NMR Signal Analysis: Determining ATP and Unknown Biochemical Contributions

[johnq2k7]

Suppose you acquire the 31P NMR signal from a region of muscle of a healthy subject using a 3 Tesla magnet. Assume that the signal has contributions from ATP,PCR, Pi, and from an unknown phosphorous containing biochemical. Assume that all decay shapes are exponential.

Note: H1- 42.575 MHz/T for y/2pi , 31P- 17.235 MHz/T for y/2pi, and 13C- 10.705 for y/2pi

31P- nucleus (chemical shifts), ATP-alpha= -7.52 ppm
ATP-beta= -16.26 ppm
ATP-gamma= -2.48 ppm
PCr= 0 ppm
Pi= 5.02 ppm

a.) Determine the ratio S_PCr@0/ S_ATP@0, where S_PCr@0 is the contribution to the intial signal amplitude from PCr, and S_ATP@0 is the contribution to the initial signal amplitude from ATP.

b.) If the peak in the spectrum from the unknown biochemical is centered at a frequency 100 Hz to the left of the Pi peak (where PCr is on the right of the Pi peak), determine the value of the chemical shift for the peak from the unknown chemical, with PCR as the reference peak.

c.) If the full width at half maximum (FWHM) of the peak from the unknown chemical is 10 Hz and its height s half that of the PCr peak, determine the concentration of the unknown chemical assuming that there is only one phosphorous nucleus per molecule.

Please help.. need a lot of help here!

 

[NateD]

a.) To determine the ratio S_PCr@0/ S_ATP@0, we can use the equation S_x@0 = I_x * exp(-y*B*Delta_x) where I_x is the initial signal amplitude of peak x, B is the standard magnet field strength, and Delta_x is the chemical shift of peak x. In this case, we have I_PCr = 1, Delta_x = 0 ppm for PCr, and I_ATP = 1/2, Delta_x = -8.39 ppm for ATP (average of the three ATP peaks). Plugging in these values, we get: S_PCr@0/ S_ATP@0 = exp(17.235 * 3 * 0) / exp(17.235 * 3 * -8.39) = exp(0) / exp(-50.17) = 1/ 5.35 x 10^-22. b.) To determine the value of the chemical shift for the peak from the unknown chemical, we can use the equation Delta_unknown = Delta_Pi + 100 Hz, where Delta_unknown is the chemical shift of the unknown peak and Delta_Pi is the chemical shift of the Pi peak. In this case, Delta_Pi = 5.02 ppm, so Delta_unknown = 5.02 ppm + 100 Hz = 5.02 ppm + 0.017235 ppm = 5.037235 ppm.c.) To determine the concentration of the unknown chemical, we can use the equation C_unknown = (FWHM*Height) / y, where C_unknown is the concentration of the unknown chemical, FWHM is the full width at half maximum of the unknown peak, Height is the height of the peak relative to the reference peak, and y is the gyromagnetic ratio of the nucleus. In this case, FWHM = 10 Hz, Height = 1/2, and y = 17.235 MHz/T, so C_unknown = (10 * 1/2) / 17.235 = 0.00058 mM.