Noncompetitive inhibition: The reciprocal-rate equation can be rearranged to yield a straight-line relation used in which classic inhibitor-constant (Ki) plotting method?

Introduction:
Graphical methods are often used to estimate inhibitor constants (Ki) and diagnose inhibition type. This question asks which plotting method follows from rearranging the reciprocal-rate equation for noncompetitive inhibition.

Given Data / Assumptions:

• Initial-rate data at several inhibitor concentrations [I] and at least two substrate concentrations [S].
• Noncompetitive mechanism under Michaelis–Menten assumptions.
• Interest in a linear relation to extract Ki.

Concept / Approach:
The Dixon method plots 1/v versus [I] at fixed [S]. For many inhibition types (including noncompetitive), lines from different [S] intersect at a point on the x-axis (−Ki) or in a common region, allowing graphical Ki estimation. This follows from the reciprocal form of the rate law with inhibitor terms grouped linearly in [I].

Step-by-Step Solution:
Start from the inhibited rate equation in reciprocal form 1/v = (Km/Vmax) * (1/[S]) * f([I]) + (1/Vmax) * g([I]).For noncompetitive inhibition, terms in [I] can be reorganized to yield 1/v linear in [I] at fixed [S].Plot 1/v (y) against [I] (x) for several [S]; lines intersect near x = −Ki.Extract Ki from the intersection point, and assess goodness by line convergence.

Verification / Alternative check:
Secondary replots or global nonlinear fitting can confirm Ki and mechanism; however, the Dixon plot remains a standard quick diagnostic from the reciprocal formulation.

Why Other Options Are Wrong:
Woolf–Augusteinsson–Hofstee: typically v versus v/[S]; substrate-focused linearization, not inhibitor-axis plotting.

Eadie–Scatchard: v/[S] versus v; again not an inhibitor-concentration plot.

Hanes–Woolf: [S]/v versus [S]; used for Km, Vmax estimates, not a primary Ki versus [I] straight line.

Common Pitfalls:

• Using only one [S], which can misidentify mechanism.
• Ignoring curvature due to tight-binding or mixed mechanisms.

Final Answer:
Dixon plot