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. 2015 Jan 20;112(3):E259-66.
doi: 10.1073/pnas.1410424112. Epub 2015 Jan 6.

Modulation of folding energy landscape by charge-charge interactions: linking experiments with computational modeling

Franco O Tzul  1 , Katrina L Schweiker  1 , George I Makhatadze  2
Affiliations

Modulation of folding energy landscape by charge-charge interactions: linking experiments with computational modeling

Franco O Tzul et al. Proc Natl Acad Sci U S A. .

Abstract

The kinetics of folding-unfolding of a structurally diverse set of four proteins optimized for thermodynamic stability by rational redesign of surface charge-charge interactions is characterized experimentally. The folding rates are faster for designed variants compared with their wild-type proteins, whereas the unfolding rates are largely unaffected. A simple structure-based computational model, which incorporates the Debye-Hückel formalism for the electrostatics, was used and found to qualitatively recapitulate the experimental results. Analysis of the energy landscapes of the designed versus wild-type proteins indicates the differences in refolding rates may be correlated with the degree of frustration of their respective energy landscapes. Our simulations indicate that naturally occurring wild-type proteins have frustrated folding landscapes due to the surface electrostatics. Optimization of the surface electrostatics seems to remove some of that frustration, leading to enhanced formation of native-like contacts in the transition-state ensembles (TSE) and providing a less frustrated energy landscape between the unfolded and TS ensembles. Macroscopically, this results in faster folding rates. Furthermore, analyses of pairwise distances and radii of gyration suggest that the less frustrated energy landscapes for optimized variants are a result of more compact unfolded and TS ensembles. These findings from our modeling demonstrates that this simple model may be used to: (i) gain a detailed understanding of charge-charge interactions and their effects on modulating the energy landscape of protein folding and (ii) qualitatively predict the kinetic behavior of protein surface electrostatic interactions.

Keywords: charge–charge interaction; computational design; energy landscape; protein folding; protein stability.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Comparison between experimental and modeling results of the thermodynamics and kinetics for the four protein pairs shows good qualitative agreement. (A) Experimentally determined difference in stabilities between WT and des proteins (data and experimental details from refs. 17, 21). (B) chevron plots comparison of the refolding and unfolding kinetics. (C) Comparison of computed heat capacity (Cv) profiles. (D) Comparison of computed folding and unfolding kinetics. Data for the WT proteins and des variants are shown as black circles–lines and red squares–lines, respectively. See Materials and Methods for experimental and computational details. Protein identity is indicated in each plot.
Fig. 2.
Fig. 2.
Characterization of native contacts in the TSE shows that des proteins have higher fraction of native contacts than the corresponding WT proteins. (A, C, E, and G) The PMF versus global reaction coordinate Q. These plots were used to identify the TSE. Solid black and red lines are for the WT and des, respectively, at their corresponding Tm values, whereas dashed red line is for the des protein at the Tm of the corresponding WT protein. See Materials and Methods for computational details. (B, D, F, and H) Difference in the fraction of native contacts formed in the transition state for the four studied proteins. Open symbols show all native contacts, whereas colored represents contacts in the TSE that differ between WT and des variants. Color scheme changes from blue (more contacts in the WT) to red (more contacts in the des). Protein identity is indicated in each plot.
Fig. 3.
Fig. 3.
des proteins have less frustrated energy landscape than the corresponding WT proteins. (A, C, E, and G) Changes in the local order parameter <Qi> relative to the global reaction coordinate Q, Q − <Qi>, as a function of Q for the four studied proteins. Colors of the lines correspond to the colors on the contact plot. Colored lines are for the des proteins, black lines are for the corresponding WT. Numbers represent parameter Θi (Eq. 1). Positive values indicate that particular local order parameter for des proteins tracks closer to the global reaction coordinate Q. The absolute values of Θi qualitatively describe the differences between des and WT and cannot be directly compared. (B, D, F, and H) Contact maps with color coding matching the colors in A, C, E, and G. See Materials and Methods for computational details.
Fig. 4.
Fig. 4.
Comparison of all pairwise distances in the TSE identifies significant changes for residues that are not involved in the native contacts. (A, C, E, and G) Difference in all pairwise distances formed in the TSE for the four studied proteins. Gray symbols show all native contacts, whereas colored shows values Δij that represent the difference in distances in the TSE between WT and des variants (Eq. 2). Color scheme changes from cyan (shorter distances in the WT) to magenta (shorter distances in the des). Black rectangles show areas that have significant changes but lack native contacts. (B, D, F, and H) The <Δrel> for the regions outlined by rectangles in A, C, E, and G as a function of global reaction coordinate Q.
Fig. 5.
Fig. 5.
Comparison of all pairwise distances in the unfolded state shows a decrease in net compactness of the des proteins relative to the corresponding WT proteins. (A, C, E, and G) Difference in all pairwise distances formed in the unfolded state for the four studied proteins. Gray symbols show all native contacts, whereas colored shows values Δij that represent the difference in distances in the TSE between WT and des variants (Eq. 2). Color scheme changes from yellow (shorter distances in the WT) to green (shorter distances in the des). (B, D, F, and H) Probability distribution of pairwise distances P(Rij) as a function of Rij. Data for the WT proteins and des variants are shown as black and red lines, respectively.
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