Molecular Understanding of Calorimetric Protein Unfolding Experiments (original) (raw)
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Protein unfolding. Thermodynamic perspectives and unfolding models
Protein unfolding is a dynamic cooperative process with many short-lived intermediates. Cooperativity means that similar molecular elements act dependently on each other. The thermodynamics of protein unfolding can be determined with differential scanning calorimetry (DSC). The measurement of the heat capacity provides the temperature profiles of enthalpy, entropy and free energy. The thermodynamics of protein unfolding is completely determined with these thermodynamic properties. We emphasise the model-independent analysis of the heat capacity. The temperature profiles of enthalpy H(T), entropy S(T) and free energy G(T) can be obtained directly by a numerical integration of Cp(T). In evaluating different models for protein unfolding. It is essential to simulate all thermodynamic properties, not only the heat capacity. A chemical equilibrium two-state model is a widely used approximation to protein unfolding. The model assumes a chemical equilibrium between only two protein conforma...
Statistical mechanics of warm and cold unfolding in proteins
The European Physical Journal B, 1998
We present a statistical mechanics treatment of the stability of globular proteins which takes explicitly into account the coupling between the protein and water degrees of freedom. This allows us to describe both the cold and the warm unfolding, thus qualitatively reproducing the known thermodynamics of proteins.
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 ...
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.
Kinetics and thermodynamics of folding in model proteins
Proceedings of the National …, 1993
Monte Carlo simulations on a class of lattice models are used to probe the thermodynamics and kinetics of protein folding. We find two transition temperatures: one at To, when chains collapse from a coil to a compact phase, and the other at Tf (< TO), when chains adopt a conformation corresponding to their native state. The kinetics are probed by several correlation functions and are interpreted in terms ofthe underlying energy landscape. The transition from the coil to the native state occurs in three distinct stages. The initial stage corresponds to a random collapse of the protein chain. At intermediate times i¢, during which much of the native structure is acquired, there are multiple pathways. For longer times rr (>> r,) the decay is exponential, suggestive of a late transition state. The folding time scale (= rr) varies greatly depending on the model. Implications of our results for in vitro folding of proteins are discussed.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2015
Motivated by single molecule experiments, we study thermal unfolding pathways of four proteins, chymotrypsin inhibitor, barnase, ubiquitin, and adenylate kinase, using bond network models that combine bond energies and elasticity. The protein elasticity is described by the Gaussian network model (GNM), to which we add prescribed bond binding energies that are assigned to all (nonbackbone) connecting bonds in the GNM of native state and assumed identical for simplicity. Using exact calculation of the Helmholtz free energy for this model, we consider bond rupture single events. The bond designated for rupture is chosen by minimizing the free-energy difference for the process, over all (nonbackbone) bonds in the network. Plotting the free-energy profile along this pathway at different temperatures, we observe a few major partial unfolding, metastable or stable, states, that are separated by free-energy barriers and change role as the temperature is raised. In particular, for adenylate ...
Simple Two-State Protein Folding Kinetics Requires Near-Levinthal Thermodynamic Cooperativity
Proteins-structure Function and Bioinformatics, 2003
Simple two-state folding kinetics of many small single-domain proteins are characterized by chevron plots with linear folding and unfolding arms consistent with an apparent two-state description of equilibrium thermodynamics. This phenomenon is hereby recognized as a nontrivial heteropolymer property capable of providing fundamental insight into protein energetics. Many current protein chain models, including common lattice and continuum Gō models with explicit native biases, fail to reproduce this generic protein property. Here we show that simple two-state kinetics is obtainable from models with a cooperative interplay between core burial and local conformational propensities or an extra strongly favorable energy for the native structure. These predictions suggest that intramolecular recognition in real two-state proteins is more specific than that envisioned by common Gō-like constructs with pairwise additive energies. The many-body interactions in the present kinetically two-state models lead to high thermodynamic cooperativity as measured by their van't Hoff to calorimetric enthalpy ratios, implying that the native and denatured conformational populations are well separated in enthalpy by a high free energy barrier. It has been observed experimentally that deviations from Arrhenius behavior are often more severe for folding than for unfolding. This asymmetry may be rationalized by one of the present modeling scenarios if the effective many-body cooperative interactions stablizing the native structure against unfolding is less dependent on temperature than the interactions that drive the folding kinetics.