Fuzziness and Frustration in the Energy Landscape of Protein Folding, Function, and Assembly

Abstract

Are all protein interactions fully optimized? Do suboptimal interactions compromise specificity? What is the functional impact of frustration? Why does evolution not optimize some contacts? Proteins and their complexes are best described as ensembles of states populating an energy landscape. These ensembles vary in breadth from narrow ensembles clustered around a single average X-ray structure to broader ensembles encompassing a few different functional "taxonomic" states on to near continua of rapidly interconverting conformations, which are called "fuzzy" or even "intrinsically disordered". Here we aim to provide a comprehensive framework for confronting the structural and dynamical continuum of protein assemblies by combining the concepts of energetic frustration and interaction fuzziness. The diversity of the protein structural ensemble arises from the frustrated conflicts between the interactions that create the energy landscape. When frustration is minimal after folding, it results in a narrow ensemble, but residual frustrated interactions result in fuzzy ensembles, and this fuzziness allows a versatile repertoire of biological interactions. Here we discuss how fuzziness and frustration play off each other as proteins fold and assemble, viewing their significance from energetic, functional, and evolutionary perspectives.We demonstrate, in particular, that the common physical origin of both concepts is related to the ruggedness of the energy landscapes, intramolecular in the case of frustration and intermolecular in the case of fuzziness. Within this framework, we show that alternative sets of suboptimal contacts may encode specificity without achieving a single structural optimum. Thus, we demonstrate that structured complexes may not be optimized, and energetic frustration is realized via different sets of contacts leading to multiplicity of specific complexes. Furthermore, we propose that these suboptimal, frustrated, or fuzzy interactions are under evolutionary selection and expand the biological repertoire by providing a multiplicity of biological activities. In accord, we show that non-native interactions in folding or interaction landscapes can cooperate to generate diverse functional states, which are essential to facilitate adaptation to different cellular conditions. Thus, we propose that not fully optimized structures may actually be beneficial for biological activities of proteins via an alternative set of suboptimal interactions. The importance of such variability has not been recognized across different areas of biology.This account provides a modern view on folding, function, and assembly across the protein universe. The physical framework presented here is applicable to the structure and dynamics continuum of proteins and opens up new perspectives for drug design involving not fully structured, highly dynamic protein assemblies.

Figure 1

(A) Local frustration of the bound complex correlates to protein interaction fuzziness. Interactions between the two partners exhibit minimal frustration in rigid docking, which is coupled to moderate conformational changes upon interactions (represented by the RNase/barstar complex) and high frustration in disordered binding, when the bound partners are conformational heterogeneous in the complex (represented by the AF4/AF9 complex). Templated and conditional foldings, which are accompanied by a transition from disordered to ordered forms upon binding (represented by TADs of transcription factors GCN4 and p53), have intermediate local frustration, reflecting that the interactions of the folded elements are suboptimal. Indeed, in the case of conditional folding, the same protein region may remain disordered in complex with other proteins. (B) Folding and binding energy landscapes. The contour plots illustrate how folding frustration relates to interaction fuzziness by showing the energy landscapes in the free state (monomer) and the bound state (complex) along the folding and binding coordinates. In rigid docking, interactions take place between folded partners, resulting in a structured bound complex. In templated folding, the disordered partner(s) adopt a well-defined structure upon binding. Similar to templated folding, conditional folding may result in a structured complex upon binding with some partners (complex 2), but folding may not be induced upon assembly with other partners (complex 1). In the case of disordered binding, the energy landscapes of the monomeric and bound states overlap, as no folding takes place upon binding.

Figure 2

Specificity in a frustrated complex leads to different contact patterns with different partners. (A) Human serum albumin binds the natural ligand prostaglandin (PDB: 3a73) and a drug compound (PDB: 3lu6) in alternative binding modes via an extensive set of aromatic and electrostatic interactions. These contacts and the level of frustration can vary depending on the target and fine-tune affinities with different ligands. Local frustration values associated with the contacts are shown in Table S1. Local frustration patterns of thc are shown with minimally frustrated interactions in green and highly frustrated interactions in red. The fuzzy region (77–90 residues) is displayed as a yellow backbone. In the contact map, minimally frustrated contacts are shown in green, highly frustrated contacts are shown in red, and neutral contacts are shown in gray (as shown in the horizontal bar below the contact map). Some contacts are not displayed for better visualization. (B) Frustration in magnets also leads to alternative spin arrangements. A triangular ferromagnetic lattice is represented with the spins as arrows, and the favorable antiferromagnetic interactions are represented with lines. There is no way to arrange the spins such that they are all satisfied; in any case, an unfavorable interaction remains (red dot). This triangular lattice is thus energetically frustrated.

Figure 3

Fuzzy interactions with coevolutionary signals. (A) N-terminal regulatory region of c-Src, where the SH4 (teal), Unique (light orange), and SH3 (salmon) domains form a compact but highly dynamic, supramodular structure due to alternative long-range interactions. (B) Residues belonging to different domains with high coevolutionary probability on a single conformer. The three domains are shown by different shades of gray, which is gradually increasing from SH4 toward SH3. Residue pairs are displayed by identical colors.