Bayesian Inference Applied to NMR-Based Configurational Assignments by Floating Chirality Distance Geometry Calculations

Abstract

Using NMR data, the assignment of the correct 3D configuration and conformation to unknown natural products is of pivotal importance in pharmaceutical and medicinal chemistry. In this report, we quantify the quality and probability of structural elucidations using Bayesian inference in combination with floating chirality distance geometry simulations. Here, we will discuss the configurational analysis of three complex natural products including isopinocampheol (1), plakilactone H (2), and iodocallophycoic acid A (3) using NMR restraints of various types and in different combinations (residual dipolar couplings (RDCs) and NOE-derived distances). Our results quantitatively demonstrate how reliably molecular geometries can be inferred from experimental NMR data, unequivocally unveiling remaining assignment ambiguities. The methodology presented here can dramatically reduce the risk of incorrect structural assignments based on the overinterpretation of incomplete data in chemistry.

NMR-Based Configurational Assignments of Natural Products: How Floating Chirality Distance Geometry Calculations Simplify Gambling with 2N–1 Diastereomers

“…It is exactly this assignment probability P(Θ|D) (or certainty) that we call the "diastereomeric differentiability" (dd) of the configuration Θ. 62,63 In Bayesian statistics 79−81 applied to problems in chemistry and physics, 82−84 there are always two probability distributions: The so-called "prior" probability P(Θ) reflects someone's knowledge about a molecular structure or configuration Θ before experimental data becomes available. In contrast, the "posterior" probability P(Θ|D) corresponds to the updated knowledge, given (indicated by the "|" symbol) that the NMR data D have become available.…”

“…receive equal weights (probabilities) P(θ) = 1/N DG a priori, where N DG is the total number of structures generated in the entire DG ensemble of all structures. 62,63 The computed weights of "conf igurations Θ" are then sums over all conformations of each configuration (cf. eq 5) and depend on their sampling probabilities, respectively.…”

“…This seems in discord with an earlier report on configurational assignments of artemisinin (2) derived from this RDC data set. 5 However, these conclusions were based on a misinterpretation of likelihood functions and probabilities P(D|θ)�in Bayesian statistics P(θ|D) needs to be evaluated 62,63 �and wrong estimates of uncertainties σ X on (vibrationally averaged) NMR parameters. 87 A study using alternate non-Bayesian statistical models�and equivalent dd values derived from a totally different formalism�showed that the discriminating power of this RDC data set is indeed as low as dd(2a) ≈ 20−30%, 88 which is approximately in accord with the results obtained here from rDG calculations.…”

“…Effective force constants on holonomic distances and chiral volumes were used as specified in the original DG version (K dist = 2.0 Å −2 and K chir = 2.0 Å −6 ), and force constants on NMR restraints were set to K NOE = 100 (this is dimensionless for log-normal potentials), K RDC = 1.0 Hz −2 , and K RQC = 0.1 Hz −2 in order to appropriately account for typical ranges of different types of NMR parameter violations (Δd ≈ 0.1−0.5 Å for NOEs, ΔD ≈ 0.5−2.0 Hz for RDCs, and Δν Q ≈ 5−10 Hz for RQCs). 62,63 In ConArch + , all configurations are evaluated via the "chiral volume" of tetrahedral centers, which corresponds to the triple product of the three vectors spanning the tetrahedron. This value is signed and changes sign upon inversion or reflection.…”

“…Apart from the bias-free evolution of molecular structures from fc-DG simulations, this method further not only provides dimensionless quality-of-fit factors but moreover yields quantitative Bayesian assignment probabilities, which in particular describe the quality of the underlying NMR data and especially their decidedness in view of structure elucidation. 62,63 In this report, we show how the relative configurations of jatrohemiketal (1), artemisinin (2), and Taxol (3) can be derived unambiguously from fc-rDG/DDD simulations using NMR-derived NOE/ROE data, which optionally can be amended by additional information obtained from RDCs or RQCs (Chart 1).…”