Elasticity coefficient

The rate of a chemical reaction is influenced by many different factors, such as temperature, pH, reactant and product concentrations and other effectors. The degree to which these factors change the reaction rate is described by the elasticity coefficient. This coefficient is defined as follows:

${\displaystyle \varepsilon _{S}^{v}={\frac {\partial v}{\partial S}}{\frac {S}{v}}={\frac {\partial \ln v}{\partial \ln S}}}$

where ${\displaystyle v}$ denotes the reaction rate and ${\displaystyle S}$ denotes the substrate concentration. The partial derivative in the definition indicates that the elasticity is measured with respect to changes in a factor S while keeping all other factors constant. The most common factors include substrates, products and effectors. The scaling of the coefficient ensures that it is dimensionless and independent of the units used to measure the reaction rate and magnitude of the factor. The elasticity coefficient is an integral part of metabolic control analysis and was introduced in the early 1970s and possibly earlier by Henrik Kacser and Burns in Edinburgh and Heinrich and Rapoport in Berlin.

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