The thermal decay of each enzyme is given in

*Muller *J Inst Brewing* 1991* "The effects of Mashing Temperature and Mash Thickness on Carbohydrate Composition" with the activity being governed by the equation A = Ao e^-kt. The given values of k are 0.0163 for alpha and 0.0434 for beta, both at 65 oC. Use t 1/2 = k/ln(2), we can derive half lives of about 42 minutes and about 16 minutes, again both at 65 oC, which correspond reasonably well with the data in Fig 1 of the paper.

The data in figs 2a to 2d aren't nearly as neat: according to the results given the degradation of beta after 10 min at 75 oC is somehow less than at 65 oC, which is simply not possible.

We can, however, get some useful insight by looking at the changes in activity between temperatures, which shows that the degradation rate of alpha roughly doubles for each 10 oC whilst that of beta roughly triples. Using this to estimate new values of k using the equations

k = 0.0163 * e ^ (0.07* (t-65)) for alpha and k = 0.0434 * e ^ (0.1* (t-65)) for beta and converting this value to a half life as before:

Temperature:....65...70...75...80...85...90

Half life Alpha....42...30...21...15...10...7

Half life Beta.....16...10.....6....3.5...2....1.5

Using piecewise linear approximation and integration, this says that mashing at 68 and allowing to cool to 64 over two hours will give beta activity equivalent to about 24 minutes at 65 degrees.