A functional enzyme displays activity with at least one substrate and can be represented by a vector in substrate–activity space. Many enzymes, including GSTs (glutathione transferases), are promiscuous in the sense that they act on alternative substrates, and the corresponding vectors operate in multidimensional space. The direction of the vector is governed by the relative activities of the diverse substrates. Stochastic mutations of already existing enzymes generate populations of variants, and clusters of functionally similar mutants can serve as parents for subsequent generations of enzymes. The proper evolving unit is a functional quasi-species, which may not be identical with the ‘best’ variant in its generation. The manifestation of the quasi-species is dependent on the substrate matrix used to explore catalytic activities. Multivariate analysis is an approach to identifying quasi-species and to investigate evolutionary trajectories in the directed evolution of enzymes for novel functions.

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