Pressure-modulated differential scanning calorimetry. An approach to the continuous, simultaneous determination of heat capacities and expansion coefficients.

A new method is described that permits the continuous and synchronous determination of heat capacity and expansibility data. We refer to it as pressure-modulated differential scanning calorimetry (PMDSC), as it involves a standard DSC temperature scan and superimposes on it a pressure modulation of preselected format. The power of the method is demonstrated using salt solutions for which the most accurate heat capacity and expansibility data exist in the literature. As the PMDSC measurements could reproduce the parameters with high accuracy and precision, we applied the method also to an aqueous suspension of multilamellar DSPC vesicles for which no expansibility data had been reported previously for the transition region. Excellent agreement was obtained between data from PMDSC and values from independent direct differential scanning densimetry measurements. The basic theoretical background of the method when using sawtooth-like pressure ramps is given under Supporting Information, and a complete statistical thermodynamic derivation of the general equations is presented in the accompanying paper.

Folding energetics of ligand binding proteins. I. Theoretical model.

Heat capacity curves as obtained from differential scanning calorimetry are an outstanding source for molecular information on protein folding and ligand-binding energetics. However, deconvolution of C(p) data of proteins in the presence of ligands can be compromised by indeterminacies concerning the correct choice of the statistical thermodynamic ensemble. By convent, the assumption of constant free ligand concentration has been used to derive formulae for the enthalpy. Unless the ligand occurs at large excess, this assumption is incorrect. Still the relevant ensemble is the grand canonical ensemble. We derive formulae for both constraints, constancy of total or free ligand concentration and illustrate the equations by application to the typical equilibrium Nx <=> N + x <=> D + x. It is demonstrated that as long as the thermodynamic properties of the ligand can be completely corrected for by performing a reference measurement, the grand canonical approach provides the proper and mathematically significantly simpler choice. We demonstrate on the two cases of sequential or independent ligand-binding the fact, that similar binding mechanisms result in different and distinguishable heat capacity equations. Finally, we propose adequate strategies for DSC experiments as well as for obtaining first estimates of the characteristic thermodynamic parameters, which can be used as starting values in a global fit of DSC data.

Folding energetics of ligand binding proteins II. Cooperative binding of Ca2+ to annexin I.

The calcium binding properties of annexin I as observed by thermodynamic DSC studies have been compared to the structural information obtained from X-ray investigation. The calorimetric experiment permitted to evaluate both the reaction scheme - including binding of ligand and conformational changes - and the energetics of each reaction step. According to published X-ray data Annexin I has six calcium binding sites, three medium-affinity type II and three low-affinity type III sites. The present study shows that at 37 degrees C annexin I binds in a Hill type fashion simultaneously two calcium ions in a first step with medium affinity at a concentration of 0.6 mM and another three Ca(2+) ions again cooperatively at 30 mM with low affinity. Therefore it can be concluded that only two medium-affinity type II binding sites are available. The third site, that should be accessible in principle appears to be masked presumably due to the presence of the N terminus. In view of the large calcium concentration needed for saturation of the binding sites, annexin I may be expected to be Ca(2+) free in vivo unless other processes such as membrane interaction occur simultaneously. This assumption is consistent with the finding, that the affinity of annexins to calcium is usually markedly increased by the presence of lipids.

Response functions of proteins.

The thermodynamics of protein folding can be studied by a variety of different techniques such as differential scanning calorimetry, differential scanning densimetry and sound velocity measurements. These three methods monitor the different response functions heat capacity, expansion coefficient and compressibility that characterise various aspects of protein dynamics such as equilibrium energy and volume fluctuations and energy-volume correlations. For the development of a comprehensive thermodynamic description of protein behaviour information on these response functions should be combined. As a starting point we provide in the present paper analytical solutions for the determination of the response functions and demonstrate on several examples how to extract a maximum of thermodynamic information on proteins from the measurements of Cp, alpha p and kappa T.

Slow unfolding and refolding kinetics of the mesophilic Rop wild-type protein in the transition range.

We describe the guanidinium hydrochloride induced folding kinetics of the four-helix-bundle protein Rop wild-type (wt) under equilibrium conditions at three temperatures. The choice of appropriate denaturant conditions inside the transition range permitted, in combination with equilibrium transition curves, the determination of both unfolding and refolding rate constants. The ratio of the rate constants at zero denaturant concentration provided equilibrium constants and standard free energy changes that are in good agreement with values obtained in previous differential scanning calorimetry studies. The DeltaG0D values for 19, 25 and 40 degrees C calculated from the present kinetic studies are, respectively, 66.8, 70.8 and 57.2 kJ.mol-1. The unfolding reactions are extremely slow under these conditions. Equilibrium was reached only after 18, 12 and 6 days at 19, 25 and 40 degrees C. These results demonstrate that for Rop wt high stability correlates with slow folding kinetics.

A comparison of the energetics of annexin I and annexin V.

The annexins comprise a family of soluble Ca2+- and phospholipid-binding proteins. Although highly similar in three-dimensional structure, different annexins are likely to exhibit different biochemical and functional properties and to play different roles in various membrane related events. Since it must be expected that these functional differences arise from differences in the characteristic thermodynamic parameters of these proteins, we performed high-sensitivity differential scanning microcalorimetry (DSC) and isothermal guanidinium hydrochloride (GdnHCl)-induced unfolding studies on annexin I and compared its thermodynamic parameters with those of annexin V published previously. The DSC data were analyzed using a model that permits quantitative treatment of the irreversible reaction. It turned out, however, that provided a heating rate of 2 K min-1 is used, unfolding of annexin I can be described satisfactorily in terms of a simple two-state reaction. At pH 6.0 annexin I is characterized by the following thermodynamic parameters: t1/2=61.8 degrees C, DeltaHcal=824 kJ mol-1 and DeltaCp=19 kJ mol-1 K-1. These parameters result in a stability value of DeltaG0D (20 degrees C)=51 kJ mol-1. The GdnHCl induced isothermal unfolding of annexin I in Mes buffer (pH 6.0), yielded DeltaG0D (buffer) values of 48, 60 and 36 kJ mol-1 at 20, 12 and 5 degrees C, respectively. These DeltaG0D values are in reasonable agreement with the values obtained from the DSC studies. The comparison of annexin I and annexin V under identical conditions (pH 8.0 or pH 6.0) shows that despite the pronounced structural homology of these two members of the annexin familiy, the stability parameters are remarkably different. This difference in stability is consistent with and provides a thermodynamic basis for the potential different in vivo functions proposed for these two annexins.

The 'Janus' nature of proteins: systems at the verge of the microscopic and macroscopic world.

Direct measurement of the heat capacity of proteins by microcalorimetry has had a decisive impact on understanding the behaviour of these biopolymers. Statistical mechanics allow a straightforward calculation and prediction of the enthalpy and heat capacity curves from the partition function. We show that these predictions can differ from the more intuitive models used so far for the description of the thermodynamic behaviour of proteins if the transition involves a stoichiometry other than 1:1. Furthermore, we delineate that the characteristics of protein unfolding are governed by the fluctuations associated with the small size of these molecules. Therefore it may be necessary to modify the picture of the unfolding of small proteins in the light of statistical physics, while for very large proteins the current view may be maintained as a useful limiting approximation.