The measured and calculated affinity of methyl and methoxy substituted benzoquinones for the Q_A site of bacterial reaction centers

Abstract

Quinones play important roles in mitochondrial and photosynthetic energy conversion acting as intramembrane, mobile electron and proton carriers between catalytic sites in various electron transfer proteins. They display different affinity, selectivity, functionality and exchange dynamics in different binding sites. The computational analysis of quinone binding sheds light on the requirements for quinone affinity and specificity. The affinities of ten oxidized, neutral benzoquinones (BQs) were measured for the high affinity Q_A site in the detergent solubilized Rhodobacter sphaeroides bacterial photosynthetic reaction center. Multi-Conformation Continuum Electrostatics (MCCE) was then used to calculate their relative binding free energies by Grand Canonical Monte Carlo sampling with a rigid protein backbone, flexible ligand and side chain positions and protonation states. Van der Waals and torsion energies, Poisson-Boltzmann continuum electrostatics and accessible surface area dependent ligand-solvent interactions are considered. An initial, single cycle of GROMACS backbone optimization improves the match with experiment as do coupled ligand and side chain motions. The calculations match experiment with an RMSD of 2.29 and a slope of 1.28. The affinities are dominated by favorable protein-ligand van der Waals rather than electrostatic interactions. Each quinone appears in a closely clustered set of positions. Methyl and methoxy groups move into the same positions as found for the native quinone. Difficulties putting methyls into methoxy sites are observed. Calculations using an SAS dependent implicit van der Waals interaction smoothed out small clashes, providing a better match to experiment with a RMSD of 0.77 and a slope of 0.97.

Introduction

Quinones are the most important lipid-soluble electron and proton carriers in the membranes of mitochondria, chloroplasts and oxygenic bacteria.^1,2 They transfer electrons between proteins carrying out the proton-coupled electron transfer reactions that generate transmembrane proton gradients.^3,4 Quinone redox chemistry occurs in specific binding sites in these proteins, which favor binding different quinones⁵ and modulate in situ quinone chemistry.^6-8 The biological quinone redox reactions shift the quinone between stable quinone and hydroquinone (quinol) species, requiring two electron and two proton transfers. The tuning of affinity, specificity and electrochemistry in protein is of prime importance since the intermediate, singly reduced semiquinone is a source of harmful reactive oxygen species (ROS).^9-12

As quinones function as intermediaries in the bioenergetic transfer chain there are quinone binding sites in many proteins. The Krebs cycle products yield QH₂ via NADH₂ or succinate oxidation in NADH dehydrogenase (complex I) and succinate dehydrogenase (complex II).¹³ In aerobic respiration, the cytochrome bc₁ complex gives electrons from QH₂ to cyt c,^8,14 which in turn reduces O₂ to water in cytochrome c oxidase. Different organisms can use different quinones. Animals and plants use only ubiquinone (UQ) in their mitochondrial membrane electron transfer proteins, while plants and algae use plastoquinone and phylloquinone in their chloroplast photosynthetic reactions. Bacteria use a mixture of quinones including UQ, menaquinone and rhodoquinone for photosynthetic and other transmembrane, bioenergetic reaction. Quinone binding sites are also the targets for anti-malarial drug,¹⁵ antibiotics such as nafuredin,¹⁶ and various herbicides.¹⁷

Quinones are seen in a slowly growing list of membrane protein crystal structures, including in photosynthetic reactions centers of bacteria (RCs) (Q_A, Q_B),¹⁸ PSI and PSII,¹⁹ cytochrome bc₁ and b₆f oxidoreductases (Q_o, Q_i),^20,21 quinol-fumarate reductase (Q_P,Q_D),²² succinate dehydrogenase¹² and the enzyme DsbB.²³ However, inspection of these quinone binding sites does not provide a well-defined binding motif.²⁴ Binding sites have from 1 to 6 aromatic residues (Phe, Tyr and Trp) within 4Å of the quinone ring and tail. These can be parallel extensions of the quinone ring or lie over the ring in tilted or parallel orientations. The two quinone oxygens are hydrogen bond acceptors when the quinone is oxidized (Q) or donors in the neutral reduced cofactor (QH₂). Hydrogen bond partners found in the crystal structures include the ionizable Glu, Asp, Lys; the polar His, Ser, Tyr, and backbone NH. The number of hydrogen bond partners varies from 0 as for one of the two quinone binding sites in Escherichia coli fumarate reductase to 5 as in RCs. Water molecules are seen in about two thirds of the quinone binding sites.

The bacterial reaction centers of photosynthetic bacteria have proved to be a useful and robust system for experimental studies of quinone electrochemistry and binding.^25-27 The electrochemical midpoints, E_ms, of Q_A⁶ and Q_B^28,29 of Rb. sphaeroides RC have been measured, even down to cryogenic temperature.^30,31 Computational analysis has followed. The Q to Q^·- E_m of the native UQ in the Q_A and Q_B sites have been satisfactorily calculated in wild type^32-36 and mutant RCs.³⁷ Likewise, the affinity of many compounds for the Q_A site of Rb. sphaeroides RCs have been measured, providing a qualitative picture of the importance of the quinone ring substituents and the tail structure.^5,38-44 However, there has been little computational analysis of quinone affinity. This is largely because calculations of binding affinity^45-48 are far more challenging than for E_ms and pK_as.^49-51

The aim here is to measure and compute binding affinities to shed light on the native binding sites that are observed to accommodate quinones. The initial target is the primary quinone (Q_A) binding site of the photosynthetic reaction centers of Rps. sphaeroides. Methods to calculate ligand affinities need to combine search functions to generate ligand poses in the protein and scoring functions to rank their energies. All methods introduce simplifications in protein and ligand degrees of freedom and in the complexity of the scoring functions to increase the computational speed.^52-54 The fastest techniques use a rigid receptor and ligand, allowing only translation and rotation.⁵⁵ More refined methods such as DOCK,⁵⁶ AutoDock,⁵⁷ FlexE,⁵⁸ GOLD⁵⁹ provide the ligand with flexibility and the protein with limited flexibility. Inevitably conformational freedom greatly expands the size of the problem. The relative protein-ligand interaction energies are evaluated with functions that range from simple statistical functions as found in QSAR,⁶⁰ to MM-PBSA or MM-GBSA^61,62 methods which use standard Molecular Dynamics (MD) bonded and non-bonded parameters and continuum electrostatics (CE) analysis⁶³ to more complete physics-based approaches with significant computational cost, such as alchemical free energy calculations⁶⁴ or DFT analysis.^65,66

MCCE, a new MC-PBSA type method, which carries many novel features will be used here. It was initially developed for analysis of E_m and pK_a values and has been used extensively in the analysis of the quinone electrochemistry in RCs.^32,33,67,68 Recently MCCE has also been applied to analyze ion binding,⁶⁹ which represents an extension of the program to determine small molecule affinity. The binding of ten fully oxidized neutral benzoquinones (BQ) to the Q_A site of the Rhodobacter sphaeroides photosynthetic reaction center will be measured and then calculated. The considered interactions between the protein and the ligand combine molecular mechanics non-electrostatic interactions and Poisson-Boltzmann continuum electrostatics interactions. The binding affinity is determined with Grand Canonical Monte Carlo sampling (GCMC), which is ideal for studying binding as it allows the bound and free quinone to come to equilbrium.^70,71 MCCE allows flexible side chains⁷² and multiple ligand binding poses⁷³ within a rigid backbone. Unlike almost all simulations, which need to pre-assign the ionization states of the protein and ligand, all protonation and redox states for each residue and cofactor can change in the Monte Carlo sampling that determines the ligand affinity. The importance of optimizing the backbone position, of the flexibility of the ligand position and the contribution of ligand rearrangement to the free energy of binding are evaluated. The results with a full AMBER van der Waals analysis of the quinone-protein non-electrostatic interactions is compared with an implicit, surface area dependent energy function.

Method

Measurement of quinone affinity

Rhodobacter sphaeroides bacteria, strain R-26, were grown anaerobically, photosynthetically, on succinate media. The RCs were extracted from the bacterial membrane with the detergent lauryldimethylamine oxide (LDAO), and purified by ammonium sulfate precipitation, followed by chromatography on a DEAE-cellulose column.⁷⁴ The bound primary and secondary quinones, Q_A, and Q_B, are removed from the protein by the method of Okamura⁷⁵ with minor modifications.⁶ All Q_B is removed. The fraction residual Q_A is preparation dependent and varied from 0.01 to 0.15.

The source of the quinones can be found in ref 76. The following abbreviations will be used henceforth: BQ: 1,4-benzoquinone; DQ: tetramethyl-BQ; Q₀: 2,3-dimethoxy-5-methyl-BQ and methyl-Q₀: 2,3-dimethoxy-5,6-methyl-BQ. Quinone purity was determined by HPLC chromatography, monitored at 220 and 250 nm.⁷⁷ Quinones were dissolved in ethanol or dimethylsulfoxide. Solutions of BQs with less than three substituents were made fresh immediately before use.

RC activity is monitored by the oxidation state of the bacteriochlorophyll dimer at 605 nm, as previously described.^78-80 If there is no active quinone present at the time of the flash the protein decays back to the ground state in 10 ns and no reaction is seen. Thus, this assay determines the K_d for quinone bound prior to the flash. If there is an active quinone correctly oriented, the state P⁺Q_A^- is formed, which lasts for milliseconds with the quinones tested here. The fraction of RCs with quinone bound is proportional to the ΔA₆₀₅.

The reaction mixture contains 0.10 to 0.35 μM Q_A-depleted RCs, solubilized by 2×10^-4 to 10^-3% LDAO in 10 mM Tris-HCl at pH 8.0. The detergent in the assay mixture represents a dilution of that present in the RC stock solution. Measurements are initiated 30μs after a 10μs (full width at half maximum) xenon flash masked with an IR transmitting Kodak 88A wratten filter. Under these conditions ≈90% of the RC population absorbs at least one photon. The cuvette temperature is maintained at 22± l°C by a circulating water bath.

Calculation of quinone affinity

In MCCE analysis, the term ‘conformer’ specifies a specific position, protonation and redox state of a side chain or ligand. These are preselected during an initial sampling and optimization cycle (see reference ⁸¹ for a more complete description) and residues can have 1 to 100’s of conformers to choose from. The protein backbone is held fixed. Monte Carlo sampling then determines the Boltzmann distribution of conformers. Thus, all acidic and basic amino acids throughout the protein can be either protonated or deprotonated unless otherwise stated, while the side chains and ligands sample all, preselected positions. The conformer distribution is determined given the Poisson-Boltzmann electrostatic interactions and ligand solvation energies, full AMBER Lennard-Jones and torsion energies⁸² and an SAS based non-electrostatic ligand-solvent interaction energy. The ligand affinity is derived from Grand Canonical Monte Carlo (GCMC) Sampling where the ligand can be bound to the protein or free in solution.⁸³ A similar GCMC analysis has been applied previously to calculate the chloride affinity to three proteins using MCCE.⁶⁹

The generation of the pre-selected side chain conformers for final Monte Carlo sampling uses a multi-scale approach. This aspect of optimization of side chain and ligand positions is novel in MCCE and is described in detail below. MCCE QUICK conformer placing is the default for the protein as a whole.⁸¹ This retains the input non-hydrogen (C,O,N,S) positions, while allowing additional, essentially isosteric positions for hydroxyls, His tautomers, and the interchange of the O and N in the Asn and Gln side chains. MCCE analysis then focuses more sampling of side chain positions near the quinone as described below. The program screens, optimizes and prunes these initial position conformers with an analytical energy function that includes AMBER torsion and Lennard-Jones energies as described in detail previously.⁸¹ The electrostatic energies in the prescreening step are obtained using Coulomb’s law with a dielectric constant of 6. In the GCMC ligand binding analysis, DelPhi⁸⁴ is applied to solve the Poisson-Boltzmann equation with a protein dielectric of 4 and 80 for water at pH 7 and with 150 mM salt using Parse charges and radii.⁸⁵ AMBER⁸² non-electrostatic parameters are applied for the Lennard-Jones and torsion energies. The quinone affinities are measured with solubilized protein, with the detergent kept below its critical micelle concentration so no membrane is included in the calculations.

During each Monte Carlo titration of ligand binding, the position of the four His (M266, M219, L190 and L230) and one Glu (M234) that are ligands to the RC iron atom are fixed in the crystal structure position and maintained with the His neutral, Glu ionized and Fe²⁺ state. This fixes the position and tautomer for His M219, which also makes a hydrogen bond to the quinone. All the bacteriochlorophylls, bacteriopheophytins and the ubiquinone at the Q_B site are fixed in their neutral ground state. There is an acidic cluster of Glu L212 and Asp L213 near the Q_B site. The acidic pair interacts strongly and the total net charge of the cluster remains -1.^33,36 Here Glu L212 is set to be neutral. In addition, Glu L104, which makes a hydrogen bond to the ring V keto carbonyl of bacteriopheophytin, is fixed in its protonated state. The ionization states of all other protonatable residues are determined by MCCE Monte Carlo sampling.

I. Preparation of protein structure file

Identical quinone docking and affinity calculations are carried out on 1AIJ⁸⁶ and 2UWU⁸⁷ structures taken from the Protein Data Bank (PDB).⁸⁸ They have a resolution of 2.20 and 2.04 Å respectively. All crystallographic water molecules, lipid and detergent molecules are removed.

Each of the ten BQs to be docked in the protein is optimized and its atomic electrostatic potential (ESP) partial charge distribution calculated using DFT analysis in the Gaussian98 program⁸⁹ with the UB3LYP/6-31G basis sets. This charge set was used in MCCE for the ligand within the protein and for reference calculations of the solvation energy in water.

One cycle of minimization is carried out for each ligand with the GROMACS molecular dynamics program.⁹⁰ These calculations use a reduced atomic model, where there are no hydrogens, so the quinone proton partial charge from the Gaussian98 analysis are redistributed to the closest carbon atom. The ab initio RC cofactor parameters derived by Ceccarelli, Procacci and Marchi⁹¹ were converted to GROMACS format and used here. The bonded parameters for the other BQs needed for GROMACS were derived from the parameters for the native UQ.

II. Ligand Docking

The calculations start with the native quinone in the crystal structure stripped of substituents, leaving only the flat, six membered ring with the two para-carbonyl groups. MCCE adds the substituent methyl and methoxy groups to the ring, building the ten 1,4 BQs by applying information in topology files that define bond angles and length, and proton positions. Each BQ is docked in the protein in all possible poses taking into account the symmetry of the substituents. For example, while maintaining the positions of the two carbonyls, the methyl-1,4-BQ has four starting orientations with its methyl group docked into the four quadrants, while there is only one starting position needed for the 4-fold symmetrical DQ. This procedure initiates all subsequent calculations.

Each quinone undergoes one cycle of GROMACS optimization to relax the backbone (Figure 1,S1). GROMACS molecular dynamics can consider only one starting conformation for each residue and cofactor. As is unlikely that the cofactor can change substituent orientation during the short simulations used here, the most occupied MCCE quinone replacement orientation is added to the RC crystal structure as the GROMACS starting structure.⁹⁰ In addition, the side chain protonation states are fixed given the MCCE results. Ten cycles of energy minimization, each consisting of 500 0.002 ps steps are carried out on the whole protein for each quinone. Energy minimization uses the method of steepest descent. All runs converge in less than 500 steps. The RMSD for the changes in backbone generated by GROMACS in all structures is less than 0.11 Å for the whole protein and less than 0.14 Å in the region of the protein within15Å of the binding site. MCCE calculations with the different resultant protein backbone structures yield negligible differences in ionization state of the protein residues in the final calculations.

Figure 1.

Overview of K_d calculations. Gaussian generates ESP charges for quinone in a given redox and protonation state. MCCE finds lowest energy substituent orientation starting from native quinone ring. This conformer is added to GROMACS energy minimization of backbone and side chains. The GROMACS derived backbone will be used for all subsequent MCCE runs with this ligand. MCCE generates potential side chain and ligand conformers through cycles of translation, out-of-plane and then in-plane rotation. Good poses are further optimized with smaller motions. MCCE K_ds are obtained by competing bound and free ligands in Grand Canonical Monte Carlo sampling as a function of quinone concentration. This uses the full energy function and all protein and ligand conformers selected in any round of conformer optimization merged onto the same backbone.

Multiple MCCE runs are used to generate many side chain rotamers and quinone positions for calculation of the relative affinity of each ligand. Each conformer generation cycle starts with the final GROMACS side chain and backbone positions for that ligand and the lowest energy ligand position found in the previous cycle of MCCE optimization (Figure 1). Side chain conformers are generated and optimized. Ligand conformers are constructed by a cycle of translation, out-of-plane rotation and then in-plane rotation. These are carried out independently to avoid an explosion of conformers (Figure S1). First ligand translation is carried out in 2 to 5 0.2~0.5 Å steps in each ±x,y,z directions. Four step translations create a 9³ grid with ≈730 conformers. The final, lowest energy position is rotated out-of plane in 30° steps around three axes through the opposite carbons of the quinone ring plane (C1-C4, C3-C6 and C2-C5), yielding 12³ conformers for each BQ orientation in the site. Finally, the best position is subjected to in-plane rotation in 30° steps along each of the six axes perpendicular to the quinone plane through every ring carbon atom. Nearby side chain conformers are created and sampled with the quinone conformers in each cycle of optimization. Each type of ligand rotation is coupled to the swing function which allows each rotatable bond to move by 3.0°~ 5.0° for finer sampling. For each transformation stage 12 rotamers are created for each methoxy substituent’s two rotatable bonds. In each cycle tens of thousands of conformers are made, screened with an analytical function leading to 10-30 positions that are subjected to Monte Carlo sampling with the complete energy function using Poisson-Boltzmann electrostatics and AMBER non-electrostatics parameters. All side chain and ligand conformers that are chosen to be bound to the protein in Monte Carlo sampling are saved and pooled.

The search for conformers is first conducted in an isolated 15Å protein sphere including the 160 residues around the quinone headgroup (Figure S1). For the ≈12 residues within 4Å of the quinone headgroup, 12 rotamers are made for each rotatable bond. QUICK rotamer making is used for the other residues.⁸¹ For each quinone the ligand is translated and rotated as described above, side chain rotamers are made and their goodness assessed by MC sampling as described above. Then the same cycle of optimization is carried out in the full 840 residue protein. The calculation again starts with the protein residue positions taken from the GROMACS minimized structure. The ligand conformation is in a low energy position taken from the previous optimization cycle built in the 15Å sphere. The region where 12 side chain rotamers are considered for each bond is increased to ≈7Å from the quinone, now encompassing ≈35 residues. With the exception of the first pre-GROMACS calculations all occupied conformers from each stage of optimization are pooled and added to the subsequent cycles of Delphi calculation and Monte Carlo sampling. This builds up an extensive set of conformers to be included in the final Monte Carlo sampling that gives the quinone K_d. For each quinone the cycle of translation, in plane rotation, out of plane rotation and swing angular displacement is carried out 3 times in the 15Å sphere surrounding the quinone and then twice in the whole protein. The initial complete protein calculation starts with 10-30 thousand conformers. Analytical energy pre-screening functions reduce this to ≈2300 conformers, of which ≈450 are for the quinone and nearby residues. This increases to ≈2700 conformers after the first cycle and ≈3300 conformers following the second cycle of conformer optimization with ≈1500 conformers for the quinone and surroundings. Additional cycles of optimization are not found to increase the affinity showing the process has converged. Currently the entire procedure takes 3~5 days on a single 3.06 GHz processor.

III. Calculating the ligand binding energy

All protein and ligand conformers selected during the MCCE conformer generation cycles are preserved for the final analysis of the binding energy for that ligand. The bound ligand conformers compete against a conformer in solution, which has torsion, van der Waals self-energy and solvation energy of an isolated quinone in water and no interactions with the protein. The van der Waals and torsion energy for the solution conformer are taken from the most occupied conformer in the protein so that these non-electrostatic self-energy terms do not affect the affinity. The quinone titration is modeled by a series of Monte Carlo runs. An energy that is proportional to the effective chemical potential is added to the solution conformer to represent the effective concentration of the quinone.⁶⁹ When the calculated occupancy of the bound and free ligand is equal, the energy difference between the apo and holo states is zero. The quinone solution chemical potential that gives 50% bound ligand is compared for the various quinones to obtain the relative K_d.

The binding free energy is the change in the system free energy when a ligand in water binds to the RC Q_A site. Using the Boltzmann distribution of ligand and side chain conformers found in the ligand titration, the binding energy can be decomposed in a mean field analysis as:⁴⁷

$$\begin{array}{lll}\mathrm{\Delta }{\mathrm{G}}_{\mathrm{bind}}& =& \mathrm{\Delta }{\mathrm{G}}_{\mathrm{solv}}+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{P}-\mathrm{L}}+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{entropy}}+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{strain}}\\ & =& (\mathrm{\Delta }{\mathrm{G}}_{\mathrm{solv},\mathrm{ele}}+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{solv},\mathrm{np}})+(\mathrm{\Delta }{\mathrm{G}}_{\mathrm{prot},\mathrm{ele}}+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{prot},\mathrm{vdW}})+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{entropy}}+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{strain}}\end{array}$$ (1)

ΔG_solv accounts for the loss of ligand-solvent interactions and ΔG_P-L the gain of new ligand-protein interactions. These terms may be favorable or unfavorable depending on the ligand, the solvent and the binding site. ΔG_entropy is a generally unfavorable term that accounts for the loss of degrees of freedom of the ligand on binding. ΔG_strain, accounts for the strain that builds up in the protein or ligand on binding.

ΔG_solv

The interaction of water and ligand is decomposed into three terms. The electrostatic component (ΔG_solv,ele) accounts for the favorable interaction of water with the dipolar ligand. It is calculated by MCCE using DelPhi,⁸⁴ in which the solvent is modeled implicitly as a medium with a dielectric constant of 80 and the solute with an interior dielectric constant of 4. Experimentally it is expected that some water will occupy a site that is empty of quinone. No water enters the empty binding site and the dielectric constant remains 4 in the calculation. However, any errors that this yields should be the same for all quinones.

The non-polar solvation term consists of the unfavorable free energy required to form a cavity for the ligand in water (ΔG_cav), which is the basis of the hydrophobic effect⁹² and the favorable solute-solvent van der Waals interaction (ΔG_vdW).^93,94 Both terms are estimated by an empirical linear relationship between the total non-polar solvation free energy (ΔG_solv,np) and the solvent accessible area (A) so they cannot be readily separated. Here:

$$\begin{array}{lll}\mathrm{\Delta }{\mathrm{G}}_{\mathrm{solv}}& =& \mathrm{\Delta }{\mathrm{G}}_{\mathrm{solv},\mathrm{ele}}+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{solv},\mathrm{np}}\\ & =& \mathrm{\Delta }{\mathrm{G}}_{\mathrm{solv},\mathrm{ele}}+({\mathrm{\gamma }}_1\mathrm{A}+\mathrm{B})=\mathrm{\Delta }{\mathrm{G}}_{\mathrm{solv},\mathrm{ele}}+(\mathrm{\Delta }{\mathrm{G}}_{\mathrm{cav}}+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{vdW}})\end{array}$$ (2)

where γ₁ is -5 cal·mol^-1·Å^-2 and B is zero (Calc1 in Table 1).^95,96

Table 1.

A,B: Relative experimental and calculated binding energies using methyl-Q₀ as the reference compound. Results of multiple calculations vary by <0.4 kcal/mol, while the experimental results have errors of ≈0.25 kcal/mol. A: Calculation in crystal structure 1AIJ. B: 2UWU. C: absolute experimental and calculated binding energies in 1AIJ. Calc¹ with vdW¹ represents full MCCE binding calculations with AMBER protein-ligand van der Waals interactions and -5 cal/mol/Ų surface area dependent ligand-solvent non-electrostatic interactions (Eqn. 2). Electrostatic desolv: the loss of the DelPhi calculated solvation energy when the ligand is moved into the protein. Calc² with vdW² uses a -55 cal/mol/Ų SAS dependent implicit van der Waals energy for both ligand to protein and ligand to solvent interaction (Eqn. 4). TΔS: entropy correction due to expected loss of methoxy rotation degrees of freedom. All energy values are in kcal/mol.

A.	1AIJ	Expt	Calc1	Calc2	SAS	TΔS	Electrostatics				vdW1				vdW2
							De-solv	bkbn	side chain	total	SAS	bkbn	side chain	total	total
	unsub	4.90	9.70	6.06	-134	-0.80	-0.96	0.44	0.00	-0.52	0.67	6.11	3.12	9.90	7.37
	methyl	4.60	6.62	4.04	-107	-0.80	-0.62	0.11	-0.54	-1.06	0.54	6.58	-0.16	6.96	5.90
	2,3-dimethyl	3.45	2.49	3.41	-89	-0.80	-0.79	0.10	0.00	-0.70	0.45	4.86	-2.83	2.48	4.91
	2,5-dimethyl	3.64	4.26	3.08	-86	-0.80	-0.78	0.34	-0.41	-0.85	0.43	4.87	-0.50	4.80	4.73
	2,6-dimethyl	3.63	3.96	3.42	-79	-0.80	-1.04	0.88	0.00	-0.16	0.40	2.26	0.94	3.60	4.37
	tri-methyl	1.52	2.04	1.87	-61	-0.80	-0.94	0.37	-0.14	-0.70	0.31	3.22	-2.10	1.43	3.37
	tetra-methyl (DQ)	-0.14	1.74	0.51	-41	-0.80	-1.20	0.25	0.00	-0.95	0.21	5.97	-4.49	1.68	2.26
	2,6-dimethoxy	2.73	-0.99	1.31	-36	0.60	-0.10	0.20	-1.36	-1.26	0.18	1.11	-3.09	-1.80	1.98
	2,3-dimethoxy, 5-methyl (Q0)	1.59	2.60	0.71	-14	0.00	0.05	0.17	-0.27	-0.06	0.07	2.18	0.18	2.43	0.77
	2,3-dimethoxy, 5,6-dimethyl (methyl-Q0)*	0.00	0.00	0.00	0	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
	Absolute energies methyl Q0						2.67	-1.49	-1.77	-0.59	-1.93	-14.01	-14.82	-30.76
B.	2UWU	Expt	Calc1	Calc2	SAS Å2	TΔS	Electrostatics				vdW1				vdW2
							De-solv	bkbn	side chain	total	SAS	bkbn	side chain	total	total
	Unsub	4.90	7.15	6.83	-134	-0.80	-1.17	0.61	0.82	0.26	0.67	4.71	1.21	6.59	7.37
	Methyl	4.60	4.32	4.39	-107	-0.80	-0.60	0.02	-0.13	-0.71	0.54	3.88	0.81	5.23	5.90
	2,3-dimethyl	3.45	1.53	3.57	-89	-0.80	-0.80	-0.01	0.27	-0.54	0.45	2.34	-1.11	1.68	4.91
	2,5-dimethyl	3.64	1.86	3.25	-86	-0.80	-0.74	0.20	-0.14	-0.68	0.43	1.72	0.28	2.43	4.73
	2,6-dimethyl	3.63	3.28	3.35	-79	-0.80	-1.12	0.49	0.41	-0.22	0.40	1.42	1.30	3.11	4.37
	tri-methyl	1.52	1.89	1.28	-61	-0.80	-0.91	-0.10	-0.27	-1.29	0.31	3.82	-0.77	3.35	3.37
	tetra-methyl (DQ)	-0.14	-0.21	0.83	-41	-0.80	-1.16	0.26	0.27	-0.63	0.21	0.19	0.54	0.94	2.26
	2,6-dimethoxy	2.73	-2.84	1.39	-36	0.60	-0.05	0.09	-1.22	-1.18	0.18	-0.26	-3.17	-3.25	1.98
	2,3-dimethoxy, 5-methyl (Q0)	1.59	3.45	0.65	-14	0.00	-0.06	0.48	-0.54	-0.12	0.07	-2.28	5.23	3.01	0.77
	2,3-dimethoxy, 5,6-dimethyl (methyl-Q0)*	0.00	0.00	0.00	0	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
	Absolute energies methyl Q0						2.68	-1.23	-1.77	-0.33	-1.93	-12.29	-15.22	-29.44
C.	1AIJ	Expt	Calc1	Calc2	SAS	TΔS	Electrostatics				vdW1				vdW2
							De-solv	bkbn	side chain	total	SAS	bkbn	side chain	total	total
	Unsub	-3.54	-21.76	-14.98	252	0.00	1.71	-1.05	-1.77	-1.11	-1.26	-7.89	-11.70	-20.86	-13.88
	Methyl	-3.84	-24.85	-17.00	279	0.00	2.04	-1.38	-2.31	-1.65	-1.40	-7.42	-14.98	-23.80	-15.35
	2,3-dimethyl	-4.98	-28.98	-17.63	297	0.00	1.87	-1.39	-1.77	-1.29	-1.49	-9.14	-17.66	-28.29	-16.34
	2,5-dimethyl	-4.79	-27.20	-17.96	300	0.00	1.88	-1.14	-2.18	-1.44	-1.50	-9.14	-15.33	-25.97	-16.52
	2,6-dimethyl	-4.80	-27.50	-17.62	307	0.00	1.63	-0.61	-1.77	-0.75	-1.53	-11.74	-13.88	-27.16	-16.88
	tri-methyl	-6.91	-29.43	-19.17	325	0.00	1.73	-1.12	-1.90	-1.29	-1.63	-10.78	-16.93	-29.34	-17.88
	tetra-methyl (DQ)	-8.57	-29.73	-20.53	345	0.00	1.47	-1.24	-1.77	-1.54	-1.73	-8.04	-19.31	-29.08	-19.00
	2,6-dimethoxy	-5.70	-32.45	-19.73	350	1.40	2.57	-1.29	-3.13	-1.85	-1.75	-12.89	-17.92	-32.56	-19.27
	2,3-dimethoxy, 5-methyl (Q0)	-6.84	-28.86	-20.32	372	0.80	2.72	-1.32	-2.04	-0.65	-1.86	-11.82	-14.64	-28.33	-20.48
	2,3-dimethoxy, 5,6-dimethyl (methyl-Q0)*	-8.43	-31.46	-21.04	386	0.80	2.67	-1.49	-1.77	-0.59	-1.93	-14.01	-14.82	-30.76	-21.25

^*methyl Q₀ is chosen as the reference compound. The Calc¹ energies are derived from the quinone solution chemical potential needed to have equal amounts of quinone bound and free in Monte Carlo sampling. The energy breakdown is obtained using equation 1. This uses a mean field analysis given the conformer distribution generated by the Monte Carlo sampling under conditions where half of the proteins have quinone bound.

ΔG_P-L

The protein-ligand contribution to the binding energy is also decomposed into electrostatic and non-electrostatic terms:

$$\mathrm{\Delta }{\mathrm{G}}_{\mathrm{P}-\mathrm{L}}=\mathrm{\Delta }{\mathrm{G}}_{\mathrm{prot},\mathrm{ele}}+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{prot},\mathrm{vdW}}$$ (3)

Both contributions are treated explicitly in the full MCCE analysis. The electrostatic pair-wise interactions with the protein (ΔG_prot,ele) are calculated by DelPhi.⁸⁴ The pair-wise van der Waals interactions (ΔG_prot,vdW) are calculated using standard AMBER parameters.⁸² Torsion energies are bundled into the latter term. Pair-wise terms are further decomposed into side chain and backbone interactions in the mean field analysis of the calculated quinone affinity.⁸¹

In addition, binding is analyzed using an implicit van der Waals protein-ligand interaction that is proportional to the ligand surface area (Calc2 in Table 1). Eqn 1 can be reorganized as:

$$\mathrm{\Delta }{\mathrm{G}}_{\mathrm{bind}}=(\mathrm{\Delta }{\mathrm{G}}_{\mathrm{solv},\mathrm{np}}+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{prot},\mathrm{vdW}})+(\mathrm{\Delta }{\mathrm{G}}_{\mathrm{solv},\mathrm{ele}}+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{prot},\mathrm{ele}})+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{entropy}}+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{strain}}$$ (4a)

$$={\mathrm{\gamma }}_2\mathrm{A}+(\mathrm{\Delta }{\mathrm{G}}_{\mathrm{solv},\mathrm{ele}}+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{prot},\mathrm{elec}})+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{entropy}}+\mathrm{\Delta }{\mathrm{G}}_{\mathrm{strain}}$$ (4b)

The coefficient (γ₂) derived from the best fit line for the solvent accessible area (A) term is -55 cal·mol^-1·Å^-2.⁹⁷ This adds the favorable protein-ligand van der Waals interaction (ΔG_prot,vdW) to the implicit water-ligand non-polar interactions (Eqn. 2). The electrostatic part of the binding energy (ΔG_solv,ele+ΔG_prot.ele), the change in entropic energy and the strain energy are the same in equations 4a and 4b.

ΔG_entropy

Changes in entropy can make significant contributions to the overall free energy of ligand binding.^47,98,99 For extended ligands, simulations estimate that as much as 25 kcal/mol can be lost so the entropy loss can oppose binding nearly as strongly as the enthalpy favors it. However, the BQs considered here are flat six-member rings with at most two rotatable methoxy groups. The loss of rotational/translational entropy on being confined in the binding site is assumed to be the same for all ligands. Neglecting this term will contribute to the absolute calculated binding energies being more favorable than those measured. The configurational entropy loss is assumed to be proportional to the number of rotatable bonds affected by binding.^100-102 A range of values from 0.3,¹⁰³ 0.45,¹⁰⁴ to 0.7¹⁰⁵ kcal/mol per rotatable bond have been used in ligand binding simulations. Assuming the methoxy trans and ±gauche orientations yield three states of equal energy, when they are fixed in one location the entropy loss is:¹⁰⁵

$$\mathrm{T}\mathrm{\Delta }{\mathrm{S}}_{\mathrm{rot}}=\mathrm{RTln}3\approx 0.7\mathrm{kcal}/\mathrm{mol}/\mathrm{methoxy}$$ (5)

A correction of 0.7 kcal/mol/methoxy is used here for the 2,6-dimethoxy BQ. A smaller energy penalty of 0.4 kcal/mol/methoxy is used for the Q₀ and methyl-Q₀ because the adjacent methoxy groups restrict each other, so that one is in plane and the other out of plane even in solution.⁵

MCCE also makes an entropy correction when there are different numbers of conformers for distinguishable states.⁸¹ Each quinone ligand has ≈20 different bound conformers competing with a single conformer representing the unbound state. The disparity in the number of conformers artificially favors the bound state. The entropy correction is calculated dynamically during Monte Carlo sampling to renormalize the number of low energy bound and free conformers.⁸¹ The correction is generally less than 2 kcal/mol.

ΔG_strain

Upon binding, the protein and/or ligand may be distorted.⁴⁷ This costs energy, favoring the ligand in water. The strain energy is included in MCCE calculation when different conformations for the protein and ligand are adopted in the bound and unbound states. Thus, the Grand Canonical Monte Carlo sampling naturally includes this contribution to the free energy change.

Results & Discussion

The affinity of ten neutral benzoquinones (BQ) for the Q_A site of the Rhodobacter sphaeroides photosynthetic reaction center was measured with protein solubilized in detergent suspension below the critical micelle concentration. The relative binding free energies were then calculated using MCCE. The native quinone found in the crystal structure is Ubiquinone-10 (UQ₁₀), a 2,3-dimethoxy-5-methyl-6-isoprenyl-BQ with a 10 unit, 50 carbon, isoprene tail. Methyl-Q₀, a UQ analogue with a methyl group in place of the isoprene tail, is chosen as the reference compound. Its K_d is measured to be 0.63 μM. All the values discussed below are relative to this quinone unless noted.

MCCE was developed to allow extensive rotamer sampling during calculations of residue and ligand pK_as and E_ms in proteins.⁸¹ It has thus focused on processes that change the charge of the protein so electrostatic interactions are dominant. However, as side chain motions accompany protonation or redox changes, state energies also include Lennard-Jones and torsion terms. More recent calculations have used the Monte Carlo sampling of multiple positions and charge states to study proton coupled chloride binding.⁶⁹ In the work reported here the calculations of the affinities of quinones represent an extension of the program into the analysis of a redox active ligand. These binding free energy calculations compare affinities determined using implicit and explicit Lennard-Jones intra-protein interactions in two independent RC crystal structures. The computed results are in good agreement with the experimental affinity measurements, permitting an evaluation of the factors that generate the different affinities of the different compounds.

Experimental vs. Calculated relative binding free energies

Measured affinities

The measured affinities of the quinones for the Q_A binding site span 5.04 kcal/mol, from -0.14 kcal/mol for DQ to 4.90 kcal/mol for the unsubstituted BQ (Table 1). The standard deviation of the measurements is ≈0.25 kcal/mol. The overall trend is that the smaller quinones bind more weakly than the larger ones. The first methyl adds 0.3 kcal/mol to the affinity. Comparing the affinity of 2,3 dimethyl-BQ with the 2,5 and 2,6 isomers shows the second methyl adds ≈1.0 kcal/mol irrespective of its position. The third and fourth methyl raise the affinity by an additional ≈2 kcal/mol and ≈1.6 kcal/mol. Thus, the experimental results suggest that the first substituent to BQ adds less to the affinity than do the latter ones. Changing 2,6 dimethyl to 2,6-dimethoxy increases the affinity by 0.9 kcal/mol, while the methyl-Q₀ essentially binds as tightly as DQ.

Calculated affinities

The analysis presented here focuses on the relative rather than the absolute affinity of the BQs. The binding free energy calculations were compared in two crystal structures, 1AIJ and 2UWU (Table 1, Figure S2).^86,87 On average the binding energies relative to Methyl-Q₀, are 1.1 kcal/mol less favorable in 1AIJ than in 2UWU. This value is taken from the best-fit line in Figure S2. In 1AIJ the average error of the relative affinity is 0.72 kcal/mol, while it is -0.6 kcal/mol in 2UWU. With either structure the standard deviation of the error is 2.3 kcal/mol. The slope of the best-fit comparison between experiment and calculations is 1.28 for 1AIJ and 0.92 for 2UWU (Table 2). The results in the two crystal structures are highly correlated, with a slope of 1.0, R² of 0.83, and with no individual K_d differences >±2.5 kcal/mol (See Figure S2). Values in the text will refer to 1AIJ unless noted and will focus on the explicit van der Waals simulation (Calc1 in Table 1), since it provides the most structural information. The calculations are reasonably successful in reproducing the experimental values (Figure 2, Table 1). Seven out of nine calculated relative binding energies have errors with absolute value ≤ 2.0 kcal/mol. All side chain and ligand conformations selected by Monte Carlo sampling during multiple cycles of conformer generation are included in the final affinity calculation. The binding energy is found to increase relatively smoothly as additional conformers are added. However, when cycles of conformer additions beyond those described in the Methods sections were tested the calculated affinity varies by less than 0.4 kcal/mol, showing the process has converged (Supplementary Table 1).

Table 2.

Expt: measured values; Calc^single: Single GROMACS minimized backbone, side chain and quinone position is evaluated with a QUICK calculation where only side chain isosteric and protonation conformers are sampled (see table S1); Calc¹ and Calc² are defined as in Table 1. Calc^scale: a scaling factor of 0.62 is applied to all protein-ligand van der Waals interactions. Range is the difference in affinity between the tightest and weakest binding quinone in kcal/mol. The other terms characterize the correspondence between the calculated and experimental relative affinities.

	Expt	Calcsingle	Calc1	Calcscale	Calc2
range	5.04	10.7	10.7	6.7	5.5
slope	n/a	0.016	1.28	0.81	0.97
R2	n/a	0	0.54	0.78	0.84
avg. abs. error	n/a	3.46	1.76	1.14	0.64
RMSD	n/a	4.2	2.29	1.4	0.77

Figure 2.

Experimental vs. calculated binding free energies (kcal/mol). (●): Explicit AMBER Lennard- Jones energies. Dashed-dotted lines show errors of ±2 kcal/mol. Eight out of ten quinones are within this range. The best fit slope is 1.28 with a RMSD of 2.29. (○): Implicit SAS term for protein-ligand Lennard-Jones interactions. The average ∣error∣ is now 0.64±0.44 kcal/mol. Dashed line: best fit line with a slope of 0.97 and R² of 0.84.

Relaxation of the quinone in the binding site

The importance of protein flexibility in modulating site recognition in protein-ligand binding is well established.^53,106 However, a full analysis of all possible ligand protein conformations is computationally very expensive. Additional degrees of freedom also introduce noise in the calculations due to fluctuations in the protein conformation that are unrelated to ligand binding. Here MCCE starts the calculation with ligand positions near the UQ₁₀ bound in the structure rather than doing an exhaustive search for the best global ligand position. Following a single GROMACS relaxation of the protein, the protein backbone is fixed, while the side chains and ligands can sample multiple positions. This is similar to programs such as GLIDE,¹⁰⁷ which allow the protein side chains and ligand to make small movements to relieve the van der Waals clashes.

The analysis of the quinone affinity starts with the generation of conformers for the ligand and the protein. The quinones are first bound with the substituent added to the crystal structure Q_A ring. The quinone has two carbonyl groups, hydrogen bonded to Ala M260 (position 1) and His M219 (position 4), methoxy groups at ring carbons 3 (pointed towards Ile M265) and 2 (near Thr M261), a methyl group at carbon 5 (towards Met M218) and the tail at carbon 6 (near Met M256) (Figure 3,5). These numbers will be associated with the 6 orientations in the protein throughout the discussion. Asymmetric substituents are allowed to sample all 4 orientations in the proteins keeping the carbonyls fixed, yielding from one (BQ and DQ) to four (methyl-BQ, tri-methyl-BQ and Q₀) starting positions. A QUICK MCCE calculation of the energies of the distinguishable substituent orientations give differences in affinity for the best and worst orientations in the original crystal structure ranging from 11 (2,6-dimethyl BQ) to 28 kcal/mol (either dimethoxy BQ)(Table S1).

Figure 3.

(a) The headgroup of the native quinone. The carbons on the ring are labeled from 1 to 6. The native ubiquinone has two carbonyl groups, hydrogen bonded to Ala M260 (position 1) and His M219 (position 4), methoxy groups at ring carbons 2 (near Thr M261) and 3 (near Ile M265) and, a methyl group at carbon 5 (towards Met M218) and the tail at carbon 6 (near Met M256). These orientations are used throughout the paper. (b-d) The energy in kcal/mol of each orientation is in the protein is underlined. (b) Energies for methyl groups in methyl-BQ docked into the four quadrants onto the crystal structure ring. Position 6 is the most favorable. (c) The 2,6 di-methoxy BQ is docked with the Methoxyls in the 2,6 or the 3, 5 positions. The first is at lower energy. (d) The Methyl-Q₀ is docked with the methoxys in the 2,3 or the 5,6 positions. The former is favored.

Figure 5.

Residues within 4Å of the Q_A headgroup. A and B are both views close to the ring plane but from slightly different angles. The same residues are shown in the two figures. The two H-bond partners to the ubiquinone are Ala M260 and His M219, which are highlighted in magenta in A. The black arrows label the quadrant designation. Figure B shows the binding site is too flat to allow significant rotation of the quinone out of plane.

The crystal structure, with the ligand substituent pose at the lowest energy in an initial MCCE run, is minimized with GROMACS to relax the backbone. The affinity of the various BQs in their GROMACS optimized structures, were determined with a QUICK run with the quinone position fixed. This QUICK run binding energy is in some ways similar to a MM-PBSA analysis of a single protein docked ligand conformation with pre-assigned ionization states. However, the MCCE calculation still allows isosteric conformer positions and acidic and basic residue protonation states to be optimized in the calculation that determines the affinity.⁸¹ A number of the smaller quinones show less than 1 kcal/mol difference in their affinity compared with that found for this quinone orientation in the original crystal structure. However, the backbone relaxation increases the affinity of DQ and 2,6-dimethoxy-BQ by ≈6 kcal/mol (Table S1). For Q₀ and methyl-Q₀ the single pose recovered from the GROMACS minimized structure binds 3~4 kcal/mol more weakly than the best quinone pose in the crystal structure. In both cases, the backbone van der Waals interactions are ≈5 kcal/mol more favorable in the minimized structure. However the 3-methoxy group, which is fixed in the QUICK run clashes with Thr M222 raising the energy by ≈7.5 kcal/mol. This will be relaxed when MCCE side chain optimization is added. The RMSD between experiment and the MCCE QUICK calculation following GROMACS backbone relaxation is 4.2 kcal/mol and the slope and R² are close to zero (Table 2).

DQ is the tightest binding quinone studied here with an affinity similar to methyl-Q₀, the analogue of the native UQ. However, it has the smallest affinity, 13 kcal/mol weaker than methyl-Q₀, when the methyl substituents are simply built onto the quinone ring in the crystal structure (Table S1). The MCCE QUICK run shows GROMACS optimization increases the DQ affinity by ≈6.7 kcal/mol by improving the van der Waals interactions, with negligible changes in the electrostatic energy. This is mostly due to changes in position of the Ala M249 and M260, which increases the affinity by ≈7.3 kcal/mol. The interaction of the DQ with the backbone of these two residues becomes ≈7.9 kcal/mol more favorable, while there are small unfavorable interactions with the side chain groups. The C_α hydrogen of M249 starts 1.6 Å from the DQ 2-methyl resulting in a 15.4 kcal/mol van der Waals clash (Figure 4). GROMACS relaxation increases this distance to 1.9 Å, reducing the energy to 4.8 kcal/mol. However, this pulls M260 closer, increasing the unfavorable interaction from 1.7 kcal/mol to 4.4 kcal/mol. These compromises represent an example of the strain energy built up on binding. The RMSD changes for the two Ala backbones are each ≈0.45 Å. The significant GROMACS relaxation of 2,6-dimethoxy BQ results from the release of a similar clash between a methoxy and the backbone of Ala M260 (Figure 4).

Figure 4.

The overlap of DQ and the backbone of Ala M249 and Ala M260 in crystal structure (magenta), GROMACS minimized structure (cyan) and MCCE optimized structure (yellow). The backbone amides are identical in GROMACS and MCCE structures so only the cyan is seen. Dashed lines label the distance between the quinone and the backbones of the two Ala residues. Black: crystal structure and GROMACS structure. Red: MCCE structure. The black arrows label the direction of the quadrants. Position 6 is occupied by the quinone tail in the native UQ₁₀.

Each GROMACS structure, optimized for each quinone, is now subjected to MCCE sampling of the side chain and ligand positions. This further increases the binding affinity by 0.3 to 7 kcal/mol. BQ, with the smallest van der Waals interactions, has the smallest and DQ the largest change. Small movements of DQ away from the GROMACS position considered above relieve clashes with the Ala M249 and Ala M260 backbone by ≈6 kcal/mol each. However the van der Waals interactions with the protein side chains, in particular Ile M265, become ≈4 kcal/mol less favorable. In total, the MCCE ensemble of accepted ligand and side chain position increases the DQ binding affinity by ≈7 kcal/mol. Thus, for the group of BQs coupled ligand, side chain and backbone relaxation is needed. While no dramatic conformational changes are found, small changes in the positions of the side chains of Ile M265, Met M262, Met M218, Thr M222 and Ile M223 lead to notable increase in the binding affinity.

Energy decomposition in the calculation of the quinone affinity

MCCE considers both explicit interactions, which depend on the atomic positions of the protein and ligand, and implicit energy terms, which depend on the atomic solvent-accessible surface area (SAS) or on the dielectric constant assigned to the protein and solvent. The implicit desolvation energy, and explicit electrostatic pair-wise interactions between the ligand and protein are obtained using DelPhi⁸⁴ to solve the Poisson Boltzmann equation. Explicit non-electrostatic Lennard-Jones and torsion energies are calculated with the AMBER force field.⁸² An implicit non-polar solvation energy term combines the hydrophobic energy, favoring quinone binding and favorable Lennard-Jones interaction between the quinone and the solvent. A value of -5 cal·mol^-1·Å^-2, used here, is taken from an earlier analysis of the vacuum to water transfer free energy of 67 molecules, including analogs to the polar amino acid side chains and protein amide backbone, using Delphi electrostatic energy with PARSE charges as does MCCE.^95,96

Electrostatic energies

The BQs whose affinities are calculated here are all neutral. As each has two carbonyls they are quadrapoles. The absolute total electrostatic contributions to binding range from -0.59 to -1.85 kcal/mol (Table 1). The biggest contributors are the ferrous non-heme iron that lies between Q_A and Q_B and His M219, which individually stabilize binding by up to 2.1 kcal/mol. The neutral His is both a ligand to the iron and a hydrogen bond donor to the quinone O₄. No other individual residue or backbone dipole has electrostatic interactions of more than 0.7 kcal/mol with any BQ. The loss in solvation energy, which opposes binding, is also not large, contributing from 1.5 to 2.7 kcal/mol. While the electrostatic interactions contribute a small amount to the affinity, they add 1.3 kcal/mol to the range of relative affinities of the different quinones. (See Table 1A) If the electrostatic interactions were ignored the average absolute error would increase from 1.75 to 2.0 kcal/mol.

One unique feature of the MCCE program is to be able to couple protein ionization with ligand binding. However, the quinone ligands studied here are neutral and situated at a relatively hydrophobic binding site. Thus calculated ionization states of the residues change little upon binding.

Non-electrostatic energies

The protein-ligand van der Waals interactions and the non-polar part of the solvation energy are the most significant contributors to the binding affinity, both in magnitude and in their differences between different quinones (Table 1). These strongly distance sensitive interactions are the most dependent on the optimization of the quinone position in the binding site. After relaxation the favorable van der Waals interactions range from -20.86 (BQ) to -32.56 kcal/mol (2,6 dimethoxy BQ).

As the size of the ligand increases, these interactions generally become more favorable. The most important contributions are from Trp M252 and Ile M265, ≈3.5 Å away from the Q_A ring plane in the original crystal structure. The interactions with the Trp M252 side chain range from -2.0 (BQ) to -5.3 kcal/mol (methyl-Q₀). Mutation of this conserved Trp leads to an RC that will not bind Q_A.^108,109 The interactions with Ile M265 can be as favorable as -3 kcal/mol. Thr M222 and His M219 can also contribute ≈-2 kcal/mol each.

Two energies are summed in the implicit non-polar interaction of the ligand with the solvent. One is the unfavorable energy to create a cavity for the ligand in solution, which is the source of the hydrophobic effect.¹¹⁰ The second is the favorable van der Waals interaction between the solvent and the ligand. Each of these is treated as being proportional to the surface area of the ligand (Eqn 2).⁹³ A value of -5 cal·mol^-1·Å^-2 is used,^95,96 which favors moving the ligand out of the water. This provides a small contribution to the affinity ranging from 0.67 for unsubstituted BQ to 0.07 kcal/mol for Q₀ relative to methyl-Q₀ (Table 1).

BQ orientation in the Q_A site

Ligand conformers

MCCE generates multiple conformations for the ligands at the RC Q_A site. In the final analysis of affinity, there are usually ≈20 conformers available for each ligand. Monte Carlo sampling assigns occupancy for each one, ranking the quinone orientations in the binding site. All ten BQs have several closely clustered conformers occupied in the Boltzmann distribution of states (Figure 6). The optimized orientations provide a view of the local interactions around the quinone. When the original crystal structure with the substituted BQs in place of the native quinone is compared with the optimized protein structure with all selected ligand conformers, no large conformational changes are found. The binding site is quite flat, restricting rotation around the carbonyl axis so only positions in the native quinone plane are found (Figure 5B). The smallest quinone studied is the unsubstituted BQ, which is 4.9 Å wide including hydrogens, while 2,6 dimethoxy is the widest stretching ≈9 Å. The smaller BQ and methyl-BQ occupy a number of positions near the native quinone. As the quinone gets larger its position is better defined. Comparing only the six carbons in the quinone ring and two carbonyl oxygens, the RMSD between the crystal structure Q_A ring and the most favorable conformer of each ligand ranges from 0.17 Å in Q₀ to 2.6 Å in unsubstituted BQ. This clustering of the quinone in the binding site is not unexpected given that all of these BQs can reconstitute UQ function, which requires them to be in position to be reduced within 10 ns of the excitation of the reaction center.^79,80

Figure 6.

The overlap of the crystal structure (magenta) with the final MCCE minimized structures with all selected protein and ligand conformers (blue). a: unsubstituted BQ, b: methyl-BQ, c: 2,5 di-methyl-BQ, d: tri-methyl-BQ, e: DQ, f: 2,6 di-methoxy BQ, g: Q₀, h: methyl-Q₀. The two H-bond partners to the ubiquinone, Ala M260 and His M219 and the most occupied ligand conformer are thicker sticks. As the ligand gets smaller more ligand poses are observed.

H-bonds to the ligand

The calculations can analyze the importance of specific interactions between the ligand and binding site. The two quinone carbonyls are hydrogen bond acceptors, O₄ from HN_δ of His M219 and O₁ from the backbone HN of Ala M260. However, a number of experiments have shown that the para-carbonyl arrangement is not required for binding or function.^42,79,111 A single carbonyl is sufficient for quinone binding.⁴² The ortho-napthoquinone reconstitutes Q_A activity¹¹² and ortho-phenanthroline is an often-used competitive inhibitor for quinone binding.¹¹³ Nevertheless, calculations here generally yield selected conformers with the two carbonyls pointing towards the native hydrogen partners (Figure 6).

The unsubstituted BQ was used to study the importance of the two H-bonds by rotating the ring moving the carbonyls from 1,4 to 2, 5 or 3, 6 orientations in the binding site (see Fig 5a). With the carbonyls in the 2,5 positions, overlaying a methyl and a methoxy in the native quinone, the quinone binds as tightly as in the 1,4 orientation. While the two H-bonds are lost weakening its electrostatic interactions with the protein by 2 and 1.2 kcal/mol respectively, there is now ≈3 kcal/mol more favorable van der Waals interactions with the protein. The affinity in the 3,6 orientation is 2 kcal/mol less. Thus for the unsubstituted neutral BQ, the carbonyl H-bonds are not indispensable for binding, though the rearrangement could change the reactivity.

The preferred methyl group positions

The first methyl increases the measured affinity by only 0.3 kcal/mol while the third increases it by 2.1 kcal/mol (Table 1). One challenge of the calculations is to explain these preferences. Methyl-1,4-BQ was built with its methyl group docked in each of the four quadrants (2, 3, 5 and 6) onto the UQ ring in the crystal structure. The relative affinity of each of the 4 orientations was determined by four separate binding calculations with only one conformer available in a QUICK MCCE calculation. The BQ with the methyl group in position 5 or 6 show very similar binding affinities (Figure 3). Adding a methyl group at position 3 is 4 kcal/mol less favorable. However the methyl is strongly disfavored at position 2, towards ThrM261, due to a clash between the methyl hydrogen and the C_α hydrogen of Ala M249 backbone. In the crystal structure there is a methoxy group at this position and the ether oxygen fits where the methyl does not. Thus the methyl, di-methyl and tri-methyl BQs place the first methyl group at position 5 or 6, with position 5 favored. Position 2 is filled only with DQ and requires backbone rearrangement and ligand movement. While this analysis was carried out with limited conformer sampling the same orientation preferences are found when the protein and ligand are allowed multi-conformer sampling. The calculated results do not fully explain the trend in binding affinity when adding methyl groups to the quinone ring. However it does show a strong preference for a methoxy rather than a methyl in this position, which contributes to the specificity of the binding site.

The distribution and orientation of the methoxy groups

There are three di-methoxy BQs studied here. In Q₀ and methyl-Q₀ the two methoxys are adjacent to each other. Monte Carlo sampling places these in protein positions 2, and 3, the same as the native quinone. This orientation binds ≈2 kcal/mol better than with the methoxys in protein positions 5 and 6 (Figure 3). The methoxy in the 2 position is required to reconstitute electron transfer from Q_A to Q_B in the RC.⁵ The methoxy groups in the 2,6-dimethoxy-BQ each situated adjacent to the same carbonyl prefer protein positions 2 and 6 rather than 3 and 5 by ≈6 kcal/mol due to clashes with Ala M248 and Met M218. In addition, protein position 2 strongly prefers to bind a methoxy group rather than a methyl group sorting the methyl and methoxy groups into the same quadrants as found with the native UQ.

When a methoxy group lies in plane the oxygen lone pairs are conjugated with the π-orbital of the ring system. This increases the ring electron density, decreasing the quinone E_m and lowering the energy of the system, while an out of plane methoxy is electron withdrawing and at higher energy.⁵ One consequence is that the methoxy position can tune the quinone redox potential, with an in plane substitution making the quinone harder to reduce.^5,114 For one methoxy group either with or without an adjacent methyl group, the in-plane conformation should be favored.¹¹⁵ When there are two adjacent methoxy groups, steric hindrance only allows one to be in-plane at a time. Despite the potential importance of the methoxy position, recent investigation of 34 RC structures at better than 2.8Å resolution shows that the methoxy groups are not well anchored in the binding site by either a hydrogen bond to the ether oxygen or by strongly defined contacts.¹¹⁶ The 3-methoxy group was found at an angle of -77±8° while the 2-methoxy’s position at 139±25° lies closer to being in plane, but is more variable.

Calculations were made with no special energy function applied to the methoxy positions. The standard van der Waals interactions will not allow two methoxys to both lie in plane, but did not account for the π electron donation into the ring that favors the in-plane orientation. The result is that all methoxy groups tend to lie out of plane with angles of 135.3±3.5°, 121±12.7° and 139.7±1° in the protein 3, 2 and 6 positions. Orientation 5 towards Met M218 is never occupied with a methoxy group.

Modification of the van der Waals terms

The van der Waals interactions, given by A/r¹² – B/r⁶, are exquisitely sensitive to the precise position of ligand and protein. Thus, small changes in orientation can change the ligand affinity by more than 20 kcal/mol (Table S1). The modest errors in the calculations with full MCCE treatment shows that this physics-based approach, developed for examining electrostatic interactions can also handle energies dominated by van der Waals interactions reasonably well. However, two alternative approaches that smooth these non-polar interactions were also investigated. In one the van der Waals energies were scaled, reducing the A and B coefficients by the same amount. In the second the non-polar energies were added solely with an implicit energy that is dependent on the surface area. The electrostatic desolvation energy and protein-ligand interactions continue to be taken from MCCE calculation based on the same multi-conformation protein structure and ligand positions.

The standard MCCE calculations use the full AMBER van der Waals potential. The slope for the comparison of experimental and calculated data is 1.28 implying MCCE overestimates the difference in interaction energy of the different compounds with the binding site (Table 2). The average explicit van der Waals energy is ≈ -81 cal·mol^-1·Å^-2. As described below an average van der Waals interaction of 50 cal·mol^-1·Å^-2 appears to provide a better estimate of the protein-ligand interactions, so both the A and B coefficients were reduced to 62% of their original values. The range of calculated binding affinities is now reduced from 10.7 kcal/mol to 6.7 kcal/mol, closer to the 5.0 kcal/mol found experimentally (Table 2). The RMSD is reduced from 2.29 to 1.4 and eight out of ten ligands have smaller errors.

A more extreme change is to treat the non-polar part of the protein-ligand interaction with another implicit, surface area dependent term, which is added to the non-polar solvation energy (Eqn 4). The best fit of the data and simulation comes with a surface area energy of -55 cal·mol^-1·Å^-2. Honig and coworkers have used a coefficient with a value of ≈-58 cal·mol^-1·Å^-2 for a similar analysis of the MHC class I protein-peptide binding.⁹⁷ Their calculated non-polar contribution to the binding free energy also favors ligand binding. The slope of the plot of experimental versus calculated relative binding free energy is now 0.97 with a R² of 0.84. As shown in Table 2 all measures of the correspondence between experimental and calculated affinities are improved (Figure 2, Table 2). The outliers remain the 2,6-dimethoxy BQ, with calculated value 1.4 kcal/mol more favorable and the unsubstituted BQ, which is 1.2 kcal/mol weaker than the measured value. While the analysis with the explicit van der Waals interactions shows that the MCCE sampling is able to generally find relatively good docked positions for each quinone, the excellent agreement with an implicit Lennard-Jones attraction shows that the Q_A binding site can easily accommodate the small quinones studied here.

The use of the fully implicit non-polar model mixes three surface dependent terms: the penalty for forming a cavity in water, the van der Waals interactions between solvent and solute and now the protein-ligand non-polar interactions. Here -5 cal·mol^-1·Å^-2 was used for γ₁ to represent the non-polar solvation energy, a value that favors pushing the quinone into the protein (Eqn 2). Increasing this to -55 cal·mol^-1·Å^-2 (γ₂) indicates an average of -50 cal·mol^-1·Å^-2 for the protein-ligand van der Waals interactions. The water- cyclohexane partition coefficients (log P) have been measured for these ten BQs.^76,77 The best fit line for surface area dependence of the non-polar transfer free energy has a slope of ≈ -21 cal·mol^-1·Å^-2, which is the difference in the dispersion energy between water and hexane plus the unfavorable cavity term in water (Figure S3). This independently calculated value is smaller than the -55 cal·mol^-1·Å^-2, which is the best fit for the binding calculations using the implicit protein-ligand van der Waals energy. Thus, the average non-electrostatic protein-ligand interaction is approximately twice as favorable as the average interaction of the ligand with hexane.

Outliers in the calculations

The unsubstituted BQ, which binds too weakly and 2,6-dimethoxy, which binds too tightly are the two outliers in the calculations in both crystal structures. The analysis of the small, unsubstituted BQ turns out to be the most challenging. The affinity calculated with explicit Lennard Jones interactions is 2.2 (2UWU) to 4.8 (1AIJ) kcal/mol weaker than measured. It is the smallest BQ included here and is thus the most mobile in the binding site. More conformers are accepted with bigger movements than for any of the other BQ (Figure 6) so it may be we do not find the full range of favorable poses. Given its greater mobility in the site, the calculations may also overestimate the entropy loss. As the weakest binding quinone, it also contains more uncertainty in its measured affinity, as it can be difficult to achieve the necessary amounts of mono-disperse quinone in solution.

The 2,6-dimethoxy BQ binds especially tightly when compared with the 2,3-dimethoxy containing quinones with error from -3.7 (1AIJ) to -5.5 (2UWU) kcal/mol. One source of error can be not properly accounting for the cost of pushing the methoxy groups out of plane when they are bound. When the methoxy is forced to take conformations in the ring plane the affinity is weakened by ≈1 kcal/mol reducing the error.

Concluding Comments

Numerous different approaches have been used for calculating binding by docking and scoring,^54,117-119 each with their own strengths and limitations. Calculations can come to within 0.5 kcal/mol of the experimental values using time-intensive, advanced MD methods.¹¹⁹ Faster methods using standard molecular-mechanics potential energy function can have a slope as steep as 1.77 with R² of 0.57 comparing experiment an calculation.¹¹⁸ Recent explorations of different scoring functions in MM-GBSA yielded poor to modest results with R² values of 0.21-0.36.¹¹⁷ All these indicate that protein-ligand binding remains a very challenging problem.

In this paper we describes a novel but computationally relatively inexpensive method to calculated binding affinities. MCCE combines pose generation and scoring. Flexibility is allowed for both ligand and protein side chains (but not backbone) using subroutines developed for exploration of side chain rotamer positions. The final calculation of affinity is carried out by Monte Carlo sampling of selected poses for ligand and side chains. Unlike almost all methods, which need to pre-assign the ionization states of the protein and ligand, all protonation and redox states for each residue and cofactor can also change in the Monte Carlo sampling that determines the ligand affinity. This unique feature allows study of the changes in the ionization states of the protein upon binding, which did not prove to be important here. However, it will permit analysis of the coupling of the changes in quinone electrochemistry to the differences in the binding affinity of the quinone and semiquinone.

With implicit protein ligand van der Waals interactions, the numerical results are improved, with a nearly ideal slope of 0.97 and a very good R² of 0.84. The success with implicit van der Waals interactions indicates that the solvent-accessible surface area correlates well with the protein-ligand van der Waals interactions as well as with the non-polar solvation energies. The Q_A binding site can generally accommodate these small compounds. The challenge then is to recover equally good results with a more complete model, which will provide more information about local interactions. A QUICK calculation of quinone binding affinity in the GROMACS optimized structure has an RMSD of 4.2 kcal/mol and an R² of ≈0 (Table 2). However, adding MCCE optimized conformers and calculating binding by Grand Canonical Monte Carlo sampling yield good results for the 10 quinones. The linear regression line comparing all measured and calculated K_ds has a slope of 1.28 with an R² of 0.54 using explicit van der Waals interactions. Thus, a single cycle of GROMACS backbone relaxation and full MCCE optimization of the ligand and side chain position is needed to relax small clashes that result within any rigid structure. The driving force for binding the neutral benzoquinone to the Q_A site is identified via calculation to be the protein-ligand van der Waals interaction, while the electrostatic energies contribute little. The favored distribution of the methyl and methoxy substitute on the benzoquinone ring is the same as the native quinone. In particular, quadrant 2 near ThrM261, binds a methoxy in the native UQ. A methyl will not bind in this position without changes in the backbone structure. Smaller quinones are more mobile at the binding site and allow more binding poses than larger quinones. In summary, calculations provide insight into how the Q_A binding site accommodates different type of quinones.

Abbreviations

MCCE

Multi-conformation Continuum Electrostatics

MC

Monte Carlo

MM-PBSA

Molecular Mechanics-Poisson Boltzmann Surface Area method

MM-GBSA

Molecular Mechanics-Generalized Poisson Boltzmann Surface Area method

ESP

electrostatic potential charge

GCMC

Grand Canonical Monte Carlo

UQ

ubiquinone

BQ

benzoquinone

DQ

tetramethyl-BQ

Q₀

2,3-dimethoxy, 5-methyl-BQ

methyl-Q₀

2,3-dimethxy, 5,6-methyl-BQ

RC

reaction center