REGULATION OF ENZYME-ACTIVITY IN ADSORPTIVE SYSTEMS .6. MODEL FOR ADSORPTION OF A HYSTERETIC ALLOSTERIC ENZYME

A kinetic model for an enzyme adsorptive system including a hysteretic allosteric enzyme is considered. It is assumed that one of the enzyme conformers is adsorbed to a support but does not bind the substrate, whereas the other binds the substrate but is not adsorbed to the suppo rt. The rate of the conformational change in the enzyme molecule is co mparable to the rate of catalytic breakdown of the enzyme-substrate co mplex, while the steps of enzyme adsorption and binding of the substra te to the enzyme are in rapid equilibrium. The transient enzyme kineti cs for this model are characterized by the appearance of lag period on the curves of product accumulation, Equations describing the dependen ce of the duration of the lag period on the parameters of the system ( concentrations of enzyme, substrate, and enzyme-binding sites of the s upport; equilibrium and kinetic constants; number of monomers in the e nzyme molecule) have been obtained by an analytical procedure for the following cases: 1) enzyme concentration low compared to the concentra tion of binding sites of the support; 2) concentration of binding site s of the support low compared to the enzyme concentration; 3) substrat e used at saturating concentrations. The dependences of the duration o f the lag period on the parameters of the system have been obtained fo r the general case by a numerical method. A linear approximation of th e dependence of the duration of a lag period on enzyme concentration w hich is valid at low enzyme concentrations has been obtained by an emp irical method.