An experimentally determined protein folding energy landscape

Abstract

Energy landscapes have been used to conceptually describe and model protein folding but have been difficult to measure experimentally, in large part because of the myriad of partly folded protein conformations that cannot be isolated and thermodynamically characterized. Here we experimentally determine a detailed energy landscape for protein folding. We generated a series of overlapping constructs containing subsets of the seven ankyrin repeats of the Drosophila Notch receptor, a protein domain whose linear arrangement of modular structural units can be fragmented without disrupting structure. To a good approximation, stabilities of each construct can be described as a sum of energy terms associated with each repeat. The magnitude of each energy term indicates that each repeat is intrinsically unstable but is strongly stabilized by interactions with its nearest neighbors. These linear energy terms define an equilibrium free energy landscape, which shows an early free energy barrier and suggests preferred low-energy routes for folding.

Fig. 1.

The structure of the Drosophila Notch ankyrin domain. Shown is a ribbon representation of chain A (Protein Data Bank ID code 1OT8), with each of the seven sequence repeats colored differently. This figure was prepared by using molscript (12) and raster3d (13).

Fig. 2.

Deletions of the Notch ankyrin domain. (A) Structural transitions of Notch ankyrin deletion constructs monitored by CD. ×, Nank1–7*; ▴, Nank2–7*; ▵, Nank1–6*; □, Nank1–5*; ▪, Nank2–6*; ⊠, Nank3–7*; •, Nank1–4*; ○, Nank2–5*; ⊚, Nank4–7*. Solid lines are the result of fitting a two-state denaturation model to the data. (B) Relationship between repeat number and free energy of folding. The equation for the linear regression line is ΔG° = 7.53 – 1.96n_rep, with a correlation coefficient of 0.925.

Fig. 3.

A linear heterogeneous model for the stability of the Notch ankyrin domain. (A) Linear model ascribing a free energy contribution of each repeat (ΔG₁° through ΔG₇°), as defined by end deletion. (B) Observed vs. predicted folding free energies of Notch deletion constructs. Predicted values were estimated from a jackknife procedure in which coefficients were iteratively calculated from subsets of the data in which different constructs were omitted. Coefficients were then used to calculate the folding free energies of each omitted construct. The correlation coefficient is 0.9556. Inset shows observed vs. predicted folding free energies of Notch ankyrin deletion constructs from a simple multiple-linear regression on all constructs. The correlation coefficient is 0.9975. (C) Coefficients for the energetic contribution of each ankyrin repeat calculated from the linear heterogeneous model. The coefficient for ankyrin repeat 4 reflects only the intrinsic stability of the repeat, whereas the other coefficients capture both the intrinsic and interfacial stabilities (see Results and Discussion).

Fig. 4.

A 1D Ising model captures equilibrium two-state unfolding of the Notch ankyrin domain. (A) The fully folded (solid line), partly folded (dashed line), and fully denatured (dotted line) conformations account for most (>85%) of the polypeptide chains. (B) Although partly folded conformations (defined as chains that are neither fully folded nor fully unfolded) are populated to ≈15% in the transition, the majority (13% of the total conformations) is made up of conformations that contain six of seven folded repeats (solid line with circles), with partly folded conformations containing fewer than six folded repeats populated to ≈2% (dashed line with X's).

Fig. 5.

Equilibrium energy landscape for the Notch ankyrin domain. Free energies were calculated from the linear heterogeneous model with experimentally determined coefficients. Free energies of each partly folded conformation are represented by the height along the vertical axis and by color. The denatured ensemble is presented as a flat tier (aqua) at a free energy of 0. Shown are the views from the native side (A) and the opposite side (B) showing the denatured ensemble and the early barrier. The diagonal surfaces connecting neighboring conformations are meant to aid the eye but do not represent the energetics of partial folding of single repeats. Diagonal surfaces connecting partly folded conformations that contain a folded fourth repeat are represented with gray shading; those connecting conformations lacking a folded fourth repeat are unshaded. This figure was prepared with mathematica (Wolfram Research, Champaign, IL).