Metabolic Control Analysis

The metabolic control analysis quantifies how variables, such as fluxes and species concentrations, depend on the systems parameters. If the systems consists of r reactions and m species, then the matrices of control coefficients includes m-by-r elasticity matrix E, m-by-r concentration control matrix C ^S and r-by-r flux control matrix C ^J calculating by the formulas

Here v is a vector of reaction rates, S is a vector of species concentrations, N = L × N_R is the stiochiometric matrix decomposition generated by the mass conservation analysis, and Id is r-by-r identity matrix¹. We also scaled all elements E_i,j, C^S_i,j and C^J_i,j of these matrices with the coefficients S_j / v_i, v_j / S_i and v_j / v_i respectively.

References

1. C Reder, "Metabolic control theory: a structural approach". J. Theor. Biol., 135:175-201, 1988.