Cooperative Site Binding (11.8)
• Binding of ligands to a biomolecule can affect the ability of other active
sites to bind ligands and is called cooperative binding
– Full cooperativity occurs when either all sites are occupied or unoccupied
P  NL  PLN
K
CPLN
CP CLN
• In full cooperativity,
the number of free sites is related to the number of


free biopolymer molecules
– Ratio of occupied to unoccupied sites is related to the ratio of bound biopolymer to free
biopolymer
CPLN
CP


N  
K

C N  
N
L
• The Hill equation
is used to determine the binding constant and the

number of active sites on a biopolymer that exhibits full cooperativity
– A normalized saturation parameter can be defined and is related to the fraction of active
sites occupied on the biopolymer

KCLN
 
N 1 KCLN
  
ln
 lnK  N lnCL
1  
Real World Cooperativity (11.8-11.9)
• Fully cooperative binding is an idealized situation
– Intermediate cooperativity can be described using the Hill parameter (α)
– Hill parameter can range from 1 (independent binding) to N (fully cooperative), called
positive cooperativity
– Hill parameter can also be less than 1, called negative cooperativity

KCL
1 KCL
• Allosterism is the property of a protein where ligand binding regulates the
activity of the protein 
– Structural changes in the protein as ligands bind are responsible for allosterism
– Allosteric effects are often described by one of two models: concerted or sequential
• Oxygen transport by hemoglobin and myoglobin are examples of
cooperative and independent binding
– Myoglobin exhibits independent binding (α=1 in a Hill plot)
– Hemoglobin exhibits cooperative binding at intermediate partial pressures of oxygen
– Hemoglobin exhibits independent binding at high and low oxygen concentrations
Concerted and Sequential Models (11.9)
• The concerted model describes ligand binding in a two-state model
– Binding sites are either in a tense state (T) or a relaxed state (R), with the relaxed state
having a higher binding affinity
– All sites on the protein exist in either the T or R state
– An equilibrium exists between the T and R forms, with the value of the equilibrium
constant depending on the number of ligands bound to protein
K0 
CT
CR
• As the number of ligands bound to the protein increases, the equilibrium
shifts to the relaxed form
– High and low concentration binding of hemoglobin is explained well using the concerted
model (binding becomes independent at high and low concentrations of oxygen)
• Sequential model states that the binding of each active site is affected by
the successive binding of ligands
– A mix of tight and relaxed active sites is allowed
– This model can be used to explain negative cooperativity
Independent vs. Cooperative Binding
Hemoglobin
Myoglobin
Binding in Hemoglobin and Myoglobin
Hill Plot for Hemoglobin and Myoglobin
Concerted Model
Sequential Model