Before revision: Constraint-based modelling of metabolic networks often gives rise to a linear programming problem. Mathematically, there always exists a dual to any linear programming problem, with dual variables known as shadow prices. Here we analyse the structure of the dual problem and the properties of the shadow prices, for typical constraint-based metabolic models. We apply our results to a representative set of recent genome-scale metabolic reconstructions. The dual problem is found to have an elegant structure. The shadow prices are to be interpreted as yield coefficients Varma and Palsson, J. theor.
After revision:  Varma and Palsson, J. theor.