Multiple Intramolecular Hydrogen Bonding in Large Biomolecules: DFT Calculations and Deuterium Isotope Effects on 13 C Chemical Shifts as a Tool in Structural Studies

: Large biomolecules often have multiple intramolecular hydrogen bonds. In the cases where these interact, it requires special tools to disentangle the patterns. Such a tool could be deuterium isotope effects on chemical shifts. The use of theoretical calculations is an indispensable tool in such studies. The present paper illustrates how DFT calculations of chemical shifts and deuterium isotope effects on chemical shifts in combination with measurements of these effects can establish the complex intramolecular hydrogen bond patterns of rifampicin as an example) The structures were calculated using DFT theoretical calculations, performed with the Gaussian 16 software. The geometries were optimized using the B3LYP functional and the Pople basis set 6-31G(d) and the solvent (DMSO) was taken into account in the PCM approach. Besides the 6-31G(d) basis set, the 6-31 G(d,p) and the 6-3111G(d,p) basis sets were also tested. The nuclear shieldings were calculated using the GIAO approach. Deuteriation was simulated by shortening the X-H bond lengths by 0.01 Å.


Introduction
Intramolecular hydrogen bonding is a very important structural parameter in many biomolecules, e.g., peptides, proteins, RNA, DNA and smaller molecules with specific biological effects such as rifampicin. [1]. Furthermore, the correct structure is a prerequisite for binding studies of molecules with biological activity [2] such as rifampicin. Rifampicin has important biological actions and is mentioned as a possible remedy against tuberculosis in combination with other drugs [3]. The introduction of deuterium in OH and NH groups is straightforward and is a minimal perturbation but still one that creates easily observable changes, e.g., in 13 C chemical shifts. Therefore, deuterium isotope effects on chemical shifts have turned out to be a useful tool in establishing the presence and the characteristics of intramolecular hydrogen bonds [4]. Examples include the use of deuterium isotope effects on 13 C chemical shifts as well as on 15 N chemical shifts in proteins [5,6]. Such isotope effects also have advantages in studies of DNA [7,8]. Intramolecular hydrogen bonding may also lead to tautomerism. This can also be studied with deuterium isotope effects on chemical shifts [9]. The situation can be complex in the cases in which several donors and acceptors forming hydrogen bonds with each other. Such a situation is found in rifampicin [2,10]. The use of theoretical calculations to calculate structures and NMR parameters have reached a very high level [11]. DFT calculations of structures, chemical shifts and isotope effects on chemical shifts combined with experimental values is particularly useful in the present study to disentangle the hydrogen bonding pattern of such a complex system as rifampicin and to determine if tautomerism is at play. Rifampicin has shown the very interesting feature that it may take up a zwitterionic form in polar solvents ( Figure 1) [8]. Density functional theory (DFT) calculations [12] are a very useful tool to analyze the complex situations both with regard to hydrogen bonding [13] and tautomerism [7]. Both nuclear shieldings and isotope effects on nuclear shieldings can be calculated [1]. Numerous examples of multiple hydrogen bonding involving biologically relevant structures can be found. Examples of calculations of structures and hydrogen bond energies including compounds with pyrroles were performed by the Afonin group [14][15][16]. each other. Such a situation is found in rifampicin [Error! Bookmark not defined., Reference source not found. ]. The use of theoretical calculations to calculate structures and NMR parameters have reached a very high level [Error! Reference source not found.]. DFT calculations of structures, chemical shifts and isotope effects on chemical shifts combined with experimental values is particularly useful in the present study to disentangle the hydrogen bonding pattern of such a complex system as rifampicin and to determine if tautomerism is at play. Rifampicin has shown the very interesting feature that it may take up a zwitterionic form in polar solvents ( Figure 1) [8]. Density functional theory (DFT) calculations [ Error! Reference source not found. ] are a very useful tool to analyze the complex situations both with regard to hydrogen bonding [ Error! Reference source not found. ] and tautomerism [7]. Both nuclear shieldings and isotope effects on nuclear shieldings can be calculated [1]. Numerous examples of multiple hydrogen bonding involving biologically relevant structures can be found. Examples of calculations of structures and hydrogen bond energies including compounds with pyrroles were performed by the Afonin group [14][15][16]. The measurement of deuterium isotope effects on chemical shifts can be performed in two different ways. If exchange of the label is slow, the measurement can be performed in a one-tube NMR experiment containing both isotopomers. However, if the exchange is fast, e.g., with presence of water, one can use a variation of the percentage of deuterium in the solvent, typically H2O/D2O or CH3OH/CH3OD, or use these as co-solvents in DMSO-d6. Having performed experiments using 0 to 100% D2O, the isotope effects can be obtained as the difference between these two situations. For systems showing changes upon the addition of water, the solvent effect of adding water must be determined. It is of course important to realize that the measured isotope effects are the sum of all possible unresolved isotope effects. The measurement of deuterium isotope effects on chemical shifts can be performed in two different ways. If exchange of the label is slow, the measurement can be performed in a one-tube NMR experiment containing both isotopomers. However, if the exchange is fast, e.g., with presence of water, one can use a variation of the percentage of deuterium in the solvent, typically H 2 O/D 2 O or CH 3 OH/CH 3 OD, or use these as co-solvents in DMSO-d 6 .
Having performed experiments using 0 to 100% D 2 O, the isotope effects can be obtained as the difference between these two situations. For systems showing changes upon the addition of water, the solvent effect of adding water must be determined. It is of course important to realize that the measured isotope effects are the sum of all possible unresolved isotope effects.
In the case of a tautomeric equilibrium, deuteriation will lead to a change in the chemical equilibrium. This, in turn, will lead to a change in the chemical shifts. This type of isotope effect mainly depends on the chemical shift differences of the same nucleus in the two equilibrating species and is hence a very good monitor of the existence of a tautomeric equilibrium.
The use of a combination of DFT calculations, and measurements of chemical shifts and isotope effects on 13 C chemical shifts is a general method that can be used in other biological systems, e.g., more complex derivatives of rifampicin such as the aldehyde [2].

Calculations
The structures are calculated using DFT theoretical calculations [9] performed with the Gaussian 16 software [17]. The geometries were optimized using the B3LYP functional [18,19] and the Pople basis set 6-31G(d) [20], and the solvent (DMSO) was taken into account in the PCM [21,22] approach. X, Y, Z coordinates of structure A (see Section 3.4) are given in the Supplementary Materials. Besides the 6-31G(d) basis set, the 6-31 G(d,p) and the 6-3111G(d,p) basis sets were also tested. The nuclear shieldings were calculated using the GIAO approach [23,24]. Deuteriation was simulated by shortening the X-H bond lengths by 0.01 Å [3].

NMR
One-dimensional 1 H and 13 C NMR spectra were recorded using a 300 MHz spectrometer (Bruker, Fallaenden, Germany) recorded at 300.08 MHz and 75.46 MHz, respectively in DMSO-d 6 using TMS as a reference. Examples of the 1 H and 13 C NMR spectra are shown in Sections 3.1 and 3.2.

Deuteriation
Deuteriation was achieved in a series of experiments by adding 2, 4 or 9 µL, and in some cases 20 or 30 µL, D 2 O to the DMSO-d 6 solutions. The latter additions were used just to confirm that the effects at such high additions were linear. The solvent effects were estimated by the addition of 10 µL H 2 O (see Section 3.4).

1 H NMR Spectrum
Both the OH-1 (15.6 ppm) and the NH+ (9.5 ppm) resonances were broad, indicating that they were in exchange. Those of OH-4 (12.5 ppm) and the NH amide (8.4 ppm) protons were sharp suggesting that these were not in exchange. An example of a 1 H NMR spectrum of a partially deuteriated species is shown in Figure 2. The degree of deuteriation was determined from the integrals of the exchangeable protons.

13 C NMR Spectrum
The 13 C NMR spectrum of rifampicin in CDCl3 is given in [9]. The assignments use in this paper are very similar except for C-2, C-9 and C-10. A number of the resonanc showed splittings due to deuteriation (see Table 1). The signs of the deuterium isotop

13 C NMR Spectrum
The 13 C NMR spectrum of rifampicin in CDCl 3 is given in [9]. The assignments used in this paper are very similar except for C-2, C-9 and C-10. A number of the resonances showed splittings due to deuteriation (see Table 1). The signs of the deuterium isotope effects on 13 C chemical shifts can be determined by knowing the degree of deuteriation. Other resonances showed a shift as a function of addition of D 2 O (Table 1) (see Figure 3).

13 C NMR Spectrum
The 13 C NMR spectrum of rifampicin in CDCl3 is given in [9]. The assignments used in this paper are very similar except for C-2, C-9 and C-10. A number of the resonances showed splittings due to deuteriation (see Table 1). The signs of the deuterium isotope effects on 13 C chemical shifts can be determined by knowing the degree of deuteriation. Other resonances showed a shift as a function of addition of D2O (Table 1) (see Figure 3).     [10]. e Slightly larger than 0.04 ppm.

Assignment of Isotope Effects on 13 C Chemical Shifts
In a system with several protons, which can be deuteriated, in this case OH-1, OH-4, NH+, OH-21, OH-23 and the NH amide proton, it is important to be able to determine which deuterium is causing which effect. In the 1 H spectrum, OH-1 and NH+ were broad, showing that they were easily exchanged and did not giving rise to observable deuterium isotope effects as doublets. This leaves the observable doublets as being due to OH-4, NHC=O, OH-21 and OH-23. The carbons of the latter two were in the aliphatic region and can be assigned. OH-21 and OH-23 were in a different part of the molecule and will not give rise to isotope effects on carbons of the aromatic rings. In an aliphatic system, the isotope effects are only transmitted over few bonds are thus very local. The effects due to NHC=O were local and restricted to C-2, C=O(NH) and C=C-16.

Isotope Effects
In a system like the present one, deuterium isotope effects on 13 C chemical shifts can be of different kinds. If the deuterium is slowly exchanged or not exchanged at all, intrinsic isotope effects are observed as splittings of the 13 C resonances. However, if the deuterium label is exchanged quickly, one observes only a change in the chemical shifts (see Table 2). Both these effects are intrinsic. Intrinsic isotope effects in aliphatic systems are only transmitted over a few bonds, whereas they can be transmitted over many bonds in conjugated systems like aromatic systems. [3] Intrinsic isotope effects are defined as: where n is the number of bonds between the label and the carbon in question. However, if the system is tautomeric between two species, A and B, equilibrium isotope effects are observed. These are defined as: In this case, X is 13 C and x is the mole fraction of B. ∆x is the change in the equilibrium upon deuteration. The interesting part is that the equilibrium isotope effect depends on the chemical shift difference between the two sites (δX B − δX A ). The isotope effects on 13 C chemical shifts that are observed as doublets or doublets of doublets can be ascribed to deuteriation either at H-4, the NH or at OH-21 or OH-23 (see assignments, Section 3.3). As described earlier, the effects of deuteriation at the NH are restricted to C-2, C=O(NH) and C=C-16. The remaining observed isotope effects seen in Table 1 were due to deuteriation of OH-4. A plot of the experimental values vs. the calculated ones (see Section 3.5.2) showed a very good agreement (the structure is A of Figure 4). In contrast, a plot based on values of the structure C gave a correlation coefficient (R 2 ) as low as 0.38. In that case, see also the discussion on tautomerism.
doublets can be ascribed to deuteriation either at H-4, the NH or at OH-21 or OH-23 (see assignments, Section 3.3). As described earlier, the effects of deuteriation at the NH are restricted to C-2, C=O(NH) and C=C-16. The remaining observed isotope effects seen in Table 1 were due to deuteriation of OH-4. A plot of the experimental values vs. the calculated ones (see Section 3.5.2) showed a very good agreement (the structure is A of Figure  4). In contrast, a plot based on values of the structure C gave a correlation coefficient (R 2 ) as low as 0.38. In that case, see also the discussion on tautomerism. Deuteriation at OH-1 did not lead to observable doublets. However, as described in Section 2.2, the isotope effects can be observed by measuring the shift as a function of D2O addition. An example is shown for C-1 in Figure 5. From this plot, it can be seen that the addition of water in itself gave rise to a shift to a higher frequency. This has to be taken Deuteriation at OH-1 did not lead to observable doublets. However, as described in Section 2.2, the isotope effects can be observed by measuring the shift as a function of D 2 O addition. An example is shown for C-1 in Figure 5. From this plot, it can be seen that the addition of water in itself gave rise to a shift to a higher frequency. This has to be taken into account when estimating the isotope effect. The data are given in Table 2. Clearly, the largest observed isotope effects due to deuteriation occurred at OH-1. The other effects are given in Table 1. The smaller effects were somewhat more uncertain but the signs could, in all the mentioned cases, be determined. The observation of isotope effects for C-40, 41 and 43 was a clear confirmation that the structure was a zwitterion.   In Table 2 it is important to notice that the C-2 doublet of doublets were observed due to isotope effects due to deuteriation both at OH-4 and NH.

Calculations
The structures were calculated using a truncated version of the molecule leaving out most of the long bridge. In one end, the double bond was kept and in the other end, the chain was replaced by a OCH 3 group (see Figure 4). Several structures were tested to obtain the optimal truncation. The test involved the fitting of calculated nuclear shieldings vs. observed 13 C chemical shifts (see Section 3.5.1). To determine the best basis set, 6-31G(d,p) and 6-311(G,p) were also tested. For structure 4A, the R 2 values were 0.9963 and 0.9935, respectively. If need be, the piperazine ring can be replaced by a NH 2 ( Figure 4E) producing an R 2 of 0.9962. The structures were calculated with and without water molecules close to the O − atom. The solvent was also taken into account (see Section 2).

13 C Nuclear Shieldings
The calculated 13 C nuclear shieldings for structures C and D of Figure 4 are given in Table 3. The very large differences were related to C-4 and C-38.
A plot of the calculated 13 C nuclear shieldings vs. experimental 13 C chemical for structure A of Figure 4 is given in Figure 6 (R 2 = 0.9949). The carbons included are the core carbons C1-C10 and C-11. As carbons one and two bonds away heavily influence the chemical shifts, only the core carbons were involved as we were using the truncated version of the molecule. For the structure with a water molecule added to the O − , R 2 = 0.9819. In other words, water did not seem to be bonded in the C1-C8 region. For structure C, R 2 = 0.9675, and for structure D, R 2 = 0.7884.

Isotope Effects on Chemical Shifts
The calculation of deuterium isotope effects on nuclear shieldi Jameson theory [Error! Reference source not found.,Error! R not found.]. In the present case, the OH bond lengths were reduced the deuteriation [1]. This will lead to "standard" isotope effects that m by plotting those vs. the observed isotope effects. As seen in Table 1

Isotope Effects on Chemical Shifts
The calculation of deuterium isotope effects on nuclear shieldings is based on the Jameson theory [25,26]. In the present case, the OH bond lengths were reduced by 0.01 Å to mimic the deuteriation [1]. This will lead to "standard" isotope effects that may need to be scaled by plotting those vs. the observed isotope effects. As seen in Table 1 and Figure 7, no scaling was needed for deuteriation of OH-4. A plot of the corresponding situation with water attached to O − gave a slightly lower R 2 of 0.9723.
The calculation of deuterium isotope effects on nuclear shieldings is based on the Jameson theory [Error! Reference source not found.,Error! Reference source not found.]. In the present case, the OH bond lengths were reduced by 0.01 Å to mimic the deuteriation [1]. This will lead to "standard" isotope effects that may need to be scaled by plotting those vs. the observed isotope effects. As seen in Table 1 and Figure 7, no scaling was needed for deuteriation of OH-4. A plot of the corresponding situation with water attached to O − gave a slightly lower R 2 of 0.9723.

Discussion
A breakthrough in understanding the structure of rifampicin (Figure 1) was the finding that the structure is a zwitterion in polar solvents with water added [8]. Taking this into account, a number of intramolecularly hydrogen bonded structures can be formulated as seen in Figure 4 (the structures are truncated versions of rifampicin).
These structures clearly demonstrate that changes in the intramolecular hydrogen bonding in one region will influence the hydrogen bonding pattern in another region. More structures with fewer hydrogen bonds can be drawn, but these are clearly less realistic.
Rifampicin is a large molecule. Here, the calculations were based on a truncated version including all essential features as seen in

Discussion
A breakthrough in understanding the structure of rifampicin (Figure 1) was the finding that the structure is a zwitterion in polar solvents with water added [8]. Taking this into account, a number of intramolecularly hydrogen bonded structures can be formulated as seen in Figure 4 (the structures are truncated versions of rifampicin).
These structures clearly demonstrate that changes in the intramolecular hydrogen bonding in one region will influence the hydrogen bonding pattern in another region. More structures with fewer hydrogen bonds can be drawn, but these are clearly less realistic.
Rifampicin is a large molecule. Here, the calculations were based on a truncated version including all essential features as seen in Figure 4. As water plays an important role in the formation of the zwitterionic form [7,8,27], water was added to the structure hydrogen bonding to C-O − . This turned out to have very little effect on the calculated deuterium isotope effects of C-1 or C-4 or the 13 C nuclear shieldings (see Section 3.5.1). However, as water is important for the formation of the zwitterionic structure, the effect of water is to solvate the N + ammonium ion. This is very important as the counter ion is far away.
From the very high chemical shift of OH-1 (15.6 ppm), it can be concluded that OH-1 was hydrogen bonded to O − . It was also seen that the OH-1 resonance was broad due to exchange.
With respect to OH-4, this can hydrogen bond to C=O in a seven-membered ring arrangement ( Figure 4A or Figure 4E) or to the C=N in a six-membered arrangement ( Figure 4C). However, in the latter case, it was very similar to o-hydroxy Schiff bases and can in principle be tautomeric [27] (see Figure 4D). However, in this case, one would expect distinctive equilibrium isotope effects at C-3, C-4, C-10 and C-38 proportional to the chemical shift differences between the carbons in the two equilibrating structures (see Equations (3) and (4)) [28]. The differences in calculated nuclear shielding are given in Table 3. Large isotope effects at C-3, C-4, C-10 and C-38 were clearly not seen in Table 1. Based on the finding that structure C was not fitting, that no equilibrium was established and the fact that the deuterium isotope effects on the 13 C chemical shifts of Figure 4A fits nicely (See Figure 5) makes 4A the likely structure. As OH-4 is hydrogen bonded to C-11=O, then the NH logically forms an intramolecular hydrogen bond to the nitrogen of the C=N bond. The observed 2 ∆C-2(ND) isotope effect of 0.133 ppm clearly showed that the NH was hydrogen bonded. Values of 2 ∆C-2(ND) for non-hydrogen bonded cases are typically 0.08-0.1 ppm [29,30]. Based on these arguments, a full structure similar to structures A or E of Figure 4 is the preferred one. Furthermore, this was confirmed by a comparison of experimental 13 C chemical shifts vs. calculated 13 C nuclear shieldings, as seen from the R 2 of 0.9949, as discussed in Section 3.5.1. The isotope effects at C-40, 41 and 43 (Table 1) confirmed that rifampicin was in a zwitterionic form. These finding are similar to the full structure found in the crystal [9].

Conclusions
The search for a suitable basis set to use with the B3LYP functional resulted in G(d) giving good NMR nuclear shieldings and being suitable for the study of large biological systems. The DFT calculations were performed using the mentioned functional and basis set. The calculated nuclear shielding and deuterium isotope effects on 13 C nuclear shieldings combined with experimental 1 H and 13 C chemical shifts and deuterium isotope effects on the latter enabled an analysis of the complex hydrogen bonding pattern of the zwitterionic form of rifampicin. The result was an extended hydrogen bonding network determined to a large extent on the hydrogen bond between O − and OH-1. The deuterium isotope effects on nuclear shieldings also confirmed the zwitterionic nature of rifampicin in polar solvents.