Differential scanning microcalorimetry measures the heat capacity of a solution as a continuous function of temperature. In a typical differential measurement, the heat capacity of a sample cell, containing a dilute biomolecule solution in a given solvent, is measured relative to a reference cell, which contains only the solvent, at a constant pressure, as the temperature is continuously changed.
Measurements must be performed under dilute conditions where the proteins do not interact. The partial specific heat capacity of the protein (that is, the protein’s heat capacity in the solute) is extremely small as compared to water and requires a highly precise and sensitive instrument to measure it.
To understand the sensitivity and precision needed for measurements, let us consider a back-of-the-envelope calculation of the calorimetric signal coming from a protein solution containing 3.3 mg mL−1 protein dissolved in water. For a differential measurement, the
observed difference between the heat capacity of the reference cell filled with water and the 3.3 mg mL−1protein solution solution will be:
∆Cpobsv =Cpproteinmprotein−Cpwater∆mwater (6.1)
where the mass of water the protein displaces is∆mwater =mprotein×v¯protein/¯vwater,v¯is
the partial specific volume.
the cell ismprotein=1 mg. Plugging in typical values of these constants[4] for the protein and
water:Cprotein
p =2 J K−1g−1,Cpwater = 4.2 J K−1g−1,v¯protein = 0.73 cm3/g,¯vwater =1 cm3/g
we find: ∆Cpobsv = 2 J gK 10−3g L 3×10−8L− 4.2 J gK 10 −3 g× 0.73 1 =−3.0×10−3J K
However the heat capacity measured for the 300 µL of water is Cwater
p ×
mwater=1.3 J K−1. Quite amazingly, the heat capacity difference due to the protein is
just 1/1000 that of the water’s heat capacity. To make a measurement with a preci- sion of 0.1%, we would require an instrument sensitive to changes on the order of of 1×10−6J K−1[4, 279, 280, 284]. In reality, modern differential scanning calorimeters can
easily measure as small as 10 µg protein in a 300 µL cell, with 10 µJ K−1sensitivity.
Traditionally, DSC instruments contain a reference and and sample cell which are heated in an adiabatic (or quasi-adiabatic) environment. The cells are heated with a constant power and the adiabatic jacket is controlled to closely follow the cell temperature. The system contains two feedback loops, one to maintain a near-zero temperature difference between the sample and reference cell as they are both heated at a constant power (power-compensation) and a second to ensure that the thermal adiabatic jacket closely follows the cell temperature and prevents heat flow between the environment and the sample (adiabatic control loop).
The temperature difference between each cell and the adiabatic jacket are measured by thermoelectric sensors. The thermoelectric sensor between the reference and sample cell produces a voltage proportional to the temperature difference. This voltage is used as the input to a feedback circuit which powers an auxiliary heating element, located in the sample cell. The feedback circuit is designed to reduce the temperature difference between the
sample and reference cell. The power needed to maintain a near-zero temperature difference between the two cells is recorded as a function of temperature. This technique is called a power-compensation technique and measures the additional power needed to keep the sample cell at the same temperature as the reference cell as they are both heated at a constant rate[4, 285]
This power can then be converted to the apparent molar excess heat capacity, Cp, using
the temperature scan rate,dT /dt, molar concentration of the biomolecule,M, and the power supplied to the heaterdQp/dt, whereQp is the heat absorbed at a constant pressure[286]:
Cp =M−1 dQp dt dT dt −1 (6.2)
In recent years nonadiabatic DSCs have become commercially available[4]. The nona- diabatic calorimetric block, shown in figure 6.1, contains two identical platinum capillary cells, one reference and one for the sample, which are connected together through a thermal shunt and contained with a thermally shielded chamber. The thermal shunt effectively fixes the operation volume of the calorimetry cells by shunting them to the thermal shield. In contrast to adiabatic DSC, non-adiabatic DSC controls the temperature outside of the cells through a series of Peltier elements and the thermal jacket leads the heating or cooling of the cell.
During a calorimetric experiment, the temperature of the calorimetric block (thermostat) is modulated to ensure that it is consistently larger than the cells. In this temperature- leading setup, heat flows to the cells from the heated calorimetric block and the cells follow the temperature of the heated surroundings. The temperature difference between the two reference and sample cells is monitored with bismuth telluride thermopiles[3]. The cells are
A
B
C
D
E
F
G
H
I
Figure 6.1:Schematic of non-adiabatic DSC. (A) Resistive heater for sample cell. (B) Re-
sistive heater for reference cell. (C) Thermoelectric sensor to detect temperature difference between cells. (D) Thermal Shield. (E) Peltier elements (F) Peltier elements. (G) Sample inlet tubes and wound capillary cells at bottom. (H) Top of manifold containing manostat and pressure sensors. (I) Thermal shunt. Schematic drawn after Privalov[3, 4].
heated at a controlled rate, which is determined by the temperature shift between the cells and the calorimetric block.
This setup also enables the sample to be cooled. Both the sample and reference cell contain Peltier elements which are controlled by a computer to minimize the temperature difference between the two cells. The power difference between these two is recorded by the computer and used to convert to the molar heat capacity as described above. Furthermore, the Peltier elements can be heated appropriately to compensate for differences in the thermal properties of the two cells, determined using a calibration run prior to the experiments. These modifications significantly improve the stability, temperature control, and baseline[3, 4]. Current commercial instruments have a typical heating and cooling rate of 0.1◦C min−1to
2.0◦C min−1and have an accessible temperature range of −10◦C to 120◦C.
To avoid bubbles which could interfere with the signal, and to prevent the solvent from boiling, the cells are connected to a common manostat which can apply an excess pressure of 1 atm to 3 atm using a dry nitrogen supply. An excess pressure of 6 atm will increase the boiling temperature of water to approximately 120◦C[4].
In addition to the non-adiabatic design and manostat, additional improvements are found by utilizing a capillary cell, which permits the cells to be permanently placed in the calori- metric block and the volume to be fixed. The capillary cells generally consist of a narrow capillary wound into coils. This enables sample volumes (typically 300 µL) to be used and allows the cells to be easily reloaded using a pipette and removed using suction. The capil- laries have a high surface to volume ratio which also reduces sample temperature gradients and enables faster scanning rates.
Another benefit is that capillary cells do not suffer from thermal gradients induced by fluid convection during heating, which ampules and cylindrical cells suffer from[279, 280, 285]. This is critical because the viscosity of a protein solution is strongly temperature dependent. As the viscosity changes during heating, fluid convection introduces temperature gradients which induce calorimetric artifacts[4].