Conformational Preferences of Pyridone Adenine Dinucleotides from Molecular Dynamics Simulations

Pyridone adenine dinucleotides (ox-NADs) are redox inactive derivatives of the enzyme cofactor and substrate nicotinamide adenine dinucleotide (NAD) that have a carbonyl group at the C2, C4, or C6 positions of the nicotinamide ring. These aberrant cofactor analogs accumulate in cells under stress and are potential inhibitors of enzymes that use NAD(H). We studied the conformational landscape of ox-NADs in solution using molecular dynamics simulations. Compared to NAD+ and NADH, 2-ox-NAD and 4-ox-NAD have an enhanced propensity for adopting the anti conformation of the pyridone ribose group, whereas 6-ox-NAD exhibits greater syn potential. Consequently, 2-ox-NAD and 4-ox-NAD have increased preference for folding into compact conformations, whereas 6-ox-NAD is more extended. ox-NADs have distinctive preferences for the orientation of the pyridone amide group, which are driven by intramolecular hydrogen bonding and steric interactions. These conformational preferences are compared to those of protein-bound NAD(H). Our results may help in identifying enzymes targeted by ox-NADs.


Introduction
Nicotinamide adenine dinucleotide and nicotinamide adenine dinucleotide phosphate (NAD and NADP, respectively) are cofactors and substrates for numerous enzymes and have a multitude of redox and non-redox roles in cells [1,2]. NAD(P)(H) plays an essential role in oxidoreductase catalyzed reactions, where the C4 of the nicotinamide ring ( Figure 1A) is the direct hydride acceptor for dehydrogenases or the hydride donor for reductases. NAD(P)H is also the hydride donor to the flavin cofactors, FAD and FMN, in a large class of enzymes known as flavin-dependent monooxygenases, which catalyze the addition of O atoms from O 2 to substrates [3]. The Sir2 family of deacetylases use NAD + as a substrate to catalyze the deacetylation of acyllysine residues of protein substrates to reveal the free amino form of the lysine sidechain and 2 -O-acyl-ADP-ribose [4]. ADP-ribosyltransferases use NAD + as the source of an adenosine diphosphoriboside (ADPribose) unit to covalently link single or multiple ADP-ribose units to protein substrates [5], while glycohydrolases are responsible for the loss of the nicotinamide unit and formation of ADP-ribose. The ubiquity of NAD(P) in the metabolism is reflected in the Protein Data Bank, where over 4000 entries contain NAD + , NADH, NADP + , or NADPH complexed to the protein.
The structural properties of NAD(H) have been measured by a variety of experimental techniques, including solution NMR and fluorescence, and X-ray crystallography. Early NMR studies have indicated that NAD(H) adopts a folded conformation in solution that is in rapid equilibrium with an open form [6][7][8]. Measurements of fluorescence anisotropy decay have indicated NADH has an apparent hydrodynamic radius in solution of about 6 Å [9]. Estimates of the hydrodynamic volume of NADH in aqueous solution are in cence anisotropy decay have indicated NADH has an apparent hydrodynamic radius in solution of about 6 Å [9]. Estimates of the hydrodynamic volume of NADH in aqueous solution are in the range of 500-600 Å 3 [10,11]. The relative population of folded NADH in aqueous solution is estimated to be 25-35% [6,9]. Another NMR study suggested NAD + is 15% folded in solution [12]. A crystal structure of the Li + salt of NAD + shows an extended molecule with an inter-base distance of 12 Å [13,14]. The crystal structure shows a dimer in which the adenine of one molecule is stacked intermolecularly on the nicotinamide of a neighboring molecule. Pyridone adenine dinucleotides (ox-NAD(P)) are oxidized derivatives of NAD(P) possessing a carbonyl group on the nicotinamide ring at the C2 N , C4 N , or C6 N position ( Figure 1B). These aberrant forms of NAD(P) accumulate in cells under stress conditions when cells build up an overabundance of electrons, in turn causing an abnormally high ratio of NADH to NAD + and the generation of reactive oxygen species [15][16][17]. Pyridone adenine dinucleotides can be detected at concentrations within the nmol/mg of protein range of NAD(P)(H) concentrations in tissues and cultured cells [18,19]. There, they have the potential to inhibit NAD(P)-dependent enzymes, causing further metabolic dysfunction and pathogenic oxidative damage.
The association of pyridone adenine dinucleotides and their catabolites in agerelated diseases, including cancer and cancer metastasis [19], and the potential for their inhibition of metabolic enzymes motivated us to study the in-solution conformations of the three major pyridone adenine dinucleotides. Herein, we report molecular dynamics simulations of NAD + , NADH, 2-ox-NAD, 4-ox-NAD, and 6-ox-NAD ( Figure 1). The Pyridone adenine dinucleotides (ox-NAD(P)) are oxidized derivatives of NAD(P) possessing a carbonyl group on the nicotinamide ring at the C 2 N , C 4 N , or C 6 N position ( Figure 1B). These aberrant forms of NAD(P) accumulate in cells under stress conditions when cells build up an overabundance of electrons, in turn causing an abnormally high ratio of NADH to NAD + and the generation of reactive oxygen species [15][16][17]. Pyridone adenine dinucleotides can be detected at concentrations within the nmol/mg of protein range of NAD(P)(H) concentrations in tissues and cultured cells [18,19]. There, they have the potential to inhibit NAD(P)-dependent enzymes, causing further metabolic dysfunction and pathogenic oxidative damage.
The association of pyridone adenine dinucleotides and their catabolites in age-related diseases, including cancer and cancer metastasis [19], and the potential for their inhibition of metabolic enzymes motivated us to study the in-solution conformations of the three major pyridone adenine dinucleotides. Herein, we report molecular dynamics simulations of NAD + , NADH, 2-ox-NAD, 4-ox-NAD, and 6-ox-NAD ( Figure 1). The presence of a carbonyl group on the nicotinamide ring profoundly alters the conformational landscape compared to NAD(H), most notably the compactness of the dinucleotide and the preferences of the pyridone ribose glycosidic bond dihedral angle and pyridone amide group orientation. We also compare the conformations of ox-NADs in solution with enzyme-bound NAD(H) to assess the compatibility of these cofactor mimics with enzyme active sites. Our results may be useful for identifying enzymes targeted by ox-NADs.

Conformational Preferences of NAD + and NADH
Ten 100 ns MD simulations (1 µs total) for both NAD + and NADH ( Figure 1A,B) were performed as references for the simulations of ox-NADs. The spatial extent of NAD(H) was assessed by monitoring the distance between the centroids of the nicotinamide and adenine rings. The time evolution of this parameter reveals that NAD(H) underwent multiple opening/closing events during the simulation (Supplementary Figure S1A,B). The inter-base distance varied from a minimum of 3.2 Å to a maximum of 17.2 Å for NAD + , and a minimum of 3.4 Å to a maximum of 17.9 Å for NADH. The distribution of this parameter was trimodal for both NAD + and NADH, with peaks near <6 Å, 8-10 Å, and 12-15 Å, which we refer to as folded, semi-extended, and extended, respectively (Figure 2A,B). The folded peak was much more prominent for NADH, suggesting a greater propensity for adopting compact conformations in solution.  Folded NAD(H) tends to have bases stacked in near-parallel arrangements. This feature is evident in the scatter plot of inter-base distance versus the normal-normal inter-base plane angle ( Figure 3A,B). For reference, parallel base stacking corresponds to normal-normal plane angles of 0 • and 180 • . The most common folded NAD + conformation ( Figure 4A) was identified as the event where the distance between atoms O 4 N -C 4 A was <=4.0 Å. Rarely, the most common folded NAD + transitioned to a highly base-stacked conformation ( Figure 4B). This conformation corresponds to the small population with inter-base distances less than 4 Å and an inter-base angle of 160-180 • (upper left of Figure 3A). Compared to NAD + , NADH displayed a stronger population density in its folded regions, which is characterized by two clusters with inter-base angles of 0-45 • or 135-180 • ( Figure 3B). Examples of these folded NADH conformations are shown in Figure 4E (inter-base angle of 30 • ) and Supplementary Figure S5D   The amide angle (θ) for NAD(H) also shows very distinct preferences. Two large populations near 0° and 180° are observed for NAD + (Figure 5B), whereas NADH strongly prefers θ near 0° ( Figure 5B). Poses with θ near 0° are shown in Figure 4.  Finally, the adenosine in NAD(H) strongly preferred anti over syn. This is expected for a purine base due to its larger size compared to pyrimidines (Supplementary Figure  S3A,B).  The conformational space of the nicotinamide riboside group of NAD(H) is of particular interest for comparison to ox-NADs. The conformation of the nicotinamide riboside was assessed by monitoring the N-glycosidic bond dihedral angle (χ N in Table 1) and the amide dihedral angle (θ in Table 1). NAD(H) showed a preference for χ N in the range of −160 • ±~70 • ( Figure 5A,B), which corresponds to the anti conformation of the base [20]. In the anti conformation, the base is rotated away from the sugar, as shown in Figure 4A for NAD + and Figure 4E for NADH. A somewhat smaller population with χ N of 0-45 • corresponded to the syn conformation. In the syn conformation, the base is rotated about the glycosidic bond to occupy a space closer to the sugar ring (examples of syn NAD + /NADH are provided in Supplementary Figure S5A,C, respectively). The preference for anti reflects a lower steric clash between the nicotinamide base and ribose compared to syn. The data suggest slightly greater syn occurrence for NADH compared to NAD + ( Figure 5A,B). Table 1. Dihedral angle definitions.  The amide angle (θ) for NAD(H) also shows very distinct preferences. Two large populations near 0 • and 180 • are observed for NAD + ( Figure 5B), whereas NADH strongly prefers θ near 0 • ( Figure 5B). Poses with θ near 0 • are shown in Figure 4.

Foldedness of ox-NADs
Finally, the adenosine in NAD(H) strongly preferred anti over syn. This is expected for a purine base due to its larger size compared to pyrimidines (Supplementary Figure S3A,B).

Foldedness of ox-NADs
MD simulations of ox-NADs were performed to understand how the presence of a carbonyl group at the C 2 N , C 4 N , or C 6 N of the nicotinamide ( Figure 1B) affects the conformational landscape of the dinucleotides. The inter-base distance was monitored to determine how the oxidation of the nicotinamide affects dinucleotide foldedness. Similar to NAD + and NADH, the distribution of inter-base distance for ox-NADs is trimodal; however, the relative populations of folded, semi-extended, and extended differ dramatically from those in NAD(H) (Figure 2). For example, the inter-base distance distributions for 2-ox-NAD and 4-ox-NAD show a major peak at 4-5 Å, indicating a greater tendency to fold compared to NAD + or NADH ( Figure 2). This increase in the folded population comes at the expense of fewer extended conformations. Interestingly, the peak representing folded 2-ox-NAD and 4-ox-NAD is shifted by −1 Å compared to NAD + , indicating greater compactness and likeness to NADH. Similar to NADH, the folded conformations of ox-NADs exhibit base stacking, as indicated by the dense populations with inter-base distance <5 Å and inter-base plane angle near 30 • and 160 • ( Figure 3C,D).
Oxidation at the nicotinamide C6 results in significant variability in folding potential. Interestingly, individual plots of the inter-base distance distribution for each simulation of 6-ox-NAD highlight one simulation, S1, where the number of folded conformations of 6-ox-NAD reached nearly 12,000, far more than in any other of the other simulations (Supplementary Figure S2E). We attribute this event to an extended specific interaction with a neutralizing Na + ion. This association appears to further stabilize a folded form observed in 6-ox-NAD ( Figure 6G), which exists at other times of the trajectory uninfluenced by Na + . Additionally, this fold pattern was observed in the other ox-NADs (not shown) as well as in NADH (Supplementary Figure S5D). While this individual simulation likely skews the standard deviation for 6-ox-NAD in bins of the folded region, we note that this strong Na + interaction was identified in only one out of the fifty simulations performed and appears to be a rare event. On average, the distribution of inter-base distance of 6-ox-NAD shows a predominant peak at 13-14 Å, representing extended conformations, while the populations of folded and semi-extended conformations are relatively minor when compared to 2and 4-ox-NAD ( Figure 2E). Thus, on average, 6-ox-NAD is more extended than the other ox-NADs.

Pyridone Ribose Conformation of ox-NADs
Oxidation of the nicotinamide at C 2 N and C 6 N profoundly affects the conformation of the N-glycosidic bond dihedral angle. 2-ox-NAD shows a very strong preference for the anti conformation (χ N~− 135 • to −180 • ) and near complete avoidance of syn ( Figure 5C). This tendency likely reflects the steric clash that arises in the syn conformation between the C 2 N -carbonyl and the ribose. The distribution of χ N for 4-ox-NAD resembles that of NAD(H) in that both anti and syn can be observed, with a preference for the former ( Figure 5D). Oxidation at the C 6 N has the opposite effect: 6-ox-NAD adopts syn far more than any of the dinucleotides ( Figure 5E). The 6-ox-NAD pyridone ribose likely experiences steric clash in either the anti or syn conformations, as both forms position atoms above the ribose. The poses in Figure 6   In addition to these large trends in χ N preferences, ox-NADs also exhibit more subtle deviations from the conformational tendencies of NAD(H). For example, 2-ox-NAD has a small population near χ N~− 60 • , which is not present in the other dinucleotides ( Figure 5C). An example of this conformation is shown in Supplementary Figure S5E. Note the approach of the C 2 N -carbonyl oxygen to the ribose oxygen O 4 N . This small population of χ N~− 60 • likely represents the high-anti pyridone ribose conformation, which corresponds to the closest approach of the C 2 N -carbonyl oxygen to the ribose O 4 N atom [21,22]. Additionally, 6-ox-NAD exhibits a small population near χ N~1 10 • (Figure 5E). An example of this conformation is shown in Supplementary Figure S5G. Similar to 2-ox-NAD, the C 6 Ncarbonyl oxygen of 6-ox-NAD is positioned near the ribose oxygen O 4 N . The population for χ N~1 10 • likely represents the high-syn pyridone ribose conformation. As 6-ox-NAD readily adopts both anti and syn conformations for its pyridone ribose, the high-syn population could be a transition state between the two main conformations of the pyridone ribose glycosidic bond angle. Conversely, 4-ox-NAD appears to sample the high-anti and high-syn regions to a very limited extent compared to 2-and 6-ox-NAD ( Figure 5D).

Conformations of Protein-Bound NAD(H)
The conformational tendencies of NAD(H) bound to proteins were studied by mining the PDB. The dataset consisted of 3965 poses of NAD + and 671 poses of NADH in crystal structures with resolution of 2.9 Å or better. The trends for NAD + and NADH were found to be similar; hence, we show results for the combined dataset of 4636 poses.
NAD(H) tends to adopt highly extended conformations when bound to proteins ( Figure 8A). The average centroid-centroid distance between the bases is 14.0 Å with standard deviation of 1.3 Å. The distribution is similar to those reported previously [23,24]  crystal structures with resolution of 2.9 Å or better. The trends for NAD and NADH were found to be similar; hence, we show results for the combined dataset of 4636 poses. NAD(H) tends to adopt highly extended conformations when bound to proteins ( Figure 8A). The average centroid-centroid distance between the bases is 14.0 Å with standard deviation of 1.3 Å. The distribution is similar to those reported previously [23,24]. Note the average of 14.0 Å is close to the typical inter-base distance of extended conformations of NAD(H) and ox-NADs in solution ( Figure 2). The glycosidic bond dihedral angle distribution of protein-bound NAD(H) resembles that of NAD(H) in solution. The adenosine is found almost exclusively in the anti conformation ( Figure 8B), whereas the nicotinamide ribose adopts both the anti and syn conformations ( Figure 8C).

Conformations of Protein-Bound NAD(H)
The amide dihedral angle (θ) of protein-bound NAD(H) is near 0 • or 180 • , with a preference for the latter ( Figure 8C). This contrasts the behavior of NAD(H) in solution, which strongly prefers θ near 0 • (Figure 5A,B). The discrepancy between solution and protein-bound NAD(H) likely reflects the fact that hydrogen bonding with the protein tends to establish the orientation of the amide group of protein-bound NAD(H). An example is aldehyde dehydrogenase 4A1, where a hydrogen bond with a backbone carbonyl fixes the amide group at~180 • [25,26].

Discussion
We compared the in-solution conformations of NAD + , NADH, and ox-NADs using MD. The results for NAD + differ from those of a much shorter, 5 ns simulation of NAD + performed by us over 20 years ago [27]. In that simulation, only a single opening and closing event was observed, and NAD + spent approximately 80% of the time in compact conformations with the inter-base distance near 5 Å. In contrast, the new multiple 100 ns simulations showed many opening and closing events and a preference for open conformations, with the inter-based distance in the range of 8-14 Å. We attribute this discrepancy to two factors: the short timescale of the previous simulation limiting the sampling of the conformational space of NAD + , and the uniqueness of the starting conformation of NAD + used for simulation from PDB 2BKJ, chain B. In that structure, NAD + is tightly folded with a syn adenine, which was not observed in our current simulation (Supplementary Figure S3A). Overlaying what we found to be the rarest folded form of NAD + ( Figure 4B) from our current simulations with the starting conformation from PDB 2BKJ, chain B shows an interesting agreement between the folds overall, aside from the flipped adenine orientation (Supplementary Figure S5B). We note that in the current simulations we observed compact conformations persisting for~5 ns, i.e., the entire duration of the previous simulation (see near t = 80, t = 200, or t = 700 ns in Supplementary Figure S1A).
We suggest the current simulation more accurately depicts the behavior of NAD + in solution because it more thoroughly sampled the available phase space compared to the previous simulation. In particular, we observed numerous opening and closing events for all five dinucleotides, suggesting that the sampling of pyrophosphate dihedral angles is adequate (Supplementary Figure S1). The consistency of the end-to-end distributions calculated from the individual 100 ns simulations also implies good sampling of these angles (Supplementary Figure S2). The average radius of the gyration of NADH from the simulation of 5.2 ± 0.6 Å is consistent with the experimental value of 6 Å [9]. Further, the glycosidic bond angles of both bases sampled both anti and syn conformations, indicating they have not been trapped in local minima. An exception is χ N of 2-ox-NAD, but this can be rationalized by the strong steric clash of the C 2 N -carbonyl with the ribose inhibiting the formation of syn. Finally, rotations around θ were observed for all five dinucleotides, indicating that this degree of freedom was also sampled adequately.
The simulations used force fields built by the chemical similarity to groups of known parameterizations using the CHARMM General Force Field generator, an approach used widely in simulations of protein complexes with organic molecules. The force fields for ox-NADs draw heavily from those developed previously by MacKerell's group for NAD(H) [28]. Although higher level force field development for ox-NADs using quantum mechanical methods is possible, we consider the current approach to be adequate given our main goal of understanding the tendencies of dihedral angles. Indeed, the preferences obtained from the simulations are in line with expectations, such as the adenosine of ox-NADs preferring anti, and the pyridone ribose glycosidic bond reflecting the potential for a steric clash between the carbonyl at C 2 N , C 4 N , or C 6 N and the ribose. These results suggest that the simulations contain useful information.
Ox-NADs exhibit distinct preferences for the conformation of the pyridone ribose. 2-ox-NAD strongly prefers the anti conformation, whereas 6-ox-NAD prefers syn. These tendencies are driven by the avoidance of steric clashes between the added carbonyl and the ribose. Ox-NADs also have preferences for the orientation of the pyridone amide group, which are driven by hydrogen bonding and steric interactions with the carbonyl at C 2 N , C 4 N , or C 6 N . The conformational preferences of the pyridone ribose appear to influence the folding of the dinucleotides. On average, 2-ox-NAD and 4-ox-NAD exhibit enhanced folding compared to NAD(H), whereas 6-ox-NAD is more extended than the other dinucleotides.
We suggest these trends reflect the unique χ N preferences of the dinucleotides, as shown in the scatter plot of inter-base distance versus χ N (Figure 9). The plots show that for all five dinucleotides, the highly compact conformations (i.e., distance < 5 Å) occur most frequently when the nicotinamide/pyridone ribose is anti, i.e., χ N in the range of 135 • to −180 • . 2-ox-NAD and 4-ox-NAD prefer the anti conformation of pyridone ribose, leading to enhanced folding. Conversely, 6-ox-NAD shows substantial syn conformation, leading to less folding. Ox-NADs have the potential to bind to enzymes and thus act as inhibitors. The comparison of the conformational preferences of ox-NADs in solution to those of protein-bound NAD(H) provides insight into proteins potentially targeted by ox-NADs. For Ox-NADs have the potential to bind to enzymes and thus act as inhibitors. The comparison of the conformational preferences of ox-NADs in solution to those of proteinbound NAD(H) provides insight into proteins potentially targeted by ox-NADs. For example, because of its strong preference for χ N anti, 2-ox-NAD may not be accommodated in the active sites of enzymes that bind NAD(H) with the nicotinamide syn. Conversely, 6-ox-NAD may have poor complementarity with enzymes that bind NAD(H) with the nicotinamide anti. NAD(H) bound to proteins strongly prefers extended conformations, and we expect that ox-NADs will bind proteins in similarly extended conformations. For this reason, there may be an energetic cost associated with unfolding for ox-NADs, particularly 2-ox-NAD and 4-ox-NAD, which seem to prefer folded conformations over 6-ox-NAD. This information may be useful for prioritizing experiments on the inhibition of enzymes by ox-NADs.

Molecular Dynamics (MD) Simulations of NAD + , NADH, and ox-NADs
The starting coordinates for the molecular dynamics (MD) simulations of NAD + and NADH were obtained from structures of an aldehyde dehydrogenase enzyme (NAD + : PDB 5KF6, chain A; NADH: PDB 7MYC, chain A). In these structures, NAD(H) adopts the classical extended conformation observed for Rossmann fold domains. The molecular editor Avogadro v1.2.0 [29] was used to generate starting coordinates for the three ox-NAD simulations by adding a carbonyl functional group at C 2 N , C 4 N , or C 6 N of the nicotinamide ring, hence eliminating the +1 formal charge on N 1 N from the starting coordinates for NAD + (Figure 1). The pyrophosphate of the dinucleotide was assumed to have a charge of −2, appropriate for pH 7.0. File formatting and topology generation for each of the dinucleotides was performed as described by [30]. The CHARMM General Force Field (CGenFF version 4.6-July 2021) [31,32] was used for toppar stream file creation, and the conversion of each stream file from CHARMM to GROMACS format was performed with the Python v2.7 [33] CGenFF program, using NetworkX v1.11 [34]. The force fields for ox-NADs are based on those developed previously by MacKerell's group for NAD(H) [28].
The following procedure was used to generate MD trajectories for each of the five dinucleotides (NAD + , NADH, 2-ox-NAD, 4-ox-NAD, 6-ox-NAD). The GROMACS 2018.3 package was used for solvation of the system, equilibration, and production [35][36][37][38][39]. The dinucleotide was solvated with the TIP3P water model [40] in a rhombic dodecahedral box of 35-41 nm 3 and neutralized with Na + ions (one Na + for NAD + , two Na + for NADH and ox-NADs). The solvated system was energy-minimized using the steepest descent algorithm until the maximum force was less than 10.0 kJ mol −1 nm −1 . A second energy minimization was performed with the inclusion of van der Waals forces using a switching function with inner and outer cutoffs of 1.0 nm and 1.2 nm, respectively. The resultant energy-minimized structure was positionally restrained by its non-hydrogen atoms and the system was subjected to a 100 ps equilibration under NVT (constant particle number, volume, and temperature) conditions at 300 K with the v-rescale thermostat [41] and using a time constant of 0.1 ps. The system was then further equilibrated for 100 ps using NPT (constant particle number, pressure, and temperature) conditions and isotropic Berendsen pressure coupling [42] with the reference pressure equal to 1 bar, isothermal compressibility set to 4.5 × 10 −5 bar −1 , and time constant set to 2 ps. Ten independent 100 ns production simulations were performed after release of positional restraints on the starting NPT-equilibrated structure. The Particle Mesh Ewald method (real space cutoff of 1.2 nm) was used for the calculation of electrostatic forces [43,44], and isotropic Parrinello-Rahman pressure coupling [45][46][47] was implemented with the same reference pressure and isothermal compressibility as in NPT equilibration. Periodic boundary conditions were applied in all three directions. All MD simulations were performed using a 2 fs time steps. Coordinates were saved every 1 ps (every 500 steps) for analysis. The details of the simulations are listed in Table 2.

Analysis of Conformations
Analyses of the MD trajectories were performed using the MDAnalysis package v2.0.0 [48,49]. For each dinucleotide, the ten 100 ns simulations were concatenated into a single, time-contiguous 1 µs trajectory. The end-to-end distance of a dinucleotide was defined as the distance between the centroids of the nicotinamide and adenine rings (i.e., the inter-base centroid-centroid distance). Dihedral angles were defined as in [24] ( Table 2). The angle between the nicotinamide and adenine rings was calculated using normal vectors, as follows. Two vectors in the plane of the nicotinamide ring were defined as the vector from atom N 1 N to C 2 N (vector a) and from N 1 N to C 6 N (vector b). The vector normal to the nicotinamide ring was calculated as a × b. Two vectors in the plane of the adenine were defined as the vector from atom C 5 A to C 4 A (vector c) and C 5 A to C 6 A (vector d). The vector normal to the adenine was calculated as c × d. The normal-normal angle between the two bases was calculated as the inverse cosine of the dot product between the two normal vectors. Graphs were created with Origin 2021 v9.85.204. Tracking folded conformations for NADH/ox-NADs was performed by tallying the number of instances in which the distance between the following atoms was less than or equal to 3 . The individual trajectory frames selected for the visualization of folded conformations were from the most prevalent of the four bins described above. The individual trajectory frames selected for the visualization of semi-extended and extended conformations were from frames immediately preceding the folded frames obtained as described above, in which the inter-base centroid-centroid distance was ±0.5 Å from the respective molecule's peak maximum in the distribution of inter-base distance (~9.0 Å for semi-extended,~13 Å for extended).
Analysis of conformational clusters was performed as follows. For each dinucleotide, the RMSD was calculated across the concatenated 1 µs simulation using a reference conformation. Clusters of conformations were obtained by selecting frames of the trajectory where the RMSD to the reference was less than or equal to 1.0 Å. Ten frames that satisfied the RMSD criterion were selected for visualization, such that the frames were >5 ns in simulation time apart from each other, except for extended conformations of 4/6-ox-NAD, which had relatively few instances.

PDB Data Mining
The conformations of NAD + and NADH bound to proteins were studied by mining the Protein Data Bank (PDB). A dataset of NAD(H) conformations was assembled by downloading X-ray crystal structures (asymmetric unit) with a resolution of 2.9 Å or better and containing either NAD + (chemical ID NAD) or NADH (chemical ID NAI) noncovalently bound to the protein. PDB entries having only C-alpha models of the protein were omitted. The resulting dataset consisted of 1445 entries with NAD + and 248 entries with NADH, and included 3965 instances of NAD + and 671 of NADH. The conformations of the dinucleotides were analyzed using CNS version 1.3 [50].

Conclusions
We investigated the structure and dynamics of NAD + , NADH, and ox-NADs in solution using MD. All five dinucleotides exhibit a rapid equilibrium of folded, semiextended, and extended conformations. Folded conformations are characterized by interbase distances of less than 6 Å and the near-parallel stacking of the bases, whereas in typical extended conformations, the bases are separated by 13-14 Å. Among the ox-NADs, 2-ox-NAD and 4-ox-NAD exhibit a greater inclination for folding than 6-ox-NAD. This trend likely reflects the strong preference of 2-ox-NAD and 4-ox-NAD to adopt anti conformations of the pyridone ribose, whereas 6-ox-NAD shows an opposite preference for syn. The higher anti character of 2-ox-NAD and 4-ox-NAD leads to more facile base stacking and hence a higher probability of folding. The preference of 2-ox-NAD for the anti conformation of the pyridone ribose is especially strong and reflects the steric clash between the pyridone carbonyl and ribose that occurs in the syn conformation. The conformations of proteinbound NAD(H) were investigated by mining the PDB. Unlike NAD(H) in solution, the dinucleotide is almost exclusively in an extended conformation when bound to proteins. The nicotinamide ribose of protein-bound NAD(H) can be found in anti or syn glycosidic bond conformations, which reflects the unique interactions in the active site and specific stereochemical requirements of catalysis. The comparison of the conformational tendencies of ox-NADs in solution with those of protein-bound NAD(H) may aid in the identification of enzymes that have the potential to be inhibited by ox-NADs. Funding: The computation for this work was performed on the high-performance computing infrastructure provided by Research Computing Support Services and in part by the National Science Foundation under grant number CNS-1429294 at the University of Missouri, Columbia MO. D.P.B. was supported by the National Institutes of Health T32 Award 5T32GM008396.

Conflicts of Interest:
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Abbreviations
MD molecular dynamics ox-NAD pyridone adenine dinucleotide