A kinetics experiment reveals that the enzyme fumarase catalyzes the dehydration of malate with a k_cat of 900 s⁻¹. If the substrate concentration is equal to the K_m of the reaction, what is the reaction velocity when the enzyme concentration is 200 nM?

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11ecba2d_0e79_f187_a3bf_3758d82a2ddf_MD0008_00 The rate V₀ of an enzymatically catalyzed reaction is determined by the enzyme concentration [E], the substrate concentration [S], the Michaelis constant K_m, and the turnover number (reactions per second per enzyme, known as k_cat). This relationship is given in the Michaelis-Menten equation: 11ecba2d_0e7a_1898_a3bf_3305436bda22_MD0008_00 V0=kcatESKm+S The product of k_cat and [E] equals the maximum velocity V_max of the reaction, which simplifies the equation to: 11ecba2d_0e7a_3fa9_a3bf_7978059b2519_MD0008_00 V0=VmaxSKm+S The question states that the concentration of malate [S] is equal to K_m. Therefore, K_m can be substituted into the equation to yield 11ecba2d_0e7a_3faa_a3bf_29c5a5785091_MD0008_00 V0=VmaxKmKm+Km=VmaxKm2Km Finally, the K_m terms in the numerator and the denominator cancel each other to yield 11ecba2d_0e7a_66bb_a3bf_0f52b979c39d_MD0008_00 V0=Vmax2 Therefore, when the substrate concentration equals the K_m of the catalyzed reaction, the reaction will proceed at half the maximum possible velocity, or ½V_max. The question says the concentration of fumarase [E] is 200 nM, and the k_cat is 900 s⁻¹. Multiplying these terms yields a V_max of 180,000 nM/s, which is equivalent to 180 µM/s (1,000 nM = 1 µM). Per the derived equation, dividing V_max by 2 yields a reaction rate V₀ of 90 µM/s, which is equal to 9.0 × 10¹ µM/s. (Choice A) 3.6 × 10² µM/s is double the maximum velocity V_max of the reaction at the given enzyme concentration. The question states that the concentration of malate is equal to the K_m of fumarase, so the reaction will proceed at ½V_max. (Choice C) 4.5 × 10⁻³ µM/s results from incorrectly calculating V_max by dividing k_cat by the fumarase concentration [E] instead of multiplying. (Choice D) 2.2 × 10⁻⁴ µM/s results from incorrectly calculating V_max by dividing the fumarase concentration [E] by k_cat instead of multiplying. Educational objective: The rate of an enzymatic reaction at any given substrate concentration is described by the Michaelis-Menten equation. The maximum velocity V_max equals the product of k_cat and enzyme concentration [E]. When the substrate concentration equals the Michaelis constant K_m, the reaction proceeds at ½V_max.

A Kinetics Experiment Reveals That the Enzyme Fumarase Catalyzes the Dehydration