Hydrogen Tunneling and Conformational Motions in Nonadiabatic Proton-Coupled Electron Transfer between Interfacial Tyrosines in Ribonucleotide Reductase

Abstract

Ribonucleotide reductase is essential for DNA synthesis and repair in all living organisms. The mechanism of E. coli RNR requires long-range radical transport through a proton-coupled electron transfer (PCET) pathway spanning two different protein subunits. Herein, the direct PCET reaction between the interfacial tyrosine residues, $\mathrm{Y}356$ and $\mathrm{Y}731$, is investigated with a vibronically nonadiabatic theory that treats the transferring proton and all electrons quantum mechanically. The input quantities to the PCET rate constant expression are computed with a combination of density functional theory and molecular dynamics simulations. The calculations highlight the importance of hydrogen tunneling in this PCET reaction. Compression of the distance between the proton donor and acceptor oxygen atoms of the interfacial tyrosine residues is essential to facilitate hydrogen tunneling by increasing the overlap between the reactant and product proton vibrational wavefunctions. This compression occurs by thermal conformational fluctuations of these interfacial tyrosine residues. N733 and R411 are identified as key residues that can hydrogen bond to $\mathrm{Y}731$ and $\mathrm{Y}356$, respectively, and thereby compete with the hydrogen-bonding interaction between $\mathrm{Y}731$ and $\mathrm{Y}356$ required for direct PCET. Understanding the roles of hydrogen tunneling and conformational motions in this interfacial PCET reaction, as well as identifying other residues that may impact the kinetics, is important for targeted protein engineering efforts to modulate RNR activity.

Graphical Abstract

INTRODUCTION

Ribonucleotide reductase (RNR) is a critical enzyme for DNA synthesis and repair, given that its primary function is to convert ribonucleotides into deoxyribonucleotides.^1–4 It is an essential component for the survival and function of all living organisms, and its elevated activity and expression in many types of cancer have led to the clinical use of chemotherapeutic agents that inhibit RNR.^5–6 In E. coli RNR, the catalytic process is initiated through a cysteine radical that is generated via a proton-coupled electron transfer (PCET) pathway spanning ~32 Å across the α and β subunits of the enzyme.^{2, 4} This pathway starts with a tyrosyl radical at residue Y122 in the β subunit, which is transferred through the β subunit, across the interface, and then through the α subunit via a series of reversible PCET reactions, ultimately generating a cysteine radical at C439 in the α subunit (Figure 1).⁷

Figure 1.

3.6 Å resolution cryo-EM structure of the E. coli RNR active α₂β₂ complex and its ~32 Å PCET pathway consisting of Y122 ↔ [W48] ↔ Y356 ↔ Y731 ↔ Y730 ↔ C439. The blue arrows show proton transfer (PT), the red arrows show electron transfer (ET), and the collinear PCET reactions are also labeled as PCET in purple. The interfacial PCET step is highlighted with a purple square bracket. Adapted from Ref. 12. Copyright 2023 American Chemical Society.

A major challenge in the study of RNR is uncovering the specific mechanisms of individual PCET reactions along this pathway.^8–16 This challenge is complicated by the rate-limiting conformational changes that obscure the individual steps^{4, 7, 17} and the transient nature of tyrosyl radicals.¹⁸ A crucial component of the PCET pathway is the interfacial PCET between $\mathrm{Y}356$ in the β subunit and $\mathrm{Y}731$ in the α subunit. This PCET reaction is influenced by the highly dynamic nature of the residues at the interface, allowing them to adopt multiple conformations.^{12–13, 15, 19} A 3.6 Å resolution cryo-EM structure of the E. coli RNR active α₂β₂ complex²⁰ shows that $\mathrm{Y}731$ is stacked with Y730 within the α subunit, with an 8.3 Å distance between the hydroxyl oxygen atoms of $\mathrm{Y}731$ in the α subunit and $\mathrm{Y}356$ in the β subunit. Our previous molecular dynamics¹¹ and quantum mechanical/molecular mechanical (QM/MM) free energy simulations¹⁵ indicate that $\mathrm{Y}731$ can reorient by flipping so that it points toward the α/β subunit interface, a finding supported by both spectroscopic experiments and crystal structures.^{19, 21}

Our QM/MM free energy simulations also revealed that direct PCET between $\mathrm{Y}356$ and $\mathrm{Y}731$ becomes feasible when $\mathrm{Y}731$ flips toward the interface but that the water-mediated double proton transfer mechanism between $\mathrm{Y}356$ and $\mathrm{Y}731$ is thermodynamically and kinetically unfavorable.¹⁵ The direct PCET mechanism between $\mathrm{Y}356$ and $\mathrm{Y}731$, as shown in Figure 2, is approximately isoergic with a relatively low free energy barrier. In these QM/MM free energy simulations, the distance between the hydroxyl oxygen atoms on $\mathrm{Y}356$ and $\mathrm{Y}731$ is ~2. 9 – 3.0 Å for the reactant and product and ~2.5 Å at the top of the free energy barrier. This finding is consistent with ENDOR experiments on mutants incorporating unnatural amino acids showing a conformation in which the distance between the hydroxyl oxygen atoms on $\mathrm{Y}356$ and $\mathrm{Y}731$ is 3.0 ± 0.2 Å.²² Furthermore, our recent analysis of vibronic and electron–proton nonadiabaticity^23–24 indicates that the interfacial PCET between $\mathrm{Y}356$ and $\mathrm{Y}731$ is both vibronically and electronically nonadiabatic.¹⁶ This analysis indicates that vibronically nonadiabatic PCET theory^25–27 can be used to calculate the rate constant for this interfacial PCET reaction.

Figure 2.

Reactant and product conformations obtained from QM/MM free energy simulations for the direct radical transfer from $\mathrm{Y}356$ to $\mathrm{Y}731$. The proton donor-acceptor distance $R$ is labeled by a black double-headed arrow for the reactant state. Adapted from Ref. 12. Copyright 2023 American Chemical Society.

Herein, we use vibronically nonadiabatic PCET theory to calculate the rate constant for direct PCET between $\mathrm{Y}356$ and $\mathrm{Y}731$:

$$\mathrm{Y}356{\mathrm{O}}^{•}+\mathrm{Y}731\mathrm{O}\mathrm{H}\to \mathrm{Y}356\mathrm{O}\mathrm{H}+\mathrm{Y}731{\mathrm{O}}^{•}$$

This theory treats the transferring hydrogen nucleus quantum mechanically and includes the effects of hydrogen tunneling and excited vibronic states. It also includes the proton donor-acceptor motion, which in this case is the motion between the hydroxyl oxygen atoms of $\mathrm{Y}356$ and $\mathrm{Y}731$. Our analysis highlights the importance of the decrease of the distance between these two oxygen atoms to facilitate hydrogen tunneling in this PCET reaction. Additionally, a more extensive analysis of molecular dynamics simulations allows us to identify key residues that influence this compression. These insights into the structural and dynamical aspects of the interface between the α and β subunits are crucial for understanding this PCET process, as well as its impact on the overall long-range radical transfer pathway in RNR. Such insights will not only advance mechanistic knowledge but will also guide targeted protein engineering efforts aimed at modulating RNR function.

METHODS

As mentioned above, our previous work indicates that the interfacial PCET reaction between $\mathrm{Y}356$ and $\mathrm{Y}731$ is vibronically and electronically nonadiabatic.¹⁶ In this analysis, we used a classification scheme²⁸ in which the PCET system is divided into electrons, transferring protons, and the environment. In the vibronically nonadiabatic limit, the electron-proton subsystem does not respond instantaneously to the motion of the other nuclei, and excited vibronic states participate. A PCET reaction is typically determined to be vibronically nonadiabatic when the vibronic coupling between the reactant and product diabatic electron-proton vibronic states is much less than the thermal energy, $k_{\mathrm{B}}T$, where $k_{\mathrm{B}}$ is the Boltzmann constant and $T$ is the temperature. Within this regime, the form of the vibronic coupling depends on electron-proton nonadiabaticity. When the electron does not respond instantaneously to the proton motion, the reaction is electronically nonadiabatic, and the vibronic coupling is the product of the electronic coupling between the diabatic electronic states and the overlap between the reactant and product proton vibrational wavefunctions. A PCET reaction is determined to be electronically nonadiabatic when the adiabaticity parameter corresponding to the ratio of an effective proton tunneling time and the electronic transition time, as computed with a semiclassical formulation,^23–24 is much less than unity. We computed the vibronic coupling and the adiabaticity parameter for PCET between $\mathrm{Y}356$ and $\mathrm{Y}731$ and found that the vibronic coupling is much less than the thermal energy, and the adiabaticity parameter is much less than unity. Additional details about this analysis are given in Ref. 16.

For vibronically and electronically nonadiabatic PCET reactions, the reaction rate constant at a specific proton donor-acceptor distance $R$ is expressed as^{25–26, 29}

$$k(R)=\sqrt{\frac{\pi }{\lambda k_{\mathrm{B}}T}}\sum _{\mu }{P}_{\mu }\sum _v\frac{{\left|V^{\mathrm{e}\mathrm{l}}{S}_{\mu v}\right|}^2}{\hslash }\mathrm{e}\mathrm{x}\mathrm{p}\left[-\frac{{\left(\mathrm{\Delta }{G}^0+{\epsilon }_v-{\epsilon }_{\mu }+\lambda \right)}^2}{4\lambda k_{\mathrm{B}}T}\right]$$ (1)

Here $\mu$ and $\nu$ indicate the vibronic states of the reactant and product, respectively, with $P_{\mu }$ indicating the Boltzmann population of the reactant vibronic state $\mu$. In the electronically nonadiabatic limit, the vibronic coupling is the product of the electronic coupling, $V^{\mathrm{e}\mathrm{l}}$, and the overlap integral, $S_{\mu v}$, of the proton vibrational wave functions associated with the vibronic states $\mu$ and $\nu$. Moreover, $\lambda$ is the total reorganization energy, $\mathrm{\Delta }{G}^0$ is the reaction free energy for the ground vibronic states, and ${\epsilon }_{\mu }$ and ${\mathrm{\epsilon }}_v$ are the energies of the reactant and product vibronic states relative to the energies of their respective ground vibronic states. The overall PCET rate constant is then obtained by thermal averaging of the rate constant over the proton donor–acceptor distance $R$:

$$k={\int }_0^{\mathrm{\infty }}k(R)P(R)dR$$ (2)

where $P(R)$ is the probability distribution function for $R$, which in this case is the distance between the hydroxyl oxygen atoms of $\mathrm{Y}356$ and $\mathrm{Y}731$, for the reactant state.

To obtain the energies and proton vibrational wavefunctions associated with the reactant and product vibronic states, we calculated the diabatic proton potential energy curves for a series of different $R$ values. These curves were computed with constrained density functional theory (CDFT)^30–32 using the ωB97X-D functional³³ and the 6–31+G** basis set.^34–36 This functional and basis set have been shown to produce similar proton potential energy curves as the multireference complete active space self-consistent field with second-order perturbative corrections (CASSCF+NEVPT2) method for PCET between two tyrosine residues in previous work.¹² In the CDFT calculations, we imposed spin constraints ensuring that the spin is ½ on $\mathrm{Y}356$ and zero on $\mathrm{Y}731$ for the reactant and zero on $\mathrm{Y}356$ and ½ on $\mathrm{Y}731$ for the product. The CDFT configuration interaction (CDFT-CI) approach was shown previously to provide qualitatively similar diabatic proton potential energy curves and electronic couplings as those obtained with the CASSCF approach for radical transfer between phenoxyl and phenol.³⁷

The proton potential energy curves were computed for structures corresponding to the average of the reactant and product geometries for each $R$ value. This average structure represents the approximate structure at which PCET is expected to occur within the vibronically nonadiabatic PCET theory. To generate these average structures, we started by selecting a hydrogen-bonded complex of $\mathrm{Y}356$ and $\mathrm{Y}731$ obtained from the final iteration of our previous QM/MM free energy string simulations.¹⁵ Specifically, we chose a configuration corresponding to the image at the top of the free energy barrier with a proton donor-acceptor distance close to the average value for this image. Using this configuration as a starting point, we then optimized the reactant and product states with DFT in the gas phase at a series of fixed $R$ values ranging from 2.42 Å to 3.12 Å in increments of 0.10 Å. During each optimization, the $R$ distance was constrained, and the proton was initially placed near the donor oxygen for the reactant and near the acceptor oxygen for the product to obtain the corresponding minimum-energy geometries.

For each $R$ value, the optimized reactant and product structures were aligned by superimposing their proton donor and acceptor oxygen atoms and then minimizing the root-mean-square deviation (RMSD) of the remaining atoms by rotating one of the structures around the donor-acceptor axis. The average structure was obtained by averaging the Cartesian coordinates of the aligned reactant and product structures. To determine the proton transfer coordinate axis, the transferring proton was optimized near the donor oxygen atom and then near the acceptor oxygen atom, while keeping all other atoms fixed. The proton coordinate axis was defined as the line connecting the optimized positions of the proton on the donor and acceptor oxygen atoms. A grid with a spacing of 0.05 Å was then generated along this proton coordinate axis, centered at the midpoint between the two optimized proton positions. CDFT-CI calculations were performed with the hydrogen atom placed at each grid point along the proton axis, generating electronically diabatic reactant and product proton potential energy curves in the gas phase. As mentioned above, the unpaired spin was constrained to $\mathrm{Y}356$ for the reactant and to $\mathrm{Y}731$ for the product. Our previous studies¹⁶ showed that including the protein environment through electrostatic embedding produces qualitatively similar diabatic proton potential energy curves as those calculated in the gas phase. The proton vibrational wavefunctions were subsequently computed for each diabatic proton potential energy curve using the Fourier Grid Hamiltonian method.^38–39 These proton vibrational wavefunctions and associated energy levels relative to their ground vibrational states were used to compute the Boltzmann populations $P_{\mu }$, the energy levels ${\epsilon }_{\mu }$ and ${\epsilon }_{\mathrm{v}}$, and the overlap integrals $S_{\mu v}$.

The electronic coupling, $V^{\mathrm{e}\mathrm{l}}$, was obtained from the CDFT-CI calculations at several different $R$ values. For each $R$ value, the diabatic curves were shifted to align the reactant and product ground vibrational energy levels, and the electronic coupling was obtained from the CDFT-CI calculation at the crossing point. We confirmed that the electronic coupling does not change significantly along the proton coordinate near this crossing point or for different $R$ values within the relevant range, 2.4 – 2.6 Å (Table S2). We used a constant electronic coupling of 0.8 kcal/mol, which was the same within one significant figure over this range of $R$ values, for the calculations herein. Given the known challenges of CDFT for computing electronic couplings,^40–41 this value should be viewed only as a qualitative estimate.

The total reorganization energy can be expressed as the sum of the outer-sphere (solvent/protein) and inner-sphere (solute) components. For this system, the outer-sphere reorganization energy is considered to be negligible because the net hydrogen atom transfer between two tyrosine residues does not entail a significant change in the charge distribution. Therefore, the total reorganization energy is approximated as the inner-sphere reorganization energy, ${\lambda }_{\mathrm{i}}$, related to structural changes within the two tyrosine residues upon PCET. We calculated ${\lambda }_{\mathrm{i}}$ using a variant of the four-point method extended to PCET.⁴² In this approach, the geometries of the reactant and product are optimized in the gas phase, and then the energy is computed for each geometry in the other state, where the state is defined by the localization of both the electron and the proton on their donors for the reactant and on their acceptors for the product.

In this case, the reactant consists of a tyrosine and a tyrosyl radical, and the product consists of a tyrosyl radical and a tyrosine. If we compute the inner-sphere reorganization energy for the individual fragments, the reactant and product are equivalent, and the expression for the inner-sphere reorganization energy simplifies to

$${\lambda }_{\mathrm{i}}=E_{\mathrm{T}\mathrm{y}\mathrm{r}•}\left(Q_{\mathrm{T}\mathrm{y}\mathrm{r}}\right)-E_{\mathrm{T}\mathrm{y}\mathrm{r}}\left(Q_{\mathrm{T}\mathrm{y}\mathrm{r}}\right)+E_{\mathrm{T}\mathrm{y}\mathrm{r}}\left(Q_{\mathrm{T}\mathrm{y}\mathrm{r}•}\right)-E_{\mathrm{T}\mathrm{y}\mathrm{r}•}\left(Q_{\mathrm{T}\mathrm{y}\mathrm{r}•}\right)$$ (3)

In this expression, $E_{\mathrm{T}\mathrm{y}\mathrm{r}}\left(Q_{\mathrm{T}\mathrm{y}\mathrm{r}}\right)$ and $E_{\mathrm{T}\mathrm{y}\mathrm{r}•}\left(Q_{\mathrm{T}\mathrm{y}\mathrm{r}•}\right)$ are the energies of the optimized geometries for tyrosine and the tyrosyl radical, respectively. $E_{\mathrm{T}\mathrm{y}\mathrm{r}•}\left(Q_{\mathrm{T}\mathrm{y}\mathrm{r}}\right)$ is the energy of the tyrosyl radical at the optimized geometry for tyrosine, where the electron and proton have been removed. $E_{\mathrm{T}\mathrm{y}\mathrm{r}}\left(Q_{\mathrm{T}\mathrm{y}\mathrm{r}•}\right)$ is the energy of tyrosine at the optimized geometry for the tyrosyl radical, where an electron and proton have been added and the proton has been optimized with all other nuclei fixed.

The final quantity to be computed is $P(R)$, the probability distribution function for the proton donor-acceptor distance $R$, which is the distance between the hydroxyl oxygen atoms of $\mathrm{Y}356$ and $\mathrm{Y}731$ (Figure 2). We computed this probability distribution function using both unrestrained and restrained classical molecular dynamics (MD) for the reactant (i.e., with the radical on $\mathrm{Y}356$) including the solvated enzyme environment. For the restrained simulations, we performed umbrella sampling simulations with restraints on both $R$ and the distance between the transferring hydrogen and the $\mathrm{Y}356$ oxygen atom (Figures S2 and S3). The second restraint ensured that only conformations with an orientation that would allow hydrogen bonding were considered. We performed two separate umbrella sampling simulations with different force constants for that restraint. For the unrestrained MD simulation, 1 μs of sampling was obtained by propagating 10 independent 100 ns trajectories following the same MD simulation procedure as used in our previous RNR study.¹⁵ We applied a filter to only include conformations with hydrogen-bonding angles (O–H–O) greater than 135°. The resulting probability distribution functions from the unrestrained MD and the two different umbrella simulations are qualitatively similar (Figure S4). All the MD simulations were conducted with the AMBER ff14SB force field^43–46 and explicit TIP3P water⁴⁷ molecules. Additional computational details are provided in the SI.

This work focuses on forward radical transfer from $\mathrm{Y}356$ to $\mathrm{Y}731$, where the radical is localized on $\mathrm{Y}356$ in the reactant state. In the vibronically nonadiabatic PCET theory, $P(R)$ is computed for the reactant state and therefore is calculated from MD simulations with the radical localized on $\mathrm{Y}356$. The cryo-EM structure²⁰ used as the starting point for the MD simulations corresponds to the pre-turnover state and is most relevant to forward radical transport. The conformations corresponding to the reactant for reverse radical transfer from $\mathrm{Y}731$ to $\mathrm{Y}356$, where the radical is localized on $\mathrm{Y}731$, could be significantly different due to conformational changes that occur in the post-turnover state (i.e., between the forward and reverse radical transport processes).

Finally, we performed a hydrogen-bonding analysis of the unrestrained 1 μs classical MD simulation to understand the effects of the local protein environment on the proton donor-acceptor distance $R$. To examine the sampling most relevant to the PCET reaction between $\mathrm{Y}356$ and $\mathrm{Y}731$, the MD data was filtered to include only conformations in which the $\mathrm{N}-{\mathrm{C}}_{\mathrm{\alpha }}-{\mathrm{C}}_{\mathrm{\beta }}-{\mathrm{C}}_{\mathrm{\gamma }}$ dihedral angle in $\mathrm{Y}731$ is between the range of 150–250°. This range corresponds to the flipped-out conformation of $\mathrm{Y}731$ and excludes its off-pathway conformations.^{11, 15}

RESULTS AND DISCUSSIONS

The goal of this work is to compute the vibronically nonadiabatic PCET rate constant corresponding to radical transfer from $\mathrm{Y}356$ to $\mathrm{Y}731$ and to analyze the contributions to this rate constant to elucidate the fundamental mechanism and underlying physical principles. We obtained the input quantities to the vibronically nonadiabatic PCET rate constant expression using a variety of computational methods, as described in Methods. Our previous QM/MM string free energy simulations suggest that the reaction free energy for radical transfer from $\mathrm{Y}356$ to $\mathrm{Y}731$ is within the range from ca. 0 to 1.0 kcal/mol.¹⁵ This finding is consistent with pulsed electron-electron double resonance and EPR spectroscopy experiments that estimated this reaction free energy to be 2.6 ± 1.2 kcal/mol.⁴⁸ Based on this information, we computed the PCET rate constant with $\mathrm{\Delta }{G}^0=0$ and with $\mathrm{\Delta }{G}^0=\pm 2.0\mathrm{k}\mathrm{c}\mathrm{a}\mathrm{l}/\mathrm{m}\mathrm{o}\mathrm{l}$ for comparison. The outer-sphere reorganization energy due to protein and solvent reorganization is assumed to be zero because no net charge transfer is involved. However, the inner-sphere reorganization energy due to structural changes within the tyrosine is calculated using the extended four-point method to be 18.86 kcal/mol, with the individual terms in Eq. (3) provided in Table S1. Our analysis indicates that this reorganization energy is due mainly to a change in the C–O distance of 0.12 Å as well as changes in the C–C distances of ~ 0.02 Å – 0.06 Å upon net hydrogen atom transfer (Figure S5). The electronic coupling calculated using the CDFT-CI method for the most relevant $R$ values is ~0.8 kcal/mol (Table S2).

The proton potential energy curves for the reactant and product diabatic states exhibit significant variation across different $R$ values (Figure 3). At small $R$ values, the potential energy curves display a single well on the donor or acceptor side with a slight shoulder on the other side. As $R$ increases, the curves develop a high-energy minimum on the other side and attain double-well character. As $R$ continues to increase, the barrier height and separation between the minima increase. For each of these proton potential energy curves, we computed the proton vibrational wavefunctions to obtain the Boltzmann populations $P_{\mu }$, the energy levels ${\epsilon }_{\mu }$ and ${\epsilon }_{\mathrm{v}}$, and the overlap integrals $S_{\mu v}$. Figure S6 shows the proton vibrational wavefunctions for the diabatic reactant and product proton potential energy curves at $R=2.62\AA$. All these input quantities were used to compute the vibronically nonadiabatic PCET rate constant given in Eq. (1) at each $R$ value. The resulting plot of $k(R)$ in Figure 4 shows that the rate constant increases dramatically as $R$ decreases, mainly because the overlap integral increases as the proton donor and acceptor become closer to each other.

Figure 3.

Diabatic reactant and product proton potential energy curves. (Top) Average reactant/product structure for $R=2.62\AA$ with the proton coordinate axis shown as a blue dashed line. Although the optimized positions of the transferring proton on the donor and acceptor oxygen atoms are shown in this figure to illustrate the generation of the proton coordinate axis, only one transferring proton is included in the calculation of the proton potential energy curves. (Bottom) Proton potential energy curves for the reactant (left) and product (right) diabatic states computed with CDFT at different proton donor–acceptor distances $R$. The reactant corresponds to the radical on $\mathrm{Y}356$, and the product corresponds to the radical on $\mathrm{Y}731$.

Figure 4:

$P(R),k(R)$, and their product $k(R)P(R)$, which is the integrand for the thermal averaging procedure used to compute $k^{\mathrm{P}\mathrm{C}\mathrm{E}\mathrm{T}}.P(R)$ is calculated from umbrella sampling simulations and fit to the exponential of a fourth-order polynomial (Figure S3). The natural logarithm of $k(R)$ was fit to a quadratic equation (Figure S7) and then exponentiated to produce this curve. There are no units on the y-axis because the various quantities are scaled to fit on the same plot.

The calculation of the overall rate constant requires thermal averaging over $R$, as given in Eq. (2). The probability distribution function $P(R)$ obtained from an umbrella sampling simulation is shown in Figure 4. The $P(R)$ obtained from two different umbrella sampling simulations are qualitatively similar to each other and to the results from the unrestrained MD simulations (Figures S3 and S4). Figure 4 also depicts the product $k(R)P(R)$, which is the integrand in Eq. (2). The maximum of $P(R)$ is at $R=2.81\AA$, whereas the maximum of the integrand, $k(R)P(R)$, is at $R=2.53\AA$. Although the probability of sampling this short distance is small, the rate constant is very high when such short distances are sampled. This analysis suggests that the PCET reaction requires compression of the distance between the hydroxyl oxygen atoms of $\mathrm{Y}356$ and $\mathrm{Y}731$. The calculated rate constant $k^{\mathrm{P}\mathrm{C}\mathrm{E}\mathrm{T}}$ is 1.58 × 10³ s⁻¹ using $P(R)$ from an umbrella sampling simulation and is 1.09 × 10⁴ s⁻¹ using $P(R)$ from the unrestrained MD simulation. The similarity of these rate constants shows that the qualitative results are not sensitive to the specific method for calculating $P(R)$.

We also analyzed the contributions from the different pairs of vibronic states to the PCET rate constant. For each $R$ value in the relevant range, the $(\mu ,\nu )=(\mathrm{0,0})$ pair of reactant and product vibronic states dominates the rate constant by contributing over 96% to $k(R)$ (Table S3). Figure 5 shows the reactant and product diabatic proton potential energy curves, along with their corresponding ground state proton vibrational wavefunctions, for $R$ values between 2.42 and 2.62 Å. At these $R$ values, the proton potential energy curves exhibit single-well character with a small shoulder. These properties of the proton potential energy curves lead to highly localized ground state proton vibrational wavefunctions, resulting in relatively small overlap integrals. As $R$ increases, the separation between the minima of the reactant and product proton potential energy curves increases, reducing the overlap integral and decreasing $k(R)$ (Figure 5 and Table S3). Compression of the proton donor-acceptor distance is necessary to facilitate hydrogen tunneling by increasing the overlap between the ground-state proton vibrational wavefunctions.

Figure 5.

Diabatic proton potential energy curves for the reactant (blue) and product (red) with associated ground state proton vibrational wavefunctions for proton donor–acceptor distances $R$ as indicated. The diabatic proton potential energy curves are shifted to align their zero-point energy levels.

We calculated the kinetic isotope effect (KIE) for this PCET reaction by changing the mass of the transferring particle to the mass of deuterium rather than hydrogen. All other input quantities were assumed to be the same. We computed a value of 86 or 13 using $P(R)$ from the umbrella sampling simulations or the unrestrained MD simulations, respectively. The KIE is sensitive to $P(R)$, particularly the equilibrium proton donor-acceptor distance and the sampling of the shorter $R$ values. As discussed elsewhere,^{27, 49} smaller overlap integrals between the reactant and product proton vibrational wavefunctions typically lead to larger KIEs. Thus, the KIE is often decreased by contributions from excited vibronic states, which tend to exhibit larger proton vibrational wavefunction overlaps than the ground vibronic states. For this PCET reaction, the ground reactant and product vibronic states are dominant, and the proton vibrational wavefunction overlap is relatively small. The KIE is lower when computed with the $P(R)$ that has greater contributions from smaller $R$ values, which correspond to larger proton vibrational wavefunction overlaps. However, the KIE is very sensitive to the proton potential energy curves as well as $P(R)$, and therefore these estimates should be viewed with caution. Moreover, it will be difficult to measure the KIE experimentally for this single PCET step in wild-type RNR, as discussed further below. On the other hand, these large KIEs are similar to those measured experimentally^50–51 and calculated using our vibronically nonadiabatic PCET theory^52–54 for the PCET reaction catalyzed by soybean lipoxygenase. We found that the PCET reaction in soybean lipoxygenase is also dominated by tunneling between the ground vibronic states with relatively small proton vibrational wavefunction overlaps.

We also examined the sensitivity of $k^{\mathrm{P}\mathrm{C}\mathrm{E}\mathrm{T}}$ to $\lambda$ and $\mathrm{\Delta }{G}^0$. Our previous QM/MM free energy simulations showed that the reaction is approximately isoergic, and we assumed $\mathrm{\Delta }{G}^0=0$ in the calculations discussed above. Calculating the PCET rate constant with $\mathrm{\Delta }{G}^0=\pm 2.0\mathrm{k}\mathrm{c}\mathrm{a}\mathrm{l}//\mathrm{m}\mathrm{o}\mathrm{l}$ changes $k^{\mathrm{P}\mathrm{C}\mathrm{E}\mathrm{T}}$ by less than an order of magnitude (Table S4). Similarly, increasing $\lambda$ from 18.86 kcal/mol to 25 kcal/mol decreases $k^{\mathrm{P}\mathrm{C}\mathrm{E}\mathrm{T}}$ by around an order of magnitude (Table S4). In all of these test cases, the qualitative picture remains the same in that hydrogen tunneling between the ground reactant and product vibronic states represents the dominant contribution to the rate constant, and the $R$ value decreases to facilitate hydrogen tunneling. Based on the above analyses, we find that the elementary PCET rate constant $k^{\mathrm{P}\mathrm{C}\mathrm{E}\mathrm{T}}$ is on the order of 10³ – 10⁴ s⁻¹ when $\mathrm{Y}731$ and $\mathrm{Y}356$ adopt conformations conducive to direct PCET. Often the apparent rate constant can be expressed as the product of a pre-equilibrium constant corresponding to forming a conducive conformation for PCET and the elementary PCET rate constant: $k_{\text{app}}=K_{\text{eq}}{k}^{\text{PCET}}$. This expression is valid when the local thermal fluctuations are faster than the PCET rate constant, and therefore the region around $\mathrm{Y}731$ and $\mathrm{Y}356$ can be assumed to be at quasi-equilibrium during PCET. Experimental studies have indicated that the conformational changes of $\mathrm{Y}731$ occur on the nanosecond to microsecond timescale,²¹ which is faster than our calculated PCET rate constant or experimentally measured rate constants for photoactivated RNRs, as discussed below. Our MD simulations in previous work¹¹ and this current work have also shown relatively fast local thermal motions of $\mathrm{Y}356$ and $\mathrm{Y}731$. The pre-equilibrium constant $K_{\text{eq}}$ is unknown, and therefore we are unable to predict the apparent PCET rate constant, which would presumably be significantly lower. In any case, it would be challenging to experimentally measure the rate constant for this PCET reaction independently from the rest of the long-range radical transfer mechanism without mutations, as discussed below.

To explore the effect of the local protein environment surrounding $\mathrm{Y}356$ and $\mathrm{Y}731$ on the proton donor–acceptor distance $R$ as well as the equilibrium constant $K_{\text{eq}}$, we examined the hydrogen-bonding interactions over the 1 μs unrestrained MD simulation in the reactant state (i.e., with the radical on $\mathrm{Y}356$). For this analysis, the MD data was filtered to include only conformations in which the $\mathrm{N}-{\mathrm{C}}_{\mathrm{\alpha }}-{\mathrm{C}}_{\mathrm{\beta }}-{\mathrm{C}}_{\mathrm{\gamma }}$ dihedral angle in $\mathrm{Y}731$ is between the range of 150–250°. Table 1 shows that the hydrogen-bonding interaction between $\mathrm{Y}356$ and $\mathrm{Y}731$ is present for less than 5% of the trajectory, corresponding to a relatively small $K_{\text{eq}}$. Moreover, this analysis does not account for the stacked and off-pathway conformations of $\mathrm{Y}731$, which would decrease $K_{\text{eq}}$ even more.

Table 1.

Hydrogen-Bonding Interactions Involving $\mathrm{Y}356$ and $\mathrm{Y}731$ Analyzed from MD Simulations^a

Distance cutoff	Y356-Y731	Y356-R411b	Y731-N733c
3.0 Å	3.6%, 2.83 Å	10.4%, 2.90 Å	9.8%, 2.81 Å
3.2 Å	4.8%, 2.89 Å	20.1%, 2.99 Å	13.4%, 2.89 Å

^aHydrogen-bonding interaction is defined as the hydrogen-bond angle greater than 135° and the donor-acceptor distance less than 3.0 Å or 3.2 Å, as indicated in the first column. The percentages refer to the fraction of sampled conformations that exhibit the hydrogen-bonding interaction, and the distances in Angstroms are the average donor-acceptor distances for the hydrogen bond.

^bPercentages include hydrogen-bonding interactions between the oxygen on $\mathrm{Y}356$ and all three nitrogen atoms on the R411 sidechain. Distances are averaged over all occurrences of all hydrogen bonds.

^cPercentages include hydrogen-bonding interaction between the oxygen on $\mathrm{Y}731$ and both the nitrogen and oxygen on the N733 sidechain. Distances are averaged over all occurrences of both hydrogen bonds.

Previous work identified the flipping of $\mathrm{Y}731$ in the α subunit between conformations,¹¹ in which it is either stacked with Y730 or pointing toward the α/β interface to enable PCET with $\mathrm{Y}356$. In the current analysis, $\mathrm{Y}731$ remains flipped toward the α/β interface. Interestingly, we found that $\mathrm{Y}356$ in the β subunit also samples two distinct conformations, in which its oxygen atom is pointing either toward or away from the α/β interface (Figures 6A and 6B). Additionally, we observed that the sampled reactant conformations are distributed between two main clusters, one with an average $R$ value of ~4 Å and the other with an average $R$ value of ~9.5 Å (Figure S1). The two distinct conformations of $\mathrm{Y}356$ correspond to the two clusters of $R$ values, as shown by the correlation of the $\mathrm{Y}356$ sidechain solvent-accessible surface area (SASA) with $R$ (Figure S9). A recent cryo-EM structure shows evidence of more subtle movement of $\mathrm{Y}356$.⁵⁵ Thus, both $\mathrm{Y}356$ and $\mathrm{Y}731$ exhibit dynamic motion at the interface.

Figure 6.

Representative conformations obtained from the 1 μs MD simulation showing different conformations of $\mathrm{Y}356$ and hydrogen-bonding interactions. (A) $\mathrm{Y}356$ is oriented with its oxygen atom pointed toward the α/β interface and hydrogen-bonded to $\mathrm{Y}731$ with $R=3.0$ Å. (B) $\mathrm{Y}356$ is oriented with its oxygen atom pointed away from the α/β interface with $R=9.6$ Å. (C) $\mathrm{Y}356$ is oriented with its oxygen atom pointed toward the α/β interface, with dashed lines indicating hydrogen-bonding interactions between $\mathrm{Y}356$ and R411 and between $\mathrm{Y}731$ and N733. Although $\mathrm{Y}356$ is oriented in the same direction as in the conformation shown in (A), this conformation shows different hydrogen-bonding interactions. (D) Same conformation as in (B) but with dashed lines indicating the hydrogen-bonding interactions between $\mathrm{Y}356$ and R411 and between $\mathrm{Y}731$ and N733. The α subunit is shown in red, and the β subunit is shown in blue. The distance $R$ between the oxygen atoms of $\mathrm{Y}356$ and $\mathrm{Y}731$, as well as the distance between the donor and acceptor atoms of each hydrogen bond in parts (C) and (D), are indicated.

Our hydrogen-bonding analysis also identified hydrogen-bonding interactions between $\mathrm{Y}356\beta$ and R411α and between $\mathrm{Y}731\alpha$ and N733α, where we are specifying the subunit in this part of the discussion for clarity. As shown in Figures 6C and 6D, these two hydrogen-bonding interactions are present when $R$ is both relatively small (~3.6 Å) and large (~9.6 Å), corresponding to the two distinct conformations of $\mathrm{Y}356\beta$. These hydrogen-bonding interactions persist for a wide range of $R$ values, indicating that the pairs of hydrogen-bonded residues are moving together (Figure S10). These hydrogen-bonding interactions could be competing with the hydrogen-bonding interaction between $\mathrm{Y}356\beta$ and $\mathrm{Y}731\alpha$ required for direct PCET. As a result, such interactions could potentially shift the maximum of the probability distribution function $P(R)$ to a larger proton donor-acceptor distance $R$, thereby decreasing $k^{\text{PCET}}$, or decrease the pre-equilibrium constant $K_{\text{eq}}$. Previous experimental studies combined with DFT calculations have suggested that R411α may hydrogen bond to an aminotyrosine (NH₂Y) substituted $\mathrm{Y}731\alpha$,^{19, 21, 56} whereas our simulations suggest that R411α may hydrogen bond to $\mathrm{Y}356\beta$. Moreover, experimental studies on a photochemically activated RNR (photoRNR) imply that mutating R411α to alanine leads to a modest rate enhancement of radical transfer from $\mathrm{Y}356\beta$ to $\mathrm{Y}731\alpha$.²¹ According to our simulations, by eliminating the competing hydrogen-bonding interaction, the R411A mutation could potentially either increase $k^{\text{PCET}}$ by altering $P(R)$ or increase $K_{\text{eq}}$, thereby increasing the apparent rate constant $k_{\text{app}}$. The hydrogen-bonding interaction between N733α and $\mathrm{Y}731\alpha$ could also impact $P(R)$ and $K_{\text{eq}}$ in a similar manner.

The turnover frequency for conversion of nucleotides to deoxynucleotides by E. coli RNR is 2 – 10 s⁻¹, which is associated with a rate-limiting conformational change. Since the radical transport process is conformationally gated, experimental measurement of the rate constants of the individual radical transfer steps is challenging. PhotoRNRs with a rhenium photo-oxidant attached to a cysteine residue at position 355β have been developed to address this challenge.^{21, 57–58} In transient absorption experiments, photoexcitation of the rhenium photosensitizer oxidizes $\mathrm{Y}356\beta$, which instigates radical transfer toward the α subunit. Monitoring the $\mathrm{Y}356\beta$ radical decay kinetics provides information about the conformational dynamics at the interface and radical transfer from $\mathrm{Y}356\beta$ to $\mathrm{Y}731\alpha$. According to these experiments, the rate constant for radical transfer from $\mathrm{Y}356\beta$ to $\mathrm{Y}731\alpha$ is ~6000 s⁻¹.²¹ However, these experiments were performed with 2,3,6-F₃Y at position 356β to render it spectroscopically distinct and with NH₂Y at position 730α to create a radical sink that facilitates the interpretation of the transient absorption spectra. Due to these mutations, as well as the attachment of the rhenium photo-oxidant, a direct comparison to our calculated PCET rate constant is not meaningful. As mentioned above, we computed $k^{\text{PCET}}$ to be 10³ – 10⁴ s⁻¹ when $\mathrm{Y}731$ and $\mathrm{Y}356$ adopt conformations conducive to direct PCET, and therefore the apparent rate constant is expected to be lower. We also emphasize that this calculated rate constant is associated with a significant degree of uncertainty due to the approximations underlying all the input quantities, including a possible underestimation of the electronic coupling (see Figure S8).

Although a direct comparison of the computed rate constant to experimentally measured values is challenging, other aspects of these calculations can be connected to experiments. Spectroscopic experiments^{19, 21} have observed the flipping motion of $\mathrm{Y}731$ observed in MD simulations.¹¹ ENDOR experiments on mutant E. coli RNR²² have identified a conformation in which the distance between the hydroxyl oxygen atoms on $\mathrm{Y}356\beta$ and $\mathrm{Y}731\alpha$ is 3.0 ± 0.2 Å, which is consistent with the distances observed in our MD simulations and in the calculated P(R) (Figure 4). Moreover, our work predicts that mutating N733α and R411α will impact the conformational motions of $\mathrm{Y}356\beta$ and $\mathrm{Y}731\alpha$ and therefore the radical transfer rate between these residues. As discussed above, experimental studies on photoRNRs indicate a modest rate enhancement of radical transfer from $\mathrm{Y}356\beta$ to $\mathrm{Y}731\alpha$ upon mutation of R411α.²¹ Our predictions may motivate additional experiments mutating N733α as well as R411α.

CONCLUSIONS

In this paper, we examined the nonadiabatic direct PCET reaction between $\mathrm{Y}356$ and $\mathrm{Y}731$ in E.coli RNR, corresponding to radical transfer from $\mathrm{Y}356$ in the β subunit to $\mathrm{Y}731$ in the α subunit in the long-range radical transfer pathway. Our kinetic analysis suggests that hydrogen tunneling plays an important role in this PCET reaction and that compression of the distance between the hydroxyl oxygen atoms of these two tyrosine residues is essential to facilitate this hydrogen tunneling. In particular, the distance between these two oxygen atoms is ~2.8 – 2.9 Å in equilibrated reactant conformations with a hydrogen-bonding interaction between $\mathrm{Y}356$ and $\mathrm{Y}731$, but the dominant distance for PCET is estimated to be ~2.5 – 2.6 Å. Although these relatively short distances are not sampled often, the larger overlap between the reactant and product proton vibrational wavefunctions leads to much faster PCET. Thus, conformational fluctuations of these interfacial tyrosine residues are critical for this PCET reaction.

Both our MD simulations and spectroscopic experiments have implicated dynamic structural fluctuations at the α/β interface.^{11–13, 15, 19, 21} We have identified N733 and R411 to be two key residues that play significant roles in the hydrogen-bonding network surrounding $\mathrm{Y}731$ and $\mathrm{Y}356$. According to our MD simulations, N733 can hydrogen bond to $\mathrm{Y}731$ and R411 can hydrogen bond to $\mathrm{Y}356$ both for conformations in which $\mathrm{Y}356$ and $\mathrm{Y}731$ are hydrogen bonded to each other and for conformations in which $\mathrm{Y}356$ and $\mathrm{Y}731$ are relatively far apart. These hydrogen-bonding interactions with N733 and R411 may influence the conformational motions of $\mathrm{Y}356$ and $\mathrm{Y}731$ and potentially compete with the hydrogen-bonding interaction between them required for direct PCET. Such effects could be used to control the PCET reaction. Our work predicts that mutation of N733 as well as further mutation of R411 may impact the rate of PCET between $\mathrm{Y}356$ and $\mathrm{Y}731$.

The interfacial PCET reaction between $\mathrm{Y}356$ and $\mathrm{Y}731$ is a key step in the long-range radical transfer pathway in RNR. Understanding the fundamental physical principles underlying this reaction and identifying residues that may influence the kinetics opens up avenues for targeted protein engineering to modulate RNR activity. Thus, this molecular level understanding could assist in the development of chemotherapeutic strategies targeting elevated RNR activity in cancerous cells. More generally, this work provides a deeper understanding of how hydrogen tunneling and conformational motions impact PCET in enzymatic processes.