Invited Reviews
Stability of proteins: Temperature, pressure and the role of the solvent

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Abstract

We focus on the various aspects of the physics related to the stability of proteins. We review the pure thermodynamic aspects of the response of a protein to pressure and temperature variations and discuss the respective stability phase diagram. We relate the experimentally observed shape of this diagram to the low degree of correlation between the fluctuations of enthalpy and volume changes associated with the folding–denaturing transition and draw attention to the fact that one order parameter is not enough to characterize the transition. We discuss in detail microscopic aspects of the various contributions to the free energy gap of proteins and put emphasis on how a cosolvent may either enlarge or diminish this gap. We review briefly the various experimental approaches to measure changes in protein stability induced by cosolvents, denaturants, but also by pressure and temperature. Finally, we discuss in detail our own molecular dynamics simulations on cytochrome c and show what happens under high pressure, how glycerol influences structure and volume fluctuations, and how all this compares with experiments.

Introduction

The stability of proteins against changes in the thermodynamic as well as in the chemical conditions of the solvent is only marginal. In some cases the free energy gap which separates the native from the denatured state can be small enough so that even spontaneous denaturation, followed by irreversible association or dissociation reactions, may occur with severe consequences concerning certain diseases (e.g. [1]). The reason for a rather small free energy difference of proteins between their native and denatured state is due to the fact that the entropic contribution and the enthalpic contribution to the folding process almost cancel [2], [3]. Both contributions are large, but have opposite signs: The total entropy of the protein plus the associated water shell decreases as the protein folds, hence, the respective contribution to the free energy change is positive. The enthalpic part is negative, mostly due to hydrogen bond formation. A typical order of magnitude of the free energies of unfolding is just some tens of kJ/mol [4]. In addition, the solvent plays a crucial role in protein stability. The natural solvent for proteins is water, but it is always mixed with cosolvents which influence the ionic strength, the pH values, the chemical affinity to certain molecular groups on the protein surface, etc. All these properties have a tremendous influence on protein stability, they can induce unfolding or folding, and may as well lead to significant changes of the critical physical parameters, i.e. the critical temperature and the critical pressure which determine the phase boundaries between the native and the denatured states. The physical properties of water, such as its ability to form hydrogen bonds, the hydrophobic and hydrophilic interaction with respective amino acids, the high specific heat of locally ordered structures, structure and density variations, etc., have a strong influence on the stability boundaries [5].

In this paper, we want to address the problem of protein stability under various aspects: First, we will discuss the stability of proteins against changes of thermodynamic variables, like pressure and temperature, and will focus on the physics of the stability phase diagram of proteins [6]. We will address the role of the solvent in thermally or pressure-induced denaturation processes. An important aspect concerns the microscopic processes involved in protein denaturation. We will also consider the thermodynamic fluctuation quantities which determine the pressure–temperature stability phase diagram and will, based on a correlation analysis of these quantities, trace the roots of the experimentally observed elliptic shape of the phase diagram. We will also present a brief survey of experiments on protein stability including our own on a modified cytochrome c. Finally we try to back up our reasoning, conclusions and model considerations by computer simulations.

Section snippets

The 2-state model and the phase transition picture

The folding–denaturing transition in proteins is a highly cooperative process. In certain cases, as a rule for smaller proteins, it suffices to describe this transition within a 2-state approach involving the native state N and the denatured state D, only. We stress that both states are rather characterized by huge areas in structural phase space than by just two single points. We associate all those states in which the protein is working with the native state N, and all those states in which

General remarks

Since the stability of proteins results from a large number of counteracting enthalpic and entropic contributions which favor the folded state as compared to the unfolded state only marginally, it is clear that changes in the interactions of the protein with the solvent, for instance by adding a cosolvent, may have a severe influence on protein stability. The nature and the magnitude of the individual contributions of the protein solvent interactions to the free energies GD and GN of the

Survey of experiments

Experiments on protein stability as a function of the various control parameters like pressure, temperature, cosolvent, pH, etc., are numerous. However, experiments in which the complete stability phase diagram was determined are still quite scarce. The literature on the influence of pressure and temperature on protein stability was recently comprehensively reviewed [6], [50], [51].

We first focus on the stability phase diagram of proteins in the PT plane. The first experiments in this respect

Molecular interactions

The most interesting observables in the investigation of the folding–unfolding transition via fluorescence spectroscopy are the 1st and the 2nd moments of the fluorescence 00-transition. These moments contain all probe solvent interactions. Although the absolute magnitude of the solvent shift is not easily accessible, in an unfolding experiment, it is only the relative changes which matter. Since the probe–solvent interactions are known in great detail [67], [68], [69], [70], it is, in some

Fluctuations and thermodynamic parameters

The description of the stability phase boundary via a general 2nd order curve in P and T (Eq. (2.2)) is strongly dependent on the assumption that entropy and volume of the system under consideration are well described by linear dependencies on pressure and temperature. An equivalent statement is that the 2nd derivatives of the Gibbs-free energy, G, are well-defined system constants, i.e. do not depend anymore on pressure and temperature. These 2nd order derivatives of G(P,T) are intimately

Roots of the elliptic shape of the stability PT-phase diagram and glass-like features of the folding–denaturing transition

The simple phase transition picture for the folding–denaturing transition of proteins as reflected in Eq. (2.1) yields a 2nd order curve (Eq. (2.2)) for the phase boundary. Practically all experiments on stability phase diagrams of proteins performed so far suggest that the phase boundary has an elliptic shape. This shape may be subject to some distortions in case the material parameters CP, κ, and α are still dependent on pressure and temperature [74], but this would not imply an essential

Microscopic aspects of protein denaturation

As we have been stressing several times, the stability/instability balance of native proteins is related to a large number of small cooperative contributions and subtle compensations of attractive and repulsive interactions. These interactions involve not only the conformational degrees of freedom of the polypeptide chain, but also the degrees of freedom of internal and external hydration waters as well as the close interplay between protein and solvent [16]. Apart from enthalpic contributions,

Computer simulations: The response of cytochrome c to external pressure and the role of the cosolvent as seen by a local sensor in the heme pocket

The structural, dynamical and energetical properties of proteins in solution can be studied in atomic detail by molecular dynamics simulations (MD) (for recent reviews on methods and developments, see, e.g. [114], [115], [116], [117], [118]; some applications in relation to the subject of this review can be found in [119], [120], [121], [122], [123], [124], [125], [126], [127], [128]). In the following, we focus on classical MD simulations of cytochrome c to calculate radial distribution

Acknowledgement

We acknowledge financial support from the DFG (Fr 456/25-4, A1 and SFB 533, B5 and C2) and from the Fonds der Chemischen Industrie. We want to thank our friends Jane Vanderkooi, Wolfgang Doster and Harald Lesch who have contributed a lot to this work through stimulating discussions and through experimental support.

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