Temperature-dependent solvation modulates the dimensions of disordered proteins

Significance

A large number of naturally occurring proteins are now known to be unstructured under physiological conditions. Many of these intrinsically disordered proteins (IDPs) bind other biological macromolecules or ligands and are involved in important regulatory processes in the cell. For understanding the structural basis of these functional properties, it is essential to quantify the balance of interactions that modulate the heterogeneous conformational distributions of IDPs and unfolded proteins in general. In contrast to the behavior expected for simple polymers with temperature-independent intramolecular interactions, unfolded proteins become more compact when the temperature is raised. Here, we show that the temperature dependence of the interactions of the constituent amino acid residues with the aqueous solvent have a dominant effect on this behavior.

Abstract

For disordered proteins, the dimensions of the chain are an important property that is sensitive to environmental conditions. We have used single-molecule Förster resonance energy transfer to probe the temperature-induced chain collapse of five unfolded or intrinsically disordered proteins. Because this behavior is sensitive to the details of intrachain and chain–solvent interactions, the collapse allows us to probe the physical interactions governing the dimensions of disordered proteins. We find that each of the proteins undergoes a collapse with increasing temperature, with the most hydrophobic one, λ-repressor, undergoing a reexpansion at the highest temperatures. Although such a collapse might be expected due to the temperature dependence of the classical “hydrophobic effect,” remarkably we find that the largest collapse occurs for the most hydrophilic, charged sequences. Using a combination of theory and simulation, we show that this result can be rationalized in terms of the temperature-dependent solvation free energies of the constituent amino acids, with the solvation properties of the most hydrophilic residues playing a large part in determining the collapse.

The properties of unfolded proteins have recently attracted renewed interest (1), triggered in particular by the realization that a large fraction of naturally occurring polypeptides are unstructured under physiological conditions (2, 3). Some of them fold into well-defined structures upon interaction with a ligand or binding partner, whereas others may remain unstructured under all conditions. Many of these “intrinsically disordered proteins” (IDPs) are involved in cellular signaling networks and are thus of great medical interest (4). Given the presence of varying degrees of disorder in unbound and bound states (5), a general framework for the description of the physicochemical properties of IDPs will aid our understanding of the molecular mechanisms underlying their function. Such a framework is beginning to emerge from recent work in which concepts from polymer physics have been found to capture very successfully key aspects of the global conformational and dynamic properties of IDPs and unfolded proteins in general (6). These include the role of charge interactions (7, 8), protein–solvent interactions (9–13), scaling laws (14–16), reconfiguration dynamics (17), and the effect of internal friction (18–21).

An aspect that is less well understood is the effect of temperature on unfolded and intrinsically disordered proteins. Recent single-molecule Förster resonance energy transfer (FRET) experiments showed that the small cold shock protein from Thermotoga maritima (CspTm) and the IDP prothymosin α (ProTα) become more compact with increasing temperature (22), even after the effect of denaturant present in solution (23) is taken into account. The results were in good agreement with dynamic light-scattering experiments on unlabeled protein, demonstrating that the effect is independent of the presence of the fluorophores (22). This result is in line with previous laser temperature jump experiments on acid-denatured BBL protein (24) and recent light- and small-angle X-ray–scattering results on the disordered N-terminal part of p53 (25) and several other IDPs (26). All of these observations are in contrast to the behavior expected for a polymer chain with a temperature-independent monomer–monomer interaction energy, which will expand with increasing temperature owing to the increasing entropic contribution to the free energy (27, 28). The observation of temperature-induced collapse in proteins thus implies the existence of temperature-dependent interactions, presumably with contributions from the hydrophobic effect (29–33) or, more generally, changes in solvation free energy as a function of temperature. A critical role for the solvent contribution is supported by molecular simulations of unfolded proteins with different water models (22, 34), and even simulations of hydrophobic homopolymers (35–39) and simple heteropolymers (40) in explicit water models exhibit a similar behavior. However, the detailed origin of the temperature-induced compaction has remained elusive. To address this question, two key ingredients are required: a larger dataset from experiments on different proteins that enables us to probe the effect of sequence composition more systematically (and in the absence of effects from denaturants), and a simulation model that provides realistic chain dimensions and allows us to investigate the role of solvation free energies.

Here, we investigate the generality and origin of the temperature-induced collapse of unfolded polypeptides by studying five natural proteins with very different sequence compositions, ranging from very hydrophobic foldable sequences to very hydrophilic IDPs. A key feature of our study is the choice of proteins with sufficiently low conformational stability to ensure that the properties of the unfolded state can be observed directly under near-physiological conditions, without using additional denaturants (22) or nonneutral pH (24). Using single-molecule FRET experiments, we are able to specifically monitor the dimensions of the unfolded state as a function of temperature. For all of the sequences, we observe a decrease in chain dimensions with increasing temperature. Remarkably, the largest amplitude of collapse is observed for the most hydrophilic, charged sequences. We use a combination of polymer theory, empirical solvation free-energy data, and implicit solvent simulations to rationalize the observations in terms of the different properties of the underlying sequences. We show that the differences in collapse can be correlated with average solvation free energies of the residues, and that by parameterizing an implicit solvent model using these solvation free energies, we can semiquantitatively reproduce both the absolute radii of gyration and the extent of collapse with temperature. The unexpected result from our work is that, even though the classical hydrophobic effect undoubtedly plays a role in our observations, we find that large variations in solvation free energy with temperature for polar and charged residues also play a very important role. This has significant implications for the properties of IDPs, which are enriched in these residue types.

Results and Discussion

To probe the temperature-dependent protein collapse, we used single-molecule FRET, a technique that has recently been used very successfully for investigating the distance distributions and dynamics of unfolded proteins and IDPs (41–43). A particular advantage of this approach is the ability to separate subpopulations in heterogeneous systems. In our case, this means that we can quantify the properties of the unfolded subpopulation even in the presence of a majority of folded molecules (Fig. 1). Each protein was labeled with Alexa 488 and Alexa 594 as FRET donor and acceptor fluorophores, respectively, via maleimide derivatives that react with cysteine residues introduced by site-directed mutagenesis (SI Materials and Methods). Single-molecule observations were made on freely diffusing molecules in a confocal instrument with accurate temperature control of the sample (22).

Fig. 1.

Transfer efficiency histograms obtained in confocal single-molecule FRET experiments on λ-repressor as a function of temperature (representative dataset). (A) Histograms were analyzed in terms of three populations, with the fits indicated as solid lines (red: native; blue: unfolded; black: sum of all populations). The population at E ∼ 0 corresponds to molecules without an active acceptor chromophore. (B) The same data were processed with recurrence analysis (47) before fitting the subpopulations to enrich the population of the unfolded state and minimize uncertainty from peak overlap.

An example of the results of such an experiment is shown in Fig. 1 for the helical N-terminal λ-repressor domain, a popular model system for protein-folding studies (44–46). At low temperature, two relevant populations are observed: a folded subpopulation with a mean transfer efficiency 〈E_F〉 of ∼0.9 and an unfolded subpopulation with a mean transfer efficiency 〈E_U〉 between ∼0.6 and ∼0.8; a third population at E ∼ 0 originates from molecules that do not contain an active acceptor chromophore. With increasing temperature, two effects are observed: the folded population decreases, and the population of unfolded molecules increases accordingly, as expected from the typical temperature-induced unfolding of proteins; at 319 K and above, all molecules are unfolded. More importantly for the present study, however, the mean transfer efficiency of the unfolded state changes with temperature (in contrast to the folded state, whose transfer efficiency remains constant). Up to 319 K, 〈E_U〉 increases, corresponding to a compaction of the unfolded molecules. Above 319 K, no further increase in 〈E_U〉 is observed; in fact, a slight decrease in 〈E_U〉 even suggests a reexpansion of unfolded λ-repressor. To exclude an effect on our analysis from the incomplete separation of unfolded and folded subpopulations between ∼300 and ∼320 K, we additionally used recurrence analysis (47), a method that allows us to enrich individual subpopulations in a model-free manner, and obtained very similar results (Fig. 1B). Fig. 2A shows the resulting values of 〈E_U〉 as a function of temperature.

Fig. 2.

Average transfer efficiencies of the unfolded proteins (A), their radii of gyration (B), and the effective intrachain interaction energies (C), as determined from the transfer efficiencies using Sanchez theory, as a function of temperature. Uncertainties in C are SDs estimated from two to three independent measurements. Fits (solid lines) are used to extract enthalpic and entropic components of ε, whose temperature dependences are determined by a heat capacity term (Table 1). Note that ε > 0 corresponds to attractive intrachain interactions, resulting in chains more compact than an excluded volume chain without additional interactions (ε = 0), and ε < 0 corresponds to repulsive intrachain interactions, resulting in chains more expanded than an excluded volume chain.

To determine whether the temperature dependence of the unfolded state dimensions is a general phenomenon, and to relate its characteristics to the amino acid composition of the chain, we extended the study to other proteins (Table 1 and SI Materials and Methods): two variants of the highly charged IDP ProTα, which allow us to probe the N- and C-terminal halves of the polypeptide (ProTαN and ProTαC, respectively), whose charge content is very different (8); the N-terminal domain of HIV integrase (8), an IDP in which the folded structure is formed upon binding of Zn²⁺ (48); and a 34-aa fragment of CspTm, which is not folding competent (18) (CspM34). The average hydrophobicities of the sequences according to the Kyte–Doolittle score (49) are −2.44 for ProTαC, −1.5 for ProTαN, −0.6 for integrase and CspM34, and −0.25 for λ-repressor. In all cases, we can investigate the unfolded state under near-physiological conditions in the absence of denaturants, in contrast to the previous experiments, where extrapolation to zero denaturant was required (22). Even though these proteins vary considerably in amino acid composition, average hydrophobicity, and charge distribution, they all exhibit an increase in 〈E_U〉 with increasing temperature (Fig. 2A), corresponding to a compaction of the unfolded state.

Table 1.

Thermodynamic parameters describing the interaction free energy –ε between monomers

Protein	/	/	/	/
ProTαC	19.6	0.056	−0.27	368.5 ± 3.6
ProTαN	9.8	0.031	−0.18	355.7 ± 1.6
Integrase	2.4	0.011	−0.07	350.8 ± 4.8
Csp M34	1.4	0.09	−0.05	354.9 ± 3.8
λ-Repressor	3.5	0.017	−0.24	320.5 ± 0.8

Data in Fig. 2C were fitted to a thermodynamic model, , where and are the enthalpic and entropic contributions to the collapse process, respectively, at the reference temperature = 298 K, and assuming a temperature-independent heat capacity . T_M is the temperature where ε(T) is a maximum.

For a quantitative analysis of the measured values of 〈E_U〉 in terms of distance distributions in the unfolded state and the magnitude of intramolecular interactions, we used the mean-field theory of Sanchez (27), as first applied to unfolded proteins by Haran and co-workers (11, 12), and with the radius of gyration at the θ state of 0.22 nm N^1/2 as a reference point (where N is the number of peptide bonds in the chain segment probed), as determined by Hofmann et al. (14) (see SI Materials and Methods for details). Briefly, the theory treats the dye-to-dye distance distribution in terms of a Flory–Fisk distribution weighted by a Boltzmann factor whose value depends on the average effective interaction free energy, ε, between the monomers. A variation of ε as a function of solution conditions or temperature can then be used to account for the observed continuous changes in chain dimensions (11, 12, 14, 27).

Fig. 2 shows the resulting values for the average radii of gyration, R_g, and ε for all protein variants investigated as a function of temperature. All unfolded proteins exhibit temperature-induced collapse. Only λ-repressor shows a slight reexpansion of the chain at high temperature; all other proteins show a monotonic compaction. Correspondingly, the average interaction energy between the amino acids in the chain becomes more favorable with increasing temperature, but with pronounced curvature. For λ-repressor, the temperature dependence of ε exhibits a maximum at ∼320 K. This type of turnover in the temperature dependence is reminiscent of the hydrophobic effect (30, 50–55), suggesting that it plays an important role in the compaction of the chain. However, the pronounced collapse and large change in ε of the IDPs, in particular the extremely hydrophilic ProTα variants, indicates that the collapse does not arise from the classical hydrophobic effect alone. We can describe the temperature dependence by treating −ε as a free energy of interaction with enthalpic and entropic contributions, whose temperature dependences are determined by a heat capacity term (56) (Fig. 2C and Table 1). This analysis shows that the monomer association leading to chain collapse is favored by entropy, as expected for the classical hydrophobic effect. However, there is also a large unfavorable enthalpy of association for the hydrophilic sequences, which is not expected for hydrophobic solutes. The decreasing solvation free energy of the chain with increasing temperature, which collapses the unfolded state, might also be expected to stabilize the folded protein. Indeed, the resultant destabilization as the temperature is lowered results in the “cold unfolding,” which can be observed for certain proteins (35, 37, 38, 57–60). However, at higher temperatures, unfolding is driven by the large increase in chain entropy on unfolding (61); at these temperatures, the unfolded chain may nonetheless continue to collapse (driven by unfavorable solvation free energy) because the variation in configurational entropy for a reduction in chain dimensions is much smaller than that for folding.

Can we rationalize the temperature-dependent ε in terms of the polypeptide sequence composition? The interaction free energy ε between two isolated residues can in general be divided into the direct interaction of those residues in the gas phase and a solvation free energy resulting from transferring the residues to water. The contribution from the solvation free energy to ε is the difference between the solvation free energy of the associated and dissociated residues, assuming the chain is sufficiently expanded that many-body effects can be neglected.

We explore this aspect by first considering the empirical solvation free energies for amino acid analogs and for the peptide group (62, 63), which fall approximately into five classes with different temperature dependences (Fig. 3A; see SI Materials and Methods for details), with the hydration of the aliphatic side chains being unfavorable and hydration of other residues being favorable. Interestingly, the hydrophobic aliphatic amino acids all exhibit a turnover in free energy because at low temperature the solvation entropy is unfavorable, but it becomes less so with increasing temperature. However, for almost all of the other amino acids, the solvation free energy becomes monotonically less favorable with increasing temperature, and the amplitude of this change is most pronounced for the most hydrophilic amino acids. These trends are clearly reminiscent of the differences in the temperature dependences of ε observed for the proteins with different mean hydrophobicity (Fig. 2C). In this connection, we note that, as all of the amino acid side chains have a positive solvation heat capacity (64), the sign of the heat capacity for contact formation is expected to be negative, as also observed in all cases (Table 1). This confirms that the sign of the heat capacity alone need not be an indication of hydrophobic effects (65).

Fig. 3.

Solvation free energies derived from small molecules. (A–E) Group solvation free energies of each amino acid side chain, and of the peptide backbone (BB), grouped by magnitude of solvation free energy. (F) Average residue solvation energies (Eq. S7) for each protein sequence.

To connect these individual residue solvation free energies to the effective intrachain interactions as determined from Sanchez theory, it would be necessary to know also the solvation free energy of the associated residue pairs. In a first approach, we approximate this effect by assuming that the solvation free energy of a buried residue is reduced (in magnitude) in proportion to the volume excluded by its neighbors (66) [as is done in the ABSINTH (67) and EEF1 models (68)]. Therefore, the change in solvation free energy upon forming a single residue–residue contact should be approximately proportional to the sum of the solvation free energies of the corresponding isolated residues, assuming each to exclude a similar volume from the other upon contact, and neglecting many-body effects. Following this reasoning, a simple approximation is that the solvation contribution to ε is proportional to the average solvation free energy per residue . This approach accounts for sequence composition, but not sequence order. Remarkably, the resulting temperature dependencies of the average residue solvation free energies (Fig. 3B) already resemble some of the key aspects observed in the temperature dependencies of the mean-field interaction energies fitted to the experimental data (Fig. 2C), in particular the pronounced curvature, the larger slope for more charged sequences, and the approximate rank order of the protein variants (only the adjacent Csp M34 and HIV integrase are switched).

Despite the qualitative success of this approach, it does not capture the maximum in ε seen for λ-repressor, and the large differences in the amplitudes of the change in ε with temperature for the different sequences seen in experiment (Fig. 2C). To make a closer connection between empirical solvation free energies and chain dimensions, we have used molecular simulations with the ABSINTH force field (67), thus capturing the effects of chain connectivity and sequence correlations, many-body solvation effects, as well as an explicit model of electrostatic interactions. The ABSINTH energy function includes an implicit solvent model in which the short-range contribution to the solvation free energy, W_solv, is written as a sum over group contributions, i.e., , where the sum runs over N_SG “solvation groups”, each with solvation free energy when fully solvent-exposed, and where f_i is the degree of solvent exposure of residue i as defined in ref. 67. The motivation for this expression is that the solvation free energy of a group of atoms will be approximately reduced in proportion to the volume excluded by neighboring residues. The solvation groups are subsets of atoms in each residue, which may be identified with small model compounds, and the solvation free energies are taken unmodified (for the most part) from experimental data for these compounds. We used the standard ABSINTH model, but with two changes: (i) we computed temperature-dependent solvation free energies using published thermodynamic data, as described in SI Materials and Methods, and (ii) we additionally considered the effect of the temperature dependence of the dielectric constant. In principle, explicit solvent simulations should be the most accurate method for treating unfolded proteins. However, unfolded states in all current force fields are too collapsed, having comparable, or sometimes smaller, radii of gyration than the folded protein (69, 70). However, ABSINTH results in a good correlation with experimental radii of gyration (Fig. 4A), as discussed below.

Fig. 4.

Results from simulations with the OPLS/ABSINTH force field. (A) Correlation between experimental single-molecule FRET (smFRET) estimate of radius of gyration with that calculated from ABSINTH calculations. Linear correlation coefficients are 0.95 and 0.92 at 300 and 350 K, respectively. (B) For each protein, the average temperature-dependent radius of gyration is plotted for simulations in which (i) the solvation free energies and solvent dielectric constants were fixed to those at 300 K (black symbols); (ii) the dielectric constant varied with temperature (red symbols); (iii) both the dielectric constant and solvation free energies were made temperature dependent (blue symbols). The unshaded region represents the temperature range probed in experiments.

Replica exchange Monte Carlo simulations were run for each of the five proteins using the modified ABSINTH model, over a wide range of temperatures. In addition, we considered two reference models: the original ABSINTH model (temperature-independent solvation free energies and dielectric constant) and a model in which only the dielectric constant varied with temperature. The radius of gyration of each peptide is shown as a function of temperature in Fig. 4B. The original ABSINTH model, although capturing very well the dimensions near 300 K, shows a large expansion with temperature in all cases, as expected from entropic considerations. The less pronounced expansion of the prothymosin variants with increasing temperature is expected in view of the large electrostatic repulsion present in these molecules (8). The modest influence of a temperature-dependent dielectric indicates that this is not an important effect. However, the model including temperature-dependent solvation free energies results in a dramatic shift in observed properties relative to the former models. Instead of rapidly expanding at low temperatures, the radius of gyration initially shows only a weak temperature dependence, or modest collapse for HIV integrase, Csp M34, and λ-repressor, thereby linking the temperature dependence of the solvation free energy with temperature-induced chain collapse. For both ProTαN and ProTαC, there is a marked collapse, reflecting the larger amplitude reduction in radius of gyration for these sequences in experiment. In Fig. 4A, we show that the average radii of gyration for each sequence correlate well with the experimental values at both 300 and 350 K when temperature-dependent solvation free energies are used.

Although the change in radius of gyration in the simulations is relatively modest for HIV integrase, Csp M34, and λ-repressor, the two prothymosin fragments appear to collapse monotonically until very high temperature. This difference appears to correlate with overall sequence hydrophobicity and is consistent with the different trends in solvation free energies of hydrophobic and polar groups in Fig. 3A. The properties of the more hydrophobic chains, and observation of hydrophobic clusters for some unfolded proteins by NMR (71, 72), suggest that a description similar to a classic hydrophobic collapse mechanism may be appropriate in these cases (30, 31, 73). A second effect that needs to be taken into account is that the amplitudes of chain collapse with temperature will be affected by the sign of the interactions within the polypeptide. For a chain with overall attractive interactions between the monomers, an increase in temperature will favor chain expansion (assuming the interactions are temperature independent). However, for a chain with overall repulsive interactions, as in the case of ProTα (14), an increase in temperature will favor chain compaction, because in the limit of high temperature, only the excluded volume part of the interactions remains important; therefore, the effect of temperature-dependent solvation free energy will be amplified.

In summary, we have shown with a combination of advanced single-molecule methods that temperature-induced collapse is a common feature of five intrinsically disordered or unfolded proteins with very different sequences. The corresponding variation in sequence composition allows us to reveal details of the temperature-dependent interactions within the chains. By analyzing the data with the polymer model of Sanchez, we can interpret intrachain interactions in terms of temperature-dependent free energies and thus link experiment, theory, and simulations. Although the hydrophobic effect is clearly a contributing factor to the collapse, an unexpected finding is the pronounced compaction of the most hydrophilic chains with increasing temperature. Ultimately, it should be possible to address all of these aspects quantitatively in explicit-solvent molecular dynamics simulations. However, only recently are force fields and water models emerging that provide a reliable description of unfolded and disordered proteins (34, 74–78). We have shown that the temperature effects on unfolded state dimensions can be understood at a semiquantitative level by means of a molecular model with implicit solvent by including a temperature-dependent solvation free energy for the constituent amino acid residues. This combination should enable a wide range of simulations for which explicit solvent models are either not accurate enough or prohibitively expensive. Finally, data of the type presented here will be an important benchmark for further improving simulations and our understanding of solvation effects on the structure and dynamics of unfolded and intrinsically disordered proteins.

Materials and Methods

Proteins were expressed recombinantly, purified, and labeled with fluorophores as described in SI Materials and Methods. Single-molecule measurements were performed using a MicroTime 200 confocal instrument (PicoQuant). For details of the simulations and their parameterization, see SI Materials and Methods.