Binding Equilibria (11.6) Binding of ligands to proteins is prevalent in biochemistry – Catalytic behavior of proteins can be described through binding – Inhibitors bind to proteins to perturb activity – Ligands bind to transport proteins (e.g., oxygen to hemoglobin) – Binding is an equilibrium process (i.e., ligands are not permanently bound to protein) Since some biopolymers have the ability to bind more than one ligand (i.e., multiple active sites), it is convenient to think in terms of average number of ligands bound to a biopolymer – The saturation parameter is related to the number of ligands bound to a polymer – Many different forms of the polymer may exist (e.g., free polymer, singly bound, doubly bound, etc.) For a single-site biopolymer, the saturation parameter is related to the equilibrium constant for the binding processsingle-site biopolymer

Equilibrium Dialysis (11.6) Binding equilibria can be determined using equilibrium dialysisequilibrium dialysis – Biopolymer is placed inside a semi-permeable membrane – Ligand is placed in solution outside membrane and can pass through membrane – Some ligand that enters membrane binds to biopolymer, some does not The amount of free ligand inside the membrane can be determined based on chemical potentials – At equilibrium, the chemical potential of the free ligand must be the same inside and outside the membrane (i.e., the concentrations must be the same) The total amount of ligand in the membrane can be elucidated in a number of ways – Monitor the change of concentration of ligand outside of the membrane – Leech out ligand from membrane by placing membrane in pure solvent

Independent Site Binding (11.7) Independent binding occurs when the binding of a ligand to a single site has no affect on the binding of ligands to other sites – For biopolymers with multiple sites (N), one can monitor the saturation parameter for a specific site (each site has its own equilibrium constant) – The overall saturation parameter is a sum of the individual saturation parameters If the sites are equivalent, the overall saturation parameter has a simple form – Only one equilibrium constant is observed The equilibrium constant and number of sites on the biopolymer can be deduced from the Scatchard equationScatchard equation – Different starting concentrations of ligand in the experiment gives different values of C L and thus different saturation parameters

Plot of Saturation Parameter vs. Ligand Concentration

Equilibrium Dialysis Experiment

Scatchard Plot of Independent Site Binding