Membrane adsorption,folding, insertion and translocation of synthetic trans-membrane peptides

Spontaneous membrane adsorption, folding and insertion of the synthetic WALP16 and KALP16 peptides was studied by computer simulations starting from completely extended conformations. The peptides were simulated using an unmodified all-atom force field in combination with an efficient Monte Carlo sampling algorithm. The membrane is represented implicitly as a hydrophobic zone inside a continuum solvent modelled using the generalized Born theory of solvation. The method was previously parameterized to match insertion energies of hydrophobic side chain analogs into cyclohexane and no parameters were optimized for the present simulations. Both peptides rapidly precipitate out of bulk solution and adsorb to the membrane surface. Interfacial folding into a helical conformation is followed by membrane insertion. Both the peptide conformations and their location in the membrane are strongly temperature dependent. The temperature dependent behaviour can be summarized by fitting to a four-state model, separating the system into folded and unfolded conformers, which are either inserted into the membrane or located at the interfaces. As the temperature is lowered the dominant peptide conformation of the system changes from unfolded surface bound configurations to folded surface bound states. Folded trans-membrane conformers represent the dominant configuration at low temperatures. The analysis allows direct estimates of the free energies of peptide folding and membrane insertion. In the case of WALP the quality of the fit is excellent and the thermodynamic behaviour is in good agreement with expected theoretical consideration. For KALP the fit is more problematic due to the large solvation energies of the charged lysine residues.     

On the accuracy of metadynamics and its variations in a protein folding process

Metadynamics and its variations are powerful tools for exploring the free energy landscape of physical, chemical and biophysical systems. However, previous tests of their accuracy were based on either low-dimensional systems or complicated systems without exact answers. Therefore their accuracy, particularly when used for high-dimensional biophysical systems, has not been rigorously tested. In this work we performed a series of simulations with metadynamics and its variations for a typical biophysical process – the folding of protein chymotrypsin inhibitor 2 (CI2) based on a coarse-grained structure-based model. The results revealed the power as well as limitations of the algorithms and provided some guidelines for using metadynamics and its variations in high-dimensional biological systems.     

Predicting repeat protein folding kinetics from an experimentally determined folding energy landscape

The Notch ankyrin domain is a repeat protein whose folding has been characterized through equilibrium and kinetic measurements. In previous work, equilibrium folding free energies of truncated constructs were used to generate an experimentally determined folding energy landscape (Mello and Barrick, Proc Natl Acad Sci USA 2004;101:14102–14107). Here, this folding energy landscape is used to parameterize a kinetic model in which local transition probabilities between partly folded states are based on energy values from the landscape. The landscape‐based model correctly predicts highly diverse experimentally determined folding kinetics of the Notch ankyrin domain and sequence variants. These predictions include monophasic folding and biphasic unfolding, curvature in the unfolding limb of the chevron plot, population of a transient unfolding intermediate, relative folding rates of 19 variants spanning three orders of magnitude, and a change in the folding pathway that results from C‐terminal stabilization. These findings indicate that the folding pathway(s) of the Notch ankyrin domain are thermodynamically selected: the primary determinants of kinetic behavior can be simply deduced from the local stability of individual repeats.     

Apparent local stability of the secondary structure of Azotobacter vinelandii holoflavodoxin II as probed by hydrogen exchange: implications for redox potential regulation and flavodoxin folding.

As a first step to determine the folding pathway of a protein with an alpha/beta doubly wound topology, the 1H, 13C, and 15N backbone chemical shifts of Azotobacter vinelandii holoflavodoxin II (179 residues) have been determined using multidimensional NMR spectroscopy. Its secondary structure is shown to contain a five-stranded parallel beta-sheet (beta2-beta1-beta3-beta4-beta5) and five alpha-helices. Exchange rates for the individual amide protons of holoflavodoxin were determined using the hydrogen exchange method. The amide protons of 65 residues distributed throughout the structure of holoflavodoxin exchange slowly at pH* 6.2 [kex < 10(-5) s(-1)] and can be used as probes in future folding studies. Measured exchange rates relate to apparent local free energies for transient opening. We propose that the amide protons in the core of holoflavodoxin only exchange by global unfolding of the apo state of the protein. The results obtained are discussed with respect to their implications for flavodoxin folding and for modulation of the flavin redox potential by the apoprotein. We do not find any evidence that A. vinelandii holoflavodoxin II is divided into two subdomains based on its amide proton exchange rates, as opposed to what is found for the structurally but not sequentially homologous alpha/beta doubly wound protein Che Y.     

Nucleation‐based prediction of the protein folding rate and its correlation with the folding nucleus size

The problem of protein self‐organization is in the focus of current molecular biology studies. Although the general principles are understood, many details remain unclear. Specifically, protein folding rates are of interest because they dictate the rate of protein aggregation which underlies many human diseases. Here we offer predictions of protein folding rates and their correlation with folding nucleus sizes. We calculated free energies of the transition state and sizes of folding nuclei for 84 proteins and peptides whose other parameters were measured at the point of thermodynamic equilibrium between their unfolded and native states. We used the dynamic programming method where each residue was considered to be either as folded as in its native state or completely disordered. The calculated and measured folding rates showed a good correlation at the temperature mid‐transition point (the correlation coefficient was 0.75). Also, we pioneered in demonstrating a moderate (‐0.57) correlation coefficient between the calculated sizes of folding nuclei and the folding rates. Predictions made by different methods were compared. The established good correlation between the estimated free energy barrier and the experimentally found folding rate of each studied protein/peptide indicates that our model gives reliable results for the considered data set. Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Consistency in structural energetics of protein folding and peptide recognition.

We report a new free energy decomposition that includes structure-derived atomic contact energies for the desolvation component, and show that it applies equally well to the analysis of single-domain protein folding and to the binding of flexible peptides to proteins. Specifically, we selected the 17 single-domain proteins for which the three-dimensional structures and thermodynamic unfolding free energies are available. By calculating all terms except the backbone conformational entropy change and comparing the result to the experimentally measured free energy, we estimated that the mean entropy gain by the backbone chain upon unfolding (delta Sbb) is 5.3 cal/K per mole of residue, and that the average backbone entropy for glycine is 6.7 cal/K. Both numbers are in close agreement with recent estimates made by entirely different methods, suggesting a promising degree of consistency between data obtained from disparate sources. In addition, a quantitative analysis of the folding free energy indicates that the unfavorable backbone entropy for each of the proteins is balanced predominantly by favorable backbone interactions. Finally, because the binding of flexible peptides to receptors is physically similar to folding, the free energy function should, in principle, be equally applicable to flexible docking. By combining atomic contact energies, electrostatics, and sequence-dependent backbone entropy, we calculated a priori the free energy changes associated with the binding of four different peptides to HLA-A2, 1 MHC molecule and found agreement with experiment to within 10% without parameter adjustment.     

Protein folding and association: insights from the interfacial and thermodynamic properties of hydrocarbons.

We demonstrate in this work that the surface tension, water-organic solvent, transfer-free energies and the thermodynamics of melting of linear alkanes provide fundamental insights into the nonpolar driving forces for protein folding and protein binding reactions. We first develop a model for the curvature dependence of the hydrophobic effect and find that the macroscopic concept of interfacial free energy is applicable at the molecular level. Application of a well-known relationship involving surface tension and adhesion energies reveals that dispersion forces play little or no net role in hydrophobic interactions; rather, the standard model of disruption of water structure (entropically driven at 25 degrees C) is correct. The hydrophobic interaction is found, in agreement with the classical picture, to provide a major driving force for protein folding. Analysis of the melting behavior of hydrocarbons reveals that close packing of the protein interior makes only a small free energy contribution to folding because the enthalpic gain resulting from increased dispersion interactions (relative to the liquid) is countered by the freezing of side chain motion. The identical effect should occur in association reactions, which may provide an enormous simplification in the evaluation of binding energies. Protein binding reactions, even between nearly planar or concave/convex interfaces, are found to have effective hydrophobicities considerably smaller than the prediction based on macroscopic surface tension. This is due to the formation of a concave collar region that usually accompanies complex formation. This effect may preclude the formation of complexes between convex surfaces.     

Mechanisms of protein folding

The strong correlation between protein folding rates and the contact order suggests that folding rates are largely determined by the topology of the native structure. However, for a given topology, there may be several possible low free energy paths to the native state and the path that is chosen (the lowest free energy path) may depend on differences in interaction energies and local free energies of ordering in different parts of the structure. For larger proteins whose folding is assisted by chaperones, such as the Escherichia coli chaperonin GroEL, advances have been made in understanding both the aspects of an unfolded protein that GroEL recognizes and the mode of binding to the chaperonin. The possibility that GroEL can remove non-native proteins from kinetic traps by unfolding them either during polypeptide binding to the chaperonin or during the subsequent ATP-dependent formation of folding-active complexes with the co-chaperonin GroES has also been explored.     

A collection of programs for one‐dimensional Ising analysis of linear repeat proteins with point substitutions

A collection of programs is presented to analyze the thermodynamics of folding of linear repeat proteins using a 1D Ising model to determine intrinsic folding and interfacial coupling free energies. Expressions for folding transitions are generated for a series of constructs with different repeat numbers and are globally fitted to transitions for these constructs. These programs are designed to analyze Ising parameters for capped homopolymeric consensus repeat constructs as well as heteropolymeric constructs that contain point substitutions, providing a rigorous framework for analysis of the effects of mutation on intrinsic and directional (i.e., N‐ vs. C‐terminal) interfacial coupling free‐energies. A bootstrap analysis is provided to estimate parameter uncertainty as well as correlations among fitted parameters. Rigorous statistical analysis is essential for interpreting fits using the complex models required for Ising analysis of repeat proteins, especially heteropolymeric repeat proteins. Programs described here are available at https://github.com/barricklab-at-jhu/Ising_programs .     

Association energetics of membrane spanning alpha-helices

Since Popot and Engelman proposed the 'two-stage' thermodynamic framework for dissecting the energetics of helical membrane protein folding, scientists have endeavored to measure the free energies of helix-helix associations to better understand how interactions between helices stabilize and specify native membrane protein folds. Chief among the biophysical tools used to probe these energies are sedimentation equilibrium analytical ultracentrifugation, fluorescence resonance energy transfer, and thiol disulfide interchange experiments. Direct and indirect comparisons of thermodynamic results suggest that differences in helix-helix stabilities between micelles and bilayers may not be as large as previously anticipated. Genetic approaches continue to become more quantitative, and the propensities for helices to interact in bacterial membranes generally correlate well with in vitro measurements.     

Using DNA mechanics to predict in vitro nucleosome positions and formation energies

In eukaryotic genomes, nucleosomes function to compact DNA and to regulate access to it both by simple physical occlusion and by providing the substrate for numerous covalent epigenetic tags. While competition with other DNA-binding factors and action of chromatin remodeling enzymes significantly affect nucleosome formation in vivo, nucleosome positions in vitro are determined by steric exclusion and sequence alone. We have developed a biophysical model, DNABEND, for the sequence dependence of DNA bending energies, and validated it against a collection of in vitro free energies of nucleosome formation and a set of in vitro nucleosome positions mapped at high resolution. We have also made a first ab initio prediction of nucleosomal DNA geometries, and checked its accuracy against the nucleosome crystal structure. We have used DNABEND to design both strong and weak histone- binding sequences, and measured the corresponding free energies of nucleosome formation. We find that DNABEND can successfully predict in vitro nucleosome positions and free energies, providing a physical explanation for the intrinsic sequence dependence of histone–DNA interactions.     

The major outer membrane protein of Fusobacterium nucleatum (FomA) folds and inserts into lipid bilayers via parallel folding pathways

Membrane protein insertion and folding was studied for the major outer membrane protein of Fusobacterium nucleatum (FomA), which is a voltage-dependent general diffusion porin. The transmembrane domain of FomA forms a beta-barrel that is predicted to consist of 14 beta-strands. Here, unfolded FomA is shown to insert and fold spontaneously and quantitatively into phospholipid bilayers upon dilution of the denaturant urea, which was shown previously only for outer membrane protein A (OmpA) of Escherichia coli. Folding of FomA is demonstrated by circular dichroism and fluorescence spectroscopy, by SDS-polyacrylamide gel electrophoresis, and by single-channel recordings. Refolded FomA had a single-channel conductance of 1.1 nS at 1 M KCl, in agreement with the conductance of FomA isolated from membranes in native form. In contrast to OmpA, which forms a smaller eight-stranded beta-barrel domain, folding kinetics of the larger FomA were slower and provided evidence for parallel folding pathways of FomA into lipid bilayers. Two pathways were observed independent of membrane thickness with two different lipid bilayers, which were either composed of dicapryl phosphatidylcholine or dioleoyl phosphatidylcholine. This is the first observation of parallel membrane insertion and folding pathways of a beta-barrel membrane protein from an unfolded state in urea into lipid bilayers. The kinetics of both folding pathways depended on the chain length of the lipid and on temperature with estimated activation energies of 19 kJ/mol (dicapryl phosphatidylcholine) and 70 kJ/mol (dioleoyl phosphatidylcholine) for the faster pathways.     

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.     

Comparison of fragments comprising the first two helices of the human y4 and the yeast ste2p g-protein-coupled receptors

Solution NMR techniques are used to determine the structure and the topology of micelle integration of a large fragment of the Y4 receptor, a human G-protein-coupled receptor, that contains the entire N-terminal domain plus the first two transmembrane (TM) segments. The structure calculations reveal that the putative TM helices are indeed helical to a large extent, but that interruptions of secondary structure occur close to internal polar or charged residues. This view is supported by ¹⁵N relaxation data, amide-water exchange rates, and attenuations from micelle-integrating spin labels. No contacts between different helices are observed. This is in contrast to a similar TM1-TM2 fragment from the yeast Ste2p receptor for which locations of the secondary and the tertiary structure agreed well with the predictions from a homology model. The difference in structure is discussed in terms of principal biophysical properties of residues within central regions of the putative TM helices. Overall, using the biophysical scale of Wimley and White the TM regions of Ste2p display much more favorable free energies for membrane integration. Accordingly, the full secondary structure and the tertiary structure in TM1-TM2 of the Y4 receptor is likely to be formed only when tertiary contacts with other TM segments are created during folding of the receptor.     

Optimal combination of theory and experiment for the characterization of the protein folding landscape of S6: how far can a minimalist model go?

The detailed characterization of the overall free energy landscape associated with the folding process of a protein is the ultimate goal in protein folding studies. Modern experimental techniques provide accurate thermodynamic and kinetic measurements on restricted regions of a protein landscape. Although simplified protein models can access larger regions of the landscape, they are oftentimes built on assumptions and approximations that affect the accuracy of the results. We present a new methodology that allows to combine the complementary strengths of theory and experiment for a more complete characterization of a protein folding landscape. We prove that this new procedure allows a simplified protein model to reproduce remarkably well (correlation coefficient > 0.9) all experimental data available on free energies differences upon single mutations for S6 ribosomal protein and two circular permutants. Our results confirm and quantify the hypothesis, recently formulated on the basis of experimental data, that the folding landscape of protein S6 is strongly affected by an atypical distribution of contact energies.     

Simple physical models connect theory and experiment in protein folding kinetics

Our understanding of the principles underlying the protein-folding problem can be tested by developing and characterizing simple models that make predictions which can be compared to experimental data. Here we extend our earlier model of folding free energy landscapes, in which each residue is considered to be either folded as in the native state or completely disordered, by investigating the role of additional factors representing hydrogen bonding and backbone torsion strain, and by using a hybrid between the master equation approach and the simple transition state theory to evaluate kinetics near the free energy barrier in greater detail. Model calculations of folding phi-values are compared to experimental data for 19 proteins, and for more than half of these, experimental data are reproduced with correlation coefficients between r=0.41 and 0.88; calculations of transition state free energy barriers correlate with rates measured for 37 single domain proteins (r=0.69). The model provides insight into the contribution of alternative-folding pathways, the validity of quasi-equilibrium treatments of the folding landscape, and the magnitude of the Arrhenius prefactor for protein folding. Finally, we discuss the limitations of simple native-state-based models, and as a more general test of such models, provide predictions of folding rates and mechanisms for a comprehensive set of over 400 small protein domains of known structure.