Frustration in protein complexes leads to interaction versatility

Disordered proteins can fold into a well-defined structure upon binding but these complexes are often fuzzy: the originally disordered partner adopts different binding modes when bound to different partners. Here we perform a systematic analysis of 160 proteins that form fuzzy complexes and demonstrate that the disordered partner displays a high degree of frustration in both the free and bound states. Although the folding of disordered regions upon binding reduces frustration relative to that of the unbound state, the interactions at the binding interface do not become fully optimized. In addition, we show that sub-optimal interactions lead to alternative frustration patterns in the complexes with different partners. These results demonstrate that disordered proteins do not always achieve fully optimal interactions in their complexes and their residual frustration leads to interaction versatility with different partners.

The discovery of disordered proteins has challenged the highly successful 2 structure-function paradigm of molecular biology by raising the question of how 3 biomolecular recognition can be achieved without a specific well-defined tertiary 4 structure [24] [2]. Disordered proteins often function as interaction hubs in which the 5 binding of multiple partners controls the specificity of signaling pathways [30]. While in 6 the past two decades a series of experimental and computational methods have begun to 7 characterise the conformational ensembles of disordered proteins in their free states [14], 8 their properties in the bound state are less well understood. Disordered proteins often 9 display different structures when they are bound with different partners. This 10 phenomenon is termed "fuzzy binding" [8]. The observed binding modes of disordered 11 proteins range from becoming nearly fully ordered to forming rather disordered states in 12 the bound complex. The structures can also change through posttranslational 13 modification or by varying cellular conditions [19]. Fuzzy binding enables disordered 14 proteins to interact not with every biomolecule but specifically only with a defined set 15 of partners. The physical basis of this controlled promiscuity has not yet been revealed. 16 Figure 1. Schematic representation for folding and binding landscapes. When local frustration is low, the folded proteins associate as rigid bodies. When local frustration is high, folding is coupled to binding, templating the folding of the disordered region. If local frustration remains in the bound state, many conformations are still accessible leading to fuzziness. The structures illustrate different binding modes derived from structures of glycogen-synthase kinase 3 (GSK-3). The right side (vertical) represents rigid docking, when a folded protein binds to a folded partner, which in this case is the LRP6 peptide (orange) (PDB: 4nm5). The left side (vertical) represents disordered binding, when the disordered N-terminal region of GSK3 makes transient interactions with the active site. The different conformations are schematically represented by colored lines. The process displayed on top (from left to right) is the conditional folding, when the N-terminal peptide folds upon phosphorylation and binds the active site with a welldefined conformation. This structure (PDB: 4nm3) superimposes well on the complex with the LRP6 peptide (PDB: 4nm5). The orange line (top right) emphasizes that a part of the N terminal region remains to be disordered in the complex. The diagonal (from bottom left to top right) represents the templated folding, when the disordered region adopts a well-defined structure upon binding, which can be achieved via conformational selection or induced fit. This scenario is different from conditional folding when both ordered and disordered bound states can be observed.

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Disordered proteins occupy a broad range of their energy landscapes. It has been 17 established that conformational ensembles of disordered proteins are however not fully 18 random. They rather form secondary structure elements [25], with many alternative 19 intramolecular interactions leading to numerous but somewhat structurally distinct 20 conformational sub-states in the native ensemble (Fig. 1). It is the entropic penalty of 21 folding, which is a bottleneck for folding of disordered proteins. 22 Disordered proteins, can undergo templated folding upon binding with their 23 partners, leading to a more well-defined conformation in the bound state [32]. 24 Templated folding can be described by a funnel-like free energy landscape, which is 25 made up from both intra-and intermolecular interactions, in contrast to autonomously 26 folding proteins, whose funnel can be generated by intramolecular interactions alone 27 (Fig. 1). Templated folding can sometimes be described as conformational selection [29], 28 when one of the conformational sub-states already dominant in the free state is 29 stabilized or may be termed induced fit, when the new conformation promoted by the 30 partner is present only in very low concentration in the free ensemble [11]. According to 31 either description the intermolecular interactions of disordered proteins with their 32 partners are thought to contrast with the rugged landscape that would arise from their 33 intramolecular interactions alone. with the pre-formed conformational elements in the unbound state [9], distinct 39 conformations turn out to be sampled when the protein binds to different partners. 40 Furthermore, mutations, which stabilize binding competent secondary structure 41 elements in the bound form may not always improve binding affinity [23]. Surprisingly, 42 in these cases mutations outside the binding region often contribute to the affinity or 43 specificity of binding [4]. These results suggest that heterogeneous nucleation in the 44 templated folding pathway differs somewhat from the homogeneous nucleation of single 45 globular proteins [28] [15].These results also suggest that the energy landscape of the 46 bound complex is more rugged than for more fully folded species.

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Disordered proteins can also undergo disordered binding, displaying many 48 conformational sub-states in the bound forms, generating a rugged energy landscape.

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Conformational exchange between these sub-states can be observed both within and 50 outside the binding region, [8] [20]. This pattern facilitates transient interactions at the 51 binding interface with other functional motifs [22]. All these observations prompt the 52 idea that the interactions of disordered proteins can be fuzzy, and that their functional 53 versatility exploits the diversity of many different sub-states [27]. Although the 54 biological significance of fuzziness has been established, understanding how diversity and 55 specificity are reconciled requires the quantitative application of energy landscape theory. 56 One's intuition that interactions mediated by disordered regions must be always weak is 57 contradicted by the existence of disordered protein complexes with high affinities [2].

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Here we examine this problem using energy landscape theory tools that analyze local 59 frustration in proteins [5]. These approaches were originally developed to describe how 60 individual parts of a protein guide the folding of globular proteins towards their 61 minimally frustrated native state [3]. Localizing frustration has given insights into their 62 conformational motions and into their functional adaptations that conflict with 63 folding [6]. In this paper we expand the theory of frustration to complexes of disordered 64 proteins, showing consistency with the energy landscape theory. In this paper we 65 systematically analyze frustration in the free and bound states of 160 disordered 66 proteins that have been found to form fuzzy complexes. We find that the interactions 67 display a high degree of frustration in both the more structured and unfolded parts of 68 3/13 disordered proteins. We also show that while templated folding reduces the level of 69 frustration, it does not eliminate frustration entirely, reflecting the fact that 70 intermolecular interactions in the distinct fuzzy protein complexes are sub-optimal. We 71 find there are often distinct frustration patterns in complexes with different partners, 72 which indicates that using sub-optimal interactions provides some selectivity but also 73 enables versatility. Our results provide a consistent physical model by which energetic 74 frustration explains the functional versatility of fuzzy protein complexes on the basis of 75 the energy landscape theory.

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The protocols underlying the datasets have been published, as well as the datasets 78 themselves. Therefore here we only provide a brief description of the methods, which 79 are detailed in previous works [12,18]. 80 Regions representing templated folding (disorder-to-order 81 binding mode, DORs, Table S1) 82 We collected crystal structures from the PDB that have resolution higher than 3Å, but 83 that have missing electron density for at least 5 residues. We excluded protein 84 sequences with post-translational modifications or that contained non-standard amino 85 acids. We then collected all available bound-state structures, and filtered those, to find 86 the disordered region in all the complexes. We analyzed the interface residues, and  (Table S1).

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Regions representing context-dependent binding modes (CDRs, 92 Table S2) 93 Disordered regions that were observed to be as both folded and disordered in different  (Table S1).

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We calculate the local frustration patterns using the Frustratometer server [21] which corresponding distributions for residues as classified by mutational frustration index are 119 shown in Fig.S1 for all the complexes generated by templated folding. The distributions 120 also include disordered regions which fold, but which do not mediate interactions with 121 the partner. We found that protein regions that were originally disordered but that now 122 adopt a well-defined structure upon binding still exhibit highly frustrated interactions 123 between 2 and 4Å. The density of minimally frustrated contacts is also lower in these 124 bound but fuzzy regions (Fig. 2B (Left)). These results indicate that the folding of 125 disordered regions upon binding often remains far from being optimal. We have also 126 found that those disorder-to-order regions (DORs) which have taken on order by 127 templated folding, also display an enrichment in highly frustrated interactions with 128 respect to the rest of the molecule (Fig. S1A). The interactions found in the structured 129 regions of the same proteins (chosen as random controls, Methods) also show an 130 enrichment of highly frustrated contacts which are slightly less frustrated than those of 131 disordered regions (Fig. 2B (Right)). The frustration of the interactions of the ordered 132 regions remains significantly higher than what is usually found in complexes formed 133 from fully structured proteins [5]. These results indicate that templated folding of fuzzy 134 regions also imposes constraints on the folded part of the protein. 135 We next compared the level of frustration of those residues which are involved in the 136 binding interface (binding) to those, which do not mediate intermolecular interactions 137 (non-binding). Fig. 3A compares the density of the configurational frustration index for 138 fuzzy residues involved in binding (blue) and non-binding contacts (pink), in the 139 complexes generated by templated folding. We observed that those residues which do 140 not form contacts with the partner exhibit higher frustration index than do those which 141 directly form intermolecular contacts (Fig. 3A) indicating that the binding itself does 142 ameliorate the high frustration of disordered proteins. These results indicate that 143 folding of disordered regions is less optimal than their frustrated interface interactions. 144 Templated folding decreases the overall frustration of disordered regions 145 relative to the free monomeric state 146 Without simulating the intrinsically disordered protein ensemble it is difficult to 147 assess precisely the local frustration of the disordered protein regions in their free 148 (unbound) forms. We can get an idea of the frustration level however by examining the 149 frustration in the structure of the disordered monomers simply by removing the 150 interaction partner, thus generating a hypothetical single structure representative of the 151 ensemble without intermolecular interactions. Both the finally disordered and 152 structured regions display a higher density of frustrated contacts in the absence of the 153 partner (Fig. S2). When we compare the frustration in monomers and complexes we see 154 that the level of frustration is lowered upon binding: partner interactions do reduce the 155 number of sub-optimal contacts.

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For templated folding ( Fig S3) and context-dependent binding modes (Fig S4) we 157 observe that fuzzy binding also reduces frustration as compared with the free state.

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These results suggest that highly frustrated interactions are related to changes in 159 binding modes. 160 We also analyzed some monomers that are found to be ordered in the free form but 161 Figure 2. Local frustration in complexes of disordered proteins generated by templated folding where the regions undergoes transition from a disordered to an ordered state. A) Examples of frustration patterns in a protein undergoing disorder-to-order transition upon binding. The backbones of the protein are shown as gray cartoons, minimally frustrated contacts are depicted with green lines, highly frustrated interactions with red lines. Neutral interactions were omitted for clarity. The disorder-to-order region is colored yellow. B) On the left we show the pair distribution function of the contacts between the protein and the residues in the disorder-to-order region. On the right we show the pair distribution function of the contacts between residues of structured regions. Green: minimally frustrated contacts, red: highly frustrated, gray: neutral contacts, black: all contacts. In all cases g(r) values were normalized such that g(20)=1. that become fuzzy in the bound form (Fig. S5). For these 52 regions we also observe an 162 enrichment of highly frustrated interactions around the fuzzy regions.

Conditional folding increases frustration of disordered regions 164
Increasing experimental evidence indicates that the frustrated interactions of 165 disordered proteins [18] often manifest themselves by forming ordered complexes with 166 some partners but forming disordered complexes with other partners [26]. We term 167 these examples as displaying "conditional folding". In this scenario, the folding of 168 disordered proteins depends on the binding context (context-dependent regions, CDRs), 169 such as the interaction partner, posttranslational modification or cellular conditions [16]. 170 Here we analyzed 77 complexes (93 fuzzy regions), generated by conditional folding and 171 found that these complexes exhibit more highly frustrated interactions (Fig. 4A) than 172 the complexes generated by templated folding (Figure 2B). The distributions for the 173 mutational frustration index are shown in Fig.S1. These indicate a small enrichment in 174 frustrated interactions around the fuzzy regions. Frustrated contacts can be found both 175 in the structured regions of the proteins (Figure 4B), and in the fuzzy regions outside 176 the binding interface ( Figure 3B). Thus, varying the degrees of folding with different 177 partners results in sub-optimal interactions in the bound state.  Another example (Fig 5B), that illustrates the nature of fuzzy binding is the 369 -  Figure 4. Local frustration in conditionally folding proteins. Those proteins which do not have a well-defined structure as monomer, but that may adopt a structure in a partner-or context-dependent manner or remain disordered in their complexes. A) Examples of frustration patterns in a conditionally folding protein. The backbone of the protein is shown as gray cartoons, minimally frustrated contacts are depicted with green lines, highly frustrated interactions with red lines. Neutral interactions were omitted for clarity. The context-dependent region is marked in yellow. B) On the left the pair distribution function of the contacts between the protein and residues of the context-dependent regions. On the right the pair distribution function of the contacts between residues of structured regions. Green: minimally frustrated contacts, red: highly frustrated, gray: neutral contacts, black: all contacts. g(r) values were normalized such that g (20). Figure 5. A) Structures for Translation initiation factor 2 subunit gamma (eif2g), PdbID: 3cw2 (above), and PdbID: 3i1f (below). Contact map of 3cw2 (above the diagonal), and 3i1f (below the diagonal). B) Protein structure for Mitogen-activated protein kinase 10, PdbID: 3v6r (above), and PdbID: 4h3b (below). Contact map of 3v6r (above the diagonal), and 4h3b (below the diagonal). The local frustration patterns of the protein, with the minimally frustrated interactions in green, the neutral in gray and highly frustrated interactions in red. The fuzzy region is shown with yellow backbone. For contact map, green: minimally frustrated contacts, red: highly frustrated, gray: neutral contacts. We see that which contacts are frustrated change in the alternate structures.

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Some frustration in the energy landscapes is required for the functional adaptability of 211 proteins [6]. As a consequence of those frustrated interactions, the energy landscape is 212 rugged encompassing distinct local minima enabling multiple biological activities [7]. To 213 control their interactions generally proteins have evolved to optimize frustration 214 allowing specificities to be compromised for functional needs [17]. This is brought to the 215 extreme for disordered proteins, which even lack a well-defined conformation on their 216 own and must always be described as an ensemble of conformers [30]. The structured 217 character of complexes of disordered proteins with their specific partners however, has 218 lead to the misleading impression that, in the end, functioning always requires a single 219 well-defined conformation to be dominant. The presence of a well defined structure, 220 however, does not correlate with the affinity of the interactions.

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Here we have performed a systematic analysis of the complexes of many disordered 222 proteins. This analysis demonstrates that even after binding, the interaction energetics 223 are far from optimal in the fuzzy regions. Consistent with earlier results for individual 224 cases [28], we have found that both the disordered and structured regions of complexes 225 are enriched in highly frustrated interactions in the bound complexes of disordered 226 proteins. The interface contacts do decrease the frustration level in the disordered 227 protein once bound as compared to the frustration of the free state, but the interactions 228 often still remain sub-optimal and energetic conflicts remain to be resolved. These 229 results corroborate the ruggedness of the energy landscape, which describes complexes 230 of disordered regions. We demonstrate that the fuzzy regions display distinct frustration 231 patterns with different partners, rationalizing how residual frustration allows both 232 specificity and versatility to be encoded. These observations can be exploited upon 233 targeting disordered regions by small molecules. Our work shows that specificity of the 234 interaction is not solely encoded in a given contact pattern, but also by the way 235 frustration is ameliorated. These observations highlight the importance of conflicting, 236 sub-optimal interaction in drug design for disordered regions.

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The coupled folding and binding of disordered regions leads to sub-optimal contacts, 238 which thus allows binding to different partners. This is fully consistent with the original 239 10/13 notion of local frustration in spin glasses and systems like the triangular 240 antiferromagnet where many structures compete as global minima [6] [31]. The high 241 residual frustration explains why disordered regions are capable of manifesting several 242 different binding modes [12]. The frustration of interactions in disordered proteins and 243 their bound complexes allows binding to be fuzzy by being sub-optimal thereby 244 enabling multifunctionality. Frustration and the ruggedness of the energy landscape 245 thus enables functional versatility along with specificity.