User`s manual

16 Chapter 3: Theory of Operation

Calorimetry Sciences Corp.

CSC 5300 N-ITC III 17

User’s Manual

shows that increased overall curvature of the thermogram is generated with decreasing

values of the association constant, K

The total heat observed is directly proportional to ∆H

, as illustrated in Figure 3-5b. It

follows that the lower the K value, the higher ∆H

must be to calculate K

and ∆H values

with a given reliability.

The limiting values of K and ∆H must simultaneously yield a curved plot of q

versus

moles of titrant and an accurately measured heat.

Mathematical Modeling

Introduction to Equilibrium Models

The thermodynamics of ligands binding to macromolecules have been thoroughly

investigated and described. Here we discuss only simple models and present the

framework for developing more complex ones. Interested users should refer to the

literature for more advanced discussions.

Relating Heat, Enthalpy, and Binding Constants

In a calorimetric experiment, the heat measured for a given titration is equal to the

difference in the enthalpy of the system after and before the injection. The system is

dened as the contents of the sample cell after the injection, and as the contents of the

sample cell plus the material to be injected before the injection. The enthalpy of the

system is given as the average excess enthalpy, <∆H>, times the moles of protein. Thus,

the heat observed for the i

injection is given as:

where C is the concentration of protein and V is the volume. If there is no protein in the

injection syringe, and assuming ideal solutions (i.e. no dilution heat), then the last term in

Equation 3-1 is zero. The cumulative heat at the i

injection is given as:

injinj

inj

1i1i

VCHVCHVCH ∆−∆∆=

−−

−

Equation 3-1