# Quantified Maximum Entropy and Biological EPR Spectra

## S.M. Glidewell and B.A. Goodman

Scottish Crop Research Institute

Invergowrie

Dundee DD2 5DA

##
J. Skilling

Cavendish Laboratory

Madingley Road

Cambridge CB3 0HE

### Abstract

Free radicals are of importance in the functioning of all biological
systems. Many biologically important free radicals have very short
lifetimes and do not accumulate in tissues to levels which are readily
detectable directly. In consequence, their presence is either
determined indirectly by assay of stable end-products of radical
reactions or by EPR spectroscopic detection of adducts with spin
traps. This technique of spin-trapping has proved valuable in the
study of reactions involving biological fluids and tissues, but its
usefulnes is often limited by the low levels of adducts which are
formed and the requirement for small amounts of aqueous material in
the cavity of the spectrometer. Improvements in the signal to noise
ratio of spectra can sometimes be effected by accumulation of the
spectrum over time, but this is not an option in dynamic systems. In
such situations, numerical methods are the only way of optimising the
information which can be derived from the spectral data.
This work describes the use of a quantified maximum entropy method for
the optimisation of analytical information from EPR spectra. EPR
spectra are normally recorded as first derivatives of absorptions
and, like all experimental data, are distorted from the ideal
lineshape by a combination of systematic and instrumental factors. The
first and crucial step in the analysis of a spectrum by maximum
entropy methods is the definition of a function --- the point spread
function (PSF) which represents the *spread* of the data around a
point, or the distortion from ideality. For EPR spectra, the PSF is
selected by differentiating a lineshape comprising Gaussian,
Lorentzian and square wave contributions. Using this inital estimate
of the PSF, the most probable result is calculated as the frequency
disitribution of intensities which, convolved with the PSF, gives the
best fit to the experimental data. Discrepancies between calculated
and experimental data are used to guide the calculation by an
iterative procedure and exploration around the optimum result allows
the determination of the error associated with each line's frequency
and intensity. The ability to use composite PSFs lends further
refinement, either for the disentangling of multiline spectra or for
the determination of the intensity of weak spectra of known radicals,
a problem often encountered in biological EPR spectroscopy.

Quantified maximum entropy reconstruction of the complex multiline EPR
spectrum of paraquat allows the accurate determination of the 4
hyperfine splittings. The approach is then used on a system involving
unknown radical species formed by crushing lettuce in the presence of
a spin trap. This reconstruction reveals the presence of at least 2
radicals and the parameters derived suggest that one of them is a
hydroxyl radical adduct --- a result not obtainable by inspection.

MaxEnt 94 Abstracts / mas@mrao.cam.ac.uk