Thermodynamics of a diffusional protein folding reaction

The folding reactions of several proteins are well described as diffusional barrier crossing processes, which suggests that they should be analyzed by Kramers' rate theory rather than by transition state theory. For the cold shock protein Bc-Csp from Bacillus caldolyticus, we measured stability and folding kinetics, as well as solvent viscosity as a function of temperature and denaturant concentration. Our analysis indicates that diffusional folding reactions can be treated by transition state theory, provided that the temperature and denaturant dependence of the solvent viscosity is properly accounted for, either at the level of the measured rate constants or of the calculated activation parameters. After viscosity correction the activation barriers for folding become less enthalpic and more entropic. The transition from an enthalpic to an entropic folding barrier with increasing temperature is, however, apparent in the data before and after this correction. It is a consequence of the negative activation heat capacity of refolding, which is independent of solvent viscosity. Bc-Csp and its mesophilic homolog Bs-CspB from Bacillus subtilis differ strongly in stability but show identical enthalpic and entropic barriers to refolding. The increased stability of Bc-Csp originates from additional enthalpic interactions that are established after passage through the activated state. As a consequence, the activation enthalpy of unfolding is increased relative to Bs-CspB.     

Spatially resolved free-energy contributions of native fold and molten-globule-like Crambin

The folding stability of a protein is governed by the free-energy difference between its folded and unfolded states, which results from a delicate balance of much larger but almost compensating enthalpic and entropic contributions. The balance can therefore easily be shifted by an external disturbance, such as a mutation of a single amino acid or a change of temperature, in which case the protein unfolds. Effects such as cold denaturation, in which a protein unfolds because of cooling, provide evidence that proteins are strongly stabilized by the solvent entropy contribution to the free-energy balance. However, the molecular mechanisms behind this solvent-driven stability, their quantitative contribution in relation to other free-energy contributions, and how the involved solvent thermodynamics is affected by individual amino acids are largely unclear. Therefore, we addressed these questions using atomistic molecular dynamics simulations of the small protein Crambin in its native fold and a molten-globule-like conformation, which here served as a model for the unfolded state. The free-energy difference between these conformations was decomposed into enthalpic and entropic contributions from the protein and spatially resolved solvent contributions using the nonparametric method Per|Mut. From the spatial resolution, we quantified the local effects on the solvent free-energy difference at each amino acid and identified dependencies of the local enthalpy and entropy on the protein curvature. We identified a strong stabilization of the native fold by almost 500 kJ mol⁻¹ due to the solvent entropy, revealing it as an essential contribution to the total free-energy difference of (53 ± 84) kJ mol⁻¹. Remarkably, more than half of the solvent entropy contribution arose from induced water correlations.     

Spatially resolved free-energy contributions of native fold and molten-globule-like Crambin

The folding stability of a protein is governed by the free-energy difference between its folded and unfolded states, which results from a delicate balance of much larger but almost compensating enthalpic and entropic contributions. The balance can therefore easily be shifted by an external disturbance, such as a mutation of a single amino acid or a change of temperature, in which case the protein unfolds. Effects such as cold denaturation, in which a protein unfolds because of cooling, provide evidence that proteins are strongly stabilized by the solvent entropy contribution to the free-energy balance. However, the molecular mechanisms behind this solvent-driven stability, their quantitative contribution in relation to other free-energy contributions, and how the involved solvent thermodynamics is affected by individual amino acids are largely unclear. Therefore, we addressed these questions using atomistic molecular dynamics simulations of the small protein Crambin in its native fold and a molten-globule-like conformation, which here served as a model for the unfolded state. The free-energy difference between these conformations was decomposed into enthalpic and entropic contributions from the protein and spatially resolved solvent contributions using the nonparametric method Per|Mut. From the spatial resolution, we quantified the local effects on the solvent free-energy difference at each amino acid and identified dependencies of the local enthalpy and entropy on the protein curvature. We identified a strong stabilization of the native fold by almost 500 kJ mol⁻¹ due to the solvent entropy, revealing it as an essential contribution to the total free-energy difference of (53 ± 84) kJ mol⁻¹. Remarkably, more than half of the solvent entropy contribution arose from induced water correlations.     

Helical junctions as determinants for RNA folding: origin of tertiary structure stability of the hairpin ribozyme

Helical junctions are ubiquitous structural elements that govern the folding and tertiary structure of RNAs. The tobacco ringspot virus hairpin ribozyme consists of two helix-loop-helix elements that lie on adjacent arms of a four-way junction. In the active form of the hairpin ribozyme, the loops are in proximity. The nature of the helical junction determines the stability of the hairpin ribozyme tertiary structure [Walter, N. G., Burke, J. M., and Millar, D. P. (1999) Nat. Struct. Biol. 6, 544-549] and thus its catalytic activity. We used two-, three-, and four-way junction hairpin ribozymes as model systems to investigate the thermodynamic basis for the different tertiary structure stabilities. The equilibrium between docked and extended conformers was analyzed as a function of temperature using time-resolved fluorescence resonance energy transfer (trFRET). As the secondary and tertiary structure transitions overlap, information from UV melting curves and trFRET had to be combined to gain insight into the thermodynamics of both structural transitions. It turned out that the higher tertiary structure stability observed in the context of a four-way junction is the result of a lower entropic cost for the docking process. In the two- and three-way junction ribozymes, a high entropic cost counteracts the favorable enthalpic term, rendering the docked conformer only marginally stable. Thus, two- and three-way junction tertiary structures are more sensitive toward regulation by ligands, whereas four-way junctions provide a stable scaffold. Altogether, RNA folding and stability appear to be governed by principles similar to those for the folding of proteins.     

Entropy-driven folding of an RNA helical junction: an isothermal titration calorimetric analysis of the hammerhead ribozyme

Helical junctions are extremely common motifs in naturally occurring RNAs, but little is known about the thermodynamics that drive their folding. Studies of junction folding face several challenges: non-two-state folding behavior, superposition of secondary and tertiary structural energetics, and drastically opposing enthalpic and entropic contributions to folding. Here we describe a thermodynamic dissection of the folding of the hammerhead ribozyme, a three-way RNA helical junction, by using isothermal titration calorimetry of bimolecular RNA constructs. By using this method, we show that tertiary folding of the hammerhead core occurs with a highly unfavorable enthalpy change, and is therefore entropically driven. Furthermore, the enthalpies and heat capacities of core folding are the same whether supported by monovalent or divalent ions. These properties appear to be general to the core sequence of bimolecular hammerhead constructs. We present a model for the ion-induced folding of the hammerhead core that is similar to those advanced for the folding of much larger RNAs, involving ion-induced collapse to a structured, non-native state accompanied by rearrangement of core residues to produce the native fold. In agreement with previous enzymological and structural studies, our thermodynamic data suggest that the hammerhead structure is stabilized in vitro predominantly by diffusely bound ions. Our approach addresses several significant challenges that accompany the study of junction folding, and should prove useful in defining the thermodynamic determinants of stability in these important RNA motifs.     

Coarse-grained strategy for modeling protein stability in concentrated solutions

We present a coarse-grained approach for modeling the thermodynamic stability of single-domain globular proteins in concentrated aqueous solutions. Our treatment derives effective protein-protein interactions from basic structural and energetic characteristics of the native and denatured states. These characteristics, along with the intrinsic (i.e., infinite dilution) thermodynamics of folding, are calculated from elementary sequence information using a heteropolymer collapse theory. We integrate this information into Reactive Canonical Monte Carlo simulations to investigate the connections between protein sequence hydrophobicity, protein-protein interactions, protein concentration, and the thermodynamic stability of the native state. The model predicts that sequence hydrophobicity can affect how protein concentration impacts native-state stability in solution. In particular, low hydrophobicity proteins are primarily stabilized by increases in protein concentration, whereas high hydrophobicity proteins exhibit richer nonmonotonic behavior. These trends appear qualitatively consistent with the available experimental data. Although factors such as pH, salt concentration, and protein charge are also important for protein stability, our analysis suggests that some of the nontrivial experimental trends may be driven by a competition between destabilizing hydrophobic protein-protein attractions and entropic crowding effects.     

Thermodynamic analysis of cavity creating mutations in an engineered leucine zipper and energetics of glycerol-induced coiled coil stabilization

Protein stability in vitro can be influenced either by introduction of mutations or by changes in the chemical composition of the solvent. Recently, we have characterized the thermodynamic stability and the rate of folding of the engineered dimeric leucine zipper A(2), which has a strengthened hydrophobic core [Dürr, E., Jelesarov, I., and Bosshard, H. R. (1999) Biochemistry 38, 870-880]. Here we report on the energetic consequences of a cavity introduced by Leu/Ala substitution at the tightly packed dimeric interface and how addition of 30% glycerol affects the folding thermodynamics of A(2) and the cavity mutants. Folding could be described by a two-state transition from two unfolded monomers to a coiled coil dimer. Removal of six methylene groups by Leu/Ala substitutions destabilized the dimeric coiled coil by 25 kJ mol(-1) at pH 3.5 and 25 degrees C in aqueous buffer. Destabilization was purely entropic at around room temperature and became increasingly enthalpic at elevated temperatures. Mutations were accompanied by a decrease of the unfolding heat capacity by 0.5 kJ K(-1) mol(-1). Addition of 30% glycerol increased the free energy of folding of A(2) and the cavity mutants by 5-10 kJ mol(-1) and lowered the unfolding heat capacity by 25% for A(2) and by 50% for the Leu/Ala mutants. The origin of the stabilizing effect of glycerol varied with temperature. Stabilization of the parent leucine zipper A(2) was enthalpic with an unfavorable entropic component between 0 and 100 degrees C. In the case of cavity mutants, glycerol induced enthalpic stabilization below 50 degrees C and entropic stabilization above 50 degrees C. The effect of glycerol could not be accounted for solely by the enthalpy and entropy of transfer or protein surface from water to glycerol/water mixture. We propose that in the presence of glycerol the folded coiled coil dimer is better packed and displays less intramolecular fluctuations, leading to enhanced enthalpic interactions and to an increase of the entropy of folding. This work demonstrates that mutational and solvent effects on protein stability can be thermodynamically complex and that it may not be sufficient to only analyze changes of enthalpy and entropy at the unfolding temperature (T(m)) to understand the mechanisms of protein stabilization.     

Does alpha-helix folding necessarily provide an energy source for the protein-lipid binding?

Lipid-induced alpha-helix folding, which occurs in many lipid surface-binding proteins and peptides such as apolipoproteins and synucleins, has been proposed to provide an energy source for protein-lipid interactions. We propose that in a system comprised of a phospholipid surface and a small polypeptide that is unfolded in solution and binds reversibly to lipid surface, helical folding involves expenditure of free energy as compared to a similar polypeptide that is alpha-helical in solution. This is a consequence of the entropic cost of helix folding that is illustrated in a simple thermodynamic model and exemplifies the general "key-into-lock" paradigm of protein-ligand binding. Even though this simple model does not explicitly address the protein-induced lipid re-arrangement and may not directly apply to large proteins that undergo significant tertiary structural changes upon lipid binding, it suggests that the notion of helix folding as an energy source for lipid binding should be treated with caution.     

Folding is not required for bilayer insertion: replica exchange simulations of an alpha-helical peptide with an explicit lipid bilayer

We implement the replica exchange molecular dynamics algorithm to study the interactions of a model peptide (WALP-16) with an explicitly represented DPPC membrane bilayer. We observe the spontaneous, unbiased insertion of WALP-16 into the DPPC bilayer and its folding into an alpha-helix with a transbilayer orientation. The free energy surface suggests that the insertion of the peptide into the DPPC bilayer precedes secondary structure formation. Although the peptide has some propensity to form a partially helical structure in the interfacial region of the DPPC/water system, this state is not a productive intermediate but rather an off-pathway trap for WALP-16 insertion. Equilibrium simulations show that the observed insertion/folding pathway mirrors the potential of mean force (PMF). Calculation of the enthalpic and entropic contributions to this PMF show that the surface bound conformation of WALP-16 is significantly lower in energy than other conformations, and that the insertion of WALP-16 into the bilayer without regular secondary structure is enthalpically unfavorable by 5-10 kcal/mol/residue. The observed insertion/folding pathway disagrees with the dominant conceptual model, which is that a surface-bound helix is an obligatory intermediate for the insertion of alpha-helical peptides into lipid bilayers. In our simulations, the observed insertion/folding pathway is favored because of a large (>100 kcal/mol) increase in system entropy that occurs when the unstructured WALP-16 peptide enters the lipid bilayer interior. The insertion/folding pathway that is lowest in free energy depends sensitively on the near cancellation of large enthalpic and entropic terms. This suggests the possibility that intrinsic membrane peptides may have a diversity of insertion/folding behaviors depending on the exact system of peptide and lipid under consideration.     

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.     

Enthalpic and entropic contributions mediate the role of disulfide bonds on the conformational stability of interleukin-4

The role of disulfide bridges in the structure, stability, and folding pathways of proteins has been the subject of wide interest in the fields of protein design and engineering. However, the relative importance of entropic and enthalpic contributions for the stabilization of proteins provided by disulfides is not always clear. Here, we perform a detailed analysis of the role of disulfides in the conformational stability of human Interleukin-4 (IL4), a four-helix bundle protein. In order to evaluate the contribution of two out of the three disulfides to the structure and stability of IL4, two IL4 mutants, C3T-IL4 and C24T-IL4, were used. NMR and ANS binding experiments were compatible with altered dynamics and an increase of the nonpolar solvent-accessible surface area of the folded state of the mutant proteins. Chemical and thermal unfolding experiments followed by fluorescence and circular dichroism revealed that both mutant proteins have lower conformational stability than the wild-type protein. Transition temperatures of unfolding decreased 14 degrees C for C3T-IL4 and 10 degrees C for C24T-IL4, when compared to WT-IL4, and the conformational stability, at 25 degrees C, decreased 4.9 kcal/mol for C3T-IL4 and 3.2 kcal/mol for C24T-IL4. Interestingly, both the enthalpy and the entropy of unfolding, at the transition temperature, decreased in the mutant proteins. Moreover, a smaller change in heat capacity of unfolding was also observed for the mutants. Thus, disulfide bridges in IL4 play a critical role in maintaining the thermodynamic stability and core packing of the helix bundle.     

Apparent two-state tendamistat folding is a sequential process along a defined route

The small all-beta-sheet protein tendamistat folds and unfolds rapidly in apparent two-state reactions. Kinetic measurements of two tendamistat variants under various solvent conditions reveal, however, that folding occurs in at least two sequential steps through a metastable obligatory intermediate. Depending on the solvent conditions either step can become rate limiting. The activation parameters indicate that the first step represents an enthalpic barrier whereas the second step is an entropic barrier at 25 degrees C. Our results suggest that initial non-specific collapse precedes formation of native secondary and tertiary structure in tendamistat folding. This points at a distinct route in tendamistat folding and indicates that partially folded metastable intermediates might play an important role in the mechanism of apparent two-state folding.     

Analysis of the factors that stabilize a designed two-stranded antiparallel beta-sheet

Autonomously folding beta-hairpins (two-strand antiparallel beta-sheets) have become increasingly valuable tools for probing the forces that control peptide and protein conformational preferences. We examine the effects of variations in sequence and solvent on the stability of a previously designed 12-residue peptide (1). This peptide adopts a beta-hairpin conformation containing a two-residue loop (D-Pro-Gly) and a four-residue interstrand sidechain cluster that is observed in the natural protein GB1. We show that the conformational propensity of the loop segment plays an important role in beta-hairpin stability by comparing 1 with (D)P--> N mutant 2. In addition, we show that the sidechain cluster contributes both to conformational stability and to folding cooperativity by comparing 1 with mutant 3, in which two of the four cluster residues have been changed to serine. Thermodynamic analysis suggests that the high loop-forming propensity of the (D)PG segment decreases the entropic cost of beta-hairpin formation relative to the more flexible NG segment, but that the conformational rigidity of (D)PG may prevent optimal contacts between the sidechains of the GB1-derived cluster. The enthalpic favorability of folding in these designed beta-hairpins suggests that they are excellent scaffolds for studying the fundamental mechanisms by which amino acid sidechains interact with one another in folded proteins.     

Stability Curve Prediction of Homologous Proteins Using Temperature-Dependent Statistical Potentials

The unraveling and control of protein stability at different temperatures is a fundamental problem in biophysics that is substantially far from being quantitatively and accurately solved, as it requires a precise knowledge of the temperature dependence of amino acid interactions. In this paper we attempt to gain insight into the thermal stability of proteins by designing a tool to predict the full stability curve as a function of the temperature for a set of 45 proteins belonging to 11 homologous families, given their sequence and structure, as well as the melting temperature () and the change in heat capacity () of proteins belonging to the same family. Stability curves constitute a fundamental instrument to analyze in detail the thermal stability and its relation to the thermodynamic stability, and to estimate the enthalpic and entropic contributions to the folding free energy. In summary, our approach for predicting the protein stability curves relies on temperature-dependent statistical potentials derived from three datasets of protein structures with targeted thermal stability properties. Using these potentials, the folding free energies () at three different temperatures were computed for each protein. The Gibbs-Helmholtz equation was then used to predict the protein''s stability curve as the curve that best fits these three points. The results are quite encouraging: the standard deviations between the experimental and predicted ''s, ''s and folding free energies at room temperature () are equal to 13 , 1.3 ) and 4.1 , respectively, in cross-validation. The main sources of error and some further improvements and perspectives are briefly discussed.     

How Difficult Is It to Fold a Knotted Protein? In Silico Insights from Surface-Tethered Folding Experiments

We explore the effect of surface tethering on the folding process of a lattice protein that contains a trefoil knot in its native structure via Monte Carlo simulations. We show that the outcome of the tethering experiment depends critically on which terminus is used to link the protein to a chemically inert plane. In particular, if surface tethering occurs at the bead that is closer to the knotted core the folding rate becomes exceedingly slow and the protein is not able to find the native structure in all the attempted folding trajectories. Such low folding efficiency is also apparent from the analysis of the probability of knot formation, p_knot, as a function of nativeness. Indeed, p_knot increases abruptly from ∼0 to ∼1 only when the protein has more than 80% of its native contacts formed, showing that a highly compact conformation must undergo substantial structural re-arrangement in order to get effectively knotted. When the protein is surface tethered by the bead that is placed more far away from the knotted core p_knot is higher than in the other folding setups (including folding in the bulk), especially if conformations are highly native-like. These results show that the mobility of the terminus closest to the knotted core is critical for successful folding of trefoil proteins, which, in turn, highlights the importance of a knotting mechanism that is based on a threading movement of this terminus through a knotting loop. The results reported here predict that if this movement is blocked, knotting occurs via an alternative mechanism, the so-called spindle mechanism, which is prone to misfolding. Our simulations show that in the three considered folding setups the formation of the knot is typically a late event in the folding process. We discuss the implications of our findings for co-translational folding of knotted trefoils.     

Importance of context in protein folding: secondary structural propensities versus tertiary contact-assisted secondary structure formation

Molecular dynamics simulations can be used to reveal the detailed conformational behaviors of peptides and proteins. By comparing fragment and full-length protein simulations, we can investigate the role of each peptide segment in the folding process. Here, we take advantage of information regarding the helix formation process from our previous simulations of barnase and protein A as well as new simulations of four helical fragments from these proteins at three different temperatures, starting with both helical and extended structures. Segments with high helical propensity began the folding process by tethering the chain through side chain interactions involving either polar interactions, such as salt bridges, or hydrophobic staples. These tethers were frequently nonnative (i.e., not i --> i + 4 spacing) and provided a scaffold for other residues, thereby limiting the conformational search. The helical structure then propagated on both sides of the tether. Segments with low stability and propensity formed later in the folding process and utilized contacts with other portions of the protein when folding. These helices formed via a tertiary contact-assisted mechanism, primarily via hydrophobic contacts between residues distant in sequence. Thus, segments with different helical propensities appear to play different roles during protein folding. Furthermore, the active role of nonlocal side chains in helix formation highlights why we must move beyond simple hierarchical models of protein folding.     

Streptavidin-biotin binding energetics

The high affinity energetics in the streptavidin-biotin system provide an excellent model system for studying how proteins balance enthalpic and entropic components to generate an impressive overall free energy for ligand binding. We review here concerted site-directed mutagenesis, biophysical, and computational studies of aromatic and hydrogen bonding interaction energetics between streptavidin and biotin. These results also have provided insight into how streptavidin builds a large activation barrier to dissociation by managing the enthalpic and entropic activation components. Finally, we review recent studies of the biotin dissociation pathway that address the fundamental question of how ligands exit protein binding pockets.     

Denaturing and refolding of protein molecules on surfaces

Keeping protein molecules in the active state on a solid surface is essential to protein microarrays and other protein-based biosensors. Here, we show that the 2-D chemical environment controls the refolding of the denatured green fluorescent proteins tethered to solid surfaces. Refolding occurs readily on the repulsive PEG functionalized surface but is inhibited on the attractive--NH(2) functionalized surface. This result shows the critical importance of the 2-D chemical environment in the maintenance and revival of protein activity on surfaces and opens the door to designing 2-D molecular chaperones for protein folding.     

Early events in protein folding

Recent advances have significantly increased the time and spectroscopic resolution of protein folding experiments. We can now study the timescale and nature of polypeptide collapse, and how this correlates with secondary and tertiary structure formation. Studies on ultrafast folding proteins and peptides provide experimental benchmarks on a timescale that overlaps directly with that of molecular dynamics simulations. This makes possible direct tests of both simulations and current models of protein folding.     

Rescuing a destabilized protein fold through backbone cyclization

We describe the physicochemical characterization of various circular and linear forms of the approximately 60 residue N-terminal Src homology 3 (SH3) domain from the murine c-Crk adapter protein. Structural, dynamic, thermodynamic, kinetic and biochemical studies reveal that backbone circularization does not prevent the adoption of the natural folded structure in any of the circular proteins. Both the folding and unfolding rate of the protein increased slightly upon circularization. Circularization did not lead to a significant thermodynamic stabilization of the full-length protein, suggesting that destabilizing enthalpic effects (e.g. strain) negate the expected favorable entropic contribution to overall stability. In contrast, we find circularization results in a dramatic stabilization of a truncated version of the SH3 domain lacking a key glutamate residue. The ability to rescue the destabilized mutant indicates that circularization may be a useful tool in protein engineering programs geared towards generating minimized proteins.