Optimal metabolic control design

In a previous work [Acerenza, L. (1993). Metabolic Control Design. J. theor. Biol. 165, 63-85] we devised a procedure to design metabolic systems that respond according to pre-established patterns. This procedure includes the mandatory structural and kinetic constraints that narrow the spectrum of responses. In an evolutionary context, the structural and functional features shown during the history of the system would also be conditioned by other factors. Here we incorporate to the Metabolic Control Design procedure two additional requirements that could have influenced metabolic evolution. These are constraints that result from the adaptation to the environment (represented by independent control coefficients that take fixed values) and optimization of metabolic variables at constant total enzyme concentration. To illustrate the general strategy we consider metabolic systems consisting of r reaction steps where the variables are the fluxes, internal metabolite concentrations, enzyme concentrations and control coefficients. In our conditions the number of degrees of freedom, calculated as number of variables minus number of number of relationships, is r - 1. A detailed analysis of three particular schemes, unbranched chain of two and three steps and branch point, with simple linear rate laws is given. Novel results are obtained for the optimization of the input flux of the simple branch point. In the well studied case where there are no evolutionary constraints one of the limbs of the branch point disappears. However, for particular independent control coefficients, when we impose to the control coefficient a fixed value, the branched structure may or may not persist depending on the range to which the fixed value belongs.