Non-linear arrhenius plots and the analysis of reaction and motional rates in biological membranes

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Abstract

We have systematically derived the rate-temperature relationships for a variety of models of membrane rate processes (particularly enzymic reactions) in order to predict the Arrhenius plot shape(s) appropriate to each model. We have explicitly considered the fact that most thermotropic changes in biological systems extend over finite and sometimes very broad temperature ranges. The rate-temperature relationships for most of the models considered can be expressed in a common, rather simple mathematical form suitable for application in computer data analysis. Only a few models predict Arrhenius plots with the “biphasic linear” form commonly reported in studies of membrane enzymes. However, many of the models yield plots which can be fitted to two intersecting lines within a quite modest experimental error, especially if the change in the slope of the plot around its “break” corresponds to a change in activation enthalpy of less than 15–20 kcal mol−1. In general, Arrhenius-type plots of motional and reaction rates in membranes are found to be capable of indicating the midpoint but not the endpoints or the overall width of thermotropic transitions in the state of membrane components. Our findings clearly indicate a need for a more rigorous analysis of Arrhenius plot data in terms of graph shapes other than sets of intersecting lines and for more cautious interpretation of Arrhenius plot “breaks” with regard to their physical basis.

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