Articles | Volume 2, issue 1
https://doi.org/10.5194/mr-2-421-2021
https://doi.org/10.5194/mr-2-421-2021
Research article
 | 
15 Jun 2021
Research article |  | 15 Jun 2021

Extended Bloch–McConnell equations for mechanistic analysis of hyperpolarized 13C magnetic resonance experiments on enzyme systems

Thomas R. Eykyn, Stuart J. Elliott, and Philip W. Kuchel

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Cited articles

Albers, M. J., Bok, R., Chen, A. P., Cunningham, C. H., Zierhut, M. L., Zhang, V. Y., Kohler, S. J., Tropp, J., Hurd, R. E., Yen, Y. F., Nelson, S. J., Vigneron, D. B., and Kurhanewicz, J.: Hyperpolarized 13C lactate, pyruvate, and alanine: noninvasive biomarkers for prostate cancer detection and grading, Cancer Res., 68, 8607–8615, https://doi.org/10.1158/0008-5472.Can-08-0749, 2008. 
Allard, P., Helgstrand, M., and Hard, T.: The complete homogeneous master equation for a heteronuclear two-spin system in the basis of cartesian product operators, J. Magn. Reson., 134, 7–16, https://doi.org/10.1006/jmre.1998.1509, 1998. 
Andersson, L., Karlsson, M., Gisselsson, A., Jensen, P., Hansson, G., Månsson, S., in 't Zandt, R., and Lerche, M.: Hyperpolarized 13C-DNP-NMR allow metabolic in vitro studies over minutes, Proc. Intl. Soc. Mag. Reson. Med., Berlin, Germany, 19–25 May 2007, 15, 542, 2007. 
Ardenkjaer-Larsen, J. H., Fridlund, B., Gram, A., Hansson, G., Hansson, L., Lerche, M. H., Servin, R., Thaning, M., and Golman, K.: Increase in signal-to-noise ratio of >10,000 times in liquid-state NMR, P. Natl. Acad. Sci. USA, 100, 10158–10163, https://doi.org/10.1073/pnas.1733835100, 2003. 
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Short summary
An approach is described for formulating the kinetic master equations of the time evolution of hyperpolarized NMR signals in reacting (bio)chemical systems. We take a stepwise approach to formulate mathematical models of enzyme systems that agree with standard descriptions of (bio)chemical kinetics while remaining capable of describing the time evolution of magnetization described by the Bloch–McConnell equations.