For an enzyme catalyzed reaction, a Lineweaver-Burk plot gave the slope value = 40 s and intercept = 4 (mmoldm-3s-1)-1. If initial concentration of enzyme is 2.5× 10-9 moldm-3, catalytic efficiency is 10x. Calculate the value of ‘x’.a)5b)6c)7d)8Correct answer is option 'C'. Can you explain this answer?

Question

For an enzyme catalyzed reaction, a Lineweaver-Burk plot gave the slope value = 40 s and intercept = 4 (mmoldm-3s-1)-1. If initial concentration of enzyme is 2.5&times; 10-9 moldm-3, catalytic efficiency is 10x. Calculate the value of &lsquo;x&rsquo;.a)5b)6c)7d)8Correct answer is option 'C'. Can you explain this answer?

Answer

To determine the maximum velocity (Vmax) and the Michaelis-Menten constant (Km) for the enzyme-catalyzed reaction, we need to use the Lineweaver-Burk plot equation:

1/Vo = (Km/Vmax) x (1/[S]) + 1/Vmax

where Vo is the initial velocity of the reaction, [S] is the substrate concentration, Km is the Michaelis-Menten constant, and Vmax is the maximum velocity of the reaction.

From the Lineweaver-Burk plot, we know that the slope value = 40 s and intercept = 4 (mmoldm-3s-1)-1. The slope value corresponds to 1/Vmax, and the intercept corresponds to Km/Vmax.

So, we can calculate:

1/Vmax = 40 s
Vmax = 1/40 s = 0.025 (mmoldm-3s-1)

Km/Vmax = 4 (mmoldm-3s-1)-1
Km = Km/Vmax x Vmax = 4 (mmoldm-3s-1)-1 x 0.025 (mmoldm-3s-1) = 0.1 mmol dm-3

Therefore, the Vmax is 0.025 (mmoldm-3s-1) and the Km is 0.1 mmol dm-3 for the enzyme-catalyzed reaction with an initial concentration of enzyme of 2.5.

Answer

ANS :- from Enzyme kinetics

R = K₂ [E]. [s]. /Km [E].

1/R = (km /K₂ [E]. ) 1/S. + 1/ K₂ [E].

Slope. intercept

Catalytic efficiency =K₂/ km

=1/{(Km /K₂)([E]./[E].}

=1/Slope [E].

=1/ 40*2.5*10-⁹

=10⁷

:: Correct option is C ) 7 {because 10 to the power x =7}

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