Transition states in protein folding kinetics: modeling phi-values of small beta-sheet proteins

Small single-domain proteins often exhibit only a single free-energy barrier, or transition state, between the denatured and the native state. The folding kinetics of these proteins is usually explored via mutational analysis. A central question is which structural information on the transition state can be derived from the mutational data. In this article, we model and structurally interpret mutational Φ-values for two small β-sheet proteins, the PIN and the FBP WW domains. The native structure of these WW domains comprises two β-hairpins that form a three-stranded β-sheet. In our model, we assume that the transition state consists of two conformations in which either one of the hairpins is formed. Such a transition state has been recently observed in molecular dynamics folding-unfolding simulations of a small designed three-stranded β-sheet protein. We obtain good agreement with the experimental data 1), by splitting up the mutation-induced free-energy changes into terms for the two hairpins and for the small hydrophobic core of the proteins; and 2), by fitting a single parameter, the relative degree to which hairpins 1 and 2 are formed in the transition state. The model helps us to understand how mutations affect the folding kinetics of WW domains, and captures also negative Φ-values that have been difficult to interpret.     

Engineered Bi-Histidine Metal Chelation Sites Map the Structure of the Mechanical Unfolding Transition State of an Elastomeric Protein Domain GB1

Determining the structure of the transition state is critical for elucidating the mechanism behind how proteins fold and unfold. Due to its high free energy, however, the transition state generally cannot be trapped and studied directly using traditional structural biology methods. Thus, characterizing the structure of the transition state that occurs as proteins fold and unfold remains a major challenge. Here, we report a novel (to our knowledge) method that uses engineered bi-histidine (bi-His) metal-binding sites to directly map the structure of the mechanical unfolding transition state of proteins. This method is adapted from the traditional ψ-value analysis, which uses engineered bi-His metal chelation sites to probe chemical (un)folding transition-state structure. The ϕ^M2+_U-value is defined as ΔΔG_‡-N/ΔΔG_U-N, which is the energetic effects of metal chelation by the bi-His site on the unfolding energy barrier (ΔG_‡-N) relative to its thermodynamic stability (ΔG_U-N) and can be used to obtain information about the transition state in the mutational site. As a proof of principle, we used the small protein GB1 as a model system and set out to map its mechanical unfolding transition-state structure. Using single-molecule atomic force microscopy and spectrofluorimetry, we directly quantified the effect of divalent metal ion binding on the mechanical unfolding free energy and thermodynamic stability of GB1, which allowed us to quantify ϕ^M2+_U-values for different sites in GB1. Our results enabled us to map the structure of the mechanical unfolding transition state of GB1. Within GB1’s mechanical unfolding transition state, the interface between force-bearing β-strands 1 and 4 is largely disrupted, and the first β-hairpin is partially disordered while the second β-hairpin and the α-helix remain structured. Our results demonstrate the unique application of ψ-value analysis in elucidating the structure of the transition state that occurs during the mechanical unfolding process, offering a potentially powerful new method for investigating the design of novel elastomeric proteins.     

Statistical mechanical treatment of α-helices and extended structures in proteins with inclusion of short- and medium-range interactions

A statistical mechanical model of protein conformation with medium-range interactions between theith and (i+k)^th residues (k<-4) is presented. Two two-state models, an α-helix-coil and an extended-structure-coil model, are formulated using the same form of the partition function, but the two models are applied independently to predict the locations of α-helical, extended, and coil segments; in the relatively few cases (<2%) where the predictions from the two models are in conflict, the prediction is scored as an incorrect one. Two independent sets of statistical weights (one set for each model) are derived to describe the interactions between the 20 amino acid residues for each range of interactionk; they are evaluated by minimizing an objective function so that the probability profiles for the α-helix or extended structure, respectively, in proteins computed from these statistical weights correlate optimally with the experimentally observed native conformations of these proteins. Examination of the resulting statistical weights shows that those for the interactions between hydrophobic residues and between a hydrophobic and a hydrophilic residue have reasonable magnitudes compared to what would be expected from the spatial arrangements of the side chains in the α-helix and the extended structure, and that those for the α-helix-coil model correlate well with experimentally determined values of the Zimm-Bragg parameterss and σ of the helix-coil transition theory. From the point of view of a method to predict the conformational states (i.e., α-helix, extended structure, and coil) of each residue, the statistical weights (as inall empirical prediction schemes) depend very much on the proteins used for the data base, since the presently available set of proteins of known structure is still too small for very high predictability; as a result, the correctness of the prediction is not very good for proteins not included in the data base. However, the correctness of the prediction, at least for the 37 proteins utilized as the data base in this study, is 91% and 87% for the α-helix-coil and the extended-structure-coil models, respectively; further, 79% of all the residues are predicted correctly when both the α-helix-coil and extended-structure-coil models are applied independently.     

More than one way to spin a crystallite: multiple trajectories through liquid crystallinity to solid silk

Arthropods face several key challenges in processing concentrated feedstocks of proteins (silk dope) into solid, semi-crystalline silk fibres. Strikingly, independently evolved lineages of silk-producing organisms have converged on the use of liquid crystal intermediates (mesophases) to reduce the viscosity of silk dope and assist the formation of supramolecular structure. However, the exact nature of the liquid-crystal-forming-units (mesogens) in silk dope, and the relationship between liquid crystallinity, protein structure and silk processing is yet to be fully elucidated. In this review, we focus on emerging differences in this area between the canonical silks containing extended-β-sheets made by silkworms and spiders, and ‘non-canonical’ silks made by other insect taxa in which the final crystallites are coiled-coils, collagen helices or cross-β-sheets. We compared the amino acid sequences and processing of natural, regenerated and recombinant silk proteins, finding that canonical and non-canonical silk proteins show marked differences in length, architecture, amino acid content and protein folding. Canonical silk proteins are long, flexible in solution and amphipathic; these features allow them both to form large, micelle-like mesogens in solution, and to transition to a crystallite-containing form due to mechanical deformation near the liquid–solid transition. By contrast, non-canonical silk proteins are short and have rod or lath-like structures that are well suited to act both as mesogens and as crystallites without a major intervening phase transition. Given many non-canonical silk proteins can be produced at high yield in E. coli, and that mesophase formation is a versatile way to direct numerous kinds of supramolecular structure, further elucidation of the natural processing of non-canonical silk proteins may to lead to new developments in the production of advanced protein materials.     

Noninteracting local-structure model of folding and unfolding transition in globular proteins. I. Formulation

A statistical-mechanical model (a noninteracting local structure model) of folding and unfolding transition in globular proteins is described and a formulation is given to calculate the partition function. The process of transition is discussed in this model within the framework of equilibrium statistical mechanics. In order to clarify the range of applicability of such an approach, the characteristics of the folding and unfolding transition in globular proteins are analyzed from the statistical-physical point of view. A theoretical advantage is pointed out in studying folding and unfolding processes taking place as conformational fluctuations in individual protein molecules under macroscopic equilibrium at the melting temperature. In this case, paths of folding and unfolding are shown to be identical in the statistical sense. A key to the noninteracting local structure model lies in the concept of local structures and the assumption of the absence of interactions between local structures. A local structure is defined as a continuous section of the chain which takes the same or similar local conformation as in the native conformation. The assumption of the absence of inter-actions between local structures endows the model with the remarkable character that its partition function can be calculated exactly; thereby the equilibrium population of various conformations along the folding and unfolding paths can be discussed only by a knowledge of the folded native conformation.     

Effects of Topology and Sequence in Protein Folding Linked via Conformational Fluctuations

Experiments have compared the folding of proteins with different amino acid sequences but the same basic structure, or fold. Results indicate that folding is robust to sequence variations for proteins with some nonlocal folds, such as all-β, whereas the folding of more local, all-α proteins typically exhibits a stronger sequence dependence. Here, we use a coarse-grained model to systematically study how variations in sequence perturb the folding energy landscapes of three model sequences with 3α, 4β + α, and β-barrel folds, respectively. These three proteins exhibit folding features in line with experiments, including expected rank order in the cooperativity of the folding transition and stability-dependent shifts in the location of the free-energy barrier to folding. Using a generalized-ensemble simulation approach, we determine the thermodynamics of around 2000 sequence variants representing all possible hydrophobic or polar single- and double-point mutations. From an analysis of the subset of stability-neutral mutations, we find that folding is perturbed in a topology-dependent manner, with the β-barrel protein being the most robust. Our analysis shows, in particular, that the magnitude of mutational perturbations of the transition state is controlled in part by the size or “width” of the underlying conformational ensemble. This result suggests that the mutational robustness of the folding of the β-barrel protein is underpinned by its conformationally restricted transition state ensemble, revealing a link between sequence and topological effects in protein folding.     

Kinetic model of primary energy transfer and trapping in photosynthetic membranes

The picosecond time-domain incoherent singlet excitation transfer and trapping kinetics in core antenna of photosynthetic bacteria are studied in case of low excitation intensities by numerical integration of the appropriate master equation in a wide temperature range of 4-300 K. The essential features of our two-dimensional-lattice model are as follows: Förster excitation transfer theory, spectral heterogeneity of both the light-harvesting antenna and the reaction center, treatment of temperature effects through temperature dependence of spectral bands, inclusion of inner structure of the trap, and transition dipole moment orientation. The fluorescence kinetics is analyzed in terms of distributions of various kinetic components, and the influence of different inhomogeneities (orientational, spectral) is studied.

A reasonably good agreement between theoretical and experimental fluorescence decay kinetics for purple photosynthetic bacterium Rhodospirillum rubrum is achieved at high temperatures by assuming relatively large antenna spectral inhomogeneity: 20 nm at the whole bandwidth of 40 nm. The mean residence time in the antenna lattice site (it is assumed to be the aggregate of four bacteriochlorophyll a molecules bound to proteins) is estimated to be ~12 ps. At 4 K only qualitative agreement between model and experiment is gained. The failure of quantitative fitting is perhaps due to the lack of knowledge about the real structure of antenna or local heating and cooling effects not taken into account.

     

Rotation-Activated and Cooperative Zipping Characterize Class I Viral Fusion Protein Dynamics

Class I viral fusion proteins are α-helical proteins that facilitate membrane fusion between viral and host membranes through large conformational transitions. Although prefusion and postfusion crystal structures have been solved for many of these proteins, details about how they transition between these states have remained elusive. This work presents the first, to our knowledge, computational survey of transitions between pre- and postfusion configurations for several class I viral fusion proteins using structure-based models to analyze their dynamics. As suggested by their structural similarities, all proteins share common mechanistic features during their transitions that can be characterized by a diffusive rotational search followed by cooperative N- and C-terminal zipping. Instead of predicting a stable spring-loaded intermediate, our model suggests that helical bundle formation is mediated by N- and C-terminal interactions late in the transition. Shared transition features suggest a global mechanism in which fusion is activated by slow protein-core rotation.     

Two-intermediate model to characterize the structure of fast-folding proteins

This paper introduces a new model that enables researchers to conduct protein folding simulations. A two-step in silico process is used in the course of structural analysis of a set of fast-folding proteins. The model assumes an early stage (ES) that depends solely on the backbone conformation, as described by its geometrical properties—specifically, by the V-angle between two sequential peptide bond planes (which determines the radius of curvature, also called R-radius, according to a second-degree polynomial form). The agreement between the structure under consideration and the assumed model is measured in terms of the magnitude of dispersion of both parameters with respect to idealized values. The second step, called late-stage folding (LS), is based on the “fuzzy oil drop” model, which involves an external hydrophobic force field described by a three-dimensional Gauss function. The degree of conformance between the structure under consideration and its idealized model is expressed quantitatively by means of the Kullback-Leibler entropy, which is a measure of disparity between the observed and expected hydrophobicity distributions. A set of proteins, representative of the fast-folding group - specifically, cold shock proteins - is shown to agree with the proposed model.     

Computation and Functional Studies Provide a Model for the Structure of the Zinc Transporter hZIP4

Members of the Zrt and Irt protein (ZIP) family are a central participant in transition metal homeostasis as they function to increase the cytosolic concentration of zinc and/or iron. However, the lack of a crystal structure hinders elucidation of the molecular mechanism of ZIP proteins. Here, we employed GREMLIN, a co-evolution-based contact prediction approach in conjunction with the Rosetta structure prediction program to construct a structural model of the human (h) ZIP4 transporter. The predicted contact data are best fit by modeling hZIP4 as a dimer. Mutagenesis of residues that comprise a central putative hZIP4 transmembrane transition metal coordination site in the structural model alter the kinetics and specificity of hZIP4. Comparison of the hZIP4 dimer model to all known membrane protein structures identifies the 12-transmembrane monomeric Piriformospora indica phosphate transporter (PiPT), a member of the major facilitator superfamily (MFS), as a likely structural homolog.     

Energetics of MazG Unfolding in Correlation with Its Structural Features

MazG is a homodimeric α-helical protein that belongs to the superfamily of all-α NTP pyrophosphatases. Its function has been connected to the regulation of the toxin-antitoxin module mazEF, implicated in programmed growth arrest/cell death of Escherichia coli cells under conditions of amino acid starvation. The goal of the first detailed biophysical study of a member of the all-α NTP pyrophosphatase superfamily, presented here, is to improve molecular understanding of the unfolding of this type of proteins. Thermal unfolding of MazG monitored by differential scanning calorimetry, circular dichroism spectroscopy, and fluorimetry at neutral pH in the presence of a reducing agent (dithiothreitol) can be successfully described as a reversible four-state transition between a dimeric native state, two dimeric intermediate states, and a monomeric denatured state. The first intermediate state appears to have a structure similar to that of the native state while the final thermally denatured monomeric state is not fully unfolded and contains a significant fraction of residual α-helical structure. In the absence of dithiothreitol, disulfide cross-linking causes misfolding of MazG that appears to be responsible for the formation of multimeric aggregates. MazG is most stable at pH 7-8, while at pH < 6, it exists in a molten-globule-like state. The thermodynamic parameters characterizing each step of MazG denaturation transition obtained by global fitting of the four-state model to differential scanning calorimetry, circular dichroism, and fluorimetry temperature profiles are in agreement with the observed structural characteristics of the MazG conformational states and their assumed functional role.     

Toward resolution of ambiguity for the unfolded state

The unfolded states in proteins and nucleic acids remain weakly understood despite their importance in folding processes; misfolding diseases (Parkinson's and Alzheimer's); natively unfolded proteins (as many as 30% of eukaryotic proteins, according to Fink); and the study of ribozymes. Research has been hindered by the inability to quantify the residual (native) structure present in an unfolded protein or nucleic acid. Here, a scaling model is proposed to quantify the molar degree of folding and the unfolded state. The model takes a global view of protein structure and can be applied to a number of analytic methods and to simulations. Three examples are given of application to small-angle scattering from pressure-induced unfolding of SNase, from acid-unfolded cytochrome c, and from folding of Azoarcus ribozyme. These examples quantitatively show three characteristic unfolded states for proteins, the statistical nature of a protein folding pathway, and the relationship between extent of folding and chain size during folding for charge-driven folding in RNA.     

Crystal Structure of the Shrimp Proliferating Cell Nuclear Antigen: Structural Complementarity with WSSV DNA Polymerase PIP-Box

DNA replication requires processivity factors that allow replicative DNA polymerases to extend long stretches of DNA. Some DNA viruses encode their own replicative DNA polymerase, such as the white spot syndrome virus (WSSV) that infects decapod crustaceans but still require host replication accessory factors. We have determined by X-ray diffraction the three-dimensional structure of the Pacific white leg shrimp Litopenaeus vannamei Proliferating Cell Nuclear Antigen (LvPCNA). This protein is a member of the sliding clamp family of proteins, that binds DNA replication and DNA repair proteins through a motif called PIP-box (PCNA-Interacting Protein). The crystal structure of LvPCNA was refined to a resolution of 3 Å, and allowed us to determine the trimeric protein assembly and details of the interactions between PCNA and the DNA. To address the possible interaction between LvPCNA and the viral DNA polymerase, we docked a theoretical model of a PIP-box peptide from the WSSV DNA polymerase within LvPCNA crystal structure. The theoretical model depicts a feasible model of interaction between both proteins. The crystal structure of shrimp PCNA allows us to further understand the mechanisms of DNA replication processivity factors in non-model systems.     

Structural changes accompanying the irreversible oxidation of the chromatophore membrane from Rhodospirillum rubrum G9

The structure of the chromatophore membrane of the carotenoid-free mutant Rhodospirillum rubrum G9 and the effect of irreversible photooxidation upon this structure have been investigated using several physical techniques. Native chromatophore membranes undergo endothermic transitions in two temperature regions; at temperatures of about 0°C a broad reversible transition and between approx. 50 and 90°C several endothermic transitions are observed which are irreversible. The first transition can be assigned to the gel-to-liquid crystal transition of the lipid bilayer present in chromatophores; the irreversible one is attributed to changes mainly in the quarternary and possibily tertiary structure of membrane proteins. CD measurements showed that heating of chromatophores up to 70°C has no effect upon the protein secondary structure. Photooxidation has little effect on the structure and dynamics of the lipid bilayer in the chromatophore membrane. The order (or average conformation) of both the lipid polar groups and the hydrocarbon chains is hardly changed. However, the lipid phase transition is dramatically broadened and the protein-associated endothermic transitions are greatly reduced. This indicates that the major effect of photooxidation is upon lipid-protein and protein-protein interactions. Electron microscopy studies support this interpretation. It can be shown that the dense and regular packing of protein particles observed in the chromatophore membrane is lost as an effect of photooxidation. Instead, randomly distributed particles of varying size and shape are seen. These results are interpreted to mean that pigment-protein interactions are responsible for maintaining the native long-range order in the chromatophore membrane of R. rubrum G9. Destruction of the pigments by photooxidation leads to irreversible protein dissociation which in turn is followed probably by random protein reaggregation.     

Interactions between model proteins and deoxyribonucleic acids.

Interactions between DNA and model proteins, poly(L-Lys(m)L-Ala(n)), where m + n = 100%, have been investigated using thermal denaturation and circular dichroism (CD). All complexes of DNA with these proteins precipitate in a small range of input ratios, protein to DNA, with the midpoints of all precipitation curves close to a 1:1 ratio of lysine to phosphate. The melting temperature of model protein-bound DNA regions decreases slightly as the alanine content of the model protein is increased, which can be explained as a result of insufficient charge neutralization of phosphates by lysine residues in the model proteins. In the free state, these model proteins possess varying amounts of alpha helix, random coil, or a mixture of these two, depending upon the relative lysine/alanine content. When bound to DNA, the CD of the complex shows a substantial increase in alpha-helical structure for those model proteins with 40-60% alanine, while there is no significant change in alpha-helical structure when the percent alanine is either substantially higher or lower (i.e., 81 or 19% alanine). Only those complexes formed with model proteins having 40-60% alanine undergo a drastic transition from a B-type CD to an A-type in the presence of intermediate ionic strength (0.2 M NaCl, for example). Poly(Lys19Ala81)-DNA complexes show a slight transition toward A-type CD at 0.4 M NaCl or higher. Apparently other factors, in addition to alanine and alpha-helical content, must be responsible for this B leads to A transition. At the other extreme of lysine/alanine ratio, with high lysine content, poly(Lys81Ala19) or polylysine, the presence of NaCl produces a B leads to psi transition. The possible significance of these differences in response to the binding of these model proteins is discussed.     

Interaction of two intrinsically disordered plant stress proteins (COR15A and COR15B) with lipid membranes in the dry state

COR15A and COR15B form a tandem repeat of highly homologous genes in Arabidopsis thaliana. Both genes are highly cold induced and the encoded proteins belong to the Pfam LEA_4 group (group 3) of the late embryogenesis abundant (LEA) proteins. Both proteins were predicted to be intrinsically disordered in solution. Only COR15A has previously been characterized and it was shown to be localized in the soluble stroma fraction of chloroplasts. Ectopic expression of COR15A in Arabidopsis resulted in increased freezing tolerance of both chloroplasts after freezing and thawing of intact leaves and of isolated protoplasts frozen and thawed in vitro. In the present study we have generated recombinant mature COR15A and COR15B for a comparative study of their structure and possible function as membrane protectants. CD spectroscopy showed that both proteins are predominantly unstructured in solution and mainly α-helical after drying. Both proteins showed similar effects on the thermotropic phase behavior of dry liposomes. A decrease in the gel to liquid-crystalline phase transition temperature depended on both the unsaturation of the fatty acyl chains and lipid headgroup structure. FTIR spectroscopy indicated no strong interactions between the proteins and the lipid phosphate and carbonyl groups, but significant interactions with the galactose headgroup of the chloroplast lipid monogalactosyldiacylglycerol. These findings were rationalized by modeling the secondary structure of COR15A and COR15B. Helical wheel projection indicated the presence of amphipathic α-helices in both proteins. The helices lacked a clear separation of positive and negative charges on the hydrophilic face, but contained several hydroxylated amino acids.     

A thermodynamic model for the helix-coil transition coupled to dimerization of short coiled-coil peptides.

A simple thermodynamic formalism is presented to model the conformational transition between a random-coil monomeric peptide and a coiled-coil helical dimer. The coiled-coil helical dimer is the structure of a class of proteins also called leucine zipper, which has been studied intensively in recent years. Our model, which is appropriate particularly for short peptides, is an alternative to the theory developed by Skolnick and Holtzer. Using the present formalism, we discuss the multi-equilibriatory nature of this transition and provide an explanation for the apparent two-state behavior of coiled-coil formation when the helix-coil transition is coupled to dimerization. It is found that such coupling between multi-equilibria and a true two-state transition can simplify the data analysis, but care must be taken in using the overall association constant to determine helix propensities (w) of single residues. Successful use of the two-state model does not imply that the helix-coil transition is all-or-none. The all-or-none assumption can provide good numerical estimates when w is around unity (0.35 < or = w < or = 1.35), but when w is small (w < 0.01), similar estimations can lead to large errors. The theory of the helix-coil transition in denaturation experiments is also discussed.