This is a general answer for all three of your related questions:
Since you said:
I want to simulate the evolution of genetic architecture when after a
sudden change in temperature or in an environment that is temporally
heterogeneous in terms of the temperature
You should see this paper. They have studied the dependence of growth rate on temperature. This was measured for different organisms (all poikilotherms).
See this figure:
Figure S1 from Dell et. al 2011. PNAS
The unimodal thermal response of radial growth rate of sac fungi (m/(colony*s)). Green and brown curves are OLS regressions to the Boltzmann-Arrhenius model (Eq. 1) for the subset of data that are the rise and fall components, respectively. These components were extracted by the algorithm described in the Materials and Methods. For
this particular response, the rise was obtained by the algorithm
through removal of the measurements at the 4 highest temperatures and
the fall through removal of measurements at the 5 lowest temperatures.
The blue curve is the best fit to the Johnson & Lewin model (SI
Methods) (1). Values shown are estimated activation energies with 95%
confidence intervals for the respective response components. Dotted
vertical arrows are estimated temperatures for Topt –the temperature
at which the trait value is optimal–calculated from the direct method
(red) and Johnson & Lewin model (blue). See SI for more details. Data
are from Fargues et al. (9)
As you can see, the curve is skewed. The left side of the curve from Topt follows the activation energy model (Arrhenius/Boltzmann). The right side, though they say in the figure legend also fits the model, it seems to me that the phenomenon is somewhat different. The steepness of the curve is perhaps because of denaturation of enzyme active site and therefore a loss of activity. For different enzymes the denaturation kinetics would vary.
I happened to stumble into the author of this paper and that is how I got to know of this work. He seemed to agree that the right half steepness might be because of enzyme denaturation.
Also have a look at this article which is about the temperature dependence of the activity of the proteasome of a thermophile (same principles apply for mesophiles).
Figure 2 of the article:
Normalized Cbz-Ala-Ala-Leu-pNA hydrolysis activity of (filled squares)
purified native and (filled circles) 70°C heat-purified recombinant (α
+ β) Mj proteasome. To normalize recombinant activity to native activity a multiplier of 1.92 was used. Error bars for the native
sample represent one standard deviation for triplicate assays.
Measured temperature errors were ±2°C.
Bottomline (From my comments)
You can assume that the enzymes are at their optimum. You can model the loss of activity due to increased temperature (protein denaturation) as gamma/chi square or exponential function (or the fitted function on the denaturation kinetics) and the effect of low temperature using the chemical thermodynamic equations. But the point is that we don't know if they are at their optimum or not or how each of they may perform at different temperatures.