Considering the association of enzyme (GOx in my case) with substrate (glucose), how is binding Free Gibbs Energy affected by immobilization? Is there a direct way to calculate the ΔG of this step (enzyme-substrate complex formation)?
Hello Rafael:
There is a theory called the collision that provides the limits of an enzymatic catalysed reaction and relates the velocity constant of a bimolecular reaction with the activation energy. You can check this paper for an idea:
Catalytic Behaviors of Enzymes Attached to Nanoparticles: The Effect of Particle Mobility, BIOTECHNOLOGY AND BIOENGINEERING, VOL. 84, NO. 4, NOVEMBER 20, 2003.
regards
Huge amount of information here -- possibly has the info you are looking for. BRENDA database is a great resource.
https://www.brenda-enzymes.org/enzyme.php?ecno=1.1.3.4
You could always perform a simple 'classical' enzyme characterization. Measure enzyme activity as a function of a range of substrate concentrations, and probably using (separately) a few different enzyme concentrations also. If you do this twice: once for free-in-solution enzyme and once for immobilized -- gives you two delta-G, and then you can calculate the effect of immobilization.
Carola's answer is interesting (I will look at that paper myself). However, if the information is critical for you, I would always favor making the measurement with your exact enzyme in the context of your specific overall reaction scheme.
In addition to abovementioned answers. You will need to evaluate the binding free energy for both free enzyme and immobilized enzyme separately, for the following steps:
1. Carry out thermal stability of your enzyme at specific time t (e.g 20mins) over range of temperature (I.e from optimum temperature to the temperature where there is still activity not complete denature state, e.g 40C to 70C.)
2. Record the initial activity at time zero (Ao) then activity at time t (A).
1. Evaluate the dissociation constant (Kd) using log(A/Ao) = - (kd/2.303)t
2. Evaluate Arrhenius equation to get activation energy (-Ea/R) from the slope of the Inkd against 1/T, where T are now in Kelvin. Intercept will be InAc where Ac is Arrhenius constant.
3. Use the Ea to evaluate enthapy (∆H) and entropy (∆S)
4. ∆G = ∆H - T∆S
Then compare the ∆G of immobilized enzyme to free enzyme.
5. Search for journals on kinetic and thermodynamic studies of enzyme e.g Sant'Anna et al., 2012
Thank you all for the helpful information.
Craig, I do have measurements from my specific system. However, I am struggling to find references in literature that measure ΔG of GOx + Substrate binding.
I'll check the references mentioned.
Regards
Thanks Carola Bahamondes
for the reference. It is really interesting.
The point is ∆G is a state property, it only depends on the difference from final state and initial state. Kinetic properties such as diffusional rates and enzyme efficiency are definitely modified by the immobilization of the protein. But ∆G is measured at equilibrium and should not be affected by this. However, the chemical modification bought about by the immobilization procedure may change the chemical environment at the active site, and have an effect on binding affinity at equilibrium, and thus on ∆G. For instance, many oligomeric proteins with multiple independent binding sites for the same ligand (not communicated by allostery), behave as is one has as many individual active sites as total subunit concentration there is (as if subunits where individual proteins). Here, the final number may change, depending on how you consider the protein concentration, if as [total binding sites] or [total protein molecules].
In the light of this, the paper mentioned by Carola offer a very surprising conclusion:
"Compared to KM, kcat appeared to be less sensitive to particle size and viscosity"
because kcat is a completely kinetic constant, while KM also includes the dissociation on and off rates, at the steady state. One might expect KM to behave more like the true dissociation constant, but it apparently does not.
The difficult part here is to measure the equilibrium, because the concentration term becomes very difficult to calculate once the molecule has become part of a very large particle. Even using a calorimeter, How do you handle the protein concentration to fit the data?
Best wishes,
Rogelio
Thank you Rogelio for the insightful comments. In our approach, we monitor the active site response during interaction with the substrate.
Then, my guess is you should not see a large effect in affinity (∆G binding), although most changes in the protein would affect its binding properties to some extent.
This is mainly because immobilization should modify the T∆S component (probable reduce it), as restrains cut down the degrees of freedom of the protein molecule.
Instead the ∆H should change very little, and only when ∆S dominates the binding process, the affinity should shown large changes, as in the case of proteins suffering a significant conformation change upon ligand binding.
Best wishes
Rogelio
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