The heat capacity paradox of ligand binding proteins: reconciling the microscopic and macroscopic world

The effect of denaturants on protein thermal stability analyzed through a theoretical model considering multiple binding sites

A novel mathematical development applied to protein ligand binding thermodynamics is proposed, which allows the simulation, and therefore the analysis of the effects of multiple and independent binding sites to the Native and/or Unfolded protein conformations, with different binding constant values. Protein stability is affected when it binds to a small number of high affinity ligands or to a high number of low affinity ligands. Differential scanning calorimetry (DSC) measures released or absorbed energy of thermally induced structural transitions of biomolecules. This paper presents the general theoretical development for the analysis of thermograms of proteins obtained for n-ligands bound to the native protein and m-ligands bound to their unfolded form. In particular, the effect of ligands with low affinity and with a high number of binding sites (n and/or m > 50) is analyzed. If the interaction with the native form of the protein is the one that predominates, they are considered stabilizers and if the binding with the unfolded species predominates, it is expected a destabilizing effect. The formalism presented here can be adapted to fitting routines in order to simultaneously obtain the unfolding energy and ligand binding energy of the protein. The effect of guanidinium chloride on bovine serum albumin thermal stability, was successfully analyzed with the model considering low number of middle affinity binding sites to the native state and a high number of weak binding sites to the unfolded state.

Differential scanning calorimetry as a tool to estimate binding parameters in multiligand binding proteins

The stability of proteins and their interactions with other molecules is a topic of special interest in biochemistry because many cellular processes depend on that. New methods and approaches are constantly developed to elucidate the energetics of biomolecular recognition. In this sense, the application of the theory of macromolecular unfolding linked to ligand binding to differential scanning calorimetry (DSC) has proved to be a useful tool to simultaneously characterize the energetics of unfolding and binding. Although the general theory is well known, the applicability of DSC to study the interaction of biomolecules is not common. In the current work, we estimated the binding parameters of 8-anilinonaphthalene-1-sulfonic acid to human serum albumin using DSC. This model system was chosen due to both the complex stoichiometry and the moderate binding constants. From DSC curves acquired at different ligand concentrations, we obtained the number of bound ligands, the binding constants, and the binding enthalpy for each independent binding site. Compared with those parameters determined by titration calorimetry, the results highlight the potentiality of DSC to estimate binding parameters in multiligand binding proteins.

Pressure-Modulated Differential Scanning Calorimetry: Theoretical Background

We demonstrate in this work and in the accompanying paper that it is possible to measure simultaneously heat capacity and expansibility of biomolecules in a single DSC experiment. In this study, we provide the theoretical basis for this new method based on rigorous statistical thermodynamics. The theoretical treatment presented here demonstrates that there are two additive contributions to the heat capacity at variable pressure, viz. (1) the isobaric heat capacity and (2) an expansibility term, and that these contributions can be experimentally separated to obtain simultaneously both heat capacity and expansibility in continuous DSC temperature scans preformed under pressure modulation. Equations that describe the mixed heat capacity and expansibility signal are derived, and experimental strategies as well as data extraction procedures are discussed.

Phase diagrams: a graphical representation of linkage relations

It is shown here that phase diagrams of ligand-binding biological macromolecules provide a powerful tool for the analysis of reaction mechanisms. The present study provides simple rules for the construction and interpretation of such phase diagrams. We give examples for the derivation of reaction schemes for macromolecules that can bind two different kinds of ligands. By sampling one dimension of a phase diagram it is possible to reconstruct the second dimension, including the correct stoichiometry, positive and negative linkage between the ligands and equilibrium binding constants for the complete series of reactions. The discussion is generalised to temperature and pressure-dependent phase diagrams. To exemplify the new diagram method we analyse the pH-dependent binding of trans-beta-indole acrylic acid to apo-Trp repressor, the pH-dependent thermal denaturation of alpha-chymotrypsinogen A, calcium binding and denaturation of annexin I, high affinity zinc binding to a metallo-beta-lactamase and high-pressure and temperature denaturation of RNase A and staphylococcal nuclease.