Monte Carlo sampling and principal component analysis of flux distributions yield topological and modular information on metabolic networks

The work presented here uses Monte Carlo random sampling combined with flux balance analysis and linear programming to analyse the steady-state flux distributions on the surface of the glucose–ammonia phenotypic phase plane of an Escherichia coli system grown on glucose-minimal medium. The distribution of allowable glucose and ammonia uptake rates showed a triangular shape, the apex corresponding to maximum growth rate. The exact shape, e.g. the diagonal boundary is determined by the relative amounts of nutrients required for growth. The logarithm of flux values has a normal distribution, e.g. there is a log normal distribution, and most of the reactions have an order of magnitude between 10−1 and 1. The increase in the number of blocked reactions as growth switched from aerobic to micro-aerobic phase and the presence of alternate networks for a single optimal solution were both reflections of the variability of pathway utilization for survival and growth. Principal component analysis (PCA) provided us with significant clues on the correlations between individual reactions and correlations between sets of reactions. Furthermore, PCA identified the most influential reactions of the system. The PCA score plots clearly distinguish two different growth phases, micro-aerobic and aerobic. The loading plots for each growth phase showed both the impact of the reactions on the model and the clustering of reactions that are highly correlated. These results have proved that PCA is a promising way to analyse correlations in high-dimensional solution spaces and to detect modular patterns among reactions in a network.