Binding of Small Molecules to a Polymerizing Protein System'

1
Binding of Small Molecules to a Polymerizing
Protein System.

• A Model for Allosteric Effects.

2
General Formulations
We will consider a system in equilibrium
(1)
where A is a protein monomer and C is a single
high polymer
Both the monomer and the polymer bind a low
molecular weight solute (S)
3
Equilibrium Constants For Monomer
where p is the number of binding sites per mole
of monomer
4
Equilibrium Constants For Polymer
where q is the number of binding sites per mole
of polymer
5
A Binding Function
A binding function, r, is defined on a weight
concentration scale as the concentration of S
bound divided by the initial protein
concentration
Substitution of expressions for all Li , and Mi
gives
where
,
.
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By making the assumption that all binding sites
within a molecular entity are equivalent except
for a statistical effect in binding we obtain
and
where and are defined as intrinsic
binding constants.
Thus the final form of the binding function is
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Special Cases

• A binding site is identical or close to a
  polymerization site
• The equilibrium constant is given by
  XC/An and we can obtain the polynomial in
  A equation
• 
  where and
• - the initial concentration of protein
• Binding sites are distinct from polymerizing
  sites
• The equilibrium constant is given by
  and equation
  for A is

8
Application of Theory
L.W Nichol, W.J.Jackson, and D.J Winzor
,Biochem.,vol.6,no.8,1967
9
L.W Nichol, W.J.Jackson, and D.J Winzor
,Biochem.,vol.6,no.8,1967
10
Conclusions
From this study of ligand binding to polymers
coexisting in equilibrium it is clear that
double-reciprocal plots of binding curves at
several concentrations of macromolecule suffice
theoretically to distinguish between the various
combinations of polymerization and ligand
binding. Six possible forms that these plots may
assume, and the type(s) of system yielding such
data may be summarized as follows.
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• 1) A straight line with slope and intercept
  independent of protein concentration a single
  protein or series of polymers with polymerization
  and binding occurring independently.
• 2) A family of straight lines with different
  intercepts on the 1/r axis but common on the
  1/S axis noncompetitive polymerization
• 3) A curve convex 1/S axis, independent of
  protein concentration noncompetitive
  izomerization and binding
• 4) A series of curves convex to the 1/S axis
  with common 1/r intercept noncompetitive
  polymerization and binding
• 5) A curve initially concave to the 1/S axis,
  independent of protein concentration
  competitive izomerization and ligand binding
• 6) A series of curves initially concave to the
  1/S axis with common 1/r intercept
  competitive polymerization and ligand binding
• Reference L.W Nichol, W.J.Jackson, and D.J
  Winzor , Biochem. , vol.6, no.8,1967