Protein phase diagrams: the physics behind their elliptic shape

Pressure, motion, and conformational entropy in molecular recognition by proteins

The thermodynamics of molecular recognition by proteins is a central determinant of complex biochemistry. For over a half-century, detailed cryogenic structures have provided deep insight into the energetic contributions to ligand binding by proteins. More recently, a dynamical proxy based on NMR-relaxation methods has revealed an unexpected richness in the contributions of conformational entropy to the thermodynamics of ligand binding. Here, we report the pressure dependence of fast internal motion within the ribonuclease barnase and its complex with the protein barstar. In what we believe is a first example, we find that protein dynamics are conserved along the pressure-binding thermodynamic cycle. The femtomolar affinity of the barnase-barstar complex exists despite a penalty by -TΔS_conf of +11.7 kJ/mol at ambient pressure. At high pressure, however, the overall change in side-chain dynamics is zero, and binding occurs with no conformational entropy penalty, suggesting an important role of conformational dynamics in the adaptation of protein function to extreme environments. Distinctive clustering of the pressure sensitivity is observed in response to both pressure and binding, indicating the presence of conformational heterogeneity involving less efficiently packed alternative conformation(s). The structural segregation of dynamics observed in barnase is striking and shows how changes in both the magnitude and the sign of regional contributions of conformational entropy to the thermodynamics of protein function are possible.

Pressure and temperature dependence of fluorescence anisotropy of green fluorescent protein

We have studied the effect of high hydrostatic pressure and temperature on the steady state fluorescence anisotropy of Green Fluorescent Protein (GFP). We find that the fluorescence anisotropy of GFP at a constant temperature decreases with increasing pressure. At atmospheric pressure, anisotropy decreases with increasing temperature but exhibits a maximum with temperature for pressure larger than 20 MPa. The temperature corresponding to the maximum of anisotropy increases with increasing pressure. By taking into account of the rotational correlation time changes of GFP with the pressure–temperature dependent viscosity of the solvent, we argue that viscosity increase with pressure is not a major contributing factor to the decrease in anisotropy with pressure. The decrease of anisotropy with pressure may result from changes in H-bonding environment around the chromophore.

Effect of high hydrostatic pressure and temperature on the steady state fluorescence anisotropy of Green Fluorescent Protein (GFP).

Interrogating the Structural Dynamics and Energetics of Biomolecular Systems with Pressure Modulation

High hydrostatic pressure affects the structure, dynamics, and stability of biomolecular systems and is a key parameter in the context of the exploration of the origin and the physical limits of life. This review lays out the conceptual framework for exploring the conformational fluctuations, dynamical properties, and activity of biomolecular systems using pressure perturbation. Complementary pressure-jump relaxation studies are useful tools to study the kinetics and mechanisms of biomolecular phase transitions and structural transformations, such as membrane fusion or protein and nucleic acid folding. Finally, the advantages of using pressure to explore biomolecular assemblies and modulate enzymatic reactions are discussed.

Hyperbolic Pressure-Temperature Phase Diagram of the Zinc-Finger Protein apoKti11 Detected by NMR Spectroscopy

For a comprehensive understanding of the thermodynamic state functions describing the stability of a protein, the influence of the intensive properties of temperature and pressure has to be known. With the zinc-finger-containing Kti11, we found a suitable protein for this purpose because folding and unfolding transitions occur at an experimentally accessible temperature (280-330 °K) and pressure (0.1-240 MPa) range. We solved the crystal structure of the apo form of Kti11 to reveal two disulfide bonds at the metal-binding site, which seals off a cavity in the β-barrel part of the protein. From a generally applicable proton NMR approach, we could determine the populations of folded and unfolded chains under all conditions, leading to a hyperbolic pressure-temperature phase diagram rarely observed for proteins. A global fit of a two-state model to all derived populations disclosed reliable values for the change in Gibbs free energy, volume, entropy, heat capacity, compressibility, and thermal expansion upon unfolding. The unfolded state of apoKti11 has a lower compressibility compared to the native state and a smaller volume at ambient pressure. Therefore, a pressure increase up to 200 MPa reduces the population of the native state, and above this value, the native population increases again. Pressure-induced chemical-shift changes in two-dimensional ¹H-¹⁵N NMR spectra could be employed for a molecular interpretation of the thermodynamic properties of apoKti11.

Practical aspects of high-pressure NMR spectroscopy and its applications in protein biophysics and structural biology

Pressure and temperature are the two fundamental variables of thermodynamics. Temperature and chemical perturbation are central experimental tools for the exploration of macromolecular structure and dynamics. Though it has long been recognized that hydrostatic pressure offers a complementary and often unique view of macromolecular structure, stability and dynamics, it has not been employed nearly as much. For solution NMR applications the limited use of high-pressure is undoubtedly traced to difficulties of employing pressure in the context of modern multinuclear and multidimensional NMR. Limitations in pressure tolerant NMR sample cells have been overcome and enable detailed studies of macromolecular energy landscapes, hydration, dynamics and function. Here we review the practical considerations for studies of biological macromolecules at elevated pressure, with a particular emphasis on applications in protein biophysics and structural biology.

Monitoring protein folding through high pressure NMR spectroscopy

High-pressure is a well-known perturbation method used to destabilize globular proteins. It is perfectly reversible, which is essential for a proper thermodynamic characterization of a protein equilibrium. In contrast to other perturbation methods such as heat or chemical denaturant that destabilize protein structures uniformly, pressure exerts local effects on regions or domains of a protein containing internal cavities. When combined with NMR spectroscopy, hydrostatic pressure offers the possibility to monitor at a residue level the structural transitions occurring upon unfolding and to determine the kinetic properties of the process. High-pressure NMR experiments can now be routinely performed, owing to the recent development of commercially available high-pressure sample cells. This review summarizes recent advances and some future directions of high-pressure NMR techniques for the characterization at atomic resolution of the energy landscape of protein folding.

Putting the Piezolyte Hypothesis under Pressure

A group of small molecules that stabilize proteins against high hydrostatic pressure has been classified as piezolytes, a subset of stabilizing cosolutes. This distinction would imply that piezolytes counteract the effects of high hydrostatic pressure through effects on the volumetric properties of the protein. The purpose of this study was to determine if cosolutes proposed to be piezolytes have an effect on the volumetric properties of proteins through direct experimental measurements of volume changes upon unfolding of model proteins lysozyme and ribonuclease A, in solutions containing varying cosolute concentrations. Solutions containing the proposed piezolytes glutamate, sarcosine, and betaine were used, as well as solutions containing the denaturants guanidinium hydrochloride and urea. Changes in thermostability were monitored using differential scanning calorimetry whereas changes in volume were monitored using pressure perturbation calorimetry. Our findings indicate that increasing stabilizing cosolute concentration increases the stability and transition temperature of the protein, but does not change the temperature dependence of volume changes upon unfolding. The results suggest that the pressure stability of a protein in solution is not directly affected by the presence of these proposed piezolytes, and so they cannot be granted this distinction.

Temperature and pressure dependence of protein stability: the engineered fluorescein-binding lipocalin FluA shows an elliptic phase diagram

We have measured the equilibrium constant for the denaturation transition of the engineered fluorescein-binding lipocalin FluA as a function of pressure and temperature, taking advantage of the fact that the ligand's fluorescence is almost fully quenched when complexed with the folded protein, but reversibly reappears on denaturation. From the equilibrium constant as a function of pressure and temperature all of the involved thermodynamic parameters of protein folding, in particular the changes in entropy and volume, compressibility, thermal expansion, and specific heat, were deduced in a global fitting procedure. Assuming that these parameters are independent of temperature and pressure, we can demonstrate from the ratio of Deltabeta, Deltaalpha(2), DeltaC(p) that the phase diagram of protein folding assumes an elliptic shape. Furthermore, we can show that the thermodynamic condition for such an elliptic phase diagram is related to the degree of correlation between the fluctuations of the changes in volume and enthalpy at the phase boundary. For the protein investigated this correlation is low, as generally expected for highly degenerate systems. Our study suggests that the elliptic phase diagram is a consequence of the inherent conformational disorder of proteins and that it may be viewed as the thermodynamic manifestation of the high degeneracy of conformational energies that is characteristic for this class of macromolecules.

Protein stability and dynamics in the pressure–temperature plane

The pressure-temperature stability diagram of proteins and the underlying assumptions of the elliptical shape of the diagram are discussed. Possible extensions, such as aggregation and fibril formation, are considered. An important experimental observation is the extreme pressure stability of the mature fibrils. Molecular origins of the diagram in terms of models of the partial molar volume of a protein focus on cavities and hydration. Changes in thermal expansivity, compressibility and heat capacity in terms of fluctuations of the enthalpy and volume change of the unfolding should also focus on these parameters. It is argued that the study of water-soluble polymers might further our understanding of the stability diagram. Whereas the role of water in protein behaviour is unquestioned, the role of cavities is less clear.

High-pressure studies of aggregation of recombinant human interleukin-1 receptor antagonist: thermodynamics, kinetics, and application to accelerated formulation studies

Recombinant human interleukin-1 receptor antagonist (IL-1ra) in aqueous solutions unfolds and aggregates when subjected to hydrostatic pressures greater than about 180 MPa. This study examined the mechanism and thermodynamics of pressure-induced unfolding and aggregation of IL-1ra. The activation free energy for growth of aggregates (DeltaG-/+(aggregation)) was found to be 37 +/- 3 kJ/mol, whereas the activation volume (DeltaV-/+(aggregation)) was -120 +/- 20 mL/mol. These values compare closely with equilibrium values for denaturation: The free energy for denaturation, DeltaG(denaturation), was 20 +/- 5 kJ/mol, whereas the partial specific volume change for denaturation, DeltaV(denaturation), was -110 +/- 30 mL/mol. When IL-1ra begins to denature at pressures near 140 MPa, cysteines that are normally buried in the native state become exposed. Under oxidizing conditions, this results in the formation of covalently cross-linked aggregates containing nonnative, intermolecular disulfide bonds. The apparent activation free energy for nucleation of aggregates, DeltaG-/+(nuc), was 42 +/- 4 kJ/mol, and the activation volume for nucleation, DeltaV-/+(nuc),was -175 +/- 37 mL/mol, suggesting that a highly solvent-exposed conformation is needed for nucleation. We hypothesize that the large specific volume of IL-1ra, 0.752 +/- 0.004 mL/g, coupled with its relatively low conformational stability, leads to its susceptibility to denaturation at relatively low pressures. The positive partial specific adiabatic compressibility of IL-1ra, 4.5 +/- 0.7 +/- 10(-12) cm2/dyn, suggests that a significant component of the DeltaV(denaturation) is attributable to the elimination of solvent-free cavities. Lastly, we propose that hydrostatic pressure is a useful variable to conduct accelerated formulation studies of therapeutic proteins.

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

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.