1 H NMR z-spectra of acetate methyl in stretched hydrogels: Quantum–mechanical description and Markov chain Monte Carlo relaxation-parameter estimation Dmitry Shishmarev a , Bogdan E. Chapman a , Christoph Naumann a , Salvatore Mamone b , Philip W. Kuchel a,⇑ a School of Molecular Bioscience, University of Sydney, NSW 2006, Australia b School of Chemistry, Southampton University, SO17 1BJ, United Kingdom article info Article history: Received 8 August 2014 Revised 28 October 2014 Available online 18 November 2014 Keywords: Sodium acetate Stretched gelatin gel Residual dipolar couplings NMR spectroscopy z-Spectra Irreducible spherical tensors abstract The 1 H NMR signal of the methyl group of sodium acetate is shown to be a triplet in the anisotropic envi- ronment of stretched gelatin gel. The multiplet structure of the signal is due to the intra-methyl residual dipolar couplings. The relaxation properties of the spin system were probed by recording steady-state irradiation envelopes (‘z-spectra’). A quantum–mechanical model based on irreducible spherical tensors formed by the three magnetically equivalent spins of the methyl group was used to simulate and fit experimental z-spectra. The multiple parameter values of the relaxation model were estimated by using a Bayesian-based Markov chain Monte Carlo algorithm. Ó 2014 Elsevier Inc. All rights reserved. 1. Introduction A z-spectrum is derived from an NMR experiment that is a var- iant of the saturation-transfer experiment, involving a radio-fre- quency (RF) field applied to the sample over a range of frequencies, prior to conventional pulse-and-acquire detection [1]. As the RF field perturbs the populations of various quantum states of the nuclear spin system, some of the corresponding reso- nances in the NMR spectrum are suppressed. The outcome of the experiment is presented as a graph of the overall integral of the probed signal as a function of the offset frequency of the RF irradi- ation field. The measured integral is proportional to the residual z- magnetisation of the corresponding NMR spin population after the saturation pulse has been applied, hence the name ‘z-spectrum’. Studies, in which z-spectra have been employed, include defin- ing conditions that affect the formation of hydrogels [2], measuring T 2 relaxation times [3], studying radiation damping effects [4], and chemical exchange processes [5]. The MRI counterpart of z-spectra is the widely used chemical exchange saturation transfer (CEST) spectroscopy; it can be used to quantify metabolites and proteins in tissues by means of amplification of their NMR signal via satura- tion transfer to the water resonance [6–9]. Recently, an adaptation of the CEST method has been called ‘‘dark-state exchange saturation transfer’’ (DEST) and it can be used to study populations and kinetics of NMR-invisible macromolecular states [10,11]; this experiment was used previously to quantify the otherwise spectroscopically invisible calcium complex of 5-FBAPTA (5-fluoro1,2-bis(o-amino- phenoxy)ethane-N,N,N 0 ,N 0 -tetraacetic acid) in haemolysates [12]. z-Spectra of quadrupolar nuclei in the anisotropic environment of stretched hydrogels, display a characteristic feature: sharp dips located between the frequencies of the main Zeeman transitions [13–15]. The presence of the dips is due to multiple-quantum tran- sitions, as has been shown in the quantum–mechanical description of the relaxation properties of several quadrupolar nuclei: 2 H (spin quantum number, I = 1) [14], 23 Na (I = 3/2) [13] and 7 Li (I = 3/2) [16,17]. Similar effects are observed for dipolar-coupled spins of the methylene group of glycine [13,18]. These peculiar features of z-spectra of quadrupolar- and dipo- lar-split resonances can lead to a pitfall when conducting conven- tional saturation-transfer experiments [19], and they can be used http://dx.doi.org/10.1016/j.jmr.2014.11.001 1090-7807/Ó 2014 Elsevier Inc. All rights reserved. Abbreviations: NMR, nuclear magnetic resonance; RF, radio-frequency; MRI, magnetic resonance imaging; CEST, chemical exchange saturation transfer; DEST, dark-state exchange saturation transfer; I, spin quantum number; RDC, residual dipolar coupling; IST, irreducible spherical tensor; J-coupling, scalar coupling; DD- coupling, dipole–dipole coupling; MCMC, Markov chain Monte Carlo. ⇑ Corresponding author at: School of Molecular Bioscience, Building G08, University of Sydney, NSW 2006, Australia. Fax: +61 2 9351 4726. E-mail address: philip.kuchel@sydney.edu.au (P.W. Kuchel). Journal of Magnetic Resonance 250 (2015) 29–36 Contents lists available at ScienceDirect Journal of Magnetic Resonance journal homepage: www.elsevier.com/locate/jmr