Protein unfolding. Thermodynamic perspectives and unfolding models (original) (raw)
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Evaluation of thermodynamic properties of irreversible protein thermal unfolding measured by DSC
Journal of Thermal Analysis and Calorimetry, 2005
We assessed the applicability of the extrapolation procedure at infinite scanning rate to differential scanning calorimetry (DSC) data related to irreversible protein unfolding. To this aim, an array of DSC curves have been simulated on the basis of the Lumry-Eyring model N↔U→F. The results obtained confirmed that when the apparent equilibrium constant K app (T=T1/2) is lower than 3, the application of the extrapolation procedure provides accurate thermodynamic parameters. Although this procedure applies only to monomeric proteins for which the Lumry-Eyring model is a reasonable approximation, it will hopefully contribute to increase the potential of DSC in obtaining reliable thermodynamic information regarding the folding/unfolding equilibrium.
Thermochimica Acta, 2010
A reliable estimation of heat capacity of denaturation (C p) is necessary to calculate the free energy of unfolding of proteins. For marginally stable proteins, such as mutants of a protein or proteins at low pH or under denaturating conditions, the pre-transition region is not fully populated by the native state. Analysis of differential scanning calorimeter (DSC) data under such conditions may not yield a reliable value of C p and other associated thermodynamic parameters of unfolding. Analysis of denaturation profiles of (a) cytochrome c at pH 2.5, 3 and 8 and (b) myoglobin at pH 4, show that an accurate value of C p can be extracted from a single unfolding profile obtained spectroscopically by including low temperature data.
Molecular Understanding of Calorimetric Protein Unfolding Experiments
SSRN Electronic Journal, 2021
Protein unfolding is a dynamic cooperative equilibrium between short lived protein conformations. The Zimm-Bragg theory is an ideal algorithm to handle cooperative processes. Here, we extend the analytical capabilities of the Zimm-Bragg theory in two directions. First, we combine the Zimm-Bragg partition function Z(T) with statistical-mechanical thermodynamics, explaining the thermodynamic system properties enthalpy, entropy and free energy with molecular parameters only. Second, the molecular enthalpy h0 to unfold a single amino acid residue is made temperaturedependent. The addition of a heat capacity term cv allows predicting not only heat denaturation, but also cold denaturation. Moreover, it predicts the heat capacity increase 0 p C ∆ in protein unfolding. The theory is successfully applied to differential scanning calorimetry experiments of proteins of different size and structure, that is, gpW62 (62aa), ubiquitin (74aa), lysozyme (129aa), metmyoglobin (153aa) and mAb monoclonal antibody (1290aa). Particular attention was given to the free energy, which can easily be obtained from the heat capacity Cp(T). The DSC experiments reveal a zero free energy for the native protein with an immediate decrease to negative free energies upon cold and heat denaturation. This trapezoidal shape is precisely reproduced by the Zimm-Bragg theory, whereas the so far applied non-cooperative 2-state model predicts a parabolic shape with a positive free energy maximum of the native protein. We demonstrate that the molecular parameters of the Zimm-Bragg theory have a well-defined physical meaning. In addition to predicting protein stability, independent of protein size, they yield estimates of unfolding kinetics and can be connected to molecular dynamics calculations.
Proteins: Structure, Function, and Bioinformatics, 2008
The change in heat capacity, ΔC p , upon protein unfolding has been usually determined by calorimetry. A non-calorimetric method which employs the Gibbs-Helmholtz relationship to determine ΔC p has seen some use. Generally, the free energy change upon unfolding of the protein is determined at a variety of temperatures and the temperature at which ΔG is zero, T m , and change in enthalpy at T m are determined by thermal denaturation and ΔC p is then calculated using the Gibbs-Helmholtz equation. We show here that an abbreviated method with stability determinations at just two temperatures gives values of ΔC p consistent with values from free energy change upon unfolding determination at a much wider range of temperatures. Further, even the free energy change upon unfolding from a single solvent denaturation at the proper temperature, when coupled with the melting temperature, T m , and the van't Hoff enthalpy, ΔH vH , from a thermal denaturation, gives a reasonable estimate of ΔC p , albeit with greater uncertainty than solvent denaturations at two temperatures. We also find that non-linear regression of the Gibbs-Helmholtz equation as a function of stability and temperature while simultaneously fitting ΔC p , T m , and ΔH vH gives values for the last two parameters that are in excellent agreement with experimental values.
Physical Chemistry Chemical Physics, 2010
Interpretations of data in the extensive literature on the unfolding of proteins in aqueous solution follow a variety of methods involving assumptions leading to estimates of thermodynamic quantities associated with the unfolding transition. Inconsistencies and thermodynamic errors in these methods are identified. Estimates of standard molar free energies and enthalpies of unfolding using incompletely defined equilibrium constants and the van't Hoff relation are unsound, and typically contradict model-free interpretation of the data. A widely used routine for estimating the change in heat capacity associated with unfolding based on changes in the unfolding temperature and enthalpy co-induced by addition of denaturant or protective additives is thermodynamically incorrect by neglect of the Phase Rule. Many models and simulations predicting thermodynamic measures of unfolding are presently making comparisons with insecure quantities derived by incorrect thermodynamic analyses of experimental data. Analysis of unfolding via the Gibbs-Duhem equation with the correct Phase Rule constraints avoids the assumptions associated with incomplete equilibrium constants and misuse of the van't Hoff relation, and applies equally to positive, negative, sitewise or diffuse solute binding to the protein. The method gives the necessary relations between the thermodynamic parameters for thermal and isothermal unfolding and is developed for the case of two-state unfolding. The differences in binding of denaturants or stabilizers to the folded and unfolded forms of the protein are identified as major determinants of the unfolding process. The Phase Rule requires the temperature and enthalpy of unfolding to depend generally on the protein concentration. The available evidence bears out this expectation for thermal unfolding, indicating that protein-protein interactions influence folding. A parallel dependence of the denaturant concentrations for isothermal unfolding on the protein concentration is anticipated. The degree of unfolding as measured by UV, CD, fluorescence and other non-calorimetric methods may not show the same temperature and concentration ranges for unfolding among themselves or as compared to DSC or isothermal calorimetry. Such disparities indicate distinct stages in unfolding detectable by particular methods.
The Journal of Chemical Physics, 2005
Thermal unfolding of proteins is compared to folding and mechanical stretching in a simple topology-based dynamical model. We define the unfolding time and demonstrate its low-temperature divergence. Below a characteristic temperature, contacts break at separate time scales and unfolding proceeds approximately in a way reverse to folding. Features in these scenarios agree with experiments and atomic simulations on titin.
The Journal of Physical Chemistry B, 2004
The quasi-Gaussian entropy (QGE) theory was used to formulate a statistical mechanical model describing the thermodynamics of the folding/unfolding process of single-domain proteins. The model was parametrized using experimental data obtained from differential scanning calorimetry (DSC) of a set of proteins. The results showed that the model is able to reproduce the experimental behavior in the usual temperature range, for all the analyzed proteins. Furthermore, a remarkable similarity of some parameters of the model, when normalized per residue and corresponding to well-defined physical properties, was found. Interestingly, at low temperature, the model provides cold denaturation features for all the proteins. Finally, a general description of the folding/ unfolding process and stability, based on the physical view provided by the model, is discussed.
Journal of Molecular Biology, 2002
To what extent do general features of folding/unfolding kinetics of small globular proteins follow from their thermodynamic properties? To address this question, we investigate a new simplifed protein chain model that embodies a cooperative interplay between local conformational preferences and hydrophobic burial. The present four-helix-bundle 55mer model exhibits proteinlike calorimetric two-state cooperativity. It rationalizes native-state hydrogen exchange observations. Our analysis indicates that a coherent, self-consistent physical account of both the thermodynamic and kinetic properties of the model leads naturally to the concept of a native state ensemble that encompasses considerable confomational fluctuations. Such a multiple-conformation native state is seen to involve conformational states similar to those revealed by native-state hydrogen exchange. Many of these conformational states are predicted to lie below native baselines commonly used in interpreting calorimetric data. Folding and unfolding kinetics are studied under a range of intrachain interaction strengths as in experimental chevron plots. Kinetically determined transition midpoints match well with their thermodynamic counterparts. Kinetic relaxations are found to be essentially single exponential over an extended range of model interaction strengths. This includes the entire unfolding regime and a significant part of a folding regime with a chevron rollover, as has been observed for real proteins that fold with non-two-state kinetics. The transition state picture of protein folding and unfolding is evaluated by comparing thermodynamic free energy profiles with actual kinetic rates. These analyses suggest that some chevron rollovers may arise from an internal frictional effect that increasingly impedes chain motions with more native conditions, rather than being caused by discrete deadtime folding intermediates or shifts of the transition state peak as previously posited.
Thermodynamic Model for the Analysis of Calorimetric Data of Oligomeric Proteins
The Journal of Physical Chemistry B, 2008
The thermodynamic parameters for the process of protein unfolding can be obtained through differential scanning calorimetry. However, the unfolding process may not be a two-state one. Between the native and the unfolded state, there may be association or dissociation processes or the formation of an intermediate state. As a consequence of this, the precise interpretation of the calorimetric data should be done with a specific thermodynamic model. In this work, we present two general models for the unfolding process of an oligomeric protein: N n h nN h nD (model A) and N n h I n h nD (model B). In model A, the first step represents the dissociation of the oligomer into the monomeric native species, and the second step represents the denaturation process. In model B, the first step represents the conformational change of the oligomer, and the second step represents the dissociation of this species with the concomitant unfolding process. A canonical ensemble was employed to describe these systems, by considering that the total protein concentration remains constant. In the present work, we show and analyze the behavior of these systems in different conditions and how this analysis could help with the identification of the unfolding mechanism experimentally observed.
2002
To what extent do general features of folding/unfolding kinetics of small globular proteins follow from their thermodynamic properties? To address this question, we investigate a new simplifed protein chain model that embodies a cooperative interplay between local conformational preferences and hydrophobic burial. The present four-helix-bundle 55mer model exhibits proteinlike calorimetric two-state cooperativity. It rationalizes native-state hydrogen exchange observations. Our analysis indicates that a coherent, self-consistent physical account of both the thermodynamic and kinetic properties of the model leads naturally to the concept of a native state ensemble that encompasses considerable confomational fluctuations. Such a multiple-conformation native state is seen to involve conformational states similar to those revealed by native-state hydrogen exchange. Many of these conformational states are predicted to lie below native baselines commonly used in interpreting calorimetric data. Folding and unfolding kinetics are studied under a range of intrachain interaction strengths as in experimental chevron plots. Kinetically determined transition midpoints match well with their thermodynamic counterparts. Kinetic relaxations are found to be essentially single exponential over an extended range of model interaction strengths. This includes the entire unfolding regime and a significant part of a folding regime with ...