Analysis of metabolism by mathematical programming techniques

A method is presented for analyzing metabolic interactions by procedures based on mathematical programming techniques. In the procedures described it is assumed that the organism has (through natural selection) maximized (within the constraints imposed on it by its genetic constitution) its fitness to the environment. A practical experimental procedure is described through which the constraints imposed on reaction rates can be observed and from which the metabolic objective function which, it is presumed, metabolism has optimized can be calculated. A method for testing the validity of the objective function is given. Discussion is carried out in terms of a two-dimensional example but the procedures are valid for any number of dimensions. The results of the procedures are expressed by statements of the sort: the metabolic interactions of the cell are such that Q is maximized where Q = a₁x₁ + a₂x₂ + ... + a_nx_n, where a₁, ..., a_n are constants and x₁, ..., x_n are reaction rates. Some possible uses of metabolic objective functions are given.