Desolvation Barrier Effects Are a Likely Contributor to the Remarkable Diversity in the Folding Rates of Small Proteins

The variation in folding rate among single-domain natural proteins is tremendous, but common models with explicit representations of the protein chain are either demonstrably insufficient or unclear as to their capability for rationalizing the experimental diversity in folding rates. In view of the critical role of water exclusion in cooperative folding, we apply native-centric, coarse-grained chain modeling with elementary desolvation barriers to investigate solvation effects on folding rates. For a set of 13 proteins, folding rates simulated with desolvation barriers cover ∼ 4.6 orders of magnitude, spanning a range essentially identical to that observed experimentally. In contrast, folding rates simulated without desolvation barriers cover only ∼ 2.2 orders of magnitude. Following a Hammond-like trend, the folding transition-state ensemble (TSE) of a protein model with desolvation barriers generally has a higher average number of native contacts and is structurally more specific, that is, less diffused, than the TSE of the corresponding model without desolvation barriers. Folding is generally significantly slower in models with desolvation barriers because of their higher overall macroscopic folding barriers as well as slower conformational diffusion speeds in the TSE that are ≈ 1/50 times those in models without desolvation barriers. Nonetheless, the average root-mean-square deviation between the TSE and the native conformation is often similar in the two modeling approaches, a finding suggestive of a more robust structural requirement for the folding rate-limiting step. The increased folding rate diversity in models with desolvation barriers originates from the tendency of these microscopic barriers to cause more heightening of the overall macroscopic folding free-energy barriers for proteins with more nonlocal native contacts than those with fewer such contacts. Thus, the enhancement of folding cooperativity by solvation effects is seen as positively correlated with a protein's native topological complexity.     

Desolvation is a likely origin of robust enthalpic barriers to protein folding

Experimental data from global analyses of temperature (T) and denaturant dependence of the folding rates of small proteins led to an intrinsic enthalpic folding barrier hypothesis: to a good approximation, the T-dependence of folding rate under constant native stability conditions is Arrhenius. Furthermore, for a given protein, the slope of isostability folding rate versus 1/T is essentially independent of native stability. This hypothesis implies a simple relationship between chevron and Eyring plots of folding that is easily discernible when both sets of rates are expressed as functions of native stability. Using experimental data in the literature, we verify the predicted chevron-Eyring relationship for 14 proteins and determine their intrinsic enthalpic folding barriers, which vary approximately from 15 kcal/mol to 40 kcal/mol for different proteins. These enthalpic barriers do not appear to correlate with folding rates, but they exhibit correlation with equilibrium unfolding enthalpy at room temperature. Intrinsic enthalpic barriers with similarly high magnitudes apply as well to at least two cases of peptide-peptide and peptide-protein association, suggesting that these barriers are a hallmark of certain general and fundamental kinetic processes during folding and binding. Using a class of explicit-chain C(alpha) protein models with constant elementary enthalpic desolvation barriers between C(alpha) positions, we show that small microscopic pairwise desolvation barriers, which are a direct consequence of the particulate nature of water, can act cooperatively to give rise to a significant overall enthalpic barrier to folding. This theoretical finding provides a physical rationalization for the high intrinsic enthalpic barriers in protein folding energetics. Ramifications of entropy-enthalpy compensation in hydrophobic association for the height of enthalpic desolvation barrier are discussed.     

Chevron behavior and isostable enthalpic barriers in protein folding: successes and limitations of simple Gō-like modeling

It has been demonstrated that a "near-Levinthal" cooperative mechanism, whereby the common Gō interaction scheme is augmented by an extra favorability for the native state as a whole, can lead to apparent two-state folding/unfolding kinetics over a broad range of native stabilities in lattice models of proteins. Here such a mechanism is shown to be generalizable to a simplified continuum (off-lattice) Langevin dynamics model with a Calpha protein chain representation, with the resulting chevron plots exhibiting an extended quasilinear regime reminiscent of that of apparent two-state real proteins. Similarly high degrees of cooperativity are possible in Gō-like continuum models with rudimentary pairwise desolvation barriers as well. In these models, cooperativity increases with increasing desolvation barrier height, suggesting strongly that two-state-like folding/unfolding kinetics would be achievable when the pairwise desolvation barrier becomes sufficiently high. Besides cooperativity, another generic folding property of interest that has emerged from published experiments on several apparent two-state proteins is that their folding relaxation under constant native stability (isostability) conditions is essentially Arrhenius, entailing high intrinsic enthalpic folding barriers of approximately 17-30 kcal/mol. Based on a new analysis of published data on barnase, here we propose that a similar property should also apply to a certain class of non-two-state proteins that fold with chevron rollovers. However, several continuum Gō-like constructs considered here fail to predict any significant intrinsic enthalpic folding barrier under isostability conditions; thus the physical origin of such barriers in real proteins remains to be elucidated.     

Water as a conformational editor in protein folding

As molecules approach one another in aqueous solution, desolvation free energy barriers to association are encountered. Experiments suggest these (de)solvation effects contribute to the free energy barriers separating the folded and unfolded states of protein molecules. To explore their influence on the energy landscapes of protein folding reactions, we have incorporated desolvation barriers into a semi-realistic, off-lattice protein model that uses a simplified physico-chemical force-field determined solely by the sequence of amino acids. Monte Carlo sampling techniques were used to study the effects on the thermodynamics and kinetics of folding of a number of systems, diverse in structure and sequence. In each case, desolvation barriers increase the stability of the native conformation and the cooperativity of the major folding/unfolding transition. The folding times of these systems are reduced significantly upon inclusion of desolvation barriers, demonstrating that the particulate nature of the solvent engenders a more defined route to the native fold.     

Native Topology of the Designed Protein Top7 is Not Conducive to Cooperative Folding

Many single-domain proteins with <100 residues fold cooperatively; but the recently designed 92-residue Top7 protein exhibits clearly non-two-state behaviors. In apparent agreement with experiment, we found that coarse-grained, native-centric chain models, including potentials with and without elementary desolvation barriers, predicted that Top7 has a stable intermediate state in which the C-terminal fragment is folded while the rest of the chain remains disordered. We observed noncooperative folding in Top7 models that incorporated nonnative hydrophobic interactions as well. In contrast, free energy profiles deduced from models with desolvation barriers for a set of thirteen natural proteins with similar chain lengths and secondary structure elements suggested that they fold much more cooperatively than Top7. Buttressed by related studies on smaller natural proteins with chain lengths of ∼40 residues, our findings argue that the de novo native topology of Top7 likely imposed a significant restriction on the cooperativity achievable by any design for this target structure.     

Solvation effects and driving forces for protein thermodynamic and kinetic cooperativity: how adequate is native-centric topological modeling?

What energetic and solvation effects underlie the remarkable two-state thermodynamics and folding/unfolding kinetics of small single-domain proteins? To address this question, we investigate the folding and unfolding of a hierarchy of continuum Langevin dynamics models of chymotrypsin inhibitor 2. We find that residue-based additive Gō-like contact energies, although native-centric, are by themselves insufficient for protein-like calorimetric two-state cooperativity. Further native biases by local conformational preferences are necessary for protein-like thermodynamics. Kinetically, however, even models with both contact and local native-centric energies do not produce simple two-state chevron plots. Thus a model protein's thermodynamic cooperativity is not sufficient for simple two-state kinetics. The models tested appear to have increasing internal friction with increasing native stability, leading to chevron rollovers that typify kinetics that are commonly referred to as non-two-state. The free energy profiles of these models are found to be sensitive to the choice of native contacts and the presumed spatial ranges of the contact interactions. Motivated by explicit-water considerations, we explore recent treatments of solvent granularity that incorporate desolvation free energy barriers into effective implicit-solvent intraprotein interactions. This additional feature reduces both folding and unfolding rates vis-à-vis that of the corresponding models without desolvation barriers, but the kinetics remain non-two-state. Taken together, our observations suggest that interaction mechanisms more intricate than simple Gō-like constructs and pairwise additive solvation-like contributions are needed to rationalize some of the most basic generic protein properties. Therefore, as experimental constraints on protein chain models, requiring a consistent account of protein-like thermodynamic and kinetic cooperativity can be more stringent and productive for some applications than simply requiring a model heteropolymer to fold to a target structure.     

Probing possible downhill folding: native contact topology likely places a significant constraint on the folding cooperativity of proteins with approximately 40 residues

Experiments point to appreciable variations in folding cooperativity among natural proteins with approximately 40 residues, indicating that the behaviors of these proteins are valuable for delineating the contributing factors to cooperative folding. To explore the role of native topology in a protein's propensity to fold cooperatively and how native topology might constrain the degree of cooperativity achievable by a given set of physical interactions, we compared folding/unfolding kinetics simulated using three classes of native-centric C^α chain models with different interaction schemes. The approach was applied to two homologous 45-residue fragments from the peripheral subunit-binding domain family and a 39-residue fragment of the N-terminal domain of ribosomal protein L9. Free-energy profiles as functions of native contact number were computed to assess the heights of thermodynamic barriers to folding. In addition, chevron plots of folding/unfolding rates were constructed as functions of native stability to facilitate comparison with available experimental data. Although common Gō-like models with pairwise Lennard-Jones-type interactions generally fold less cooperatively than real proteins, the rank ordering of cooperativity predicted by these models is consistent with experiment for the proteins investigated, showing increasing folding cooperativity with increasing nonlocality of a protein's native contacts. Models that account for water-expulsion (desolvation) barriers and models with many-body (nonadditive) interactions generally entail higher degrees of folding cooperativity indicated by more linear model chevron plots, but the rank ordering of cooperativity remains unchanged. A robust, experimentally valid rank ordering of model folding cooperativity independent of the multiple native-centric interaction schemes tested here argues that native topology places significant constraints on how cooperatively a protein can fold.     

Molecular simulations of cotranslational protein folding: fragment stabilities, folding cooperativity, and trapping in the ribosome

Although molecular simulation methods have yielded valuable insights into mechanistic aspects of protein refolding in vitro, they have up to now not been used to model the folding of proteins as they are actually synthesized by the ribosome. To address this issue, we report here simulation studies of three model proteins: chymotrypsin inhibitor 2 (CI2), barnase, and Semliki forest virus protein (SFVP), and directly compare their folding during ribosome-mediated synthesis with their refolding from random, denatured conformations. To calibrate the methodology, simulations are first compared with in vitro data on the folding stabilities of N-terminal fragments of CI2 and barnase; the simulations reproduce the fact that both the stability and thermal folding cooperativity increase as fragments increase in length. Coupled simulations of synthesis and folding for the same two proteins are then described, showing that both fold essentially post-translationally, with mechanisms effectively identical to those for refolding. In both cases, confinement of the nascent polypeptide chain within the ribosome tunnel does not appear to promote significant formation of native structure during synthesis; there are however clear indications that the formation of structure within the nascent chain is sensitive to location within the ribosome tunnel, being subject to both gain and loss as the chain lengthens. Interestingly, simulations in which CI2 is artificially stabilized show a pronounced tendency to become trapped within the tunnel in partially folded conformations: non-cooperative folding, therefore, appears in the simulations to exert a detrimental effect on the rate at which fully folded conformations are formed. Finally, simulations of the two-domain protease module of SFVP, which experimentally folds cotranslationally, indicate that for multi-domain proteins, ribosome-mediated folding may follow different pathways from those taken during refolding. Taken together, these studies provide a first step toward developing more realistic methods for simulating protein folding as it occurs in vivo.     

An all-atom structure-based potential for proteins: bridging minimal models with all-atom empirical forcefields

Protein dynamics take place on many time and length scales. Coarse-grained structure-based (Go) models utilize the funneled energy landscape theory of protein folding to provide an understanding of both long time and long length scale dynamics. All-atom empirical forcefields with explicit solvent can elucidate our understanding of short time dynamics with high energetic and structural resolution. Thus, structure-based models with atomic details included can be used to bridge our understanding between these two approaches. We report on the robustness of folding mechanisms in one such all-atom model. Results for the B domain of Protein A, the SH3 domain of C-Src Kinase, and Chymotrypsin Inhibitor 2 are reported. The interplay between side chain packing and backbone folding is explored. We also compare this model to a C(alpha) structure-based model and an all-atom empirical forcefield. Key findings include: (1) backbone collapse is accompanied by partial side chain packing in a cooperative transition and residual side chain packing occurs gradually with decreasing temperature, (2) folding mechanisms are robust to variations of the energetic parameters, (3) protein folding free-energy barriers can be manipulated through parametric modifications, (4) the global folding mechanisms in a C(alpha) model and the all-atom model agree, although differences can be attributed to energetic heterogeneity in the all-atom model, and (5) proline residues have significant effects on folding mechanisms, independent of isomerization effects. Because this structure-based model has atomic resolution, this work lays the foundation for future studies to probe the contributions of specific energetic factors on protein folding and function.     

Energetic and structural consequences of desolvation/solvation barriers to protein folding/unfolding assessed from experimental unfolding rates

Theoretical work has suggested the existence of solvation/desolvation barriers in protein folding/unfolding processes. We propose that the energetic and structural consequences of such barriers for the folding transition state can be assessed from experimental unfolding rates using well-established structure-energetics relationships. For a set of proteins of size within the 60-130 number-of-residues range, we find energetic effects associated to solvation/desolvation on the order of 10(2) kJ/mol. This supports that the folding transition states may be characterized by large networks of water-unsatisfied, broken internal contacts. In terms of buried surface, we estimate the typical network size to be on the order of several thousands of A2, or approximately 50% of the total change in accessible surface area upon unfolding. The analyses reported here thus suggest a clear structural picture for the different energetic balance of native and folding transition states.     

Relationship between the native-state hydrogen exchange and the folding pathways of barnase

The previous native-state hydrogen exchange experiment with barnase failed to detect any partially unfolded intermediate state which was contrary to the experimental results from kinetic deuterium hydrogen exchange pulse labeling and protein engineering studies. This has been taken to suggest that the native-state hydrogen exchange method cannot be used alone as an analytical tool to study the folding pathways of proteins. Here, we revisited the pulse labeling experiment with barnase and detected no stable folding intermediate. This finding allows a reconciliation of the native-state HX data and the folding pathway of barnase. Along with alternative theoretical interpretations for a curved chevron plot of protein folding, these data suggest that further investigation of the nature of the intermediate of barnase is needed.     

The influence of intrinsic folding mechanism of an unfolded protein on the coupled folding-binding process during target recognition

Intrinsically disordered proteins (IDPs) are extensively involved in dynamic signaling processes which require a high association rate and a high dissociation rate for rapid binding/unbinding events and at the same time a sufficient high affinity for specific recognition. Although the coupled folding-binding processes of IDPs have been extensively studied, it is still impossible to predict whether an unfolded protein is suitable for molecular signaling via coupled folding-binding. In this work, we studied the interplay between intrinsic folding mechanisms and coupled folding-binding process for unfolded proteins through molecular dynamics simulations. We first studied the folding process of three representative IDPs with different folded structures, that is, c-Myb, AF9, and E3 rRNase. We found the folding free energy landscapes of IDPs are downhill or show low barriers. To further study the influence of intrinsic folding mechanism on the binding process, we modulated the folding mechanism of barnase via circular permutation and simulated the coupled folding-binding process between unfolded barnase permutant and folded barstar. Although folding of barnase was coupled to target binding, the binding kinetics was significantly affected by the intrinsic folding free energy barrier, where reducing the folding free energy barrier enhances binding rate up to two orders of magnitude. This accelerating effect is different from previous results which reflect the effect of structure flexibility on binding kinetics. Our results suggest that coupling the folding of an unfolded protein with no/low folding free energy barrier with its target binding may provide a way to achieve high specificity and rapid binding/unbinding kinetics simultaneously.     

Protein dynamics: From the native to the unfolded state and back again

Simulations to study protein unfolding and folding were performed. The unfolding simulations make use of molecular dynamics and treat an atomic model of barnase in aqueous solvent. The cooperative nature of the unfolding transition and the important role of water are described. The folding simulations are based on a bead model of the protein on a cubic lattice. It is shown for the 27-mer model that a large energy gap between the lowest energy (native) state and the excited states is a necessary and sufficient condition for fast folding.     

The folding pathway of barnase: the rate-limiting transition state and a hidden intermediate under native conditions

The nature of the rate-limiting transition state at zero denaturant (TS(1)) and whether there are hidden intermediates are the two major unsolved problems in defining the folding pathway of barnase. In earlier studies, it was shown that TS(1) has small phi values throughout the structure of the protein, suggesting that the transition state has either a defined partially folded secondary structure with all side chains significantly exposed or numerous different partially unfolded structures with similar stability. To distinguish the two possibilities, we studied the effect of Gly mutations on the folding rate of barnase to investigate the secondary structure formation in the transition state. Two mutations in the same region of a beta-strand decreased the folding rate by 20- and 50-fold, respectively, suggesting that the secondary structures in this region are dominantly formed in the rate-limiting transition state. We also performed native-state hydrogen exchange experiments on barnase at pD 5.0 and 25 degrees C and identified a partially unfolded state. The structure of the intermediate was investigated using protein engineering and NMR. The results suggest that the intermediate has an omega loop unfolded. This intermediate is more folded than the rate-limiting transition state previously characterized at high denaturant concentrations (TS(2)). Therefore, it exists after TS(2) in folding. Consistent with this conclusion, the intermediate folds with the same rate and denaturant dependence as the wild-type protein, but unfolds faster with less dependence on the denaturant concentration. These and other results in the literature suggest that barnase folds through partially unfolded intermediates that exist after the rate-limiting step. Such folding behavior is similar to those of cytochrome c and Rd-apocyt b(562). Together, we suggest that other small apparently two-state proteins may also fold through hidden intermediates.     

Stability and folding of the protein complexes of barnase.

Native-like complexes of proteins, formed by the association of two complementary fragments comprising the entire sequence of the protein, can be used to gain insight into the stability and folding of the intact protein. We have studied the structural, thermodynamic and kinetic properties of four barnase complexes, with the cleavage site at different positions of the amino-acid chain (CB36, at position 36; CB56, at position 56; CB68, at position 68; and CB79, at position 79). The four barnase complexes have native-like structure as shown by fluorescence, far-and near-UV CD, size-exclusion chromatography and NMR. The NMR characterization indicated that the structural changes were mainly located in regions close to the cleavage site. The main core of the protein was fully formed and the overall structure was similar to that of intact barnase. The thermal and chemical denaturation showed that all complexes were substantially destabilized. CB56 displayed two denaturation transitions, probably because of the presence of partially folded conformations around the cleavage site. The rate constant for the association/folding of fragments decreased with the decreasing length of the C-terminal fragment. Thus, the larger the fragment (and, consequently, the larger the amount of residual native-like structure), the faster the association. These findings are consistent with the proposed model of barnase folding.     

Lack of definable nucleation sites in the rate-limiting transition state of barnase under native conditions.

It has been shown that the burst-phase (submillisecond) intermediate of barnase, if it exists, can be only marginally more stable than the fully unfolded state at pH 6.3 and 25 degrees C. In the study reported here, no stable burst-phase intermediate could be detected, even in the presence of stabilizing salt (0.4 M Na(2)SO(4)). These results suggest that a burst-phase intermediate with even marginal stability does not exist. The absence of such an intermediate in turn suggests the need for re-examination of the rate-limiting transition state (RLTS) under native conditions, which was previously characterized by using a three-state model with a stable intermediate and protein engineering. Surprisingly, mutations throughout the structure of barnase do not significantly affect the folding rate, suggesting a lack of specific favorable interactions among the side-chains in the RLTS. This RLTS is clearly different from that previously characterized under denaturing conditions, indicating that changes take place in the RLTS under native and denaturing conditions. The occurrence of such changes is further supported by the observation that the unfolding rate constants of barnase and its mutants were divergent or convergent as a function of denaturant concentrations. Consistent with changes in the RLTS, a re-analysis of data from native-state hydrogen exchange studies has shown that the logarithm of the unfolding rate constant inflects down under low concentrations of denaturant. Here, we discuss in detail the question of whether changes in the RLTS involve a kinetically silent intermediate that occurs after the initial RLTS.     

Anti-cooperativity and cooperativity in hydrophobic interactions: Three-body free energy landscapes and comparison with implicit-solvent potential functions for proteins

Potentials of mean force (PMFs) of three-body hydrophobic association are investigated to gain insight into similar processes in protein folding. Free energy landscapes obtained from explicit simulations of three methanes in water are compared with that predicted by popular implicit-solvent effective potentials for the study of proteins. Explicit-water simulations show that for an extended range of three-methane configurations, hydrophobic association at 25 degrees C under atmospheric pressure is mostly anti-cooperative, that is, less favorable than if the interaction free energies were pairwise additive. Effects of free energy nonadditivity on the kinetic path of association and the temperature dependence of additivity are explored by using a three-methane system and simplified chain models. The prevalence of anti-cooperativity under ambient conditions suggests that driving forces other than hydrophobicity also play critical roles in protein thermodynamic cooperativity. We evaluate the effectiveness of several implicit-solvent potentials in mimicking explicit water simulated three-body PMFs. The favorability of the contact free energy minimum is found to be drastically overestimated by solvent accessible surface area (SASA). Both the SASA and a volume-based Gaussian solvent exclusion model fail to predict the desolvation barrier. However, this barrier is qualitatively captured by the molecular surface area model and a recent "hydrophobic force field." None of the implicit-solvent models tested are accurate for the entire range of three-methane configurations and several other thermodynamic signatures considered.     

Optimization of binding electrostatics: charge complementarity in the barnase-barstar protein complex

Theoretical and experimental studies have shown that the large desolvation penalty required for polar and charged groups frequently precludes their involvement in electrostatic interactions that contribute strongly to net stability in the folding or binding of proteins in aqueous solution near room temperature. We have previously developed a theoretical framework for computing optimized electrostatic interactions and illustrated use of the algorithm with simplified geometries. Given a receptor and model assumptions, the method computes the ligand-charge distribution that provides the most favorable balance of desolvation and interaction effects on binding. In this paper the method has been extended to treat complexes using actual molecular shapes. The barnase-barstar protein complex was investigated with barnase treated as a target receptor. The atomic point charges of barstar were varied to optimize the electrostatic binding free energy. Barnase and natural barstar form a tight complex (K(d) approximately 10(-14) M) with many charged and polar groups near the interface that make this a particularly relevant system for investigating the role of electrostatic effects on binding. The results show that sets of barstar charges (resulting from optimization with different constraints) can be found that give rise to relatively large predicted improvements in electrostatic binding free energy. Principles for enhancing the effect of electrostatic interactions in molecular binding in aqueous environments are discussed in light of the optima. Our findings suggest that, in general, the enhancements in electrostatic binding free energy resulting from modification of polar and charged groups can be substantial. Moreover, a recently proposed definition of electrostatic complementarity is shown to be a useful tool for examining binding interfaces. Finally, calculational results suggest that wild-type barstar is closer to being affinity optimized than is barnase for their mutual binding, consistent with the known roles of these proteins.     

Kinetic characterization of the recombinant ribonuclease from Bacillus amyloliquefaciens (barnase) and investigation of key residues in catalysis by site-directed mutagenesis

Barnase, the ribonuclease from Bacillus amyloliquefaciens, has been cloned and expressed in Escherichia coli [Hartley, R. W. (1988) J. Mol. Biol. 202, 913-915], thus enabling the overproduction and site-directed mutagenesis of one of the smallest enzymes (Mr equals 12,382). As barnase is also composed of just a single polypeptide chain with no disulfide bridges and has a reversible folding transition, it affords a fine system for studying protein folding and design. We show here that the recombinant enzyme has properties identical with those of the authentic enzyme, characterize the basic kinetics and specificity of the enzyme, and, using site-directed mutagenesis, identify key residues involved in catalysis to provide evidence that supports the classic ribonuclease mechanism. The wild-type enzyme catalyzes the hydrolysis of dinucleotides of structure GpN. There is a prime requirement for G and a preference for A greater than G greater than C greater than U for N. The pH-activity curve for the transesterification step of dinucleotides is bell shaped with an optimum for kcat/KM and kcat at about pH 5. The enzyme is far more active toward long RNA molecules, and the pH optimum for kcat is at 8.5. The activity of barnase toward dinucleotide substrates is about 0.5% of that of the highly homologous T1 nuclease at pH 5.9, but barnase is twice as active as T1 toward RNA at pH 8.5. There must be important subsite interactions that contribute to catalysis in barnase in addition to those immediately on either side of the scissile bond.(ABSTRACT TRUNCATED AT 250 WORDS)