Collapse Transitions of Proteins and the Interplay Among Backbone, Sidechain, and Solvent Interactions

Abstract

Proteins can collapse into compact globules or form expanded, solvent-accessible coil-like conformations. Additionally, they can fold into well-defined three-dimensional structures or remain partially or entirely disordered. Recent discoveries have shown that the tendency for proteins to collapse or remain expanded is not intrinsically coupled to their ability to fold. These observations suggest that proteins do not have to form compact globules in aqueous solutions. They can be intrinsically disordered, collapsed, or expanded, and even form well-folded, elongated structures. This ability to decouple collapse from folding is determined by the sequence details of proteins. In this review, we highlight insights gleaned from studies over the past decade. Using a polymer physics framework, we explain how the interplay among sidechains, backbone units, and solvent determines the driving forces for collapsed versus expanded states in aqueous solvents.

INTRODUCTION

Polypeptide chains undergo either collapse or expansion transitions in response to stimuli (20). These stimuli include changes to temperature and pressure, and changes to concentrations of osmolytes, salts, and pH (18, 38, 42, 73, 109, 139, 143). Other stimuli include mechanical forces that can be applied directly in vitro or through work done by molecular machines in vivo (52). The conformational response of compaction/expansion to various stimuli is fundamental to disorder–order transitions of proteins. It is also central to the various reactions and quality control programs that regulate the concentrations of proteins in vivo.

Uncovering the physicochemical details of collapse/expansion transitions of polypeptide chains remains at the forefront of protein biophysics. The emergence of insights over the past decade has required the deployment of advanced methodologies for experimental investigations that have gone hand in hand with synergistic advances in theory and computation. Through concerted efforts from many labs, built on pioneering earlier work, there appears to be a coherent set of answers to questions regarding the generic and sequence-specific molecular driving forces for the collapse/expansion transitions of proteins (20, 32, 33, 125, 127, 148).

Here, we review evidence suggesting that the driving forces for collapse/expansion originate from a fine interplay among backbone, sidechain, and solvent-mediated interactions. Further, simple extrapolations from studies of model systems fail to account for all the nuances of heteropolymeric collapse/expansion. Sequence-specific complexities must be embraced while simultaneously looking for universality. Indeed, the aphorism, often paraphrased and attributed to Einstein that “Everything [especially models] should be made as simple as possible, but not simpler” rather succinctly captures the emerging views regarding the molecular driving forces of collapse/expansion transitions.

POLYMER PHYSICS AS THE LINGUA FRANCA FOR COLLAPSE TRANSITIONS

Polypeptide chains can undergo collapse or expansion in response to stimuli (148). For brevity, we shall designate collapse/expansion transitions as collapse transitions. The conceptual foundations of polymer physics are helpful for describing the physics of collapse transitions. In the polymer physics literature, collapse transitions are referred to as coil-to-globule transitions (Figure 1a) (112). These transitions have been explored extensively in the context of protein folding (32). However, it is important to recognize that the collapse transition is in no way a protein-specific phenomenon and is observed with simple homopolymers as well as complex heteropolymers (30, 146).

Figure 1.

(a) The coil-to-globule transition curve for a 100-residue homopolymer as a function of monomer–monomer interaction strength with representative ensemble snapshots. The sigmoidal shape is characteristic of a cooperative transition, as observed for complex heteropolymers and simple homopolymers alike. (b) The molecular structure of a polypeptide. A single backbone peptide unit is highlighted at the top; this structure repeats down the chain. Various sidechains are circled in red.

The dimensions of a chain, which define the extent of collapse or expansion vis-à-vis a well-defined reference state, such as a non-interacting Flory random coil, are governed by the interplay between intrachain and chain–solvent interactions (41). Bona fide order parameters for monitoring collapse transitions include the radius of gyration$\left(R_g\right)$, the hydrodynamic radius $\left(R_{\text{h}}\right)$, the radial density profile $\left[\text{ρ}\left(r\right)\right]$, and the scaling of spatial separation as a function of sequence separation $(\langle \langle R_{ij}\rangle \rangle )$ (50, 77, 112, 126). Although, the mean end-to-end distance $\left(R_e\right)$ is often used, early theoretical work showed that $R_e$ can be a poor order parameter for describing global scaling behavior (50). In heteropolymers, a more pronounced decoupling of $R_g$ and $R_e$ can occur in both globule and coil-like states owing to the chemical heterogeneity of interactions (34, 43, 113, 124).

In mean-field and scaling theories, these order parameters are captured in terms of the excluded volume ($V_{ex}$, the chain length $\left(N\right)$, the effective monomer size or Kuhn length $\left(b\right)$, and the correlation length for the amplitude of conformational fluctuations quantified in terms of a scaling exponent $\left(\text{ν}\right)$ (31, 40, 112). The excluded volume quantifies the effective volume set aside per residue for interactions with the surrounding solvent. It can be negative, zero, or positive depending on whether the effective interactions with the solvent are repulsive, indifferent, or attractive, respectively (53, 112). In physical chemistry, excluded volume is typically used to describe steric overlap. To avoid confusion, we follow recent precedent and use the term effective solvation volume $\left(V_{es}\right)$ for the polymer physics definition of excluded volume (53).

Generic proteins are unbranched, linear polymers of amino acids. In polymers, each repeating unit or monomer consists of a repeating backbone unit and an additional functional group (R-group). For homopolymers, each R-group is the same. For heteropolymers, the R-groups associated with different monomers along a single polymer are different. Polypeptides consist of a backbone peptide unit with sidechains as the polymer R-groups (Figure 1b). For a given set of solution conditions, we can decompose the determinants of collapse transitions into a combination of intrinsic backbone preferences and sequence-specific effects due to the sidechains. In this formulation, every protein sequence in solvent is, at a minimum, a three-component system consisting of the backbone repeating units, the sidechains, and the solvent (109). In biological systems, the solvent is typically a mixture of water, ions, and various organic and inorganic osmolytes.

Determinants of Chain Dimensions of Homopolymers

Physical descriptions of collapse transitions require a quantitative framework that captures the effects of the three-way interplay among polypeptide backbone units, sidechain moieties, and solvent components. The framework for describing this interplay can be borrowed from the polymer physics literature. Coil-to-globule transitions of flexible homopolymers can be described in terms of the interplay between effective intrachain and chain–solvent interactions. Mean-field theories provide a convenient route to arrive at phenomenological descriptions, and this is achieved in terms of the sign and magnitude of $V_{es}$ (112).

The effective, solvent-mediated potential of mean force denoted as $W\left(r\right)$ is the free-energy change associated with bringing a pair of monomeric units from a noninteracting reference point to distance $r$ of one another in an aqueous solvent (112). If $r$ is small enough to allow direct interaction between the two monomeric units, then one of three possible scenarios will result: If the residues “like” one another more than they “like” the solvent, then the effective inter-residue interactions will be attractive. If the residues “like” the solvent more than they “like” one another, then the effective inter-residue interactions will be repulsive. If the residues “like” the solvent and one another equally, neither attractive nor repulsive interaction is experienced. The probability that a pair of chain monomers will be a distance $r$ from one another is proportional to $\text{exp}\left[–\text{β}W\left(r\right)\right]$, where $\text{β}={\left(RT\right)}^{–1}$, $T$ is the temperature, and $R$ is the ideal gas constant. Because residues cannot sterically overlap with one another, $\text{exp}\left[–\text{β}W\left(r\right)\right]$ is zero for short inter-residue distances, while $\text{exp}\left[–\text{β}W\left(r\right)\right]\approx 1$ for large separations where the inter-residue interactions are effectively zero. Between these two limits, $\text{exp}\left[–\text{β}W\left(r\right)\right]$ can be large and positive for separations $r$ where the inter-residue interactions are attractive. Conversely, $\text{exp}\left[–\text{β}W\left(r\right)\right]$ is negligibly small at inter-residue separations $r$ where the effective interactions are repulsive (112).

For each pair of monomers, $V_{es}$ is defined as the negative of the integral of the Mayer $f$-function $f\left(r\right)$ over the volume available to the pair of residues (112). Here, $f\left(r\right)=\text{exp}\left[–\text{β}W\left(r\right)\right]–1$, and the integral is performed over all pairs of inter-monomer separations. Depending on the inter-monomer separation $r$ and the type of interactions, the $f$-function will be negative (short-range steric overlaps or effective inter-residue repulsions), positive (effective inter-residue attractions), or zero (large separations). The Mayer $f$-function is dimensionless, and the integral has units of volume. It quantifies the effective pairwise inter-monomer interactions for the polymers in solution.

In a poor solvent, $V_{es}$ is negative; each monomer, on average, excludes itself from interactions with the solvent and instead interacts with other monomers. We can consider this to represent the fact that the chain relinquishes solvent in exchange for inter-residue interactions (i.e., the solvent now has a negative volume). In a good solvent, $V_{es}$ is positive because, on average, each residue interacts favorably with the solvent, such that there is a positive contribution $V_{es}$. Depending on the sign, the magnitude of $V_{es}$ quantifies the poorness or the goodness of the solvent. If the inter-monomer interactions exactly counterbalance the monomer–solvent interactions, then $V_{es}\approx 0$ and this is achieved in a theta solvent (20, 112).

The size of a chain, quantified in terms of $R_g$, may be written as

$$R_{\text{g}}=R_0\left(V_{\text{es}},w,b\right)N^{\text{ν}}.$$ 1.

Here, the pre-factor $R_0$ is a function of the effective solvation volume $V_{es}$; the three-body interaction parameter $w$, which is defined by the thickness of the chain; and the effective monomer size $b$ (112). The three-body interaction parameter $w$ is always positive and represents the steric volume occupied by the chain, preventing this model from undergoing collapsing to a single point in the limit of $\text{ν}=0.33$. The effective monomer size (or Kuhn length) defines the chain persistence length. In this way, all the chemistry of the repeating units is subsumed in the pre-factor $R_0$, which captures the effective bulk of the monomer as well as the chain connectivity. It should be clear form this formalism that $R_0$ will vary with $V_{es}$.

In good, theta, and poor solvents, $\text{ν}=0.5885$, 0.50, and 0.33, respectively (31, 40, 86). In poor solvents, homopolymers form compact globules, maximizing inter-residue contacts and minimizing the residue–solvent contacts. In good solvents, polymers adopt expanded coil-like conformations, minimizing inter–residue contacts and amplifying residue–solvent contacts in a way that maximizes chain entropy. In theta solvents, chain–solvent and chain–chain interactions are exactly counterbalanced and chain dimensions as well as the distribution of conformations are governed entirely by chain connectivity and conformational entropy (30, 31, 40).

Scaling laws hold for polymers that are infinitely long. Finite-size artifacts will lead to deviations from the canonical scaling exponents, and the presence of these artifacts can be discerned via analytical/numerical calculations or measurements as a function of chain length (126). For finite-length polymers, approaching the tricritical point, defined by the point where $\text{ν}=0.5$, sets a threshold to distinguish between good ($\text{ν}>0.5$) and poor ($\text{ν}<0.5$) solvent behavior. The inferred value of $\text{ν}$ will represent a convolution of contributions from the apparent goodness versus poorness of the solvent as well the contributions to the amplitudes of fluctuations that come from the underlying chemical details and finite-size considerations.

Given a combination of polymer and solvent, how might we discern solvent quality? One approach is to quantify the sign and magnitude of $V_{es}$ from direct measurements, such as light scattering that yields estimates of the second virial coefficient, which is proportional to $V_{es}$ (102, 112). Alternatively, one can measure the scaling of $R_g$ or $R_h$ as a function of chain length $N$ using pulse-field gradient nuclear magnetic resonance (NMR), small angle X-ray scattering (SAXS), fluorescence correlation spectroscopy (FCS), two-focus FCS, or related measurements (4, 25, 56, 73, 139). If the accuracy and sampling of molecular mechanics–based simulations can be relied upon, then these provide a route to extracting the scaling exponent and in principle the sign and magnitude of $V_{es}$ (47, 53, 63, 91, 134, 147). Instead of simulating the conformational distributions for multiple chain lengths, it suffices to perform simulations for one suitably long chain length and compare the resultant conformational distributions to those obtained from simulations based on reference potentials (58, 86, 89). With these reference distributions in hand, one can compare a variety of order parameters from the simulation of interest with the reference to obtain inferences regarding solvent quality and even proxies for $V_{es}$ (53).

WATER IS A POOR SOLVENT FOR POLYPEPTIDE BACKBONES

A well-reasoned question to ask is whether water at room temperature is a good, indifferent, or poor solvent for polypeptide backbones? In order to answer this question, the constructs used should not yield confounding results due to the interplay between backbone and sidechain interactions. Over the past decade, several investigations have focused on glycine-rich sequences, including polyglycine of different chain lengths (2, 58, 64, 65, 128, 131). Results from these investigations may be summarized as follows: Polyglycine is a poly-secondary-amide. N-methylacetamide (NMA) is a model compound mimic of glycine, and vapor pressure osmometry measurements indicate a favorable free energy of solvation at room temperature of approximately –10 kcal/mol (141). The free energy of solvation quantifies the free-energy change associated with transferring the solute from the gas phase into water (10). Naive extrapolation predicts that polyglycine should be favorably solvated, and these molecules should favor expanded, coil-like conformations characterized by a scaling exponent of $\text{ν}\approx 0.59$. However, molecular simulations, exceedingly poor solubility, and FCS experiments unequivocally show that polyglycine forms compact globules in water, implying that water is a poor solvent for polypeptide backbones (2, 58, 64, 65, 128).

What is the origin of the behavior of polyglycine in water? The free energy of solvation of model compounds does not account for the competition that arises from the high local concentration of other backbone moieties. Preference for compact, globular conformations derives from the ability of amides to solvate one another through favorable amide–amide interactions in globules, where the effective concentration of amides around one another is ~20 M (58). Pettitt and coworkers (2, 64, 65) have argued that the preference for self-solvation by polypeptide backbones is driven by amide mediated dipole–dipole interactions and a favorable entropic component through water release. Support for these inferences comes from denaturation experiments performed on polyglycine, which show that the extent of expansion that polyglycine undergoes in aqueous mixtures with 8 M urea ($\text{ν}\approx 0.4$) or 7 M GdmCl ($\text{ν}\approx 0.37$) is rather modest (58). Therefore, even high concentrations of a diamide such as urea are insufficient to outcompete the intrachain amide–amide interactions that give rise to the preference for compact globules in dilute solutions of polyglycine and the poor solubility of polyglycine in general.

Given that water is a poor solvent for polypeptide backbones, what does this result mean for protein sequences in general? Two diverging hypotheses emerge: According to the backbone- hypothesis, sidechains amplify the intrinsic properties of polypeptide backbones (3, 14, 111). Alternatively, the true nature of protein sequences derives from the three-way interplay among the intrinsic preferences of polypeptide backbones, sidechain-mediated interactions, and solvent-mediated effects (20, 32).

According to the backbone-centric view, the intrinsic preference for the collapse of globular proteins derives from the properties of polypeptide backbones in water. Sidechains essentially act as conformational selectivity filters, choosing the optimal collapsed backbone conformation that accommodates the partitioning between hydrophilic versus hydrophobic sidechains. This view is anchored by extrapolations from three sets of observations; dissection of the transfer free energies of model compounds from water into 1 M urea suggests that the backbone contributes most significantly to protein denaturation, whereas sidechains are passive bystanders (3). This is taken to mean that interactions other than intra-backbone interactions are refractory to stabilizing protein structures. Secondly, the hydrogen-bonding potential of backbone units is considered to be so strong that these amides would have to always hydrogen bond to themselves or to the surrounding solvent (111). And third, the coarse-grain tube model for polypeptide backbones, which is based on an elegant generalization of the Edwards continuum model for polymers, generates canonical hydrogen-bonded structures as so-called platonic folds of backbones without any consideration of sidechains (9, 35).

The backbone-centric model was introduced 2006 and was based on a synthesis of different types of data (14, 111). As discussed below, research over the past decade has diverged from the backbone-centric view. Although water is a poor solvent for polypeptide backbones, sidechains play a central role in modulating and even radically altering the intrinsic preferences of polypeptide backbones (29, 45, 85, 87, 98, 111a, 138).

HETEROPOLYMERIC PROTEIN SEQUENCES IN AQUEOUS SOLVENTS

Naturally occurring proteins are neither polyglycine nor simple homopolymers. Instead, they are finite-sized heteropolymers. How do concepts of solvent quality, effective solvation volumes, and scaling exponents transfer to finite-sized heteropolymeric sequences? The effective solvation volume per residue will be modified by the intrinsic and context-dependent free energies of solvation of each sidechain, the modulation of the backbone solvation by each sidechain, and the repulsive or attractive interactions between pairs of residues. Therefore, the effective solvation volume for a heteropolymeric sequence may be written as: $V_{\text{es}}^{\text{het}}=\mathrm{sgn}\left(s\right)s{V}_{\text{es}}^{\text{bb}}$ where $V_{\text{es}}^{\text{bb}}$ is the effective solvation volume of backbone units, $\text{sgn}\left(s\right)$ is the signum function such that $\text{sgn}\left(s\right)=-1$, 0, or +1, respectively, for $s<0,=0$, and > 0, and $s$ is a sequence-specific modifier that renormalizes the effective solvation volume. This leads to the approach of an apparent sequence-specific solvent quality, and the scaling relationship takes the form

$$R_{\text{g}}=R_0\left(V_{\text{es}}^{\text{het}},w,\langle b\rangle \right)N^{{\text{ν}}_{\text{app}}}.$$ 2.

The pre-factor $R_0$ captures the sequence- and composition-specific modulation of the effective solvation volume of the backbone, including sequence-specific solvation volume and the average size of a monomer unit $\langle b\rangle$. The difference beween Equations 1 and 2 is the appearance of a renormalized effective solvation volume $\left(V_{\text{es}}^{\text{het}}\right)$ and an apparent scaling exponent, $v_{\text{app}}$, which can be quite different from the intrinsic scaling exponent of $\text{ν}\approx 0.33$ for polypeptide backbones in isolation. As in Equation 1, $v_{\text{app}}$ is also a function of $V_{\text{es}}^{\text{het}}$.

The interplay among sidechain, solvent, and backbone interactions will be sequence is reflected in the values of $V_{\text{es}}^{\text{het}}$ and consequently $v_{\text{app}}$. The major advance over the past decade has been the ability to uncover a set of heuristics that enable qualitative inferences regarding $v_{\text{app}}$ based on amino-acid compositions, although much work remains (29, 57).

CATEGORIES OF PROTEIN SEQUENCES

We propose that individual domains of proteins can be classified into one of four distinct ground states in aqueous solutions (17, 25, 60, 75, 104, 107, 108, 148). In dilute facsimiles of physiological milieus, which we refer to as native conditions, proteins can be (a) ordered (also known as folded) and collapsed; (b) disordered and collapsed; (c) ordered and expanded; or (d) disordered and expanded (Figure 2). Although this discretization is convenient, it is worth emphasizing that depending on the solution conditions, any chain can, in theory, adopt a continuum of values along both axes (e.g., the degree of order/disorder and global dimensions).

Figure 2.

Conformational classifications of polypeptides based on the two-dimensional space of conformational heterogeneity and global dimensions. Examples for each are the crystal structure of SasG (top left), the conformational ensemble of Ash1 (top right), the conformational ensemble for polyglutamine (bottom right), and the crystal structure of lysozyme (bottom left) (PDB: 1IEE) (51, 89, 140). The decoupling of global dimensions and conformational heterogeneity is formally addressed in Reference 82.

Proteins that Are Collapsed and Folded (Ordered) in Aqueous Solvents

Dima & Thirumalai (34) showed that the scaling of $R_g$ with chain length for folded globular proteins yields values consistent with $v_{\text{app}}\approx 0.33$. This is concordant with the compact, globular nature of folded domains. We repeated this analysis with 2,392 nonredundant protein structures taken from PDBSELECT25 and found similar results, which are also consistent with other analyses (Figure 3a) (49, 87, 139). The inset in Figure 3a also demonstrates the decoupling between $R_g$ and $R_e$, a result recently observed in flexible heteropolymers (43).

Figure 3.

(a) Scaling behavior for folded proteins based on ~2,400 nonredundant structures taken from PDBSELECT25 (49). While the radius of gyration shows reasonable agreement with $v_{\text{app}}\approx 0.33$, the end-to-end distance shows a poor correlation (inset). (b) Scaling behavior for chemically denatured proteins based on data from Reference 73. The unfolded state under strongly denaturing conditions is well described by a self-avoiding random chain ($v_{\text{app}}\approx 0.59$).

The similarity between $v_{\text{app}}$ and the scaling exponent derived for polyglycine suggests that, like polypeptide backbones, water is a poor solvent for folded states of globular proteins. Therefore, in the folded state, the sidechains maintain the intrinsic preference of backbones for collapse, although the accommodation of sidechains should change the packing density, degree of solvent penetration, and the surfaces of globules. As shown in Figure 3b, it is well established that foldable proteins under high concentrations of denaturant show conformational behavior consistent with a self-avoiding random coil ($v_{\text{app}}\approx 0.59$) (73, 139). With this in mind, what does the scaling of $R_g$ with chain length for folded proteins tell us about the dimensions of unfolded proteins under folding conditions? The answer to this question is directly relevant to details of collapse transitions for autonomously foldable proteins. One might envisage two limiting behaviors.

The poorness of the solvent in the folded state could mean that $v_{\text{app}}$ is always approximately 0.33 for foldable proteins under native conditions, such that global dimensions of a foldable protein should be approximately equal irrespective of folding status. In this scenario, the folding transition is conceptualized as a conformational rearrangement between (wet or dry) molten globules and a compact folded globule, akin to a crystallization process (39, 121). The case for the distinct classes of molten globules, first introduced via theoretical work, has received some support from recent experiments (7, 17, 48, 55, 62, 99, 108, 115, 120, 148). Support for this model also comes from molecular dynamics simulations with compact unfolded states, although it is unclear whether these are legitimate observations or force-field artifacts (106). In this model, the poorness of the solvent for the backbone governs the dimensions of the folded and unfolded states, and these states are distinguishable mainly by the extent of internal hydration, the acquisition of secondary and tertiary structure, and the packing of sidechains. Given the finite-size nature of natural polypeptides, $v_{\text{app}}$ could be beyond the globule limit but still in the poor-solvent regime (0.33 < $v_{\text{app}}<0.5$), a prediction consistent with some data (24, 90, 93, 94).

Alternatively, if water is a good solvent for unfolded proteins, then we would expect scaling behavior consistent with $v_{\text{app}}>0.5$. This could be at the limit of a self-avoiding random coil ($v_{\text{app}}\approx 0.59$), meaning the unfolded state in high concentrations of denaturant is identical to the unfolded state under native or near-native conditions. Inferences from SAXS-based experiments seem to support this model (60, 67, 107, 118, 119, 145, 111a). In this scenario, water is a good solvent for generic protein sequences. The tradeoff between chain–solvent hydrogen bonds for chain–chain hydrogen bonds can be accommodated through a combination of packing of specific elements such as foldons and the hydrophobic effect (36, 37, 59, 137).

Single-molecule Förster resonance energy transfer (smFRET) experiments and more recent simulation studies arrive at a somewhat different conclusion. These experiments show a continuous contraction of proteins upon dilution from denaturant (4, 15, 56, 83, 110, 117, 122, 129, 145, 147). This result is broadly consistent with water being a good or theta solvent for unfolded states ($v_{\text{app}}>=0.5$) but suggests that a continuous worsening in solvent quality accompanies the dilution of denaturant. Although Hofmann et al. report $v_{\text{app}}$ of 0.46 ± 0.05, we suggest that within all reasonable expectations of experimental error this can be taken to imply that water is a generic theta-like ($v_{\text{app}}\approx 0.5$) solvent for unfolded proteins under native conditions (56). The discrepancies between inferences based on SAXS and smFRET measures proved to be confounding and became the focus of intense scrutiny given the direct implications for the description of unfolded states under native conditions. Recent multiplexed experiments, numerical assessments, and analysis of SAXS/smFRET data on the same sets of molecules, aided by atomistic simulations, show that the discrepant inferences between SAXS and smFRET measurements originate, at least in part, from the decoupling between $R_g$ and $R_e$, which is amplified for heteropolymeric sequences (43, 113, 124). When this is taken into account, SAXS and smFRET show reasonable agreement and suggest a general model for the unfolded state under native conditions. In this model, water is a theta-like or marginally good solvent for the unfolded state under native conditions (0.50 ≤ $v_{\text{app}}<0.55$), but there is a dependence of $v_{\text{app}}$ on the concentration of denaturant. It is noteworthy that recent analysis of full scattering curves taken from SAXS experiments using a novel approach (111a) suggests that unfolded proteins under native conditions are characterized by $v_{\text{app}}$ of 0.54. The $v_{\text{app}}$ for the unfolded state under native conditions is expected to show some sequence dependence, and the decoupling of $R_g$ and $R_e$ at lower denaturant concentrations may also be a confounding factor for the interpretation of certain experiments

Samanta et al. (114) recently developed a heteropolymeric theory for chain compaction parameterized using native-state topology. This predicts a continuous transition in chain dimensions as a function of denaturant concentration and that native-state topology has a significant impact on the so-called collapsibility of a given protein sequence. In this work, based on analysis of over two thousand structures, the authors make the important comment that one cannot arrive at proteome-wide inferences from experiments on a handful of systems. Nevertheless, there appears to be a growing consensus that water is a theta-like or marginally good solvent for unfolded states under native conditions.

There are numerous advantages that one can envisage for an unfolded state that behaves like it is in theta-like or marginally good solvents (70). These pertain to the amplitudes of conformational fluctuations, the ability to enable backtracking when folding errors are made, and direct encoding of cooperativity in folding–unfolding transitions by making the unfolded state distinct from the folded state (19, 69, 70). Such a result can reconcile numerous seemingly disparate observations, including the presence of foldons, the robustness of the linear extrapolation model for assessing protein stability, the impact of unfolded states on phi value analysis, and the modest global contraction observed in both SAXS and smFRET measurements when one accounts for the decoupling between $R_g$ and $R_e$ (22, 37, 103).

Proteins that Are Disordered and Collapsed in Aqueous Solvents

The discovery of intrinsically disordered proteins (IDPs) led to the recognition that proteins can be functional even while displaying significant conformational heterogeneity (132, 142). A surprising finding, arrived at via very different biophysical investigations, is that IDPs can form collapsed, globular ensembles while simultaneously exhibiting significant conformational heterogeneity (29, 132). Chain collapse in IDPs has been observed in many different systems. These include polyglutamine and polyglycine tracts, low-complexity sequences rich in Gly, Ser, Asn, and Gln, bacterial protamine-like domains, the amyloid beta peptides, the Islet amyloid polypeptide, and the P domain of Pab1 (58, 61, 85, 97, 101, 128, 133, 111b). These IDPs accentuate the intrinsic preferences of polypeptide backbones in water but do so without undergoing a folding transition. The energy landscapes associated with collapsed globules are expected to be rugged and resemble the topology of an egg carton, whereby distinct, albeit compact, conformations are of equivalent stability (134).

On the basis of heuristics gathered from simulations of a large number of sequences, a diagram of states was proposed for IDPs (28). According to this proposal, collapsed globules would be preferred for sequences with a fraction of charged residues (FCR) below 25%, which represent roughly 25% of all IDPs (29, 57). More recently, various lines of experimental evidence suggest that the determinants of collapse in IDPs are more complex than simple FCR-based thresholds. Many sequences with low FCR values are expanded relative to globules (43, 46, 89). Therefore, it seems likely that the fraction of sequences across the disordered proteome that form collapsed globules is smaller than would be predicted using composition-based heuristics. However, it is noteworthy that the study of IDPs that undergo collapse is inherently challenging. Techniques such as NMR and SAXS require high protein concentrations, and this opens the door to confounding inferences due to aggregation and poor solubility of globule-forming IDPs. In contrast, the observation of collapsed ensembles in simulations might not necessarily imply problems with force fields (12). IDPs that form globules readily become trapped in various metastable compact states, and broken ergodicity becomes a major challenge with respect to conformational sampling. These concerns emphasize the extant practical bias against studying collapsed IDPs. With this in mind, one should be cautious to not interpret the paucity of ensemble studies as evidence that these types of IDPs do not exist. In this context, single-molecule fluorescence and force spectroscopy measurements have a particularly useful role to play in concert with molecular simulations and theoretical analysis.

Proteins that Are Expanded and Folded in Aqueous Solvents

It is important to recognize that the folded states of proteins need not always be collapsed. As an example, while globular proteins are typically associated with a $v_{\text{app}}\approx 0.33$, the polypeptides that make up the collagen triple helix show scaling behavior consistent with a rod, $v_{\text{app}}\approx 1.0$ (11). Other examples of folded structures that are more consistent with rodlike states in water include alpha helical rods formed by block copolypeptides of the form [(Glu)₄-(Lys)₄]_n and the highly charged extracellular bacterial protein SasG (6). Various fibrous proteins or those with large coiled-coil segments are also inconsistent with global dimensions associated with chain collapse, although helices could be considered collapsed on an extremely local level (51, 81). Repeat proteins are another archetype of well-folded, highly stable, nonglobular proteins that lack the micellar organization of globular, folded proteins (1, 71, 72). Sequences that fold into elongated structures seem to bypass the collapse transition altogether, such that their folding likely involves a coil-to-rod transition, as opposed to coil-to-globule transition. There is much to learn from these systems that have the sequence characteristics or compositional biases of IDPs and yet fold into elongated structures via fundamentally different rules when compared to canonical globular proteins. A compact hydrophobic core is a convenient scaffold for protein stability, where that stability may help engender so-called evolvability (13). However, the discussion in this section emphasizes the point that a collapsed folded state is by no means the only mechanism through which a well-defined structure can be achieved.

Proteins that Are Expanded and Disordered in Aqueous Solvents

Many of the well-studied IDPs studied fall into this category. Marsh & Forman-Kay (87) found that, for a set of 32 IDPs, their global scaling behavior is consistent with an effective theta solvent ($v_{\text{app}}=0.51$). In the eight years since that study, many more IDPs have been characterized, and this empirical scaling relationship seems to be reasonably robust. As for exceptions, we have already discussed the case of IDPs that are disordered albeit collapsed. Interestingly, there are many examples of IDPs that are considerably more expanded than the proteins in the Marsh & Forman-Kay data set. For these sequences, $v_{\text{app}}$ can be larger than even 0.6, and these sequences include IDPs with high fractions of charged residues (85, 98). These sequences are either polyelectrolytes or polyampholytes, and changes to their dimensions as a function of salt concentration are predictable using generalizations of mean-field theories (54, 85, 98). Sequences that show increased expansion may also be rich proline residues. The combination of local stiffness, a marginal charge density, and the context-dependent solvation properties are thought to drive expansion (16, 23, 46, 87, 89, 107a, 144).

It is worth emphasizing that heteropolymers with $v_{\text{app}}\ge 0.50$ can have well-defined local and long-range attractive and repulsive interactions (21, 76, 89, 91, 123). As a result, $v_{\text{app}}$ should be thought of as a mean-field descriptor of the average polypeptide behavior but should not be taken as proof that the polypeptide is well described by a homopolymer model across all length scales. A prime example of this is the unfolded state of Ntl9, which under strongly denaturing conditions shows conformational behavior consistent with a scaling exponent of 0.59, yet complementary analysis by simulations and NMR find strong evidence for long-range and local interactions in the unfolded ensemble (91). Similarly, biophysical characterization of an intrinsically disordered region from the protein Ash1 found that although its expanded global dimensions are insensitive to phosphorylation, compensatory local changes lead to a reconfiguration of local and long-range intramolecular interactions (89).

We speculate that there may be an evolutionary bias toward expanded IDPs. According to conventional homopolymer theory, IDPs that undergo collapse would be expected to undergo aggregation, while those that show behavior consistent with a good solvent should remain soluble (112). If native environments were effective poor solvents for all disordered regions, then maintaining proteomic solubility would be an enormous energetic burden on the cell. Of course, this assumes that aggregation is detrimental. Recent work suggests the formation of biomolecular condensates through nonstoichiometric interactions among disordered proteins is a ubiquitous mechanism for cellular organization (8, 121a). Given the prevalence of polar-rich disordered regions in proteins that drive intracellular phase transitions, we suspect that at least in some cases the macroscopic self-assembly behavior of these disordered regions reflects a nanoscopic tendency for collapse (8, 95, 105).

THE INTERPLAY AMONG BACKBONE, SIDECHAINS, AND SOLVENT AS CAPTURED IN THE SIDECHAIN-PRIMING MODEL

The properties of IDPs that mimic the statistics of chains where $v_{\text{app}}\ge 0.50$ can be attributed to a dominance of the sidechain properties over the intrinsic preferences of backbones in water. Surprisingly, this sidechain dominance can be manifest even in sequences with large glycine contents, such as the RGG domain of the Caenorhabditis elegans protein LAF-1 (35% Gly) or the glycine-rich snow-flea antifreeze protein (45% Gly), both of which show behavior that is consistent with $v_{\text{app}}>0.50$ (45, 138). How can glycine drive chain compaction in polyglycine, while showing little apparent impact on the dimensions of glycine-rich heteropolymers?

The sidechain-priming model provides a plausible explanation for this behavior (58). Here, the presence of sidechains has two effects on the properties of the backbone. First, sidechains can engage in either attractive or repulsive interactions with backbone, sidechains, and solvent. Second, the sidechains have a steric impact; they prevent compaction of the peptide backbone thus inhibiting the solvation of backbone amides by one another. This steric effect is significant. Starting with a maximally compact polyglycine globule as a reference, the sidechains can dilute the effective local concentration of backbone amides by ~10 M, thus reducing self-solvation of backbone amides and limiting backbone-driven collapse. Therefore, the key interplay is between the polyglycine effect intrinsic to all sequences, which concentrates backbone amides around one another, and the sidechain-mediated amplification or dilution of the effective backbone amide concentration. Hence, even the conformational properties of disordered ensembles such as unfolded states under native conditions and IDPs in physiological milieus will be determined by the amino acid composition and primary sequence. For example, certain sidechains can drive chain compaction via sidechain–sidechain and sidechain–backbone interactions, such as in the case of polyglutamine (25, 135, 140). Conversely, in other sequences, including those with glycine-rich stretches interrupted by nonglycine residues, the intrinsic tendency of the backbone to collapse on itself is reversed by the interplay among sidechain, backbone, and solvent units.

The sidechain-priming model also helps explain apparently confounding results regarding the effects of denaturants on protein collapse/expansion. Various models to explain the denaturation mechanism of GdmCl and urea have been proposed, each of which suggests that a different balance of denaturant–backbone and denaturant–sidechain interaction is key (3, 18, 78, 92). In the sidechain-priming model, denaturant–sidechain interactions enable interactions between denaturants and backbone amides, such that in the absence of sidechains, denaturant–backbone interactions are unable to outcompete backbone–backbone interactions. This model is consistent with a two-stage mechanism for protein unfolding in which denaturant–sidechain interaction leads to a so-called dry-molten globule before denaturant–backbone interactions occur, as proposed and predicted from theory and subsequently observed experimentally (62, 96, 136). While denaturant–backbone interactions play an important role, and could be the dominant mode of peptide–denaturant interaction, sidechain-based interactions are necessary to facilitate denaturant accessibility to the backbone.

THE OVERALL ROLE OF SIDECHAINS AS MODULATORS—EVEN DETERMINANTS OF COLLAPSE

Given our preceding discussion, it becomes clear that sidechains play a dominant role in dictating the apparent solvent quality for different protein states. Accordingly, the amino acids can be divided into distinct classes on the basis of their physicochemical properties.

Hydrophobic Residues

Arguably the most well-studied amino acid class, hydrophobic sidechains include Ala, Ile, Leu, Val, Met, Phe, Tyr, and Trp. As commonly described, the hydrophobic effect reflects the fact that there is an energetic penalty associated with the solvent exposure of hydrophobic moieties, driving them into more buried orientations. The role of hydrophobic residues in protein folding is well studied. The Matthews lab (44, 66, 100) has explored the impact of isoleucine, leucine, and valine residues in driving protein folding. Unsurprisingly, the impact of hydrophobic residues on the unfolded state is not limited to protein folding. The formation of hydrophobic clusters in the unfolded state has been observed in many proteins, both under native conditions and nonnative conditions (26, 68, 74, 84, 88). Although IDPs are generally depleted in hydrophobic residues, this need is not always the case. Riback et al. (111a) found a direct correlation between hydrophobicity and the degree of collapse in the hydrophobic and proline-rich P domain of Pab1. Similarly, work from the Schüler lab (98) has shown a direct relationship between hydrophobicity and chain dimensions.

Polar Residues

Although polar residues (Gly, Ser, Thr, Asn, Gln, and Cys) are typically abundant in IDPs, they are also found extensively in folded proteins. Experimental and computational analysis of polyglutamine found that, despite the absence of conventional hydrophobic residues, it undergoes robust collapse and shows scaling behavior consistent with a polymer in a poor solvent (25, 134). Although not directly characterized, the length-dependent self-assembly of polyasparagine is consistent with it undergoing nonspecific collapse (80). In agreement with this, the glutamine/asparagine-rich N-terminal domain of the yeast prion protein Sup35 forms compact ensembles, and many polar rich IDPs drive self-assembly, gelation, and phase separation (95, 97, 105). The drive for collapse associated with polar tracts appears to be a combination of intramolecular hydrogen bonding, dipole–dipole interactions, and an entropic component from water upon collapse as solvent–amide hydrogen bonds are replaced by amide–amide hydrogen bonds (2, 63–65). The impact of other polar residues, such as serine and threonine in particular, remains less well understood, although the absence of an amide group is expected to reduce their ability to drive collapse in the same manner as glutamine. Similarly, the interplay between different types of polar sidechains requires further study.

Charged Residues

The energy scales associated with the interactions mediated by charged residues (Asp, Glu, Lys, Arg, and His) imply that they play important roles as determinants of the conformational behavior of proteins. For unfolded proteins and IDPs, the net charge per residue shows a direct correlation with global dimensions of polypeptides, in agreement with polyelectrolyte theory (85, 87, 98). The origins of this expansion are twofold: the electrostatic repulsions of like-charge residues and the extremely favorable free energies of solvation of charged sidechains. In conjunction, these two factors drive unfolded proteins with a high net charge toward expanded, coil-like ensembles. However, charge interactions can also drive compaction. As a prime example of this, phosphorylation of an unfolded protein 4E-BP2 drives compaction and folding via the formation of a network of hydrogen bonds that drive protein folding and compaction (5).

For an IDP of fixed composition with approximately equal numbers of positively and negatively charged residues, the patterning of charged residues can also directly dictate the global dimensions and amplitudes of conformational fluctuations (27, 28, 116). Patches of oppositely charged residues will engender electrostatic attractions; in well-mixed sequences, the electrostatic repulsions are screened by attractions and the preference for chain solvation dominates typically lack the ability to overcome charge repulsion and favorable solvation. In naturally occurring proteins, the extent of charge patterning may be also be important for mediating intermolecular interactions (79, 101). Finally, the temperature dependence of charge interactions may also prove to be important. Highly charged chains can undergo compaction as temperature increases owing to the increase in entropic cost of solvating charged groups (143).

Proline

Proline imparts several distinct features. Despite its purported hydrophobicity, L-proline is the most soluble amino acid (3). This is true of high polymers of proline, which show lower critical solution temperature in that they are highly soluble below ~70°C and form liquid crystalline assemblies above this temperature (130). It has been proposed that the patterning of proline and charged residues may play a role in determining the degree of expansion in disordered proteins (89). Consistent with this hypothesis, several well-patterned proline sequences are highly expanded (16, 46, 107a, 144).

CONCLUDING REMARKS

In this review, we have highlighted emerging ideas regarding the collapse transitions of proteins. Our perspective has been guided by the recognition that the sequences of proteins are diverse enough to accommodate at least four distinct categories of states in aqueous solvents. Different flavors of IDPs and rod like protein sequences have led to the realization that there is more to the collapse/expansion transition than just the canonical hydrophobic effect. A topic not explored here, but of direct relevance to collapse transitions in the cell, is how different types of osmolytes influence conformational behavior (29a, 109). As new approaches and combinations of theory and experiments are deployed, ideally in a high-throughput manner, we will learn more about the intricate details of the interplay among backbone units, sidechain moieties, and solvent molecules and the extent of coupling/decoupling between collapse/expansion and folding. The authors are not aware of any affiliations, memberships, funding, or financial holdings that might be perceived as affecting the objectivity of this review.