The kinetics of uptake and breakdown: antibiotic resistance

Abstract

where it is proposed that allosteric enzymes, which usually possess co-operative kinetics, are the sites of highest flux control. What possible advantages can one attach to systems which contain such enzymes but do not, as these results indicate, possess high flux control? According to the flux Control Coefficient summation theorem (Kacser & Burns, 1973), if some enzyme sites have low flux Control Coefficients then other sites must compensate by having higher flux Control Coefficients. In the example studied here, it has been shown that enzyme sites which display positive co-operativity cannot simultaneously have high flux Control Coefficients. This must mean that other sites take up flux control in order to satisfy the summation theorem. In this example it can be shown that enzymes upstream from the co-operative enzyme gain in flux control at the expense of flux control at the co-operative enzyme. The Response Coefficient which is a measure of the response of the pathway flux to changes in external effectors, is the product of the flux Control Coefficient and elasticity of the external effector at the entry point into the pathway. In the example here, this would equal the flux Control Coefficient of first enzyme multiplied by the elasticity of the first enzyme with respect to the starting metabolite, &. Since the presence of positive co-operativity in the fourth enzyme transfers flux control upstream, this will result in a higher value for the Response Coefficient. Moreover, the closer the allosteric enzyme is to the start of the pathway, the greater is the rise in the Response Coefficient. We conclude: (1) The presence of positive co-operativity in a linear pathway results in the transfer of flux control upstream away from the effected enzyme. In contrast, negative co-operativity tends to draw flux control towards the affected enzyme at the expense of other enzyme sites in the pathway. (2) As a result of the effects occuring in (l), the response coefficient with respect to the starting metabolite will tend to rise in the case of positive co-operativity and fall in the case of negative co-operativity. (3) The closer the allosteric enzyme is to the start of the pathway the greater the rise or fall in the Response Coefficient. This final conclusion gives some credence to the common notion of the so-called ‘committed step’ hypothesis.