Interpretation of 31P MRS Spectra in Determining Intracellular Free Magnesium and Potassium Ion Concentrations

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Abstract
The current paper develops a simple mathematical model for the determination of the concentration of ionic species using the chemical shifts of ATP from phosphorus magnetic resonance spectroscopy (31P MRS) spectra. An iterative method is used to evaluate the equilibrium constants for a range of Mg/ATP equilibria. Initially, an expression for free magnesium concentration is determined by consideration of four equilibria. We then demonstrate how any number of equilibria may be included using this simplified analysis, by incorporation of pseudo equilibrium constants. This approach may be applied to the interpretation of both ex vivo and, more importantly, in vivo MRS spectra. Furthermore, the authors suggest that the commonly used equation for determining free intracellular magnesium concentration as presented by Gupta and colleagues is an oversimplification, particularly under conditions of fluctuating pH.