Electrostatics and water occlusion regulate covalently-bound FMN cofactors of Vibrio cholerae respiratory complex NQR

Abstract

Proteins like NADH:ubiquinone oxidoreductase (NQR), an essential enzyme and ion pump in the physiology of several pathogenic bacteria, tightly regulate the redox properties of their cofactors. Although flavin mononucleotide (FMN) is fully reduced in aqueous solution, FMN in subunits B and C of NQR exclusively undergo one-electron transitions during its catalytic cycle. Here, we perform ab initio calculations and molecular dynamics simulations to elucidate the mechanisms that regulate the redox state of FMN in NQR. QM/MM calculations show that binding site electrostatics disfavor anionic forms of FMNH₂, but permit a neutral form of the fully reduced flavin. The potential energy surface is unaffected by covalent bonding between FMN and threonine. Molecular dynamics simulations show that the FMN binding sites are inaccessible by water, suggesting that further reductions of the cofactors are limited or prohibited by the availability of water and other proton donors. These findings provide a deeper understanding of the mechanisms used by NQR to regulate electron transfer through the cofactors and perform its physiologic role. They also provide the first, to our knowledge, evidence of the simple concept that proteins regulate flavin redox states via water occlusion.

1. Introduction

The ion pumping NADH:ubiquinone oxidoreductase (NQR) plays a critical role, both as a respiratory complex and as the main ion pump, in the physiology of several types of pathogenic bacteria, including Vibrio cholerae (1), Klebsiella pneumoniae (2), Chlamydia trachomatis (3), Pseudomonas aeruginosa (4) and others (5). NQR catalyzes electron transfer from NADH to ubiquinone, feeding the lower part of the respiratory chain (6, 7). The electron transfer reaction releases a large amount of energy that NQR harnesses to pump ions, creating a gradient that is used by the cell to support a wide variety of homeostatic and bioenergetic roles. While earlier reports indicated that NQR is a sodium-specific ion pump (8-11), we have recently shown that NQR from P. aeruginosa is a proton pump (12).

NQR is composed of six subunits (A-F) and five confirmed redox cofactors (Figure 1A and 1B): FAD (flavin adenine dinucleotide), a 2Fe-2S center, two covalently-bound FMN (flavin mononucleotide) molecules, and a riboflavin molecule (8-11, 13-18). Crystallographic data indicate that a sixth cofactor, a non-heme iron center, could also participate in electron transfer (19, 20). However, its participation in the electron transfer pathway has not been experimentally corroborated. NQR is a remarkable protein family with many unique characteristics. It is the only known enzyme that uses riboflavin (vitamin B₂) directly as a cofactor (15, 16); all other flavin-dependent enzymes use FMN or FAD (21, 22). In addition, the two-covalently bound FMN molecules, located in subunits B (FMN_B) and C (FMN_C), are attached through an uncommon phosphodiester bond between the phosphate moiety of FMN and a conserved threonine residue (14, 23). In contrast with all other reported cases, in which covalent flavins are attached through the isoalloxazine ring by an autocatalytic process, the formation of the phosphoester bond in NQR is catalyzed by the only known flavin transferase, ApbE (24-27).

Figure 1.

A) Electron transfer pathway, subunit and cofactor composition of Na⁺-NQR, and role of subunits B, D and E in sodium transport. B) Crystal structure of Na⁺-NQR. C) Internal electron transfer chain and redox steps linked to sodium transport.

Studies performed by several groups have shed light into NQR’s internal electron transfer pathway (7, 16, 28-30). The electrons move downhill (31-33) through a linear pathway (Figure 1C): two electrons from NADH are donated to FAD (located in subunit F); the electrons then move one by one to the 2Fe-2S center in subunit F, to FMN_C, to FMN_B, and then are finally delivered to riboflavin, the final internal electron carrier. Riboflavin delivers the redox equivalents to ubiquinone (28), which binds to subunit B (19, 20, 34-36).

Strikingly, electron transfer during NQR catalysis is characterized by one-electron transitions. All physiological redox transitions for the two covalently-bond FMN and riboflavin molecules are one-electron transitions (28, 31, 37). Moreover, all redox reactions involved in the ion pumping mechanism of this enzyme are also one-electron transitions (31, 38). For instance, the redox reactions involved in the capture and release of sodium are the one-electron reductions of FMN_C and Riboflavin (38) (Figure 1C).

The presence of multiple semiquinone flavin radicals is another characteristic feature of NQR. The riboflavin cofactor carries a stable neutral radical (RibH^•) that is resistant to air and strong oxidants (15, 16, 30). Moreover, during the physiologic electron transfer reactions, the two FMN molecules are found as anionic semiquinone radicals (FMN^•−) (28). While FMN_C can also be found in a two-electron reduced anionic monoprotonated form (FMNH⁻), this state is not part of the catalytic cycle due to its low redox potential. The full reduction of FMN_B is not observed; the most reduced state found in the NQR complex is the one-electron reduced anionic semiquinone radical (F^•−) (31, 37).

The observed one-electron transitions and redox states indicate that the two covalently-bound FMN molecules only undergo one or two of six possible transitions. As in other flavins, the reduction of FMN can in principle follow six basic steps (Figure 2): A) the one-electron reduction of the oxidized form coupled to the uptake of a proton, to produce a neutral semiquinone radical (F→FH^•), B) the one-electron reduction and protonation of the neutral radical to produce the fully reduced form (FH^•→FH₂), C) the one-electron proton-independent reduction of the oxidized state to produce an anionic semiquinone radical (F→F^•−), D) the subsequent one-electron reduction of the anionic radical and the uptake of two protons to produce the fully reduced state (F^•−→FH₂). E) the two-electron reduction and di-protonation of the oxidized state (F→FH₂), and F) the protonation/ deprotonation of the neutral/anionic radicals (FH^•↔ F^•−). In the enzymatic mechanism of NQR, however, the FMN molecules only carry out step C) (28, 31).

Figure 2. Redox steps involved in the reduction of oxidized FMN.

Pathways a and b show proton-dependent one- electron reductions of FMN to produce the neutral semiquinone radical (FH^•) and the fully reduced form (FH₂), respectively. Pathways c and d show one-electron reductions of FMN to produce the anionic semiquinone radical (F^•−) and the fully reduced form, respectively. The protonation/deprotonation of the anionic/ neutral semiquinone flavin radical is represented in path f. The two-electron reduction of FMN is found in reaction e.

Although the redox states and mechanistic role of NQR cofactors have been extensively studied, very little is known about the factors that dictate these properties. In this work, we use ab initio calculations and molecular dynamics simulations to study the factors that determine the redox states of the covalently-bound FMN cofactors and the electron transfer reactions between these molecules.

2. Results

2.1. Homology models for every subunit were generated with strong confidence

The I-TASSER web server (39-41), which was used to build complete models of every subunit, computes a C-score to quantify the degree of confidence of a generated model. The range of a typical C-score is between −5 and 2, with a higher score signifying greater confidence in the model. The C-scores of the first model for each subunit were 0.42 for A, −0.10 for B, 1.47 for C, 0.53 for D, 1.72 for E, and 1.95 for F. Subunit B has a lower C-score because no template was found for 38 residues at the N terminus. In all of the other subunits, regions lacking a template were shorter than 10 residues. The lack of a template at the N terminus of subunit B is highly unlikely to affect the quality of modeling at the FMN binding site, which involves residue numbers 200 and above.

2.2. Covalent bonding and modification have negligible effects on the potential energy surface of FMN reduction

Potential energy differences between FMNH_n in three forms – truncated, native, and long chain (Figure S2) – indicate that covalent bonding and modification have a negligible effect on the relative stability of the redox states (Table S1). While the truncated form only includes the isoalloxazine ring capped by a methyl group, the native chain includes the linker and phosphate group, and the long chain includes the side chain of threonine, a 2-propyl group (Figure S2). The negligible difference between the relative stability of forms indicates that the uncommon covalent attachment of the FMN molecules does not modify or regulate their redox potentials. Rather, by elimination, the likely role of the covalent bonds is to attach the molecule to the binding site. Subsequent results are based on FMN with a native chain.

2.3. Complete reduction of FMN occurs prior to protonation in gas phase and implicit solvent

To understand the pathway that electrons traverse to reach the stable redox states of FMN, we carried out potential energy calculations of diverse redox and protonation states of this molecule. The calculations consider three redox states, fully oxidized (e⁻=0), one- (e⁻=1) and two-electron (e⁻=2) reduced states. Moreover, we carried out calculations in which each of these states exist in three protonation states, fully protonated (H⁺=2), semi-deprotonated state (H⁺=1) and fully deprotonated (H⁺=0), for a total of 9 intermediates. It should be clarified that while some of these states are nonphysical (i.e., e⁻=1, H⁺=2), these calculations help us map theoretically possible redox pathways and the stability of the intermediates. Furthermore, it should be noted that the calculations shown in Figures 3A-C do not take into account the energy of the electron donor for each of these cofactors. Thus, they do not represent the complete physiological electron transfer process. Nonetheless, the information obtained improve our understanding of the electron transfer pathway.

Figure 3.

Potential energy surfaces of the redox states as a function of the protonation and redox state of the FMN molecule for (a) FMN in the implicit solvent with no electron donor, (b) FMN_B in a relaxed protein with no electron donor, (c) FMN_C in a relaxed protein with no electron donor, and (d) FMN_B in a relaxed protein with FMN_C^•− as electron donor.

Figure 3A shows the potential energy surface of the redox states of the isolated FMN molecule in implicit solvent, as a function of the protonation state (H⁺) and redox state (e⁻). Oxidized FMN is found at the coordinate (0, 0); the neutral radical FMNH^• at (1, 1); the anionic radical FMN^•− at (0, 1) and the reduced FMNH₂ at (2,2). Figure 3A indicates that the optimal reaction route from the oxidized FMN to the reduced FMNH₂ involves these steps: oxidized FMN (0, 0) → anionic semiquinone radical FMN^•− (0, 1) → fully reduced di-anionic FMN²⁻ species (0, 2) → mono-protonated fully reduced anionic FMNH⁻ (1, 2) → di-protonated reduced FMNH₂ (2, 2). Interestingly, the energy calculations indicate that in the implicit solvent without an electron donor, the reduction processes precede the protonation of FMN, which is not obvious. Qualitative trends for the relative energy levels of FMNH_n are consistent with gas-phase calculations (Figure S1), suggesting that the most energetically favorable path is not an artifact of the implicit solvent model.

2.4. Complete reduction of FMN in NQR requires proton-coupled electron transfer

In addition to the calculations with the FMN molecule in implicit solvent, we carried out calculations of the covalently-attached FMN_B and FMN_C centers in the protein context, embedded in the FMN sites in subunits B and C with no electron donor. The potential energy surfaces of FMN_B and FMN_C reduction and protonation are found in Figures 3B and 3C. These energy surfaces differ significantly from that of FMN in the implicit solvent. In particular, the reaction route FMN→FMN^•−→FMN²⁻→FMNH⁻→FMNH₂ is not allowed in the embedded cofactor. Instead, FMN_B reduction follows an alternate pathway: oxidized FMN (0, 0) → anionic semiquinone radical FMN^•− (0,1) → neutral semiquinone radical FMNH^• (1,1) → protonated neutral semiquinone radical FMNH₂^• (2,1) → di-protonated reduced FMNH₂ (2,2). The main difference compared to the gas phase and implicit solvent calculations is that the fully reduced anionic species, FMNH⁻ (1,2) and FMN²⁻ (0,2), are relatively instable in the electrostatic environment of the enzyme. For this reason, the pathway is rerouted through the neutral semiquinone radical (1, 1) and the protonated semiquinone radical FMNH₂^• (2, 1).

2.5. The FMN_B reduction pathway with its physiologic electron donor is similar

To further characterize the electron transfer pathways in the enzyme, we carried out calculations using FMN_C, which in the physiologic context is found as an anionic semiquinone radical (FMN_C^•−), as the redox donor of FMN_B (Figure 3D). Accordingly, the potential energy surface of the embedded FMN_B includes the contribution of the donor (ΔE_ET). Although the energy landscape is very different compared to previous calculations, the pathway of electron transfer obtained is similar, involving the neutral semiquinone radical and two subsequent protonation steps: FMN→FMN^•−→FMNH^•→FMNH₂^•→FMNH₂. The main difference is that the transition from the oxidized state to the anionic radical is slightly unfavored. This transition could be favorable in a slightly different protein conformation. The energy landscape also suggests that an alternative pathway through the monoprotonated oxidized cofactor (1,0) is feasible. However, this intermediate has not been experimentally observed.

2.6. Water accessibility regulates reduction of the covalently-bound FMN cofactors

While the QM/MM calculations clarify that the protein electrostatic environment precludes fully reduced anionic FMN, they do not explain how the NQR catalytic cycle limits FMN to the fully oxidized and anionic semiquinone redox states. We suspected that further reduction of FMN is restricted by the lack of a nearby proton donor such as water.

To assess whether the availability of water could regulate the reduction of FMN cofactors in NQR, we evaluated the solvent accessible surface area (SASA) and water density near the cofactors (Figure 4). The SASA of the initial configuration of the MD simulation, which is similar to the crystal structure, suggests that possible protonation sites of FMN are not accessible to water. The water density from 100 ns of molecular dynamics simulation provides further evidence that, even after accounting for thermal fluctuations of the NQR structure, both FMN molecules are shielded from the aqueous environment. Taken together with the potential energy calculations, these results suggest that the full reduction of the FMN molecules is prevented by the availability of proton donors in the FMN sites. They explain the experimental observation that the most stable intermediate is the anionic radical.

Figure 4. Water accessibility of FMN_B and FMN_C binding sites.

The solvent-accessible surface area of FMN_B (A) and FMN_C (B) binding sites from NQR crystal structure. Water density in the FMN_B (C, front view; Left bottom, side view) and FMN_C (D, front view; Left bottom, side view) binding sites calculated after molecular dynamics simulations.

3. Discussion

We have performed QM/MM calculations and molecular dynamics simulations to elucidate how NQR regulates the redox state of its covalently bonded FMN molecules. Our work contributes to scientific understanding in several ways. First, the QM/MM results clearly show that the phosphoester bond between the conserved threonine in the binding site and the phosphate moiety of FMN does not modify the thermodynamic properties of the cofactor, and thus the role of this bond is exclusively for covalent attachment. This question has eluded the groups involved in this field for several years. Second, the QM/MM calculations show that the reduction pathway of FMN is significantly altered by the electrostatic environment of the binding sites. In particular, anionic fully reduced FMN is destabilized and the energy landscape forms a wedge that directs the electrons to the neutral semiquinone radical. Finally, the molecular dynamics simulations show that full reduction of FMN is restricted by the unavailability of water as a proton donor.

Changes to the reduction pathway of FMN relative to solvent are explained by the amino acid composition of the binding sites (Figures 5A and 5B). The sites are filled with hydrophobic residues, which generally favor electrically neutral ligands opposed to anionic ones. Remarkably, the FMN_B and FMN_C sites appear to have distinct mechanisms for stabilizing the anionic semiquinone. The binding site for FMN_B carries a positively charged arginine residue (R209) that can stabilize negative charges. On the other hand, the binding site of FMN_C positions the hydroxyl group of a conserved threonine 173 to donate a hydrogen bond to N5. This mechanism of stabilizing the anionic semiquinone of FMN has also been observed in iodotyrosine deiodinase (42, 43). Ultimately, the energy landscapes of both cofactors are nearly identical.

Figure 5.

Binding sites of the covalently- attached FMN_B and FMN_C. Carbon atoms in the protein are shown in white.

The potential energy landscapes of FMN shown in Figure 3 are consistent with previously measured midpoint potentials. In the case of FMN_B, we were able to calculate the energy landscape for the physiologic reaction using FMN_C^•− as an electron donor (28), as shown in Figure 3D. (For FMN_C analogous calculations were difficult due to the complex electron configuration of the one-electron reduced 2Fe-2S center, the physiologic electron donor). The reduction of FMN_B to the anionic radical involves an energy difference of nearly zero, consistent with the almost identical midpoint potential of both centers (31). In the case of FMN_C, Figure 3C shows that the potential energy of the neutral radical (1,1) is lower than the two-electron reduced anionic monoprotonated form, FMNH⁻ (1,2). This calculation is consistent with the observation that while FMNH⁻ is found in subunit C of NQR, its midpoint potential too negative to participate in the mechanism of the enzyme (E_m= −215 mV) (31, 37), requiring an uphill electron transfer due to the higher potential of the anionic radicals (E_m = −125 mV for both in the presence of sodium (31)).

Although they are informative, the energy landscapes are not sufficient to explain the observed redox states of FMN in NQR; the availability of protons must also be considered. Molecular dynamics simulations indicate that water is unavailable as a proton donor in either cofactor binding site. Neighboring side chains are another possible source of protons. The binding site of FMN_B lacks proton donors near the protonation sites of FMN (Figure 5A). The lack of protons in subunit B, combined with the high potential energy of the two-electron reduced state FMN²⁻, explains why only the fully oxidized and anionic semiquinone forms of FMN have been observed in subunit B. In the binding site of FMN_C, on the other hand, a proton can be abstracted from threonine 173 (Figure 5B). Although threonine (pKa = 13) is not a strong proton donor compared to the hydronium ion (pKa = 7) or tyrosine (pKa = 10.5), it could still participate in the protonation reaction, allowing the uphill two-electron reduction of FMN_C.

The potential energy landscapes also highlight the importance of occluding water from the FMN binding sites. If protonation were to occur in FMN_B, producing the neutral semiquinone radical, an electron would be trapped in a thermodynamic valley, slowing down downstream reactions and likely wasting some of the energy that would otherwise be used for the conformational changes involved in sodium transport.

Although conceptually simple, the notion that full reduction of semiquinone radicals is precluded by the unavailability of protons is apparently, to our knowledge, novel. A number of mechanisms have been proposed to explain the stabilization of semiquinones, including modifications to the electrostatic environment, π stacking, and hydrogen bonding, especially involving N5. For example, in many flavodoxins, the stabilization of neutral semiquinones is driven by several factors (44): a negative electrostatic environment that disfavors anionic radicals; a conserved tyrosine residue that forms more favorable π stacking interactions with the semiquinone than fully reduced form; and hydrogen bonding between FMN N5H and a carboxyl group on the backbone of a glycine (45). A similar glycine carbonyl interaction is also important for stabilizing a neutral semiquinone in NADPH-cytochrome P450 oxidoreductase (46). Some of these mechanisms are inappropriate for stabilizing the anionic semiquinone; an unusual archeal flavodoxin that stabilizes the anionic semiquionone does not contain as many acidic residues near the FMN binding site or a glycine that can flip to participate in hydrogen bonding (47). The anionic semiquinone also is stabilized by donating hydrogen bonds to the FMN N5, as in iodotyrosine deiodinase (42, 43). As mentioned above, this mechanism is likely to apply to the FMN binding site in NQR subunit C. Stabilization of various semiquinone radicals has been proposed to be coupled with conformational changes (48) or small molecule binding (49). However, we have not seen a discussion of flavin redox being regulated by water accessibility.

Previous reports indicate that NQR undergoes multiple conformational changes during the catalytic cycle that allow the enzyme to capture the ions and translocate them through the plasma membrane (31, 38, 50). Moreover, it has been reported that the two FMN cofactors participate exclusively as anionic semiquinone radicals (29-31). Thus, our results suggest that the covalently-bound FMN binding sites are not significantly altered during the catalytic cycle or that the sites remain hydrophobic after structural rearrangements, which would limit the entry of water into the site and stabilize the anionic state of the radical. This hypothesis is an important addition to the kinetic model that we have proposed for the catalytic mechanism of NQR (50), which must be tested experimentally in future studies.

4. Conclusions

In this work we have unveiled the underlying structural factors that determine the redox states and pathways of two of NQR redox cofactors, FMN_B and FMN_C. Our results show that the anionic semiquinone radical form of the two cofactors, their physiologic state, is readily formed and that other transitions are blocked by the lack of proton donors or by the presence of weak donors. These results offer a deeper understanding about the way in which electron transfer is modulated by the cofactors’ environment.

5. Materials and Methods

5.1. Molecular dynamics simulation of the NQR system

The force field for molecular dynamics simulations were based on AMBER(51) with special modifications for cofactors and nonstandard residues. The V. cholerae Na⁺-NQR crystallographic structure (PDB ID: 4P6V) contains six cofactors (FAD, FMN_B, FMN_C, Riboflavin, the Fe and 2Fe-2S centers) and a Ca²⁺ ion. In this study, the AMBER ff14SB force field (51) was used for standard residues and the Generalized AMBER force field 2 (52) for organic cofactors. For the Fe and 2Fe-2S centers, we used the force fields provided by Carvalho et. al. (53). The Austin Model 1-Bond Charge Corrections (AM1-BCC) method (54, 55) was used for partial charges of the other cofactors. All redox centers were modeled in the fully oxidized form. 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine (DPPE) lipid (56-58) and the OPC3 water model (59) were used to build a membrane and aqueous environment, respectively. V. cholerae Na⁺-NQR has 10 non-standard residues that are covalently bound to cofactors. FMN_B and FMN_C are attached to atoms OG1 of T236 in subunit B and T225 in subunit C, respectively. The non-heme Fe center is attached to residues C29 and C112 in subunit D, and C26 and C120 in subunit E. The 2Fe-2S center is attached to C70, C76, C79 and C111 in subunit F. Covalent bonds between residues and cofactors are represented as harmonic bonds. Bond, angle, and torsional potential energy terms for these iron-containing centers were obtained from Carvalho et. al. (53). OpenMM was modified to add these additional potential energy terms when generating AMBER input (prmtop and inpcrd) files from the PDB file. The modified code and force fields that were used in this study are available on GitHub (https://github.com/swillow/pdb2amber).

The initial structure for simulation was based on fitting homology models to the crystal structure of NQR. The crystal structure 4P6V does not provide the atomic coordinates for 163 residues located in the periplasmic and cytosolic loops connecting transmembrane helices. Complete models for every NQR subunit, including these missing residues, were built using the I-TASSER web server(39-41). The complete models were rotated and translated to minimize the root mean square deviation between alpha carbons of the model and crystal structure using UCSF Chimera 1.14(60). All heavy atoms of the protein and cofactors without hydrogen atoms were slightly minimized using a steepest (gradient) decent minimization with a maximum displacement Δx of 0.05 Å: x(t+1) = x(t) + dt x(t+1)= x(t)+ dt Δx and Δx = f/m, where f, m, and dt represent the force, the mass, and the time step (dt = 2.0 fs). We performed 1000 steps of this minimization to remove overlapping heavy atoms. The code for the minimization of heavy atoms without hydrogen atoms is available on GitHub (https://github.com/swillow). Default protonation states (AMBER residue types ASP, GLU, LYS, HIE, and CYS) were used for titratable residues. The complete NQR protein model was translated and rotated in order to align three atoms, the alpha carbons of TRP 134, TRP 166, LUE 64 of subunit E, to the structure of crystallographic protein atomic positions in a DPPE membrane from the OPM database(61-63). Two systems were prepared, each containing the protein complex model with 6 cofactors, one Ca²⁺ ion, 301 DPPE molecules and 48945 OPC3 water molecules. One of the systems lacked salts and contained 27 Na⁺ ions. The second system was modeled with 0.1 M NaCl, 69 Cl⁻ and 96 Na⁺ ions. The python codes used to build the system are available on GitHub, too.

Isothermal isobaric molecular dynamics simulations were performed using the Langevin integrator at P = 1 bar and T = 300 K with a time step of 2 fs using OpenMM(64). Over the course of 20 ns, restraints on atomic positions were progressively relaxed using python codes provided in the Membrane Builder of CHARMM-GUI(65), described at the end of the CHARMM-GUI article. This equilibration procedure uses the MonteCarloMembraneBarostat in OpenMM with options of XYIsotropic and ZFree, which makes the X and Y axes isotropic. For production (20 ns ~ 100 ns), we performed NPT simulations with the MonteCarloBarostat, in which all axes are isotropically scaled every 100 steps. The average of the system box size was 108.3 x 108.3 x 174.9 ų. Particle-mesh Ewald (PME) summation was used to compute the long-range Coulomb interactions. A 12 Šcutoff distance was used for the Coulomb and Lennard-Jones interactions(41) as short-range interactions. All bonds involving a hydrogen atom were constrained. Water molecules are constrained using SETTLE(66). The Constant Constraint Matrix Approximation (CCMA) algorithm is used for constraining the other bonds involving a hydrogen atom(67).

5.2. Potential energy calculations of FMN molecules

QM, QM/MM, and QM/solvent calculations were performed with the PySCF 1.7.0 python package(68), in which the evaluation of molecular integrals of many-body operators over Gaussian functions were obtained using libcint 3.0.19(69). Potential energies were calculated using the restricted/unrestricted Hartree-Fock method in conjunction with the 6-311G** basis set.

The ddCOSMO model(70, 71) was used as the implicit solvent model for QM/solvent calculations. The solvent-accessible surface on the QM molecule was generated with the van der Waals radii (72) scaled by a factor 1.2. The solvent dielectric constant is 78.3553 for water. The points and weights of a Lebedev integration grid were generated with a lebedev_order of 7.

QM/MM calculations were based on an additive scheme in which the electron density of the QM region is polarized due to an embedding field of atomic charges from the MM region (73). The QM region included the FMN isoalloxazine ring by itself (truncated) or with the covalently attached phosphate group capped with either a hydrogen atom or isopropyl group based on the threonine side chain (Figure S2); in the latter two, the link atoms are hydrogen. Because partial charges of MM atoms linked via bonds and angles to atoms in the QM region can cause overpolarization, the charges of these atoms was set to zero. Depending on the protonation state of FMNH_n (n = 0, 1, 2), the QM region also included hydronium ions or water molecules adjacent to the FMN protonation sites on the isoalloxazine ring (Figure S3 for FMN by itself and Figure S4 for FMN in NQR); this scheme ensures that the number of atoms is equivalent in all QM calculations of ground-state potential energy differences with the same chain.

Coordinates for QM calculations were based on the NQR crystal structure or on molecular dynamics simulations. For QM and QM/solvent calculations of FMN by itself, coordinates of FMNH_n were extracted from subunit B of the crystal structure and minimized using the antechamber program in the AMBER(51) package (Figure S3 and Table S2). For QM/MM calculations, FMN coordinates were taken from the last snapshot of the 4 ns NQR simulation with no salt. Either a hydronium ion or water molecule was placed near the nitrogen atom (N5) of the FMN molecule with a distance of 3 Å between the oxygen atom of hydronium and the nitrogen atom (N5) of the FMN molecule. The embedding field included all residues and water in which at least one atom is within a cutoff distance (10 Å) of any QM atom (Figure S5). Atomic charges in the embedding field were provided by the AMBER ff14SB force field. In summary, calculations were performed for the FMN and threonine configuration from chain B and C, with a native or long chain, with or without an embedding field based on the protein environment, and with or without implicit solvent.

5.3. Solvent-accessible surface area (SASA) and water density

The water accessibility of FMN cofactors was evaluated based on the solvent-accessible surface area of the crystallographic structure and the water density observed in after molecular dynamics simulation. The SASA of the whole NQR was calculated using Visual Molecular Dynamics (VMD) 1.9.3 with a spherical probe of 1.4 Å (the radius of a water molecular probe). The python package MDAnalysis.analysis.density was used to calculate the water density around FMN_B and FMN_C(74). First, all frames from 20 to 100 ns from the simulation trajectories were aligned by minimizing the α carbon RMSD relative to the cofactors. Then a three-dimensional map of the water density, relative to the bulk water density, within 20 Å of FMN_B and of FMN_C was calculated based on grids with a spacing of 0.5 Å. VMD was used to visualize the results using an isosurface representation with an isovalue of 1.0, rendering a surface where the density is equal to the bulk density(75).