Synopsis Intrinsically disordered proteins participate in important protein-protein and protein-nucleic acid interactions and control cellular phenotypes through their prominence as dynamic organizers of transcriptional, post-transcriptional, and signaling networks. These proteins challenge the tenets of the structure-function paradigm and their functional mechanisms remain a mystery given that they fail to fold autonomously into specific structures. Solving this mystery requires a first principles understanding of the quantitative relationships between information encoded in the sequences of disordered proteins and the ensemble of conformations they sample. Advances in quantifying sequence-ensemble relationships have been facilitated through a four-way synergy between bioinformatics, biophysical experiments, computer simulations, and polymer physics theories. Here, we review these advances and the resultant insights that allow us to develop a concise quantitative framework for describing sequence-ensemble relationships of intrinsically disordered proteins.

SUMMARY Sequences rich in glutamine (Q) and asparagine (N) residues often fail to fold at the monomer level. This, coupled to their unusual hydrogen-bonding abilities, provides the driving force to switch between disordered monomers and amyloids. Such transitions govern processes as diverse as human protein-folding diseases, bacterial biofilm assembly, and the inheritance of yeast prions (protein-based genetic elements). A systematic survey of prion-forming domains suggested that Q and N residues have distinct effects on amyloid formation. Here we use cell biological, biochemical, and computational techniques to compare Q/N-rich protein variants, replacing Ns with Qs and Qs with Ns. We find that the two residues have strong and opposing effects: N-richness promotes assembly of benign self-templating amyloids; Q-richness promotes formation of toxic non-amyloid conformers. Molecular simulations focusing on intrinsic folding differences between Qs and Ns suggest that their different behaviors are due to the enhanced turn-forming propensity of Ns over Qs.

The sizes of unfolded proteins under highly denaturing conditions scale as N 0.59 with chain length. This suggests that denaturing conditions mimic good solvents, whereby the preference for favorable chain-solvent interactions causes intrachain interactions to be repulsive, on average. Beyond this generic inference, the broader implications of N 0.59 scaling for quantitative descriptions of denatured state ensembles (DSEs) remain unresolved. Of particular interest is the degree to which N 0.59 scaling can simultaneously accommodate intrachain attractions and detectable long-range contacts. Here we present data showing that the DSE of the N-terminal domain of the L9 (NTL9) ribosomal protein in 8.3 M urea lacks detectable secondary structure and forms expanded conformations in accord with the expected N 0.59 scaling behavior. Paramagnetic relaxation enhancements, however, indicate the presence of detectable long-range contacts in the denatured-state ensemble of NTL9. To explain these observations we used atomistic thermal unfolding simulations to identify ensembles whose properties are consistent with all of the experimental observations, thus serving as useful proxies for the DSE of NTL9 in 8.3 M urea. Analysis of these ensembles shows that residual attractions are present under mimics of good solvent conditions, and for NTL9 they result from low-likelihood, medium/longrange contacts between hydrophobic residues. Our analysis provides a quantitative framework for the simultaneous observation of N 0.59 scaling and low-likelihood long-range contacts for the DSE of NTL9. We propose that such low-likelihood intramolecular hydrophobic clusters might be a generic feature of DSEs that play a gatekeeping role to protect against aggregation during protein folding.atomistic simulations | denatured proteins | paramagnetic relaxation Q uantitative descriptions of unfolded proteins are important for understanding collapse transitions (1), protein folding mechanisms (2), misfolding, aggregation (3, 4), and the effects of macromolecular crowding on protein stability (5, 6). Expanded unfolded states are sampled in high concentrations of chemical denaturants such as urea and guanidinium chloride. The sizes of these denatured proteins, quantified using hydrodynamic radii (〈R h 〉) or radii of gyration (〈R g 〉), scale as N 0.59 with chain length (7-9). This N 0.59 scaling arises because denatured proteins expand to make favorable contacts with the surrounding solvent, implying that high concentrations of denaturants are good solvents for generic proteins.In good solvents, the ensemble-averaged interresidue pair interaction coefficient is positive, suggesting that the preference for favorable chain-solvent interactions leads to intrachain interactions being repulsive on average (10). The validity of this inference for denatured proteins has been demonstrated recently using a combination of single-molecule experiments and polymer theory (11). Quantitative descriptions of chain statistics for polymers in good solvents rely on the so-ca...

In aqueous solutions with high concentrations of chemical denaturants such as urea and guanidinium chloride (GdmCl) proteins expand to populate heterogeneous conformational ensembles. These denaturing environments are thought to be good solvents for generic protein sequences because properties of conformational distributions align with those of canonical random coils. Previous studies showed that water is a poor solvent for polypeptide backbones and therefore backbones form collapsed globular structures in aqueous solvents. Here, we ask if polypeptide backbones can intrinsically undergo the requisite chain expansion in aqueous solutions with high concentrations of urea and GdmCl. We answer this question using a combination of molecular dynamics simulations and fluorescence correlation spectroscopy. We find that the degree of backbone expansion is minimal in aqueous solutions with high concentrations denaturants. Instead, polypeptide backbones sample conformations that are denaturant-specific mixtures of coils and globules, with a persistent preference for globules. Therefore, typical denaturing environments cannot be classified as good solvents for polypeptide backbones. How then do generic protein sequences expand in denaturing environments? To answer this question, we investigated the effects of sidechains using simulations of two archetypal sequences with amino acid compositions that are mixtures of charged, hydrophobic, and polar groups. We find that sidechains lower the effective concentration of backbone amides in water leading to an intrinsic expansion of polypeptide backbones in the absence of denaturants. Additional dilution of the effective concentration of backbone amides is achieved through preferential interactions with denaturants. These effects lead to conformational statistics in denaturing environments that are congruent with those of canonical random coils. Our results highlight the role of sidechain-mediated interactions as determinants of the conformational properties of unfolded states in water and in influencing chain expansion upon denaturation.

The role of beta-sheets in the early stages of protein aggregation, specifically amyloid formation, remains unclear. Interpretations of kinetic data have led to a specific model for the role of beta-sheets in polyglutamine aggregation. According to this model, monomeric polyglutamine, which is intrinsically disordered, goes through a rare conversion into an ordered, metastable, beta-sheeted state that nucleates aggregation. It has also been proposed that the probability of forming the critical nucleus, a specific beta-sheet conformation for the monomer, increases with increasing chain length. Here, we test this model using molecular simulations. We quantified free energy profiles in terms of beta-content for monomeric polyglutamine as a function of chain length. In accord with estimates from experimental data, the free energy penalties for forming beta-rich states are in the 10-20 kcal/mol range. However, the length dependence of these free energy penalties does not mirror interpretations of kinetic data. In addition, although homodimerization of disordered molecules is spontaneous, the imposition of conformational restraints on polyglutamine molecules does not enhance the spontaneity of intermolecular associations. Our data lead to the proposal that beta-sheet formation is an attribute of peptide-rich phases such as high molecular weight aggregates rather than monomers or oligomers.