User`s manual

18 Chapter 3: Theory of Operation

Calorimetry Sciences Corp.

CSC 5300 N-ITC III 19

User’s Manual

In order to determine binding constants and enthalpy changes from the calorimetric data

we need to have a model for the average excess enthalpy terms. The simplest binding

model is for one ligand binding to each protein with a binding constant of K and a

binding enthalpy of ∆H. K for this system is expressed as:

where M represents the protein (or any other macromolecule) and X represents the

ligand. For this system the protein can exist in two states, either bound or free. By

rearranging Equation 3-3 and substituting, the sum of the accessible states of the protein,

expressed as concentrations, is given as:

Note that [M]

tot

is the same as C in Equation 3-1. The population of bound protein, P

is the proportion of the bound protein to the total protein. Applying Equation 3-3 and

Equation 3-4 yields:

In general, the average excess enthalpy is given as the sum of the population of each

state, j, times the change in enthalpy to get to that state, ∆H

For this case then:

VCH∆==

∑

Equation 3-2

[ ]

[ ][ ]

K =

Equation 3-3

[ ] [ ] [ ] [ ] [ ]( )

XK1MMXMM

tot

+=+=

Equation 3-4

[ ]

[ ] [ ]

[ ]

XK1

Equation 3-5

[ ]

XK1

HHPH

∆=∆=∆

∑

Equation 3-6