Effect of Substrate Concentration
At a low substrate concentration, the initial velocity of an enzyme catalyzed reaction is proportional to the substrate concentration. However, as the substrate concentration is increased, the initial velocity increases less as it is no longer proportional to the substrate concentration. With a further increase in the substrate concentration the reaction rate becomes independent of the substrate concentration and assumes a constant rate as a result of enzyme being saturated with its substrate.
It was Michaelis and Menten who suggested an explanation of these findings by postulating that at low substrate concen-trations, the enzyme is not saturated with the substrate and the reaction is not proceeding at maximum velocity whereas when the enzyme is saturated with substrate, maximum velocity is observed. They further visualized the combination of enzyme with the substrate to form an enzyme-substrate complex and assumed that the rate of decomposition of the substrate being proportional to the concentration of enzyme-substrate complex. The velocity of the reaction at this high
substrate concentration is termed as maximum velocity. The substrate concentration at which the velocity is half of the maximum velocity is called the Michaelis constant and is termed as Km.
Km indicates the affinity of the substrate towards the enzyme and is inversely proportional to the affinity.
m
K 1
Affinity
∝
Higher the affinity the smaller will be the Km and lower the affinity, the higher will be the Km.
The Michaelis-Menten equation is given by the expression V0 = max
m
V [S]
K +[S]
where V0 = Initial velocity Vmax = Maximum velocity Km = Michaelis constant [S] = Substrate concentration
The Michaelis-Menten equation relates the initial velocity, the maximum velocity and the initial substrate concentration through Michaelis-Menten constant.
When the initial velocity is exactly half of the maximum velocity the Michaelis-Menten equation assumes the form
max
Thus Michaelis-Menten constant is equal to the substrate concentration at which the initial velocity is half of the maximum velocity.
Determination of important physical constants of an enzyme such as V and Km would be difficult from the curve that would be obtained by plotting [V] against [S]. So the Michaelis-Menten equation can be transformed into the form which is useful in plotting experimental data.
Taking the reciprocals of both the sides of Michaelis-Menten equation.
0
This equation is called Line-weaver Burk equation and is the equation for a straight line y = mx + c, where m is the slope of the straight line, c is the intercept on the y-axis and x is the intercept on x-axis.
When 1
Since, Line-weaver-Burk equation is in the form of a straight line, so it requires few points to define, Km. By using small concentrations of substrate it is possible by this double reciprocal plot to determine Km.
Significance of Km and Vmax Values
The Michaelis constant [Km] has two meanings:
One is that it is equal to that substrate concentration at which half of the active sites are filled and so once the Km is shown, the fractions of sites filled (fs) at any substrate concentration can be calculated by:
fs =
Second, Km is related to rate constant of the individual steps disso-ciation constant of the ES complex, a reversible reaction, i.e.
1
(the equilibrium constant of ES) Km = 1
1
K K
−
So when this condition is met, Km indicates the strength of ES complex and at such conditions a high Km indicates weak binding and a low Km indicates strong binding. But this is true only when the K2 is much less then K-1.
Vmax
Vmax indicates the turn over number of the enzyme if the con-centration of active sites, i.e. the total enzyme (Et) is known since Vmax = K2[Et].
Here, in this relation K2 is called the turn over number of an enzyme which is defined as number of substrate molecules converted into product per unit time when the enzyme is fully saturated with the substrate and the time required for each round of catalysis is thus given by 1/K2. Method of Determining Km
Km can be determined by double reciprocal Line-weaver-Burk method. In this the velocity of reaction is noted with different
1
[ ]S and 1
[ ]V from the graph, the value of Km is determined.
Another advantage of this equation is that it is used to differentiate certain type of inhibitors of enzyme system.
Effect of Enzyme Concentration
The rate of an enzyme catalyzed reaction is directly pro-portional to the concentration of the enzyme. The greater the concentration of enzyme, the faster will be reaction taking place.
Effect of pH
Most enzymes have a characteristic pH at which their activity is maximum. Above or below that pH, the enzyme activity decreases. If a curve is drawn between the activity of an en-zyme on a given substrate with the pH of the reaction mixture, it will reveal a maximum activity at a definite pH. This value is known as optimum pH. See Diagram on Page No. 129.
This is probably due to the changes in the net charge on enzy-mes, (as they are protein in nature) resulting from changes in pH. Excessive changes of pH brought on by the addition of strong acids or bases may completely denature and inactivate enzymes.
Effect of Temperature
The rate of an enzyme catalyzed reaction generally increases with temperature, within the temperature range in which the enzyme is stable and retains its full or maximum activity.
Enzyme catalyzed reactions have an optimum temperature at which the reaction is most rapid.
Above this temperature the reaction rate decreases as enzymes being protein in nature are denatured by heat and becomes inactive.
The increase in rate below optimal temperature results from increased kinetic energy of the reacting molecules.