Fig. 11.22 temperature response of an injection calorimeter time
Fig. 11.22 temperature response of an injection calorimeter
The temperature spikes following each injection of ligand are due to the heat released by binding of ligands to sites on the macromolecules and the heat removed by the cooling apparatus immersed in the solution. The rate of heat removal from the solution is proportional to the departure of the temperature from the reference temperature, which is also the temperature of the cooling system: Q = E x AT . Here E is the product of the heat transfer coefficient between the cooling surface and the solution and the heat transfer area. The integral of the heat removal rate is the heat released during an injection pulse:
Q j = E JaT dt j is the injection number, which in Fig. 11.22, runs from 1 to 11. The conditions of the experiment are:
[Linj] = ligand concentration in injected solution = 16 mM Vinj = volume of each injection, liters = 0.4 liter
[So]o = concentration of binding sites in the fresh macromolecule solution = 10 mM Vo = volume of the fresh macromolecule solution = 4 liters
After j injections, the volume of the solution is Vo + jVinj and a total of jVinj[Linj] moles of ligand have been added. The total ligand concentration (corresponding to [Lo] in Eq (11.15)) is:
After j injections of ligand, the total concentration of sites is:
With these concentrations, and an assumed value of the binding equilibrium constant K, the quantities X and Y of Eqs (11.18) are computed and the ratio of bound ligand to total ligand, y/(1+y), is obtained from Eqs (11.17) and (11.20). Once done, the number of moles of bound ligand at the end of injection j is given by:
nbj = [S.L]j(Vo + jVinj) = ^[Lo ]j (Vo + jV^ ) 1 + y and the heat released during injection j is:
In order to reproduce the injection pulses shown in Fig. 11.22, the required binding properties are: K = 0.72 mM-1 and Aha = 58 kJ/mole. The comparison of the energies of each injection from the "data" in Fig. 11.22 with the model predictions are shown in Fig. 11.23.
The objective of the above exercise was to demonstrate that data such as those shown schematically in Fig 11.22 can be utilized to provide information not only on the energetics of the biological reaction of interest, but on the equilibrium properties as well.
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