#
Conformational Investigations in Flexible Molecules Using Orientational NMR Constraints in Combination with ^{3}J-Couplings and NOE Distances

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

**1**with a single rotatable bond as well as a 24-ring macrolide related to the natural product mandelalide A

**2**.

## 1. Introduction

_{i}> are joined in a set of linear equations (e.g., SVD [13]) to determine an order matrix

**A [14]**which describes the alignment of a molecular fixed frame relative to the static magnetic field and which enables the back-prediction of all RDCs from this structure model [8,15,16,17]. Despite the structural assumptions and the often “under-determination” of

**A**, this method can deliver clear-cut validation of stereochemistry even with imperfect correlation.

_{i}and an order matrix

**A**fixed within the molecular frame becomes much more ill-defined. Though some level of success can be achieved using a small set of minimized geometries combined with an overall average alignment tensor or with discrete number of order tensors [10,18], these methods cannot be generalized to all flexible molecules, encompassing all dynamic amplitudes, timescales and complexity. Besides the steep increase in complication in fitting data in this way, one additional challenge here is to properly access the full conformational space.

_{2}(cos ϑ) > relating the RDC internuclear vector to the laboratory frame is used to restrain a replica-averaged MD simulation [28]. The appeal of this approach is that the approximations and assumptions associated with the determination of an alignment tensor is avoided. Instead, the orientational bias is calculated along with the conformational fluctuations within the restrained MD simulation. Still, the implicit overall scaling of the dipolar coupling clearly marks a delineation between the whole-molecule reorientation and the internal fluctuations. Using a bias-exchange metadynamics approach, the authors illustrated the method on the small molecule, strychnine, to determine its major conformational states and populations based on RDCs [29].

_{2}(cos ϑ) derived from that component [28] with respect to the z-direction of the external magnetic field (directly or via the director of the sample alignment). In reality, the full dynamics of the molecular motion requires that the time and ensemble mean value of the tensor’s off-diagonal elements vanish. Consequently, using all elements of the dipolar coupling second-order tensor (rather than only their scalar values) as a MD-restraint should autonomously drive the full internuclear orientational dynamics.

**1**were undertaken to generate rotamer distributions. The much more complex second example uses a pair of stereoisomers of mandelalide A, a 24-ring macrolactone including nine main-chain chiral centers [35] for which a rich set of NMR data was available. These examples validate the MDOC approach towards generating realistic thermodynamic structural ensemble and show encouraging potential towards guiding the correct configuration assignment.

## 2. Results and Discussion

#### 2.1. Single-Bond Dynamics in Diketone **1**

#### 2.1.1. NMR Datasets

**1**was synthesized as a coupling product between 2-methylnaphth-1-yl hydrazine and 1-indanone in an asymmetric Brønsted acid catalyzed dearomatizing redox cross coupling reaction [34] (Figure 1). Characteristic for this molecule are the two chiral and relatively rigid subgroups (a naphthalenone group and an indenone group) connected by a single rotatable bond. The modest stereoselectivity (dr < 2.5) during the trials of this reaction resulted in both diastereomers of the 1,4-diketone

**1**being available for this study. The labels

**1-SR**and

**1-SS**are applied henceforth to represent the two diastereomers, differing only in the chirality at carbon C12, for simplicity. The diastereomers were separated by chromatography and provided two samples for dynamic investigation by NMR.

**1**were first geometry-optimized and their relative energies calculated using DFT (see Supporting Information). Table S1 shows that the trans and the gauche (-) geometries are the most stable among the conformers of

**1-SS**and

**1-SR**, respectively, which both correspond to the configuration where the small indenone H12 is simultaneously gauche to the bulkier methyl (C11) and carbonyl (C1) groups. Nevertheless, the other rotamers should also be accessible, especially for

**1-SR**with all three relative energies within 1 kcal/mol. For

**1-SS**, the theoretical differences are somewhat larger (E

_{tr}− E

_{g+}= 3.6 kcal/mol) due to the combination of the repulsive effect of the ketones and overall steric effect of the other 2 rotamers. It is expected however that these differences could be mitigated by the polar solvent. These optimized structures provide already theoretical evidence for significant rotameric exchange and will serve also as starting structures for the dynamical evaluations.

**(1-SS)**and 1B for (

**1-SR**)) comprising carefully evaluated NOESY cross-peaks integrals and converted to interproton distances and a set of

^{3}J-coupling constants related to torsion angle distribution (for datasets, see Supplementary Information). Both the measured NOE contacts as well as the homo- and heteronuclear

^{3}J couplings in the initial NMR analysis indicate some level of rotameric exchange, fast on the NMR timescale. For instance, there are no distinctly large

^{3}J

_{CH}couplings (>9 ppm) from H12 to C1, C9 or C11 across the rotatable C10-C12 bond that would clearly hint to a static trans relation. Furthermore, the semi-quantitative evaluation of the interannular NOEs from H13 or H12 to H11 or H9 show that all pairs correlate with NOEs of similar magnitudes which also imply some form of dynamic averaging.

_{3}) and the anisotropic (PMMA/CDCl

_{3}) sample for each diastereomer. An RDC-fitting procedure using MSPIN (SVD) against the corresponding three DFT rotamers identified the 1A and 1B dataset to fit best to

**1-SS-tr**(Q = 0.19) and

**1-SR-g(-)**(Q = 0.21) conformation, respectively (see Supporting Information). These rotamers match with those with the lowest calculated DFT energies. However, the quality of the best fits were less than optimal as indicated by the quality criterion (n/χ

^{2}) and outlier criterion (1/χ

^{2}

_{min}) far below unity (1A: n/χ

^{2}= 0.07, 1/χ

^{2}

_{min}= 0.013 and 1B: n/χ

^{2}= 0.05, 1/χ

^{2}

_{min}= 0.006), as well as only $\mathcal{F}$ = 6/22 (27%) and 5/24 (21%) of the computed RDCs being valid, i.e., having values within the estimated error margins. These observations indicate that overall, a majority of RDCs cannot be accurately rationalized by a lone rotamer.

^{2}= 0.11, 1/χ

^{2}

_{min}= 0.01 and $\mathcal{F}$ = 41% (9/22) and 1B: n/χ

^{2}= 0.08, 1/χ

^{2}

_{min}= 0.015 and $\mathcal{F}$ = 54%(13/24)). It should be mentioned that these only modest improvements may be in part due to the assumption of an existing average alignment tensor; indeed, since the overall shape of the molecule changes substantially from one rotamer to the other, a strong dependence of the alignment to the rotameric state is to be expected. Unfortunately, the sparseness of the RDC dataset did not allow the use of multiple alignment tensors since this procedure would have required at a minimum 17 independent RDC values (3 × 5 for the Saupe (alignment) matrix + 2 for the three populations). A further extension of the dataset (e.g., with less accessible long-range HC RDC couplings) would not have improved the required low condition number since a large portion of the RDC vector orientations are confined within or close to the aromatic planes and are therefore not completely independent. The inclusion of the NOE interproton information and the

^{3}J-coupling (CH) in the stereofitter module of MSPIN did not give significantly better results (data not shown).

**1**demonstrates, as for many molecules previously studied in past, that the linear fitting approaches like SVD constitute a powerful tool to roughly discriminate structures especially between a finite number of possible conformers; however, as a molecule exhibits increasingly more disorder, the method becomes progressively more deficient towards accurately explaining dynamic exchange. The aim of the MDOC approach introduced in the next section therefore presents a novel tool to obtain an ensemble of structures based on NMR observables that describe the conformational space for each diastereomer.

#### 2.1.2. MDOC Simulation

**1-SR**and the

**1-SS**with their corresponding NMR constraints from datasets 1A and 1B (for the details of the simulations see Tables S10 and S11 in Supplementary Information). Datasets 1A and 1B included 1-bond CH RDCs (1A:14, 1B:14) and long-range HH RDCs (1A:8, 1B:10)), NOEs (1A: 7, 1B:5), 3J-couplings (1A: 5, 1B:5), each translated into a pseudo-force term for the MDOC simulations. The outcome was independent of the initial conformation, since the pseudo-forces calculated from the RDC have the ability to rapidly generate all possible rotamers as well as reorient the molecule as a whole, on a timescale related to the memory time τ of the mean value calculation (in this case 200 ps, Equation (3)).

^{13}C-

^{1}H dipolar splittings are displayed. The left panel shows the fluctuation of the dipolar coupling of the aromatic C-H group at position C6 calculated using the exponential function with a memory time τ of 200 ps, according to Equation (3). After a short simulation time of about 1 ns—approximately 5 times the exponential rise constant of the pseudo-forces—the time mean value of the dipolar coupling fluctuates mostly within a range of about ±1 Hz. The experimental error of 1.2 Hz is indicated in Figure 2 with green lines. The pseudo-force width constant ΔD (Equation (5)) was set to 0.5 Hz which is close to the error ranges of most experimental values. Figure 2 also shows the convergence of the running mean value (red) of the trajectory towards a value close to the experimental RDC and reaching a constant value after about 10 ns, indicating that this MDOC simulation period was sufficient to average the dipolar coupling through combined whole-molecule reorientation and internal dynamics.

_{3}group which involves one additional mode of motion—the axial reorientation of the CH

_{3}group. Though the local order parameters for freely rotating methyl groups are typically much smaller than in the case of the aromatic CH groups, the conditions for a successful convergence are also fulfilled within these time limits.

**1-SS**and

**1-SR**are in good accord with the entire corresponding measured datasets, which include four categories of NMR parameter types (one-bond and long-range RDCs,

^{3}J-couplings and NOEs). In stark contrast to the outcome of the linear analysis based only on RDC values fit to static rotameric DFT models, the aforementioned quality criterion (n/χ

^{2}) exceeds unity for all but one parameter type, the only exception being the “long-range” (

^{n}D, n > 1) RDCs for the

**1-SS**configuration with n/χ

^{2}= 0.76 (Figure 3). This exception is specifically affected by the calculated H6-H8 coupling, with a deviation of 1.4 Hz from the measured RDC, whose error was estimated to be ± 0.9 Hz. In the case of the MDOC simulation of the

**1-SS**and

**1-SR**configurations with dataset 1A and 1B, there are 6 ($\mathcal{F}$ = 34/40 (85%)) and 4 ($\mathcal{F}$ = 37/41 (90%)) outliers observed, with ${\chi}_{min}^{-2}$ values of 0.29 and 0.13 respectively (see supplementary information). Though these numbers represent a large improvement over the corresponding values in the static SVD study (black in Figure 3: 1A: #outliers = 13/22 and ${\chi}_{min}^{-2}$ = 0.015; 1B: #outliers = 11/22 and ${\chi}_{min}^{-2}$ = 0.010), it will be important to determine the factors contributing most to the remaining incongruity.

**1**corresponding to trans, gauche(-) and gauche(+) subensembles. In the

**1-SS**form the trans-conformation is clearly favored whereas in the

**1-SR**form the gauche(-) conformation is the dominant conformation. This is in general accordance with the relative DFT energies from the geometry optimized DFT models and with the results of the SVD analysis (see Supporting Information). More specifically, however, a statistical analysis showed that the relative population of the individual rotameric states ratios (trans:gauche(-):gauche(+)) are more balanced for the minor components (

**1-SS**: {0.617: 0.281: 0.101} and

**1-SR**{0.165: 0.730: 0.105}

**1-SR**in gauche(-) conformation obtained from a DFT geometry optimization, a static torsion angle of ${\tau}_{1}$ = −6.4° and ${\tau}_{2}$ = 13.5° are observed, which are not dominant in the MDOC simulation. This raises the question whether this ring-twist dynamic behavior represented by this ensemble distribution is real or rather an artifact of the MDOC method. For the ${\tau}_{2}$ dihedral angle, this question could be investigated, by considering the

^{3}J

_{HH}couplings of H13a and H13b to H11. Using the Altona equation [4], the

**1-SR-g(-)**DFT model gives a value of

^{3}J

_{H13b-H12}= 8.5 Hz. The MDOC simulation which was run at a mean temperature of 313 K gave rise to a mean value of 5.8 Hz within the estimated error range (±0.75 Hz) of the experimental value of 5.1 Hz, so that one can suppose that this isomeric exchange occurs also in reality.

#### 2.2. Mandelalide A

#### 2.2.1. NMR Datasets

**2p**in Figure 6). The tedious syntheses ultimately led to the correction of the configuration, reallocating the entire northern part to the inverted configuration (

**2r**in Figure 6).

**2p**and its 11-epi

**-2p**were synthesized in larger scale in a local laboratory and characterized using NMR, this excellent material was made available to test the MDOC methodology on a challenging, larger-sized and flexible molecule.

^{3}J couplings. In the case of structure

**2p (**11-epi-

**2p),**a full unambiguous

^{1}H and

^{13}C assignment was obtained (including the prochiral

^{1}H assignment 7 CH

_{2}), and complemented with 45 (48) CH RDC values, 38 (38)

^{3}J

_{HH}couplings and 129 (106) NOE distances (see Supplementary Information). Any attempt to obtain alignment tensor evaluation using the SVD approach on calculated structural models failed (data not shown). The NMR-based structural information, however, was used as constraints in a 41-ns MDOC simulations (see Supplementary Information).

^{2}quality criteria (Figure 7), values back-calculated from the MDOC trajectory are on average well within the experimental error bounds (n/χ

^{2}> 1). As for the MDOC simulation of the 1,4-diketone

**1**, inspection of the individual data reveals however the occasional parameter were not completely fulfilled (see labels representing the fidelity $\mathcal{F}$ in Figure 7). The outliers represent generally less than 10% of the overall NMR constraints. Furthermore, based on the magnitude of the outlier criterion, ${\chi}_{min}^{-2}$, the worst of these outliers deviate by less than one error margin. Whereas the error margins for the RDC values were determined individually, those for the NOE distances were estimated to 0.5Å. In the case of

^{3}J couplings, the errors were assessed to be about 1.0 Hz taking into account also the possible uncertainties of the equation of Haasnoot et al. [4]. The RMS deviation of the NOE distances was lower than 0.3 Å and that of the

^{3}J couplings below 0.6 Hz.

^{3}J couplings and NOE distances) as averaged according to the memory function as given in Equation (3). In other words, the snapshots contain average information from every time step of the trajectory. Considering the n/χ

^{2}criteria (Equation (7)) or the calculated data (see Supplementary Information), it can be stated that the MDOC results are mostly within the estimated error bounds and no severe outliers are observed. Since the NMR data are both time- and ensemble-averaged values, it can also be stated that the MDOC simulation for a single molecule behaves to a good approximation in an ergodic manner. In this sense, the 2000 coordinate and data snapshots represent the final result of the simulations. Since this larger flexible molecules may undergo many conformational changes, the population of these states may be of high interest and therefore advanced methods need to be employed to analyze these populations.

#### 2.2.2. Torsion Angle Distributions

**2p**with torsion angles commonly populated within the 1000 MDOC coordinate snapshots (the Supplementary Information contains a collection of 10 typical conformers). This conformer also exhibits the lowest total force field energy among all snapshots. Also displayed Figure 8 are the torsion distributions of some σ-bonds that display highest variability throughout the trajectory. As can be seen, many bonds sample a wide range of dihedral angles even within a closed 24-membered macrolide ring, indicating large amplitude motions and complex conformation exchange. Noteworthily, the oxane 6-ring (-C5-C6-C7-C8-C9-O-) did not change from its chair conformation throughout the simulation although the oxolane 5-ring displayed two twist states as demonstrated by σ

_{19}with a slight preference of g(-) conformation (Figure 9, top-right inset).

_{3}group (Figure 8). The dominant rhamnose ring conformation was characterized by the O-CH

_{3}in axial position of the ring and the two OH groups and the CH

_{3}group in equatorial positions. This conformation is strongly supported by the

^{3}J couplings of the protons of the rhamnose ring and rendered by the MDOC simulation, although nearly 10% rhamnose ring inversions were also generated.

**2p**selected from a set of 1000 snapshots of an 40-ns MDOC simulation is presented, along with the distribution of key dihedral angles. It is instructive to compare the significantly different rotameric distribution of torsion angles with the values given for configuration

**2p**in Figure 8. Not surprisingly, the dynamics present in the smaller rings are almost identical in both diastereomers (e.g., ${\sigma}_{19}$). In the larger macrolide ring, however, not only are the torsion angle distributions in the direct vicinity of the epimerization site affected (${\sigma}_{11}$ and ${\sigma}_{12}$) but also those at moderately and very distant sites (e.g., ${\sigma}_{0}$, ${\sigma}_{4}$, ${\sigma}_{5}$ and ${\sigma}_{17})$. This is indicative of long-range trans-annular steric interactions of the methyl group at position C11. However, a clearer conformational picture can only emerge from the examination of the entire structural ensemble generated by the MDOC simulation.

#### 2.2.3. Principal Component Analysis

**1**, it would be desirable to rationalize the dynamics of the mandelalide A isomers

**2**in terms of population of major conformers with representative torsion angle combinations. Instead of only three rotameric states as in

**1**, there are nine “rotatable” σ-bond (Figure 6) each with roughly three main rotamers, leading to nearly 20,000 possible combinations of angles. Though the MDOC simulations indicate that very broad distribution of angles is sampled by all of these nine key bonds, all combinations of angles are, of course, not accessible in reality. The challenge here lies in the complexity of the conformational space, and in finding the right tools to describe its essence.

**2p**isomer of mandelalide A, all 24 of the macrolide dihedral angles within the large ring were selected as the basis for the dPCA. Results are shown in Figure 10, where the relative contribution of each of the 24 dihedral angles to the angular variance is displayed for the first two principal components. Further components (n

_{pc}> 2) were already less significant. Out of the 24 bonds, five contribute very significantly to the overall conformational fluctuations within the MDOC ensemble, namely ${\sigma}_{0}$, ${\sigma}_{1}$, ${\sigma}_{4}$, ${\sigma}_{11}$ and ${\sigma}_{12}$, which according to Figure 8 are involved in fluctuations of large amplitude.The product of each eigenvector n with the dihedral angle matrix deliver a single angular value θ

_{n}for a given MD snapshot. In Figure 11, the (θ

_{1}, θ

_{2}) distribution for the first two principal components obtained for the dPCA of mandelalide A

**2p**is presented from all 8000 data points each corresponding to an MDOC snapshot taken every 5 ps. The resulting distribution identifies three sub-regions at approximately (θ

_{1}, θ

_{2}) = (+100, +130) [45%], (+100, −150) [40%] and (170, −150) [~5%]. In principle, these describe the subsets of large amplitude fluctuations contributing the most to the overall dynamics within the large ring system. Though the θ

_{1}and θ

_{2}angles bear no direct geometrical representation in the macrolide, they correspond to a linear combination of the angles highlighted in Figure 10. The major conformational exchanges between the three sub-regions thus involve correlated variations of these angles. Structural representation of typical conformers for the two principal subregions are also shown in Figure 11.

^{2}criterion. Further investigations will however be required to establish the relationship between the abundance of short- and long-range constraints and the representation of low-energy conformations. There are several experimental and theoretical investigations that discuss precisely measured NMR parameters, especially NOE distances, as sensitive indicators on sparsely populated conformers to elucidate conformer equilibria [39,40].

**-2p**(Supplementary Information). The corresponding dominantly contributing torsion angles are different to those of

**2p**: whereas ${\sigma}_{1}$, ${\sigma}_{4}$, ${\sigma}_{11}$ and ${\sigma}_{12}$ have similarly important co-variation, ${\sigma}_{0}$ and ${\sigma}_{17}$ are relatively more involved. Since the eigenvectors have different angular linear contributions, the dihedral landscapes for (θ

_{1}, θ

_{2}) cannot be directly compared; still, one can notice that the 11-epi

**-2p**conformational equilibrium is constituted of two major sub-regions ((θ

_{1}, θ

_{2}) = (120°,160°) and (175°,120°)) with well-defined distributions. The results here show that transannular steric influence reaching the opposite part of the 24-membered ring seems to favor an overall more open ring conformation for 11-epi

**-2p**.

**2p**and its isomer 11-epi

**-2p**, whose configurations only differ in the chirality of a single methyl group, and these differences would be expected to be manifest mainly in the NMR data of nuclei in the direct vicinity of the C11-CH

_{3}group, but based on Figure 8 and Figure 9 as well as in the PCA results, this is not the case - the disparities hint to divergent conformer distributions. Though it is perhaps unexpected that a single methyl group epimerization leads to considerable change in the conformer distribution of the entire ring system, the significantly different NMR spectra and datasets corroborates with this finding. By contrast, the oxolane 5-ring, the oxane 6-ring and the rhamnose ring displayed no significant difference comparing

**2p**and 11-epi-

**2p.**

#### 2.3. Configuration Determination with MDOC

#### 2.3.1. Discriminating 1,4-Diketone 1-SS vs. 1-SR

^{2}, 1/χ

^{2}

_{min}and $\mathcal{F}$) with the corresponding

**1-SS**configuration and, conversely, those with dataset 1B scored better (or equally well (1/χ

^{2}

_{min})) with the

**1-SR**form. More importantly, the wrong configuration does not pass the quality criterion in both cases. The individual parameter types taken individually (1-bond RDCs, long-range RDCs, NOE distances and

^{3}J-couplings) also follow the trend that the criteria are consistently better for the correct configuration (Table S6 and Figure S12 in Supporting Information). The only exception regards the

^{3}J-couplings of dataset 1A for which the three values are satisfied almost equally for both diastereomers. Note that the three

^{3}J-couplings entered as constraints into the simulation influence the ω dihedral angle, and that these values are more characteristic of the conformational exchange than of the configuration. By contrast, the NOE distances seems to be highly sensitive to the configuration.

#### 2.3.2. Discriminating between 4 Stereoisomers of Mandelalide A 2

**2**were tested in MDOC simulation against the incorrect configurations to address the diastereomeric discriminating ability of MDOC in more complex flexible molecules with various chiral centers. To this end, MDOC simulations with identical parameters (see SI) were applied to four configurations

**2p**, 11-epi-

**2p**,

**2r**and 11-epi-

**2r**, and the accuracy of the simulated NMR parameters were examined based again on the three aforementioned criteria. The results are displayed in Figure 13. Although the quality criterion is met (>1) for all configurations, the isomers

**2r**and 11-epi-

**2r**with their inverted northern part show a substantial drop in the quality of fit relative to the correct ones (

**2p**and 11-epi

**-2p**, respectively). However, the inversion of the methyl group at position 11 does not lead to a large deterioration of the quality - especially with NMR dataset

**2p**(4.64 to 4.20). Closer inspection however showed that the small drop in quality is caused mainly by a number of long-range NOE distances, whereas the simulated RDCs and J-coupling could not readily distinguish either configurations. In contrast, a more distinct drop in quality is observed for the 11-epi-

**2p**dataset applied to configuration

**2p**.

## 3. Conclusions

^{3}J couplings, which are easily measured in solution and which should limit the generation of unrealistic rotamers. The entire NMR dataset can be brought together in a single simulation to generate a consistent picture regarding the structure of molecules in solution and their dynamic equilibrium. For the

**2p**isomer of mandelalide A, for instance, it can at least be stated that the resulting ensemble are in accordance with no less than 212 NMR constraints. Further investigations will show to what extent this method can be generalized.

**1-SS**and

**1-SR**, differing at a single chiral position, the MDOC results fit the incorrect diastereomer quite well by conventional standard testing (e.g., RMS or Q), but according to the n/χ

^{2}and 1/χ

^{2}criteria, the outcome is much clearer. In the case of the much larger mandelalide A, configuration

**2p**can readily be distinguished from

**2r**but in the case of the epimers

**2p**and 11-epi-

**2p**the difference is barely significant. Nevertheless, all 4 configurations pass the n/χ

^{2}test and have similar in 1/χ

^{2}values. This is not surprising since a majority of the short-range constraints (NOEs and J) are only weakly affected by the chiral difference at distant positions. It would thus be desirable to take these aspects into consideration and develop more advanced statistical tools in order to confidently use MDOC for configurational evaluations in flexible molecules.

## 4. Materials and Methods

#### 4.1. NMR

#### 4.1.1. Materials

_{6}and chloroform-d

_{1}(99.9% of D atoms) were purchased from Cambridge Isotope Laboratories (Tewksbury, MA, USA). Twenty five mg of a single diastereomer of the 1,4 diketone was kindly donated by the List group, and was a product of an asymmetric cross coupling catalysis reaction [34]. About 2 mg of “pseudo”-mandelalide and 11-epi-“pseudo”-mandelalide (recognized as isomers of mandelalide A as a result of its synthesis, following the inversion of the northern part) were obtained from the Fürstner group as the end product of a multistep synthesis by Willwacher et al. [41]

#### 4.1.2. Sample Alignment

_{1}, inserted into a 5-mm NMR tube. Residual monomers were washed out of the polymer stick gel by applying several compession-and-release cycles in the deuterated solvent (chloroform-d

_{1}) using a home-made Teflon plunger. This was repeated until no monomer could be observed in the 1D

^{1}H NMR spectrum. The gels exhibited quadrupolar splitting (Δν

_{Q}) of the solvent signal of form 40 to 47 Hz when maximally compressed, and no quadrupolar splitting (Δν

_{Q}= 0) when fully relaxed as assessed by 1D 2H NMR. The homogeneity of the alignment was also assessed using

^{2}H-mapping approaches [43]. The dissolved analytes (diketones or mandelalides) were dispersed into the gel using a pumping actions as described above. Samples could be measured immediately.

#### 4.1.3. NMR Experiments

^{1}H, and 125.69 MHz for

^{13}C and equipped with a broad band observe (incl.

^{19}F) probehead (BBFO) with Z gradients. NMR experiments for the mandelalide samples were collected on a Bruker Avance NMR instrument operating at 600.22 MHz for

^{1}H, and 150.93 MHz for

^{13}C and equipped with cryogenically cooled triple channel (

^{1}H/

^{13}C/

^{15}N) inverse probehead (CPTCI) with Z gradients. Complete

^{1}H and

^{13}C assignments, including stereotopic

^{1}H in methylene groups, were obtained at 25 °C from standard 1D experiments as well as 2D correlation experiments. The correlation experiments included

^{1}H,

^{1}H-DQF-COSY,

^{1}H,

^{1}H-NOESY,

^{1}H,

^{13}C-HSQC,

^{1}H,

^{13}C-HMBC. The

^{1}H and

^{13}C spectra were referenced by setting the residual solvent signal at their known chemical shift relative to TMS. Homonuclear

^{1}H scalar coupling constants were measured directly on 1D

^{1}H NMR spectra in resolved cases and using selective 1D NOE experiments in cases where

^{1}H signals were overlapped. Cross-relaxation NOEs were evaluated from a

^{1}H,

^{1}H NOESY experiments measured with 2048 × 1024 points in the acquisition matrix, 6(8) scans per increment and 1(0.7) s mixing time and 3(6) s relaxation delay for the diketone (mandelalide) sample. CLIP-HSQC experiments [44] were recorded to measure the CH splittings corresponding to scalar couplings (

^{1}J

_{CH}) or to scalar plus residual dipolar couplings (

^{1}T

_{CH}=

^{1}J

_{CH}+

^{1}D

_{CH}) in the isotropic and anisotropic samples. This experiment was typically parametrized with 16k x 512 points in the acquisition matrix, 8 scans per increment and 3-s relaxation delay. A homo-decoupled CLIP-RESET-HSQC [45] was also measured in the case of the mandelalide sample as a 3D matrix of 512 × 512 × 12 (chunks) points, with chunk duration of 16.255 ms, 8 scans per increment and relaxation delay of 1 s. All raw, processed and analysed data are made available as NMReDATA records [46].

#### 4.1.4. Conformational Analysis

**1-SS**and

**1-SR**) in three different rotamers (trans, gauche+ and gauche-) were generated with the hybrid density function B3LYP, cc-pVTZ as a basis set in Gaussian-09. For the conformation analysis of these structures against the measured RDCs based on the classical alignment method using SVD, the program Mspin (Mestrelabs, Santiago de Compostela, Spain) was employed. All inputs are given in the Supporting Informations.

#### 4.2. MDOC Simulations

#### 4.2.1. Theory: RDC-Based Orientation Constraints

**D**and all tensor components are regarded as constraints. Other pseudo-energies for scalar constraints like NOE distances or scalar J couplings have only the second summation over the experimental values (denoted with i). The constant k is used to convert the expression into kJ/mol and to adjust the strength of the pseudo-forces. Measured RDC values represent the z-components of diagonal traceless tensors whereas the off-diagonal elements are averaged to zero by the rapid reorientation of the molecule around the director. The measured tensors

**D**

^{exp}are given in the laboratory coordinate system, oriented with its z-axis relative to the direction of the external magnetic field. The calculation of dipolar coupling tensor

**D**

^{theo}can easily be performed in the coordinate system that is oriented parallel to the vector that connects the two coupled nuclei. In this case the dipolar tensor is diagonal and its principal values can be calculated from the product of the gyromagnetic ratios of the two nuclei divided by the third power of their distance (also see Supplementary Information). To calculate the differences between the calculated and experimental tensor components, the tensor

**D**

^{theo}has to be transformed from its principal axis system to the laboratory coordinate system using proper transformation matrices

**T**

^{i}:

^{1}H and a

^{13}C nucleus in a C-H bond is chosen as example. This coupling is nearly the same for all C-H bonds since the bond distance is nearly constant (in the present simulations, different values only for C(sp

^{3})-H and C(sp

^{2})-H couplings are used—see Supplementary Information). The double sum in Equation (2) runs over all components of the transformation matrices

**T**

^{i}being mostly different for all sites i because of the different orientation of the bonds with respect to the laboratory system.

**D**is left and the pseudo-forces change on the same time scale τ because of the mismatch of calculated and experimental data. In this respect, MDOC can be regarded as an accelerated MD simulation and orientational averages can be reached in moderate simulation times. A value of τ of 200 picoseconds was generally used whereas the simulations were performed over durations one or two order of magnitudes longer than τ − i.e., over several nanoseconds.

_{i}and B

_{i}:

**T**

^{i}in Equation (2) with respect to the coordinates coupling nuclei. The transformation matrices can be obtained from sets of orthogonal unit vectors that span the local bond (or interconnection) coordinates systems and therefore the derivatives can be obtained from these unit vectors (see Sternberg et al. [31]). In contrast to 1-bond RDCs(

^{1}D), long-range RDCs (

^{n}D) can also be used as distance constraints in analogy to NOE distances, providing the mean distribution of orientations of nuclear connection vectors (or alignment tensor) is known. However, in this investigation, only the orientational derivatives of the RDC pseudo-energies are used.

^{−2}to 10

^{−3}. Therefore an order parameter S

_{am}is introduced into the calculations that accounts for the reduction of the dipolar splitting caused by the alignment medium (in analogy to the order parameter S

_{bilayer}introduced by Marsan et al. [53]). S

_{am}is multiplied to the calculated dipolar couplings to prevents too high pseudo-forces by shifting the dipolar splittings from the kHz range to several Hertz. S

_{am}should be chosen large enough that its product with the maximum splitting is in any case much larger than any observed splitting. If, for example, the static C-H splitting of 47.96 kHz is multiplied with S

_{am}(0.004, see Table S10 in Supplementary Information) a maximum attainable CH splitting of 191.8 Hz is obtained, that is much larger than any observed splitting.

#### 4.2.2. Theory: Scalar Constraints

^{3}J

_{HH}indirect scalar couplings are used as constraints. For the calculation of the time mean values in both cases the average with an exponential memory as given in Equation (3) was used. The pseudo-forces are augmented with hyperbolic tangent weight function as given in Equation (5). For the calculation of the distances the following average is applied [54]:

_{3}groups as constraints. If for the CH

_{3}protons also one bond RDC are used as constraints these groups rotate fast in the MDOC simulations and therefore the same distance constraint can be applied to all three protons of a CH

_{3}group.

^{3}J

_{HH}couplings the equation according to Haasnoot et al. [4] was used. In this Karplus-like equation a correction term is added that accounts for the influence of the electronegativity of neighbor substituents on the coupling protons. Using this equation an RMS (root mean square) deviation between calculation and experiment in the range of ca. 0.6 Hz should be possible.

#### 4.2.3. Evaluation of Quality

^{2}criterion is used, as introduced by Intelmann et al. [55]:

^{2}(with n the number of measured values of the property P) giving values larger than 1.0 when the calculations are on average within the experimental error bounds.

_{outliers})/n will also be employed.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Sample Availability: Samples of are no longer available from the authors. |

**Figure 1.**(

**A**) Synthesis of

**1 [34]**. (

**B**) The

**1-SR**(C10-S and C12-R) and

**1-SS**(C10-S and C12-S) forms. Bond rotation (defined by torsion angle ω (C1-C10-C12-C20), red) is not restricted. Conjugated double bonds are displayed in red and single bonds in cyan.

**Figure 2.**Selected

^{13}C-

^{1}H dipolar splittings of an 80-ns MDOC simulation of the

**1-SS**configuration with dataset 1A. The trajectories display the mean values with exponential memory according to Equation (3) (blue) and the running mean over the former values (red). Extreme values at beginning of the trajectory are later cut off. The orange line indicates the experimental splitting and the lower and upper error bounds are indicated by green lines. (

**A**): C

_{6}-H

_{6}bond dipolar splitting and (

**B**): C-H splitting of the CH

_{3}group at position C11.

**Figure 3.**criterion n/χ

^{2}(Equation (7)), “smallest outlier” criterion 1/χ

^{2}

_{min}and fidelity $\mathcal{F}$ (labels) for MDOC simulations of the 1,4-diketone

**1-SS**and

**1-SR**with the experimental datasets 1A and 1B, respectively. On average, all interaction types are very well reproduced by ensembles, with n/χ

^{2}> 1 (overall 1A: 1.9, 1B: 1.8) and fidelity $\mathcal{F}$ above 85% (overall 1A: 34/40, 1B: 37/40).

**Figure 4.**Angle analysis of the C1-C10-C12-C20 torsion angle (ω) from an MDOC simulation of the

**1-SR**and

**1-SS**form of the 1,4-diketon. Upper panel:

**1-SR**form: torsion statistics for the ω torsion angle. The {trans, gauche(-), gauche(+)} ratios are {0.165, 0.730, 0.105} Lower panel:

**1-SS**form: torsion statistics for the ω torsion angle. The {trans, gauche(-), gauche(+)} ratios are {0.617, 0.281, 0.101}.

**Figure 6.**Proposed

**2p**and revised

**2r**isomers of the natural product mandelalide A. During the search for the right configuration, 11-epi

**-2p,**for which the bond indicated in red was inverted, was also synthesized.

**Figure 7.**Criterion n/χ

^{2}(top), outlier criterion1/χ

^{2}

_{min}(bottom) and fidelity $\mathcal{F}$ (labels) of the MDOC simulations of the configurations

**2p**and 11-epi

**-2p.**Data is presented for each type of NMR parameters.

**Figure 8.**Conformer of mandelalide A configuration

**2p**including some torsion distributions around single bonds (π-bonds are displayed in red). Dihedral angles are denoted with ${\sigma}_{n}$, where n refers to the 3rd atom of the dihedral angle definition (e.g., ${\sigma}_{1}\equiv $ C23-O-C1-C2). The torsion distributions involve only carbons or oxygens of the large ring system. Inset labels indicate {trans, gauche-, gauche+} ratios.

**Figure 9.**Conformer of mandelalide A configuration 11-epi-

**2p**including selected occupation numbers of torsional states around single bonds (π-bonds are displayed in red). Dihedral angles are denoted with ${\sigma}_{n}$, where n refers to the 3rd atom of the dihedral angle definition (e.g., ${\sigma}_{1}\equiv $ C23-O-C1-C2). The torsion distributions involve only carbons or oxygens of the ring system. Inset labels indicate {trans, gauche-, gauche+} ratios.

**Figure 10.**Contribution of the selected 24 σ dihedral angles along the mandelalide A ring main-chain to the first 2 principal components with highest ranked eigenvalues. Dominant contributions (>0.3) are indicated with the shorthand ${\sigma}_{n}$, where n refers to the 3rd atom of the dihedral angle definition (e.g., ${\sigma}_{12}\equiv $ C10-C11-C12-C13, also: ${\sigma}_{0}\equiv $ C22-C23-O-C1).

**Figure 11.**Dihedral landscape of the first two principal components of the mandelalide A isomer

**2p**with two typical molecules according their contribution to the principal components (Figure 10). The left conformation is selected according to the lower θ

_{2}maximum of the dihedral distribution and the right molecule according to the upper θ

_{2}maximum. The side chains of the large ring system are displayed transparent. The arrows indicate the largest contributions to the first two principal components: both bonds to methyl-group-bearing C11 (${\sigma}_{11}$ and ${\sigma}_{12}$), the bond to the ring oxygen O1 (${\sigma}_{0}$) and the bond the methylene C4 (${\sigma}_{4}$).

**Figure 12.**The MDOC outcome based on datasets 1A and 1B against the correct (green) and incorrect (red) diketone

**1**configuration. Displayed are the three criteria (quality criterion n/χ

^{2}, outlier criterion (1/χ

^{2}

_{min}) and data validity $\mathcal{F}$ (labels)). For the breakdown of these parameters based on data type, see Figure S2 in the Supporting Information).

**Figure 13.**Quality criteria (n/χ

^{2}, 1/χ

^{2}

_{min}and $\mathcal{F}$) for MDOC simulations of four configurations with two different NMR data sets. The configuration that belongs to the data is indicated in green.

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Farès, C.; Lingnau, J.B.; Wirtz, C.; Sternberg, U.
Conformational Investigations in Flexible Molecules Using Orientational NMR Constraints in Combination with ^{3}*J*-Couplings and NOE Distances. *Molecules* **2019**, *24*, 4417.
https://doi.org/10.3390/molecules24234417

**AMA Style**

Farès C, Lingnau JB, Wirtz C, Sternberg U.
Conformational Investigations in Flexible Molecules Using Orientational NMR Constraints in Combination with ^{3}*J*-Couplings and NOE Distances. *Molecules*. 2019; 24(23):4417.
https://doi.org/10.3390/molecules24234417

**Chicago/Turabian Style**

Farès, Christophe, Julia B. Lingnau, Cornelia Wirtz, and Ulrich Sternberg.
2019. "Conformational Investigations in Flexible Molecules Using Orientational NMR Constraints in Combination with ^{3}*J*-Couplings and NOE Distances" *Molecules* 24, no. 23: 4417.
https://doi.org/10.3390/molecules24234417