Spin counting

The EPR spectrum is a reflection of the electronic structure of the paramagnet. The latter may be complicated (especially in low-symmetry biological systems), and the precise relation between the two may be very difficult to establish. As an intermediate level of interpretation, the concept of the spin Hamiltonian was developed, which will be dealt with later in Part 2 on theory. For the time being it suffices to know that in this approach the EPR spectrum is described by means of a small number of parameters, the spin-Hamiltonian parameters, such as g-values, A-values, and )-values. This approach has the advantage that spectral data can be easily tabulated, while a demanding interpretation of the parameters in terms of the electronic structure can be deferred to a later date, for example, by the time we have developed a sufficiently adequate theory to describe electronic structure. In the meantime we can use the spin-Hamiltonian parameters for less demanding, but not necessarily less relevant applications, for example, spin counting. We can also try to establish... 

Molecular spectra can be analyzed for spectrometric or for spectroscopic purposes. The term spectrometric usually refers to compound identification (linking a signal to a known structure) and to the determination of its concentration. The term spectroscopic stands for interpretation of the spectrum in terms of structure (chemical, electronic, nuclear, etc.). In this chapter we will look as some theoretical and practical aspects of a key spectrometric application of bioEPR, namely, the determination of the concentration of paramagnets, also known as spin counting. Subsequently, we consider the generation of anisotropic powder EPR patterns in the computer simulation of spectra, a basic technique that underlies both spectrometric and spectroscopic applications of bioEPR. 

The procedure of spin counting is then to use the EPR spectrum of another paramagnetic compound as an external standard (which we will label K to avoid confusion with the spin S) of known concentration (cK) to obtain the unknown (U) concentration (cv) of the paramagnetic compound of interest as... 

It is well possible to do a spin counting when only part of the EPR powder spectrum is available, for example, because some features are broadened beyond detection or are at field values beyond the maximum limit of the magnet, or because the spectrum is disturbed by overlap of spectra from other paramagnets. Two conditions... 

Figure 12.5. If desired, these small effects can easily be exactly included by letting the simulation program output all the relative energy levels for the experimentally used frequency and for the canonical orientation that corresponds to geff = 10.4, and then using these values in Equation 12.3. The outcome of Equation 12.3 for a given experimental temperature is required for spin counting (determination of the concentration of the S = 7/2 system) using the single-peak integration procedure explained in Section 6.2.

Equation 12.3 is readily rewritten for any other half-integer spin. For integer spins we have one singulet (the ms = 0 level) and S doublets, but we do not bother writing down the modified equation, because spin counting for integer-spin systems in the weak-field limit is near-to-impossible (Hagen 2006). 

The pH-dependence is of particular relevance for groups that occur in three subsequent oxidation states because the two reduction potentials j° and E° in Equation 13.14 in general have different pH dependence. For example, the paramagnetic Wv state of the tungsto-enzyme DMSO reductase affords an EPR signal with a maximal spin count of 40% of protein concentration at pH = 5 when E° - E° +10 mV, whereas at pH = 8 no signal is detected at all because E° E° (Hagedoorn et al. 2003). 

The 13C NMR study utilized cross polarization-magic angle spinning (CP-MAS) with spin counting. The elemental and functional group analyses provided input for a series of analytical constraints calculations that yield an absolute upper limit for the amount of aromatic carbon and most probable estimates of both aromatic and non-carboxyl aliphatic carbon in each sample. Spin counting experiments demonstrate that less than 50% of the... 

PHYSICAL ORGANIC CHEMISTRY NOMENCLATURE Spin counting,... 

It is important to note the quantitative character of NMR spectroscopy. By use of an internal or external intensity standard, a spin counting via the comparison of the signal intensities can be performed. In the case of an external intensity standard, the same spectroscopic parameters must be used, and the effect of Curie s law (Eq. (25)) in experiments at elevated temperatures has to be taken into account. 

Smernik, R. J., and Oades, J. M. (2000a). The use of spin counting for determining quantitation in solid state C-13 NMR spectra of natural organic matter 1. Model systems and the effects of paramagnetic impurities. Geoderma 96,101-129. 

Figure 15.8 Examples of spectral integration and normalization. Spectra shown were obtained with nitroxide label 14 (Fig. 15.3C). Acquisition parameters are listed in Table 15.1, except that number of scans = 4 and number of points = 1024. (A) Spectrum of an aqueous sample of a 23-nt RNA, together with its 1st and 2nd integrals. (B) Spectral comparison between a 23-nt RNA (40 gM, dotted line) and a 49-nt RNA (30 jiM, sobd Une). Comparison of the normalized spectra is not skewed by the different amount of labeled RNAs used in the measurement, and reports different nitroxide behavior due primarily to the difference in RNA size. (C) An example of spin counting. The calibration curve was generated by linear fitting (solid Une) of data points (sobd square) obtained using tempol solutions of various concentrations. Using this calibration curve, the sample measured in (A) was found to contain 37.5 gM of spins ( sample = 2.5). Based on an RNA concentration of 40 jiM, the nitroxide labeling efficiency was determined to be 93.6%.

Create a Hahn-echo sequence with 16/32 ns in one channel and optimize the echo intensity. Do the same in a second channel and adjust its phase 180° to the first cannel. Both channels are used for the two-step phase cycle. Running the experiment with the two-step phase cycle eliminates receiver offsets and allows reading off the real echo signal intensity, which is important for accurately determining Vx in spin counting experiments (Section 5.1). 

Figure 4.8 Spin orientation in d-multiplets with up to 10 electrons in spherical atoms that obey the exclusion principle. The spin count is defined as a = 2 Ylms.

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