Mash Enzyme Temperature and Duration

[Lyrebird_Cycles]

In a recent thread on mash enzymes I posted some information on the rate of thermal degradation of the enzymes which was possibly a little maths heavy for many readers.


Thinking about ways of making this info more accessible, I came up with the idea of the enzyme Degradation Unit (DU), analogous to the Pasteurisation Unit (PU) used for estimating thermal death rates of spoilage organisms. The two phenomena are governed by the same sets of equations as could be expected given that thermal death is the result of the denaturation (coagulation) of essential proteins. In keeping with the premise of this thread I'll go into the background maths in a later post.


I propose that 10 DU is the net thermal dose that reduces enzyme activity to 1/10 its former level (eg 90% of activity is lost) so 1 DU is equivalent to roughly 20% activity loss and 3 DU is equivalent to 50% activity loss. Again the maths behind this will follow.


Just like pasteurisation, you add the DUs but multiply the effect: if 5 minutes at a particular temperature gives 10 DU and 3 minutes at another temperature also gives 10 DU, the total is 20 DU and the enzyme activity will be reduced to 1/100th ( = 1/10 x 1/10) its initial level.


There are two ways of presenting the required information: the number of minutes at each temperature to reach 1 DU and the number of DUs per minute at each temperature. Of course these are simply the inverses of one another.


Minutes for 1 DU at various temperatures:

temp C...55.....60.....65.....70.....75.....80.....85.....90.....95.....100

alpha......28.....20.....14.....10.....7.1....5.0....3.5....2.5....1.8.....1.2

beta........16.....9.2....5.3...3.1....1.8....1.0....0.59...0.34...0.20...0.11



DU/minute at various temperatures:

temp C....55.......60.......65.......70.......75......80.......85.......90.......95......100

alpha.....0.035..0.050...0.071..0.10....0.14....0.20....0.28....0.40....0.57....0.80

beta.......0.063..0.11.....0.19.....0.33....0.57...0.98.....1.7......2.9......5.1......8.8.


As an illustration of how this information might be used, let us take the common supposition that a 10 minute mash out at 75 oC will kill off the mash enzymes.

From the table we can see that at 75 oC 10 minutes will provide 1.4 DU for alpha and 5.7 DU for beta. This will result in a loss of about 30% of enzyme activity for alpha and 70% for beta: a moderate reduction in the first case and a significant reduction (but not complete elimination) in the second.

 

[Mardoo]

Fantastic work. Thank you! You're one hell of a valuable member of this forum. It appears the table hasn't come across, at least on mobile.

 

[Lyrebird_Cycles]

Sorry about the tables, I made a mistake and forgot that the forum software destroys tables when they are copy / pasted so I took them out and re-edited. You may have viewed the post during the editing window, I hope they are OK now.

 

[Lyrebird_Cycles]

As promised,a bit of a follow up to flesh out someof the detail.

The decay follows the standard logarithmic decay curve At = A0 e^-kt, where A0 is activity at time0 (start) and At activity at time t. The exponential factor k thus describes the decay rate at a given temperature. The data given in the reference is for 65 oC.


To derive decay units we need two bits of data: the decimal decay time at the reference temperature (eg the time taken at that temperature for At = A0 /10), known as the D factor, and the temperature resistance coefficient (the temperature difference required for the D factor to reduce by ten times), known as the z coefficient.


Since the decay is logarithmic, D is given by ln(10) / k so the D factor at 65 oC can be estimated directly from the k values in the reference giving D65 = 141 minutes for alpha amylase and D65 = 53 minutes for beta amylase. This means that 1 DU at reference temp is given directly by ln(10)/ 10*k.


The data given in figs 2a to 2d of the reference allow us to estimate that the decay rate increases by a factor of about 2 for each 10 degrees C for alpha amylase and about 3 for each 10 degrees for beta. Again a simple formula allows us to derive z for each of these: z = Delta t. Ln (10) / Ln (rate), giving z = 33 min for alpha and z = 21 min for beta*.


We can then derive D values at different temperatures (DT) from Log(DT / Dref) = (Tref – T) / z. Which is equivalent to DT = Dref * 10^((Tref-T)/z). Note the change from natural logs to decimal in this last eqn. This is because z is given as the decimal temperature reduction coefficient.

Lastly, I decided to use 10 DU = heat load required to casue a 90% diminution in activity by analogy to the decibel (dB). The actual unit of sound pressure is the Bel(l) named after Alexander Graham Bell and defined as the log to base 10 of the sound pressure referred to a base level. This unit is so unwieldy that everybody divides it by ten and uses the result (decibel) instead.



* Strictly z is itself dependent on the square of the absolute temperature but at the temperature ranges we are using the use of a linear approximation gives a small error.