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

• 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

• 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

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P + NL ↔ PLN

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K =CPLN

CPCLN

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θ =ν N

=KCL

N

1+ KCLN

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CPLN

CP

=ν

N −ν

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K =ν

CLN N −ν ( )

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lnθ

1−θ

⎛

⎝ ⎜

⎞

⎠ ⎟= lnK + N lnCL

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

• 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

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θ =KCL

α

1+ KCLα

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

• 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

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K0 =CT

CR

Independent vs. Cooperative Binding

Hemoglobin

Myoglobin

Binding in Hemoglobin and Myoglobin

Hill Plot for Hemoglobin and Myoglobin

Concerted Model

Sequential Model