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