Determination of Enantiomeric Excess and Diastereomeric Excess via Optical Methods. Application to α-methyl-β-hydroxy-carboxylic acids

Abstract

Characterization of chiral molecules in solution is paramount for measuring reaction success. However, techniques to distinguish between chiral molecules containing more than one stereocenter through the use of optical techniques remains a challenge. Herein, we report a techique using a series of circular dichroism spectra to train multivariate regression models that are capable of predicting the complete speciation of 3-hydroxy-2-methylbutanoic acid stereoisomers. From this, it is possible to rapidly and accurately determine the enantiomeric excess and diastereomeric excess of the solution without the need for chiral chromatography.

Graphical Abstract

Introduction

The development of catalytic asymmetric transformations is crucial for the production of pharmaceuticals and agrochemicals. With modern advances in parallel synthesis, thousands of reaction conditions can be screened by the systematic variation of reaction parameters, e.g., metal precursor, ligand, solvent, temperature, etc., to find ideal conditions for a given asymmetric transformation. Thus, the use of high-throughput experimentation (HTE) and, subsequently, high-throughput screening (HTS), is becoming ubiquitous throughout academic and industrial settings.^1–4 The use of HTE and HTS has facilitated the discovery of novel noble metal catalysts,^5–7 organocatalysts,^{8, 9} and biocatalysts,^9,10 for a variety of asymmetric transformations.

Two metrics of success for asymmetric reactions are the enantiomeric excess (ee) and, when two or more stereocenters are present in the target molecule, the diastereomeric excess (de). The production of enantiopure drugs is of utmost importance to the pharmaceutical industry as pairs of enantiomers can show variation in their pharmacological activity.^{11, 12} The importance of developing enantio- and diastereoselective reactions has garnered significant attention, but developing such methods can pose a considerable challenge.^13,14 To monitor these values, chromatography is the academic and industry standard to characterize stereoselective transformations; however, the serial nature of chromatography limits the method when analyzing large numbers of samples during HTE.¹⁵ Additionally, method development is required for each structure of interest, where slight changes of the molecule’s functionalities may require different chromatographic methods.^16,17 In contrast, optical methods are compatible with existing parallel synthetic approaches and are generally applicable to an entire class of compound, e.g., amines, carboxylic acids, albeit a different sensor is needed for each class, and a different calibration curve is needed for each analyte within a class.^18–21

To expand the capabilities of optical screening techniques, researchers have started investigating a variety of machine learning (ML) techniques to use in tandem with current ee and de sensing workflows. Through this combination, researchers have been able to pull information from circular dichroism (CD) spectra that would otherwise not be discernible. These discoveries range from predicting the ee and de of chiral alcohols to the generation of calibration curves constructed using Charton parameters.^10,22,23 Such advances have been exciting developments in the field of HTE, but improvements are needed in both functional group diversity as well as the ML techniques used to analyze CD data.

Recently, our group reported a general workflow for the use of CD and UV/Vis spectroscopy for the determination of reaction yield, ee values, and de values (Figure 1A).²² We demonstrated its applicability by determining the complete stereoisomeric speciation of 2-aminocyclohexanol. The concentration of the solution was determined using a simple hydrazone condensation (1) after oxidizing the alcohol of the 2-aminocyclohexanol to a ketone. To determine the ee and de, two previously published assemblies, one comprised of an octahedral iron(II) complex (2) and a second using an ECCD-active trigonal bipyramidal complex with a zinc(II) center (3), that bind secondary alcohols and amines, respectively, were used to generate CD and absorbance spectra for varying ratios of each of the four stereoisomers.^24,25 Differentiation of the diastereomers was enabled through their distinct differences in absorbance spectra from the alcohol-sensing assembly (1), with the trans-isomers having significantly lower absorbance values than their cis-counterparts (1.0 a.u. vs. 1.3 a.u.). Importantly, as previously described, mathematical relationships between stereoisomers reveal that only when special circumstances are met is it possible to determine the ee of a species using the de.²⁶ When this relationship is not met, the trans or cis relationship of the stereocenters influences the spectroscopic signal of both the alcohol (1) and amine (2) assemblies. Therefore, the relationships between ee and de must be drawn from the experimental CD spectrum of mixtures of all four stereoisomers. Using machine learning (ML) techniques, specifically sequential and orthogonalized covariance selection (SO-CovSel), it was possible to generate a trained model that distinguishes the two stereocenters, which would not have been possible using typical linear approaches to quantify ee and de, and thereby determine the percent composition of all four stereoisomers in unknown mixtures.

Figure 1.

(A) Three sensors used to determine de optically, (B) Approach used by Wolf to achieve complete speciation using two CD-active Cu(II) complexes, (C) Potential conversion of 3-hydroxy-2-methylbutanoyl-N-acetylcysteamine thioester into sensor-compatible alcohol and carboxylic acid, (D) Tandem sensing and kernel partial least squares regression (KPLSR) strategy employed in this work.

An alternative approach to complete speciation of amino alcohols was accomplished by the Wolf group (Figure 1B).²⁷ A mix-and-measure workflow was designed that implements the use of Schiff base formation and Cu(II) coordination chemistry, which can be read out through UV and CD spectroscopy. To begin the speciation, the amino alcohol analyte, specifically 1-amino-2-indanol (4), was condensed onto salicylaldehyde (5). The UV/Vis spectrum of the resultant Schiff base (6) could be used to concurrently determine the de and concentration of analyte in solution by monitoring two wavelengths (420 nm and 340 nm, respectively). This is possible through a distinct decrease in absorbance (0.3 a.u.) between the threo- and erythro-stereoisomers at 420 nm. Additionally, at 340 nm the absorbance is independent of stereochemistry and decreases in absorbance can be attributed to lower analyte concentrations through a calibration curve. To determine the ee and de of the solution, subsequent addition of Cu(II) in the absence (7) and presence of base (8) yielded distinct ee values for each diastereomeric pair. To minimize the error associated with this technique, linear programming and parameter sweep algorithms were implemented, which enabled unbiased identification of optimal wavelength ranges for the most accurate and robust analysis. By taking these three measurements, the concentration, de, and ee of aminoindanol was determined in less than an hour.

Since this work, the use of ML in extracting information from CD and UV spectra has proliferated throughout the field of optical sensing. Recently, a complex mixture of eight enantiomers (four chiral amino alcohols) was deconvoluted using an optimized ML algorithm which allowed the absolute configuration, enantiomeric ratios, and individual concentrations to be determined.²⁸ Despite the convoluted spectra, the data was faithfully interpreted with a variety of amino alcohols in varying complexity of mixtures by the ML algorithm. This breakthrough shows great promise in further expediting sample analysis and potentially precluding the need for purification for analysis. Beyond interpreting data, ML has been used to optimize sensors. One example²⁹ involved a combination of computational parameterization, statistical modeling, and high-level density functional theory calculations to optimize an existing sensor, previously only capable of sensing secondary alcohols at the α- and β-stereocenters, to determine chirality at a γ-position^{24, 30}

The three examples of spectral deconvolution discussed above for speciation of compounds with two stereocenters inspired us to further extend ML capabilities for chiroptical sensing of ee and de. We identified the Keatinge-Clay chemoenzymatic method to be a prime candidate for reaction development and product characterization via optical methodologies.³¹ This group has extensive experience utilizing ketoreductases (KRs) to generate synthetically useful, chiral building blocks.^31–33 In one example, a chemoenzymatic platform was developed by employing KRs from modular polyketide synthases (PKSs).³¹ PKSs are enzymatic assembly lines that control the stereochemistries of substituents during the biosynthesis of polyketide natural products such as 6-deoxyerythronolide B (6-dEB). The chemoenzymatic platform is driven by an NADPH-regeneration system that couples KR-mediated reduction to the oxidation of glucose. This biocatalytic transformation yields α-alkyl, β-hydroxy N-acetylcysteamine thioesters that possess stereocenters at the α- and β-positions. Typically, the enantio- and diastereoselectivities of the transformations were determined via chiral HPLC methods that ranged in time from 55 to 125 minutes. However, it is known that thioesters are readily hydrolyzed to carboxylic acids in mild acid or base,^34,35 as it is a step in the citric acid cycle, which would render in this case β-hydroxyl-α-alkyl carboxylic acids. Hence, these analytes were deemed a useful choice for further exploring and improving methods that simultaneously determine ee and de.

Workflow Design

Thus, we adopted a strategy which utilized two well-understood sensors that could accommodate derivatives of 3-hydroxy-2-methylbutanoyl-N-acetylcysteamine thioester (9) which could be accessed through hydrolysis and methanolysis (Figure 1C). To expedite model development for ultimate use in enzymatic screening, the carboxylic acids (10) and methyl esters (11) were synthesized according to the procedure in SI section 2.1.

We opted to use the aforementioned chiral secondary alcohol assembly (3) in tandem with a sensor for α-chiral carboxylic acids (12). The carboxylic acid can be analyzed with our previously reported sensing system for α- or β-chiral carboxylic acids (Scheme 1).³⁶ The tripodal Cu(II) complex (12) exists as a racemic mixture of M- and P- helical twists as a result of the orientation of the pyridyl- and quinolyl- chromophores around the copper (II) center. Upon addition of a chiral carboxylic acid, diastereomeric complexes (13) are formed with a preferred M- or P- helical twist, with the preferred twist being indicative of the stereochemistry of the carboxylate guest. The twist imparted to the two quinoline chromophores leads to exciton-coupled circular dichroism couplets in the resulting CD spectra. Calibration curves can be constructed relating the CD intensity at 240 nm to the ee of the carboxylate analyte, with errors of ±3%. The copper (II) host (12) is readily synthesized, analyte binding occurs quickly upon mixing, and the CD spectrum can be immediately measured - making this method a simple mix-and-measure approach, ideal for use in HTS assays.

Scheme 1.

The tripodal [(BQPA)Cu(ClO₄)₂] complex (12) for the enantiomeric differentiation of chiral carboxylic acids, where the perchlorate anions (ClO₄⁻) have been omitted for clarity. BQPA corresponds to the tripodal ligand, 1- (pyridin-2-yl)-N,N-bis(quinolin-2-ylmethyl)methanamine.

Lastly, to construct a de relationship from CD spectra, we aimed to capitalize on the diastereomeric interactions our analyte would have with the two assemblies (3 and 13). If one assembly interacted differently with one diastereomeric pair versus the other, through ML it could be possible to use this difference to predict the de of each analyte through their CD spectra. This approach is different, and more direct, than our previous report on amino-alcohol stereoisomer speciation (using 1, 2, and 3), in that a de assay is not required (Figure 1D).

Results and Discussion

We aimed to elucidate how we could further advance the field of optical HTS by using ML trained on CD values to determine the ee of the individual stereocenters of the threo and erythro isomers, and from those measurements predict both the ee and de of unknown mixtures of this new class of analyte, thus expanding the scope of optical methods for stereoisomer speciation. We hypothesized that the tandem use of previously reported chiroptical assays for the ee of α- and β-chiral carboxylic acids³⁶ and chiral mono-ols,²⁴ along with ML-derived relationship for de,²² would be suitable for differentiation of the four stereoisomers (Figure 2).

Figure 2.

The four possible stereoisomers of the carboxylic acid (10) and methyl ester (11) analytes.

Alcohol ee Determination

As carboxylic acids do not interact with the alcohol sensing assembly and vice versa, the analytes are compatible with both the alcohol and carboxylic acid chirality-sensing systems. However, upon assembly formation of the alcohols, we observed that the magnitudes of the CD signals were significantly higher for the methyl esters [methyl-3-hydroxy-2-methylbutanoate (11)] than the carboxylic acids [3-hydroxy-2-methylbutanoic acid (10)]. Further, the efficiency of the hemiaminal ether zinc (II) complex 3 to incorporate β-hydroxy carboxylate substrates could not be determined. This was due to the presence of a broad -OH resonance in the 5–6 ppm region that coincidentally overlapped with the chemical shifts of the hemiaminal ether hydrogens, which are used to determine the yield as well as the dr of the complex. Thus, the methyl ester derivatives of the four stereoisomers were used for stereochemical analysis of the β-hydroxy position. Each stereoisomer of methyl-3-hydroxy-2-methylbutanoate was found to efficiently incorporate into the alcohol assembly (3).

Characteristic Cotton effects were observed at 270 nm, and initial tests found that the threo- and erythro- diastereomers gave identical CD signals using assembly 3. To verify that the methyl substituent at the 2-position does not affect chiroptical analysis, CD spectra were gathered for each diastereomeric set ((2R,3R)/(2S,3S) and (2R,3S)/(2S,3R)) by creating solutions with various ee values (−100, −80, −60, −40, −20, 0, 20, 40, 60, 80, 100%). Additionally, CD spectra were acquired for solutions of diastereomeric mixtures ((2R,3S)/(2S,3S) and (2S,3R)/(2R,3R)), thus varying the ee values for this set at only the α-position. Essentially identical CD spectra were found for the same ee values for these different sets of diastereomerically pure compounds (SI Figure 1). It was concluded that the ee at the 3-position could be determined regardless of the stereochemistry at the adjacent position.

Because the CD intensity at 270 nm for assembly 3 is not influenced by the stereochemistry of the α-stereocenter at 270 nm, all four stereoisomers should correspond to the same calibration curve for the ee at the β-center. Thus, CD was plotted versus ee and linear calibration curves were found for each of the four combinations of stereoisomers described above (SI Figure 1). The average of these four curves is shown in SI Figure 2.

Although a difference in the CD response between the diastereomers might be expected, the fact that the 2-position has minimal impact on the CD signal can be rationalized by considering the preferred M- or P- twists of the hemiaminal ether zinc assembly 3. The preferred helical twist is the stereoisomer that results in the alcohol pointing away from the interior of the zinc complex.²⁴ In this conformation, the α-stereocenter must not be close enough to the hemiaminal ether stereocenter to impart an effect on the preferred orientation of the pyridyl chromophores.

Carboxylic Acid ee Determination

As with the alcohol assembly, CD spectra for 13 were collected for each diastereomeric set ((2R,3R)/(2S,3S) and (2R,3S)/(2S,3R)) and mixtures ((2R,3S)/(2S,3S) and (2S,3R)/(2R,3R)). Unlike the use of chiral alcohol sensing assembly 3 where the diastereomers responded the same, the diastereomers of 2-methyl-3-hydroxybutryic acid gave different CD signals at 240 nm using the assembly 13, as shown in SI Figure 3 (|CD|_erythro = 5 mdeg and |CD|_threo = 9 mdeg). Because this copper (II) complex has been used to determine the ee of carboxylic acids with α- and β- stereogenic centers, it was not surprising that the stereochemistry at the β-position affected the chiroptical analyses. The stereochemistry at the 3-position of the threo-isomers must be arranged in such a manner that there is a larger overall twist in the quinoline chromophores relative to the erythro-isomers.

De Determination

Having collected CD spectra for all four stereoisomers using both assemblies 3 and 13, we developed a model that would allow us to determine the de of complex mixtures of stereoisomers. Researchers frequently turn to the use of linear regression methods to model similar relationships.³⁷ For high-dimensional datasets, partial least squares (PLS) regression is an appealing option as it is relies on compressing the multivariate information in a reduced set of components, obtained by maximizing the covariance between predictor variables and measured responses.³⁸ This technique is widely used throughout chemistry, as well as social sciences and marketing,^{39, 40} to create predictive models. PLS regression assumes that some predictor variables have different impact on the responses and subsequently adjusts the weight or influence of those predictor variables accordingly.⁴¹ While this is often a very helpful method, it becomes ineffectual if the relationship between the predictor variables and responses is nonlinear. When our data was analyzed as if it were linearly related, we found the resulting R-squared to be low and inaccurate in de predictions. Thus, we assumed the relation between the spectroscopic variables and the responses to be nonlinear. To accommodate non-linear relationships, we turned to kernel partial least squares (KPLS) regression. KPLS regression implements non-linear modeling by projecting the spectroscopic data onto a higher-dimensional feature space using a non-linear transformation of the original variables (in the present case, polynomial). The relationship between the newly transformed spectral data and the responses (% composition of each stereoisomer) can be considered linear.⁴² In this respect, the fundamental characteristic of KPLS is that the non-linear transformation of the input data is accomplished in an implicit way, via the so-called kernel trick.

Having identified the KPLS approach as the most optimal for our dataset, we randomly split the data containing spectra from both the alcohol and carboxylic acid assemblies into a training and test set in a representative way via the Kennard-Stone algorithm,⁴³ which ensures that the data used for model building representatively span the variability of the entire data set. The test set was comprised of 70% of the dataset where the percent composition of each stereoisomer and the corresponding CD data were known. The model can correlate changes in CD intensity to changes in percent composition of the four stereoisomers. The model was then validated using our test set. For the test set, 30% of the data is fed into the model, solely as CD spectral data and the resulting percent composition of each stereoisomer is predicted (Figure 3A). After training this model, it is possible to predict the de as well as the ee of unknown mixtures of 3-hydroxy-2-methylbutanoic acid from this workflow (Figure 3B). From the screening of nine unknown samples, the error in composition for each isomer found to be ±6%. This means that each of the four isomers can be quantitated in unknown mixtures with an error of 6% out of a total 100% (sum of all isomers), which is comparable to ¹H-NMR spectroscopy and HPLC analysis. Such an error is adequate for use in HTS techniques for following changes in ee and de values during optimization routines.

Figure 3.

(A) Tabulated KPLS regression model predictions for the total speciation of 3-hydroxy-2-methylbutanoyl N-acetylcysteamine thioester derivates (RR, RS, SR, and SS configurations) and (B) graphical representation of predicted vs. measured % composition. The red circles are training values whereas the black squares are test values.

Conclusions

In summary, we have demonstrated an ee and de determination workflow by using alcohol- and carboxylic acid-sensing assemblies to quantify four stereoisomers of unknown mixtures, without the requirement of a separate de assay. These simple mix-and-measure assemblies use minimal solvent and only optical measurements to acquire data, making them amenable to HTS. Using KPLS regression we were able to accurately predict stereoisomer composition in solution with a 6% error by using a tandem sensor approach with two previously developed sensors. The accuracy of this technique could release researchers from needing to use chiral chromatography to characterize analytes during HTS because optical methods now routinely allow ~100 analyses in under five minutes²⁰, albeit the conversion of thioester analytes from PKSs to a sensor-compatible form would add an additional step. The impact of this additional processing time would diminish as the number of reactions analyzed increases. Additionally, the simplicity of this workflow makes it adaptable to other compounds containing multiple stereocenters. Potential future studies could be executed to determine the generality of this workflow for substituents at the γ-position and beyond. Optical-based workflows are advancing due to the surge of ML techniques in chemistry, making them very promising techniques for future use in academia and industry.