Exploration of two-dimensional hydrophobic-polar lattice model by combining local search with elastic net algorithm

Determining the functional conformation of a protein from its amino acid sequence remains a central problem in computational biology. In this paper, we establish the mathematical optimal model of protein folding problem (PFP) on two-dimensional space based on the minimal energy principle. A novel hybrid of elastic net algorithm and local search method (ENLS) is applied successfully to simulations of protein folding on two-dimensional hydrophobic-polar (HP) lattice model. Eight HP benchmark instances with up to 64 amino acids are tested to verify the effectiveness of proposed approach and model. In several cases, the ENLS method finds new lower energy states. The numerical results show that it is drastically superior to other methods in finding the ground state of a protein.     

Facile synthesis of @-tide beta-strand peptidomimetics: improved assembly in solution and on solid phase

The synthesis of @-tide beta-strand peptidomimetics has been improved such that oligomers now can be obtained from solution- and solid-phase synthesis protocols approaching the efficiency and flexibility of peptide chemistry. These methods enable the synthesis of @-tide oligomers with a variety of amino acids and with lengths up to 13 units. [reaction: see text]     

Ribonuclease T1: Structure,Function, and Stability

Proteins carry out the most important and difficult tasks in all living organisms. To do so, they must often interact specifically with other small and large molecules. This requires that they fold to a globular conformation with a unique active site that is used for the specific interaction. Consequently, protein folding can be regarded as the “secret of life”. Biochemists and chemists have a great interest in elucidating the mechanism by which proteins fold and in predicting the folded conformation and its stability given just the amino acid sequence. This challenge is sometimes called the “protein folding problem”. The ability to construct proteins differing in sequence by one or more amino acids and to analyze their three-dimensional structures by X-ray crystallography and NMR spectroscopy is a powerful tool for investigating the conformational stability and folding of proteins. Several proteins are now under intensive study by this approach. One of these is ribonuclease T1.     

Peptide backbone folding induced by the C(alpha)-tetrasubstituted cyclic alpha-amino acids 4-amino-1,2-dithiolane-4-carboxylic acid (Adt) and 1-aminocyclopentane-1-carboxylic acid (Ac5c). A joint computational and experimental study

The conformational study of a new group of synthetic peptides containing 4-amino-1,2-dithiolane-4-carboxylic acid (Adt), a cysteine-related achiral residue, has been carried out through a joint application of computational and experimental methodologies. Molecular Dynamics simulations clearly suggest the tendency of this molecule to adopt a gamma-turn conformation in vacuum and help in analyzing the complex and crucial conformational behaviour of the dithiolane ring which appears to preferentially adopt a C(S)-like structure. Electronic structure calculations carried out in solution using the Density Functional Theory also indicate the preservation of the gamma-like folding in apolar solvents and the helix-like one in more polar solvents. A comparison with the achiral 1-aminocycloalkane-1-carboxylic acid (Ac5c) has been carried out using the same computational tools. NMR and IR data on dipeptide derivatives containing the Adt or Ac5c residue show that in chloroform solution all the models prefer a gamma-turn structure, centered at the cyclic residue, stabilized by an intramolecular H-bond, whereas in a more polar solvent, i.e. dimethyl sulfoxide, this folding is not maintained. The experimental conformational studies, extended to N-Boc protected tripeptides, clearly indicate the remarkable tendency of both the five-membered C(alpha)-tetrasubstituted cyclic amino acids Adt and Ac5c to induce the gamma-turn structure also in models able to adopt the beta-bend conformation.     

Side-chain dynamics of an alpha-helical polypeptide monitored by fluorescence

The "blob" model, developed to analyze the fluorescence decays of polymers randomly labeled with pyrene, has been applied to a series of pyrene-labeled poly(glutamic acid)s (PyPGA) in DMF and carbonated buffer solutions at pH 9. Poly(glutamic acid) (PGA) exists in the ionized form in the buffer solutions as poly(sodium glutamate) (PGNa). PGA adopts an alpha-helical conformation in DMF, whereas in aqueous solution PGNa is a random coil. Fluorescence, UV-vis absorption, and circular dichroism measurements indicate that in our studies pyrene pendants attached themselves along PGA in a clustered manner. Simulations were carried out to establish that the geometry of the PGA alpha-helix induces the high level of pyrene clustering. Since the level of pyrene clustering decreased with lower pyrene content, information about naked PGA was retrieved by extrapolating the trends obtained by fluorescence to zero pyrene content. Analysis of the fluorescence decays demonstrated that during its lifetime an excited pyrene probes a 32 amino acid section of the PGA alpha-helix. This result was supported by molecular mechanics optimizations. This study establishes that the blob model, originally used to monitor the encounters between pyrenes attached randomly onto a polymer adopting a random coil conformation, can also be applied to study the dynamics of the side chains of structured proteins. Since the blob model helps in monitoring the encounters between amino acids in the initial state (i.e., random coil) and in the final state (i.e., structured protein) of the folding pathway of a protein, it could be applicable to the study of protein folding.     

Predicting protein folding rates using the concept of Chou's pseudo amino acid composition

One of the most important challenges in computational and molecular biology is to understand the relationship between amino acid sequences and the folding rates of proteins. Recent works suggest that topological parameters, amino acid properties, chain length and the composition index relate well with protein folding rates, however, sequence order information has seldom been considered as a property for predicting protein folding rates. In this study, amino acid sequence order was used to derive an effective method, based on an extended version of the pseudo-amino acid composition, for predicting protein folding rates without any explicit structural information. Using the jackknife cross validation test, the method was demonstrated on the largest dataset (99 proteins) reported. The method was found to provide a good correlation between the predicted and experimental folding rates. The correlation coefficient is 0.81 (with a highly significant level) and the standard error is 2.46. The reported algorithm was found to perform better than several representative sequence-based approaches using the same dataset. The results indicate that sequence order information is an important determinant of protein folding rates.     

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.     

Design of amino acid sequences to fold into C(alpha)-model proteins

In order to extend the results obtained with minimal lattice models to more realistic systems, we study a model where proteins are described as a chain of 20 kinds of structureless amino acids moving in a continuum space and interacting through a contact potential controlled by a 20x20 quenched random matrix. The goal of the present work is to design and characterize amino acid sequences folding to the SH3 conformation, a 60-residue recognition domain common to many regulatory proteins. We show that a number of sequences can fold, starting from a random conformation, to within a distance root-mean-square deviation between 2.6 and 4.0 A from the native state. Good folders are those sequences displaying in the native conformation an energy lower than a sequence-independent threshold energy.     

Protein secondary structure preferencs

This paper addresses the question to what extent steric properties of sequence neighbors effect the preferences of an amino acid residue to assume the-helical or some other secondary structure conformation. We find that an amino acid has increased tendency to be in-helical conformation when its sequence neighbors are bulky. This result is an outcome of our automated method for finding conformational preferences as functions of physical parameters important for protein folding. The steric environment for a given residue in a protein is defined as an average of water-accessible surface areas of its primary structure neighbors in extended conformation for model tripeptides. For all amino acids, including non-helix formers like glycine and arginine, the preference for the helical structure increases if their primary structure neighbors form a larger steric environment.     

Modulation of the folding energy landscape of cytochrome C with salt

The folding reaction of acid-unfolded cytochrome c in the presence of various amounts of KCl was investigated with Trp fluorescence and resonance Raman spectroscopies. It was found that the too-early-too-much polypeptide chain collapse induced by KCl yields some stable folding intermediates, which need to overcome a higher energy barrier to fold into their native conformation. We propose that the charge distribution on the polypeptide chain is part of the folding codon encoded in the linear amino acid sequence. The charge screening effect introduced by KCl alters the shape of the energy landscape by raising the slope of the upper rim and introduces a rugged energy surface toward the bottom of the folding funnel.     

Importance of native-state topology for determining the folding rate of two-state proteins

Understanding the relationship between amino acid sequences and folding rate of proteins is a challenging task similar to protein folding problem. In this work, we have analyzed the relative importance of protein sequence and structure for predicting the protein folding rates in terms of amino acid properties and contact distances, respectively. We found that the parameters derived with protein sequence (physical-chemical, energetic, and conformational properties of amino acid residues) show very weak correlation (|r| < 0.39) with folding rates of 28 two-state proteins, indicating that the sequence information alone is not sufficient to understand the folding rates of two-state proteins. However, the maximum positive correlation obtained for the properties, number of medium-range contacts, and alpha-helical tendency reveals the importance of local interactions to initiate protein folding. On the other hand, a remarkable correlation (r varies from -0.74 to -0.88) has been obtained between structural parameters (contact order, long-range order, and total contact distance) and protein folding rates. Further, we found that the secondary structure content and solvent accessibility play a marginal role in determining the folding rates of two-state proteins. Multiple regression analysis carried out with the combination of three properties, beta-strand tendency, enthalpy change, and total contact distance improved the correlation to 0.92 with protein folding rates. The relative importance of existing methods along with multiple-regression model proposed in this work will be discussed. Our results demonstrate that the native-state topology is the major determinant for the folding rates of two-state proteins.     

Real value prediction of protein folding rate change upon point mutation

Prediction of protein folding rate change upon amino acid substitution is an important and challenging problem in protein folding kinetics and design. In this work, we have analyzed the relationship between amino acid properties and folding rate change upon mutation. Our analysis showed that the correlation is not significant with any of the studied properties in a dataset of 476 mutants. Further, we have classified the mutants based on their locations in different secondary structures and solvent accessibility. For each category, we have selected a specific combination of amino acid properties using genetic algorithm and developed a prediction scheme based on quadratic regression models for predicting the folding rate change upon mutation. Our results showed a 10-fold cross validation correlation of 0.72 between experimental and predicted change in protein folding rates. The correlation is 0.73, 0.65 and 0.79, respectively in strand, helix and coil segments. The method has been further tested with an extended dataset of 621 mutants and a blind dataset of 62 mutants, and we observed a good agreement with experiments. We have developed a web server for predicting the folding rate change upon mutation and it is available at .     

Predictive in silico all-atom folding of a four-helix protein with a free-energy model

We report the predictive all-atom folding of the 60 amino acid four-helix bacterial ribosomal protein (BRP) L20 with a stochastic evolutionary optimization method in a free-energy force field. The energetically best, as well as six of the 10 lowest conformations, converge to a near-native structure. All of the 10 best energy conformations share the secondary structure elements of the native conformation, but differ in their tertiary alignment. The best conformation has a backbone root-mean-square deviation of 4.6 A to the native conformation and reproduces most distance constraints of the NMR experiment to 1.5 A resolution. Starting from random initial conditions, the native content of the simulated population increases more than 60-fold in the course of the simulation. These data demonstrate the feasibility of predictive unbiased all-atom protein folding with present day computational resources for the BRP L20.     

Mapping tertiary interactions in protein folding reactions: a novel mass spectrometry- and chemical synthesis-based approach

A novel mass spectrometry- and chemical synthesis-based approach for studying protein folding reactions is described, and its initial application to study the folding/unfolding reaction of a homo-hexameric enzyme 4-oxalocrotonate (4OT) is reported. This new approach involves the application of total chemical synthesis to prepare protein analogues that contain a photoreactive amino acid site-specifically incorporated into their primary amino acid sequence. To this end, a photoreactive amino acid-containing analogue of 4OT in which Pro-1 was replaced with p-benzoyl-l-phenylalanine (Bpa) was prepared. This analogue can be used to map structurally specific protein-protein interactions in 4OT's native folded state. These photocrosslinking studies and peptide mapping results with (PlBpa)4OT indicate that this construct is potentially useful for probing the structural properties of equilibrium and kinetic intermediates in 4OT's folding reaction.     

Intrinsic energy landscapes of amino acid side-chains

Amino acid side-chain conformational properties influence the overall structural and dynamic properties of proteins and, therefore, their biological functions. In this study, quantum mechanical (QM) potential energy surfaces for the rotation of side-chain χ(1) and χ(2) torsions in dipeptides in the alphaR, beta, and alphaL backbone conformations were calculated. The QM energy surfaces provide a broad view of the intrinsic conformational properties of each amino acid side-chain. The extent to which intrinsic energetics dictates side-chain orientation was studied through comparisons of the QM energy surfaces with χ(1) and χ(2) free energy surfaces from probability distributions obtained from a survey of high resolution crystal structures. In general, the survey probability maxima are centered in minima of the QM surfaces as expected for sp(3) (or sp(2) for χ(2) of Asn, Phe, Trp, and Tyr) atom centers with strong variations between amino acids occurring in the energies of the minima indicating intrinsic differences in rotamer preferences. High correlations between the QM and survey data were found for hydrophobic side-chains except Met, suggesting minimal influence of the protein and solution environments on their conformational distributions. Conversely, low correlations for polar or charged side-chains indicate a dominant role of the environment in stabilizing conformations that are not intrinsically favored. Data also link the presence of off-rotamers in His and Trp to favorable interactions with the backbone. Results also suggest that the intrinsic energetics of the side-chains of Phe and Tyr may play important roles in protein folding and stability. Analyses on whether intrinsic side-chain energetics can influence backbone preference identified a strong correlation for residues in the alphaL backbone conformation. It is suggested that this correlation reflects the intrinsic instability of the alphaL backbone such that assumption of this backbone conformation is facilitated by intrinsically favorable side-chain conformations. Together our results offer a broad overview of the conformational properties of amino acid side-chains and the QM data may be used as target data for force field optimization.     

A reverse turn structure induced by a D,L-alpha-aminoxy acid dimer

Our previous work revealed that two adjacent D-alpha-aminoxy acids could form two homochiral N-O turns, with the backbone folding into an extended helical structure (1.8(8)-helix). Here, we report the conformational studies of linear peptides 3-6, which contain a D,L-alpha-aminoxy acid dimer segment. The NMR and X-ray analysis of 3 showed that it folded into a loop conformation with two heterochiral N-O turns. This loop segment can be used to constrain tetrapeptides 4 and 6 to form a reverse turn structure. (1)H NMR dilution studies, DMSO-d6 addition studies, and 2D-NOESY data indicated that tetrapeptides 4 and 6 folded into reverse turn conformations featured by a head-to-tail 16-membered-ring intramolecular hydrogen bond. In contrast, tetrapeptide 5 with L-Ala instead of Gly or D-Ala as the N-terminal amino acid could not form the desired reverse turn structure for steric reasons. Quantum mechanics calculations showed that model pentamide 7, with the same substitution pattern of 4, adopted a novel reverse turn conformation featuring two heterochiral N-O turns (each of an 8-membered ring hydrogen bond), a cross-strand 16-membered ring hydrogen bond, and a 7-membered ring gamma-turn.     

Mapping tertiary interactions in protein folding reactions: a novel mass spectrometry- and chemical synthesis-based approach

A novel mass spectrometry- and chemical synthesis-based approach for studying protein folding reactions is described, and its initial application to study the folding/unfolding reaction of a homo-hexameric enzyme 4-oxalocrotonate (4OT) is reported. This new approach involves the application of total chemical synthesis to prepare protein analogues that contain a photoreactive amino acid site-specifically incorporated into their primary amino acid sequence. To this end, a photoreactive amino acid-containing analogue of 4OT in which Pro-1 was replaced with p-benzoyl-l-phenylalanine (Bpa) was prepared. This analogue can be used to map structurally specific protein-protein interactions in 4OT’s native folded state. These photocrosslinking studies and peptide mapping results with (P1Bpa)4OT indicate that this construct is potentially useful for probing the structural properties of equilibrium and kinetic intermediates in 4OT’s folding reaction.     

Secondary Structures in Synthetic Poly(Amino Acids): Homo- and Copolymers of Poly(Aib), Poly(Glu), and Poly(Asp)

The secondary structure of poly(amino acids) is an excellent tool for controlling and understanding the functionality and properties of proteins. In this perspective article the secondary structures of the homopolymers of oligo- and poly-glutamic acid (Glu), aspartic acid (Asp), and α-aminoisobutyric acid (Aib) are discussed. Information on external and internal factors, such as the nature of side groups, interactions with solvents and interactions between chains is reviewed. A special focus is directed on the folding in hybrid-polymers consisting of oligo(amino acids) and synthetic polymers. Being part of the SFB TRR 102 “Polymers under multiple constraints: restricted and controlled molecular order and mobility” this overview is embedded into the cross section of protein fibrillation and supramolecular polymers. As polymer- and amino acid folding is an important step for the utilization and design of future biomolecules these principles guide to a deeper understanding of amyloid fibrillation.     

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.     

Tuning the conformation of synthetic co‐polypeptides of serine and glutamic acid through control over polymer composition

Ring opening polymerization (ROP) of N‐carboxy anhydride (NCA) amino acids presents a rapid way to synthesize high molecular weight polypeptides with different amino acid compositions. The compositional and functional versatility of polypeptides make these materials an attractive choice for biomaterials. The functional performance of polypeptide materials is equally linked to their conformation which is determined by the amino acid sequence in the polymer chains. Here, the interplay between composition and conformation of synthetic polypeptides obtained by NCA polymerization was explored. Various copolypeptides from Glu(Bzl) and Ser(Bzl) were prepared to investigate how polypeptide composition affected the conformation of the resulting copolymer. Polymerization kinetics indicated that the copolymerization of Glu(Bzl) and Ser(Bzl) preferentially yielded alternating copolymers. Both the polydispersity and the conformation of the polypeptides were dependent on the Ser(Bzl) content in the polymer, demonstrating that polypeptide functionalities could be tuned directly by altering the relative amounts of amino acids in the chain. This work presents the first step toward an improved understanding and control over polypeptide conformation through modulating the amino acid composition of the material. Understanding this sequence–functionality relationship is essential to advancing the use of ROP as a technique to design smart polypeptide based materials with specific functions. © 2016 The Authors. Journal of Polymer Science Part A: Polymer Chemistry Published by Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 2331–2336