Unified Description of Urea Denaturation: Backbone and Side Chains

Dec 11, 2013 - Macromolecular Stabilization by Excluded Cosolutes: Mean Field Theory ... Mutual Exclusion of Urea and Trimethylamine N-Oxide from Amin...
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Unified Description of Urea Denaturation: Backbone and Side Chains Contribute Equally in the Transfer Model Beate Moeser and Dominik Horinek* Institut für Physikalische und Theoretische Chemie, Universität Regensburg, 93040 Regensburg, Germany S Supporting Information *

ABSTRACT: After studying protein denaturation by urea for many decades, conflicting views of the role of the side chains and the backbone have emerged; many results suggest that urea denatures by enhancing the solubility of both the side chains and the backbone, but the frequently applied transfer model (TM) so far ascribes denaturation exclusively to urea’s action on the backbone. We use molecular dynamics simulations to rigorously test one of the TM’s key assumptions, the proportionality of a molecule’s transfer free energy (TFE) and its solvent-accessible surface. The performance of the TM as it is usually implemented turns out to be unsatisfactory, but the proportionality is satisfied very well after an inconsistency in the treatment of the backbone contribution is corrected. This inconsistency has so far gone unnoticed as it was obscured by a compensating error in the side-chain group TFEs used so far. The revised “universal backbone” TM presented in this work shows excellent accuracy in the prediction of experimental m values of a set of 36 proteins. It also settles the conflicting views regarding the role of the side chains because it predicts that both the side chains and the backbone on average contribute favorably to denaturation by urea.

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INTRODUCTION Protein folding and unfolding relies on a subtle free-energy balance and is sensitive to temperature, pressure, and chemical environment.1−4 The latter is especially important because it affects protein stability at ambient conditions, and there has been a tremendous amount of work aiming at the understanding of stabilizing and denaturing cosolute effects on proteins.1,5−7 Probably the most studied cosolute is urea, a common denaturant that is ubiquitous in living organisms. There is much evidence that denaturation by urea is caused by direct binding of urea to polar as well as nonpolar parts of the protein, which includes both the backbone and the side chains.8 This result is corroborated by a wealth of studies with molecular dynamics (MD) simulations9−12 and by experiments.13,14 Yet, the scientific debate about urea’s denaturation mechanism is still ongoing because the widely used and wellestablished transfer model (TM) points toward a contrasting mode of action. The TM was proposed by Tanford15 and rendered implementable by Auton and Bolen.16,17 It serves to calculate the m value, an experimentally readily accessible quantity that describes the change in protein unfolding free energy per molar addition of urea. This is done in a bottom-up approach, in which the solvent-transfer properties of proteinogenic building blocks are derived from experiments on small molecules and then merged into the m-value prediction of a protein with known structure. In this framework, it is possible to keep track of the emergence of the m value on the level of individual side-chain and backbone groups.17 According to © 2013 American Chemical Society

Bolen and co-workers, the TM reveals that the denaturation by urea is entirely driven by favorable interactions of urea with the polar backbone18,19 and that the increased exposition of side chains upon unfolding, on average, opposes denaturation. It is predicted that unfolding only occurs because urea’s effect on the backbone dominates. The TM is based on a number of assumptions. So far, their validity has never been tested rigorously but has only been made plausible by the fact that predicted m values agree well with experimental m values for a manifold of proteins with different compositions and structures.20 In this work, we present an approach for a quantitative test of one of the TM’s key assumptions, which is that the contribution of a proteinogenic building block to the protein’s transfer free energy (TFE) from water to an aqueous urea solution is proportional to its solvent accessible surface area (ASA). The test is primarily based on MD simulations with a simulation protocol that we recently developed.12 Compared with experimental studies, computer simulations have the advantage that they allow for the investigation of simple model peptides of a well-defined secondary structure, ASA, and composition. Our study reveals that the ASA-scaling hypothesis is accurate, but not when the current established implementation of the TM17−19,21 is applied. We trace this back to the treatment of the backbone group contributions, which is not consistent with Received: October 7, 2013 Revised: November 27, 2013 Published: December 11, 2013 107

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Article bb sc TFE ⎞⎟ TFE ⎞⎟ est sc ⎛ bb ⎛ ⎜ ⎜ TFEaa = ASAaa + ASAaa ⎝ ASA ⎠aa ⎝ ASA ⎠aa

the ASA-scaling hypothesis. We propose an alternative “universal backbone” implementation that is better in line with the original assumption and better accounts for the chemical nature of the backbone unit. This alternative implementation yields considerably more accurate ASA-based predictions of TFEs. In a second step, we demonstrate that the universal backbone TM is also superior to the established implementation in predicting m values of proteins on the basis of experimentally determined group TFEs. Moreover, we show that analyses with the universal backbone TM in combination with correct experimental side-chain TFEs upend the established conclusion of the TM that denaturation is entirely driven by the backbone. According to our study, the backbone and the total side-chain contributions to the m value are of comparable size and favor denaturation. This finding unifies the different existing views on the side chains’ role in urea denaturation and provides a further step toward a generally accepted concept of urea’s denaturation mechanism.

The subtle but decisive difference is the index aa of the TFE per ASA ratio of the backbone: in eq 2 all backbone units are treated identically and have the same TFE per ASA value, whereas in eq 3 the TFE per ASA value of the backbone depends on the type of residue it belongs to. Hence, we call the first implementation (eq 2) universal backbone TM to distinguish it from the established TM (eq 3), which essentially operates with 20 different backbone groups. The universal backbone implementation accounts for the fact that all backbone units in a protein are chemically the same species, and that their TFE per ASA valuesin the framework of the TMshould not depend on the side chain attached to them. Therefore, in our view, eq 2 is more consistent with the basic ideas of the TM than eq 3. To understand the implications of the different treatment of the backbone units in the two implementations of the TM, it is instructive to take a closer look on the determination of the group TFE per ASA values as performed in practice; in an experiment, it is not possible to directly access the ratio of TFE to ASA. Therefore, one measures the TFEs of the different groups and separately defines a set of ASA values to which the measured TFEs are assigned. Usually, the TFEs of all side-chain groups are obtained by measuring the TFEs of the free amino acids and subtracting the TFE of a glycine molecule.24 These TFEs are then assigned17−19,25 to the ASA values that the considered side chains on average have in Gly-X-Gly sequences isolated from protein structures26 (other realizations of the TM use the maximal side-chain accessibilities in Gly-X-Gly tripeptides instead21). The TFE of the backbone unit is determined from TFE measurements of peptide containing model compounds such as, for example, N-acetylglycinamide peptides of varying length or cyclic glycylglycine.16 Results of measurements with different model compounds agree well within the experimental accuracy and usually a value of −39 cal mol−1 M−1 is used. In the universal backbone TM, we assign this TFE to the ASA of glycine in the tabulated Gly-X-Gly ASAs, which corresponds well to the ASA of the backbone in an N-acetylglycinamide peptide. Choosing from the same list of ASAs as in the established implementation ensures the maximum comparability between the universal backbone implementation and the latter. In the established TM, however, this backbone TFE is for each amino acid type X assigned to the backbone ASA of the respective Gly-X-Gly sequence average,17−19,25 which differs drastically between amino acid types; for glycine, the backbone ASA in isolated Gly-X-Gly sequences amounts to 88.1 Å2, but it is significantly smaller for all other amino acids. For isoleucine it is only 30.9 Å2.17,26 Thus, in the established TM, the absolute TFE per ASA value of the backbone unit increases with decreasing ASA in the Gly-X-Gly sequence and ranges from −0.44 to −1.26 cal mol−1 Å−2 M−1, whereas the first value seems to be the most reasonable estimate for all backbone units. Figure S1 in the Supporting Information illustrates the different TFE per ASA values of the backbone unit and their dependence on the backbone ASA of the Gly-X-Gly reference state as present in the established TM. In contrast to the TM that treats the side chains and the backbone unit as building blocks, other models13 distinguish different atom types and, therefore, have a finer resolution. Nevertheless, we also examine an even more reductionist

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OVERVIEW OF DIFFERENT TM IMPLEMENTATIONS The m value of a protein equals the difference of the TFEs of the denatured and the native state from water to a 1 M cosolute solution (here, urea).17 On the basis of this equality, in the TM, the m value is calculated via an estimate of these two TFEs. As described below in this paragraph, the calculation of the TFE in the framework of the TM requires the knowledge of the ASAs of individual side-chain and backbone groups. For the native state, these ASAs can be determined from published structural data. However, the structure of the denatured state, which might display some residual structure, is generally not known. Therefore, an assumption about the structure of the denatured state and, thus, about the solvent accessibilities of the individual groups needs to be made. Usually, it is assumed that the ASAs in the denatured state can be described by the average ASAs of the two extreme models for the denatured state that were developed by Creamer et al.17,22 For a given protein structure, the TFE is estimated in the TM by means of two major assumptions: The first is that the TFE of any protein structure can be written as a sum of the TFEs of its amino acid residues TFEprot =

∑ TFEaa aa

(1)

where the TFE of each amino acid, TFEaa, in turn is composed of two additive contributions, one from the backbone part and one from the side chain. Several studies indicate that this assumption is legitimate.12,16,23 Second, it is assumed that the TFE of each considered group (i.e., side chain or backbone) is proportional to the ASA it has in the protein structure under consideration. This ensures that groups that are not in contact with the solvent do not contribute to the free energy of the solvent change. The ASA-scaling hypothesis corresponds to the assumption that each building block of the protein has a characteristic TFE per ASA value. Thus, in a straightforward implementation of this basic idea, the TFE of an amino acid residue is given by sc ⎛ TFE ⎞bb TFE ⎞⎟ sc ⎛ bb ⎜ ⎜ ⎟ TFEaa = ASAaa + ASAaa ⎝ ASA ⎠aa ⎝ ASA ⎠

(3)

(2)

where sc stands for side chain and bb for backbone. The established realization of the TM17−19,21 that was introduced by Auton and Bolen17 uses instead 108

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Figure 1. Computed TFEs, simulation snapshots, and ASAs of the four different simulated peptide conformations (here for glycine homopeptides). The blue lines denote the computed TFEs for a transfer from water to up to 10 M aqueous urea solution, and the dashed red lines are predictions of the TFEs. The good agreement between predicted and simulated TFEs demonstrates that ASA-based predictions are reasonable.

implementation of the TM, the “united residue TM”. In this model, we do not distinguish between the side chain and the backbone of the amino acid residues. Instead, we treat the 20 different residue types as the groups of the TM and describe each residue by a characteristic TFE per ASA ratio ⎛ TFE ⎞ ⎟ TFEaa = ASAaa⎜ ⎝ ASA ⎠aa

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Predictions Based on Experimental Data. We use the three different TM implementations to predict m values on the basis of experimentally determined TFEs for a benchmark list of proteins. This enables us to compare the predictive accuracies of the different implementations and to determine the backbone and side-chain contributions to the m values. The list of proteins and their experimental m values are taken from ref 18 and the PDB IDs of the structures that we use for the proteins are listed in Table S3 in the Supporting Information. In the determination of the TFE per ASA values, we use either the GTFEapp values from ref 17 or the GTFE+ values as given in the Supporting Information for the side-chain TFEs and −39 cal mol−1 M−1 for the backbone TFE.16,17 The GTFE+ values represent a recalculation of the GTFE* values from ref 18 with a corrected version of the (previously erroneous) incorporation of the activity coefficient of glycine. A detailed derivation of the calculation of the GTFE+ values is given in the Supporting Information. The ASAs that we use in the determination of the TFE per ASA values are the average ASAs of Gly-X-Gly sequences as given in ref 17. For the determination of the TFE per ASA values of the backbone, we use the Gly-X-Gly ASA of Gly in the universal backbone TM and the amino acid type dependent Gly-X-Gly backbone ASA of X in the established TM. The differences in ASA between the native and the denatured state of the proteins are calculated with the m-value calculator.25 Thus, our implementation of the established TM is identical to the one of Auton, Holthauzen, and Bolen, and the universal backbone TM differs from that only by the assignment of ASA to TFE in the determination of the TFE per ASA value of the backbone. A more detailed description of the above-described prediction methods with equations is presented in the Supporting Information.

(4)

METHODS

Validation by Molecular Dynamics Simulations. We determine the ASAs and TFEs of amino acid residues in homopeptides of different conformations with a simulation protocol that we recently developed.12 Detailed descriptions of the simulated structures, the simulations themselves, and the TFE and ASA calculations are given in the Supporting Information. The simulations are performed with GROMACS 4.527 using the force fields GROMOS 53a628 for the peptides, SPC29 for water, and KBFF for urea.30 The validity of the different TM implementations is assessed by determining their accuracy in predicting the TFE of amino acid residues in folded peptide structures from the TFE per ASA values of residues in extended strands. These ASA-based TFE predictions are performed with eq 2−4 for which the TFE per ASA values are obtained as follows: in the united residue TM, the TFE per ASA ratio of the extended strand is used; in the universal backbone TM, the TFE per ASA value of the backbone is given by the data of the glycine strand; in the established TM, it is given by the TFE of the glycine strand and by the backbone ASA of the strand of the amino acid in question. To determine the TFE per ASA value of the side chain, in both implementations the difference between the TFE of a residue in the strand and the determined TFE of the backbone in the strand is taken and assigned to the side-chain ASA in the strand bb TFEaa − ASAaa ⎛ TFE ⎞sc ⎜ ⎟ = sc ⎝ ASA ⎠aa ASAaa

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RESULTS AND DISCUSSION

Validation by Molecular Dynamics Simulations. First, we check whether the ASA-scaling assumption holds for glycine residues. We perform MD simulations to calculate the TFE and ASA per residue of glycine homopeptides in four conformations: extended strand, 310 helix, α helix, and β sheet. Figure 1 displays simulation snapshots of the four structures along with results for their ASA and TFE. On the basis of the TFE per ASA value of the extended strand, we predict the TFEs of the three folded structures. For glycine residues, which do not have any side chain, the predictions of the established TM and of the universal backbone TM are identical to those of the united residue TM. The predictions are shown as red dotted lines in

bb

( TFE ASA )

(5)

As quantitative measures of predictive accuracies, we take the absolute and relative rms deviations of the predicted TFEs from the calculated TFEs averaged over the three folded structures and over the whole urea concentration range (200 concentrations between 0 and 10 M). 109

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Qualitatively, these results are robust to changes in the TFE and ASA determination methods (e.g., they are similar for different sets of radii for ASA calculation). This is shown in Figure S3 in the Supporting Information, and it indicates that the observed differences in deviations in Figure 2 mainly arise from the differences in the implementations. To sum up, our results indicate that ASA-based predictions of TFEs for single residues in different secondary structural elements are accurate and reasonable when performed with the universal backbone TM or the united residue TM. This finding also supports other models that are based on the ASA-scaling hypothesis and additivity (e.g., the solute partitioning model31). Predictions with the established TM implementation deviate substantially from calculated TFEs for all studied amino acids except glycine. Predictions Based on Experimental Data. The above presented validation of the TM implementations is based on simulations with a force field. As all calculations are done with the same force field, quantitative predictions within simulation results are possible. However, due to the approximative nature of complex biomolecular force fields, a quantitative comparison of MD data with experimental TFEs is less accurate.12 In a next step, we validate the three TM versions by checking how well they predict experimentally obtained m values of proteins on the basis of experimentally determined group TFEs. We use the three implementations of the TM to predict the known experimental m values of 36 proteins, which are listed in ref 18. Figure 3 displays the predicted m values in comparison to the experimental m values for all three implementations on the basis of two different sets of TFEs, which are used for the determination of the TFE per ASA value. In Figure 3A,

Figure 1 and agree well with the computed TFEs. As a quantitative measure of quality of the predictions, we calculate the rms deviation between the predictions and the computed TFEs averaged over all three conformations and over urea concentrations between 0 and 10 M. The rms deviation amounts to 0.048 kcal mol−1 per residue on an absolute scale and to 12% on a relative scale. The same analysis is performed for the amino acids alanine, leucine, serine, and phenylalanine. Figure 2 shows that for these

Figure 2. Absolute (A) and relative (B) errors of ASA-based TFE predictions of the three studied implementations of the TM. For each amino acid, the simulated TFEs of the three folded structures are predicted from the TFE per ASA values of the simulations of the extended strand. The bars display the rms deviations between the predicted and the calculated TFEs averaged over the three predictions and a urea concentration range of 0−10 M. The black lines mark the mean value. The universal backbone TM and the united residue TM outperform the established TM both on the absolute and on the relative scale.

residues, the predictions with the established TM lead to considerably larger deviations from the computed TFEs than for glycine (see also Supporting Information Figure S2). Averaged over all five studied amino acid types, the error is 0.241 kcal mol−1 per residue (48% relative error). The universal backbone TM has a much higher predictive efficiency for these amino acids. Figure 2 shows that the rms deviations are both on an absolute and on a relative scale substantially smaller than for the established TM. The average deviations for predictions with the universal backbone TM amount to only 0.078 kcal mol−1 per residue (22%). The errors obtained with the universal backbone TM are of similar size for all studied amino acids except phenylalanine, for which the error is remarkably larger. Still, the universal backbone TM predicts the phenylalanine TFEs with less than half the absolute error compared with that of the established TM. The third column in Figure 2 displays results for the united residue TM. This is the most reductionist model among the studied because it does not differentiate between side-chain and backbone groups and treats whole residues as TM groups. The predictions of the united residue TM differ from those of the universal backbone TM, but on average they agree equally well with the calculated TFEs despite of the simplicity of the model (see also Supporting Information Figure S2).

Figure 3. Predictions of the established, universal backbone and united residue TM for the m values of proteins in comparison to the experimental data (A) with the GTFEapp values from ref 17, and (B) with the GTFE+ values, which represent a correct calculation of the erroneous GTFE* data from ref 18. No simulation data were used for these predictions. The black line marks perfect agreement. In both cases, the universal backbone and the united residue TM have a higher predictive accuracy than the established TM. 110

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Figure 4. Backbone and net side-chain contributions to the predicted m value (A) for the established TM in combination with the (erroneous) GTFE*s and (B) for the universal backbone TM with the GTFE+ values. The established TM overestimates the negative backbone contribution, and the GTFE* values predict too positive side-chain contributions. Thus, in (A), the impression arises that denaturation is driven by the backbone. According to the universal backbone implementation of the TM in (B), however, denaturation is due to favorable backbone and side-chain interactions of comparable size.

apparent TFEs17,18,24 are used. On the basis of these, all three versions of the TM predict m values that are more negative than the experimental ones. The predictions of the universal backbone TM and of the united residue TM are similar to each other and are closer to the experimental data than those of the established TM because in these two implementations the backbone units contribute less. The discrepancy between the predictions of the established TM and the experimental m values was previously attributed to a systematic error in the side-chain TFEs,18 which is present in the apparent TFEs, because they are derived from molar solubilities of amino acids in aqueous urea and water without taking activity coefficients into account.18,24 For the determination of TFEs of highly soluble amino acids, the activity coefficients are important.18 As the TFE of a glycine molecule, which has a high solubility, is subtracted from the TFE of another amino acid in order to obtain its side-chain TFE, the activity coefficients of glycine affect the values of all 19 sidechain TFEsno matter whether the respective side chain is highly soluble or not. Auton, Holthauzen, and Bolen18 derived a new set of side-chain TFEs called GTFE*, which take the activity coefficients of glycine in water and 1 M urea solution into account. The GTFE* values are shifted by 40.27 cal mol−1 M−1 with respect to the apparent GTFEapp values of the side chains. Thus, many side-chain TFEs are positive or close to zero in the GTFE* set, whereas all except of those for asparagine and glutamine are negative in the apparent GTFEapp set. Predictions with the established TM based on the GTFE* values are in good agreement with experimental m values.18 However, during the calculation of the GTFE* values, a mistake was made in the conversion of activity coefficient data between concentration scales. Thus, instead of a shift of 14.47 cal mol−1 M−1, a shift of 40.27 cal mol−1 M−1 was applied (see the Supporting Information for a detailed thermodynamic derivation of the correct activity coefficient shift). Consequently, all side-chain GTFE* values are 25.8 cal mol−1 M−1 too positive and cancel the overestimation of the negative backbone contribution in the established TM. We, thus, attribute the good performance of the established TM with the GTFE* values to error compensation. The correct shift of 14.47 cal mol−1 M−1 defines the new GTFE+ values, which are listed in Table S1 in the Supporting Information. In

combination with the universal backbone TM or the united residue TM, the GTFE+ values lead to predictions that are in very good agreement with the experimental m values, whereas the established TM again predicts systematically too negative m values. This is shown in Figure 3B. It is interesting to note that the universal backbone TM and the united residue TM have comparable predictive accuracies not only in the case of simulation data but also with the experimental data. For each of the 36 proteins, both methods predict very similar m values. This indicates that the discrimination between backbone and side chains is not necessary for the prediction of denaturation thermodynamics. However, the application of the universal backbone TM seems to be more straightforward and practical because with the standard experimental procedures, TFEs are not obtained for whole residues but individually for the side chains and the backbone. Concluding, the presented assessment reveals that the universal backbone TM and the united residue TM have a markedly higher predictive accuracy than the established TM not only for simulation data but also for experimental data, provided that the correct side-chain TFEs GTFE+ are used. Many authors have discussed requirements that need to be fulfilled for the functioning of the TM. Usually, the validity of the assumed additivity, a correct measurement of group TFEs, and an apt model for the denatured state are listed as such.5,13,14,19,20 Our results indicate that the list should be extended; the TFEs not only need to be determined correctly but they also need to be assigned to an appropriate ASA. To our knowledge, the relevance of the ASAs used for the determination of the TFE per ASA values has never been pointed out before. Backbone and Side-Chain Contributions to Denaturation. The TM is a well-established method not only for mvalue prediction but also for m-value interpretation. As m values are generally correctly predicted, one assumes that the different group contributions to the m values in the prediction are also correct. Here, we demonstrate that the magnitude of the predicted group contributions crucially depends on the chosen implementation of the TM (and the used set of group TFEs). Analyses with the established TM and the GTFE* values yield the result that denaturation by urea is driven by a 111

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the other hand, urea is a potent hydrogen-bonding partner, which suggests a mechanism in which urea denatures by solvating polar groups of proteins,43−46 the most prevalent being the backbone. Both suggested effects appear to occur in model systems,11,13 leading to the conclusion that urea binds to basically any chemical motif that is found in proteinshydrophobic as well as hydrophilic. This is also corroborated by the GTFE+ set of side-chain TFEs presented here. The decisive question, however, is the relative importance of binding to different parts of a protein for denaturation. This question is hard to answer because (i) all involved effects are entangled in results from experiments or simulations of proteins and (ii) results for simple model compounds are not useful without further assumptions. The TM comprises a set of assumptions with which it is possible to link model compound data to group contributions in denaturation. Therefore, it ranks high among the available methods for the study of cosolute effects. It is widely used, is incorporated in more powerful models,21 and is applied in other contexts than cosolutes.47 As pointed out recently,5 however, the last big controversy of urea denaturation is the mismatch between results of the TM on one side and of a plethora of studies on the other side. While previous results of the TM ascribe urea denaturation entirely to interactions with the backbone, other studies indicate that the solvation of both the backbone and the side chains is crucial. The study at hand settles this controversy; we show that the TM indeed predicts that both the backbone and the side chains in total contribute equally to urea denaturationif the universal backbone implementation of the TM is used in combination with the GTFE+ set of side-chain TFEs. We present sound theoretical reasoning and empirical validations with data from MD simulations as well as from experiments that speak for the superiority of the universal backbone TM over the currently-established TM. At the same time, we provide a quantitative explanation for the previously existing mismatch. Interestingly, it is based on two inconsistencies in previous applications of the TM that, to our knowledge, have not been discussed before in any of the many qualitative attempts of explanation put forward so far (see ref 5 and references therein). Our validations and proposed improvements of the TM further consolidate the TM as a powerful and easy to use tool for the prediction and interpretation of the solvation thermodynamics of proteins in mixed solvents. Apart from the two key revisions that we introduce here, our implementations of the TM are as close as possible to the established TM in refs 17−19 because simultaneous changes in more parameters of the TM would obscure the implications of individual revisions. It is open to future studies to further improve the TM by improving the model for the denatured state, the set of ASAs used for the determination of the TFE per ASA values, and the measured TFE data by measurements that account for activity coefficients (like, for example, osmometry as used in the solute partitioning model13,31).

favorable solvation of the backbone in urea. Figure 4A shows predicted m values and their decomposition in a backbone and a net side-chain contribution for the 36 proteins of ref 18 (based on the established TM with the GTFE* values). For all studied proteins, the predicted m value in Figure 4A is mainly determined by the backbone contribution, which favors denaturation. The overall side-chain contribution is generally very small and in most cases positive (i.e., opposing denaturation). Several analyses similar to the one in Figure 4A led to the longstanding and well-known notion that the TM ascribes urea denaturation entirely to interactions with the backbone.18−20 In the previous sections, however, we presented evidence that the side-chain TFEs are too positive in the GTFE* set (because of the mistake in the activity coefficient contribution) and that the established TM overestimates the backbone contribution (due to the ASAs used for the determination of the TFE per ASA value of the backbone group). We consider the universal backbone and the united residue implementations to be more in compliance with the TM assumptions than the established implementation, and because of their good validation results in the last two sections, we are convinced that these implementations in combination with the GTFE+ values lead to a more realistic picture of denaturation. The united residue TM does not provide information about the contributions of the backbone and the side chains. Hence, we here only analyze the m values predicted with the universal backbone TM (in combination with the GTFE+ set). The dissection of these m values into backbone and side-chain contributions is shown in Figure 4B. The predicted m values are similar to those in panel A (and to the experimental m values, see Figure 3), but a fundamentally different interpretation arises: both the backbone and the side chains favor denaturation, and for most of the proteins, the backbone and the net side-chain contributions are approximately the same size. The mere fact that the side chains contribute to denaturation in this scenario is mainly due to the set of GTFE+ values. The fact that the proportions between the predicted backbone and side-chain contributions differ between panel A and panel B of Figure 4 depends on both the side-chain TFEs and on the implementation of the TM. Both the set of side-chain GTFE+ values and the predicted contributions with the universal backbone TM are in line with results of many other studies with various methods.9−14,32 For the trp-cage miniprotein, for example, it was shown by MD simulations9 and by experiments13 that the backbone and the side-chain contributions to denaturation by urea are of comparable size.

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OUTLOOK Toward a Unified Description of Urea Denaturation. The mechanism of urea denaturation has been a controversial issue for many decades. Among the early proposed mechanisms was an indirect effect33−35 that stems from modifications of the bulk solvent structure. Thermodynamic arguments rule out the significance of indirect effects for urea/water mixtures, which are close to ideality,12 and ascribe the denaturing power of urea to direct preferential binding to the protein.10,36,37 Zooming in on this direct mechanism, the question what parts of the protein are responsible for the denaturation remains. On one hand, urea attenuates the free-energy penalty of hydrophobic solvation,38−41 suggesting a mechanism in which it binds to nonpolar parts of proteins (i.e., hydrophobic side chains).42 On

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SUMMARY The mechanism by which urea denatures proteins is a highly debated topic, mainly because urea’s mode of action arising from the prominent TM so far contradicts most other studies. We provide a quantitative explanation for this mismatch. We trace it back to two inconsistencies in the implementation of the TM that have not been discussed before and demonstrate 112

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their impact by simulations and analyses of experimental data. The revision of these two inconsistencies alone brings the TM in line with other studies, which is an important step toward a unified view of urea denaturation, in which backbone and side chains play equal roles.

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ASSOCIATED CONTENT

S Supporting Information *

A detailed thermodynamic derivation of the activity coefficient contribution to the TFE of glycine and a table with the different sets of GTFE values, additional figures, and further information on the applied methods. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*D. Horinek. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Emanuel Schneck and Werner Kunz for helpful discussions. Financial support was granted by the Deutsche Forschungsgemeinschaft and supercomputing access was provided by the LRZ Munich (project pr63ca).

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REFERENCES

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