Correlations between designability and various structural characteristics of protein lattice models

Using six kinds of lattice types (4 x 4, 5 x 5, and 6 x 6 square lattices; 3 x 3 x 3 cubic lattice; and 2+3+4+3+2 and 4+5+6+5+4 triangular lattices), three different size alphabets (HP, HNUP, and 20 letters), and two energy functions, the designability of protein structures is calculated based on random samplings of structures and common biased sampling (CBS) of protein sequence space. Then three quantities stability (average energy gap), foldability, and partnum of the structure, which are defined to elucidate the designability, are calculated. The authors find that whatever the type of lattice, alphabet size, and energy function used, there will be an emergence of highly designable (preferred) structure. For all cases considered, the local interactions reduce degeneracy and make the designability higher. The designability is sensitive to the lattice type, alphabet size, energy function, and sampling method of the sequence space. Compared with the random sampling method, both the CBS and the Metropolis Monte Carlo sampling methods make the designability higher. The correlation coefficients between the designability, stability, and foldability are mostly larger than 0.5, which demonstrate that they have strong correlation relationship. But the correlation relationship between the designability and the partnum is not so strong because the partnum is independent of the energy. The results are useful in practical use of the designability principle, such as to predict the protein tertiary structure.     

Understanding the role of the topology in protein folding by computational inverse folding experiments

Recent studies suggest that protein folding should be revisited as the emergent property of a complex system and that the nature allows only a very limited number of folds that seem to be strongly influenced by geometrical properties. In this work we explore the principles underlying this new view and show how helical protein conformations can be obtained starting from simple geometric considerations. We generated a large data set of C-alpha traces made of 65 points, by computationally solving a backbone model that takes into account only topological features of the all-alpha proteins; then, we built corresponding tertiary structures, by using the sequences associated to the crystallographic structures of four small globular all-alpha proteins from PDB, and analysed them in terms of structural and energetic properties. In this way we obtained four poorly populated sets of structures that are reasonably similar to the conformational states typical of the experimental PDB structures. These results show that our computational approach can capture the native topology of all-alpha proteins; furthermore, it generates backbone folds without the influence of the side chains and uses the protein sequence to select a specific fold among the generated folds. This agrees with the recent view that the backbone plays an important role in the protein folding process and that the amino acid sequence chooses its own fold within a limited total number of folds.     

Altering the folding patterns of naphthyl trimers

Proteins can adopt helical and sheet-type secondary structures that depend on their primary sequence of amino acids. Nonnatural foldamers have been developed to emulate these protein structures as well as investigate various types of noncovalent interactions. Here we report a strategy to access two distinct folding topologies in aqueous solutions using the inherent recognition properties of aromatic donor/acceptor interactions. These oligomers are constructed of electron-rich 1,5-dialkoxynaphthalene (Dan) and electron-deficient 1,4,5,8-naphthalenetetracarboxylic diimide (Ndi) units. A trimer of the sequence Dan-Ndi-Dan was shown to adopt a pleated fold in solution, while its constitutional isomer, Dan-Dan-Ndi, adopted an intercalative or turn-type fold. UV-vis and NOESY spectroscopy analyses were consistent with the two different conformations. This study illustrates the designability of folding naphthyl oligomers and encourages the use of directed aromatic interactions to construct larger and more complex assemblies in water.     

“Topohydrophobic positions” as key markers of globular protein folds

The positions of a given fold always occupied by strong hydrophobic amino acids (V, I, L, F, M, Y, W), which we call “topohydrophobic positions”, were detected and their properties demonstrated within 153 non-redundant families of homologous domains, through 3D structural alignments. Sets of divergent sequences possessing at least four to five members appear to be as informative as larger sets, provided that their mean pairwise sequence identity is low. Amino acids in topohydrophobic positions exhibit several interesting features: they are much more buried than their equivalents in non-topohydrophobic positions, their side chains are far less dispersed; and they often constitute a lattice of close contacts in the inner core of globular domains. In most cases, each regular secondary structure possesses one to three topohydrophobic positions, which cluster in the domain core. Moreover, using sensitive alignment processes such as hydrophobic cluster analysis (HCA), it is possible to identify topohydrophobic positions from only a small set of divergent sequences. Amino acids in topohydrophobic positions, which can be identified directly from sequences, constitute key markers of protein folds, define long-range structural constraints, which, together with secondary structure predictions, limit the number of possible conformations for a given fold. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 16 November 1998     

De novo and inverse folding predictions of protein structure and dynamics

Summary In the last two years, the use of simplified models has facilitated major progress in the globular protein folding problem, viz., the prediction of the three-dimensional (3D) structure of a globular protein from its amino acid sequence. A number of groups have addressed the inverse folding problem where one examines the compatibility of a given sequence with a given (and already determined) structure. A comparison of extant inverse protein-folding algorithms is presented, and methodologies for identifying sequences likely to adopt identical folding topologies, even when they lack sequence homology, are described. Extension to produce structural templates or fingerprints from idealized structures is discussed, and for eight-membered β-barrel proteins, it is shown that idealized fingerprints constructed from simple topology diagrams can correctly identify sequences having the appropriate topology. Furthermore, this inverse folding algorithm is generalized to predict elements of supersecondary structure including β-hairpins, helical hairpins and α/β/α fragments. Then, we describe a very high coordination number lattice model that can predict the 3D structure of a number of globular proteins de novo; i.e. using just the amino acid sequence. Applications to sequences designed by DeGrado and co-workers [Biophys. J., 61 (1992) A265] predict folding intermediates, native states and relative stabilities in accord with experiment. The methodology has also been applied to the four-helix bundle designed by Richardson and co-workers [Science, 249 (1990) 884] and a redesigned monomeric version of a naturally occurring four-helix dimer, rop. Based on comparison to the rop dimer, the simulations predict conformations with rms values of 3–4 ? from native. Furthermore, the de novo algorithms can asses the stability of the folds predicted from the inverse algorithm, while the inverse folding algorithms can assess the quality of the de novo models. Thus, the synergism of the de novo and inverse folding algorthhm approaches provides a set of complementary tools that will facilitate further progress on the protein-folding problem.     

SPICKER: a clustering approach to identify near-native protein folds

We have developed SPICKER, a simple and efficient strategy to identify near-native folds by clustering protein structures generated during computer simulations. In general, the most populated clusters tend to be closer to the native conformation than the lowest energy structures. To assess the generality of the approach, we applied SPICKER to 1489 representative benchmark proteins 相似文献   

Folding Lattice HP Model of Proteins Using the Bond‐Fluctuation Model

In this paper, we find ‘good’ amino acid sequences that fold to a desired “target” structure as a ground state conformation of lowest accessible free energy using the modified bond‐fluctuation lattice model. In our protein lattice model, bond lengths are set to vary between one and √2 in three dimensions. Our results agree well with the native state energies E_N. Comparisons with the “putative native state” (PNS) energy E_PNS and the “hydrophobic zippers” (HZ) energy E_HZ are made. For every sequence, the global energy minimum is found to have multiple degeneracy of conformations, which is the same result as for the constraint‐based hydrophobic core construction (CHCC) method. The interior conformations of the ground states are also discussed.     

RNA architecture dictates the conformations of a bound peptide.

BACKGROUND: The biological function of several viral and bacteriophage proteins, and their arginine-rich subdomains, involves RNA-mediated interactions. It has been shown recently that bound peptides adopt either beta-hairpin or alpha-helical conformations in viral and phage peptide-RNA complexes. We have compared the structures of the arginine-rich peptide domain of HIV-1 Rev bound to two RNA aptamers to determine whether RNA architecture can dictate the conformations of a bound peptide. RESULTS: The core-binding segment of the HIV-1 Rev peptide class II RNA aptamer complex spans the two-base bulge and hairpin loop of the bound RNA and the carboxy-terminal segment of the bound peptide. The bound peptide is anchored in place by backbone and sidechain intermolecular hydrogen bonding and van der Waals stacking interactions. One of the bulge bases participates in U*(A*U) base triple formation, whereas the other is looped out and flaps over the bound peptide in the complex. The seven-residue hairpin loop is closed by a sheared G*A mismatch pair with several pyrimidines looped out of the hairpin fold. CONCLUSIONS: Our structural studies establish that RNA architecture dictates whether the same HIV-1 Rev peptide folds into an extended or alpha-helical conformation on complex formation. Arginine-rich peptides can therefore adapt distinct secondary folds to complement the tertiary folds of their RNA targets. This contrasts with protein-RNA complexes in which elements of RNA secondary structure adapt to fit within the tertiary folds of their protein targets.     

The effect of sequence on the conformational stability of a model heteropolymer in explicit water

We investigate the properties of a two-dimensional lattice heteropolymer model for a protein in which water is explicitly represented. The model protein distinguishes between hydrophobic and polar monomers through the effect of the hydrophobic monomers on the entropy and enthalpy of the hydrogen bonding of solvation shell water molecules. As experimentally observed, model heteropolymer sequences fold into stable native states characterized by a hydrophobic core to avoid unfavorable interactions with the solvent. These native states undergo cold, pressure, and thermal denaturation into distinct configurations for each type of unfolding transition. However, the heteropolymer sequence is an important element, since not all sequences will fold into stable native states at positive pressures. Simulation of a large collection of sequences indicates that these fall into two general groups, those exhibiting highly stable native structures and those that do not. Statistical analysis of important patterns in sequences shows a strong tendency for observing long blocks of hydrophobic or polar monomers in the most stable sequences. Statistical analysis also shows that alternation of hydrophobic and polar monomers appears infrequently among the most stable sequences. These observations are not absolute design rules and, in practice, these are not sufficient to rationally design very stable heteropolymers. We also study the effect of mutations on improving the stability of the model proteins, and demonstrate that it is possible to obtain a very stable heteropolymer from directed evolution of an initially unstable heteropolymer.     

Pattern recognition in the prediction of protein structure. III. An importance-sampling minimization procedure

A procedure that generates random conformations of a protein chain, and then applies energy minimization to find the structure of lowest energy, is described. Single-residue conformations are represented in terms of four conformational states, α, ?, α*, and ?*. Each state corresponds to a rectangular region in the ?, ψ map. The conformation of an entire chain is then represented by a sequence of single-residue conformational states. The distinct “chain-states” in this representation correspond to multidimensional rectangular regions in the conformational space of the whole protein. A set of highly-probable chain-states can be predicted from the amino acid sequence using the pattern recognition procedure developed in the first two articles of this series. The importance-sampling minimization procedure of the present article is then used to explore the regions of conformational space corresponding to each of these chain-states. The importance-sampling procedure generates a number of random conformations within a particular multidimensional rectangular region, sampling most densely from the most probable, or “important,” sections of the ?, ψ map. All values of ? and ψ are allowed, but the less-probable values are sampled less often. To achieve this, the random values of ? and Φ are generated from bivariate gaussian distributions that are determined from known X-ray structures. Separate gaussian distributions are used for proline residues in the α and ? states, for glycine residues in the α, ?, α*, and ?* states, and for ordinary residues involved in 29 different tripeptide conformations. Energy minimization is then applied to the randomly-generated structures to optimize interactions and to improve packing. The final energy values are used to select the best structures. The importance-sampling minimization procedure is tested on the avian pancreatic polypeptide, using chain-states predicted from the amino acid sequence. The conformation having the lowest energy is very similar to the X-ray conformation.     

The shape-shifting quasispecies of RNA: one sequence, many functional folds

E Unus pluribum, or "Of One, Many", may be at the root of decoding the RNA sequence-structure-function relationship. RNAs embody the large majority of genes in higher eukaryotes and fold in a sequence-directed fashion into three-dimensional structures that perform functions conserved across all cellular life forms, ranging from regulating to executing gene expression. While it is the most important determinant of the RNA structure, the nucleotide sequence is generally not sufficient to specify a unique set of secondary and tertiary interactions due to the highly frustrated nature of RNA folding. This frustration results in folding heterogeneity, a common phenomenon wherein a chemically homogeneous population of RNA molecules folds into multiple stable structures. Often, these alternative conformations constitute misfolds, lacking the biological activity of the natively folded RNA. Intriguingly, a number of RNAs have recently been described as capable of adopting multiple distinct conformations that all perform, or contribute to, the same function. Characteristically, these conformations interconvert slowly on the experimental timescale, suggesting that they should be regarded as distinct native states. We discuss how rugged folding free energy landscapes give rise to multiple native states in the Tetrahymena Group I intron ribozyme, hairpin ribozyme, sarcin-ricin loop, ribosome, and an in vitro selected aptamer. We further describe the varying degrees to which folding heterogeneity impacts function in these RNAs, and compare and contrast this impact with that of heterogeneities found in protein folding. Embracing that one sequence can give rise to multiple native folds, we hypothesize that this phenomenon imparts adaptive advantages on any functionally evolving RNA quasispecies.     

Heuristic energy landscape paving for protein folding problem in the three-dimensional HP lattice model

The protein folding problem, i.e., the prediction of the tertiary structures of protein molecules from their amino acid sequences is one of the most important problems in computational biology and biochemistry. However, the extremely difficult optimization problem arising from energy function is a key challenge in protein folding simulation. The energy landscape paving (ELP) method has already been applied very successfully to off-lattice protein models and other optimization problems with complex energy landscape in continuous space. By improving the ELP method, and subsequently incorporating the neighborhood strategy with the pull-move set into the improved ELP method, a heuristic ELP algorithm is proposed to find low-energy conformations of 3D HP lattice model proteins in the discrete space. The algorithm is tested on three sets of 3D HP benchmark instances consisting 31 sequences. For eleven sequences with 27 monomers, the proposed method explores the conformation surfaces more efficiently than other methods, and finds new lower energies in several cases. For ten 48-monomer sequences, we find the lowest energies so far. With the achieved results, the algorithm converges rapidly and efficiently. For all ten 64-monomer sequences, the algorithm finds lower energies within comparable computation times than previous methods. Numeric results show that the heuristic ELP method is a competitive tool for protein folding simulation in 3D lattice model. To the best of our knowledge, this is the first application of ELP to the 3D discrete space.     

SH3-like fold proteins are structurally conserved and functionally divergent

The folding space for all the protein sequences is limited. Therefore it was observed that many proteins, whose sequences are not related, have similar fold characteristics. The fold databases like SCOP and CATH have classified various protein folds. However, in-depth analysis of the functional features of these folds was not done. We analyzed about twenty unique SH3-like folded proteins in their structural environment and functional characteristics. From our analysis it is apparent that the SH3-like folds could carry out various functions by modulation of loops and the functional region is restricted to one side of a particular sheet helped by two or three loops. The functions vary from oligonucleotide-binding to peptide-binding and other ligand binding. Although certain degree of sequence similarity was observed among the SH3-fold proteins, the similarity was restricted to the beta-strand regions of the proteins.     

Bacterial protein structures reveal phylum dependent divergence

Protein sequence space is vast compared to protein fold space. This raises important questions about how structures adapt to evolutionary changes in protein sequences. A growing trend is to regard protein fold space as a continuum rather than a series of discrete structures. From this perspective, homologous protein structures within the same functional classification should reveal a constant rate of structural drift relative to sequence changes. The clusters of orthologous groups (COG) classification system was used to annotate homologous bacterial protein structures in the Protein Data Bank (PDB). The structures and sequences of proteins within each COG were compared against each other to establish their relatedness. As expected, the analysis demonstrates a sharp structural divergence between the bacterial phyla Firmicutes and Proteobacteria. Additionally, each COG had a distinct sequence/structure relationship, indicating that different evolutionary pressures affect the degree of structural divergence. However, our analysis also shows the relative drift rate between sequence identity and structure divergence remains constant.     

Synthetic non-peptide mimetics of alpha-helices

Proteins in nature fold into native conformations in which combinations of peripherally projected aliphatic, aromatic and ionic functionalities direct a wide range of properties. Alpha-helices, one of the most common protein secondary structures, serve as important recognition regions on protein surfaces for numerous protein-protein, protein-DNA and protein-RNA interactions. These interactions are characterized by conserved structural features within the alpha-helical domain. Rational design of structural mimetics of these domains with synthetic small molecules has proven an effective means to modulate such protein functions. In this tutorial review we discuss strategies that utilize synthetic small-molecule antagonists to selectively target essential protein-protein interactions involved in certain diseases. We also evaluate some of the protein-protein interactions that have been or are potential targets for alpha-helix mimetics.     

Kinetics of cooperative protein folding involving two separate conformational families

The master equation that describes the kinetics of protein folding is solved numerically for a portion of Staphylococcal Protein A by a Laplace transformation. The calculations are carried out with 50 local-minimum conformations belonging to two conformational families. The master equation allows for transitions among all the 50 conformations in the evolution toward the final folded equilibrium distribution of conformations. It is concluded that the native protein folds in a fast cooperative process. The global energy minimum of a native protein can be reached after a sufficiently long folding time regardless of the initial state and the existence of a large number of local energy minima. Conformations representing non-native states of the protein can transform to the native state even if they do not belong to the native conformational family. Given a starting conformation, the protein molecule can fold to its final conformation through different paths. Finally, when the folding reaches the equilibrium distribution, the protein molecule adopts a set of conformations in which the global minimum has the largest average probability.     

Folding a nonbiological polymer into a compact multihelical structure

The only molecules that are currently known to fold into unique three-dimensional conformations and perform sophisticated functions are biological polymers - proteins and some RNA molecules. Our aim is to create a nonbiological sequence-specific polymer that folds in aqueous solution. Toward that end, we synthesized sequence-specific 30mer, 45mer, and 60mer peptoid oligomers (N-substituted glycine polymers) consisting of 15mer units we chained together by disulfide and oxime linkages to mimic the helical bundle structures commonly found in proteins. Because these 15mer sequences were previously shown to form defined helical structures that aggregate together at submillimolar concentrations, we expected that by covalently linking multiple 15mers together, they might fold as helical bundles. To probe whether they folded, we used fluorescence resonance energy transfer (FRET) reporter groups. We found that certain constructs fold up with a hydrophobic core and have cooperative folding transitions. Such molecules may ultimately provide a platform for designing specific functions resembling those of proteins.     

Conformationally Programmable Chiral Foldamers with Compact and Extended Domains Controlled by Monomer Structure

Foldamers are an important class of abiotic macromolecules, with potential therapeutic applications in the disruption of protein–protein interactions. The majority adopt a single conformational motif such as a helix. A class of foldamer is now introduced where the choice of heterocycle within each monomer, coupled with a strong conformation‐determining dipole repulsion effect, allows both helical and extended conformations to be selected. Combining these monomers into hetero‐oligomers enables highly controlled exploration of conformational space and projection of side‐chains along multiple vectors. The foldamers were rapidly constructed via an iterative deprotection‐cross‐coupling sequence, and their solid‐ and solution‐phase conformations were analysed by X‐ray crystallography and NMR and CD spectroscopy. These molecules may find applications in protein surface recognition where the interface does not involve canonical peptide secondary structures.     

Sequence-structure relationships in DNA oligomers: a computational approach

A collective-variable model for DNA structure is used to predict the conformation of a set of 30 octamer, decamer, and dodecamer oligomers for which high-resolution crystal structures are available. The model combines an all-atom base pair representation with an empirical backbone, emphasizing the role of base stacking in fixing sequence-dependent structure. We are able to reproduce trends in roll and twist to within 5 degrees across a large database of both A- and B-DNA oligomers. A genetic algorithm approach is used to search for global minimum structures and this is augmented by a grid search to identify local minimums. We find that the number of local minimums is highly sequence dependent, with certain sequences having a set of minimums that span the entire range between canonical A- and B-DNA conformations. Although the global minimum does not always agree with the crystal structure, for 24 of the 30 oligomers, we find low-energy local minimums that match the experimental step parameters. Discrepancies throw some light on the role of crystal packing in determining the solid-state conformation of double-helical DNA.     

蛋白质结构的“限域下最低能量结构片段”假说与蛋白质进化的“石器时代”

蛋白质折叠问题被称为第二遗传密码,至今未破译;蛋白质序列的天书仍然是"句读之不知,惑之不解"。在最近工作的基础上,我们提出了蛋白质结构的"限域下最低能量结构片段"假说。这一假说指出,蛋白质中存在一些关键的长程强相互作用位点,这些位点相当于标点符号,将蛋白质序列的天书变成可读的句子(多肽片段)。这些片段的天然结构是在这些强长程相互作用位点限域下的能量最低状态。完整的蛋白质结构由这些"限域下最低能量结构片段"拼合而成,而蛋白质整体结构并不一定是全局性的能量最低状态。在蛋白质折叠过程中,局部片段的天然结构倾向性为强长程相互作用的形成提供主要基于焓效应的驱动力,而天然强长程相互作用的形成为局部片段的天然结构提供主要基于熵效应的稳定性。在蛋白质进化早期,可能存在一个"石器时代",即依附不同界面(比如岩石)的限域作用而稳定的多肽片段先进化出来,后由这些片段逐步进化(包括拼合)而成蛋白质。