Optimisation of enzyme concentrations for unbranched reaction chains: the concept of combined response coefficient

In the metabolic control theory, the control coefficient is a key parameter in quantifying the sensitivity of the flux towards an infinitesimal variation of enzyme activity. This concept does not apply just as it is for variations of enzyme concentrations whenever there is spatial, energy or resources limitations in the cell. Due to constraint on total enzyme concentration, the variation of concentration of any given enzyme may affect the concentrations of other enzymes. To take into account these correlations between enzyme concentrations, we propose the concept of "combined response coefficient". Its definition is similar to that of the control coefficient, but its mathematical expression is different. Its range of variation is from -infinity to +1, the null value corresponding to optimum enzyme concentration, i.e. to concentrations that maximise the flux, and the negative values to concentrations beyond the optimum value. A summation property could be derived using a simple weighting of the combined response coefficients, the sum of the weighed coefficient being 0.