Phi-value analysis of apo-azurin folding: comparison between experiment and theory

From covalent transition states in chemistry to noncovalent in biology: from β- to Φ-value analysis of protein folding

Solving the mechanism of a chemical reaction requires determining the structures of all the ground states on the pathway and the elusive transition states linking them. 2024 is the centenary of Brønsted's landmark paper that introduced the β-value and structure-activity studies as the only experimental means to infer the structures of transition states. It involves making systematic small changes in the covalent structure of the reactants and analysing changes in activation and equilibrium-free energies. Protein engineering was introduced for an analogous procedure, Φ-value analysis, to analyse the noncovalent interactions in proteins central to biological chemistry. The methodology was developed first by analysing noncovalent interactions in transition states in enzyme catalysis. The mature procedure was then applied to study transition states in the pathway of protein folding - 'part (b) of the protein folding problem'. This review describes the development of Φ-value analysis of transition states and compares and contrasts the interpretation of β- and Φ-values and their limitations. Φ-analysis afforded the first description of transition states in protein folding at the level of individual residues. It revealed the nucleation-condensation folding mechanism of protein domains with the transition state as an expanded, distorted native structure, containing little fully formed secondary structure but many weak tertiary interactions. A spectrum of transition states with various degrees of structural polarisation was then uncovered that spanned from nucleation-condensation to the framework mechanism of fully formed secondary structure. Φ-analysis revealed how movement of the expanded transition state on an energy landscape accommodates the transition from framework to nucleation-condensation mechanisms with a malleability of structure as a unifying feature of folding mechanisms. Such movement follows the rubric of analysis of classical covalent chemical mechanisms that began with Brønsted. Φ-values are used to benchmark computer simulation, and Φ and simulation combine to describe folding pathways at atomic resolution.

Significance of the Disulfide Bridge in the Structure and Stability of Metalloprotein Azurin

Metalloproteins make up a class of proteins that incorporate metal ions into their structures, enabling them to perform essential functions in biological systems, such as catalysis and electron transport. Azurin is one such metalloprotein with copper cofactor, having a β-barrel structure with exceptional thermal stability. The copper metal ion is coordinated at one end of the β-barrel structure, and there is a disulfide bond at the opposite end. In this study, we explore the effect of this disulfide bond in the high thermal stability of azurin by analyzing both the native S-S bonded and S-S nonbonded (S-S open) forms using temperature replica exchange molecular dynamics (REMD). Similar to experimental observations, we find a 35 K decrease in denaturation temperature for S-S open azurin compared to that of the native holo form (420 K). As observed in the case of native holo azurin, the unfolding process of the S-S open form also started with disruptions of the α-helix. The free energy surfaces of the unfolding process revealed that the denaturation event of the S-S open form progresses through different sets of conformational ensembles. Subsequently, we compared the stabilities of individual β-sheet strands of both the S-S bonded and the S-S nonbonded forms of azurin. Further, we examined the contacts between individual residues for the central structures from the free energy surfaces of the S-S nonbonded form. The microscopic origin of the lowering in the denaturation temperature is further supplemented by thermodynamic analysis.

Folding of copper proteins: role of the metal?

Copper is a redox-active transition metal ion required for the function of many essential human proteins. For biosynthesis of proteins coordinating copper, the metal may bind before, during or after folding of the polypeptide. If the metal binds to unfolded or partially folded structures of the protein, such coordination may modulate the folding reaction. The molecular understanding of how copper is incorporated into proteins requires descriptions of chemical, thermodynamic, kinetic and structural parameters involved in the formation of protein-metal complexes. Because free copper ions are toxic, living systems have elaborate copper-transport systems that include particular proteins that facilitate efficient and specific delivery of copper ions to target proteins. Therefore, these pathways become an integral part of copper protein folding in vivo. This review summarizes biophysical-molecular in vitro work assessing the role of copper in folding and stability of copper-binding proteins as well as protein-protein copper exchange reactions between human copper transport proteins. We also describe some recent findings about the participation of copper ions and copper proteins in protein misfolding and aggregation reactions in vitro.

Crowding-Induced Elongated Conformation of Urea-Unfolded Apoazurin: Investigating the Role of Crowder Shape in Silico

Here, we show by solution nuclear magnetic resonance measurements that the urea-unfolded protein apoazurin becomes elongated when the synthetic crowding agent dextran 20 is present, in contrast to the prediction from the macromolecular crowding effect based on the argument of volume exclusion. To explore the complex interactions beyond volume exclusion, we employed coarse-grained molecular dynamics simulations to explore the conformational ensemble of apoazurin in a box of monodisperse crowders under strong chemically denaturing conditions. The elongated conformation of unfolded apoazurin appears to result from the interplay of the effective attraction between the protein and crowders and the shape of the crowders. With a volume-conserving crowder model, we show that the crowder shape provides an anisotropic direction of the depletion force, in which a bundle of surrounding rodlike crowders stabilize an elongated conformation of unfolded apoazurin in the presence of effective attraction between the protein and crowders.

Characterization of protein folding by a Φ-value calculation with a statistical-mechanical model

The Φ-value analysis approach provides information about transition-state structures along the folding pathway of a protein by measuring the effects of an amino acid mutation on folding kinetics. Here we compared the theoretically calculated Φ values of 27 proteins with their experimentally observed Φ values; the theoretical values were calculated using a simple statistical-mechanical model of protein folding. The theoretically calculated Φ values reflected the corresponding experimentally observed Φ values with reasonable accuracy for many of the proteins, but not for all. The correlation between the theoretically calculated and experimentally observed Φ values strongly depends on whether the protein-folding mechanism assumed in the model holds true in real proteins. In other words, the correlation coefficient can be expected to illuminate the folding mechanisms of proteins, providing the answer to the question of which model more accurately describes protein folding: the framework model or the nucleation-condensation model. In addition, we tried to characterize protein folding with respect to various properties of each protein apart from the size and fold class, such as the free-energy profile, contact-order profile, and sensitivity to the parameters used in the Φ-value calculation. The results showed that any one of these properties alone was not enough to explain protein folding, although each one played a significant role in it. We have confirmed the importance of characterizing protein folding from various perspectives. Our findings have also highlighted that protein folding is highly variable and unique across different proteins, and this should be considered while pursuing a unified theory of protein folding.

Evolution, energy landscapes and the paradoxes of protein folding

Protein folding has been viewed as a difficult problem of molecular self-organization. The search problem involved in folding however has been simplified through the evolution of folding energy landscapes that are funneled. The funnel hypothesis can be quantified using energy landscape theory based on the minimal frustration principle. Strong quantitative predictions that follow from energy landscape theory have been widely confirmed both through laboratory folding experiments and from detailed simulations. Energy landscape ideas also have allowed successful protein structure prediction algorithms to be developed. The selection constraint of having funneled folding landscapes has left its imprint on the sequences of existing protein structural families. Quantitative analysis of co-evolution patterns allows us to infer the statistical characteristics of the folding landscape. These turn out to be consistent with what has been obtained from laboratory physicochemical folding experiments signaling a beautiful confluence of genomics and chemical physics.

Frustration in biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their own structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of frustration in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and especially how biomolecular structure connects to function by means of localized frustration. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding mechanisms. We review here how the biological functions of proteins are related to subtle local physical frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. In this review, we also emphasize that frustration, far from being always a bad thing, is an essential feature of biomolecules that allows dynamics to be harnessed for function. In this way, we hope to illustrate how Frustration is a fundamental concept in molecular biology.

Discrete kinetic models from funneled energy landscape simulations

A general method for facilitating the interpretation of computer simulations of protein folding with minimally frustrated energy landscapes is detailed and applied to a designed ankyrin repeat protein (4ANK). In the method, groups of residues are assigned to foldons and these foldons are used to map the conformational space of the protein onto a set of discrete macrobasins. The free energies of the individual macrobasins are then calculated, informing practical kinetic analysis. Two simple assumptions about the universality of the rate for downhill transitions between macrobasins and the natural local connectivity between macrobasins lead to a scheme for predicting overall folding and unfolding rates, generating chevron plots under varying thermodynamic conditions, and inferring dominant kinetic folding pathways. To illustrate the approach, free energies of macrobasins were calculated from biased simulations of a non-additive structure-based model using two structurally motivated foldon definitions at the full and half ankyrin repeat resolutions. The calculated chevrons have features consistent with those measured in stopped flow chemical denaturation experiments. The dominant inferred folding pathway has an “inside-out”, nucleation-propagation like character.

A variational model for oligomer-formation process of GNNQQNY peptide from yeast prion protein Sup35

Many human neurodegenerative diseases are associated with the aggregation of insoluble amyloid-like fibrous proteins. However, the processes by which the randomly diffused monomer peptides aggregate into the highly regulated amyloid fibril structures are largely unknown. We proposed a residue-level coarse-grained variational model for the investigation of the aggregation pathway for a small assembly of amyloid proteins, the peptide GNNQQNY from yeast prion protein Sup35. By examining the free energy surface, we identified the residue-level sequential pathways for double parallel and antiparallel β-peptides, which show that the central dry polar zipper structure is the major folding core in both cases. The critical nucleus size is determined to be three peptides for the homogeneous nucleation process, whereas the zig-zag growth pattern appears most favorably for heterogeneous nucleation. Consistent with the dock-and-lock mechanism, the aggregation process of free peptides to the fibril core was found to be highly cooperative. The quantitative validation with the computational simulations and experimental data demonstrated the usefulness of the proposed model in understanding the general mechanism of the amyloid fibril system.

Role of metal in folding and stability of copper proteins in vitro

Metal coordination is required for function of many proteins. For biosynthesis of proteins coordinating a metal, the question arises if the metal binds before, during or after folding of the polypeptide. Moreover, when the metal is bound to the protein, how does its coordination affect biophysical properties such as stability and dynamics? Understanding how metals are utilized by proteins in cells on a molecular level requires accurate descriptions of the thermodynamic and kinetic parameters involved in protein-metal complexes. Copper is one of the essential transition metals found in the active sites of many key proteins. To avoid toxicity of free copper ions, living systems have developed elaborate copper-transport systems that involve dedicated proteins that facilitate efficient and specific delivery of copper to target proteins. This review describes in vitro and in silico biophysical work assessing the role of copper in folding and stability of copper-binding proteins. Examples of proteins discussed are: a blue-copper protein (Pseudomonas aeruginosa azurin), members of copper-transport systems (bacterial CopZ, human Atox1 and ATP7B domains) and multi-copper ferroxidases (yeast Fet3p and human ceruloplasmin). The consequences of interactions between copper proteins and platinum-complexes are also discussed. This article is part of a Special Issue entitled: Cell Biology of Metals.

Insights into protein folding mechanisms from large scale analysis of mutational effects

Protein folding mechanisms are probed experimentally using single-point mutant perturbations. The relative effects on the folding (phi-values) and unfolding (1 - phi) rates are used to infer the detailed structure of the transition-state ensemble (TSE). Here we analyze kinetic data on > 800 mutations carried out for 24 proteins with simple kinetic behavior. We find two surprising results: (i) all mutant effects are described by the equation: DeltaDeltaG(double dagger)(unfold)=0.76DeltaDeltaG(eq) +/- 1.8kJ/mol. Therefore all data are consistent with a single phi-value (0.24) with accuracy comparable to experimental precision, suggesting that the structural information in conventional phi-values is low. (ii) phi-values change with stability, increasing in mean value and spread from native to unfolding conditions, and thus cannot be interpreted without proper normalization. We eliminate stability effects calculating the phi-values at the mutant denaturation midpoints; i.e., conditions of zero stability (phi(0)). We then show that the intrinsic variability is phi(0) = 0.36 +/- 0.11, being somewhat larger for beta-sheet-rich proteins than for alpha-helical proteins. Importantly, we discover that phi(0)-values are proportional to how many of the residues surrounding the mutated site are local in sequence. High phi(0)-values correspond to protein surface sites, which have few nonlocal neighbors, whereas core residues with many tertiary interactions produce the lowest phi(0)-values. These results suggest a general mechanism in which the TSE at zero stability is a broad conformational ensemble stabilized by local interactions and without specific tertiary interactions, reconciling phi-values with many other empirical observations.

How general is the nucleation-condensation mechanism?

We investigate the structures of the major folding transition states of nine proteins by correlation of published Phi-values with inter-residue contact maps. Combined with previous studies on six proteins, the analysis suggests that at least 10 of the 15 small globular proteins fold via a nucleation-condensation mechanism with a concurrent build-up of secondary and tertiary structure contacts, but a structural consolidation that is clearly nonuniformly distributed over the molecule and most intense in a single structural region suggesting the occurrence of a single folding nucleus. However, on average helix- and sheet-forming residues show somewhat larger Phi-values in the major transition state, suggesting that secondary structure formation is one important driving force in the nucleation-condensation in many proteins and that secondary-structure forming residues tend to be more prominent in folding nuclei. We synthesize the combined information on these 10 of 15 proteins into a unified nucleation-condensation mechanism which also accounts for effects described by the framework, hydrophobic collapse, zipper, and funnel models.

Simulations of proteins with inhomogeneous degrees of freedom: The effect of thermostats

Proteins with a long flexible polymeric tail attached at their N- or C-terminus are studied using molecular dynamics (MD) simulations of a coarse-grained model for protein folding where the temperature is regulated by either the Berendsen or the Langevin thermostat. These thermostats show different abilities to regulate the temperature of these systems that include flexible and more rigid regions. In the simulations with the Berendsen thermostat, the flexible tail is significantly hotter than the protein, both in its folded and unfolded states. Upon weakening the strength of the Berendsen thermostat, the temperature gradient between the fast and the slow degrees of freedom is significantly decreased, yet linkage between the temperatures of the flexible tail and the protein remains. The Langevin thermostat is proven to regulate the temperature of these inhomogenous systems reliably, without discriminating between the slow and fast degrees of freedom. The Langevin thermostat is less sensitive than is the Berendsen thermostat to the strength of the coupling between the protein system and the thermal bath. Our study calls for special care in choosing the thermostat for MD simulations of systems with inhomogenous degrees of freedom. Using the Berendsen thermostat with strong coupling would result in mistaken thermodynamic descriptions of such systems.

Crowded, cell-like environment induces shape changes in aspherical protein

How the crowded environment inside cells affects the structures of proteins with aspherical shapes is a vital question because many proteins and protein-protein complexes in vivo adopt anisotropic shapes. Here we address this question by combining computational and experimental studies of a football-shaped protein (i.e., Borrelia burgdorferi VlsE) in crowded, cell-like conditions. The results show that macromolecular crowding affects protein-folding dynamics as well as overall protein shape. In crowded milieus, distinct conformational changes in VlsE are accompanied by secondary structure alterations that lead to exposure of a hidden antigenic region. Our work demonstrates the malleability of "native" proteins and implies that crowding-induced shape changes may be important for protein function and malfunction in vivo.

Variationally determined free energy profiles for structural models of proteins: characteristic temperatures for folding and trapping

Characterizing the phase diagram for proteins is important both for laboratory studies and for the development of structure prediction algorithms. Using a variational scheme, we calculated the generic features of the protein thermostability over a large range of temperatures for a set of more than 50 different proteins using a model based on native structure alone. Focusing on a specific system, protein G, we further examined, using a more realistic model that includes the nonnative interaction, the thermostability of both the native state and a collection of trap structures. By surveying the native structures for many proteins and by paying closer attention to the various trap structures of protein G, we obtained an overall understanding of the folding dynamics far from the conditions usually focused on; namely, those near the folding temperature alone. Two characteristic temperatures (shown to scale with folding temperature in general) signal drastic changes in the folding mechanism. The variational calculations suggest that most proteins would, indeed, fold in a barrierless manner below a critical temperature analogous to a spinodal in crystallization. For fixed interaction strengths, this temperature, however, seems to be generally very low, approximately 50% of the equilibrium folding temperature. Likewise, native proteins, in general, would unfold in a completely barrierless way at a temperature 25% above folding temperature according to these variational calculations. We also studied the distribution of free energy profiles for escape from a set of trap structures generated by simulations.

Minimizing frustration by folding in an aqueous environment

Although life as we know it evolved in an aqueous medium, the properties of water are not completely understood. In this review, we focus on the role of water in guiding protein folding and stability. Specifically, we discuss the mechanisms of protein folding in an aqueous environment, the effects of water on the folding energy landscape as well as the transition state ensemble, and interactions of water with the folded state. We show that water cannot be viewed as a passive solvent, but rather, plays a very active role in the life of a protein.

Excluded volume, local structural cooperativity, and the polymer physics of protein folding rates

A coarse-grained variational model is used to investigate the polymer dynamics of barrier crossing for a diverse set of two-state folding proteins. The model gives reliable folding rate predictions provided excluded volume terms that induce minor structural cooperativity are included in the interaction potential. In general, the cooperative folding routes have sharper interfaces between folded and unfolded regions of the folding nucleus and higher free energy barriers. The calculated free energy barriers are strongly correlated with native topology as characterized by contact order. Increasing the rigidity of the folding nucleus changes the local structure of the transition state ensemble nonuniformly across the set of proteins studied. Nevertheless, the calculated prefactors k(0) are found to be relatively uniform across the protein set, with variation in 1/k(0) less than a factor of 5. This direct calculation justifies the common assumption that the prefactor is roughly the same for all small two-state folding proteins. Using the barrier heights obtained from the model and the best-fit monomer relaxation time 30 ns, we find that 1/k(0) approximately 1-5 mus (with average 1/k(0) approximately 4 micros). This model can be extended to study subtle aspects of folding such as the variation of the folding rate with stability or solvent viscosity and the onset of downhill folding.

Establishing the entatic state in folding metallated Pseudomonas aeruginosa azurin

Understanding how the folding of proteins establishes their functional characteristics at the molecular level challenges both theorists and experimentalists. The simplest test beds for confronting this issue are provided by electron transfer proteins. The environment provided by the folded protein to the cofactor tunes the metal's electron transport capabilities as envisioned in the entatic hypothesis. To see how the entatic state is achieved one must study how the folding landscape affects and in turn is affected by the metal. Here, we develop a coarse-grained functional to explicitly model how the coordination of the metal (which results in a so-called entatic or rack-induced state) modifies the folding of the metallated Pseudomonas aeruginosa azurin. Our free-energy functional-based approach directly yields the proper nonlinear extra-thermodynamic free energy relationships for the kinetics of folding the wild type and several point-mutated variants of the metallated protein. The results agree quite well with corresponding laboratory experiments. Moreover, our modified free-energy functional provides a sufficient level of detail to explicitly model how the geometric entatic state of the metal modifies the dynamic folding nucleus of azurin.