Contribution of Water to Pressure and Cold Denaturation of Proteins

The mechanisms of cold and pressure denaturation of proteins are matter of debate and are commonly understood as due to water-mediated interactions. Here, we study several cases of proteins, with or without a unique native state, with or without hydrophilic residues, by means of a coarse-grain protein model in explicit solvent. We show, using Monte Carlo simulations, that taking into account how water at the protein interface changes its hydrogen bond properties and its density fluctuations is enough to predict protein stability regions with elliptic shapes in the temperature-pressure plane, consistent with previous theories. Our results clearly identify the different mechanisms with which water participates to denaturation and open the perspective to develop advanced computational design tools for protein engineering.

Figure 1

$P\text{−}T$ SR of the protein from Monte Carlo simulations. Symbols mark state points with the same average residue-residue contact’s number $n_{\mathrm{rr}}/n_{\max }=30\%$, 40%, 50% and 70%. Elliptic lines are guides for the eyes. The “glass transition” line defines the temperatures below which the system does not equilibrate. The spinodal line marks the stability limit of the liquid phase at high $P$ with respect to the gas at low $P$; $k_B$ is the Boltzmann constant.

Figure 2

Typical configurations of a hydrated protein made of 30 residues (in green): (a) folded at the state point $(T{k}_B/4\epsilon ,P{v}_0/4\epsilon )=(0.25,0.1)$ and unfolded (b) at high $T$ (0.9,0.1), (c) at low $T$ (0.1,0.1), (d) at high $P$ (0.25,0.6), (e) at low $P$ $(0.25,-0.3)$. Left panels: Water molecules with (without) HBs are represented in blue (white) and bulk (interfacial) HBs in blue (red). Right panels: Color coded water density field (from black for lower $\rho$ to yellow for higher $\rho$) calculated as $v_0{\rho }_i^{(\lambda )}\equiv v_0/(v_0+n_{\mathrm{HB},i}^{(\lambda )}{v}_{\mathrm{HB}}^{(\lambda )})$ where $\lambda =b,\mathrm{\Phi }$, and $n_{\mathrm{HB},i}^{(\lambda )}$ is the number of HBs associated to the water molecule $i$, with $\sum _i{n}_{\mathrm{HB},i}^{(\lambda )}=N_{\mathrm{HB}}^{(\lambda )}$.

Figure 3

Volume change $\mathrm{\Delta }V$ for the $f\to u$ process in the $T\text{−}P$ plane. Color coded $\mathrm{\Delta }V$ (black for negative, yellow for positive) is in $v_0$ units. Solid lines connect state points with constant $\mathrm{\Delta }V$. Black points mark the SR. The locus $\mathrm{\Delta }V=0$ has a positive slope and intersects the SR at the turning points with $dT/dP{|}_{\mathrm{SR}}=0$. The dashed line, connecting the points with $dP/dT{|}_{\mathrm{SR}}=0$, corresponds to the locus where $\mathrm{\Delta }S=0$ and separates state points with $\mathrm{\Delta }S>0$ (high $T$) from those with $\mathrm{\Delta }S<0$ (low $T$) at the $f\to u$ process. The white symbol marks the error in the dashed-line slope estimate.

Figure 4

The SR for the heteropolymer with a unique native state. We set ${\epsilon }_{\mathrm{rr}}/J=0.7$, ${\epsilon }_{\mathrm{w},\mathrm{\Phi }}=0$, ${\epsilon }_{\mathrm{w},\zeta }/J=1.17$, $J_{\mathrm{\Phi }}/J=1.3$, $J_{\zeta }/J=0.5$, $v_{\mathrm{HB}}^{(\zeta )}=0$, with all the other parameters as in Fig. 1. We test that changing the parameters, within physical ranges, modifies the SR, reproducing a variety of experimental SRs [11], but preserves the elliptic shape.