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. 2008 Nov 18;105(46):17754-9.
doi: 10.1073/pnas.0804775105. Epub 2008 Nov 12.

Computing the stability diagram of the Trp-cage miniprotein

Dietmar Paschek  1 , Sascha Hempel, Angel E García
Affiliations

Computing the stability diagram of the Trp-cage miniprotein

Dietmar Paschek et al. Proc Natl Acad Sci U S A. .

Abstract

We report molecular dynamics simulations of the equilibrium folding/unfolding thermodynamics of an all-atom model of the Trp-cage miniprotein in explicit solvent. Simulations are used to sample the folding/unfolding free energy difference and its derivatives along 2 isochores. We model the DeltaG(u)(P,T) landscape using the simulation data and propose a stability diagram model for Trp-cage. We find the proposed diagram to exhibit features similar to globular proteins with increasing hydrostatic pressure destabilizing the native fold. The observed energy differences DeltaE(u) are roughly linearly temperature-dependent and approach DeltaE(u) = 0 with decreasing temperature, suggesting that the system approached the region of cold denaturation. In the low-temperature denatured state, the native helical secondary structure elements are largely preserved, whereas the protein conformation changes to an "open-clamp" configuration. A tighter packing of water around nonpolar sites, accompanied by an increasing solvent-accessible surface area of the unfolded ensemble, seems to stabilize the unfolded state at elevated pressures.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Convergence of the REMD simulations. (A) Time history of the number of replicas that have folded (rmsd ≤ 0.22 nm) at least once in the simulation (NFR). (B) Number of replicas sampling the folded state as a function of time. The total number of replicas sampling the 0.966 gcm−3 and 1.064 gcm−3 isochores is 40 and 48, respectively. After 40 ns all replicas have reached folded state at least once.
Fig. 2.
Fig. 2.
Folding/unfolding equilibrium of trp-cage. (A) Backbone atom rmsd distributions obtained from the 0.966 gcm−3-isochore for 4 selected temperatures. (B) Fraction of folded configurations (rmsd ≤ 0.22 nm) as a function of temperature for both studied isochores.
Fig. 3.
Fig. 3.
Structural aspects related to the folding/unfolding of Trp-cage. (A–C) Principal component analysis (70) of the entire REMD configurational ensemble obtained for the 0.966 gcm−3 isochore: (A) Probability distributions of the largest eigenmode m1 for 4 selected temperatures. (B) Comparison of the temperature dependence of fraction of folded states as obtained from the rmsd and m1 distributions. (C) Free energy landscape of Trp-cage (in units of kT) projected on the m1 eigenmode. Representative configurations of Trp-cage for selected states are indicated. (D) Helical content (defined as in ref. 71) of unfolded Trp-cage as a function of temperature. The helical content of the native state (PDB ID code 1L2Y) is given as a reference.
Fig. 4.
Fig. 4.
Averages of the difference upon unfolding of the (A) free energy, (B and C) total energy, and specific volume, calculated for the 2 indicated isochores. (D) Free energy surface ΔGu(P,T) obtained by fitting to a Hawley-type model the free energy and its derivatives calculated for the 2 isochores. Different grayscale colors indicate changes of ΔGu of 2 kJ mol−1.
Fig. 5.
Fig. 5.
Water packing around Trp-cage. (A–C) Proximal radial distribution functions gprox(r) between water's center of mass and the heavy atoms of the Trp-cage molecule. All data shown refers to “low temperature configurations” with T<320 K (A) gprox(r) including both, “polar” (O and N) and nonpolar “C” atoms. (B) separate gprox(r) for “polar” (O and N) and nonpolar “C” atoms. (C) gprox(r) for nonpolar “C” atoms of the Trp-sidechain, calculated for the “unfolded” configurations. (D) Solvent accessible surface area distributions (72) calculated for folded and unfolded configurations of Trp-cage for T<320 K.
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