Team:Imperial College London/Drylab/Enzyme/Analysis

Assumptions

In the standard model of enzymatic reaction, 3 sets of assumptions are made.

Enzymatic assumptions:

• The enzyme is specific only for the substrate and not for any other chemicals.

• Only one enzyme, our enzyme of interest is present and participating in the reaction.

• There is negligible formation of product without the enzyme.

• The rate of enzymatic activity remains constant over time because there is:
  • no co-operativity of the system. Binding of substrate to one enzyme binding site doesn't influence the affinity or activity of an adjacent site.
  • no allosteric regulations from either the product or the substrate.
  • no product inhibition of the enzyme.

• The enzymatic reaction can be modelled by the following set of reactions (in particular the catalysed reaction is irreversible)

ie:

Degradation assumptions:

• All proteins are very stable and thus their degradation can be neglected over the course of the experiments
• If there is no creation of substrate during the experiment (which is the most common case), we thus have [S]0=[S]+[ES]+[P] at all time
• Likewise if there is no creation of enzyme during the experiment (which is the most common case), we have [E0] =[E]+[ES] at all time

Law of mass action assumptions:

• Free diffusion ; Free unrestricted thermodynamically driven random molecular motion
• The reagents are in thermal equilibrium at a constant absolute temperature
• The reagents are well mixed. [2]

Michaelis-Menten assumption:

• The Michaelis-Menten (MM) assumption is a simplifying assumption that is commonly made with enzymatic reactions. It says that since substrate binding is very fast compared to catalysis, the enzyme complex ES is always at quasi-steady state, ie: , during the time of the experiment.

• It is straightforward to prove that combining the MM assumption with the conservation equation [E₀]=[E]+[ES] yields a new form for the fourth equation

• From the above assumptions, we know that

Model Predictions

• When substrate concentration is large, the enzyme concentration is the limiting factor, hence rate of reaction is directly proportional to [E].

• At very low [E], the reaction rate measured will be negligible as very low amounts of product will be produced.

• Increasing k1 and k3 values will increase the product synthesis rate.

The actual model...