Surveying biomolecular frustration at atomic resolution

Abstract

To function, biomolecules require sufficient specificity of interaction as well as stability to live in the cell while still being able to move. Thermodynamic stability of only a limited number of specific structures is important so as to prevent promiscuous interactions. The individual interactions in proteins, therefore, have evolved collectively to give funneled minimally frustrated landscapes but some strategic parts of biomolecular sequences located at specific sites in the structure have been selected to be frustrated in order to allow both motion and interaction with partners. We describe a framework efficiently to quantify and localize biomolecular frustration at atomic resolution by examining the statistics of the energy changes that occur when the local environment of a site is changed. The location of patches of highly frustrated interactions correlates with key biological locations needed for physiological function. At atomic resolution, it becomes possible to extend frustration analysis to protein-ligand complexes. At this resolution one sees that drug specificity is correlated with there being a minimally frustrated binding pocket leading to a funneled binding landscape. Atomistic frustration analysis provides a route for screening for more specific compounds for drug discovery.

Fig. 1. A folded biomolecule usually sits near the bottom of a funneled energy landscape.

This diagram gives a sense of the statistical arrangement of states in a two-dimensional representation. The radial coordinate reflects the configurational entropy which decreases as the protein forms native contacts. The free energy of individual configurations averaged over the solvent is represented by the vertical axis. Fully denatured configurations appear at the top of the funnel. As structures form, the molecule encounters lots of barriers and local minima that may act as traps during folding. These local minima typically possess some native structure but also may make use of statistically unlikely but energetically favorable alternative non-native contacts. Such interactions are usually frustrated. If patches of frustrated contacts are localized in space they allow hinge-like motion between functionally distinct states. The frustrated contacts can take on alternative configurations and are indicated by red lines while the minimally frustrated interactions give rigidity to subdomains of the protein.

Fig. 2. Gallery of the localized frustration and minimally frustrated networks in allosteric proteins.

A structural alignment of both experimentally determined conformations is shown at the center, colored according to the structure deviation (blue low and red high). The individual conformations are shown at the sides. The protein backbone is displayed as cartoons, the interresidue interactions with solid lines. Minimally frustrated interactions are shown in green, highly frustrated interactions in red, neutral contacts are not drawn. At right, a quantification of the minimally frustrated interactions (green) or highly frustrated interactions (red) in the vicinity of each residue in a 1XTQ and 1XTS, b 1OIV, and 1OIW, c 1KAO and 2RAP, d 1HH4 and 1MH1, and e 1H4X and 1H4Y. The local Qi of each residue is shown in black. The quantifications of the interactions in the two configurations are shown in solid lines and dashed lines separately. We can see that the two patterns are strongly correlated with most minimally frustrated regions being nearly the same in both and the location of the frustrated regions typically only shifting by a few residues or becoming minimally frustrated.

Fig. 3. Gallery of the localized frustration and highly frustrated networks in enzymatic proteins.

The protein backbone is displayed as cartoons, the interresidue interactions with solid lines. Minimally frustrated interactions are shown in green, highly frustrated interactions in red, neutral contacts are not drawn. The catalytic sites are identified from the database and shown in yellow spheres.

Fig. 4. Examples of localized frustration patterns in protein complexes.

For each binding complex, the frustration indices are shown as calculated for the complex using both all-atom frustration (left panel) and coarse-grained frustration (right panel). Binding interfaces in (a–e) are largely dry interfaces dominated by non-water-mediated contacts, while the interfaces in (f) and (g) are rich in water-mediated contacts.

Fig. 5. Examples of localized frustration patterns in EGFR-inhibitor complexes.

For each binding complex in (a–d), the frustration indices are shown as calculated and shown on the left panel, and frustrations around the ligands only are shown on the right panel. e The correlation between the number of minimally frustrated interactions in each EGFR-inhibitor complex and the logarithm of binding affinity in the picomolar unit at a base of 2 is shown. A regression line is plotted to illustrated the trends with a modest pearson correlation of 0.45.

Fig. 6. Examples of localized frustration patterns in cox-inhibitor complexes.

For each drug, the frustration indices are shown as calculated and shown on the left panel, and frustrations around the ligands only are shown on the right panel. pmi-001 (a) is a selective inhibitor for COX2. ct-3 (b) and bromfenac (c) are inhibitors without selectivity. d Box plot of the increased minimally frustrated interactions in COX2 over COX1 is shown for both the selective drugs of COX2 and non-selective drugs.