Scatchard analysis of noncooperative binding with two sites For a protein that binds two ligands independently (noncooperative), what is the x-intercept of the Scatchard plot?

Introduction / Context:The Scatchard plot (r/[L] versus r, where r is bound ligand per protein) is a traditional method to analyze binding data. For independent, identical sites, this plot provides direct access to the number of sites and the affinity constant.

Given Data / Assumptions:

• Protein has two identical, independent binding sites.
• Binding is noncooperative (no interaction between sites).
• Standard Scatchard formalism is used.

Concept / Approach:For identical independent sites, the Scatchard plot is a straight line with slope −K and x-intercept equal to the total number of binding sites n. Therefore, for two sites, the x-intercept is 2.

Step-by-Step Solution:Use Scatchard equation: r/[L] = nK − Kr.Recognize linear form: y = a − bx with slope = K and intercept = nK.Set r/[L] = 0 to find x-intercept; solve 0 = nK − Kr ⇒ r = n.With n = 2, x-intercept equals 2.

Verification / Alternative check:Fitting experimental data for noncooperative systems yields straight lines whose intercept gives n, providing a cross-check against stoichiometry.

Why Other Options Are Wrong:1 corresponds to a single site; “not defined” is incorrect for well-behaved systems; the intercept is not simply the Hill coefficient and does not depend only on ligand concentration.

Common Pitfalls:Using Scatchard plots for heterogeneous or cooperative systems leads to curvature and misinterpretation of n.

Final Answer:2.