Determination of the pKa and Concentration of NMR-Invisible Molecules and Sites Using NMR Spectroscopy

The goal of this study is to address the limitations of traditional NMR methods in measuring the dissociation constants (pKa) of molecules, especially for polymers, biomolecules, and inorganic species that lack favorable pH-dependent NMR properties. Existing methods rely on nonlinear fitting of chemical shifts across a pH range, which often fails for complex or poorly resolved spectra. This study presents an innovative approach to determine pKa values and acidic species concentrations by quantifying the removal of acidic protons along a concentration gradient of an organic base in a single, automated ^1H chemical shift imaging experiment. The method avoids the need for direct observation of analyte resonances, bypasses spectral overlap challenges, and provides a simpler, more reliable alternative to nonlinear fitting routines.

The original article

Determination of the pKa and Concentration of NMR-Invisible Molecules and Sites Using NMR Spectroscopy

Haider Hussain, Yaroslav Z. Khimyak, Matthew Wallace

Anal. Chem. 2024, 96, 50, 19858–19862

https://doi.org/10.1021/acs.analchem.4c03596

licensed under CC-BY 4.0

Selected sections from the article follow. Formats and hyperlinks were adapted from the original.

Abstract

NMR spectroscopy is a very powerful tool for measuring the dissociation constants (pK_a) of molecules, requiring smaller quantities of samples of lower purity relative to potentiometric or conductometric methods. However, current approaches are generally limited to those molecules possessing favorable pH-dependent NMR properties. Typically, a series of 1D experiments at varying pH are performed, and the pK_a is obtained by fitting the observed chemical shift of the analyte as a function of pH using nonlinear routines. However, the majority of polymers, biomolecules, and inorganic species do not present favorable NMR resonances. Either the resonances are not observable or too broad, or the unambiguous interpretation of the NMR data is impossible without resorting to complex 2D experiments due to spectral overlap. To overcome these fundamental limitations, we present a method to obtain the pK_a values and concentrations of acidic species without their direct observation by NMR. We instead determine the quantity of acidic protons removed from the species along a concentration gradient of an organic base in a single ¹H chemical shift imaging experiment that can be run under automation. The pK_a values are determined via simple linear plots, avoiding complex and potentially unreliable nonlinear fitting routines.

Introduction

The acid dissociation constant, K_a, is a fundamental property which can be used to predict whether a molecule or ion will be protonated or deprotonated under different conditions. (1) K_a, typically represented by its negative logarithm pK_a, attracts significant interest in the areas of food science, pharmaceutical chemistry, and organic synthesis among other areas. (2) In drug discovery, pK_a values are used to predict drug–target interactions and drug solubility. (3) In materials science, the pK_a of polymers provides information about their self-assembly and complexation properties. For example, an understanding of the pK_a value of nucleic acid–polymer complexes is needed to prepare stable nucleic acids for therapeutic use. (4) Additionally, inorganic ions such as phosphorus or nitrogen species play an important role in biological systems while proteins exhibit a pH-dependent charge which determines their solubility, stability, and separation properties. (5)

NMR spectroscopy is a valuable technique to measure pK_a as it offers the advantages of studying analytes using small volumes with equipment that is available in most research institutions. (6) Furthermore, we demonstrated how, when the analyte can be observed by ¹H NMR, pK_a can be determined using a combination of pH gradients and 2D chemical shift imaging (CSI). (7) This allows for a “single shot” determination of pK_a in one NMR experiment, saving material and time. (7−9) However, a restriction on most NMR methods is that they require the analyte to display chemical shifts which can be clearly observed to change as a function of pH, or else require the concentration of analyte to be known. (10) However, not all systems of interest can be characterized in this manner. A striking case is polymeric systems with molecular weights above 20,000 g/mol that typically display very broad resonances. (11) Additionally, even for systems that have a lower molecular weight, given enough complexity, the spectral overlap will make the resolution of separate resonances impractical. The ChEMBL database displays 1,913,280 small molecules that are preclinical, of which approximately 20% have a molecular weight over 600 g/mol and are therefore likely to exhibit overalpping resonances on a standard ¹H NMR spectrum. (12) Moreover, the BMRB (Biological Magnetic Resonance) databank contains more than 15,000 entries regarding peptides and proteins that can be investigated using solution-state NMR, but for which 2D NMR experiments and isotopic labeling would be needed in many cases to assess their pH-dependent behavior. (13) Such “NMR restricted” molecules and ions are of great interest in a variety of fields and would otherwise benefit from pK_a determination by NMR.

Here, we present a more general NMR method that has the capacity to encompass these restricted molecules, expanding the range of molecules that can be probed by NMR, hence providing avenues for exploring their pK_a-associated activity that was not previously possible while also enabling the analysis of species whose toxicity, volatility, or limited availability may preclude the use of conventional potentiometric titrations. The new method determines the pK_a of molecules with no or poorly observable NMR resonances by measuring the quantity of protons transferred to a basic indicator along pH gradients in 5 mm NMR tubes. We demonstrate the measurement of the pK_a values of a range of small organic and inorganic molecules in excellent agreement with the literature values. We apply our method on complex systems to determine the effective pK_a of poly(acrylic acid) and estimate the isoelectronic point, pI, of wheat germ agglutinin.

Figure 1. (a) A concentration gradient of a basic indicator is established in an NMR tube, allowing measurement of the quantity of protons transferred from acid to base as a function of pH. (b) Plot of 1/κ versus 10–pH for 60 mM H3PO4 (left) and plot of pH (black circle) and Cindicator (red diamond) versus height from tube base (right). (c) Plot of 1/κ versus 10–pH for 10 mM boric acid (left) and plot of pH and Cindicator versus height from tube base (right).

Experimental Section

NMR

Experiments were performed at 298 ± 0.5 K on a Bruker Avance III 500 MHz spectrometer operating at 500.21 MHz for ¹H. CSI experiments were performed using a gradient phase encoding sequence based on that of Trigo-Mouriño et al. (14) but incorporating double echo excitation sculpting for water suppression (Bruker library zgesgp), with the ramped gradient pulse included at the end of the water suppression block. A balancing delay to compensate for this gradient pulse and recovery delay (200 μs) were added to the last echo of the water suppression block, while a spoil gradient pulse (1 ms, 25 G/cm) was inserted at the end of the relaxation period (2.0 s) to destroy any remaining transverse magnetization (Section S14). The signal acquisition time was 2.04 s with a sweep width of 16 ppm. The encoding gradient pulse (172 μs, smoothed square) was varied between −18.8 and 18.8 G/cm in 64 steps. Here, 4 ms Gaussian 180° pulses were employed for water suppression, while the hard 90° pulse was 10 μs. Four scans were acquired at each step, while 16 dummy scans were acquired prior to signal acquisition, giving a total acquisition time of 20 min. The vertical range of the experiment (cnst0, Section S14) was set to 2.6 cm, and the spatial resolution can thus be assumed equal to 0.41 mm, such that each 1D spectrum in the data set arises from a 0.41 mm thick slice. All spectra were referenced to DSS (0 ppm). NMR data were processed using Bruker TopSpin 3.6.5. C_indicator and the pH of each row of the CSI data set were determined experimentally from the integrals and chemical shifts of the indicator resonances, respectively, on each spectrum. C_analyte was determined by linear fitting, as described below. Scripts for the acquisition and processing of NMR data are provided in Section S15–17, while a spreadsheet is supplied as additional Supporting Information.

Conclusion

We have shown how the pK_a of any substance can be determined in a single NMR experiment at a concentration of acidic sites as low as 2 mM. With a standard NMR sample volume of ca. 500 μL, our approach provides a substantial saving in sample quantity and experimental time relative to conventional workflows based on 2D heteronuclear NMR experiments and manual adjustment of the sample pH. Furthermore, by avoiding completely the requirement for direct observation of the molecule of interest, we can analyze any molecule or ion including those that do not exhibit observable NMR resonances (NH₃OH⁺), or else resonances that are too broad (PAA) or not pH responsive (WGA) for analysis based on the pH-dependence of their ¹H chemical shifts. Knowledge of pK_a of these large systems could be used to inform the design of polymer–drug conjugates or liposomal formulations. (44) Our approach could potentially be extended to study the degree of proton transfer between acidic and basic partners at different volume fractions of organic solvent, greatly accelerating the determination of the pK_a of compounds with insufficient solubility for direct analysis in water. (45−47)