Quantitative criteria for native energetic heterogeneity influences in the prediction of protein folding kinetics

Abstract

Energy landscape theory requires that the protein-folding mechanism is generally globally directed or funneled toward the native state. The collective nature of transition state ensembles further suggests that sufficient averaging of the native interactions can occur so that the knowledge of the native topology may suffice for predicting the mechanism. Nevertheless, while simple homogeneously weighted native topology-based models predict the folding mechanisms for many proteins, for other proteins knowledge of the native topology, by itself, seems not to suffice in determining the folding mechanism. Simulations of proteins with differing topologies reveal that the failure of homogeneously weighted topology-based models can, however, be completely understood within the framework of a funneled energy landscape and can be quantified by comparing the fluctuation of entropy cost for forming contacts to the expected fluctuations in contact energy. To be precise, we find the transition state ensembles of proteins with all-alpha topologies, which are more uniform in the specific entropy cost of contact formation, have transition state ensembles that are more readily perturbed by differences in energetic weights than are the transition state ensembles of proteins with significant amounts of beta-structure, where the specific entropy costs of contact formation are more widely distributed. This behavior is consistent with a random-field Ising model analogy that follows from the free energy functional approach to folding.

Fig. 1.

The folding mechanisms of the all-α lambda repressor [Protein Data Bank (PDB) ID code 1R69] (A, D, and G), the α/β CI2 (PDB ID code 2CI2) (B, E, and H), and all-β src-SH3 domain (PDB ID code 1SRL) (C, F, and I). (A–C) The matrices of the interaction energies in the vanilla and flavored native-topology-based models are plotted below and above the diagonal, respectively, with darker colors representing stronger interactions. The corresponding native structures are also shown. (D–F) From simulations of the vanilla and flavored models, the free energy profiles were generated with respect to the order parameter Q. (G–I) The Φ values from the vanilla and flavored models are compared in a plot with a best-fit line; m is the slope of the line.

Fig. 2.

The probability of a contact in the transition state of the lambda repressor, an all-α protein, with the vanilla and flavored models.

Fig. 3.

The folding mechanisms of three all-α proteins (from Left to Right, 1v54E0, 1f6vA0, and 1cy5A0) selected from the CATH database. (A–C) The matrices of the interaction energies in the vanilla and flavored models are plotted below and above the diagonal, respectively, with darker colors representing stronger interactions. The corresponding native structures are also shown. (D–F) From simulations of the vanilla and flavored models, the free energy profiles were generated with respect to the order parameter Q. (G–I) The Φ values from the vanilla and flavored models are compared in a plot with a best-fit line.

Fig. 4.

The entropy and energy lost from the formation of native contacts for all-α (red), α/β- (green), and all-β (blue) proteins. Shown are the entropy (A) and energy (B), as well as the variance of the entropy (C) and energy (D), all plotted with respect to the order parameter, Q.

Fig. 5.

The relationship between the ratio of the entropic and energetic fluctuations at the transition state with the ratio between long- and short-range native interactions for well-studied two-state folding proteins.

Fig. 6.

Flavored model simulations of src-SH3 domain protein with a range of distributions of the Miyazawa–Jernigan contact energies. The free energy profiles (A) and Φ values (B) are shown for simulations using the varying parameter, χ, in a range where the folding mechanism does not change significantly. The free energy profiles (C) and Φ values (D) are shown for simulations using the varying parameter, χ, in a range where the folding mechanism does change significantly. The dependence of the correlation between the Φ values of the vanilla model versus the flavored models, r, with a range of χ (E) and 〈δS²〉/〈δε²〉 (F) is shown in blue for the all-β src-SH3 domain protein and in red for the all-α lambda repressor, for comparison.