Ligands and reversible binding
Ligands
Kinetic experiments study the rate at which reactions happen.- how conc of reactant and product change as funct of
time.
Rate of reaction is slope. Rate of reaction decreases as reaction proceeds.
Chemical kinetics
Equilibrium
Equilibrium experiments study how conc of reaction products change as function of reactant concentrations.
A+B<---->AB. Increasing amount of A is titrated against fixed amount of B and equilibrium conc of product AB determined.
Thermodynamics
Rate constants and equilibrium constant
• Consider a process in which a ligand (L) binds reversibly to a site in the
protein (P)
ka
kd
ka
[PL]
=
Ka=
kd
[P][L]
In practice, we can often determine the fraction of occupied binding sites
Q=
[PL]
[PL]+[P]
[PL]
Ka=
[P][L]
Q=
Bound protein
Total protein
[P][L]
Kd=
[PL]
[L]
[L]+ Kd
• The fraction of bound sites depends on the free ligand concentration and Kd
• In a typical experiment, ligand concentration is the known independent variable
Ligand binding to protein
The fraction of ligand-binding sites occupied Q plotted against conc of free ligand
• Interaction strength can be expressed as:
– association (binding) constant Ka, units M‐1
– dissociation constant Kd, units M, Kd = 1/Ka
– interaction (binding) free energy DGo, units: kJ/mol
Definitions:
– DGo = DHo ‐TDSo : enthalpy and entropy
– Ka = [PL]/[P][L]
- Kd=[P][L]/[PL]
• Relationships:
– DGo = ‐RT ln Ka = RT ln Kd (RT at 25 oC is 2.48 kJ/mol)
• Magnitudes
– Strong binding: Kd < 10 nM
– Weak binding: Kd > 10 uM
Myoglobin
Myoglobin
Heme
Myoglobin, Histidine and oxygen
Carbon Monoxide
• CO has similar size and shape to O2; it can fit to the same binding site
• CO binds over 20,000 times better than O2 because the carbon in CO has a filled lone
electron pair that can be donated to vacant d-orbitals on the Fe2+
• Myoglobin Protein pocket decreases affinity for CO, but it still binds about 250 times
better than oxygen
• CO is highly toxic as it competes with oxygen. It blocks the function of myoglobin,
hemoglobin, and mitochondrial cytochromes that are involved in oxidative phosphorylation
Myoglobin Oxygen binding
Hemoglobin Oxygen binding.
Hemoglobin cycle
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Myoglobin and Hemoglobin structures
T and R structures
T and R states
Hi
K
CO2
CO2
CO2
CO2
b
a
K
Hi
T state
Tissues = low pH
Low O2 conc (4 kPa)
No oxygen bound
H+/CO2 bound
a
O
O
O
O
b
K
Hi
b
Hi
K
a
b
a
R state
Lungs = high pH
High O2 (13.3 kPa)
Oxygen bound
No H+/CO2 bound
Allosteric Interactions
Heterotropic
Protein
Protein
Ligand
Modulator
binds
Ligand induces
change in protein
and binds protein
Modulator
induces change
Homotropic
Ligand binds
protein
Myoglobin and Hemoglobin O2 binding
% bound by Ligand
100
50
Myo
Hb
Ligand concentration
Slope and degree of co-operativity
Slope is the measure of the degree of co-operativity
For Hb in the low and high affinity states, their slopes indicate no-cooperativity
For Hb in the intermediate states, the slope indicates high cooperativity
Co-operativity
Molecular models for cooperativity
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Induced fit