortunately, data about protonation equilibria or rearrangementfor the active site in N azurin are not available because protonexchanges are generally studied in aqueous solutions, and the activesite for the N protein is inserted in a hydrocarbon environment.34

The calculated copper/azurin binding free energy in the U state isunderestimated by about 8 kJ mol1 (Table 1). In this case, the copperion is embedded in an aqueous environment, therefore it is possible toadopt the ionization equilibrium data relative to the protonation ofresidues to estimate their contribution to the free energy due to copperremoval. The protonation free energies in water of the three copper

ligands at T � 25�C and pH � 7 are 0.64 for the two histidines and8.4 kJ mol1 for cysteine.35 If we bear in mind that the free energyof deprotonation of water is approximately 7.5 kJ mol1 and that atpH � 7, 50% of histidines are protonated, then the energetic contri-bution of rearrangement of the active site as a consequence of coppershould be approximately 1.5 kJ mol1. Taking into account theestimated uncertainty of calculations, calculated and experimentaldata are in good agreement.

In principle, the two parts to understanding the structural basis ofmetal-assisted protein n its competing partner, that is, the unfoldedstate. To do this, it is essential to calculate the binding affinity ofcopper to native and unfolded states, as schematically represented inFigure 2, in which G1 and G3 are the free energy differencesbetween N and U states for holo and apo azurin, respectively. G1 �59 � 4 kJ/mol and G3 � 35 � 3 kJ/mol were measured in aprevious article by thermal denaturation experiments.9 In the samearticle G2 and G4 were measured by spectroscopic protein/metaltitration experiments, and in the present article they were calculatedby means of FEP/MD calculations. According to the thermodynamiccycle reported in Figure 2:

G4 � G2 � G3 � G1 (5)

DSC experiments have pointed out that G3 G1 � 24 � 7kJ mol1 at 25°C; on the other hand, G4 G2 calculated fromthe theoretical simulations carried out in the present article, isequal to 36 � 2.2 kJ mol1. Moreover, UV titration experimentshave given a value of 38 � 2.8 kJ mol1 for the same free energydifference.

These differences on the two sides of eq. (5) would suggest thatcopper contribution to azurin stability is not additive. An attemptto explain this Gibbs free energy difference one must take intoaccount that DSC data refers to the energy required to obtainglobal protein unfolding, whereas the binding experiment providesthe energy needed to remove the copper ion from the active site.This last contribution is 14 kJ mol1 higher than the first one.9

This result suggests that the copper insertion into apo proteinrequires an energetic cost of 14 kJ mol1 for the conformationalreorganization of the polypeptide chain. This interpretation is inagreement with the results obtained by other computations,9 whichhave clearly demonstrated that the difference in the stability ofnative holo and apo azurin is about 14 kJ mol1.36

Conclusively, if we add to the right hand side of eq. (5) this“extra” contribution of 14 kJ mol1 the agreement between thetheoretical and experimental data is acceptable.

Conclusions

In the present article the CVFF, AMBER, and CFF force fieldshave been alternatively used to perform FEP/MD simulations onazurin with the aim of determining the binding free energy ofcopper to the protein either in the N or in the denatured state. Thecomparison of the calculated values with the experimental ones,evaluated on the basis of spectroscopic and DSC studies, pointedout the effectiveness of the CFF and of the methodology adopted

Table 1. Binding Gibbs Free Energy of Copper to Native andUnfolded Azurin in Water.

Azurin

Gbinding (kJ mol1)

ExperimentalAMBER CVFF CFF

Native 200.0 � 1.6 278 � 12 127.0 � 1 137.0 � 3Unfolded — — 91.0 � 1.2 99.3 � 2.0


for calculation. The whole of the results have clearly shown thatthe binding of copper to the protein stabilizes remarkably the Nstate with respect to the U one. The calculation strategy proposedin the present article could be a suitable methodology to investi-gate the metal-assisted protein stabilization for a wide variety ofproteins, and it can be particularly useful when these values are notexperimentally accessible.

Acknowledgments

This work has been financially supported by MURST (Ministerodell’ Universita e della Ricerca Scientifica e Tecnologica) (ex 40%1999). We thank Prof. U. Ryde for helpful discussions during thepreparation of calculation strategies.

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Figure 2. Thermodynamic cycle showing the linkage between copper/azurin binding and the thermody-namic stability of the holo and apo forms. The experimentally accessible quantities are: the unfolding freeenergy of the holo protein (G1), the binding free energy of copper to the native protein (G4), theunfolding free energy of the apo protein (G3), and the binding free energy of copper to the denaturedprotein (G2). The theoretically accessible quantities are G4 and G2.


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free energy perturbation and molecular dynamics calculations of copper binding to azurin

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