Energetic analysis of binding of progesterone and 5ß-androstane-3,17-dione to anti-progesterone antibody DB3 using molecular dynamics and free energy calculations

Mikael Peräkylä,1 and Nana Nordman

Department of Chemistry, University of Kuopio, PO Box 1627, FIN-70211 Kuopio, Finland


    Abstract
 Top
 Abstract
 Introduction
 Methods
 Results and discussion
 References
 
Molecular dynamics simulations and molecular mechanics–Poisson–Boltzmann surface area (MM-PBSA) free energy calculations were used to study the energetics of the binding of progesterone (PRG) and 5ß-androstane-3,17-dione (5AD) to anti-PRG antibody DB3. Although the two steroids bind to DB3 in different orientations, their binding affinities are of the same magnitude, 1 nM for PRG and 8 nM for 5AD. The calculated relative binding free energy of the steroids, 8.8 kJ/mol, is in fair agreement with the experimental energy, 5.4 kJ/mol. In addition, computational alanine scanning was applied to study the role of selected amino acid residues of the ligand-binding site on the steroid cross-reactivity. The electrostatic and van der Waals components of the total binding free energies were found to favour more the binding of PRG, whereas solvation energies were more favourable for the binding of 5AD. The differences in the free energy components are due to the binding of the A rings of the steroids to different binding pockets: PRG is bound to a pocket in which electrostatic antibody–steroid interactions are dominating, whereas 5AD is bound to a pocket in which van der Waals and hydrophobic interactions dominate.

Keywords: antibody/free energy/molecular dynamics/mutation/steroid


    Introduction
 Top
 Abstract
 Introduction
 Methods
 Results and discussion
 References
 
The immune system's ability to produce antibodies against foreign antigens has been exploited to obtain receptors for a wide range of chemical and biochemical applications (Liu and Schultz, 1999Go). For example, selective and efficient antibody catalysts have been produced for a wide range of chemical transformations (Schultz and Lerner, 1995Go; Sinha et al., 1998Go). In order to be of practical value the antibodies generated have to bind the desired antigen with high enough affinity and specificity. In addition to various methods of accelerated and directed evolution, which in several ways mimic the natural evolution in biological systems, rational design offers means to generate antibodies with improved properties (Arnold and Volkov, 1999Go; Altamirano et al., 2000Go). However, rational design of antibodies, and proteins in general, has proven to be less efficient than the evolution-mimicking approaches (Altamirano et al., 2000Go). This is at least partly due to difficulties in designing stable proteins with desired properties and quantitatively predicting the properties of an engineered protein. However, a lot of progress has been made recently in this area (Hellinge, 1998Go; Hill et al., 2000Go; Mayo and Gordon, 2000Go). Understanding the factors determining the binding of ligands to protein receptors at the atomic level is a prerequisite to successful rational design.

Characterization of antibodies by protein X-ray crystallography and other biochemical methods has provided a lot of data on structure and function of antibodies (Arevalo et al., 1994Go; Wilson and Stanfield, 1994Go; Charbonnier et al., 1997Go; Gigant et al., 1997Go; Wedemayer et al., 1997Go). The structures of several steroid-binding antibodies have been determined by X-ray crystallography, providing an atomic level understanding of steroid binding (Arevalo et al., 1994Go; Jeffrey et al., 1993Go; Trinh et al., 1997Go). The X-ray structure of the monoclonal anti-progesterone (anti-PRG) antibody DB3, which is investigated in this study, in an unliganded form and complexed with PRG and several PRG-like steroids have been determined (Arevalo et al, 1993aGo,bGo,1994Go). DB3 binds PRG with high affinity (Ka = 1x109 M) and cross-reacts with several PRG-like steroids with nanomolar affinities (Arevalo et al., 1993bGo).

The two steroids studied, PRG and 5ß-androstane-3,17-dione (5AD, Figure 1Go), are of quite different shape. PRG is a flat molecule with an angle of 25° between the planes defined by the ring carbon atoms of the steroid A ring and B, C and D rings. In the case of 5AD the corresponding angle is 110°. Furthermore, the X-ray structures revealed that the two molecules bind to the ligand-binding site of DB3 in different orientations: the D ring of both molecules binds to the same binding pocket but the faces of the steroids point in the opposite directions (Figures 2 and 3GoGo). In spite of these differences, the binding affinity of PRG (1 nM) is close to that of 5AD (8 nM, Arevalo et al., 1993bGo).



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Fig. 1. Structures and numbering of (a) PRG and (b) 5AD.

 


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Fig. 2. Stereo presentation of the ligand-binding site of the antibody–PRG complex.

 


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Fig. 3. Stereo presentation of the ligand-binding site of the antibody–5AD complex.

 
In this work we have used the molecular mechanics–Poisson–Boltzmann surface area (MM-PBSA) method (Jayaram et al., 1998Go; Vorobjev et al., 1998Go; Kollman et al., 2000Go) to calculate the free energies for the binding of PRG and 5AD to the anti-PRG antibody DB3. In the MM-PBSA method the binding free energy is calculated as a sum of molecular mechanical energies and solvation free energies of several ‘snapshot’ structures taken from an molecular dynamics (MD) simulation with explicit water. The MM-PBSA method has been applied to investigate the structure and energy of proteins (Lee et al., 2000Go) and DNA (Srinivasan et al., 1998Go) and protein–RNA (Reyes and Kollman, 2000aGo,bGo) and protein–ligand associations (Kuhn and Kollman, 2000Go). Chong et al. (Chong et al., 1999Go) have used the method to calculate the free energies of hapten binding to the germ line and mature forms of the 48G7 antibody Fab fragments. In addition to the different energy components of the total binding free energies, computational mutagenesis of selected binding-site amino acid residues were used in this work to rationalize the affinities of the two steroids to the DB3 antibody.


    Methods
 Top
 Abstract
 Introduction
 Methods
 Results and discussion
 References
 
Steroid parameters

The Cornell et al. (Cornell et al., 1995Go) force field, which was used in the MD simulations of this work, does not have some bond, angle and torsion angle parameters needed for the steroids. The missing parameters compatible with the Cornell et al. force field were developed by following the guidelines of Fox and Kollman (Fox and Kollman, 1998Go). The equilibrium bond distances were taken from the structures optimized at the HF/6-31G* and the corresponding bond stretching force constants were interpolated from similar type of bonds of the Cornell et al. force field. The angle parameters were taken from the corresponding angles of the Cornell et al. force field. The missing torsion parameters were developed using small model molecules. Torsion profiles were calculated for the models at the MP2/6-31G**//HF/6-31G* level and the torsion angle parameters were fitted to reproduce the quantum mechanical (QM) energy profile. Atomic point charges were calculated with the two-stage RESP method (Cornell et al., 1993Go) at the HF/6-31G* level for the steroids and the model compounds using the geometries optimized at the same level. The parameters added to the parm96 parameter file of the AMBER5 program (Case et al., 1997), the QM and MM energy profiles and steroid charges are available as supplementary material.

Molecular dynamics simulations

The initial coordinates for the antibody complexes were obtained from the X-ray crystal structures of the Fab' fragment of the anti-PRG monoclonal antibody DB3 complexed with PRG (Protein Data Bank code: 1DBB; Arevalo et al., 1993aGo) and 5AD (Protein Data Bank code:1DBK; Arevalo et al., 1993bGo) determined to 2.7 and 3.0 Å resolution, respectively. For the MD simulations the ligand-binding sites of the antibody–ligand complexes were solvated by adding a sphere of TIP3P (Jorgensen et al., 1983Go) water molecules with a 25 Å radius from the mass-centre of the ligands with the use of the ‘cap’ option of the LEAP program (Schafmeister et al., 1995Go). This resulted in 848 water molecules for the DB3–PRG and 874 for the DB3–5AD complex. In the simulations, residues having atoms within 12 Å from the atoms of the ligand molecules were allowed to move. This resulted in 82 moving residues for the PRG and 92 residues for the 5AD simulation. The water molecules of the solvated systems were first energy-minimized for 1000 steps with the use of the conjugate gradient algorithm and then equilibrated by a 30 ps MD simulation at a constant temperature of 300 K with the use of the Berendsen temperature coupling algorithm (Berendsen et al., 1984Go). After that, the water molecules and the moving part of the protein were energy-minimized for 1000 steps and equilibrated for 100 ps at 300 K. The production simulations of 500 ps were then started. In the simulations the non-bonded cut-off of 12 Å and a time step of 2.0 fs were used. The SHAKE algorithm (Ryckaert et al., 1977Go) was used to constrain bond distances to their equilibrium values. During the 500 ps simulations structures were saved every 5 ps for further analyses. All MD simulations were done using the AMBER5 program with the Cornell et al. force field and parameters developed in this work.

Free energy analyses

The binding free energies were calculated using the MM-PBSA method (Kollman et al., 2000Go). In the method free energies are calculated for ‘snapshot’ structures taken from the MD trajectory of the system studied. The average binding free energy ({Delta}GBIND) is calculated from the average molecular mechanical gas-phase energies (EMM), solvation free energies ({Delta}Gsolv) and entropy contributions (–TS):

(1)
In this work the molecular mechanical (EMM) energies were calculated using the ANAL program of AMBER5 with all protein pairwise interactions included using dielectric constant ({varepsilon}) of 1. The solvation free energy ({Delta}Gsolv) was estimated as the sum of electrostatic solvation, calculated by the finite-difference solution to the Poisson–Boltzmann equation ({Delta}GPB) as implemented in the Delphi program (Nicholls et al., 1990Go) and non-polar solvation energy ({Delta}Gnp), calculated from the solvent-accessible surface area (SASA):

(2)
We used {varepsilon} = 1 for the solute and {varepsilon} = 80 for the solvent in the electrostatic solvation free energy ({Delta}GPB) calculations. A probe radius of 1.4 Å and the atomic radii of the PARSE (Sitkoff et al., 1994Go) parameter set was used to determine the molecular surface. Atomic charges of the Cornell et al. force field were used for amino acid residues and RESP charges calculated at the HF/6-31G* level for the steroids. An 80% boxfill cubic lattice and a grid resolution of 0.5 Å/grid point were used in the Delphi calculations. The MSMS program (Sanner et al., 1996Go) was used to calculate the SASA for the estimation of the non-polar solvation energy ({Delta}Gnp) using Equation (3)Go and {gamma} = 0.02268 kJ/mol. Å2 and ß = 3.85 kJ/mol.

(3)
The binding free energies reported were further divided into several components: {Delta}Eelec = electrostatic part of the MM energy, {Delta}EvdW = van der Waals part of the MM energy, and {Delta}GPB,elec = {Delta}{Delta}GPB + {Delta}Eelec.

In this work the energy contribution from entropy changes upon ligand binding was not included. This was justified by the fact that it is likely that entropy does not contribute much to the relative binding free energies of the two steroids to the same receptor. More importantly, there is no straightforward way to quantitatively calculate the entropy contribution to binding. The normal mode analysis, which is often used to estimate entropy changes, gives only qualitative estimates (Kollman et al., 2000Go).

The MM-PBSA method was used for the computational alanine scanning (Reyes and Kollman, 2000aGo) of selected binding-site residues. In the scanning, the structures of the MD trajectory of the protein–ligand complex are mutated by truncating the side chains of the residues one at a time and binding free energies are calculated for each of the mutated trajectories. Binding free energies and computational mutagenesis of selected binding-site residues were calculated using single protein–ligand trajectories. This means that the snapshot structures for the energy calculations of the protein–steroid complex and separated protein and steroid were taken from the MD trajectory of the protein–steroid complex. It has been observed that the single trajectory method provides fairly good estimates for the relative binding energies (Kollman et al., 2000Go). From the 500 ps antibody–ligand MD trajectories 50 snapshots were taken at even intervals for the binding energy analyses. The binding free energies reported are averages from the 50 snapshots.


    Results and discussion
 Top
 Abstract
 Introduction
 Methods
 Results and discussion
 References
 
Structures and dynamics of the antibody–steroid complexes

The starting structures for the MD simulations of the DB3–PRG and DB3–5AD complexes were obtained from the corresponding X-ray structures. In the simulations only the residues within 12 Å from the steroids were allowed to move and the moving part was solvated with a 25 Å sphere of water molecules. The production simulations of 500 ps carried out for these systems were stable on the basis of the total and potential energies of the systems (data not show) and the root-mean square (RMS) deviations from the X-ray structures (Figure 4Go). The magnitudes of the atomic fluctuations of the two systems are similar but the structure of the antibody–5AD complex has an average RMS deviation of 1.1 Å as compared to the 0.6 Å of the antibody–PRG complex. This difference is most probably due to the larger number of moving amino acid residues in the 5AD (92) than the PRG simulation (82). The medium resolution antibody–steroid X-ray structures and use of a water sphere to solvate the simulation systems may also be responsible for the different behaviour of the systems. However, the deviations are comparable to those observed earlier for similar systems (Chong et al., 1999Go). Visual inspection of the simulation trajectories showed that the residues of the ligand-binding pocket and the ligands stayed close to the positions they have in the X-ray structures. The X-ray structures of the complexes between the DB3 antibody and the steroids studied in this work and other similar steroids have been analysed in detail by Arevalo et al. (Arevalo et al., 1993aGo,bGo,1994Go).



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Fig. 4. RMS deviations for the C{alpha} atoms from the corresponding X-ray structure in the DB3 antibody–PRG and DB3 antibody–5AD simulations. The average RMS deviations are 0.6 Å for the PRG and 1.1 Å for the 5AD complex.

 
Binding of PRG and 5AD to the native DB3 antibody

Free energies were calculated for the binding of PRG and 5AD to the DB3 antibody with the MM-PBSA method (Tables I–IIIGoGoGo). The calculated binding free energy, without the contribution of entropy, was –119.3 kJ/mol for PRG and –110.5 kJ/mol for 5AD. The experimental binding free energies are –51.4 and –46.2 kJ/mol for PRG and 5AD, respectively (Arevalo et al., 1993bGo). The calculated relative binding free energy, 8.8 kJ/mol, is in fair agreement with the relative experimental energy, 5.4 kJ/mol. Note that the standard deviations of the calculated binding energies of PRG and 5AD are of the same magnitude as the relative energy. The relatively large statistical error in calculated binding energy is an inherent feature of the MM-PBSA method because the energy is calculated from averages of several large numbers. In spite of this, good agreement between the calculated and experimental relative binding energies have been obtained in several cases with this method (Kollman et al., 2000Go). The inclusion of change in entropy upon association, T{Delta}S, would bring the calculated absolute energies closer to the experimental ones. The entropy contribution has been calculated to be 77.0 and 80.8 kJ/mol for a phosphonate hapten binding to the germ line and mature forms of the antibody 48G7 using normal-mode analysis in the gas-phase (Chong et al., 1999Go). In addition, –T{Delta}S has been calculated to be 42–84 kJ/mol for the binding of a set of nine ligands to avidin (Kuhn and Kollman, 2000Go). Since the calculation of entropy contribution requires several approximations and provides only rough estimates, especially in the case of a simulation in which only a part of the protein is moving, it was not calculated here.


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Table I. Free energy terms (kJ/mol) for the antibody–PRG complexa
 

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Table II. Free energy terms (kJ/mol) for the antibody–5AD complexa
 

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Table III. Free energy analysis (kJ/mol) of the antibody–PRG and the antibody–5AD complex formationa
 
The contributions of different force-field terms and solvation energies allow us to analyse the energetics of the ligand binding in more detail (Table IIIGo). Van der Waals energy ({Delta}EvdW) was calculated to be the most important complex formation favouring term having values of –199.5 and –174.3 kJ/mol for the binding of PRG and 5AD, respectively. The electrostatic protein–ligand interactions ({Delta}Eelec) favour the binding of PRG by –73.4 kJ/mol and that of 5AD by –41.9 kJ/mol. As a result of highly unfavourable electrostatic solvation energies ({Delta}{Delta}GPB, 173.5 and 124.7 kJ/mol), the electrostatic part of the total binding free energy ({Delta}{Delta}GPB,elec) is unfavourable for both steroids. The non-polar solvation free energies ({Delta}{Delta}Gnp) favour the complex formations. In the case of PRG it contributes –19.9 kJ/mol and in the case of 5AD –19.0 kJ/mol to binding. That the unfavourable electrostatic solvation is compensated, but not fully, by favourable electrostatic protein–ligand interactions has been observed in several earlier ligand-binding studies and seems to be a general phenomenon (Kuhn and Kollman, 2000Go). In addition, in line with the results of this work, the non-covalent association has been found to be driven by favourable van der Waals energies in several MM-PBSA studies (Kuhn and Kollman, 2000Go). It was suggested earlier by Miyamoto and Kollman (Miyamoto and Kollman, 1993Go), based on free energy perturbation calculations of absolute ligand-binding energies, to be a general scheme for non-covalent association.

The sum of the electrostatic protein–ligand interaction energy and electrostatic solvation energy ({Delta}{Delta}GPB,elec) is 17.3 kJ/mol less favourable for the binding of PRG than 5AD. However, because of the 25.2 kJ/mol more favourable {Delta}GvdW, PRG is bound tighter to DB3 than 5AD. The more favourable van der Waals and protein–ligand electrostatic interaction energies of PRG are in agreement with the larger number of van der Waals and hydrogen-bonding interactions observed in the X-ray structures of PRG than 5AD. There are 59 such interactions in the antibody–PRG complex but only 20 in the 5AD complex (Arevalo et al., 1993bGo). The number of DB3 antibody–steroid interactions has been found to correlate with the slightly higher affinities of the steroids with a 5ß substituent or a double bond to carbon 5 (like PRG) compared to steroids with a 5{alpha} substituent (like 5AD; Arevalo et al., 1993bGo). On the basis of the data for 5AD, the binding of other 5ß derivatives to the DB3 antibody is also favoured by solvation energies.

Computational alanine scanning of the ligand-binding residues

To study the role of individual amino acid residues on the cross-reactivity of DB3 with PRG and 5AD, selected residues of the ligand-binding pocket were mutated to alanines (Figure 5Go.). The residues mutated and the binding-site structures of the antibody–PRG and antibody–5AD complexes are shown in Figures 2 and 3GoGo. Arevalo et al. have made a detailed crystal structure analysis of the steroid binding to the DB3 antibody (Arevalo et al., 1994Go). They divided the binding site into four different compartments (pockets) named P1, P2, P3 and P3'. The P1 compartment is the most hydrophobic cavity of the binding site and interacts with the steroid D ring. The side chain of NH35 located at the bottom of the P1 compartment provides a hydrogen-bond donor for the bound steroids. This interaction is important for the antibody specificity by enforcing a hydrogen-bond acceptor as the functional group of the steroid D ring. There is a greater degree of flexibility and less antigen complementarity in the P2 compartment. It makes interactions with the B, C and D rings of steroids. The P3 and P3' compartments are available for the binding of the two different conformations of the A ring.



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Fig. 5. Effects of selected amino acid residues of the ligand-binding site on the calculated free energies (kJ/mol) for the binding of PRG (left, grey) and 5AD (right, black) to the DB3 antibody.

 
All the steroids whose complexes with DB3 have been determined, have their D ring bound to the bottom of the ligand-binding pocket of the antibody. Mutations NH35A, WH50A, YH97A, WH100A and FH100bA involve interactions with the D ring. These residues form the most important antibody–steroid interactions of the P1 compartment. Mutation NH35A has the largest effect on the binding energies. It decreases the binding energy of PRG by 25.1 kJ/mol and that of 5AD by 25.9 kJ/mol. This mutation removes a hydrogen bond between the carbonyl oxygen of the ligands and the amino group of the NH35 side chain, an interaction important for specificity and tight binding of steroids to DB3. There is a close contact (3.5 Å) between the phenyl ring of YH97 and the C21 methyl of PRG. Since 5AD sits deeper in the ligand-binding cavity, the corresponding interaction is between the D ring's CH2 groups and YH97. Mutation YH97 decreases the binding free energy of PRG by 8.8 kJ/mol and that of 5AD by 11.3 kJ/mol. Mutation FH100bA has a 4.2 kJ/mol larger effect on the binding of PRG than 5AD. This is due to the shorter FH100b to PRG than FH100b to 5AD distance.

There are two compartments in the ligand-binding cavity where the steroid skeleton can be placed. The walls of these compartments are mainly formed by WH50 and WH100 located on the opposite sides of the binding cavity. The two steroids are bound to the binding site in different orientations. The {alpha}-face (the face with no CH3 groups) of PRG is stacked face-to-face with WH100, whereas the ß-face (the face with CH3 groups) of 5AD makes this interaction. These interactions have large contributions to the binding free energies. Mutation WH100 decreases the binding of PRG by 23.0 kJ/mol and that of 5AD by 20.1 kJ/mol. Mutation of WH50A has a 7.9 kJ/mol larger effect on the binding of 5AD than that of PRG. In addition to the different binding orientations of PRG and 5AD, a slight twist about the long axis of the steroid skeleton differentiates the two binding modes. This rotation allows extensive interactions between the {alpha}-faces of the steroids and WH50 (in the case of 5AD) or WH100 (in the case of PRG). Mutation WH47A decreases the binding energy of 5AD 4.6 kJ/mol more than that of PRG. WH47 is <4.5 Å away from the C ring of both steroids. However, due to the bent geometry of 5AD, its A ring is <5 Å from WH47, which does not interact with the A ring of PRG. In addition to this, the A ring of 5AD makes several additional interactions with the antibody. The A ring of 5AD is bound nicely to the P3' binding pocket defined by residues WH47, WH50, VL94, PL95 and PL96. There is a tight contact between 5AD and VL94 with distances of 3.7 Å between the methyl carbons of VL94 and the A ring of 5AD. In contrast, only one of the methyl groups of VL94 interacts with PRG. These differences are seen in the calculated binding free energies. Mutation VL94A decreases the binding of 5AD 5.9 kJ/mol more than that of PRG. The carbonyl group of PRG's A ring makes a hydrogen bond with N{delta}H of HL27d (part of the P3 compartment). This interaction is absent for 5AD, whose carbonyl group of the A ring is solvated by water molecules. Therefore, mutation HL27dA decreases the binding of PRG by 8.4 kJ/mol but that of 5AD only by 3.8 kJ/mol. In addition to the hydrogen bond with HL27d, the A and B rings of PRG make several hydrogen-bonding type interactions with the main-chain carbonyl carbons of SL91 and HL93. The heavy atom distances between the carbonyl carbons and C4, C6 and C7 of PRG are 3–4 Å. In contrast, only the C19 of 5AD has a short distance (3.9 Å) to SL91.

The P3 and P3' compartments are responsible for the observed steroid cross-reactivity to the DB3 antibody. The comparison of the antibody–steroid structures shows that the compartments have different types of interactions with the bound steroids: the P3 compartment operates mainly by hydrogen-bonding and electrostatic interactions, whereas the binding to the P3' compartment is mainly hydrophobic in nature. These differences are seen in the free energy components. Although the calculated electrostatic solvation free energies of PRG and 5AD are similar (–51.9 and –54.0 kJ/mol, respectively), the solvation free energy for binding is 47.7 kJ/mol less unfavourable for 5AD. This reflects the more hydrophobic nature of the P3' compartment. That the P3 compartment has hydrogen-bonding like interactions with PRG, is seen in the larger electrostatic protein–ligand interaction energies ({Delta}Eelec) for PRG (–73.4 kJ/mol) than 5AD (–41.9 kJ/mol).

To conclude, the MM-PBSA calculations of the present study reproduced the relative binding free energy of PRG and 5AD, which bind to slightly different binding pockets of anti-PRG antibody DB3, in fair agreement with experimental values (8.8 versus 5.5 kJ/mol). Analyses of the binding energetics showed that in agreement with earlier computational ligand-binding studies the van der Waals energy is the most important complex formation favouring energy term. In addition, electrostatic antibody–steroid interactions were found to be important for the binding of PRG, whereas van der Waals and hydrophobic interactions were important for 5AD. These differences are mostly due to the binding of the A rings of the steroids to different binding pockets of DB3.


    Notes
 
1 To whom correspondence should be addressed. E-mail: mikael.perakyla{at}uku.fi Back


    Acknowledgments
 
This work was supported by the Academy of Finland.


    References
 Top
 Abstract
 Introduction
 Methods
 Results and discussion
 References
 
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Received March 13, 2001; revised July 24, 2001; accepted July 31, 2001.





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