Decoding two-dimensional complex multicomponent separations by autocovariance function.

A new method for decoding two-dimensional (2D) multicomponent separations based on the use of the 2D Autocovariance function (2D-ACVF) has been developed. Theoretical models of single component (SC) spot distributions in 2D separations, both random and structured, are developed as the basis for a nonlinear estimation of both sample and separation system parameters from experimental 2D separations. The number of SCs, the average spot size, the spot capacity, and the saturation factor can be evaluated in the case of random SC spot patterns. The procedure was validated by extensive numerical simulation under conditions close to those usually found in GC x GC or 2D-polyacrylamid gel electrophoresis of proteins. The worse precision degree was no greater than 10% in the case of maximum spot density. This imprecision was fully accounted for, and it seems acceptable owing to the intrinsic statistical character of the estimation method. Structured multicomponent 2D separations, where SCs are linked by linear relationships, give rise to specific structured patterns in 2D-ACVF plots from which the parameters (phase and frequency) of the structured SC sequences can be evaluated: the study of 2D-ACVF makes it possible to decode multicomponent 2D separation, that is, to determine the number, relative abundance, and structural similarities of the single components. Pertinent expressions of the theoretical 2D-ACVF were derived for simple cases, and a procedure for decoding cases of structured 2D separations was developed and applied. It was shown that 2D separations containing both random and structured patterns of SC spots give rise to 2D-EACVF, which is the superimposition of the two component parts. This feature allows one, in principle, to decode the two components. The relevance of these results for Giddings sample dimensionality and separation dimensionality and their effective experimental evaluation is discussed.