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Enzyme Kinetics

The Michaelis-Menten equation can be derived by making certain assumptions employing Briggs and Haldane derivation for steady state kinetics. In an enzyme catalyzed reaction, the enzyme E must combine with its substrate S to form an ES-complex which then breaks down to yield the product and the enzyme is set free to be reused.
Where k1,k2,k3 and k4 are rate constants for each reaction.
Before deriving the equation, let us make few generalizations
1. The enzyme catalyzed reaction follows a typical hyperbolic curve. The velocity of reaction increase with the concentration of the substrate to a limited extent, subsequently it falls off. The decline may be due to several factors, such as saturation of the enzyme with the substrate, exhaustion of the substrate, denaturation  of the enzyme or inhibition of the enzyme, etc.
2. The effect of substrate concentration on the velocity of enzyme reaction can be visualized by having three points A, B and C on the hyperbola.
3. A represents the stage when the velocity(v) of reaction  is dependent on the substrate concentration.
4.  At B, substrate concentration is equal to km, hence the velocity is half of Vmax.
5. At point C, substrate concentration is much greater than the Km value hence the velocity is maximum (Vmax). The enzyme at this stage is fully saturated with the substrate and any increase in its concentration  will have no effect.

Application of Michaelis-Menten Equation

The Michaelis-Menten equations is sufficient to describe most of the enzyme catalyzed reactions. It can be utilized to determine Km at various substrate concentrations and the values can be used in predicting rate –limiting steps. Therefore, Vmax and Km should be carefully determined .However, an important method in determining these values precisely is to take reciprocal of substrate concentration and velocity of reaction to draw Lineweaver-Burk polts. One of the major application of  these plots is to study enzyme inhibition.

Line-Burk Plot

The Michaelis –Menten equation can be  transformed by taking the reciprocal of both sides of the equation:

lineeaver burk plot

If a double reciprocal plot is drawn by taking 1/v values on the ordinate and 1/[s] values on the abcissa, a straight line is obtained from which Km values can be calculated the slope of the line is represented by Km/Vmax and the 1/ Vmax.

Such plots are handy in distinguishing the nature of inhibitors.

linear burk plot of the reciprocals of velocity and substrate cncentration for determining km and vmax

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