Theory and Practice of DSC Measurements on Proteins

Jörg Rösgen; Hans-Jürgen Hinz    Institut für Physikalische Chemie, Westfälische Wilhelms Universität Münster, Schloβplatz 7, 48149 Münster, Germany

1 INTRODUCTION

Proteins are fascinating biological and physical objects. The investigation of protein energetics is not only important for the understanding of their biological function, such studies have also an intrinsic heuristic value for the rationalisation of some unique physical properties of proteins that result from the small size of these macromolecules compared to the magnitude of standard classical thermodynamic systems [1]. The understanding of the physical properties of proteins will also enhance the understanding of their biological reactions.

Experimental access to the energetic properties of proteins can be obtained by several methods. However, none of these methods provide such a direct and powerful approach as differential scanning calorimetry. DSC monitors the response function “heat capacity” which is directly related to the partition function of the system. Knowledge of the partition function is sufficient to derive all the thermodynamic information on the system.

2 THE DSC-EXPERIMENT

2.1 Sample preparation

An important starting point for a successful DSC experiment is the careful preparation of all solutions. Generally the buffer should be filtered and degassed. The sample solution should be essentially free of oxygen, especially if there are free cysteines in the protein [2]. If ligands are involved, their concentrations have to be adjusted with great care. This is also true of H+ ions as ligands. For example, in some cases pH-shifts of a few tenth of a pH unit can result in remarkable shifts in the unfolding temperature of a protein [3].

The protein must be dialysed exhaustively against buffer before the measurement. Typical protein concentrations that can be measured accurately by present day DSC instrumentation are in the range of 0.1 mg/ml to 10 mg/ml. High concentrations yield a favourable signal to noise ratio, but they may favour unspecific irreversible aggregation of the samples.

2.2 Measurement and data treatment

DSC monitors the energy needed to raise the temperature of the sample. Heating rates between 0.1 and 2 K/min are routinely employed with protein solutions. The temperature scans must be done with both the sample and the equilibrium dialysis buffer solution. The difference in heat capacity between these solutions – the so-called apparent heat capacity ΔCp,app – is the basis for all Cp calculations.

This difference originates from the replacement of buffer solution by proteins. The corresponding equation is:

Cp,app=cp,buffer·mbuffer−cp,protein·mprotein,

where mbuffer and 'mprotein are, respectively, the mass of the replaced buffer and the protein. Introducing the specific volume v = V/m and solving for the heat capacity of the protein one obtains the equation

p,protein=Cp,buffer·vproteinvbuffer−ΔCp,appmprotein.

At low buffer concentration the heat capacity of the buffer is not very different from the heat capacity of water. Therefore often the heat capacity of water at room temperature (1 cal/gK = 4.184 J/gK) is used as an approximate value for the specific: heat capacity of the buffer cp,buffer. However, if accurate data are needed, a third measurement of water against buffer must be performed, which yields the difference in heat capacity between buffer and water. Since the heat capacity of water is known accurately and can be expressed by the following polynomial equation based on the data of Stimson [4]

p,water[J/gK]=4.2174−3.176894·10−3T+8.574342·10−5T2−9.3402·10−7T3+3.94926·10−9T4

(fitted to a fourth order polynomial in temperature [°C]), cp,buffer can be determined properly, if necessary. As long as no absolute values of heat capacity are required, but only transition parameters such as enthalpies or entropies are of interest, approximate values for the specific volumes may be employed. Frequently mean values of vprotein = 0.74 ml/g and vbuffer ≈ 1 ml/g have been used. However, in general it is preferable to determine experimentally the variation with temperature of both specific volumes directly [5,6] or take the individual values from data collections [7]. The specific volume of water is given by the following expression [8]

water[ml/g]=(1+16.87985·10−3T)/(0.9998395+16.945176·10−3T−7.9870401·10−6T2−46.170461·10−9T3+105.56302·10−12T4−280.54253·10−15T5).

3 THERMODYNAMIC ANALYSIS OF HEAT CAPACITY CURVES

In this section heat capacity is interpreted in a classical thermodynamical way. A more general statistical thermodynamical analysis in a later section will show some differences in interpretation, which renders the DSC method an even more powerful tool in the investigation of protein folding.

3.1 The shape of heat capacity curves

In the simplest case a heat capacity curve of a protein consists of three parts. There are two regions showing roughly a linear temperature dependence of Cp separated by a peak (Figure 1). This peak reflects a first order transition between the two common states of proteins, the so-called native and the denatured state. The native state is the biologically functional state which is populated at physiological conditions. It is also characterised by a well defined three-dimensional structure. In contrast the denatured state has no defined single structure and lacks biological function. The transition region is marked by a heat absorption peak. Its stepwise integrated area has been assumed traditionally to be proportional to the fraction of denatured molecules or equivalently to the population shift. The midpoint temperature of the transition is called T1/2 and has been traditionally defined as the temperature at which 50% of the molecules have been denatured.

3.2 Protein stability

In the present survey protein stability will be defined thermodynamically [9]. Alternatively for other purposes it may be useful to characterise protein stability by the time during which a protein population shows biological activity. Such a criterion is not based on thermodynamic grounds but is rather a question of irreversible kinetics. Therefore we shall refer in this discussion to protein stability in the strict thermodynamic manner by using the standard Gibbs energy change of unfolding NDG0(T) as a quantitative measure of protein stability.

The use of NDG0(T) as a quantitative measure of stability implies reversible experimental conditions. Therefore measurements have to be optimised to exclude the occurrence of irreversibility. Two mayor causes of irreversibility can be distinguished. First, for the establishment of equilibrium conditions the scan rate must be slow compared to the folding kinetics [10,11]. Otherwise the Cp(T)-curve will become distorted. Second, reversible unfolding may be perturbed by an irreversible step following unfolding, if the heating rate is too slow compared with the rate of the irreversible reaction. Interference by such a process can be avoided, if the measurement is completed before a significant amount of the irreversibly misfolded state has accumulated [12-14], The proper choice of the scan rate is therefore dictated by the intrinsic folding properties of the protein but also by the response time of the DSC instrument [15]. These constraints may lead to both an upper and lower limit of the heating rate.

The quantitative description of the transition curve shown in Figure 1 can be accomplished in the following manner. The overall excess heat contribution NDH0(T1/2) of the unfolding transition is represented by the area of the peak, since thermodynamically the heat capacity at constant pressure is defined by the equation

p=(∂H∂T)p.

Furthermore this means that the heat capacity difference between two states N and D, given by equation...