Proteins maximum-entropy processing

Figure 4.19 Electrospray spectra of a protein (a) after transformation, and (b) after maximum entropy processing. From applications literature published by Micromass UK Ltd, Manchester, UK, and reproduced with permission.

The raw electrospray spectrum obtained is shown in Figure 5.14. Maximum entropy processing of these data yielded the spectrum shown in Figure 5.15, which shows the presence of two species with molecular masses of 14293.6 and 14 309.6 Da, with the latter being attributed to partial oxidation of the parent protein. 

Green B.N., Hutton T., and Vinogradov S.N. (1996), Analysis of complex protein and glycoprotein mixtures by electrospray ionization mass spectrometry with maximum entropy processing, Method. Mol. Biol. 61, 279-294. 

The central engine of this data workflow is the process of spectral deconvolution. During spectral deconvolution, sets of multiply charged ions associated with particular proteins are reduced to a simplified spectrum representing the neutral mass forms of those proteins. Our laboratory makes use of a maximum entropy-based approach to spectral deconvolution (Ferrige et al., 1992a and b) that attempts to identify the most likely distribution of neutral masses that accounts for all data within the m/z mass spectrum. With this approach, quantitative peak intensity information is retained from the source spectrum, and meaningful intensity differences can be obtained by comparison of LC/MS runs acquired and processed under similar conditions. 

The solution of a protein crystal structure can still be a lengthy process, even when crystals are available, because of the phase problem. In contrast, small molecule (< 100 atoms) structures can be solved routinely by direct methods. In the early fifties it was shown that certain mathematical relationships exist between the phases and the amplitudes of the structure factors if it is assumed that the electron density is positive and atoms are resolved [255]. These mathematical methods have been developed [256,257] so that it is possible to solve a small molecule structure directly from the intensity data [258]. For example, the crystal structure of gramicidin S [259] (a cyclic polypeptide of 10 amino acids, 92 atoms) has been solved using the computer programme MULTAN. Traditional direct methods are not applicable to protein structures, partly because the diffraction data seldom extend to atomic resolution. Recently, a new method derived from information theory and based on the maximum entropy (minimum information) principle has been developed. In the immediate future the application will require an approximate starting phase set. However, the method has the potential for an ab initio structure determination from the measured intensities and a very small sub-set of starting phases, once the formidable problems in providing numerical methods for the solution of the fundamental equations have been solved. 

The maximum entropy method achieves a remarkable universality and unification based on common sense reduced to calculation . It has been applied to information theory, statistical mechanics, image processing in radio astronomy, and now to X-ray crystallography. The prospects for a computational solution to the phase problem in protein crystallography appear promising and developments in the field are awaited eagerly. 

Mehdi M, Alan SS, Wolfgang B, Glenn FK, Jeffrey CH, (2010) A non-uniformly sampled 4D HCC(CO)NH-TOCS Y experiment processed using maximum entropy frn- rapid protein sidechain assignment J Magn Reson 204 160-164... 

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