Graphical determination of mean activation energy and standard deviation in a microheterogeneity model of enzyme deactivation

Traditionally, enzyme populations have been treated as if they were either homogenous, or heterogeneous with distinct and separable subpopulations. The microheterogeneity model, however, assumes that there is a continuous distribution of properties in the population. In the area of enzyme deactivation kinetics, this model describes the heterogeneous population as having a continuous distribution of activation energy of deactivation. This distribution is characterized by mean activation energy, and a standard deviation of activation energy. The microheterogeneity model contains two parameters, (0) and sigma. Parameter (0) is the mean value of for a heterogeneous enzyme population; is the activation energy divided by absolute temperature and the ideal gas constant. Parameter sigma is the standard deviation of the Gaussian distribution of values in the population. If the population is homogeneous, then = (0) for all enzyme molecules and sigma = 0. There are certain ratios which are independent of (0) and dependent upon sigma. Two important ratios are t(1/4)/t(1/2) and t(1/2)/t(1/2) ('), where t(1/2) (') represents t(1/2) for a homogeneous enzyme population with the same mean ((0)), as the heterogeneous population. If there is experimental deactivation data for the heterogeneous population which is well behaved, the first ratio, t(1/4)/t(1/2), can be determined by estimating the time in minutes at which the enzyme has lost 25% of its activity (t(1/4)), and the time in minutes at which the enzyme has lost 50% of its activity (t(1/2)), and then taking the ratio t(1/4)/t(1/2). The corresponding value of sigma can be estimated from a graph. The ratio t(1/2)/t(1/2) (') can be found directly as a function of t(1/4)/t(1/2), and can be estimated from another graph. The value of (0) can then be calculated from the formulasgiven in the article.