Conformational entropy in molecular recognition of intrinsically disordered proteins

Broad conformational ensembles make intrinsically disordered proteins or regions entropically intriguing. Although methodo-logically challenging and understudied, emerging studies into their changes in conformational entropy ( D S (cid:1) conf ) upon complex formation have provided both quantitative and qualitative insight. Recent work based on thermodynamics from isothermal titration calorimetry and NMR spectroscopy uncovers an expanded repertoire of regulatory mechanisms, where D S (cid:1) conf plays roles in partner selection, state behavior, functional buffering, allosteric regulation


Introduction
Molecular communication relies on specific proteinprotein interactions (PPIs), where binding is a thermodynamic compromise between changes in enthalpy (DH ) and entropy (DS ).Intrinsically disordered proteins or regions (collectively IDPs) exist in broad ensembles of conformations separated by low energy barriers allowing easy transit [1,2].This gives IDPs a large conformational entropy, S conf .
Many IDPs undergo coupled folding and binding [3], resulting in changes in conformational entropy, D S conf , and contributing unfavorably to the free energy of binding, DG , as shown in Figure 1a [4].This is anticipated to enable high specificity without high affinity [5].Indeed, an unfavorable DS is documented when comparing disordered to ordered complexes [6]; although the penalty for folding is relatively small (0.7e3.5 kcal mol À1 ) [6,7], it is within a range to pivot biological outputs.Furthermore, intrinsic disorder (ID)based high-affinity interactions are amply described [8e10].So, how do IDPs meet the thermodynamic compromise?
For IDPs, the functionally relevant disorder can remain in a complex, lowering the entropic penalty for binding, as shown in Figure 1b.Also, the desolvation of protein groups with the release of water or counterions works favorably to increase the entropy through changes in solvent entropy, DS HE [11].Further contributions come from changes in the rotational and translational entropy of the protein and the ligand, DS rt , and remaining contributions, DS other , resulting in four major entropy terms for binding (BOX 1) [12,13].With the intriguing thermodynamics related to ID-based interactions, the decomposition of these entropic contributions is highly relevant for mechanistic insight.
Through recent examples, we discuss how DS conf is a source for advancing mechanistic understanding.

Methods for quantification of conformational entropy in ID-based interactions
Direct measurement of DS is challenging.It can be obtained from the measurement of DH and the equilibrium constant, K a ð ¼ K d À1 Þ, using isothermal titration calorimetry (ITC), which enables the calculation of DG and DS (BOX 1) [14].The Spolar and Record (SR) method represents an indirect approach for quantifying DS conf [12].It relies on empirical thermodynamic relationships and determination of the heat capacity change on binding, DC p , which, through the determination of DS conf enables quantification of the number of residues, R th , folding upon binding (BOX 1).Recently, the SR method was adapted to ID-based interactions (SR ID ) [15].In particular, changing the ratio of desolvation of non-polar and polar surfaces is important for ID-based interactions, adjusting also DS rt and the average per-residue DS conf for folding (BOX 1) [15].Nuclear magnetic resonance (NMR) relaxation measurements and molecular dynamics (MD) simulations are other ways to approximate DS conf .From order parameters (S2 ) [16], the changes in fast time-scale dynamics of methyl-bearing residues can be used as proxy for DS conf in PPIs [13,16,17].Using this so-called entropy meter, DS conf can vary, be significant for PPIs, and also involving ID partners [16,18].Trajectories from MD simulations sampling side-chain dynamics can be used to back-calculate S 2 , and hence extract DS  [17].As S 2 is most reliably obtained for folded states, using changes in dihedral angles on binding [19] may be a different source for an ID-entropy-meter to derive DS conf .
Linking thermodynamics and structure DC p constitutes an important link between thermodynamics and structure.Large DC p s are caused by coupled folding and binding leading to the exclusion of ordered water from hydrophobic areas [11,12].Thus, DC p can be used to estimate the contributions from different DS s in PPIs, as exemplified by evolutionary studies of complexes of the disordered CREB-binding protein (CBP) interaction domain (CID) and nuclear coactivatorbinding domain (NCBD) from transcriptional coregulators [20].Increased affinity for modern complexes is associated with new interactions and more favorable DS .Based on DC p s, the ancestral and modern complexes differ in DS conf instead of DS HE [20].Recently, DC p was key to understanding the interaction between amyloid fibrils of a-synuclein, which is associated with Parkinson's disease, and the chaperone aB-crystallin.aB-crystallin binds a-synuclein fibrils with entropydriven high affinity [21].Since the interaction is associated with a positive DC p , the entropic gain is unlikely only due to DS HE [11].Instead, the disassembly of aBcrystallin oligomers is suggested, functioning as an entropic buffer, as shown in Figure 1b [21].

Conformational ensemble modulation
IDPs employ strategies to reduce DS upon binding, including compaction and pre-folding in the free state and dynamics in the bound state, as shown in Figure 1b [2,22].For Son of Sevenless (SOS), binding to its IDregion (IDR) is entropically favorable at low temperatures, but becomes less so at increasing temperatures [23].As IDPs compact at higher temperatures [24], DS HE may be less favorable and compensate less for an unfavorable DS conf .Environmental changes thus affect S conf [25], and cellular crowding can impact compaction lowering S conf , but with elusive thermodynamics [26].For the interaction between Grb2-associated binding protein 1 (Gab1) and the SH2 domain protein tyrosine phosphatase (SHP2), crowding-induced residual structure in the disordered SHP2-binding regions of Gab1 likely results in reduced DS conf , explaining a decreased entropic penalty of binding [27], as shown in Figure 1b.
Helix propensity modulation may impact binding affinity [7,28].For the interaction between the negative BOX 1.
The thermodynamics of binding relate the Gibbs free energy difference between the free and bound states (DG ) to changes in binding enthalpy (DH ) and entropy (DS ) where R is the gas constant, and T is the temperature in Kelvin.DH reflects the changes in bonds, whereas DS depends both on the changes in protein and ligand translational and rotational entropy, DS rt , solvent entropy, DS HE , conformational entropy DS conf , and other contributions, DS other [12,13]: other DS thus reflects the difference in the number of states of the system.This is described by configurational and conformational entropy, where the configurational entropy originates from statistical mechanics and conformational entropy, used here, from chemical thermodynamics.
The SR approach can be used to quantify coupled folding and binding [12].For the ID-adapted SR approach [15], this is based on the following: where DC p ; the change in heat capacity at constant pressure, is determined from the temperature dependence of DH , and T S is the isoentropic temperature (DS ¼ 0Þ.Through this, R th , the number of residues undergoing coupled folding and binding can be calculated from the equation: regulator Radical-Induced Cell Death1 (RCD1) and the transcription factor Dehydration-Responsive Element-Binding protein 2A (DREB2A), a correlation between the amount of residual helical structure and binding affinity is seen [29].Lower affinity is associated with less favorable DH , only partly compensated by DS .
Since the amount of helix in free and bound states of DREB2A variants correlates, the thermodynamics most likely reflects differences in interactions and structural heterogeneity, which is associated with a larger S conf in the complex.Thus, the degree of helicity in the free state carries information to complex structure and thermodynamics [ [22].For rapid rewiring, high affinity is undesirable, as for the Phe-Gly nucleoporins (FG-Nups), with multiple SLiMs connected by disordered linkers.For nuclear transport factor 2 (NTF2) interactions, the favorable DH of increasing the number of SLiMs above four is counteracted by unfavorable DS due to linker structuring [31,32].Thus, enthalpyeentropy (DH:DS) compensation prevents high-affinity interactions between FG-Nups and NTF2, while multiple SLiMs ensure translocation selectivity [31].
SLiM context in long ID regions can negatively affect both S conf and DS conf .Using a proteomic screen against the EVH1 domain of ENAH, bait-peptide analyses show that binding of single and dual-SLiM peptides is driven to similar affinities by favorable DS and DH , respectively [33].DS s of the dual-SLiM interactions are an order of magnitude less favorable, leading to the proposal of a model according to which the long, disordered dual-SLiM peptides pay a S conf penalty from wrapping around the target domain.
Although protein complexes have a high degree of energetic frustration [34], structural heterogeneity may contribute favorably to affinity, as shown in Figure 1b.Thus, for the CcdA:CcdB2 antitoxin-toxin complex, mutations in CcdA promote complex heterogeneity, ensuring DS conf optimization to avoid adverse functional effects [7].Proline-cis/trans-isomerization represents a way of introducing heterogeneity.For NCBD from CBP, proline isomerization affects interactions with partner proteins as well as the conformational ensembles to different extents, enabling differential partner binding and regulation [35,36].According to a statistical thermodynamic model based on helix-coil theory [37], heterogeneous bound-state ensembles are constrained by IDP-target interactions through hotspots.Although the distribution of hotspot residues defines the allowed microstates, the helix propensity determines their probabilities in the diverse targetbound ensembles [37].

Understanding mechanisms from quantitative analyses of entropy
The relevance of DH :DS compensation in PPIs has been much debated [38].However, several studies in addition to the FG-Nup:NTF2 interactions [31] support this biochemical concept.Bona-fide DH :DS compensation was shown for the IDR of the mitogenactivated protein kinase MKK4 [39].Using the same SLiM, MKK4 forms different conformations in complexes with the kinases JNK1 and p38a associated with unfavorable and favorable DS , respectively.In this case, DH :DS compensation plays an important role in providing similar kinase-binding affinities of MKK4 [39].The association of an IDR of munc-18 interacting protein 3 (Mint3) with factor inhibiting hypoxiainducible factor-1 (FIH-1) showed large changes in DH and DS [40].Combined with NMR and CD analyses, this suggests that the IDR, in addition to primary binding sites, has touching sites, silent to affinity, but affecting the thermodynamic profiles [40] and thus likely affecting DS conf unfavorably, as shown in Figure 1a.The relative contributions of DH and DS to ID-based binding were addressed for transcriptional networks of the aa-hub RST domain from different regulators and transcription factors [41].RCD1eRST binds its biological ligands with high affinity driven by enthalpy and with considerable structuring, whereas entropy drives the binding of RCD1-RST-specific ligands to the TAF4-RST domain, but with lower affinity and less structuring.This shows how balancing DH and DS fine-tunes affinity, and, importantly, specificity.Entropically responsive partners of IDPs also play significant roles in binding energetics [8], allowing liganddependent DS conf (or S 2 ) responses, as reported for ligand selection by CBP-TAZ1 [42,43], calmodulin using the entropy meter [44], and ID-binding PDZ domains, as shown in Figure 1c [45].Contrasting compensatory DH :DS , MD simulations suggest DH :DS reinforcement for the oppositely charged H1 and ProTa [46], which form a high-affinity disordered complex governed by electrostatic mean-field type interactions [9].Changing the polyelectrolytic properties and chargepatterning changes affinity, with contributions from DH and DS conf .The favorable DS conf is suggested to be due to lower S conf of the unbound state resulting from intrachain repulsion [46].Together, this demonstrates how DS conf can be fine-tuned in ID-based interactions [47], leading to adaptation and selectivity in binding.

Quantifying folding in ID-based interactions using DS conf to reach models
In the SR method, DS conf is a tool for quantification of coupled folding and binding [12].For the cell cycleregulating p27:cyclin-dependent kinase (Cdk)2 interaction [48,49], SR pushes structural analysis showing that p27 tyrosine phosphorylation leads to the displacement of the p27-inhibitory domain from Cdk2 [49].In the interactions between CID and NCBD, the extant human interaction is suggested to involve increased structuring compared to the earlier CID:NCBD complexes [20], supported by SR ID analysis [15].For the RCD1-RST:DREB2A interaction, the inclusion of ID context of the DREB2A RST-binding SLiM induces further structuring in both the SLiM and the RCD1-RST domain, resulting in major DH :DS compensation, as shown in Figure 1c.In this case, SR ID analysis was essential for revealing the entropy-based allosteric effect of the SLiM context [15].SR ID analysis was also used to address the effect of the long linker between the two essential SLiMs of E1A, jointly essential for high-affinity binding to the host protein Rb [50].The < ID value did not increase for a SLiM-linker fragment compared to a SLiM-only fragment, suggesting linker residues not to be involved in coupled folding and binding.This supports a model where the linker functions in motif tethering by providing conformational, and thus S conf ; buffering needed for competitive hijacking of host Rb by viral E1A, as shown in Figure 1c.These examples illustrate how SR analysis can identify new features of ID-based interactions and propose models of IDbased interactions.

Conformational entropy as a regulatory source
Biomolecular phase transitions, where proteins form membrane-less non-stochiometric higher-order assemblies, are interesting entropic systems.Studies of the cancer-related speckle-type pox virus and zinc-finger protein (SPOP), which forms higher-order rod-like structures, revealed an entropically driven gel state at substoichiometric ratios with the IDR of deathassociated protein (DAXX) 6 [51].According to the proposed model, the favorable DS conf originates from distributing DAXX along the SPOP rod.Only at high concentrations of DAXX will DS conf exceed the loss in DS rt paid for gel formation, transiting to the condensed liquid state [51].According to fluorescence anisotropy experiments, a fragment, K18, of tau1 implicated in Alzheimer's disease, exhibits increased backbone dynamics in the condensed state, and is proposed to be an entropic driving force in condensation, as shown in Figure 1c [52].Such neatly balanced entropic systems are likely applicable to other IDPs undergoing phase separation.Also, in phase separation, the effect of sequence on backbone S conf was analyzed using MD simulations on model peptides, and the results indicate that the loss of S conf accompanying phase transitions is amply compensated by DH [53].This is also the case, although with opposite signs, for phase separation of cyclic peptides, which lose less S conf in the process [54].Thus, phase separation involving IDPs appears entropically diverse, likely reflecting the material properties of the different states.

Exploiting conformational entropy in drug targeting
With over 20% of human disease mutations occurring in IDRs, they are obvious therapeutic targets [64].However, flexibility and DH :DS compensation are a challenge.Penalty in coupled folding and binding was considered in targeting the interaction between nuclear receptor peroxisome-proliferator-activated receptor g (PPARg) and its cognate coactivators [65].Helical peptides from the SLiM regions of the coactivators have been used as antidiabetic PPARg antagonists through the competitive disruption of the PPARg-coactivator interaction.However, when excised from context, the peptides do not form helical structures, resulting in an entropic binding penalty.Stabilizing the helical conformation by hydrocarbon stapling restricts S conf of the peptides in the free state and ensures a more favorable Strategies for the exploitation of IDP conformational heterogeneity have been suggested for drug design.One approach is to identify small molecules, which promote entropic expansion e an increased S conf e with population of more conformations, as proposed for the IDR of the transcription factor c-Myc, as shown in

Conclusions
From the emphasized examples, it is apparent that DH : DS compensation and reinforcement play important functional roles in ID-based interactions and that quantifying DS conf can uncover new mechanistic insight, interaction sites, entropic allosteric regulation, and entropy-driven molecular regulation.Examples show compensatory changes among DS conf , DS rt , and DS HE and reveal entropic barriers of functional relevance.Although quantitative measures are emerging, it is still not evident how different thermodynamic strategies are employed by IDPs in translating entropy to function, and it will be long before we have enough data for generalization.Indeed, in many of the presented examples, we have extracted the entropic effects from studies with a different main focus.Thus, there is a strong need for directed studies focused on the role of conformational entropy in molecular recognition of IDPs.MD simulations and statistical thermodynamics represent promising approaches and one current strong method combination is that combining ITC and NMR.Probing the degree of structuring using the SR ID approach and dissecting the results on a residue level combined with dynamic measurements by NMR can make DS conf a key parameter in understanding IDbased interactions.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. conf

Figure 1 Changes
Figure 1 The ensemble volume of an IDP likely relates to S conf , and changes can be functionally exploitable.Indeed, favorable DS conf through the release of histone IDRs from DNA is suggested to drive nucleosome unwinding[55].Oppositely, tethering an IDP will reduce S conf[56].To counteract this, an entropic force is generated, and the more compact the ensemble, the larger the entropic force[56].Such change in S conf may tune binding.The ID tail of the UDP-a-d-glucose-6dehydrogenase (UGDH) shifts the conformational ensemble of the linked folded domain toward a highaffinity state for an inhibitor with a force that is solely dependent on tail length[57].Similarly, entropic brushes generated from long ID tails with large S conf drive membrane bending, as shown in Figure1a, as for the endocytic adaptor proteins, Epsin1 and AP180 [58].Recent studies of chimeras show that sequencedependent chain repulsion or attraction can determine the direction of the bend [59].Entropic regulation is seen for ActA translocation through the bacterial cell wall.Due to confinement in the cross-linked cell wall, a loss of S conf provides an entropic barrier.However, beyond a critical length, the entropic cost can be overcome from access to the unconstrained exterior, driving length-dependent translocation of ActT-like polymers [60].Large S conf can also act as entropic safety catch as in the ID-tail of E2, suppressing the activity of the E1 and E2 fusion proteins of hepatitis C virus [61].Mutations that reduce S conf in the E2 tail turn off the safety catch and generate hyper-reactive virus with enhanced entry [61].These examples demonstrate entropic allosteric effects.Similarly, statistical thermodynamics highlights that changing S conf of an IDR allosterically affects a connected IDR or folded domain through energetic coupling [62].This was addressed experimentally for the glucocorticoid receptor (GR), where coregulator binding to the GR-IDR leads to IDR folding, improved DNA binding by the DNA-binding domain, and enhanced transcriptional activity of GR in vivo [63].
Figure 1b [66,67].Similarly, binding of the small-molecule inhibitor 10,074-G5 to amyloid-b peptide (Ab) increases S conf of monomeric Ab and decreases its hydrophobic surface area, delaying disease-associated aggregation [68].For Huntingtin exon1, binding of the drug ispinesib to wildtype and pathogenic proteins leads to entropic expansion and collapse, respectively, showing an alternative targeting approach [69].Another strategy involves ID sequestration [70,71].Small molecules, which target -specific aromatic residues in p27 and promote the formation of soluble p27-oligomers, were identified [70,71].This was possible because p27 dynamically fluctuates between multiple conformations of the entropy reservoirs allowing small molecules to cross-link multiple chains.Still, with few examples, general principles remain elusive. 29].