User`s manual

20 Chapter 3: Theory of Operation
Calorimetry Sciences Corp.
CSC 5300 N-ITC III 21
User’s Manual
site per protein based on structural information, the experimental value of N may still
vary due to error in protein concentration estimation or to degradation of the protein
sample. For experiments performed under conditions in which K can be determined, the
value of N does not affect the tted value of K or ∆H.
Consider the case in which we have two independent binding sites on the protein, but
each site has a different binding constant. The sum of the accessible states of the protein,
expressed as concentrations, is then given as:
The average excess enthalpy is then:
which can be substituted into Equation 3-1 or Equation 3-2. In this case we need to solve
a cubic expression for [X]. This can be readily accomplished using standard numerical
algorithms and the result substituted into Equation 3-12.
More complex models are developed by the same approach. Based on the model
an expression is derived for the average excess enthalpy in terms of the free ligand
concentration, and then the free ligand concentration is expressed in terms of the total
concentrations of ligand and protein generally requiring numerical methods to obtain a
solution.
The following references give further detail on modeling of titration data or general
binding phenomena:
[ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ]
( )
[ ] [ ]( ) [ ]( )
XK1XK1M
XKKXKXK1M
XMXMXMMM
21
2
2121
221
tot
++=
+++=
+++=
Equation 3-11
[ ]
[ ]( ) [ ]( )
[ ]
[ ]( ) [ ]( )
( )
[ ]
[ ]( ) [ ]( )
XK1XK1
XKKHH
XK1XK1
XKH
XK1XK1
XKH
HPH
21
2121
21
22
21
11
j
jj
++
+
+
++
+
++
=
=
Equation 3-12