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For positively charged substrates, \(K_m^{app}\) is given by which of the following?

(a) Kmλ

(b) Km/λ

(c) Vmax/2

(d) Vmax

The question was posed to me in an online interview.

This intriguing question comes from Kinetics of Immobilized Enzymes in chapter Immobilized Enzymes Preparation and Kinetics of Enzyme Technology

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Correct option is (a) Kmλ

To explain: For immobilized enzymes, the Miachelis Menten equation changes to be \(V=\frac{V_max}{1+\frac{K_m^{app}}{[S_0]}}\)

\(K_m^{app}\) is apparent Km and given \(K_m^{app}\) = Kmλ for positively charged substrates. This can be calculated when the concentration of positively charged substrates in the bulk solution is known. For negatively charged substrates, the \(K_m^{app}\) = Km/λ. Km is the substrate concentration at which Vmax is reduced to half. Vmax is the maximum rate equation.

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