- Km is a measure of the affinity of an enzyme for its substrate, and they are inversely related.Low Km value → E has high affinity for [S]High Km value → E has low affinity for [S]Km = K2 + K3 /K1
Km = K2 /K1 + K3 /K1
Km = KS + K3 /K1Where KS = dissociation constant for equation 1Km = KS, provided K3/K1 is small compared to KS or K2>>K3.Under these conditions, Km is the reciprocal of the affinity of E for its substrate.As KS decreases (→Km ↓ KS), the enzymes’ affinity for the substrate increases.Example: Hexokinase and glucokinase (refer Table 6.5) are the enzymes that catalyse the phosphorylation of glucose.Glucose → glucose-6-phosphatase. (Hexokinase or glucokinase enzyme) Table 6.5 Characteristics of Hexokinase and Glucokinase Towards GlucoseHexokinase (Brain)Glucokinase (Liver)Low Km valueHigh Km valueHigh affinity for [S[i.e. glucoseLow affinity for [S] i.e. glucoseHence takes up glucose even when blood glucose levels are lowHence takes up glucose only when blood glucose level is high
- Kcat/Km is a measure of catalytic efficiencyWe may define the catalytic constant Kcat of an enzyme asKcat = Vmax /(EX)
Unit of Kcat = Vmax /(ET) = concN · time−1/concN
Unit of Kcat = time−1.This quantity is also known as the turnover number of an enzyme because it is the number of substrate molecules converted to product per unit time per active site of an enzyme (or per E molecule when E is fully saturated with [S]). For Michaelis–Menten equation, Vmax = K3(Et)(when E is fully saturated with S, Vo becomes Vmax)Vmax /(ET) = K3
K3 = Kcat; only if saturating [S] conc.Under physiological conditions, E are not fully saturated with substrate. In vivo, we have only low or optimum concentration of [S] but not high concentration. Then we have another term Kcat/Km, which gives the catalytic efficiency.Vmax = K3[ET]
Or Vmax = Kcat[ET]Kcat is sometimes known as the turnover number of the enzyme.When [S] << <<KM- Km + [S] Km
- ET = E free, at low [S] conc; as the amounts of bound E are very low, all are free forms.
Therefore, we haveV = Vmax [S]/Km + [S]
Or V = Kcat [Et][S]/Km + [S]When [S] << << KmV = Kcat /Km [E][S]Rate of the reaction varies directly with how often enzyme and substrate encounter one another in solution. The quantity Kcat /Km is, therefore, a measure of an enzyme catalytic efficiency.
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