Symbolic Control Analysis of Cellular Systems

Metabolic Control Analysis (MCA) is a powerful quantitative frame- work for understanding and explaining the relationships between the global steady-state properties of a cellular system in terms of control coefficients, and the local properties of the individual components of the system in terms of elasticities. The elasticities are apparent kinetic orders, which derive directly from the kinetic properties of the en- zymes. Since MCA relates elasticities to control coefficients through a matrix inversion, it allows one to predict and to quantify how the kinetics of individual enzymes affect the systemic behaviour of biolo- gical pathways. Most often this problem has been solved numerically, with algebraic and symbolic control analysis having been tackled less frequently. We present here a general implementation of the symbolic matrix inversion of MCA through symbolic algebraic computation. The algebraic expressions thus generated allow an in-depth analysis of where the control within a system lies and which parameters have the greatest effect on this control distribution, even if the exact values of the elasticities or control coefficients are unknown.