Competing interactions give rise to two-state behavior and switch-like transitions in charge-rich intrinsically disordered proteins

The most commonly occurring intrinsically disordered proteins (IDPs) are polyampholytes, which are defined by the duality of low net charge per residue and high fractions of charged residues. Recent experiments have uncovered nuances regarding sequence–ensemble relationships of model polyampholytic IDPs. These include differences in conformational preferences for sequences with lysine vs. arginine and the suggestion that well-mixed sequences form a range of conformations, including globules, conformations with ensemble averages that are reminiscent of ideal chains, or self-avoiding walks. Here, we explain these observations by analyzing results from atomistic simulations. We find that polyampholytic IDPs generally sample two distinct stable states, namely, globules and self-avoiding walks. Globules are favored by electrostatic attractions between oppositely charged residues, whereas self-avoiding walks are favored by favorable free energies of hydration of charged residues. We find sequence-specific temperatures of bistability at which globules and self-avoiding walks can coexist. At these temperatures, ensemble averages over coexisting states give rise to statistics that resemble ideal chains without there being an actual counterbalancing of intrachain and chain-solvent interactions. At equivalent temperatures, arginine-rich sequences tilt the preference toward globular conformations whereas lysine-rich sequences tilt the preference toward self-avoiding walks. We also identify differences between aspartate- and glutamate-containing sequences, whereby the shorter aspartate side chain engenders preferences for metastable, necklace-like conformations. Finally, although segregation of oppositely charged residues within the linear sequence maintains the overall two-state behavior, compact states are highly favored by such systems.

Significant fractions of eukaryotic proteomes are made up of intrinsically disordered regions (IDRs) (1). Conformational heterogeneity (2) is a defining hallmark of IDRs (3–5). Studies over the past decade have helped quantify relationships (6) that connect sequence-encoded information within IDRs to properties of conformational ensembles such as overall sizes and shapes, the amplitudes of spontaneous conformational fluctuations, and the dynamics of interconverting between distinct conformational states (7–19). These sequence–ensemble relationships have direct functional consequences that have been uncovered via studies based on biophysical, biochemical, and engineering approaches (5, 20–38). Our work, which is focused on physical principles underlying sequence–ensemble relationships of IDRs, is of direct relevance to understanding how IDRs function.Charged residues are key determinants of sequence–ensemble relationships of IDRs (19, 39–41). They contribute through highly favorable free energies of hydration (42) and long-range electrostatic interactions. Net charge per residue (19, 39, 40) and the patterning of oppositely charged residues (43–45) are useful order parameters for describing sequence–ensemble relationships and interactions of charge-rich IDRs (46). Both features can be modulated through posttranslational modifications (47–51), charge renormalization by solution ions (52), and charge regulation through context- and conformation-dependent uptake and release of protons (53).Polyampholytes feature roughly equivalent numbers of oppositely charged residues, and they make up more than 70% of known IDRs (7, 17). For a given amino acid composition, which sets the fraction of charged residues and the net charge per residue, it has been shown that the linear mixing vs. segregation of oppositely charged residues can have a profound impact on sequence–ensemble relationships of polyampholytic IDRs (31, 32, 43). Specifically, for a given set of solution conditions, sequences featuring uniform linear distributions of oppositely charged residues are predicted to favor more expanded conformations compared to sequences with identical amino acid compositions where the oppositely charged residues are segregated into distinct blocks along the linear sequence. These predictions made using simulation and theory (43, 44, 54) have been confirmed using different experiments (31–33, 41, 55).The ensemble-averaged radii of gyration (R_g) of flexible polymers follow scaling relationships of the form R_g ∼ N^ν. Here, N denotes the number of residues and the scaling exponent ν is a measure of the length scale over which conformational fluctuations are correlated. For homopolymers or systems that are effective homopolymers, ν has four limiting values, viz., 0.33, 0.5, 0.59, or 1, corresponding to globules, Flory random coils (FRCs), self-avoiding walks, and rod-like conformations, respectively (56). Atomistic simulations performed at fixed temperatures suggest that ν ≈ 0.59 (43) for strong, well-mixed polyampholytes (17). The explanation for this behavior is as follows. Electrostatic attractions and repulsions are realized on similar length scales for well-mixed sequences. These interactions screen one another, and the highly favorable free energies of hydration become the main determinants of overall sizes and shapes of well-mixed strong polyampholytes (17). In contrast, compact conformations are formed by strong polyampholytes where oppositely charged residues are segregated into distinct blocks. Here, the electrostatic attractions between oppositely charged blocks can outcompete opposing effects of favorable solvation. These inferences were gleaned using sequences comprising 1:1 ratios of Lys and Glu (43). In the original simulations, the reference free energies of hydration of all charged residues were treated as being quantitatively equivalent and highly favorable. This leads to the hypothesis that Lys and Arg are interoperable with one another as determinants of sequence–ensemble relationships of IDRs (17). A similar inference emerges regarding the interoperability of Asp and Glu with respect to one another. The recent work of Sørensen and Kjaergaard has challenged these inferences (57). Using a system where model IDRs were deployed as flexible linkers between interaction domains, Sørensen and Kjaergaard used their measurements to estimate the relationships between amino acid sequence and the scaling exponent ν (57). Inferences from their experiments suggest that the ν ≈ 0.33 for (GRESRE)_n and ν ≈ 0.5 for (GKESKE)_n for the specific conditions they used in their measurements. Here, n is the number of repeats of the hexapeptides GRESRE or GKESKE. The results point to significant differences between Arg- and Lys-containing sequences. Further, while globularity of (GRESRE)_n has precedent in mean-field theories for polyampholytes, the mechanism by which FRC-like behavior of (GKESKE)_n is achieved is unclear. Here, we develop a plausible physical explanation for the findings of Sørensen and Kjaergaard (57). Our work is based on atomistic simulations and the ABSINTH implicit solvation model and forcefield paradigm (58–61).