# Understanding Scatchard Plots

Im having trouble understanding Scatchard plots.

Y Axis = Bound/Free Ligand X Axis = Bound Ligand

The graph has a negative slope.

Why when there is almost no Bound (Y axis = 0) do we get a high positive number for Bound ligand on the X Axis corresponding to Receptor concentration? if there is no bound how is there a positive bound number?
it looks like the less bound ligand on the Y axis, the more bound on the X axis!

The Scatchard eqn can be written as $$\displaystyle \frac{Y}{[L]}=\frac{n}{K}-\frac{Y}{K}$$ with $$[L]$$ the free ligand concentration and $$Y$$ the fraction bound, (i.e. $$[L]$$ bound /total protein) so the x-axis intercept (when $$Y/[L]=0$$) is $$n$$ the number of ligands bound, the slope is $$-1/K$$ and the y-axis intercept is $$n/K$$. Your plot confirms this equation, the interpretation of intercepts and slope follow from the equation.

(Your plot seems to plot bound concentration not fraction bound so needs correcting with total protein to make $$Y$$ and this is presumably why $$n$$ comes out to be a small value)

Scatchard plots are intuitively difficult to grasp because the X-axis is not the "independent variable" of the experimental measurement.

When we do a binding isotherm, we measure B (bound, the dependent variable) at increasing concentrations of free (F, the independent variable). But in the Scatchard plot, F doesn't appear as the x-axis variable, and instead appears in the denominator of the y-axis variable, which is counter-intutitive. So the answer to this question is best explained by thinking about the hyperbolic binding isotherm for the reaction in three segments.

At very low F (below Kd) and very low B, B increases linearly with F. Our calculated B/F is high, and stays roughly constant as F increases. These are the points in the extreme upper left of the Scatchard plot.

As F rises to and passes Kd, larger increases in F are needed to get the same increase in B; the slope of the hyperbola is starting to level off, F is increasing faster than B, so B/F decreases. These are the points in the main part of the Scatchard plot.

At F much greater than Kd, the isotherm approaches and reaches saturation. Large increases in F are needed to produce only small increases in B. F increases much faster than B, so B/F gets even smaller.

Finally, as F theoretically approaches infinity, B reaches Bmax and can increase no further, and B/F approaches zero. These are the points in the lower right of the Scatchard plot, where the x-intercept is Bmax.