Reference deconvolution algorithms

Because online separations provide such a wealth of information about target proteins, interpretation becomes of critical importance in order to make full use of the data. The first step in any analysis of LC-MS data involves integration and deconvolution of sample spectra to determine protein mass and intensity. In manual analysis (Hamler et al., 2004), users identify protein umbrellas, create a total ion chromatogram (TIC), integrate the protein peak, and deconvolute the resulting spectrum. Deconvolution of ESI spectra employs a maximum entropy deconvolution algorithm often referred to as MaxEnt (Ferrige et al., 1991). MaxEnt calculates... 

Although a number of effective deconvolution algorithms do not use Fourier methods, these methods shed considerable light on the performance of the algorithms. For this reason, we introduce the Fourier transform and outline some of its most-useful properties. Only a brief treatment is given here. For additional detail, we again refer the reader to the excellent practical text on this subject by Bracewell (1978). 

Figure 8.2.7 Reference deconvolution applied to the methanol peak (a) original peak (b) methanol peak deconvolved to a 2 Hz Lorenzian lineshape (c) gradient-shifted methanol peak (d) gradient-shifted methanol peak deconvolved to the same 2 Hz Lorenzian lineshape (e) comparison of the sub-spectrum of the methanol sample using the subtraction algorithm with (sharp peak) and without (flattened peak) reference deconvolution. Reprinted from Hou, T., MacNamara, E. and Raftery, D., NMR analysis of multiple samples using parallel coils improved performance using reference deconvolution and multi-dimensional methods , Anal. Chem. Acta, 400, 297-305, copyright (1999), with permission of Elsevier Science...

When we speak of mathematical models for biology, we usually refer to formulae (such as the Hardy-Weinberg theorem, or the Lotka-Volterra equations) that effectively describe some features of living systems. In our case, embryonic development is not described by integrals and deconvolutions, and the formulae of the reconstruction algorithms cannot be a direct description of what happens in embryos. There is however another type of mathematical model. The formulae of energy, entropy and information, for example, apply to all natural processes, irrespective of their mechanisms, and at this more general level there could indeed be a link between reconstruction methods and embryonic development. For our purposes, in fact, what really matters are not the formulae per se, but... 

Although GC-MS spectral analyses and compound identification can be performed manually, the effort can be tedious, inefficient, and problematic for highly complex chromatograms. The authors laboratory makes productive use of a software package developed by the US Department of Defense and NIST for international treaty verification. The Automated Mass Spectral Deconvolution and Identification System (AMDIS) incorporates several algorithms to distill pure component spectra and associated data from intricate chromatograms, and then uses that information to assess whether the component can be attributed to a known compound in the reference database. 

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