Experiment-guided thermodynamic simulations on reversible two-state proteins: implications for protein thermostability

Here, we perform protein thermodynamic simulations within a set of boundary conditions, effectively blanketing the experimental data. The thermodynamic parameters, melting temperature (TG), enthalpy change at the melting temperature (DeltaHG) and heat capacity change (DeltaCp) were systematically varied over the experimentally observed ranges for small single domain reversible two-state proteins. Parameter sets that satisfy the Gibbs-Helmholtz equation and yield a temperature of maximal stability (TS) around room temperature were selected. The results were divided into three categories by arbitrarily chosen TG ranges. The TG ranges in these categories correspond to typical values of the melting temperatures observed for the majority of the proteins from mesophilic, thermophilic and hyperthermophilic organisms. As expected, DeltaCp values tend to be high in mesophiles and low in hyperthermophiles. An increase in TG is accompanied by an up-shift and broadening of the protein stability curves, however, with a large scatter. Furthermore, the simulations reveal that the average DeltaHG increases with TG up to approximately 360 K and becomes constant thereafter. DeltaCp decreases with TG with different rates before and after approximately 360 K. This provides further justification for the separate grouping of proteins into thermophiles and hyperthermophiles to assess their thermodynamic differences. This analysis of the Gibbs-Helmholtz equation has allowed us to study the interdependence of the thermodynamic parameters TG, DeltaHG and DeltaCp and their derivatives in a more rigorous way than possible by the limited experimental protein thermodynamics data available in the literature. The results provide new insights into protein thermostability and suggest potential strategies for its manipulation.     

Maximal stabilities of reversible two-state proteins

The hydrophobic effect is the major force driving protein folding. Around room temperature, small organic solutes and hydrophobic amino acids have low solubilities in water and the hydrophobic effect is the strongest. These facts suggest that globular proteins should be maximally stable around room temperature. While this fundamental paradigm has been expected, it has not actually been shown to hold. Toward this goal, we have collected and analyzed experimental thermodynamic data for 31 proteins that show reversible two-state folding <--> unfolding transitions at or near neutral pH. Twenty-six of these are unique, and 20 of the 26 are maximally stable around room temperature irrespective of their structural properties, the melting temperature, or the living temperatures of their source organisms. Their average temperature of maximal stability is 293 +/- 8 K (20 +/- 8 degrees C). These proteins differ in size, fold, and number of domains, hydrophobic folding units, and oligomeric states. They derive from the cold-loving psychrophiles, from mesophiles, and from thermophiles. Analysis of the single-domain proteins present in this set shows that the variations in their thermodynamic parameters are correlated in a way which may explain the adaptation of the proteins to the living temperatures of the organisms from which they derive. The average energetic contribution of the individual amino acids toward protein stability decreases with an increase in protein size, suggesting that there may be an upper limit for protein maximal thermodynamic stability. For the remaining proteins, deviation of the maximal stability temperatures from room temperature may be due to greater uncertainties in their heat capacity change (DeltaC(p)) values, a weaker hydrophobic effect, and/or a stronger electrostatic contribution.     

Comparative thermodynamic elucidation of the structural stability of thermophilic proteins

Differential scanning calorimetry, circular dichroism, and visible absorption spectrophotometry were employed to elucidate the structural stability of thermophilic phycocyanin derived from Cyanidium caldarium, a eucaryotic organism which contains a nucleus, grown in acidic conditions (pH 3.4) at 54°C. The obtained results were compared with those previously reported for thermophilic phycocyanin derived from Synechococcus lividus, a procaryote containing no organized nucleus, grown in alkaline conditions (pH 8.5) at 52°C. The temperature of thermal unfolding (t_d) was found to be comparable between C. caldarium (73°C) and S. lividus (74°C) phycocyanins. The apparent free energy of unfolding (ΔG_[urea]=0) at zero denaturant (urea) concentration was also comparable: 9.1 and 8.7 kcal/mole for unfolding the chromophore part of the protein, and 5.0 and 4.3 kcal/mole for unfolding the apoprotein part of the protein, respectively. These values of t_d and ΔG_[urea]=0 were significantly higher than those previously reported for mesophilic Phormidium luridum phycocyanin (grown at 25°C). These findings revealed that relatively higher values of t_d and ΔG_[urea]=0 were characteristics of thermophilic proteins. In contrast, the enthalpies of completed unfolding (ΔH_d) and the half-completed unfolding (ΔH_d)1/2 for C. caldarium phycocyanin were much lower than those for S. lividus protein (89 versus 180 kcal/mole and 62 versus 115 kcal/mole, respectively). Factors contributing to a lower ΔH_d in C. caldarium protein and the role of charged groups in enhancing the stability of thermophilic proteins were discusse.     

The thermodynamic stability of the proteins of the ccd plasmid addiction system

The two opponents, toxin (CcdB, LetB or LetD, protein G, LynB) and antidote (CcdA, LetA, protein H, LynA), in the plasmid addiction system ccd of the F plasmid were studied by different biophysical methods. The thermodynamic stability was measured at different temperatures combining denaturant and thermally induced unfolding. It was found that both proteins denature in a two-state equilibrium (native dimer versus unfolded monomer) and that CcdA has a significantly lower thermodynamic stability. Using a numerical model, which was developed earlier by us, and on the basis of the determined thermodynamic parameters the concentration dependence of the denaturation transition temperature was obtained for both proteins. This concentration dependence may be of physiological significance, as the concentration of both ccd addiction proteins cannot exceed a certain limit because their expression is controlled by autoregulation.The influence of DNA on the thermal stability of the two proteins was probed. It was found that cognate DNA increases the melting temperature of CcdA. In the presence of non-specific DNA the thermal stability was not changed. The melting temperature of CcdB was not influenced by the applied double-stranded oligonucleotides, neither cognate nor unspecific.     

Thermal stability and thermodynamic analysis of native and methoxypolyethylene glycol modified trypsin

Four methoxypolyethylene glycols (MPEG, molecular masses 350, 750, 2000 and 5000 Da), each activated by nitrophenyl chloroformate, were used to modify trypsin. Compared with the native trypsin, the MPEG-modified trypsin was more stable against temperature between 30°C and 70°C, longer chain of MPEG moiety corresponding to higher thermal stability. The T for the native and the modified trypsin (0.4 mg ml^–1) was increased from 47°C to 66°C. The stabilization effect caused by MPEG modification was the result of decreasing in both the autolysis rate and the thermal denaturation rate. The thermodynamic analysis of the thermal denaturation process showed that the activation free energy (G^*) of the native and the modified trypsin at 60°C was increased from 102.9 to 109.3 kJ mol^–1; the activation enthalpy (H^*) was increased from 57.4 to 86.9 kJ mol^–1; the activation entropy (S^*) was increased from –136 to –67 J molK^–1. A possible explanation for the decreased thermal denaturation rate caused by MPEG modification was also discussed.     

Importance of hydrophobic cluster formation through long-range contacts in the folding transition state of two-state proteins

Understanding the folding pathways of proteins is a challenging task. The Phi value approach provides a detailed understanding of transition-state structures of folded proteins. In this work, we have computed the hydrophobicity associated with each residue in the folded state of 16 two-state proteins and compared the Phi values of each mutant residue. We found that most of the residues with high Phi value coincide with local maximum in surrounding hydrophobicity, or have nearby residues that show such maximum in hydrophobicity, indicating the importance of hydrophobic interactions in the transition state. We have tested our approach to different structural classes of proteins, such as alpha-helical, SH3 domains of all-beta proteins, beta-sandwich, and alpha/beta proteins, and we observed a good agreement with experimental results. Further, we have proposed a hydrophobic contact network pattern to relate the Phi values with long-range contacts, which will be helpful to understand the transition-state structures of folded proteins. The present approach could be used to identify potential hydrophobic clusters that may form through long-range contacts during the transition state.     

Protein's native state stability in a chemically induced denaturation mechanism

In this work, we present a generalization of Zwanzig's protein unfolding analysis [Zwanzig, R., 1997. Two-state models of protein folding kinetics. Proc. Natl Acad. Sci. USA 94, 148-150; Zwanzig, R., 1995. Simple model of protein folding kinetics. Proc. Natl Acad. Sci. USA 92, 9801], in order to calculate the free energy change Delta(N)(D)F between the protein's native state N and its unfolded state D in a chemically induced denaturation. This Extended Zwanzig Model (EZM) is both based on an equilibrium statistical mechanics approach and the inclusion of experimental denaturation curves. It enables us to construct a suitable partition function Z and to derive an analytical formula for Delta(N)(D)F in terms of the number K of residues of the macromolecule, the average number nu of accessible states for each single amino acid and the concentration C(1/2) where the midpoint of the N<==>D transition occurs. The results of the EZM for proteins where chemical denaturation follows a sigmoidal-type profile, as it occurs for the case of the T70N human variant of lysozyme (PDB code: T70N) [Esposito, G., et al., 2003. J. Biol. Chem. 278, 25910-25918], can be splitted into two lines. First, EZM shows that for sigmoidal denaturation profiles, the internal degrees of freedom of the chain play an outstanding role in the stability of the native state. On the other hand, that under certain conditions DeltaF can be written as a quadratic polynomial on concentration C(1/2), i.e., DeltaF approximately aC(1/2)(2)+bC(1/2)+c, where a,b,c are constant coefficients directly linked to protein's size K and the averaged number of non-native conformations nu. Such functional form for DeltaF has been widely known to fit experimental measures in chemically induced protein denaturation [Yagi, M., et al., 2003. J. Biol. Chem. 278, 47009-47015; Asgeirsson, B., Guojonsdottir, K., 2006. Biochim. Biophys. Acta 1764, 190-198; Sharma, S., et al., 2006. Protein Pept. Lett. 13(4), 323-329; Salem, M., et al., 2006. Biochim. Biophys. Acta 1764(5), 903-912] so EZM can shed some light into the physical meaning of the experimental values for the a,b,c coefficients.     

Role of non-covalent interactions for determining the folding rate of two-state proteins

Understanding the factors influencing the folding rate of proteins is a challenging problem. In this work, we have analyzed the role of non-covalent interactions for the folding rate of two-state proteins by free-energy approach. We have computed the free-energy terms, hydrophobic, electrostatic, hydrogen-bonding and van der Waals free energies. The hydrophobic free energy has been divided into the contributions from different atoms, carbon, neutral nitrogen and oxygen, charged nitrogen and oxygen, and sulfur. All the free-energy terms have been related with the folding rates of 28 two-state proteins with single and multiple correlation coefficients. We found that the hydrophobic free energy due to carbon atoms and hydrogen-bonding free energy play important roles to determine the folding rate in combination with other free energies. The normalized energies with total number of residues showed better results than the total energy of the protein. The comparison of amino acid properties with free-energy terms indicates that the energetic terms explain better the folding rate than amino acid properties. Further, the combination of free energies with topological parameters yielded the correlation of 0.91. The present study demonstrates the importance of topology for determining the folding rate of two-state proteins.     

Additivity in both thermodynamic stability and thermal transition temperature for rubredoxin chimeras via hybrid native partitioning

Given any operational definition of pairwise interaction, the set of residues that differ between two structurally homologous proteins can be uniquely partitioned into subsets of clusters for which no such interactions occur between clusters. Although hybrid protein sequences that preserve such clustering are consistent with tertiary structures composed of only parental native-like interactions, the stability of such predicted structures will depend upon the physical robustness of the assumed interaction potential. A simple distance cutoff criterion was applied to the most thermostable protein known to predict such a seven-residue cluster in the metal binding site region of Pyrococcus furiosus rubredoxin and a mesophile homolog. Both conformational stability and thermal transition temperature measurements demonstrate that 39% of the differential stability arises from these seven residues.     

Validity of the "two-state" hypothesis for conformational transitions of proteins

The theory, character, and properties of cooperative transitions are developed with special reference to the abrupt changes of state which occur in protein solutions. Comparisons of helix–coil processes and protein conformational reactions show that though cooperation dominates both of these processes, there are important differences. Tests of two types for the validity of the two-state approximation are presented with specific applications to proteins. Available experimental evidence demonstrates that the thermally induced reversible transitions of ribonuclease, α-chymotrypsin, and chymotrypsinogen A under conditions thus far examined are two-state processes.     

Sequence optimization for native state stability determines the evolution and folding kinetics of a small protein

Investigating the relative importance of protein stability, function, and folding kinetics in driving protein evolution has long been hindered by the fact that we can only compare modern natural proteins, the products of the very process we seek to understand, to each other, with no external references or baselines. Through a large-scale all-atom simulation of protein evolution, we have created a large diverse alignment of SH3 domain sequences which have been selected only for native state stability, with no other influencing factors. Although the average pairwise identity between computationally evolved and natural sequences is only 17%, the residue frequency distributions of the computationally evolved sequences are similar to natural SH3 sequences at 86% of the positions in the domain, suggesting that optimization for the native state structure has dominated the evolution of natural SH3 domains. Additionally, the positions which play a consistent role in the transition state of three well-characterized SH3 domains (by phi-value analysis) are structurally optimized for the native state, and vice versa. Indeed, we see a specific and significant correlation between sequence optimization for native state stability and conservation of transition state structure.     

Some thermodynamic implications for the thermostability of proteins

An analysis of the thermodynamics of protein stability reveals a general tendency for proteins that denature at higher temperatures to have greater free energies of maximal stability. To a reasonable approximation, the temperature of maximal stability for the set of globular, water-soluble proteins surveyed by Robertson and Murphy occurs at T* approximately 283K, independent of the heat denaturation temperature, T(m). This observation indicates, at least for these proteins, that thermostability tends to be achieved through elevation of the stability curve rather than by broadening or through a horizontal shift to higher temperatures. The relationship between the free energy of maximal stability and the temperature of heat denaturation is such that an increase in maximal stability of approximately 0.008 kJ/mole/residue is, on average, associated with a 1 degrees C increase in T(m). An estimate of the energetic consequences of thermal expansion suggests that these effects may contribute significantly to the destabilization of the native state of proteins with increasing temperature.     

Amino acid sequence predicts folding rate for middle-size two-state proteins

The significant correlation between protein folding rates and the sequence-predicted secondary structure suggests that folding rates are largely determined by the amino acid sequence. Here, we present a method for predicting the folding rates of proteins from sequences using the intrinsic properties of amino acids, which does not require any information on secondary structure prediction and structural topology. The contribution of residue to the folding rate is expressed by the residue's Omega value. For a given residue, its Omega depends on the amino acid properties (amino acid rigidity and dislike of amino acid for secondary structures). Our investigation achieves 82% correlation with folding rates determined experimentally for simple, two-state proteins studied until the present, suggesting that the amino acid sequence of a protein is an important determinant of the protein-folding rate and mechanism.     

Solute excluded-volume effects on the stability of globular proteins: A statistical thermodynamic theory

A statistical thermodynamic theory is developed to investigate the effects of solute excluded volume on the stability of globular proteins. Proteins are modeled as two states in chemical equilibrium: the denatured state is modeled as a flexible chain of tangent hard spheres (pearl-necklace chain) while the native state is modeled as a single hard sphere. Study of model proteins bovine pancreatic trypsin inhibitor and lysozyme in a McMillan-Mayer model solution of hard spheres indicates that the excluded volume of solutes has three distinct types of effects on protein stability: (1) small-size solutes strongly denature proteins, (2) medium-size solutes stabilize proteins at low solute concentrations and destabilize them at high concentrations, and (3) large-size solutes stabilize native-state proteins across the whole liquid region. The study also finds that increasing the chain length of hard-chain polymer solutes has an effect on protein stability that is similar to increasing the diameter of spherical solutes. This work qualitatively explains why stabilizers tend to be large size molecules such as sugars, polymers, polynols, nonionic, and anionic surfactants while denaturants tend to be small size molecules such as alcohols, glycols, amides, formamides, ureas, and guanidium salts. Quantitative comparison between theoretical predictions and experimental results for folding free energy changes shows that the excluded-volume effect is at least as important as the binding and/or electrostatic effects on solute-assisted protein-denaturation processes. Our theory may also be able to explain the effect of excluded volume on the Φ condensation of DNA. © 1996 John Wiley & Sons, Inc.     

Folding rates and low-entropy-loss routes of two-state proteins

We develop a simple model for computing the rates and routes of folding of two-state proteins from the contact maps of their native structures. The model is based on the graph-theoretical concept of effective contact order (ECO). The model predicts that proteins fold by "zipping up" in a sequence of small-loop-closure events, depending on the native chain fold. Using a simple equation, with a few physical rate parameters, we obtain a good correlation with the folding rates of 24 two-state folding proteins. The model rationalizes data from Phi-value analysis that have been interpreted in terms of delocalized or polarized transition states. This model indicates how much of protein folding may take place in parallel, not along a single reaction coordinate or with a single transition state.     

Unification of the folding mechanisms of non-two-state and two-state proteins

We have collected the kinetic folding data for non-two-state and two-state globular proteins reported in the literature, and investigated the relationships between the folding kinetics and the native three-dimensional structure of these proteins. The rate constants of formation of both the intermediate and the native state of non-two-state folders were found to be significantly correlated with protein chain length and native backbone topology, which is represented by the absolute contact order and sequence-distant native pairs. The folding rate of two-state folders, which is known to be correlated with the native backbone topology, apparently does not correlate significantly with protein chain length. On the basis of a comparison of the folding rates of the non-two-state and two-state folders, it was found that they are similarly dependent on the parameters that reflect the native backbone topology. This suggests that the mechanisms behind non-two-state and two-state folding are essentially identical. The present results lead us to propose a unified mechanism of protein folding, in which folding occurs in a hierarchical manner, reflecting the hierarchy of the native three-dimensional structure, as embodied in the case of non-two-state folding with an accumulation of the intermediate. Apparently, two-state folding is merely a simplified version of hierarchical folding caused either by an alteration in the rate-limiting step of folding or by destabilization of the intermediate.