Ligand binding

What are the different types of ligand binding?

• Single binding site

• Multiple identical independent binding sites

• Multiple non-identical independent binding sites

• Multiple dependent binding sites (cooperativity)

What are the methods for detecting ligand binding?

Structural & high-resolution methods:

• X-ray Crystallography

• NMR

Physical & Thermodynamic methods:

• ITC

• Radioactivity

X-ray crystallography

Gold standard for seeing physical map of the hydrogen bonds and VdW forces that hold the ligand.

• Advantage: Atomic resolution (can reach <1Å), very accurate bond lengths/angles, widely applicable

• Disadvantage: Requires crystal (hard to get for flexible proteins, membrane proteins, large complexes)

Nuclear magnetic resonance (NMR)

Uses 2D fingerprint where each dot is an amino acid. When a ligand binds, specific dots shift, telling us which residues are in the binding pocket. By adding more ligand and wathching the dots move, the K_d (ligand binding affinity) can be calculated.

Isothermal titration calorimetry (ITC)

Measures heat released or absorbed during binding. Directly measures ΔH, Kd, stoichiometry (n) and ΔG, ΔS from a single experiment.

• No requirement of radioactive material

• Requires high protein concentration

Radioactivity

Uses a radioactive ligand and measures radioactivity (coupled with Equilibrium dialysis)

• Simple & sensitive

• Involves hazardous substance

What are experimental setups for ligand binding?

Equilibrium dialysis:

• Semi-permeable membrane separates chambers with protein and ligand; ligand is small enough to move freely

• At equilibrium, free ligand concentration is equal on both sides

• Free ligand = concentration in chamber without protein (unbound)

• Bound ligand = total in protein chamber − free ligand

• R = bound ligand / total protein concentration

Fluorescence spectroscopy:

• Competitive labelling: fluorescent probe is already bound to the protein, and once ligand binds, it kicks out the probe and a fluorescent signal change is measured

• Hyperbolic curve can be plotted (fluorescence vs [L])

• Plot inverse of (double reciprocal) curve to linearise where:

  • Y-intercept: 1/n, where “n” is no. of binding sites

  • Slope = K_d (dissociation constant), which is the ligand concentration at half-saturation of protein (half-bound)

Important equation

• [P_total] = total protein concentration, i.e., both bound and not bound

• [PL] = Bound ligand (protein-ligand complex)

• [P] = Free protein (not bound to ligand)

• [L] = Free ligand (not bound to protein)

• Kd = dissociation constant (measures the binding affinity)

  • Represents concentration of ligand at which exactly half of the binding sites are occupied

A protein has a K_d =0.1 mM. What ligand concentration is required for 90% saturation?

R = saturation fraction

• 90% Saturation → R = 0.9

• Rearrange equation and solve

• [L] = 0.9 mM

Ligand binding question with table

• Some form of ligand amount will be given, so can calculate the right axes using:

  • L_total = L_bound + L_free

• Make a scatchard plot where:

  • X-axis: bound ligand, like L_bound or [PL]

  • Y-axis: bound ligand over free ligand, so L_bound/L_free or [PL]/[L]

• Use intercepts and slope of the linear regression to find parameters:

  • Y-intercept = L_bound(Max)/K_d

  • X-intercept = L_bound(Max)

  • K_d = -1/slope

  • K_a = 1/K_d

• Plug values in this equation to find other parameter:

  • No. of binding sites (n) = L_bound(Max)/[P_total]

What do the shape of the curve tell us about the binding sites?

• Linear Scatchard: Independent equal binding sites

• Hyperbolic curve: independent multiple binding sites

• Sigmoidal curve: cooperative multiple binding sites

What does a Hill plot tell us?

Cooperativity! Where the slope = Hill coefficient n.

• n>1 → positive cooperativity

  • the binding of a ligand increases the affinity of the protein for subsequent ligands

  • Example: Haemoglobin

• n<1 → negative

  • the binding of a ligand decreases the affinity of the protein for additional ligands

• n=1 → independent

  • Affinity of the protein for a ligand remains exactly the same, regardless of how many ligands are already attached

  • Example: Myoglobin