Water-assisted Proton Transfer in Ferredoxin I

Abstract

The role of water molecules in assisting proton transfer (PT) is investigated for the proton-pumping protein ferredoxin I (FdI) from Azotobacter vinelandii. It was shown previously that individual water molecules can stabilize between Asp¹⁵ and the buried [3Fe-4S]⁰ cluster and thus can potentially act as a proton relay in transferring H⁺ from the protein to the μ₂ sulfur atom. Here, we generalize molecular mechanics with proton transfer to studying proton transfer reactions in the condensed phase. Both umbrella sampling simulations and electronic structure calculations suggest that the PT Asp¹⁵-COOH + H₂O + [3Fe-4S]⁰ → Asp¹⁵-COO⁻ + H₂O + [3Fe-4S]⁰ H⁺ is concerted, and no stable intermediate hydronium ion (H₃O⁺) is expected. The free energy difference of 11.7 kcal/mol for the forward reaction is in good agreement with the experimental value (13.3 kcal/mol). For the reverse reaction (Asp¹⁵-COO⁻ + H₂O + [3Fe-4S]⁰H⁺ → Asp¹⁵-COOH + H₂O + [3Fe-4S]⁰), a larger barrier than for the forward reaction is correctly predicted, but it is quantitatively overestimated (23.1 kcal/mol from simulations versus 14.1 from experiment). Possible reasons for this discrepancy are discussed. Compared with the water-assisted process (ΔE ≈ 10 kcal/mol), water-unassisted proton transfer yields a considerably higher barrier of ΔE ≈ 35 kcal/mol.

Introduction

Water can affect chemical and biological systems at various levels, including the formation of specific interactions through hydrogen bonding, the screening of Coulomb interactions, the mediation of proton transfer, or as an intrinsic component in the secondary structure of proteins. Usually, directly probing this role is difficult because of the transient nature of the processes involved. The difficulty also extends to probing the role of single water molecules in chemical and biological catalysis. Particularly in proton and hydrogen transfer reactions, the role (or absence of it) of water is often postulated but cannot be unequivocally proven. Examples include water involvement in ribozyme catalysis (1) where a large body of data suggests water involvement in RNA backbone trans-esterification or proton transfer in ferredoxin where the experiments were explained as a direct protein-to-[3Fe-4S] cluster transfer without participation of water (2, 3).

There are three profoundly different ways to characterize the role of water in a specific context. First, the water degrees of freedom can be essentially averaged out, and not much insight at the atomistic level can be gained. Second, a few individual water molecules are singled out, and their role can be analyzed in detail. Third, different types of water molecules can be distinguished, for example “surface-bound” versus bulk water molecules (4). Individual water molecules have been implicated in mediating proton transfer, and their role has been characterized by spectroscopic means (5). Structural studies, on the other hand, have established that individual water molecules play a central role in protein-ligand interactions such as in carbohydrate-protein binding (6) or in HIV-1 protease (7). In protein folding and protein-protein interactions, water has been found to act as a lubricant or “facilitator” in protein recognition (8, 9), and structural waters can render proteins more flexible (10). Also, it has been argued that water may even be conserved evolutionarily as an integral part of a protein structure (10).

Water has also been suggested to play important roles in proton translocation (11, 12). Two prominent examples are electron transfer processes (13) and ATP hydrolysis (14, 15). In general, proteins performing such proton transfer (PT)³ reactions are referred to as “proton pumps,” among which cytochrome c oxidase found in the mitochondrial electron-transfer chain (16–19) and bacteriorhodopsin found in photochemical reaction centers (20–23) are prime examples. Experimental observation of an enzymatic proton transfer has been found by Fourier transform infrared difference spectroscopy (24–26). However, direct experimental observation of PT at an atomistic level is generally difficult because it is a transient process.

Complementary to experimental work, theoretical and computational methods have been used to provide a more detailed understanding of PT processes (27–39). These methods are often based on empirical potentials (29–32), Car-Parrinello, or related approaches (33–37, 39). With standard force fields, it is not possible to examine in detail the dynamics of the proton transfer itself due to their inability to describe breaking and forming of chemical bonds. One way to circumvent this problem is to use mixed quantum mechanics/molecular mechanics calculations (QM/MM) (40, 41). They decompose the system into a part that is directly involved in the reaction and treat it with quantum mechanics, whereas the rest of the system is treated with a molecular mechanics force field. Other methods that use a QM/MM separation are empirical valence bond theory (42) or approximate valence bond theory (43). Recently, we introduced a new method for studying PT in protein-sized systems using molecular dynamics (MD) simulations (44, 45). This approach, named molecular mechanics with proton transfer (MMPT), is inspired by QM/MM simulations but combines a potential energy surface (PES; the “QM” part), suitable for describing the proton transfer between an acceptor and a donor atom, with a force field (the MM part) for the remaining degrees of freedom. The MMPT potential includes a modified treatment of hydrogen bonding that allows for the formation and breaking of bonds involving the proton being transferred (45). The main advantage of this approach over QM/MM is the performance, which is comparable with a force field simulation and makes it applicable for long time simulations of large systems such as proteins. In the present work, we present a generalization of MMPT to condensed phase systems and apply it to proton transfer in ferredoxin (3, 46, 47).

Ferredoxins are a family of small iron-sulfur proteins that mediate electron transfer, which are involved in such fundamental biological roles as photosynthesis and nitrogen fixation (48). One ferredoxin for which considerable amounts of structural and experimental data are available is ferredoxin I (FdI) from Azotobacter vinelandii, a nitrogen-fixating soil bacterium. It is known that the one-electron reduction of the iron-sulfur cluster in FdI is immediately followed by the uptake of a proton from the solvent. The mechanism of this proton transfer, which can be used as a model of a redox-driven proton pump, has been the subject of particular attention (46, 3, 49, 50). The kinetics of the electron-coupled proton transfer were probed experimentally using cyclic voltammetry, which, combined with site-directed mutagenesis, indicates that Asp¹⁵, a surface residue, plays an important role in catalyzing the proton transfer (51, 3). The simplest possible mechanism would involve a direct (water-unassisted) transfer of the proton from Asp¹⁵ to give the protonated [3Fe-4S]⁰H⁺ cluster. However, proton tunneling under such conditions is limited to distances of <0.25 Å (52, 53), and detailed MD and quantum chemical calculations show that the aspartic acid side chain in FdI is too far from the nearest μ₂-sulfur for efficient proton transfer to occur (45, 47). An alternative possibility is that proton transfer between Asp¹⁵ and S is mediated by a water molecule. Although no crystallographic water molecules near the iron-sulfur cluster were reported, detailed atomistic simulations showed that the active site of FdI is water-accessible and that the active site water is stabilized over extended periods of time and could potentially act as a proton relay (47, 54). It is known from experiment that when interior waters are mobile, they may not be detected in x-ray structures, and in many cases, the number of observed water molecules is smaller than that actually present (55–57). Thus, a water-mediated mechanism is plausible. The overall reaction studied with density functional theory (DFT) and free energy simulations in the present work is Asp¹⁵-COOH + H₂O + [3Fe-4S]⁰ → Asp¹⁵-COO⁻ + H₃O⁺ + [3Fe-4S]⁰ → Asp¹⁵-COO⁻ + H₂O + [3Fe-4S]H⁺. The forward barrier is found to be in good agreement with the experimentally determined rates, whereas the reverse barrier is somewhat overestimated. Contrary to this, the water-uncatalyzed reaction, which is also characterized by density functional theory methods, yields much higher barriers and is unlikely to occur.

MATERIALS AND METHODS

Electronic Structure Calculations

Following the previous study on FdI (54), electronic structure calculations were carried out at the spin-unrestricted level with the UB3LYP DFT functional and a 6–31G(d,p) basis set, using the Gaussian 03 suite of programs (58). Three model systems differing in complexity (models A to C) were considered for scanning the potential energy surface. They are shown in Fig. 1, A–C. Model A (33 atoms) includes the [3Fe-4S]⁰ cluster (total charge of the system q = −3, total spin S = 2) with thiomethoxy side chains replacing residues Cys⁸, Cys¹⁶, and Cys⁴⁹ from FdI; a water molecule coordinating to the S1 atom of the cluster; and acetic acid (AcOH) to model the Asp¹⁵ side chain from the 7FDR x-ray structure recorded at 1.4 Å resolution (59). Internal bond and angle geometries of [3Fe-4S]⁰ initially taken from 7FDR were optimized prior to proton transfer scans in this system. Model B (59 atoms, q = −3, total spin S = 2) is an extension of model A with a complete representation of residue Asp¹⁵ and parts (terminated by hydrogen atoms) of residues Cys¹⁶, Thr¹⁴, and Tyr¹³ to account for interactions of the nearby protein backbone with the proton transfer partners. The geometries of the cluster and amino acid backbone were taken from 7FDR, and the internal coordinates of the Asp¹⁵ side chain and the water molecule were optimized before the potential energy scans. A version of this model with the water molecule deleted was also used to study water-unassisted proton transfer. For the MMPT parametrization (see below) model system C, including a protonated [3Fe-4S]H⁺ cluster with the same thiomethoxy side chains attached as in model A, and a water molecule was used (26 atoms, q = −2, total spin S = 2; see Fig. 1C). Internal bonds and angles of the cluster and all degrees of freedom of the water molecule were optimized prior to calculating the interaction potentials.

FIGURE 1.

A, small model system used in the DFT energy scan. B, large model system for the DFT energy scan. C, model system used to calculate the two-dimensional PES used for fitting MMPT function. Wat, water.

Density functional theory scans for the complete proton transfer including the initial transfer (PT1) from Asp¹⁵-OH to a water molecule and a second proton transfer (PT2) from the hydronium ion intermediate H₃O⁺ to the [3Fe-4S] cluster were performed for models A and B of Fig. 1 along a reaction coordinate defined by the OD1 to HD1 distance r_OD1–HD1. For both models, internal and external coordinates of water were allowed to relax during the scans, whereas the coordinates of the cluster were kept fixed. This is a reasonable assumption as a comparison of the Fe-S distances between optimized protonated ([3Fe-4S]H⁺) and unprotonated ([3Fe-4S]⁰) clusters show only small differences (0.05 Å) (59). In model A, all external coordinates of AcOH except the donor oxygen OD1 to proton acceptor atom S1 distance (R_OD1–S1) were allowed to relax. R_OD1–S1 was constrained to three different values: R_OD1–S1 = 4.4, 4.7 (the value found in the x-ray structure of FdI), and 5.0 Å, resulting in three individual scans for model A. For the energy scan of model system B, only the degrees of freedom of the water molecule and the angle and dihedral connecting HD1 to OD1 of Asp¹⁵, were optimized at each point of the scanning coordinate. Relaxing more degrees of freedom is computationally very demanding for this structure. Each scan in model systems A and B in Fig. 1 was performed along r_OD1–HD1. Starting from r_OD1–HD1 = 0.8 Å, the distance was increased in steps of 0.1 Å until the transition state (TS) was reached, and atom H2 of the water molecule was transferred to S1 of the [3Fe-4S] cluster. Close to the transition state, the step size was reduced to improve the resolution of the potential scan in this region.

To parametrize the MMPT potential for PT2 H₃O⁺ + [3Fe-4S]⁰ → H₂O + [3Fe-4S]H⁺, a two-dimensional scan of the potential energy surface was calculated starting from the energy-optimized model C in Fig. 1C. The S1 to OH2 distance R₂ and the S1 to HS distance r₂ along the hydrogen bond were scanned, whereas all other degrees of freedom were kept rigid. A total of 347 points were calculated. The resulting energy surface (shown in Fig. 2A) has a single minimum that corresponds to having the proton closer to S1, forming a strong hydrogen bond to the water molecule (see Fig. 1C).

FIGURE 2.

A, contour plot of the potential energy surface resulting from the DFT scan on model C along ρ₂ = (r₂ − 0.8)/(R₂ − 1.6) and R₂. B, example of the fitting process used to avoid double counting of the molecular mechanics nonbonded terms. V_PT is fitted to the difference between the DFT energy and V_MM. The slice shown is for constant R₂ = 3.36 Å. Black diamonds, V^ref(x⃗), which is DFT energy; dotted black line, V_MM(y⃗), which is the MM energy calculated when V_PT is set to 0; gray triangles, V^ref (x⃗) − V_MM (y⃗); gray line, V_PT(R₂, ρ₂, θ₂), obtained from a least-squares fit of the asymmetric double minimum potential shown in the supplemental data to the gray triangles; black line, total fitted MMPT potential V^fit(x⃗).

MD Simulations and Intermolecular Interactions

All atomistic simulations were carried out with CHARMM (60) and the CHARMM22 force field (61) with provisions for the MMPT potential (45). Further details of the simulations are given below and in the supplemental data. Conventional force fields cannot describe the breaking or formation of bonds because stretching potentials are typically parametrized as harmonic oscillators. In contrast, MMPT uses a functional form for V_PT(R, ρ, θ), which is based on Morse potentials and allows for describing proton or hydrogen transfer between D and A. The total potential energy of the system with respect to all coordinates x⃗ is decomposed into a part for the proton transfer motif (V_PT(R, ρ, θ)) and the remaining degrees of freedom y⃗ of the system. Thus, the total interaction is written as shown in Equation 1,

where R is the distance between the heavy atoms, ρ is the PT progression coordinate, defined as ρ = (r − 0.8)/(R − 1.6), and θ is the hydrogen bonding angle. In the following, PT1 takes place between Asp¹⁵-COOH and water (OD1-HD1···OH2) and PT2 between [3Fe-4S] and water (S1-H2···OH2) (see Fig. 1). According to this definition, PT1 and PT2 start at each end of the overall PT reaction and develop toward the hydronium ion. Thus, for PT1, θ is the hydrogen bonding angle, OH2-HD1-OD1, and for PT2, it is OH2-H2-S1. Subsequently, the variables R₁, ρ₁, and θ₁ refer to PT1 and variables R₂, ρ₂, and θ₂ to PT2.

A consequence of using a large model system such as the one in Fig. 1C as a reference for fitting is that nonbonded interactions beyond the immediate vicinity of the proton transfer play a potentially important role. This is unlike the case of the prototype systems used previously, such as H₅O₂⁺, where these interactions are included in V_PT2 (62). As a result, it is no longer appropriate to fit V_PT directly to the DFT potential energy surface because that would result in double counting of the nonbonded interactions when V_PT is added to the CHARMM force field. Instead, V_PT has to be fitted to the difference between the DFT energy, and the energy computed using the force field when V_PT is set to zero (from Equation 1, V_PT(R₂, ρ₂, θ₂) = V(x⃗) − V_MM (y⃗). This relation is shown graphically in Fig. 2B for PT2. The difference between the potential including double-counted interactions (V_PT2, black curve in Fig. 2B) and that without it (gray curve in Fig. 2B) remains nearly constant in the region where PT takes place. V_PT2 is shifted by ≈ 6 kcal/mol after subtraction of V_MM(y⃗). For the problem studied here, this means that total energies are moderately influenced by double counting, whereas the PT barrier remains nearly unaffected. The procedure of refitting the surface to account for the double counting of nonbonded interactions is described in detail in the supplemental data.

To distinguish between the different protonation states, the following nomenclature is used: “state 1” has Asp¹⁵ protonated (-COOH), “state 2” has the water molecule protonated (H₃O⁺), and “state 3” has the iron-sulfur cluster protonated ([3Fe-4S]H⁺). As a first approximation, the transition between state 1 and state 2, and between state 2 and state 3 may be assumed to lie at ρ₁ = ρ₂ ≈ 0.5. However, this assumption can be refined based on the shape of the free energy surface obtained from the simulations.

Potentials of Mean Force

One-dimensional potentials of mean force were calculated from MD simulations using umbrella sampling (63). The simulations were started from an equilibrated structure of the reduced protein (Protein Data Bank code 7FDR) at 300 K in a 62 Å cubic TIP3P (64) water box with periodic boundary conditions. The time step in the simulations was 0.5 fs, and all bonds to hydrogen atoms except for those in the water molecule involved in the proton transfer were constrained using the SHAKE algorithm (65). The potentials of mean force are built from individual 50-ps simulations (after 2 ps of further equilibration) with harmonic biasing potentials ranging from k_umb = 30 to 600 kcal mol⁻¹ along the reaction coordinates. To follow PT1, the driving coordinate was defined as λ₁ = r₁/R₁, where r₁ is the OD1-HD1 distance, and R₁ is the OD1-OH2 distance (see Fig. 1A). The corresponding coordinate for PT2 is λ₂ = r₂/R₂, where r₂ is the S1-H2 distance, and R₂ is the S1-OH2 distance already used above. λ₁ and λ₂ were modified in intervals of 0.05 along the umbrella sampling simulation. The λ-coordinate was chosen as a proxy for ρ for practical reasons. A graphical representation for the relationship between ρ and λ is given in the supplemental data. To account for some of the charge transfer that accompanies proton transfer, atomic charges appropriate for each value of the reaction coordinates were modified (see supplemental data). The data from individual simulations was combined with a weighted histogram analysis (66).

Minimum Energy Pathway

The potential energies along λ₁ and λ₂ were also calculated starting from the MMPT-equilibrated protein structures in states 1 and 3, respectively, with both proton transfers occurring toward state 2. The absolute minimum along the PT scan was determined prior to constraining the system at different values of λ by running 1000 steps of steepest-descent minimization followed by multiple steps of adopted basis Newton-Raphson minimization with a gradient-based cut-off of 10⁻⁶. Subsequent adopted basis Newton-Raphson minimization with the same average gradient tolerance were carried out starting from the minimum energy structures by constraining the system to the average λ-geometries obtained from each individual umbrella sampling window.

RESULTS

Proton Transfer from DFT Calculations on Model Systems

Potential energy scans as described in “Materials and Methods” were carried out for model systems A and B (Fig. 1, A and B) along the OD1-HD1 distance r₁. This yields the minimum energy path (MEP) for double proton transfer and allows to identify the geometries of formation and decomposition of the intermediate H₃O⁺ species. Furthermore, it is possible to locate the transition state. The corresponding MEPs are shown in Fig. 3. The initial transfer (PT1) from acetate to the water molecule, which leads to AcO⁻···H₃O⁺, completes at r₁ = 1.40 Å, R₁ = 2.50 Å, and ρ₁ = 0.66 in all four scans. None of the potentials show a local minimum at this point, i.e. H₃O⁺ is energetically not stabilized. Rather, the energy continuously increases along the progression coordinate until the second transfer (PT2) from H₃O⁺ to [3Fe-4S]⁰ takes place. Therefore, the overall proton transfer from AcOH (or Asp) to [3Fe-4S]⁰ involves only a single TS. The initial transition to H₃O⁺ (PT1) in model A, located at r₁ ≈ 1.4 Å, has relative energies of 5.2, 6.5, and 4.7 kcal/mol for R_OD1–S1 = 4.4, 4.7, and 5.0 Å, respectively. The TS barrier for double proton transfer is located at r₁ = 1.57, 1.50, and 1.80 Å with energies of 7.6, 8.1, and 10.1 kcal/mol for R_OD1–S1 = 4.4, 4.7, and 5.0 Å, respectively. For R_OD1–S1 = 4.4 and the larger 6–311G(d,p) basis set, this increases from 7.6 kcal/mol to 10.0 kcal/mol.

FIGURE 3.

Coupled PT MEPs calculated by DFT for model systems A (black) and B (gray) as described under “Materials and Methods.” Scans of model system A were calculated for fixed OD1 to S1 distances of 4.4 Å (solid line), 4.7 Å (dashed line), and 5.0 Å (dotted line).

For model B, only one scan was carried out for R_OD1–S1 = 4.8 Å. The TS for the forward double-PT reaction is at r₁ = 1.58 Å with a barrier of 30.2 kcal/mol. The difference between models A and B is related to the fewer degrees of freedom that are allowed to relax in model B. Thus, the system has more strain, which is also indicated by the much steeper slope of the surface. On the other hand, the back transfer barrier of this model system is only 8.1 kcal/mol. Overall, the electronic structure calculations consistently find no stabilized intermediate (H₃O⁺), and the barrier for proton transfer is sensitive to rearrangements in the Asp¹⁵ side chain, which are possible only for the relaxed model A scans.

It is also possible that such a concerted PT reaction involves electronic coupling. To test this, a reverse scan was performed for R_OD1–S1 = 4.4 Å starting in state 3. The energy of the transition state differs by only 0.2 kcal/mol compared with the forward scan but because the potential energy surface is flat around the transition state, the S1-H2 distance differs by ≈ 0.25 Å between the two structures. Despite this considerable geometrical difference the largest deviation between the Mulliken charges of the atoms involved in PT does not exceed 0.07 e. Thus, the different states are not coupled electronically, and the process is ground-state proton transfer.

Reactions PT1 and PT2 from Umbrella Sampling

To validate the MMPT force field in the protein environment, constant energy MD simulations were carried out. For this, 100 ps were run starting from an equilibrated structure of solvated 7FDR. All hydrogen atoms, except for the hydrogen atoms in the water molecule as well as the proton being transferred, were constrained using SHAKE (65). A time step of 0.5 fs was used to follow the rapid H-motion explicitly. Fig. 4 reports the histogram of E_tot(t) and temperature T(t), which show no drift over the time interval studied here and establish that the computational procedure is reliable and meaningful.

FIGURE 4.

Validation for energy conservation in an MMPT MD simulation of FdI. Left, histogram of the energy fluctuations around the mean from a 100-ps simulation. Right, fluctuation of the temperature from the same simulation.

The experimental rate constant describing proton transfer from the protein (Asp¹⁵) to the [3Fe-4S]⁰ cluster was determined from fast scan protein film voltammetry at pH 8.34 as k_on^hop = 1294 ± 100 s⁻¹ and the back transfer rate from [3Fe-4S]⁰H⁺ to the protein (Asp¹⁵⁻) as k_off^hop = 332 ± 25 s⁻¹ (2). According to transition state theory, such a rate k^TST is related to the free energy of activation ΔG^‡ by Equation 2,

where k_B is the Boltzmann constant, T is the temperature in K, h is the Planck's constant, and R is the gas constant (67). From the experimental rate constants (k_on^hop and k_off^hop) free energies of activation ΔG_on^‡ = 13.3 ± 0.05 and ΔG_off^‡ = 14.1 ± 0.05 kcal/mol for the forward and backward reaction are obtained, respectively. Such barriers are too large to be accessible to unconstrained molecular dynamics simulations. Therefore, the reactive steps were in the following investigated by using umbrella sampling (63).

The first proton transfer (PT1) Asp¹⁵-COOH + H₂O → Asp¹⁵-COO⁻ + H₃O⁺ was reinvestigated with the asymmetric potential energy surface (see Ref. 45) but now included fluctuating charges on the atoms involved in the proton transfer motif (see “Materials and Methods” and supplemental Fig. S3). The potential of mean force from umbrella sampling simulations is shown in Fig. 5A (solid line). The free energy curve does not show a barrier but a characteristic flattening around λ₁ = 0.56, which is related to formation of H₃O⁺. This configuration is ΔG_PT1^‡ = 11.7 kcal/mol above the Asp¹⁵-COOH + H₂O state, which is somewhat higher than in the earlier work, which was 8.2 kcal/mol (45). This difference is related to the use of fluctuating charges in the present work, which takes into account partial charge transfer from OD1 of Asp¹⁵ to OH2 of water (for PT1) and subsequently to S1 of the cluster (for PT2), see supplemental data. The dotted and dashed curves in Fig. 5A correspond to the gas-phase minimum energy path from PES 1 and the path calculated in the condensed phase (protein) environment. The gas-phase minimum is shifted from λ₁ = 0.34 to λ₁ = 0.36 compared with the minimum energy path (from condensed phase minimizations) and the potential of mean force (from MD simulations), respectively. Fig. 5B reports a projection of the average PT coordinate from umbrella sampling onto the corresponding potential energy surface from DFT calculations from Ref. 45. In the minimum of state 1, R₁ lies between 2.8 to 2.9 Å. Decreasing λ₁ increases R₁ and thus separates the water from Asp¹⁵. As the reaction progresses, the water approaches R₁ = 2.5 Å, and as soon as the proton is completely transferred (in state 2; ρ₁ ≈ 0.7), R₁ rises again with increasing λ₁, which corresponds to the positively charged hydronium ion moving away from the deprotonated Asp¹⁵ residue.

FIGURE 5.

Shown are gas phase MEP (dotted line), condensed phase MEP from MMPT minimizations in protein (dashed line), and PMF from MMPT MD simulations in protein (solid line) described for PT1 (A) and PT2 (C) along λ₁ = r₁/R₁ and λ₂ = r₂/R₂, respectively. r₁, R₁, r₂, and R₂ are described in the insets of A and C. B and D, average trajectories followed during the PMF simulations on the ρ₁ = (r₁ − 0.8)/(R₁ − 1.6), R₁ surface for PT1 (B) and on the ρ₂ = (r₂ − 0.8)/(R₂ − 1.6), R₂ surface for PT2. The contour plot show the DFT PES. The squares represent average coordinates from each MD simulation, labeled according to the center of the umbrella potentials.

For PT2, the potential of mean force is shown in Fig. 5C as a solid line. The minimum at λ₂ = 0.36 corresponds to the proton closer to the S1 sulfur atom (although forming a strong hydrogen bond with the water molecule). For comparison, the gas-phase minimum energy path from the potential energy surface in Fig. 2A is also shown (dotted line in Fig. 5C). The two curves are qualitatively similar, although the MEP rises more steeply at higher λ₂. The dashed line represents the condensed phase minimum energy path. Between λ₂ = 0.4 and 0.5, the curve is ≈ 3 kcal/mol higher than the gas-phase MEP but for λ₂ > 0.5, it lies between the gas-phase MEP and the condensed phase PMF. This suggests that the protein environment provides additional stabilization of the hydronium ion. State 2 appears around λ₂ = 0.65 in Fig. 5C, where the gradient of the potential of mean force flattens out. The corresponding free energy difference relative to H₂O + [3Fe-4S]⁰H⁺ is ΔG_PT2^‡ = 23.1 kcal/mol. Fig. 5D shows the average trajectory of the PMF projected onto the R₂, ρ₂ surface. At small ρ₂, the water molecule is far from the S1 sulfur (R₂ = 4.0 Å). The initial increase of ρ₂ is primarily related to a reduction of R₂, i.e. the water molecule shifts toward the acceptor S1. The actual PT2 takes place at R₂ ≈ 2.5 Å. Beyond ρ₂ = 0.8, R₂ increases again, which corresponds to the completed formation of the hydronium ion. Subsequently, it is detached from the [3Fe-4S] cluster without the formation of a stable minimum. Thus, the overall proton transfer reaction is most likely concerted.

Having identified proton transfers PT1 and PT2 separately with both exhibiting a flattening of the PMF around state 2, it is also possible to connect the two processes. This amounts to a diabatic treatment around the transition state and provides an overarching description of H⁺ transport from the protein via the water molecule toward the buried iron-sulfur cluster. Fig. 6, A and B, shows typical structures from the umbrella sampling simulation for PT1 and PT2 in state 2. PT1 occurs with the proton-accepting water molecule preferentially arranged near the bulk. During PT2, the same water molecule coordinates to the S1 atom of [3Fe-4S] and the OD1 atom of Asp¹⁵. The structural transition from state 2 of PT1 (Fig. 6A) to the corresponding state for PT2 (Fig. 6B) therefore consists mainly of a rotation of the hydronium ion. The two separate potentials of mean force from Fig. 5, A and C, describing PT1 and PT2 are shown together in Fig. 6C. It should be noted that there is no a priori relationship between the two progression coordinates λ₁ and λ₂, which is illustrated by the dashed line that symbolizes the uncharacterized parts of the free energy surface. However, as the two structures of Fig. 6, A and B, demonstrate, the PES is probably very flat in this region. Because both potentials of mean force do not have a barrier for reaching state 2 (H₃O⁺) from their corresponding minima, the merged PMF also consists of only one transition state region with the previously determined forward (ΔG_PT1^‡ = 11.7 kcal/mol) and backward (ΔG_PT2^‡ = 23.1 kcal/mol) barriers.

FIGURE 6.

A, typical structure in state 2 of the PT1 reaction. B, same as A but for PT2. C, combined PMF curves for PT1 (black) and PT2 (gray) aligned to the same free energy level at λ₁ = 0.56 and λ₂ = 0.65 according to the identified H₃O⁺ states from the total PT DFT scans evaluated using model A. Error bars indicate potential energy fluctuations along λ₁ and λ₂. The postulated transition of the hydronium ion between state 2 of PT1 and PT2 is indicated as a dashed line.

In each of the density functional theory scans (models A and B), the initial transfer from OD1 to the water (PT1) is completed at an OD1-HD1 distance of r₁ = 1.4 Å and a OD1-OH2 distance of R₁ = 2.50 Å. The OH2-HD1 distance at this point therefore is 1.1 Å (θ = 180°), and PT1 is regarded to be completed. Nearly the same average geometry was sampled in the potential of mean force of PT1 using MMPT at λ₁ = 0.56. This is the region where the surface in Fig. 5A is flattening out and suggests completed formation of H₃O⁺. Geometries determining state 2 of PT2 were extracted from scans of model A with density functional theory at a S1-OD1 distance of 5.0 Å (dotted line in Fig. 3). In this scan, the H₃O⁺ species remains stable up to r₁ = 1.8 Å. The PT2-related coordinates at this point are r₂ = 1.96 Å and R₂ = 3.00 Å corresponding to λ₂ = 0.65, which is the region on the PMF of PT2 (Fig. 5C) that exhibits flattening.

DISCUSSION

In the present work, atomistic simulations with provisions to describe hydrogen- or proton-transfer reactions and electronic structure calculations were combined to characterize water-assisted proton transfer in a protein. A concrete procedure for using the MMPT potential in extended and fully solvated condensed-phase systems is presented. The strategy is based on model ab initio calculations around critical points of the interaction potential and avoids double counting of nonbonded interactions.

For proton transfer between the Asp¹⁵ side chain and the buried [3Fe-4S] cluster in FdI, both approaches (MMPT and DFT) support a concerted double PT in which PT1 is the rate-determining step. Previous computational studies also concluded that PT reactions on or near a protein surface proceed semi- to fully concerted rather than stepwise (38, 39, 68). However, these studies were carried out either at the semiempirical level with variational transition state theory (which neglects explicit dynamics) (68) or with calculation of minimum energy pathways on an ensemble of structures (39), or by using density functional theory without dynamics (38).

Computed values for ΔG_PT1^‡ and ΔG_PT2^‡ can be directly related to the free energies of activation ΔG_on^‡ and ΔG_off^‡ evaluated from experimentally measured rate constants. ΔG_PT1^‡ (Fig. 5A) underestimates ΔG_on^‡ slightly by 1.6 kcal/mol, whereas ΔG_PT2^‡ overestimates the experimental barrier ΔG_off^‡ by 9.0 kcal/mol and is only in qualitative agreement with experiment. Taking zero-point energy corrections into account, both barriers will be further lowered by ≈ 2 kcal/mol. Furthermore, the experimental rate k_on^hop = 1294 s⁻¹ was measured at a pH of 8.34. At a physiologically more relevant acidic pH (69, 70), the experimental rate for PT2 is smaller (k_off^hop = 36 ± 5 s⁻¹ at pH 5.0 (2)), which, according to transition state theory, corresponds to a barrier increase by ΔG_PT2^‡ = 1.4 kcal/mol compared with pH 8.34. In the simulations for PT2, the carboxyl group of Asp¹⁵ is deprotonated, which covers the situation down to a pH of ≈ 4.1 (the pK_a of Asp lies at 4.1 (71)). Because the measured barriers for proton transfer are pH-dependent, this has to be taken into account in comparing with the computed value. Applying both zero-point corrections (2.0 kcal/mol) and corrections due to the pH dependence (1.4 kcal/mol), the difference between the computed and the experimentally determined barrier for PT2 reduces to 5.6 kcal/mol.

Similarly to this, DFT scans (model compound A) at different R_OD1–S1 show larger variations of barrier heights for PT2 compared with PT1. A possible effect in umbrella sampling is local relaxation of the environment which can lead to an overstabilization of one state over the other (72). To assess such relaxation effects, 100 individual and unconstrained MMPT MD simulations starting in state 2 (λ₁ = 0.56 and λ₂ = 0.65; i.e. proton-transferred state) were run and the potential energy along λ₁ and λ₂ was collected until they reached the potential minima. The fluctuations δV of the potential energy (indicated as bars in Fig. 6C) remain moderate for PT2 down to λ₂ ≈ 0.55 but increase sharply up to ≈ 10 kcal/mol when approaching geometries of the [3Fe-4S]H⁺ state. Corresponding fluctuations for PT1 are of similar size for large λ₁ but remain moderate (δV ≈ 5 kcal/mol) for structures around the minimum of PT1. It is important to note that these fluctuations are not “errors;” rather, they reflect the variation in potential energy of downhill dynamics from the TS toward the respective local minimum, and thus, they also exclude entropic contributions. Similar amplitudes for instantaneous relaxation in large condensed phase systems have previously been found to lead to significant changes in barrier heights due to long range forces and global perturbations (73). In conclusion, both DFT and MMPT MD simulations suggest stronger fluctuations for PT2 compared with PT1. An additional reason for the different degrees of agreement of the forward and reverse barriers for PT1 and PT2 is the increased complexity of PT2. PT1 involves essentially PT between COOH and water, which is a relatively simple process to capture with electronic structure calculations. On the other hand, proton transfer between [3Fe-4S]H⁺ and water is much more challenging and quantitative information is likely to be more difficult to obtain.

The transition state energies calculated with models A (smaller, more degrees of freedom relaxed) and B (larger, fewer degrees of freedom relaxed) differ considerably (10.1 kcal/mol versus 30.2 kcal/mol). This can be primarily related to the increased flexibility allowed for in model A, which is also supported by the umbrella sampling simulations that find a barrier energy of ΔG_on^‡ = 13.3 kcal/mol. Comparing the structures of model A obtained in the minimum of state 1 with the one of state 3 shows that AcO⁻ reorients considerably during proton transfer. The RMSD of AcO⁻ between the two structures aligned to the [3Fe-4S] atoms is 5.8 Å for the scan with R_OD1–S1 = 5.0 Å. The important structural differences leading to such a large rearrangement are a distance increase of 1 Å between the CG atom of AcOH and the S1 atom of [3Fe-4S] in going from state 1 to state 3 and more noticeably a near inversion of AcOH along the CB-CG vector. This finding corroborates the swinging-arm conduction mechanism suggested from the rapid-scan voltammetry on FdI (2), which is also referred to as a “piggy back” mechanism. Other long range proton-shuttling systems for which the swinging-arm conduction was proposed are NADH or NADPH (74) and bacteriorhodopsin (22). Structures from umbrella sampling simulations in state 1 and state 3 also show an elongation of the CG-S1 distance by ≈ 0.5 Å. On the other hand, a complete inversion of the Asp¹⁵ side chain along the CB-CG axis in the simulations could not be observed as it is expected to induce major reorientation in the protein backbone. Electronic effects involved in reducing the barrier from 30 kcal/mol to 10 kcal/mol between models A and B can be excluded. For example, Mulliken charges on the atoms involved in PT from structures around the transition state show no significant differences (<0.05 e) between models A and B. The DFT profile from model A with R_OD1–S1 = 5.0 Å yields a forward barrier of 10.1 kcal/mol and a reverse barrier of 13.7 kcal/mol, both of which are close to the barriers derived from the experimental rates. All other DFT scans performed in this work (especially those with short R_OD1–S1) have their global minimum in state 1. These observations suggest that state 3 in FdI must have larger R_OD1–S1 compared with the 7FDR x-ray structure. These general conclusions are supported by the umbrella sampling simulations with MMPT, which find 〈R_OD1–S1〉 = 4.8 Å in state 1, 〈R_OD1–S1〉 = 4.5 Å around the TS, and 〈R_OD1–S1〉 = 5.3 Å after formation of [3Fe-4S]H⁺, all consistent with the DFT calculations.

It is worthwhile to mention that relaxed DFT scans for model B at the UB3LYP/6–31G(d,p) level for water-unassisted proton transfer from the −COOH group to the accepting sulfur atom of [3Fe-4S]⁰ yield a barrier of ΔE ≈ 35 kcal/mol, which makes such a process considerably less likely. Compared with this, water-assisted proton transfer reduces this barrier to ΔE ≤ 10 kcal/mol and brings it within the range of experimentally observed rates (2).

In summary, generalized MMPT has been applied to PT in FdI, which involves transport of one proton from the solvent-exposed Asp¹⁵ residue via a water molecule to a buried [3Fe-4S] cluster. The PMFs from MD simulations show that the hydronium ion (H₃O⁺) is not a stable intermediate in the protein cavity. Therefore, the postulated water-mediated PT from Asp¹⁵ to [3Fe-4S]⁰ is most likely a concerted process. Barriers from the present PMF curves qualitatively agree with experimentally determined rate constants of the PT process in FdI. Quantitatively, the forward PMF barrier is in good agreement with experimental data. Our DFT scans using different model systems either over- or underestimated this barrier mainly due to the difficulty of finding a model structure that balances flexibility and protein backbone constraints that affect the conformational dynamics of Asp¹⁵ (cf. swinging-arm mechanism). In addition, the DFT models include only the immediate protein environment without explicit solvent. From such models, no quantitative information can be expected. The present study establishes that it is possible to investigate PT reactions in condensed phase environments, including explicit solvation and at atomistic detail by using generalized MMPT. By studying PT in FdI, MMPT has proven to be a practical tool to simulate multistep PT processes in proteins.