A bio molecular interpretation of g-strain

Our finding that linewidth anisotropy in biomolecular EPR spectra can be described by a statistical theory in which the random variables that cause the broadening are fully correlated, does not only make analysis by simulation practical it also holds a message on the nature of the ultimate source of the broadening if the three principal elements of the p-tensor are fully correlated, then they should find their cause in a single, scalar quantity. 

A stress that is describable by a single scalar can be identified with a hydrostatic pressure, and this can perhaps be envisioned as the isotropic effect of the (frozen) medium on the globular-like contour of an entrapped protein. Of course, transduction of the strain at the protein surface via the complex network of chemical bonds of the protein 3-D structure will result in a local strain at the metal site that is not isotropic at all. In terms of the spin Hamiltonian the local strain is just another field (or operator) to be added to our small collection of main players, B, S, and I (section 5.1). We assign it the symbol T, and we note that in three-dimensional space, contrast to B, S, and I, which are each three-component vectors. T is a symmetrical tensor with six independent elements  

We can now extend the spin Hamiltonians by making combinations of T, with B, and/or S, and/or I, and since we are interested in the effect of strain on the g-value from the electronic Zeeman interaction (B S), the combination of interest here is T B S. 

The spin Hamiltonian encompassing electronic Zeeman plus strain interaction for a cubic S = 1/2 system is (Pake and Estle 1973 Equation 7-21)  

Note that the Zeeman interaction for a cubic system results in an isotropic g-value, but the combination with strain lowers the symmetry at least to axial (at least one of the 7 -, 0), and generally to rhombic. In other words, application of a general strain to a cubic system produces a symmetry identical to the one underlying a Zeeman interaction with three different g-values. In yet other words, a simple S = 1/2 system subject to a rhombic electronic Zeeman interaction only, can formally be described as a cubic system deformed by strain. 

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