Response to External Effectors


With the control coefficients we try to answer the question of "by how much does each step of a pathway control a system variable?". However it is also very important to quantify the effects of substances foreign to the pathway on its variables.

Internal and External Effectors

The enzymes of a metabolic system can be affected by two types of biochemical substances: those that are produced in the system itself (the internal effectors), and those that are added to the system from an external source (external effectors). Substances of the latter type can be, for example, drugs added to the system or hormones produced by other cells of the same organism. The internal effectors are variables of the system and, therefore, are not primary causes, but rather effects. Their role in the control of the system is that of being the "conveyor belts" of the machinery, which is taken into account by the connectivity relations, described in the previous section. On the other hand, the external effectors are causes, rather than effects (as they are under control of agents external to the system), therefore it is useful to quantify their effect on the system.

The Partitioned Response Coefficients

The primary effect of an external effector on a metabolic pathway is to affect (enhance or reduce) the rate of some of the enzymes. Such an effect is quantified by the enzyme elasticity coefficients. But as these rates change, so will the system variables of the pathway: the flux(es) and internal metabolite concentrations. How the latter change with changes in rates of the enzymes is quantified by the flux- and concentration- control coefficients. Thus the effect of the external effector (X) on a pathway variable (A) is:

C k A ε [ X ] i                                ( 9 )

where the effector X affects the enzyme k only. More generally external metabolites affect more than one enzyme of the pathway, and so the change in the system variable is the sum of the effects through all the enzymes whith which the effector interacts. This is know as the partinioned response coefficient (Kacser & Burns 1973) and is given by:

R X A = i C i A ε [ X ] i                 ( 10 )

where the summation is over all affected enzymes.