On the role of frustration in the energy landscapes of allosteric proteins

Abstract

Natural protein domains must be sufficiently stable to fold but often need to be locally unstable to function. Overall, strong energetic conflicts are minimized in native states satisfying the principle of minimal frustration. Local violations of this principle open up possibilities to form the complex multifunnel energy landscapes needed for large-scale conformational changes. We survey the local frustration patterns of allosteric domains and show that the regions that reconfigure are often enriched in patches of highly frustrated interactions, consistent both with the idea that these locally frustrated regions may act as specific hinges or that proteins may "crack" in these locations. On the other hand, the symmetry of multimeric protein assemblies allows near degeneracy by reconfiguring while maintaining minimally frustrated interactions. We also anecdotally examine some specific examples of complex conformational changes and speculate on the role of frustration in the kinetics of allosteric change.

Fig. 1.

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 structural deviation (blue low, red high). The individual conformations are shown at the sides. The protein backbone is displayed as ribbons, 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 form A (solid, 1AN0 and 1LTH_T) or form B (dashed, 1NF3 and 1LTH_R). The local Q_i of each residue is shown in black.

Fig. 2.

Local frustration and residue displacement. The pair-distribution functions between the Cα of the residues classified by displacement and the center of mass of the contacts in different frustration classes was computed. The distributions for all contacts (black), minimally frustrated (green), neutral (gray), or highly frustrated contacts (red), are shown for the mobile (A) or undisplaced (B) residues.

Fig. 3.

Local frustration in allosteric pairs. The distribution of the configurational (A) and mutational (B) frustration indices were calculated for the contacts conserved between substates (solid) or exclusive to one substate (dashed). The vertical lines indicate the cutoff used to define minimally frustrated, neutral, or highly frustrated interactions.

Fig. 4.

Local frustration in oligomeric proteins. The distribution of the configurational (A) and mutational (B) frustration indices were calculated for the contacts internal to each monomer (tertiary, solid lines) or in between monomers (quaternary, dashed lines). The vertical lines indicate the cutoff used.

Fig. 5.

Local frustration in paradigmatic examples. Frustratographs for the open and closed forms of Adenylate kinase are shown in A. The Cα of residues where hinge motions are thought to occur (24) are highlighted in blue. The local frustration pattern of CAP protein is shown in B, side to the change in NMR exchange parameter (20). The tertiary and quaternary frustration patterns of the oxy and deoxy forms of haemoglobin are shown in C.