# Generalized Arrhenius Function

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How a chemical reaction depends on temperature is often parameterized by the Arrhenius function (blue line). Enzyme-mediated reactions respond to temperature in a more complicated manner: high temperatures reduce the catalytic effect exerted by the enzymes (red line). The optimal temperature () is not always close to the temperature of enzyme denaturing. The temperature response of photosynthesis, for example, is often drawn as a bell-shaped curve (green line). This type of temperature response can be modeled with the generalized Arrhenius function, if .

Contributed by: Georgii Alexandrov (March 2011)

Open content licensed under CC BY-NC-SA

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The generalized Arrhenius function is designed to describe the effect of temperature on enzyme activity. It parametrizes the temperature response in terms of activation energy, optimal temperature (), and the ratio () between the levels of activation energy above and below the optimal temperature, as follows:

where is the normalized Arrhenius function (at the optimal temperature).

Further readings:

G. A. Alexandrov and Y. Yamagata, "A Peaked Function for Modeling Temperature Dependence of Plant Productivity," *Ecological Modelling*, 200(1–2), 2007 pp. 189–192.

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