1. Consider a metabolic pathway in which flux is 85% of Vmax for an enzyme that catalyzes the reaction of an intermediate in the pathway. What is the margin of safety for increases in the rate at which the initial metabolite enters the sequence if the concentration of the intermediate may not rise more than 50% without damaging the cell? What is the margin of safety for increases in flux if the intermediate may not increase by more than two-fold? five-fold? 2. Repeat Problem 1 while considering a metabolic pathway in which the flux is 35% of Vmax. 3. It is often noted that the concentrations of many metabotites in living cells are somewhat below the Km values of the enzymes that act upon them. What determines the physiologic steady-state levels of intermediates in motabolie pathways? (The steady-state levels of these intermediatesmust De-distinguished from the concentrations of branchpoint metabolites and ond products that are usually controlled by specific and complex regulatory interactions.) 4. In agreement with the first sentence of Problem 3, the activities of most enzymes seem to be held at levels that result in normal fluxes of between 10% and 35% of Vmax. By now you should realize that selection pressures in the course of evolution make such values reasonable. What is the concentration of substrate as a function of Km when flux is 0.30 of Vmax ? Determine the boundaries on the ratio of [S] to Km (at "normal" values of flux) if the levels of enzymes are sufficient to allow the flux to increase three-fold above "normal" values without increasing the concentrations of the intermediates by more than a factor of eight. Determine the boundaries on the ratio of [S] to Km if the levels of enzymes are sufficient to allow the flux to increase four-fold without increasing [S] by more than a factor of ten? How would you answer someone who argues that it is wasteful for a cell to make more enzyme than just enough to permit the reaction rates required by "normal" conditions