Abstract
Thermally-induced protein unfolding is commonly described with the two-state model. This model assumes only two types of protein molecules in solution, the native (N) and the denatured, unfolded (U) protein. In reality, protein unfolding is a multistep process, even if intermediate states are only sparsely populated. As an alternative approach we explore the Zimm-Bragg theory, originally developed for the α-helix-to-random coil transition of synthetic polypeptides. The theory includes intermediate structures with concentrations determined by the cooperativity of the unfolding reaction. We illustrate the differences between the two-state model and the Zimm-Bragg theory with measurements of apolipoprotein A-1 and lysozyme by differential scanning calorimetry (DSC) and CD spectroscopy. Nine further protein examples are taken from the literature. The Zimm-Bragg theory provides a perfect fit of the calorimetric unfolding transitions for all proteins investigated. In contrast, the transition curves and enthalpies predicted by the two-state model differ considerably from the experimental results. Apolipoprotein A-1 is ~50% α-helical at ambient temperature and its unfolding follows the classical α-helix-to-random coil equilibrium. The unfolding of proteins with little α-helix content, such as lysozyme, can also be analyzed with the Zimm-Bragg theory by introducing the concept of 'folded' and 'unfolded' peptide units assuming an average unfolding enthalpy per peptide unit. DSC is the method of choice to measure the unfolding enthalpy, , but CD spectroscopy in combination with the two-state model is often used to deduce the unfolding enthalpy. This can lead to erroneous result. Not only are different enthalpies required to describe the CD and DSC transition curves but these values deviate distinctly from the experimental result. In contrast, the Zimm-Bragg theory predicts the DSC and CD unfolding transitions with the same set of parameters.
Highlights
Proteins can fold spontaneously into their native conformations
Cooperative unfolding and two-state model applied to differential scanning calorimetry (DSC) and circular dichroism (CD) spectroscopy 17 5.1
A second quality criterion follows from a comparison of DSC and CD spectroscopy unfolding transitions obtained for a given protein under identical experimental conditions
Summary
2. Two-state model versus sequential protein unfolding 3 2.1. Energetics of ‘folded’ peptide units in globular proteins 6. 3. Protein unfolding measured with CD spectroscopy 7 3.1. Two-state model applied to Apo A-1 unfolding 9 3.3. Zimm–Bragg theory applied to Apo A-1 unfolding 9 3.4. A globular protein with α/β-structure 10 3.5. 4. Thermal unfolding measured with DSC 11 4.1. 5. Cooperative unfolding and two-state model applied to DSC and CD spectroscopy 17 5.1. The total heat of unfolding ΔHe0xp 17 5.2. Equivalence of DSC and CD spectroscopy unfolding transitions? 6. Zimm–Bragg theory applied to globular proteins 20 6.1. An excellent thermodynamic approach to protein unfolding 20 6.2.
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