I have to calculate the activation energy (Ea) for a thermostable enzyme (wild-type) and its mutants based on its enzyme activity (ln of activity vs 1/T). The wild-type is stable at near boiling temperature and the Arrhenius plot is linear, but the mutants are less stable (
If you have checked that the enzyme undergoes denaturation above certain temperatures, the best would be toremove from your Arrhenius plots those points at highert temperatures that give you non-linearity, because they are "contaminating" your plot. This points may include also denaturation kinetics (if the enzyme denatures irreversibly) and enzyme activity data (thus the increase in activity is less steep because a fraction of the enzyme is lost)
I don't know what's the property you want explore,
For us and for thedynamic viscosity we use the following derivative function:
Ea(T) = R.dln(etha)/d(1/T), may be you add the sign(-) for other quantities like reaction rate in kinetics, or conductivity, etc...
You may think about the pre-exponential factor (the second parameter of Arrhenius factor : lnA = lnY - 1/RT.Ea(T). It also becomes dependent on temperature in the case of non linear behavior..
You can discover surprising phenomenon or results or temperature, when you eliminate the temperature parameter (T) and You plot Ea as a function of lnA !!! I'm sure. You can also think about our new quantity "the Arrhenius temperature" !!
Good luck.
If you have checked that the enzyme undergoes denaturation above certain temperatures, the best would be toremove from your Arrhenius plots those points at highert temperatures that give you non-linearity, because they are "contaminating" your plot. This points may include also denaturation kinetics (if the enzyme denatures irreversibly) and enzyme activity data (thus the increase in activity is less steep because a fraction of the enzyme is lost)
If the Arrhenius plot is not linear, then the activation energy is temperature dependent. Why? That is what you have to discover... If it is only caused by partial denaturation, then you can try to fit the Arrhenius plot with a temperature dependent concentration of active enzyme. That concentration should agree with your data on denaturation.
An alterantive is a recent interesting proposal that deltaH and deltaS can themselves be temperature dependent. Take a look at this paper:
http://pubs.acs.org/doi/abs/10.1021/cb4005029
When analyzing the Arrhenius plot you need to focus in one reaction. If you are measuring the enzyme velocity then you should be looking at the chemical process (transformation of reactants into products). The Ea should reflect the energy required to reach the reactant ->product transition state. When the temperature range chosen includes points where your enzyme is undergoing thermal denaturation, then you have two different processes occurring at the same time reactant->product conversion, and Native_Enzyme->Denatured_Enzyme. As the reaction time evolves the reactant->product catalyzed conversion goes down along with the accumulation of denatured protein. Therefore the ln(rate) vs 1/T plot will be the result of a serious mixture of effects.
A) You assays are likely to be non-linear, therefore the estimates of initial velocities are poor, to say the least.
B) The enzyme reaction rate if a function of several variables r=f([E],[S],[P],t,...), two of which are changing in the same experiment. The corresponding Arrhenius plot is a very complex function of both the Ea of the chemical conversion, the Ea of enzyme denaturation, the enzyme assay duration, and the statistical methods used to obtain the rate estimates.
As mentioned above by Dr. Angel Pey, to assess the Ea of the chemical reaction, you should limit yourself to the section where the enzyme is stable. Check the linearity of the enzyme assays, if you do not see linear [P] vs time progress curves, inestability may already be an issue, even if the Arrhenius plot looks almost linear.
If you want to analyze the Ea of thermal denaturation, incubate your protein at several temperatures (with or without ligands), take samples at defined times and measure the remaining activity at a fixed temperature, and standard assay conditions (those where the enzyme is stable). The rate of activity loss can be equated to the rate of enzyme denaturation and the Ea of this process can be assessed just as any other transformation, the meaning of this barrier, may however, have a different theoretical meaning.
I think you can use the Volgel-Fulcher-Tammann
(VFT) expression for phase transition kinetics to calculate the activation engergy Ea, as follows: t = to* exp(Ea/(R(T-To),) where t is the relaxation time, "to" is a pre-exponential factor and To is a reference temperature (i.e., in your case To may be 60oC).
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