The half-maximal velocity (Vmax/2) occurs at the Michaelis constant Km without inhibitor and at the apparent Km (Km,app) with competitive inhibitor. The competitive inhibitor concentration [I] is 0.4 μM.

Key Concepts

Michaelis-Menten kinetics describes enzyme velocity v = Vmax [S] / (Km + [S]). Half-maximal velocity occurs when [S] = Km, so Km = 0.5 × 10-6 M. Competitive inhibitors bind the active site, increasing apparent Km to Km,app = Km (1 + [I]/Ki) while Vmax remains unchanged.

Step-by-Step Calculation

Km,app = 1.5 × 10-6 M and Ki = 2 × 10-7 M (dissociation constant for enzyme-inhibitor).

  1. Km,app / Km = 1.5×10-6 / 0.5×10-6 = 3.
  2. 3 = 1 + [I]/Ki → [I]/Ki = 2
  3. [I] = 2 × 2×10-7 = 4×10-7 M = 0.4 μM (rounded to one decimal).

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Introduction

Competitive inhibitor concentration calculation in Michaelis-Menten kinetics is essential for CSIR NET Life Sciences. This guide solves a key problem where half-maximal velocity shifts from substrate concentration 0.5 × 10-6 M to 1.5 × 10-6 M with enzyme-inhibitor dissociation constant 2 × 10-7 M, yielding inhibitor concentration of 0.4 μM rounded to one decimal.

Michaelis-Menten Basics

In enzyme kinetics, half-maximal velocity defines Km as substrate concentration [S] at v = Vmax/2. Competitive inhibition raises apparent Km (Km,app) via Km,app = Km (1 + [I]/Ki), where Ki is the inhibitor dissociation constant. Vmax stays constant as high [S] outcompetes inhibitor.

Problem Breakdown

Parameter Value
Km 0.5 μM
Km,app 1.5 μM
Ki 0.2 μM
Ratio Km,app/Km 3
[I] 0.4 μM

Verification Steps

  • No other inhibition types fit: non-competitive lowers Vmax; uncompetitive lowers both Km and Vmax.
  • Lineweaver-Burk plots confirm competitive via same y-intercept, shifted x-intercept.

CSIR NET Tips

  • Practice rearranging Km,app = Km (1 + [I]/Ki) for [I].
  • Units consistent in M; convert to μM for answer.
  • Common trap: confusing Ki with Km.