Resolving complex mixtures: trilinear diffusion data.

Complex mixtures are at the heart of biology, and biomacromolecules almost always exhibit their function in a mixture, e.g., the mode of action for a spider venom is typically dependent on a cocktail of compounds, not just the protein. Information about diseases is encoded in body fluids such as urine and plasma in the form of metabolite concentrations determined by the actions of enzymes. To understand better what is happening in real living systems we urgently need better methods to characterize such mixtures. In this paper we describe a potent way to disentangle the NMR spectra of mixture components, by exploiting data that vary independently in three or more dimensions, allowing the use of powerful algorithms to decompose the data to extract the information sought. The particular focus of this paper is on NMR diffusion data, which are typically bilinear but can be extended by a third dimension to give the desired data structure.