Osmolyte-induced protein folding free energy changes

Upon addition of protecting osmolyte to an aqueous solution of an intrinsically unstructured protein, spectral observables are often seen to change in a sigmoid fashion as a function of increasing osmolyte concentration. Commonly, such data are analyzed using the linear extrapolation model (LEM), a method that defines a scale from 0%-100% folded species at each osmolyte concentration by means of extending pre- and post-folding baselines into the transition region. Defining the 0%-100% folding scale correctly for each osmolyte is an important part of the analysis, leading to evaluation of the fraction of folded protein existing in the absence of osmolytes. In this study, we used reduced and carboxyamidated RNase T1 (RCAM-T1) as an intrinsically unstructured protein, and determined the thermodynamic stability of RCAM-T1 induced by naturally occurring osmolytes. Because the folded fraction of the protein population determined by experiments of thermal and urea-induced denaturation is nonzero in the absence of osmolytes at 15 degrees C, the commonly used LEM can lead to false values of DeltaG[stackD-->N0] for protein folding due to the arbitrary assumption that the protein is 100% unfolded in the presence of buffer alone. To correct this problem, titration of the protein solution with urea and extrapolating back to zero urea concentration gives the spectral value for 100% denatured protein. With fluorescence as the observable we redefine F/F0 to F/F0extrap = 1.0 and require that the denatured-state baseline have this value as its intercept. By so doing, the 0%-100% scale-corrected DeltaG[D-->N0] values of RCAM-T1 folding in the presence of various osmolytes are then found to be identical, with small error, demonstrating that DeltaG[D-->N0] is independent of the osmolytes used. Such a finding is an important step in validating this quantity derived from the LEM as having the properties expected of an authentic thermodynamic parameter. The rank order of osmolyte efficacies in stabilizing RCAM-T1 is sarcosine > sucrose > sorbitol > proline > betaine > glycerol.     

Mapping the folding free energy surface for metal-free human Cu,Zn superoxide dismutase

Mutations at many different sites in the gene encoding human Cu,Zn superoxide dismutase (SOD) are known to be causative agents in amyotrophic lateral sclerosis (ALS). One explanation for the molecular basis of this pathology is the aggregation of marginally soluble, partially structured states whose populations are enhanced in the protein variants. As a benchmark for testing this hypothesis, the equilibrium and kinetic properties of the reversible folding reaction of a metal-free variant of SOD were investigated. Reversibility was achieved by replacing the two non-essential cysteine residues with non-oxidizable analogs, C6A/C111S, to produce apo-AS-SOD. The metal-free pseudo-wild-type protein is folded and dimeric in the absence of chemical denaturants, and its equilibrium folding behavior is well described by an apparent two-state mechanism involving the unfolded monomer and the native dimer. The apparent free energy of folding in the absence of denaturant and at standard state is -20.37(+/- 1.04) kcal (mol dimer)(-1). A global analysis of circular dichroism kinetic traces for both unfolding and refolding reactions, combined with results from small angle X-ray scattering and time-resolved fluorescence anisotropy measurements, supports a sequential mechanism involving the unfolded monomer, a folded monomeric intermediate, and the native dimer. The rate-limiting monomer folding reaction is followed by a near diffusion-limited self-association reaction to form the native dimer. The relative population of the folded monomeric intermediate is predicted not to exceed 0.5% at micromolar concentrations of protein under equilibrium and both strongly unfolding and refolding conditions for metal-free pseudo-wild-type SOD.     

Reliable protein folding on complex energy landscapes: the free energy reaction path

A theoretical framework is developed to study the dynamics of protein folding. The key insight is that the search for the native protein conformation is influenced by the rate r at which external parameters, such as temperature, chemical denaturant, or pH, are adjusted to induce folding. A theory based on this insight predicts that 1), proteins with complex energy landscapes can fold reliably to their native state; 2), reliable folding can occur as an equilibrium or out-of-equilibrium process; and 3), reliable folding only occurs when the rate r is below a limiting value, which can be calculated from measurements of the free energy. We test these predictions against numerical simulations of model proteins with a single energy scale.     

Zinc binding modulates the entire folding free energy surface of human Cu,Zn superoxide dismutase

Over 100 amino acid replacements in human Cu,Zn superoxide dismutase (SOD) are known to cause amyotrophic lateral sclerosis, a gain-of-function neurodegenerative disease that destroys motor neurons. Supposing that aggregates of partially folded states are primarily responsible for toxicity, we determined the role of the structurally important zinc ion in defining the folding free energy surface of dimeric SOD by comparing the thermodynamic and kinetic folding properties of the zinc-free and zinc-bound forms of the protein. The presence of zinc was found to decrease the free energies of a peptide model of the unfolded monomer, a stable variant of the folded monomeric intermediate, and the folded dimeric species. The unfolded state binds zinc weakly with a micromolar dissociation constant, and the folded monomeric intermediate and the native dimeric form both bind zinc tightly, with subnanomolar dissociation constants. Coupled with the strong driving force for the subunit association reaction, the shift in the populations toward more well-folded states in the presence of zinc decreases the steady-state populations of higher-energy states in SOD under expected in vivo zinc concentrations (approximately nanomolar). The significant decrease in the population of partially folded states is expected to diminish their potential for aggregation and account for the known protective effect of zinc. The ∼ 100-fold increase in the rate of folding of SOD in the presence of micromolar concentrations of zinc demonstrates a significant role for a preorganized zinc-binding loop in the transition-state ensemble for the rate-limiting monomer folding reaction in this β-barrel protein.     

Calculation of the free energy and cooperativity of protein folding

Calculation of the free energy of protein folding and delineation of its pre-organization are of foremost importance for understanding, predicting and designing biological macromolecules. Here, we introduce an energy smoothing variant of parallel tempering replica exchange Monte Carlo (REMS) that allows for efficient configurational sampling of flexible solutes under the conditions of molecular hydration. Its usage to calculate the thermal stability of a model globular protein, Trp cage TC5b, achieves excellent agreement with experimental measurements. We find that the stability of TC5b is attained through the coupled formation of local and non-local interactions. Remarkably, many of these structures persist at high temperature, concomitant with the origin of native-like configurations and mesostates in an otherwise macroscopically disordered unfolded state. Graph manifold learning reveals that the conversion of these mesostates to the native state is structurally heterogeneous, and that the cooperativity of their formation is encoded largely by the unfolded state ensemble. In all, these studies establish the extent of thermodynamic and structural pre-organization of folding of this model globular protein, and achieve the calculation of macromolecular stability ab initio, as required for ab initio structure prediction, genome annotation, and drug design.     

Network and graph analyses of folding free energy surfaces

Protein folding is governed by a complex free energy surface whose entropic contributions are relevant because of the large number of degrees of freedom involved. Such complexity, in particular the conformational heterogeneity of the denatured state, is hidden in projections onto one or two order parameters (e.g. fraction of native contacts and/or radius of gyration), which usually results in relatively smooth surfaces. Recent approaches borrowed from network and graph theory have yielded quantitative unprojected representations of the free energy surfaces of a beta-hairpin and a three-stranded beta-sheet peptide using equilibrium folding-unfolding molecular dynamics simulations. Interestingly, the network and graph analyses of these structured peptides have revealed a very heterogeneous denatured state ensemble. It includes high-enthalpy, high-entropy conformations with fluctuating non-native secondary structure, as well as low-enthalpy, low-entropy traps.     

Exploring folding free energy landscapes using computational protein design

Recent advances in computational protein design have allowed exciting new insights into the sequence dependence of protein folding free energy landscapes. Whereas most previous studies have examined the sequence dependence of protein stability and folding kinetics by characterizing naturally occurring proteins and variants of these proteins that contain a small number of mutations, it is now possible to generate and characterize computationally designed proteins that differ significantly from naturally occurring proteins in sequence and/or structure. These computer-generated proteins provide insights into the determinants of protein structure, stability and folding, and make it possible to disentangle the properties of proteins that are the consequence of natural selection from those that reflect the fundamental physical chemistry of polypeptide chains.     

Entropy calculations on a reversibly folding peptide: changes in solute free energy cannot explain folding behavior

The configurational entropy of a beta-heptapeptide in solution at four different temperatures is calculated. The contributions of the backbone and of the side-chain atoms to the total peptide entropy are analyzed separately and the effective contribution to the entropy arising from correlations between these terms determined. The correlation between the backbone and side-chain atoms amounts to about 17% and is rather insensitive to the temperature. The correlation of motion within the backbone and within side-chains is much larger and decreases with temperature. As the peptide reversibly folds at higher temperatures, its change in entropy and enthalpy upon folding is analyzed. The change in entropy and enthalpy upon folding of the peptide alone cannot account for the observed change in free energy on folding of the peptide in solution. Enthalpic and entropic contributions of the solvent thus also play a key role. Proteins 2001;43:45-56.     

Exploring structures in protein folding funnels with free energy functionals: the denatured ensemble

We discuss the formulation of free energy functionals that describe the formation of structure in partially folded proteins. These free energy functionals take into account the inhomogeneous nature of contact energies, chain entropy and cooperative contributions reflecting the many body character of some folding forces like hydrophobicity, but do not directly account for non-native contacts because they assume the validity of the minimal frustration principle. We show how the free energy functionals can be used to interpret experiments on partially folded proteins that probe the fractional occupancy of specific local structures. In particular, we study the hydrogen protection factors in lysozyme studied in transient experiments by Gladwin and Evans and by Nash and Jonas using equilibrium pressure denaturation and the NMR order parameters measured by Dobson and Kim for the homologous protein alpha-lactalbumin.     

Protein folding: Thickening the broth

Recent results support the notion that macromolecular 'crowding' enhances protein aggregation, at the expense of correct folding. The results can be rationalised in terms of kinetic competition between distinct processes, taking into account the relative influence of crowding on each process.     

The effect of redox state on the folding free energy of azurin

 The unfolding of oxidized and reduced azurin by guanidine hydrochloride has been monitored by circular dichroism. Dilution experiments showed the unfolding to be reversible, and the equilibrium data have been interpreted in terms of a two-state model. The protein is stabilized by the strong metal binding in the native state, so that the folding free energy is as high as –52.2 kJ mol^–1 for the oxidized protein. The reduced protein is less stable, with a folding free energy of –40.0 kJ mol^–1. A thermodynamic cycle shows, as a consequence, that unfolded azurin has a reduction potential 0.13 V above that of the folded protein. This is explained by the bipyramidal site in the native fold stabilizing Cu(II) by a rack mechanism, with the same geometry being maintained in the Cu(I) form. In the unfolded protein, on the other hand, the coordination geometries are expected to differ for the two oxidation states, Cu(I) being stabilized by the cysteine thiol group in a linear or trigonal symmetry, whereas Cu(II) prefers oxygen ligands in a tetragonal geometry. Received: 15 January 1997 / Accepted: 3 April 1997     

Exploring structures in protein folding funnels with free energy functionals: the transition state ensemble

We use free energy functionals that account for the partial ordering of residues in the transition state ensemble to characterize the free energy surfaces for fast folding proteins. We concentrate on chymotrypsin inhibitor and lambda-repressor. We show how the explicit cooperativity that can arise from many body forces, such as side-chain ordering or hydrophobic surface burial, determines the crossover from folding with a large delocalized nucleus and the specific small classical nucleus of the type envisioned in nucleation growth scenarios. We compare the structural correlations present in the transition state ensemble obtained from free energy functionals with those inferred from experiment using extrathermodynamic free energy relations for folding time obtained via protein engineering kinetics experiments. We also use the free energy functionals to examine both the size of barriers and multidimensional representations of the free energy profiles in order to address the question of appropriate reaction coordinates for folding.     

Protein folding

The importance of protein folding in the biosynthesis of proteins is reviewed.     

Non-linear rate-equilibrium free energy relationships and Hammond behavior in protein folding

Non-linear rate-equilibrium relationships upon mutation or changes in solvent conditions are frequently observed in protein folding reactions and are usually interpreted in terms of Hammond behavior. Here we first give a general overview over the concept of transition state movements in chemical reactions and discuss its application to protein folding. We then show examples for genuine Hammond behavior and for apparent transition state movements caused by other effects like changes in the rate-limiting step of the folding reaction or ground state effects, i.e. structural changes in either the native state or the unfolded state. These examples show that apparent transition state movements can easily be mistaken for Hammond behavior. We describe experimental tests using self- and cross-interaction parameters to distinguish between structural changes in a single transition state following Hammond behavior and apparent transition state movements caused by other effects.     

Protein folding: pulling back the frontiers

In the past few years, it has become possible to measure the forces required to mechanically unfold single protein molecules. Recently, the mechanical properties of heteropolyproteins have been studied, shedding new light on the mechanical design of modular proteins such as titin.     

Protein free energy landscapes remodeled by ligand binding

Glucose/galactose binding protein (GGBP) functions in two different larger systems of proteins used by enteric bacteria for molecular recognition and signaling. Here we report on the thermodynamics of conformational equilibrium distributions of GGBP. Three fluorescence components appear at zero glucose concentration and systematically transition to three components at high glucose concentration. Fluorescence anisotropy correlations, fluorescent lifetimes, thermodynamics, computational structure minimization, and literature work were used to assign the three components as open, closed, and twisted conformations of the protein. The existence of three states at all glucose concentrations indicates that the protein continuously fluctuates about its conformational state space via thermally driven state transitions; glucose biases the populations by reorganizing the free energy profile. These results and their implications are discussed in terms of the two types of specific and nonspecific interactions GGBP has with cytoplasmic membrane proteins.     

Protein folding mechanisms and the multidimensional folding funnel

An important idea that emerges from the energy landscape theory of protein folding is that subtle global features of the protein landscape can profoundly affect the apparent mechanism of folding. The relationship between various characteristic temperatures in the phase diagrams and landmarks in the folding funnel at fixed temperatures can be used to classify different folding behaviors. The one-dimensional picture of a folding funnel classifies folding kinetics into four basic scenarios, depending on the relative location of the thermodynamic barrier and the glass transition as a function of a single-order parameter. However, the folding mechanism may not always be quantitatively described by a single-order parameter. Several other order parameters, such as degree of secondary structure formation, collapse and topological order, are needed to establish the connection between minimalist models and proteins in the laboratory. In this article we describe a simple multidimensional funnel based on two-order parameters that measure the degree of collapse and topological order. The appearance of several different “mechanisms” is illustrated by analyzing lattice models with different potentials and sequences with different degrees of design. In most cases, the two-dimensional analysis leads to a classification of mechanisms totally in keeping with the one-dimensional scheme, but a topologically distinct scenario of fast folding with traps also emerges. The nature of traps depends on the relative location of the glass transition surface and the thermodynamic barrier in the multidimensional funnel. Proteins 32:136–158, 1998. © 1998 Wiley-Liss, Inc.     

Calculation of mutational free energy changes in transition states for protein folding

Recent advances in experimental and computational methods have made it possible to determine with considerable accuracy the structures whose formation is rate limiting for the folding of some small proteins-the transition state ensemble, or TSE. We present a method to analyze and validate all-atom models of such structures. The method is based on the comparison of experimental data with the computation of the change in free energy of the TSE resulting from specific mutations. Each mutation is modeled individually in all members of an ensemble of transition state structures using a method originally developed to predict mutational changes in the stability of native proteins. We first apply this method to six proteins for which we have determined the TSEs with a technique that uses experimental mutational data (Phi-values) as restraints in the structure determination and find a highly significant correlation between the calculated free energy changes and those derived from experimental kinetic data. We then use the procedure to analyze transition state structures determined by molecular dynamics simulations of unfolding, again finding a high correlation. Finally, we use the method to estimate changes in folding rates of several hydrophobic core mutants of Fyn SH3. Taken together, these results show that the procedure developed here is a tool of general validity for analyzing, assessing, and improving the quality of the structures of transition states for protein folding.