Fig Comparison of injectionpulse areas from Fig with the calculated values

Differential Scanning Mode

The principal application of this technique in biological research is the determination of the thermodynamic properties of denaturation (i.e., unfolding) of macromolecules, proteins in particular. The scanning feature indicates that the temperature of the reference cell on the left of Fig. 11.21 is increased approximately linearly in time, at a rate of about 1 K/s. The temperature ramp rate needs to be slow enough for the system in the active cell to remain in equilibrium during the transient. The differential aspect refers to the comparison of the temperatures in the active cell on the right in Fig. 11.21 with that in the reference cell. The control electronics adjusts the heating or cooling rate in the active cell to maintain a zero temperature difference between the two cells at all times.

As the temperature is raised, the control electronics records the cumulative heat inputs to the two cells. Since unfolding involves breaking many bonds within the folded protein, the process is endothermic and heat must be added to the active cell in order for its temperature to match that of the reference cell.

Consider the heat inputs in a temperature interval dT. Since the reference cell contains only water (and perhaps a buffer), the heat required to achieve the temperature rise is:

dQref = nwCpwdT

where nw is the number of moles of water in both the reference cell and the active cell. CPw is the specific heat of water. In addition to nw moles of water, the active cell contains np moles of the protein. In the temperature interval dT, the fraction of protein in the unfolded state increases by df, so the heat input to the active cell for the temperature interval dT is:

CPu and Cpf are the heat capacities of the unfolded and folded states of the protein, respectively, and AH u is the enthalpy change upon unfolding. The first term in the above equation accounts for the effect of the heat capacities of the two states and their relative amounts at the current temperature. The second term is the heat that must be added to the active cell as a differential amount of unfolding (df) occurs. The third term is the heat absorbed by the water present in the active cell. The contribution of the water in the two cells is removed by combining the two heat input equations to give an apparent heat capacity:

The next step is to express f in terms of the thermodynamic properties of the denaturation reaction, namely AH £ , ASJJ and CPu and CPf. This analysis has been developed in Sect.11.5.1: Eq (11.10) gives the equilibrium constant, KU, in terms of the standard Gibbs free energy of the unfolding process, AG ° ; the latter is expressed in terms of the thermodynamic properties by Eq

(11.11); finally, the fraction unfolded, f is expressed in terms of the equilibrium constant by Eq

(11.12). These relations, plus the Van't Hoff equation Eq (10.25) relating the temperature derivative of KU to the enthalpy change on unfolding, convert the apparent heat capacity to:

Figure 11.24 is a plot of Eq (11.73) for the same thermodynamic properties that produced Fig. 11.7. These properties are for 298 K, which is the reference temperature in Eq (11.11).

At low temperature, KU ® 0 and the apparent heat capacity reduces to CPf. At the opposite limit of high temperature, KU ® ¥ and the apparent heat capacity approaches CPu. The bulk of the f ® u conversion takes place over a narrow temperature range of ~ 15oC. It is important to note that the height and width of the peak between 370 and 380 K in Fig. 11.24 depends not only upon AH u but on ASJJ and the difference in the heat capacities of the folded and unfolded states as well.

Temperature, K

Fig. 11.24 Response of a differential scanning calorimeter to unfolding of a protein in aqueous solution. The reaction properties at 298 K are: CPf = 0.2 kJ/mole-K

Temperature, K

Fig. 11.24 Response of a differential scanning calorimeter to unfolding of a protein in aqueous solution. The reaction properties at 298 K are: CPf = 0.2 kJ/mole-K

AH U = 50 kcal / mole; AS^ = 0.1kcal / mole - K; C Pu - C Pf = 1.5 kcal / mole - K

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Solar Panel Basics

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