Phenotype phase plane analysis using interior point methods

Phenotype phase plane analysis is a linear optimization procedure which can be used to study the value of the objective function (a desired phenotype) as two variables (external substrates) vary simultaneously. Existing methods for phenotype phase plane analysis are based on computing shadow prices as defined in classical linear programming duality theory. Since different bases may produce different "shadow prices", we present here an alternative way to determine the phenotype phase plane based on so-called interior point methods, which unambiguously calculates the correct shadow prices. In addition, this work constitutes the first attempt at producing a mathematically rigorous algorithm to compute phenotype phase planes in a systematic way.