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

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Abstract
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, ϵ0 and σ. Parameter ϵ0 is the mean value of ϵ for a heterogeneous enzyme population; ϵ is the activation energy divided by absolute temperature and the ideal gas constant. Parameter σ is the standard deviation of the Gaussian distribution of ϵ values in the population. If the population is homogeneous, then ϵ = ϵ0 for all enzyme molecules and σ = 0. There are certain ratios which are independent of ϵ0 and dependent upon σ. Two important ratios are t1/4/t1/2 and t1/2/t , where t represents t1/2 for a homogeneous enzyme population with the same mean ϵ (ϵ0), as the heterogeneous population. If there is experimental deactivation data for the heterogeneous population which is well behaved, the first ratio, t1/4/t1/2, can be determined by estimating the time in minutes at which the enzyme has lost 25% of its activity (t1/4), and the time in minutes at which the enzyme has lost 50% of its activity (t1/2), and then taking the ratio t1/4/t1/2. The corresponding value of σ can be estimated from a graph. The ratio t1/2/t can be found directly as a function of t1/4/t1/2, and can be estimated from another graph. The value of ϵ0 can then be calculated from the formulasgiven in the article.

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