Ligand Binding and the Scatchard Plot

#kinetics

1.0

Equations

All Very important (2)

Ligand binding equilibrium

[P] + [L] \underset{k_d}{\overset{k_a}{\rightleftharpoons}} [PL]

$[P]$ : free protein concentration, $\text{M}$
$[L]$ : free ligand concentration, $\text{M}$
$[PL]$ : protein-ligand complex concentration, $\text{M}$
$k_a$ : rate constant for complex formation (association), $\text{M}^{-1}\text{s}^{-1}$
$k_d$ : rate constant for complex breakdown (dissociation), $\text{s}^{-1}$

Association and dissociation constants

K_a = \frac{[PL]}{[P][L]} \qquad\qquad K_d = \frac{[P][L]}{[PL]} = \frac{1}{K_a}

$K_a$ : association constant, $\text{M}^{-1}$
$K_d$ : dissociation constant, $\text{M}$
$[P]$ , $[L]$ , $[PL]$ : free protein, free ligand, and complex concentrations, $\text{M}$ each

Fractional saturation

\Theta = \frac{r}{n}

$\Theta$ : fractional saturation, dimensionless
$r$ : average ligand molecules bound per protein molecule, dimensionless
$n$ : total binding sites per protein molecule, dimensionless

The Scatchard equation

Very important

\frac{\Theta}{[L]} = \frac{n}{K_d} - \frac{\Theta}{K_d}

$\Theta$ : fractional saturation, dimensionless
$[L]$ : free (unbound) ligand concentration, $\text{M}$
$n$ : total binding sites per protein molecule, dimensionless
$K_d$ : dissociation constant, $\text{M}$

The Scatchard equation

Very important

\frac{r}{[L]} = nK_a - rK_a = K_a(n - r)

$r$ : average ligand molecules bound per protein molecule, dimensionless
$[L]$ : free ligand concentration, $\text{M}$
$n$ : total binding sites per protein molecule, dimensionless
$K_a$ : association constant, $\text{M}^{-1}$

05 formulas