Molecular determinant of the effects of hydrostatic pressure on protein folding stability

Abstract

Hydrostatic pressure is an important environmental variable that plays an essential role in biological adaptation for many extremophilic organisms (for example, piezophiles). Increase in hydrostatic pressure, much like increase in temperature, perturbs the thermodynamic equilibrium between native and unfolded states of proteins. Experimentally, it has been observed that increase in hydrostatic pressure can both increase and decrease protein stability. These observations suggest that volume changes upon protein unfolding can be both positive and negative. The molecular details of this difference in sign of volume changes have been puzzling the field for the past 50 years. Here we present a comprehensive thermodynamic model that provides in-depth analysis of the contribution of various molecular determinants to the volume changes upon protein unfolding. Comparison with experimental data shows that the model allows quantitative predictions of volume changes upon protein unfolding, thus paving the way to proteome-wide computational comparison of proteins from different extremophilic organisms.

Figure 1. Pictorial definitions of volume changes upon protein unfolding.

The volume enclosed by the molecular surface (red line) is the geometric or solvent-excluded volume (shaded area, V_SE). Molecular surface is calculated by using solvent probe of 1.4 Å (blue spheres). The solvent-excluded volume consists of van der Waals volume (dark yellow area, V_vdW), that is, the volume occupied by protein atoms, and void volume (grey area, V_Void). Upon protein unfolding the molecular surface of the protein increases and some of the voids become solvent exposed.

Figure 2. Breakdown of the contributions to the total geometric volume of protein.

Contributions of van der Waals V_vdW, squares) and void (V_Void, triangles) volumes to the total geometric volume (V_SE, circles) in the native (a) and unfolded (b) state ensembles as a function of protein size. Lines show linear regression fit. AAR, amino acid residue.

Figure 3. Radii of gyration (R_g) of unfolded state ensembles generated using TraDES and SC compared with experimentally measured radii of gyration of unfolded proteins as a function of protein size.

TraDES-generated unfolded state ensemble shows a dependence of radii of gyration (R_g) on protein size similar to experimentally measured values. Red triangles show the experimentally measured (using SAXS) values of R_g of proteins of various sizes. Open squares show the R_g values calculated using SC-generated ensemble, while grey circles show the values calculated using TraDES ensemble. For clarity only every fifth data point is shown. See also Supplementary Fig. 4 that shows the results for the FM-generated ensemble.

Figure 4. Void volume changes upon unfolding as a function of protein size.

Comparison of the void volume changes expected by considering that all void volume of the native protein contributes to the ΔV_Void=−V_Void,N, upon unfolding (triangles) with the volume changes that explicitly take into account the void volume of the unfolded state ensemble ΔV_Void=V_Void,U−V_Void,N (circles).

Figure 5. Pictorial definition of hydration volume.

Volume of solute in non-polar phase (V_φ,NP) includes volume that a solute occupies in non-polar solvent (red area). The difference between the volume in the gas phase (V_SE) and the partial volume of solute in water (V_φ,aq) accounts only for the volume changes due to the interactions with water. Thus, the hydration volume can be defined as V_Hyd=V_φ,aq−V_SE.

Figure 6. Hydration volume of model compounds.

The dependence of hydration volume, V_Hyd, of model compounds at 25 °C on the total (MSA_Tot, (a)) or non-polar (MSA_NP, (b)) surface area shows that non-polar groups make a major contribution. Aromatic model compounds (▪); non-aromatic model compounds (circle); oligopeptides (n=3–5) (triangle); N-acetyl amides of amino acids (upside-down triangle); and N-acetyl amino acids (diamond). In b, the scatter in the grey circles calculated with equation (9) matches the scatter in V_Hyd data and the line shows linear regression of V_Hyd versus MSA_NP.

Figure 7. Thermodynamic cycle for separating the contributions of hydration of native (V_Hyd,N) and unfolded (V_Hyd,U) state ensembles from the contribution of geometric volume changes (ΔV_SE) to the total changes in volume (ΔV_Tot) upon protein unfolding in aqueous solution.

The sum of all three steps is equal to the volume of unfolding of the protein in aqueous solution, ΔV_Tot, as defined by equation (11). It must emphasized that this process is valid because volume as a thermodynamic parameter is a state function and there are no conformational changes in the native or unfolded state ensembles upon transfer to and from the gas phase.

Figure 8. The dependence of the total volume changes upon unfolding (ΔV_Tot calculated using equation (11)) on protein size.

(a) Contributions of void (ΔV_Void, triangles) and hydration (ΔV_Hyd, upside-down triangles) volume changes to the total volume (ΔV_Tot, circles) changes upon unfolding as a function of protein size. (b) Fractional changes in the total volume ΔV_Tot/V_Tot,N as a function of protein size.

Figure 9. Direct comparison of experimentally measured (black bars) and calculated using equation (11) (red bars) volume changes upon unfolding of eight globular proteins.

Lyz, hen egg white lysozyme PBD:4LZT; BPTI, bovine pancreatic trypsin inhibitor PBD:6PTI; RNAse, bovine pancreatic ribonuclease A PDB:7RSA; Ubq, human ubiquitin PDB:1UBQ; SNase, ΔPHS variant of staphylococcal nuclease PDB:3BDC; Egl-c, leech eglin c PDB:1EGL; Acp, human acylphosphatase PDB:2ACY; TrpZ, Tryptophan Zipper PDB:1LE3. Experimental data (25 °C SNase; 40 °C RNase; 50 °C Acp, Egl and Lyz; 90 °C BPTI; and 80 °C TrpZ) are taken from refs , , . It is important to note that volume changes are temperature dependent that can also contribute to the observed differences between experimental and calculated values. Error bars show s.d. of averaging the experimental data over measured temperature range or of the multiple (n=3–8) repeats of MD runs for the native state (see Methods section for details).