Structural correspondence between the alpha-helix and the random-flight chain resolves how unfolded proteins can have native-like properties

Implications of the unfolded state in the folding energetics of heterogeneous-backbone protein mimetics

Sequence-encoded folding is the foundation of protein structure and is also possible in synthetic chains of artificial chemical composition. In natural proteins, the characteristics of the unfolded state are as important as those of the folded state in determining folding energetics. While much is known about folded structures adopted by artificial protein-like chains, corresponding information about the unfolded states of these molecules is lacking. Here, we report the consequences of altered backbone composition on the structure, stability, and dynamics of the folded and unfolded states of a compact helix-rich protein. Characterization through a combination of biophysical experiments and atomistic simulation reveals effects of backbone modification that depend on both the type of artificial monomers employed and where they are applied in sequence. In general, introducing artificial connectivity in a way that reinforces characteristics of the unfolded state ensemble of the prototype natural protein minimizes the impact of chemical changes on folded stability. These findings have implications in the design of protein mimetics and provide an atomically detailed picture of the unfolded state of a natural protein and artificial analogues under non-denaturing conditions.

Biophysical experiments and atomistic simulation reveal impacts of protein backbone alteration on the ensemble that defines the unfolded state. These effects have implications on folded stability of protein mimetics.

Uncovering the Conformational Distribution of a Small Protein with Nanoparticle-Aided Cryo-Electron Microscopy Sampling

Here, we introduce the nanoparticle-aided cryo-electron microscopy sampling (NACS) method to access the conformational distribution of a protein molecule. Two nanogold particles are labeled at two target sites, and the interparticle distance is measured as a structural parameter via cryo-electron microscopy (cryo-EM). The key aspect of NACS is that the projected distance information instead of the global conformational information is extracted from each protein molecule. This is possible because the contrast provided by the nanogold particles is strong enough to provide the projected distance, while the protein itself is invisible due to its low contrast. We successfully demonstrate that various protein conformations, even for small or disordered proteins, which generally cannot be accessed via cryo-EM, can be captured. The demonstrated method with the potential to directly observe the conformational distribution of such systems may open up new possibilities in studying their dynamics at a single-molecule level.

A relationship between the transient structure in the monomeric state and the aggregation propensities of α-synuclein and β-synuclein

α-Synuclein is an intrinsically disordered protein whose aggregation is implicated in Parkinson's disease. A second member of the synuclein family, β-synuclein, shares significant sequence similarity with α-synuclein but is much more resistant to aggregation. β-Synuclein is missing an 11-residue stretch in the central non-β-amyloid component region that forms the core of α-synuclein amyloid fibrils, yet insertion of these residues into β-synuclein to produce the βSHC construct does not markedly increase the aggregation propensity. To investigate the structural basis of these different behaviors, quantitative nuclear magnetic resonance data, in the form of paramagnetic relaxation enhancement-derived interatomic distances, are combined with molecular dynamics simulations to generate ensembles of structures representative of the solution states of α-synuclein, β-synuclein, and βSHC. Comparison of these ensembles reveals that the differing aggregation propensities of α-synuclein and β-synuclein are associated with differences in the degree of residual structure in the C-terminus coupled to the shorter separation between the N- and C-termini in β-synuclein and βSHC, making protective intramolecular contacts more likely.

The extent of pyrene excimer fluorescence emission is a reflector of distance and flexibility: analysis of the segment linking the LDL receptor-binding and tetramerization domains of apolipoprotein E3

Pyrene is a spatially sensitive probe that displays an ensemble of monomeric fluorescence emission peaks (375-405 nm) and an additional band (called excimer) at ~460 nm when two fluorophores are spatially proximal. We examined if there is a correlation between distance between two pyrenes on an α-helical structure and excimer/monomer (e/m) ratio. Using structure-guided design, pyrene maleimide was attached to pairs of Cys residues separated by ~5 Å increments on helix 2 of the N-terminal domain of apolipoprotein E3 (apoE3). Fluorescence spectral analysis revealed an intense excimer band when the probes were ~5 Å from each other with an e/m ratio of ~3.0, which decreased to ~1.0 at 20 Å. An inverse correlation between e/m ratio and the distance between pyrenes was observed, with the probe and helix flexibility also contributing to the extent of excimer formation. We verified this approach by estimating the distance between T57C and C112 (located on helices 2 and 3, respectively) to be 5.2 Å (4.9 Å from NMR and 5.7 Å from the X-ray structure). Excimer formation was also noted to a significant extent with probes located in the linker segment, suggesting spatial proximity (10-15 Å) to corresponding sites on neighboring molecules in the tetrameric configuration of apoE. We infer that oligomerization via the C-terminal domain juxtaposes the linker segments from neighboring apoE molecules. This study offers new insights into the conformation of tetrameric apoE and presents the use of pyrene as a powerful probe for studying protein spatial organization.

Universality in the timescales of internal loop formation in unfolded proteins and single-stranded oligonucleotides

Understanding the rate at which various parts of a molecular chain come together to facilitate the folding of a biopolymer (e.g., a protein or RNA) into its functional form remains an elusive goal. Here we use experiments, simulations, and theory to study the kinetics of internal loop closure in disordered biopolymers such as single-stranded oligonucleotides and unfolded proteins. We present theoretical arguments and computer simulation data to show that the relationship between the timescale of internal loop formation and the positions of the monomers enclosing the loop can be recast in a form of a universal master dependence. We also perform experimental measurements of the loop closure times of single-stranded oligonucleotides and show that both these and previously reported internal loop closure kinetics of unfolded proteins are well described by this theoretically predicted dependence. Finally, we propose that experimental deviations from the master dependence can then be used as a sensitive probe of dynamical and structural order in unfolded proteins and other biopolymers.

Kinetics and mechanism of the unfolding native-to-loop transition of Trp-cage in explicit solvent via optimized forward flux sampling simulations

The native-to-loop (N-L) unfolding transition of Trp-cage protein was studied via optimized forward flux sampling (FFS) methods with trajectories evolved using molecular dynamics. The rate constant calculated from our simulations is in good agreement with the experimental value for the native-to-unfolded transition of this protein; furthermore, the trajectories sampled a phase region consistent with that reported in previous studies for the N-L transition using transition path sampling and transition interface sampling. A new variant of FFS is proposed and implemented that allows a better control of a constant flux of partial paths. A reaction coordinate model was obtained, at no extra cost, from the transition path ensemble generated by FFS, through iterative use of the FFS-least-square estimation method [E. E. Borrero and F. A. Escobedo, J. Chem. Phys. 127, 164101 (2007)] and an adaptive staging optimization algorithm [E. E. Borrero and F. A. Escobedo, J. Chem. Phys. 129, 024115 (2008)]. Finally, we further elucidate the unfolding mechanism by correlating the unfolding progress with changes in the root mean square deviation from the α carbons of the native state, the root mean square deviation from an ideal α-helix, and other structural properties of the protein.

Determination of the free energy landscape of alpha-synuclein using spin label nuclear magnetic resonance measurements

Natively unfolded proteins present a challenge for structure determination because they populate highly heterogeneous ensembles of conformations. A useful source of structural information about these states is provided by paramagnetic relaxation enhancement measurements by nuclear magnetic resonance spectroscopy, from which long-range interatomic distances can be estimated. Here we describe a method for using such distances as restraints in molecular dynamics simulations to obtain a mapping of the free energy landscapes of natively unfolded proteins. We demonstrate the method in the case of alpha-synuclein and validate the results by a comparison with electron transfer measurements. Our findings indicate that our procedure provides an accurate estimate of the relative statistical weights of the different conformations populated by alpha-synuclein in its natively unfolded state.

Structural insights for designed alanine-rich helices: comparing NMR helicity measures and conformational ensembles from molecular dynamics simulation

The temperature dependence of helical propensities for the peptides Ac-ZGG-(KAAAA)(3)X-NH(2) (Z = Y or G, X = A, K, and D-Arg) were studied both experimentally and by MD simulations. Good agreement is observed in both the absolute helical propensities as well as relative helical content along the sequence; the global minimum on the calculated free energy landscape corresponds to a single alpha-helical conformation running from K4 to A18 with some terminal fraying, particularly at the C-terminus. Energy component analysis shows that the single helix state has favorable intramolecular electrostatic energy due to hydrogen bonds, and that less-favorable two-helix globular states have favorable solvation energy. The central lysine residues do not appear to increase helicity; however, both experimental and simulation studies show increasing helicity in the series X = Ala --> Lys --> D-Arg. This C-capping preference was also experimentally confirmed in Ac-(KAAAA)(3)X-GY-NH(2) and (KAAAA)(3)X-GY-NH(2) sequences. The roles of the C-capping groups, and of lysines throughout the sequence, in the MD-derived ensembles are analyzed in detail.

The low-pH unfolded state of the C-terminal domain of the ribosomal protein L9 contains significant secondary structure in the absence of denaturant but is no more compact than the low-pH urea unfolded state

There is considerable interest in the properties of the unfolded states of proteins, particularly unfolded states which can be populated in the absence of high concentrations of denaturants. Interest in the unfolded state ensemble reflects the fact that it is the starting point for protein folding as well as the reference state for protein stability studies and can be the starting state for pathological aggregation. The unfolded state of the C-terminal domain (residues 58-149) of the ribosomal protein L9 (CTL9) can be populated in the absence of denaturant at low pH. CTL9 is a 92-residue globular alpha, beta protein. The low-pH unfolded state contains more secondary structure than the low-pH urea unfolded state, but it is not a molten globule. Backbone ( (1)H, (13)C, and (15)N) NMR assignments as well as side chain (13)C beta and (1)H beta assignments and (15)N R 2 values were obtained for the pH 2.0 unfolded form of CTL9 and for the urea unfolded state at pH 2.5. Analysis of the deviations of the chemical shifts from random coil values indicates that residues that comprise the two helices in the native state show a clear preference for adopting helical phi and psi angles in the pH 2.0 unfolded state. There is a less pronounced but nevertheless clear tendency for residues 107-124 to preferentially populate helical phi and psi values in the unfolded state. The urea unfolded state has no detectable tendency to populate any type of secondary structure even though it is as compact as the pH 2.0 unfolded state. Comparison of the two unfolded forms of CTL9 provides direct experimental evidence that states which differ significantly in their secondary structure can have identical hydrodynamic properties. This in turn demonstrates that global parameters such as R h or R g are very poor indicators of "random coil" behavior.

Fluorescence characterization of denatured proteins

Characterization of unfolded states, while critical to a complete understanding of protein folding, is inherently difficult due to structural heterogeneity and dynamic interchange between states. The growing body of work focusing on single molecule fluorescence techniques for the study of protein folding, also highlights their potential for studies of unfolded proteins. These methods can obtain conformational information about individual subpopulations of molecules in an ensemble, and measure dynamics without the need for synchronization. The studies highlighted here demonstrate the promise of these techniques for obtaining novel information about unfolded states in vitro and in more physiologically relevant milieu.

Folding domain B of protein A on a dynamically partitioned free energy landscape

The B domain of staphylococcal protein A (BdpA) is a small helical protein that has been studied intensively in kinetics experiments and detailed computer simulations that include explicit water. The simulations indicate that BdpA needs to reorganize in crossing the transition barrier to facilitate folding its C-terminal helix (H3) onto the nucleus formed from helices H1 and H2. This process suggests frustration between two partially ordered forms of the protein, but recent varphi value measurements indicate that the transition structure is relatively constant over a broad range of temperatures. Here we develop a simplistic model to investigate the folding transition in which properties of the free energy landscape can be quantitatively compared with experimental data. The model is a continuation of the Muñoz-Eaton model to include the intermittency of contacts between structured parts of the protein, and the results compare variations in the landscape with denaturant and temperature to varphi value measurements and chevron plots of the kinetic rates. The topography of the model landscape (in particular, the feature of frustration) is consistent with detailed simulations even though variations in the varphi values are close to measured values. The transition barrier is smaller than indicated by the chevron data, but it agrees in order of magnitude with a similar alpha-carbon type of model. Discrepancies with the chevron plots are investigated from the point of view of solvent effects, and an approach is suggested to account for solvent participation in the model.

Residual structure, backbone dynamics, and interactions within the synuclein family

The human synuclein protein family includes alpha-synuclein, which has been linked to both familial and sporadic Parkinson's disease, and the highly homologous beta and gamma-synuclein. Mutations in alpha-synuclein cause autosomal dominant early onset Parkinson's, and the protein is found deposited in a fibrillar form in hereditary and idiopathic forms of the disease. No genetic link between beta and gamma-synuclein, and any neurodegenerative disease has been established, and it is generally considered that these proteins are not highly pathogenic. In addition, beta and gamma-synuclein are reported to aggregate less readily than alpha-synuclein in vitro. Indeed, beta-synuclein has been reported to protect against alpha-synuclein aggregation in vitro, as well as alpha-synuclein-mediated toxicity in vivo. Earlier, we compared the structural properties of the highly helical states adopted by all three synucleins in association with detergent micelles in an attempt to delineate the basis for functional differences between the three proteins. Here, we report a comparison of the structural and dynamic properties of the free states of all three proteins in order to shed light on differences that may help to explain their different propensities to aggregate, which in turn may underlie their differing contributions to the etiology of Parkinson's disease. We find that gamma-synuclein closely resembles alpha-synuclein in its free-state residual secondary structure, consistent with the more similar propensities of the two proteins to aggregate in vitro. beta-Synuclein, however, differs significantly from alpha-synuclein, exhibiting a lower predisposition towards helical structure in the second half of its lipid-binding domain, and a higher preference for extended structures in its C-terminal tail. Both beta and gamma-synuclein show less extensive transient long-range structure than that observed in alpha-synuclein. These results raise questions regarding the role of secondary structure propensities and transient long-range contacts in directing synuclein aggregation reactions.

Toward an accurate theoretical framework for describing ensembles for proteins under strongly denaturing conditions

Our focus is on an appropriate theoretical framework for describing highly denatured proteins. In high concentrations of denaturants, proteins behave like polymers in a good solvent and ensembles for denatured proteins can be modeled by ignoring all interactions except excluded volume (EV) effects. To assay conformational preferences of highly denatured proteins, we quantify a variety of properties for EV-limit ensembles of 23 two-state proteins. We find that modeled denatured proteins can be best described as follows. Average shapes are consistent with prolate ellipsoids. Ensembles are characterized by large correlated fluctuations. Sequence-specific conformational preferences are restricted to local length scales that span five to nine residues. Beyond local length scales, chain properties follow well-defined power laws that are expected for generic polymers in the EV limit. The average available volume is filled inefficiently, and cavities of all sizes are found within the interiors of denatured proteins. All properties characterized from simulated ensembles match predictions from rigorous field theories. We use our results to resolve between conflicting proposals for structure in ensembles for highly denatured states.

Foldamer simulations: novel computational methods and applications to poly-phenylacetylene oligomers

We apply several methods to probe the ensemble kinetic and structural properties of a model system of poly-phenylacetylene (pPA) oligomer folding trajectories. The kinetic methods employed included a brute force accounting of conformations, a Markovian state matrix method, and a nonlinear least squares fit to a minimalist kinetic model used to extract the folding time. Each method gave similar measures for the folding time of the 12-mer chain, calculated to be on the order of 7 ns for the complete folding of the chain from an extended conformation. Utilizing both a linear and a nonlinear scaling relationship between the viscosity and the folding time to correct for a low simulation viscosity, we obtain an upper and a lower bound for the approximate folding time within the range 70 ns<tau<350 ns. This is in agreement with the experimentally measured folding time on the order of 160 ns. The kinetic model used to fit the kinetic behavior of the ensemble of trajectories provides a framework to describe the bulk folding mechanism. We were able to identify two unique clusters of conformations that provide a structural basis to account for the appearance of a kinetic intermediate in the mechanism. We discuss the implications of these findings in the context of helix-coil theory.

Identification of the PXW sequence as a structural gatekeeper of the headpiece C-terminal subdomain fold

The HeadPiece (HP) domain, present in several F-actin-binding multi-domain proteins, features a well-conserved, solvent-exposed PXWK motif in its C-terminal subdomain. The latter is an autonomously folding subunit comprised of three alpha-helices organised around a hydrophobic core, with the sequence motif preceding the last helix. We report the contributions of each conserved residue in the PXWK motif to human villin HP function and structure, as well as the structural implications of the naturally occurring Pro to Ala mutation in dematin HP. NMR shift perturbation mapping reveals that substitution of each residue by Ala induces only minor, local perturbations in the full villin HP structure. CD spectroscopic thermal analysis, however, shows that the Pro and Trp residues in the PXWK motif afford stabilising interactions. This indicates that, in addition to the residues in the hydrophobic core, the Trp-Pro stacking within the motif contributes to HP stability. This is reinforced by our data on isolated C-terminal HP subdomains where the Pro is also essential for structure formation, since the villin, but not the dematin, C-terminal subdomain is structured. Proper folding can be induced in the dematin C-terminal subdomain by exchanging the Ala for Pro. Conversely, the reverse substitution in the villin C-terminal subdomain leads to loss of structure. Thus, we demonstrate a crucial role for this proline residue in structural stability and folding potential of HP (sub)domains consistent with Pro-Trp stacking as a more general determinant of protein stability.

Shaping up the protein folding funnel by local interaction: lesson from a structure prediction study

Predicting protein tertiary structure by folding-like simulations is one of the most stringent tests of how much we understand the principle of protein folding. Currently, the most successful method for folding-based structure prediction is the fragment assembly (FA) method. Here, we address why the FA method is so successful and its lesson for the folding problem. To do so, using the FA method, we designed a structure prediction test of "chimera proteins." In the chimera proteins, local structural preference is specific to the target sequences, whereas nonlocal interactions are only sequence-independent compaction forces. We find that these chimera proteins can find the native folds of the intact sequences with high probability indicating dominant roles of the local interactions. We further explore roles of local structural preference by exact calculation of the HP lattice model of proteins. From these results, we suggest principles of protein folding: For small proteins, compact structures that are fully compatible with local structural preference are few, one of which is the native fold. These local biases shape up the funnel-like energy landscape.

Polyproline II conformation is one of many local conformational states and is not an overall conformation of unfolded peptides and proteins

The alanine-based peptide Ac-XX(A)7OO-NH2, referred to as XAO (where X, A, and O denote diaminobutyric acid, alanine, and ornithine, respectively), has recently been proposed to possess a well defined polyproline II (P(II)) conformation at low temperatures. Based on the results of extensive NMR and CD investigations combined with theoretical calculations, reported here, we present evidence that, on the contrary, this peptide does not have any significant amount of organized P(II) structure but exists in an ensemble of conformations with a distorted bend in the N- and C-terminal regions. The conformational ensemble was obtained by molecular dynamics/simulated annealing calculations using the amber suite of programs with time-averaged distance and dihedral-angle restraints obtained from rotating-frame nuclear Overhauser effect (ROE) volumes and vicinal coupling constants 3J(HN Eta alpha), respectively. The computed ensemble-averaged radius of gyration Rg (7.4 +/- 1.0) A is in excellent agreement with that measured by small-angle x-ray scattering (SAXS) whereas, if the XAO peptide were in the P(II) conformation, Rg would be 11.6 A. Depending on the pH, peptide concentration, and temperature, the CD spectra of XAO do or do not possess the maximum with positive ellipticity in the 217-nm region, which is characteristic of the P(II) structure, reflecting a shifting conformational equilibrium rather than an all-or-none transition. The "P(II) conformation" should, therefore, be considered as one of the accessible conformational states of individual amino acid residues in peptides and proteins rather than as a structure of most of the chain in the early stage of folding.

Methionine oxidation of monomeric lambda repressor: the denatured state ensemble under nondenaturing conditions

Although poorly understood, the properties of the denatured state ensemble are critical to the thermodynamics and the kinetics of protein folding. The most relevant conformations to cellular protein folding are the ones populated under physiological conditions. To avoid the problem of low expression that is seen with unstable variants, we used methionine oxidation to destabilize monomeric lambda repressor and predominantly populate the denatured state under nondenaturing buffer conditions. The denatured ensemble populated under these conditions comprises conformations that are compact. Analytical ultracentrifugation sedimentation velocity experiments indicate a small increase in Stokes radius over that of the native state. A significant degree of alpha-helical structure in these conformations is detected by far-UV circular dichroism, and some tertiary interactions are suggested by near-UV circular dichroism. The characteristics of the denatured state populated by methionine oxidation in nondenaturing buffer are very different from those found in chemical denaturant.

Scaling approach to the folding kinetics of large proteins

We study a nucleation-growth model of protein folding and extend it to describe larger proteins with multiple folding units. The model is of one of an extremely simple type in which amino acids are allowed just two states--either folded (frozen) or unfolded. Its energetics are heterogeneous and Gō-like, the energy being defined in terms of the number of atom-to-atom contacts that would occur between frozen amino acids in the native crystal structure of the protein. Each collective state of the amino acids is intended to represent a small free energy microensemble consisting of the possible configurations of unfolded loops, open segments, and free ends constrained by the cross-links that form between folded parts of the molecule. We approximate protein free energy landscapes by an infinite subset of these microensemble topologies in which loops and open unfolded segments can be viewed roughly as independent objects for the purpose of calculating their entropy, and we develop a means to implement this approximation in Monte Carlo simulations. We show that this approach describes transition state structures (phi values) more accurately and identifies folding intermediates that were unavailable to previous versions of the model that restricted the number of loops and nuclei.

Protein oligomerization: how and why

A large fraction of cellular proteins are oligomeric. Protein oligomerization may often be an advantageous feature from the perspective of protein evolution and has probably evolved by a variety of mechanisms. The study of protein oligomerization may provide insights into the early protein environment and the evolution of modern proteins. Oligomeric mini-proteins, short peptides with discrete protein-like structures, may serve as valuable models for understanding features of protein oligomerization.

Characterizing the conformational ensemble of monomeric polyglutamine

Studies of synthetic polyglutamine peptides in vitro have established that polyglutamine peptides aggregate via a classic nucleation and growth mechanism. Chen and colleagues [Proc Natl Acad Sci U S A 2002;99:11884-11889] have found that monomeric polyglutamine, which is a disordered statistical coil in solution, is the critical nucleus for aggregation. Therefore, nucleation of beta-sheet-rich aggregates requires an initial disorder to order transition, which is a highly unfavorable thermodynamic reaction. The questions of interest to us are as follows: What are the statistical fluctuations that drive beta-sheet formation in monomeric polyglutamine? How do these fluctuations vary with chain length? And why is this process thermodynamically unfavorable, that is, why is monomeric polyglutamine disordered? To answer these questions we use multiple molecular dynamics simulations to provide quantitative characterization of conformational ensembles for two short polyglutamine peptides. We find that the ensemble for polyglutamine is indeed disordered. However, the disorder is inherently different from that of denatured proteins and the average compactness and magnitude of conformational fluctuations increase with chain length. Most importantly, the effective concentration of sidechain primary amides around backbone units is inherently high and peptide units are solvated either by hydrogen bonds to sidechains or surrounding water molecules. Due to the multiplicity of backbone solvation modes the probability associated with any specific backbone conformation is small, resulting in a conformational entropy bottleneck which makes beta-sheet formation in monomeric polyglutamine thermodynamically unfavorable.

How large is an alpha-helix? Studies of the radii of gyration of helical peptides by small-angle X-ray scattering and molecular dynamics

Using synchrotron radiation and the small-angle X-ray scattering technique we have measured the radii of gyration of a series of alanine-based alpha-helix-forming peptides of the composition Ace-(AAKAA)(n)-GY-NH(2), n=2-7, in aqueous solvent at 10(+/-1) degrees C. In contrast to other techniques typically used to study alpha-helices in isolation (such as nuclear magnetic resonance and circular dichroism), small-angle X-ray scattering reports on the global structure of a molecule and, as such, provides complementary information to these other, more sequence-local measuring techniques. The radii of gyration that we measure are, except for the 12-mer, lower than the radii of gyration of ideal alpha-helices or helices with frayed ends of the equivalent sequence-length. For example, the measured radius of gyration of the 37-mer is 14.2(+/-0.6)A, which is to be compared with the radius of gyration of an ideal 37-mer alpha-helix of 17.6A. Attempts are made to analyze the origin of this discrepancy in terms of the analytical Zimm-Bragg-Nagai (ZBN) theory, as well as distributed computing explicit solvent molecular dynamics simulations using two variants of the AMBER force-field. The ZBN theory, which treats helices as cylinders connected by random walk segments, predicts markedly larger radii of gyration than those measured. This is true even when the persistence length of the random walk parts is taken to be extremely short (about one residue). Similarly, the molecular dynamics simulations, at the level of sampling available to us, give inaccurate values of the radii of gyration of the molecules (by overestimating them by around 25% for longer peptides) and/or their helical content. We conclude that even at the short sequences examined here (< or =37 amino acid residues), these alpha-helical peptides behave as fluctuating semi-broken rods rather than straight cylinders with frayed ends.

Unusual compactness of a polyproline type II structure

Polyproline type II (PPII) helix has emerged recently as the dominant paradigm for describing the conformation of unfolded polypeptides. However, most experimental observables used to characterize unfolded proteins typically provide only short-range, sequence-local structural information that is both time- and ensemble-averaged, giving limited detail about the long-range structure of the chain. Here, we report a study of a long-range property: the radius of gyration of an alanine-based peptide, Ace-(diaminobutyric acid)2-(Ala)7-(ornithine)2-NH2. This molecule has previously been studied as a model for the unfolded state of proteins under folding conditions and is believed to adopt a PPII fold based on short-range techniques such as NMR and CD. By using synchrotron radiation and small-angle x-ray scattering, we have determined the radius of gyration of this peptide to be 7.4 +/- 0.5 angstroms, which is significantly less than the value expected from an ideal PPII helix in solution (13.1 angstroms). To further study this contradiction, we have used molecular dynamics simulations using six variants of the AMBER force field and the GROMOS 53A6 force field. However, in all cases, the simulated ensembles underestimate the PPII content while overestimating the experimental radius of gyration. The conformational model that we propose, based on our small angle x-ray scattering results and what is known about this molecule from before, is that of a very flexible, fluctuating structure that on the level of individual residues explores a wide basin around the ideal PPII geometry but is never, or only rarely, in the ideal extended PPII helical conformation.

Design of a heterospecific, tetrameric, 21-residue miniprotein with mixed alpha/beta structure

The study of short, autonomously folding peptides, or "miniproteins," is important for advancing our understanding of protein stability and folding specificity. Although many examples of synthetic alpha-helical structures are known, relatively few mixed alpha/beta structures have been successfully designed. Only one mixed-secondary structure oligomer, an alpha/beta homotetramer, has been reported thus far. In this report, we use structural analysis and computational design to convert this homotetramer into the smallest known alpha/beta-heterotetramer. Computational screening of many possible sequence/structure combinations led efficiently to the design of short, 21-residue peptides that fold cooperatively and autonomously into a specific complex in solution. A 1.95 A crystal structure reveals how steric complementarity and charge patterning encode heterospecificity. The first- and second-generation heterotetrameric miniproteins described here will be useful as simple models for the analysis of protein-protein interaction specificity and as structural platforms for the further elaboration of folding and function.

How does averaging affect protein structure comparison on the ensemble level?

Recent algorithmic advances and continual increase in computational power have made it possible to simulate protein folding and dynamics on the level of ensembles. Furthermore, analyzing protein structure by using ensemble representation is intrinsic to certain experimental techniques, such as nuclear magnetic resonance. This creates a problem of how to compare an ensemble of molecules with a given reference structure. Recently, we used distance-based root-mean-square deviation (dRMS) to compare the native structure of a protein with its unfolded-state ensemble. We showed that for small, mostly alpha-helical proteins, the mean unfolded-state Calpha-Calpha distance matrix is significantly more nativelike than the Calpha-Calpha matrices corresponding to the individual members of the unfolded ensemble. Here, we give a mathematical derivation that shows that, for any ensemble of structures, the dRMS deviation between the ensemble-averaged distance matrix and any given reference distance matrix is always less than or equal to the average dRMS deviation of the individual members of the ensemble from the same reference matrix. This holds regardless of the nature of the reference structure or the structural ensemble in question. In other words, averaging of distance matrices can only increase their level of similarity to a given reference matrix, relative to the individual matrices comprising the ensemble. Furthermore, we show that the above inequality holds in the case of Cartesian coordinate-based root-mean-square deviation as well. We discuss this in the context of our proposal that the average structure of the unfolded ensemble of small helical proteins is close to the native structure, and demonstrate that this finding goes beyond the above mathematical fact.

Unassisted refolding of urea-denatured arginine kinase from shrimp Feneropenaeus chinensis: evidence for two equilibrium intermediates in the refolding pathway

The refolding process and the equilibrium intermediates of urea-denatured arginine kinase (AK) were investigated by 1-anilino-8-naphthalenesulfonate (ANS) intrinsic fluorescence, far-UV circular dichroism (CD), size-exclusion chromatography (SEC), and enzymatic activity. In dilute denaturant, two equilibrium refolding intermediates (I and N') were discovered, and a refolding scheme of urea-denatured AK was proposed. During the refolding of urea-denatured AK, the fluorescence intensity increased remarkably, accompanied by a significant blue shift of the emission maximum and a pronounced increase in molar ellipticity of CD at 222 nm. The first folding intermediate (I) was inactive in urea solution ranging between 2.4 and 3.0 M. The second (N') existed between a 0.4- and 0.8-M urea solution, with slightly increased activity. Neither the blue shift emission maximum nor the molar ellipticity of CD at 222 nm showed significant changes in these two regions. The two intermediates were characterized by monitoring the ANS binding ability in various residual urea solutions, and two peaks of the emission intensity were observed in urea solutions of 0.6 and 2.8 M, respectively. The SEC results indicated that a distribution coefficient (K(D)) platform existed in urea solutions ranging between 2.4 and 3.0 M urea, suggesting that there was a similarly apparent protein profile and size in the urea solution region. The refolding kinetics showed that the urea-denatured AK was in two-phase refolding. Proline isomerization occurred in the unfolding process of AK, which blocked the slow phase of refolding. These results suggested that the refolding process of urea-denatured AK contained at the least two equilibrium refolding intermediates.

Exploring the helix-coil transition via all-atom equilibrium ensemble simulations

The ensemble folding of two 21-residue alpha-helical peptides has been studied using all-atom simulations under several variants of the AMBER potential in explicit solvent using a global distributed computing network. Our extensive sampling, orders of magnitude greater than the experimental folding time, results in complete convergence to ensemble equilibrium. This allows for a quantitative assessment of these potentials, including a new variant of the AMBER-99 force field, denoted AMBER-99 phi, which shows improved agreement with experimental kinetic and thermodynamic measurements. From bulk analysis of the simulated AMBER-99 phi equilibrium, we find that the folding landscape is pseudo-two-state, with complexity arising from the broad, shallow character of the "native" and "unfolded" regions of the phase space. Each of these macrostates allows for configurational diffusion among a diverse ensemble of conformational microstates with greatly varying helical content and molecular size. Indeed, the observed structural dynamics are better represented as a conformational diffusion than as a simple exponential process, and equilibrium transition rates spanning several orders of magnitude are reported. After multiple nucleation steps, on average, helix formation proceeds via a kinetic "alignment" phase in which two or more short, low-entropy helical segments form a more ideal, single-helix structure.

Native and nonnative conformational preferences in the urea-unfolded state of barstar

The refolding of barstar from its urea-unfolded state has been studied extensively using various spectroscopic probes and real-time NMR, which provide global and residue-specific information, respectively, about the folding process. Here, a preliminary structural characterization by NMR of barstar in 8 M urea has been carried out at pH 6.5 and 25 degrees C. Complete backbone resonance assignments of the urea-unfolded protein were obtained using the recently developed three-dimensional NMR techniques of HNN and HN(C)N. The conformational propensities of the polypeptide backbone in the presence of 8 M urea have been estimated by examining deviations of secondary chemical shifts from random coil values. For some residues that belong to helices in native barstar, 13C(alpha) and 13CO secondary shifts show positive deviations in the urea-unfolded state, indicating that these residues have propensities toward helical conformations. These residues are, however, juxtaposed by residues that display negative deviations indicative of propensities toward extended conformations. Thus, segments that are helical in native barstar are unlikely to preferentially populate the helical conformation in the unfolded state. Similarly, residues belonging to beta-strands 1 and 2 of native barstar do not appear to show any conformational preferences in the unfolded state. On the other hand, residues belonging to the beta-strand 3 segment show weak nonnative helical conformational preferences in the unfolded state, indicating that this segment may possess a weak preference for populating a helical conformation in the unfolded state.

Efficient expansion, folding, and unfolding of proteins

We consider a nonstatistical, computationally fast experiment to identify important topological constraints in folding small globular proteins of about 100-200 amino acids. In this experiment, proteins are expanded mechanically along a path of steepest increase in the free space around residues. The pathways are often consistent with folding scenarios reported in kinetics experiments and most accurately describe obligatory or mechanic folding proteins. The results suggest that certain topological "defects" in proteins lead to preferred, entropically favorable channels down their free energy landscapes.

Trp zipper folding kinetics by molecular dynamics and temperature-jump spectroscopy

We studied the microsecond folding dynamics of three beta hairpins (Trp zippers 1-3, TZ1-TZ3) by using temperature-jump fluorescence and atomistic molecular dynamics in implicit solvent. In addition, we studied TZ2 by using time-resolved IR spectroscopy. By using distributed computing, we obtained an aggregate simulation time of 22 ms. The simulations included 150, 212, and 48 folding events at room temperature for TZ1, TZ2, and TZ3, respectively. The all-atom optimized potentials for liquid simulations (OPLS(aa)) potential set predicted TZ1 and TZ2 properties well; the estimated folding rates agreed with the experimentally determined folding rates and native conformations were the global potential-energy minimum. The simulations also predicted reasonable unfolding activation enthalpies. This work, directly comparing large simulated folding ensembles with multiple spectroscopic probes, revealed both the surprising predictive ability of current models as well as their shortcomings. Specifically, for TZ1-TZ3, OPLS for united atom models had a nonnative free-energy minimum, and the folding rate for OPLS(aa) TZ3 was sensitive to the initial conformation. Finally, we characterized the transition state; all TZs fold by means of similar, native-like transition-state conformations.