Two-enzyme active transport in vitro with pH induced asymmetrical functional structures. III. Discussions based on numerical treatments of the time-dependent evolutions.

Three complementary models have been considered in which pH gradients (step function, linear pH or linear H+) impose asymmetry on a two-enzyme mixture. If the "combined pH dependences" of enzymes is pro-asymmetrical, the pH gradient induces an asymmetrical distribution of potential activities ("latent" asymmetry of functional structure). When substrate is added, "developed" asymmetry of effective activities appears which results in "substrate space wave" and pumping when the catalysed reaction couple is "inversible". It is shown that only one steady state exists for a given boundary condition and is attained when the "combined effective activity" of enzymes is nil; the stationary flux with symmetrical boundaries or the stationary load with moving boundaries is proportional to "effective global activities" of enzymes. "Equivalent square models" could be proposed that would be able to describe "functional" or "permanent" structure pumps as well. These models belong to the thermodynamic branch and the asymmetrical "space wave" substrate concentration profiles obtained must be distinguished from dissipative structures. It appears that such primary active transport pumps are chemical equivalents of heat pumps.