Reversible Temperature and Pressure Denaturation of a Protein Fragment: A Replica Exchange Molecular Dynamics Simulation Study

We determine the reversible folding-unfolding of the C-terminal (41–56) fragment of protein G as a function of density and temperature using replica exchange molecular dynamics simulations. We employ a total of 253 replicas, covering the temperature range between 320 and 515 K and the density range between $0.96$ and $1.16\mathrm{g}{\mathrm{c}\mathrm{m}}^{-3}$. Using the root mean square deviation from the folded structure as a quantitative measure, we are able to obtain the fraction of folded states, and can thus establish the free energy difference between the folded and the unfolded states of the protein fragment as a function of temperature and pressure. For the pressure denaturation the weakening of the hydrophobic interaction between the bulky side chains is found to be crucial at lower temperatures, leading to an apparent destabilization of the folded backbone structure at elevated pressures.

Figure 1

(a) Average root mean square deviation of backbone atoms from the folded structure for three selected temperatures. (b) Average end to end distance (distance between the ${\mathrm{C}}_{\alpha }$ atoms of residues 1 and 16).

Figure 2

Thin solid lines: Density isobars for water (experimental data according to Ref. 18). Thin dashed lines: Density isobars obtained for SPC water. Filled spheres: Folding-unfolding transition of staphylococcal nuclease [19]. Filled squares: Folding-unfolding transition of ubiquitin [20]. Inset: Fraction of folded states $x_{\mathrm{f}\mathrm{o}\mathrm{l}\mathrm{d}\mathrm{e}\mathrm{d}}$ of the GB1 $\beta$ hairpin (with $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{D}<0.35\mathrm{n}\mathrm{m}$ for the backbone atoms). The experimentally determined stability lines have been transformed to the $\rho ,T$ space using the $P(\rho ,T)$-data set given in Ref. 18.

Figure 3

(a) Van't Hoff plot [with equilibrium constant $K=(1-x_{\mathrm{f}\mathrm{o}\mathrm{l}\mathrm{d}\mathrm{e}\mathrm{d}})/x_{\mathrm{f}\mathrm{o}\mathrm{l}\mathrm{d}\mathrm{e}\mathrm{d}}$] of interpolated (lower pressure) isobars. The straight line corresponds to $\Delta H_u=12\mathrm{k}\mathrm{J}{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}$ and $\Delta S_u=0.043\mathrm{k}\mathrm{J}{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}{\mathrm{K}}^{-1}$. (b) Free energy of unfolding $\Delta G_u=-RT\ln K$ as a function of pressure. The line corresponds to $\Delta V_u=-10\mathrm{m}\mathrm{l}{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}$ and $\Delta {\beta }_u=(\partial \Delta V_u/\partial P{)}_T=2\times {10}^{-2}\mathrm{m}\mathrm{l}{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}{\mathrm{M}\mathrm{P}\mathrm{a}}^{-1}$.

Figure 4

Radius of gyration $R_G$ calculated for the backbone atoms (BB, open symbols) and for the atoms forming the hydrophobic side chains of residues 3(TRP), 5(TYR), 12(PHE), and 14 (VAL) (SC, filled symbols). (a) Two lowest temperatures. (b) Two highest temperatures.