# 21 Michaelis - Menten Equation and Immobilising an enzyme

Michaelis-Menten equation describes the velocity of enzymatic reactions (v) by relating it to [S] - concentration of a substrate S.

Michaelis - Menten Equation

An example curve with parametersV_max = 3.4 and K_m = 0.4. Wikipedia. 

Here, V_max represents the maximum rate achieved by the system, at maximum (saturating) substrate concentrations.

The Michaelis constant K_m is the substrate concentration at which the reaction rate is half of V_max.

K_m is (roughly) an inverse measure of the affinity or strength of binding between the enzyme and its substrate. The lower the K_m, the greater the affinity (so the lower the concentration of substrate needed to achieve a given rate).

It permits prediction of whether or not the rate of formation of product will be affected by the availability of substrate.

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Immobilising an enzyme in alginate  

• In industry enzymes are used on a large scale.

• It is very costly to use enzymes only once, but most enzymes are only commercially available in liquid or dehydrated forms and once they have been used in solution it is very difficult and time consuming to separate them from the product. 

• To allow their re-use, enzymes may be immobilised (attached to an inert, insoluble material such as calcium alginate to form a gel capsule around them). This way, the enzymes will be hold in place throughout the reaction, easily separated from the products and may be used again.

• One way of immobilising enzymes: mixing the enzyme with sodium alginate, then dropping the mixture into calcium chloride solution. Sodium alginate will turn from liquid to solid when immersed in calcium chloride. This produces small beads with the enzyme inside. 

2 Na(Alginate) + Ca⁺⁺ -------> Ca(Alginate)₂ + 2 Na⁺

• The substrate that the enzyme acts upon is able to diffuse through the gel, although this may be quite slow. 

• Immobilised enzymes are widely used in industry because it allows the reaction to flow continuously and the product will not be contaminated with the enzyme so will not need to be purified.

Syllabus 2016 - 2018 Factors that affect enzyme action b)   explain that  the maximum rate  of reaction (Vmax) is used to derive  the Michaelis-Menten constant (Km) which is used to compare the affinity of different enzymes for their substrates d)   investigate and explain the effect of immobilising  an enzyme in alginate on its activity as compared with its activity when free in solution.