Ligands and reversible binding
Feb 07, 2016
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 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.
Equilibrium
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] [P][L]
=ka
kd
In practice, we can often determine the fraction of occupied binding sites
Ka=[PL] [P][L]
= [PL] [PL]+[P]
Bound proteinTotal protein
Kd=[P][L][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 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 Go, units: kJ/mol
Definitions:– Go = Ho ‐TSo : enthalpy and entropy– Ka = [PL]/[P][L] - Kd=[P][L]/[PL]
• Relationships:– Go = ‐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
Hi K
Hi
K
Hi
K
Hi
K
Hi
K
Hi
K
O
O O
O
T stateTissues = low pHLow O2 conc (4 kPa)No oxygen boundH+/CO2 bound
CO2
CO2CO2
CO2Hi
K
HiK
R stateLungs = high pHHigh O2 (13.3 kPa)Oxygen boundNo H+/CO2 bound
T and R states
Allosteric Interactions
ProteinModulator binds
Modulator induces change
Ligand bindsprotein
Heterotropic
Ligand
ProteinHomotropic
Ligand induces change in protein and binds protein
Ligand concentration
% b
oun
d b
y L
igan
d
50
100Myo
Hb
Myoglobin and Hemoglobin O2 binding
Slope and degree of co-operativity
Slope is the measure of the degree of co-operativityFor Hb in the low and high affinity states, their slopes indicate no-cooperativityFor Hb in the intermediate states, the slope indicates high cooperativity
Co-operativity
Molecular models for cooperativity
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Induced fit