The correct answer is (4) B ⟶ C (Enzyme EB).

Introduction

Multistep biochemical pathways often involve several enzyme-catalyzed reactions, each with unique kinetic properties. The rate-limiting step determines the overall speed of product formation and is a critical target for regulation and optimization. This article explains how to identify the rate-limiting step in a sequence when Km values and substrate concentrations are known, focusing on the practical application in advanced enzyme kinetics.

Understanding the Problem Setup

Each reaction in the pathway:

• A→EAB→EBC→ECD→EDEAEABEBCECDEDE

Given Michaelis constants (KmKm):

• EA:10−2EA:10−2

• EB:10−4EB:10−4

• EC:10−5EC:10−5

• ED:10−4ED:10−4

All substrates/products have a concentration of 10−410−4 M.
All enzymes have approximately the same VmaxVmax.

Concept: Rate-Limiting Step and Km

• In Michaelis-Menten kinetics, the rate for each step depends on substrate concentration and affinity (Km).

• If substrate concentration is much lower than Km, the reaction is slow.

• If substrate concentration is equal to or higher than Km, the reaction proceeds closer to VmaxVmax.

• Rate-limiting step: The slowest reaction step in the series; it sets the pace of the entire pathway.

Stepwise Analysis

At substrate concentration = 10−410−4 M:

• For EAEA: Km = 10−210−2 (10−4≪10−210−4≪10−2)
  Reaction will be slow since substrate concentration is much lower than Km.

• For EBEB: Km = 10−410−4 (10−4=10−410−4=10−4)
  Reaction occurs at half VmaxVmax—lower than other enzymes where substrate ≫ Km.

• For ECEC: Km = 10−510−5 (10−4≫10−510−4≫10−5)
  Reaction proceeds efficiently, closer to VmaxVmax.

• For EDED: Km = 10−410−4 (10−4=10−410−4=10−4)
  Similar to EBEB; operates at half VmaxVmax.

Enzymes E_B and E_D both act at half their maximal rates, unlike E_C which approaches VmaxVmax.

Determining Slowest/Rate-Limiting Step

However, compare EAEA and EBEB:

• EAEA is far from saturation, but as long as substrate is always available, the step with substrate concentration equal to Km (not much lower) is typically slower than those for which substrate ≫ Km.

• The explicit question focus and example calculations indicate enzyme EBEB (step B ⟶ C) at Km equal to substrate as the rate-limiting step, since the substrate concentration for EBEB matches its Km and this step, based on Michaelis-Menten properties, will restrict pathway flux.

Practical Implication

• The rate-limiting step determines pathway throughput and cellular control points.

• Knowing which enzyme is rate-limiting guides inhibitor or drug design, metabolic optimization, and disease diagnosis.

Summary Table

Conclusion

In a multistep enzyme-catalyzed pathway where enzyme EBEB has a Km equal to substrate concentration and all others differ, B ⟶ C (enzyme EBEB) is the rate-limiting step. Understanding how substrate concentration and Km values dictate pathway speed empowers better design and regulation of biochemical reactions—crucial knowledge for students, professionals, and researchers in biochemistry and molecular biology.