Zero-field nuclear magnetic resonance of chemically exchanging systems

Abstract

Zero- to ultralow-field (ZULF) nuclear magnetic resonance (NMR) is an emerging tool for precision chemical analysis. In this work, we study dynamic processes and investigate the influence of chemical exchange on ZULF NMR J-spectra. We develop a computational approach that allows quantitative calculation of J-spectra in the presence of chemical exchange and apply it to study aqueous solutions of [¹⁵N]ammonium (¹⁵N[Formula: see text]) as a model system. We show that pH-dependent chemical exchange substantially affects the J-spectra and, in some cases, can lead to degradation and complete disappearance of the spectral features. To demonstrate potential applications of ZULF NMR for chemistry and biomedicine, we show a ZULF NMR spectrum of [2-¹³C]pyruvic acid hyperpolarized via dissolution dynamic nuclear polarization (dDNP). We foresee applications of affordable and scalable ZULF NMR coupled with hyperpolarization to study chemical exchange phenomena in vivo and in situations where high-field NMR detection is not possible to implement.

Fig. 1

Chemical exchange scenarios important in the context of zero- to ultralow-field (ZULF) NMR. a Exchange affecting the entire J-coupled network. All atoms of the molecule can break chemical bonds between each other. Practically relevant examples include exchange in symmetric molecules such as H₂O, NH₄, etc. b Exchange affecting a subsystem of J-coupled network. One part of the spin system exchanges while the rest of the molecule stays intact. A practically relevant example is proton exchange in molecules containing more than a single coupled nucleus. Note that once dissociated, hydrogen (light blue) can attach to a different molecule, i.e., the exchange is intermolecular

Fig. 2

Simulated ZULF NMR spectra as a function of chemical exchange rate. a Exchange in the AX spin system (A is ¹H spin, X is ¹³C spin, J-coupling is 120 Hz). One can clearly see signal broadening as a function of dissociation exchange rate. b Exchange in the AXB spin system (X is ¹³C spin, A and B are ¹H spins, J_AX = 120 Hz, J_AB = 3 Hz, J_XB = 0 Hz). In both simulations, the forward reaction rate and the reverse reaction rate were considered to be equal: k = k_d = k_a[X] and k = k_d = k_a[B] for the case (a) and (b), respectively

Fig. 3

Chemical exchange in the ¹⁵N-labeled ammonium. a Molecular diagram of the chemical exchange in ¹⁵N${\mathrm{H}}_4^{+}$. Each of the four hydrogen atoms can dissociate with a kinetic rate constant k_d and associate back with a kinetic rate constant k_a (defined through the equilibrium constant K_a = k_d/k_a; pK_a = −log₁₀(K_a)). b Molar fractions of different forms of ammonia in solution as a function of pH. Color code is based on universal pH indicator. Note that for pH < pK_a ammonium is predominantly present in the form of ¹⁵N${\mathrm{H}}_4^{+}$ (rather than ¹⁵NH₃). c High-field (18.8 T) ¹⁵N NMR spectra as a function of pH. d ZULF NMR spectra of ¹⁵N${\mathrm{H}}_4^{+}$ as a function of pH. Note the difference in the pH range for the high-field and ZULF spectra

Fig. 4

Chemical exchange in the [2-¹³C]pyruvic acid. a ZULF NMR spectrum of [2-¹³C]pyruvic acid (single scan) hyperpolarized via dissolution dynamic nuclear polarization (dDNP). b Red circles—fraction of hydration for the pyruvic acid and its conjugate base measured with benchtop ¹H NMR (60 MHz) as a function of pH. Black line is fit with Supplementary Eq. 18. The inset demonstrates spectra at pH = −0.4 and 5.2, single and double asterisks denote ¹H NMR resonances of CH₃ group of the nonhydrated and hydrated forms of pyruvic acid, respectively. c Simulated ZULF NMR spectrum of [2-¹³C]pyruvate and [2-¹³C]lactate. Biochemical conversion of pyruvate to lactate is an important target for studies of metabolism in vivo. ZULF NMR detection of hyperpolarized molecules may endow narrow (sub-Hz) resonances separated by more than 100 Hz, a typical carbon-proton J-coupling value. Note that in the simulation, we did not consider relaxation/decoherence effects