Folding of elongated proteins: conventional or anomalous?

The complexity of the mechanisms by which proteins fold has been shown by many studies to be governed by their native-state topologies. This was manifested in the ability of the native topology-based model to capture folding mechanisms and the success of folding rate predictions based on various topological measures, such as the contact order. However, while the finer details of topological complexity have been thoroughly examined and related to folding kinetics, simpler characteristics of the protein, such as its overall shape, have been largely disregarded. In this study, we investigated the folding of proteins with an unusual elongated geometry that differs substantially from the common globular structure. To study the effect of the elongation degree on the folding kinetics, we used repeat proteins, which become more elongated as they include more repeating units. Some of these have apparently anomalous experimental folding kinetics, with rates that are often less than expected on the basis of rates for globular proteins possessing similar topological complexity. Using experimental folding rates and a larger set of rates obtained from simulations, we have shown that as the protein becomes increasingly elongated, its folding kinetics becomes slower and deviates more from the rate expected on the basis of topology measures fitted for globular proteins. The observed slow kinetics is a result of a more complex pathway in which stable intermediates composed of several consecutive repeats can appear. We thus propose a novel measure, an elongation-sensitive contact order, that takes into account both the extent of elongation and the topological complexity of the protein. This new measure resolves the apparent discrimination between the folding of globular and elongated repeat proteins. Our study extends the current capabilities of folding-rate predictions by unifying the kinetics of repeat and globular proteins.     

Secondary structures of peptides and proteins via NMR chemical-shielding anisotropy (CSA) parameters

Complete nuclear magnetic resonance (NMR) chemical-shielding tensors, sigma, have been computed at different levels of density-functional theory (DFT), within the gauge-including atomic orbital (GIAO) formalism, for the atoms of the peptide model For-L-Ala-NH2 as a function of the backbone dihedral angles phi and psi by employing a dense grid of 10 degrees. A complete set of rigorously orthogonal symmetric tensor invariants, {sigma iso, rho, tau}, is introduced, where sigma iso is the usual isotropic chemical shielding, while the newly introduced rho and tau parameters describe the magnitude and the orientation/shape of the chemical-shielding anisotropy (CSA), respectively. The set {sigma iso, rho, tau} is unaffected by unitary transformations of the symmetric part of the shielding tensor. The mathematically and physically motivated {rho, tau} anisotropy pair is easily connected to more traditional shielding anisotropy measures, like span (Omega) and skew (kappa). The effectiveness of the different partitions of the CSA information in predicting conformations of peptides and proteins has been tested throughout the Ramachandran space by generating theoretical NMR anisotropy surfaces for our For-L-Ala-NH2 model. The CSA surfaces, including Omega(phi, psi), kappa(phi, psi), rho(phi, psi), and tau(phi, psi) are highly structured. Individually, none of these surfaces is able to distinguish unequivocally between the alpha-helix and beta-strand secondary structural types of proteins. However, two- and three-dimensional correlated plots, including Omega versus kappa, rho versus tau, and sigma iso versus rho versus tau, especially for 13Calpha, have considerable promise in distinguishing among all four of the major secondary structural elements.     

Prediction of native-state hydrogen exchange from perfectly funneled energy landscapes

Simulations based on perfectly funneled energy landscapes often capture many of the kinetic features of protein folding. We examined whether simulations based on funneled energy functions can also describe fluctuations in native-state protein ensembles. We quantitatively compared the site-specific local stability determined from structure-based folding simulations, with hydrogen exchange protection factors measured experimentally for ubiquitin, chymotrypsin inhibitor 2, and staphylococcal nuclease. Different structural definitions for the open and closed states based on the number of native contacts for each residue, as well as the hydrogen-bonding state, or a combination of both criteria were evaluated. The predicted exchange patterns agree with the experiments under native conditions, indicating that protein topology indeed has a dominant effect on the exchange kinetics. Insights into the simplest mechanistic interpretation of the amide exchange process were thus obtained.     

Spatial geometric arrangements of disulfide-crosslinked loops in proteins

The classification of patterns of the three-dimensional folding of a covalently crosslinked polypeptide chain can be used to introduce long-range interactions into the theoretical search for the native conformation of a protein. This classification into Spatial Geometric Arrangements of Loops (SGAL) had been proposed earlier (H. Meirovitch and H. A. Scheraga, Macromolecules 14 , 1250, 1981). It is based on the subdivision of the protein molecule into closed loops, defined by covalent crosslinks (such as disulfide bonds). Various SGAL classes correspond to the presence or absence of mutual penetration of loops, called entanglements or thrustings. A systematic and objective method is developed here to enumerate all theoretically possible SGAL's for a protein, based only on its covalent structure, i.e., the pattern of disulfide bonds or other crosslinks, regardless of whether the three-dimensional structure is known or unknown. This information can be of use in structural predictions of folding patterns. Using a modification of the method, it is also possible to determine the SGAL class to which a protein of known structure belongs. Out of 18 proteins with known three-dimensional structure and containing more than two disulfide bonds, five have a native structure with at least one entanglement or thrusting. Thus, threaded SGAL's represent a significant structural feature of native proteins. All five involve neighboring loops in the sequences. Their presence in a protein can suggest restrictions on the possible ways of folding the protein.     

The Trp cage: folding kinetics and unfolded state topology via molecular dynamics simulations

Using over 75 mus of molecular dynamics simulation, we have generated several thousand folding simulations of the 20-residue Trp cage at experimental temperature and solvent viscosity. A total of 116 independent folding simulations reach RMSDcalpha values below 3 A RMSDcalpha, some as close as 1.4 A RMSDcalpha. We estimate a folding time of 5.5+/-3.5 mus, a rate that is in reasonable agreement with experimental kinetics. Finally, we characterize both the folded and unfolded ensemble under native conditions and note that the average topology of the unfolded ensemble is very similar to the topology of the native state.     

Influence of the native topology on the folding barrier for small proteins

The possibility of downhill instead of two-state folding for proteins has been a very controversial topic which arose from recent experimental studies. From the theoretical side, this question has also been accomplished in different ways. Given the experimental observation that a relationship exists between the native structure topology of a protein and the kinetic and thermodynamic properties of its folding process, Gō-type potentials are an appropriate way to approach this problem. In this work, we employ an interaction potential from this family to get a better insight on the topological characteristics of the native state that may somehow determine the presence of a thermodynamic barrier in the folding pathway. The results presented here show that, indeed, the native topology of a small protein has a great influence on its folding behavior, mostly depending on the proportion of local and long range contacts the protein has in its native structure. Furthermore, when all the interactions present contribute in a balanced way, the transition results to be cooperative. Otherwise, the tendency to a downhill folding behavior increases.     

人工神经网络法预测炸药组分的色谱保留值参数

 以分子拓扑指数作为炸药组分的结构描述符 ,利用反向传播算法 (BP)人工神经网络 ,以Sigmoid函数为传递函数 ,分子连接性指数0 χ ,1χ ,2 χ与边邻接指数 (ε)为输入向量 ,反相高效液相色谱保留值参数logkw 和S为输出向量 ,将输入向量归一化至 - 3～ 3区间 ,输出向量归一化至 0～ 1区间 ,网络精度取 0 5 ,学习步长 η的初始值取0 2 ,动量因子α取 0 5 ,通过对 2 0种炸药的网络模型进行训练 ,建立了炸药分子结构与logkw 和S之间的定量模型。结果表明 ,该模型较好地反映了炸药分子结构与保留值之间的关系。     

Crowding alters the folding kinetics of a β-hairpin by modulating the stability of intermediates

Crowded environments inside cells exert significant effects on protein structure, stability, and function, but their effects on (pre)folding dynamics and kinetics, especially at molecular levels, remain ill-understood. Here, we examine the latter for, as an initial candidate, a small de novo β-hairpin using extensive all-atom molecular dynamics simulations for crowder volume fractions φ up to 40%. We find that crowding does not introduce new folding intermediates or misfolded structures, although, as expected, it promotes compact structures and reduces the accessible conformational space. Furthermore, while hydrophobic-collapse-mediated folding is slightly enhanced, the turn-directed zipper mechanism (dominant in crowder-free situations) increases many-fold, becoming even more dominant. Interestingly, φ influences the stability of the folding intermediates (FI(1) and FI(2)) in an apparently counterintuitive manner, which can be understood only by considering specific intrachain interactions and intermediate (and hierarchical) structural transitions. For φ values <20%, native-turn formation is enhanced, and FI(1), characterized by a hairpin structure but slightly mismatched hydrophobic contacts, increases in frequency, thus enhancing eventual folding. However, higher φ values impede native-turn formation, and FI(2), which lacks native turns, re-emerges and increasingly acts as a kinetic trap. The change in the stability of these intermediates with φ strongly correlates with the hierarchical folding stages and their kinetics. The results show that crowding assists intermediate structural changes more by impeding backward transitions than by promoting forward transitions and that a delicate competition between reduction in configuration space and introduction of kinetic traps along the folding route is key to understanding folding kinetics under crowded conditions.     

Conformational landscape of the HIV-V3 hairpin loop from all-atom free-energy simulations

Small beta hairpins have many distinct biological functions, including their involvement in chemokine and viral receptor recognition. The relevance of structural similarities between different hairpin loops with near homologous sequences is not yet understood, calling for the development of methods for de novo hairpin structure prediction and simulation. De novo folding of beta strands is more difficult than that of helical proteins because of nonlocal hydrogen bonding patterns that connect amino acids that are distant in the amino acid sequence and there is a large variety of possible hydrogen bond patterns. Here we use a greedy version of the basin hopping technique with our free-energy forcefield PFF02 to reproducibly and predictively fold the hairpin structure of a HIV-V3 loop. We performed 20 independent basin hopping runs for 500 cycles corresponding to 7.4 x 10(7) energy evaluations each. The lowest energy structure found in the simulation has a backbone root mean square deviation (bRMSD) of only 2.04 A to the native conformation. The lowest 9 out of the 20 simulations converged to conformations deviating less than 2.5 A bRMSD from native.     

Foldable subunits of helix protein

Detection of foldable subunits in proteins is an important approach to understand their evolutions and find building motifs for de novo protein design. Using united-residue model, we simulated the folding of a six-helix protein with a length of 120 amino acids (C-terminal domain of Ku86). The folding behaviors, structural topology and sequence repetition of this protein all suggest that it may have a two-fold quasi-repetition or symmetry in its sequence and structure. Therefore, we simulated the folding of its two halves (1–60 and 61–120 amino acids) and find that they can fold into native conformations independently. It is also found that their folding behaviors are very similar to other three-helix bundles. This suggests that this protein may be divided into two foldable halves.     

Residue-specific 13C' CSA tensor principal components for ubiquitin: correlation between tensor components and hydrogen bonding

The residue-specific 13C' CSA tensor principal components, sigma(11), sigma(22), sigma(33), and the tensor orientation defined by the rotation angles beta and gamma have been determined by solution NMR for uniformly labeled ubiquitin partially aligned in four different media. Spurious chemical shift deviations due to solvent effects were corrected with an offset calculated by linear regression of the residual dipolar couplings and chemical shifts at increasing alignment strengths. Analysis of this effect revealed no obvious correlation to solvent exposure. Data obtained in solution from a protein offer a better sampling of 13C' CSA for different amino acid types in a complex heterogeneous environment, thereby allowing for the evaluation of structural variables that would be challenging to achieve by other methods. The 13C' CSA principal components cluster about the average values previously determined, and experimental correlations observed between sigma(11), sigma(22) tensorial components and C'O...H(N) hydrogen bonding are discussed. The inverse association of sigma(11) and sigma(22) exemplify the calculated and solid-state NMR observed effect on the tensor components by hydrogen bonding. We also show that 13C' CSA tensors are sensitive to hydrogen-bond length but not hydrogen-bond angle. This differentiation was previously unavailable. Similarly, hydrogen bonding to the conjugated NH of the same peptide plane has no detectable effect. Importantly, the observed weak correlations signify the presence of confounding influences such as nearest-neighbor effects, side-chain conformation, electrostatics, and other long-range factors to the 13C' CSA tensor. These analyses hold future potential for exploration provided that more accurate data from a larger number of proteins and alignments become available.     

Tryptophan-BODIPY: a versatile donor-acceptor pair for probing generic changes of intraprotein distances

We demonstrate that Tryptophan (Trp) and N-(4,4-difluoro-5,7-dimethyl-4-bora-3a,4a-diaza-s-indacene-3-yl)methyl iodoacetamide (BODIPY) is a suitable donor-acceptor (D-A) pair for intraprotein distance measurements, applicable to the study of protein folding. The suitability of the Trp-BODIPY electronic energy transfer is exemplified on the extensively-characterised two-state protein, S6, from Thermus thermophilus. This protein has proved to be useful for the elucidation of folding cooperativity and nucleation, as well as the changes upon induction of structural transitions. For a comprehensive structural coverage, BODIPY molecules were anchored by Cys insertions at four different positions on the S6 surface. Trp residues at position 33 or 62 acted as donors of electronic energy to the BODIPY groups. None of the D-A pairs show any detectable difference in the folding kinetics (or protein stability), which supports the notion that the two-state transition of S6 is a highly concerted process. Similar results are obtained for mutants affecting the N- and C-terminus. The kinetic analyses indicate that changes of the transition state occur through local unfolding of the native state, rather than by a decrease of the folding cooperativity. The distances obtained from the analysis of the time-resolved fluorescence experiments in the native state were compared to those calculated from X-ray structure. As an additional measure, molecular dynamics simulations of the different protein constructs were performed to account for variability in the BODIPY location on the protein surface. The agreement between fluorescence and X-ray data is quite convincing, and shows that energy transfer measurements between Trp and BODIPY can probe distances between ca. 17 to 34 A, with an error better than 10%.     

Frustration Sculpts the Early Stages of Protein Folding

The funneled energy landscape theory implies that protein structures are minimally frustrated. Yet, because of the divergent demands between folding and function, regions of frustrated patterns are present at the active site of proteins. To understand the effects of such local frustration in dictating the energy landscape of proteins, here we compare the folding mechanisms of the two alternative spliced forms of a PDZ domain (PDZ2 and PDZ2as) that share a nearly identical sequence and structure, while displaying different frustration patterns. The analysis, based on the kinetic characterization of a large number of site‐directed mutants, reveals that although the late stages for folding are very robust and biased by native topology, the early stages are more malleable and dominated by local frustration. The results are briefly discussed in the context of the energy‐landscape theory.     

A localized specific interaction alters the unfolding pathways of structural homologues

Reductive unfolding studies of proteins are designed to provide information about intramolecular interactions that govern the formation (and stabilization) of the native state and about folding/unfolding pathways. By mutating Tyr92 to G, A, or L in the model protein, bovine pancreatic ribonuclease A, and through analysis of temperature factors and molecular dynamics simulations of the crystal structures of these mutants, it is demonstrated that the markedly different reductive unfolding rates and pathways of ribonuclease A and its structural homologue onconase can be attributed to a single, localized, ring-stacking interaction between Tyr92 and Pro93 in the bovine variant. The fortuitous location of this specific stabilizing interaction in a disulfide-bond-containing loop region of ribonuclease A results in the localized modulation of protein dynamics that, in turn, enhances the susceptibility of the disulfide bond to reduction leading to an alteration in the reductive unfolding behavior of the homologues. These results have important implications for folding studies involving topological determinants to obtain folding/unfolding rates and pathways, for protein structure-function prediction through fold recognition, and for predicting proteolytic cleavage sites.     

A statistical model for predicting protein folding rates from amino acid sequence with structural class information

Prediction of protein folding rates from amino acid sequences is one of the most important challenges in molecular biology. In this work, I have related the protein folding rates with physical-chemical, energetic and conformational properties of amino acid residues. I found that the classification of proteins into different structural classes shows an excellent correlation between amino acid properties and folding rates of two- and three-state proteins, indicating the importance of native state topology in determining the protein folding rates. I have formulated a simple linear regression model for predicting the protein folding rates from amino acid sequences along with structural class information and obtained an excellent agreement between predicted and experimentally observed folding rates of proteins; the correlation coefficients are 0.99, 0.96 and 0.95, respectively, for all-alpha, all-beta and mixed class proteins. This is the first available method, which is capable of predicting the protein folding rates just from the amino acid sequence with the aid of generic amino acid properties and structural class information.     

End-to-end vs interior loop formation kinetics in unfolded polypeptide chains

The conformational search for favorable intramolecular interactions during protein folding is limited by intrachain diffusion processes. Recent studies on the dynamics of loop formation in unfolded polypeptide chains have focused on loops involving residues near the chain ends. During protein folding, however, most contacts are formed between residues in the interior of the chain. We compared the kinetics of end-to-end loop formation (type I loops) to the formation of end-to-interior (type II loops) and interior-to-interior loops (type III loops) using triplet-triplet energy transfer from xanthone to naphthylalanine. The results show that formation of type II and type III loops is slower compared to type I loops of the same size and amino acid sequence. The rate constant for type II loop formation decreases with increasing overall chain dimensions up to a limiting value, at which loop formation is about 2.5-fold slower for type II loops compared to type I loops. Comparing type II loops of different loop size and amino acid sequence shows that the ratio of loop dimension over total chain dimension determines the rate constant for loop formation. Formation of type III loops is 1.7-fold slower than formation of type II loops, indicating that local chain motions are strongly coupled to motions of other chain segments which leads to faster dynamics toward the chain ends. Our results show that differences in the kinetics of formation of type I, type II, and type III loops are mainly caused by differences in internal flexibility at the different positions in the polypeptide chain. Interactions of the polypeptide chain with the solvent contribute to the kinetics of loop formation, which are strongly viscosity-dependent. However, the observed differences in the kinetics of formation of type I, type II, and type III loops are not due to the increased number of peptide-solvent interactions in type II and type III loops compared to type I loops as indicated by identical viscosity dependencies for the kinetics of formation of the different types of loops.     

New fluorophores with rod-shaped polycyano pi-conjugated structures: synthesis and photophysical properties

[reaction: see text] Novel rod-shaped polycyano-oligo(phenyleneethynylene)s were synthesized by Pd cross-coupling reaction. Polycyano groups were found to greatly improve the emission efficiency (Phi(f)) of OPEs. By the end donor modification, we achieved the creation of very intense blue light-emitting fluorophore with the SMe group (Phi(f) = 0.972, log epsilon 4.89, lambda(em) 455 nm) and very intense yellow light-emitting fluorophore with the NMe(2) group (Phi(f) = 0.999, log epsilon 4.75, lambda(em) 555 nm). Contrasting Phi(f) solvent dependency of 6 and 7 and a linear relationship between Phi(f) and sigma(p)-X over the whole region of sigma(p)-X were also found.