No evidence that mRNAs have lower folding free energies than random sequences with the same dinucleotide distribution

This work investigates whether mRNA has a lower estimated folding free energy than random sequences. The free energy estimates are calculated by the mfold program for prediction of RNA secondary structures. For a set of 46 mRNAs it is shown that the predicted free energy is not significantly different from random sequences with the same dinucleotide distribution. For random sequences with the same mononucleotide distribution it has previously been shown that the native mRNA sequences have a lower predicted free energy, which indicates a more stable structure than random sequences. However, dinucleotide content is important when assessing the significance of predicted free energy as the physical stability of RNA secondary structure is known to depend on dinucleotide base stacking energies. Even known RNA secondary structures, like tRNAs, can be shown to have predicted free energies indistinguishable from randomized sequences. This suggests that the predicted free energy is not always a good determinant for RNA folding.     

mRNAs have greater negative folding free energies than shuffled or codon choice randomized sequences

An examination of 51 mRNA sequences in GenBank has revealed that calculated mRNA folding is more stable than expected by chance. Free energy minimization calculations of native mRNA sequences are more negative than randomized mRNA sequences with the same base composition and length. Randomization of the coding region of genes yields folding free energies of less negative magnitude than the original native mRNA sequence. Randomization of codon choice, while still preserving original base composition, also results in less stable mRNAs. This suggests that a bias in the selection of codons favors the potential formation of mRNA structures which contribute to folding stability.     

Failures of inverse folding and threading with gapped alignment

To calculate the tertiary structure of a protein from its amino acid sequence, the thermodynamic approach requires a potential function of sequence and conformation that has its global minimum at the native conformation for many different proteins. Here we study the behavior of such functions for the simplest model system that still has some of the features of the protein folding problem, namely two-dimensional square lattice chain configurations involving two residue types. First we show that even the given contact potential, which by definition is used to identify the folding sequences and their unique native conformations, cannot always correctly select which sequences will fold to a given structure. Second, we demonstrate that the given contact potential is not always able to favor the native alignment of a native sequence on its own native conformation over other gapped alignments of different folding sequences onto that same conformation. Because of these shortcomings, even in this simple model system in which all conformations and all native sequences are known and determined directly by the given potential, we must reexamine our expectations for empirical potentials used for inverse folding and gapped alignment on more realistic representations of proteins. © 1996 Wiley-Liss, Inc.     

Computational protein design and large-scale assessment by I-TASSER structure assembly simulations

Protein design aims at designing new protein molecules of desired structure and functionality. One of the major obstacles to large-scale protein design are the extensive time and manpower requirements for experimental validation of designed sequences. Recent advances in protein structure prediction have provided potentials for an automated assessment of the designed sequences via folding simulations. We present a new protocol for protein design and validation. The sequence space is initially searched by Monte Carlo sampling guided by a public atomic potential, with candidate sequences selected by the clustering of sequence decoys. The designed sequences are then assessed by I-TASSER folding simulations, which generate full-length atomic structural models by the iterative assembly of threading fragments. The protocol is tested on 52 nonhomologous single-domain proteins, with an average sequence identity of 24% between the designed sequences and the native sequences. Despite this low sequence identity, three-dimensional models predicted for the first designed sequence have an RMSD of < 2 Å to the target structure in 62% of cases. This percentage increases to 77% if we consider the three-dimensional models from the top 10 designed sequences. Such a striking consistency between the target structure and the structural prediction from nonhomologous sequences, despite the fact that the design and folding algorithms adopt completely different force fields, indicates that the design algorithm captures the features essential to the global fold of the target. On average, the designed sequences have a free energy that is 0.39 kcal/(mol residue) lower than in the native sequences, potentially affording a greater stability to synthesized target folds.     

Symmetric connectivity of secondary structure elements enhances the diversity of folding pathways

The influence of native connectivity of secondary structure elements (SSE) on folding is studied using coarse-grained models of proteins with mixed alpha and beta structure and the analysis of the structural database of wild-type proteins. We found that the distribution of SSE along a sequence determines the diversity of folding pathways. If alpha and beta SSE are localized in different parts of a sequence, the diversity of folding pathways is restricted. An even (symmetric) distribution of alpha and beta SSE with respect to sequence midpoint favors multiple folding routes. Simulations are supplemented by the database analysis of the distribution of SSE in wild-type protein sequences. On an average, two-thirds of wild-type proteins with mixed alpha and beta structure have symmetric distribution of alpha and beta SSE. The propensity for symmetric distribution of SSE is especially evident for large proteins with the number of SSE > or = 10. We suggest that symmetric SSE distribution in protein sequences may arise due to nearly random allocation of alpha and beta structure along wild-type sequences. The tendency of long sequences to misfold is perhaps compensated by the enhanced pathway diversity. In addition, folding pathways are shown to progress via hierarchic assembly of SSE in accordance with their proximity along a sequence. We demonstrate that under mild denaturation conditions folding and unfolding pathways are similar. However, the reversibility of folding/unfolding pathways is shown to depend on the distribution of SSE. If alpha and beta SSE are localized in different parts of a sequence, folding and unfolding pathways are likely to coincide.     

Computational design of proteins stereochemically optimized in size, stability, and folding speed

Artificial proteins potentially barrier-free in the folding kinetics are approached computationally under the guidance of protein-folding theories. The smallest and fastest folding globular protein triple-helix-bundle (THB) is so modified as to minimize or eliminate its presumed barriers in folding speed. As the barriers may reside in the ordering of either secondary or tertiary structure, the elements of both secondary and tertiary structure in the protein are targeted for prenucleation with suitable stereochemically constrained amino acid residues. The required elements of topology and sequence for the THB are optimized independently; first the topology is optimized with simulated annealing in polypeptides of highly simplified alphabet; next, the sequence in side chains is optimized using the standard inverse design methods. The resultant three best-adapted THBs, variable in topology and distinctive in sequences, are assessed by comparing them with a few benchmark proteins. The results of mainly molecular dynamics (MD) comparisons, undertaken in explicit water at different temperatures, show that the designed sequences are favorably placed against the chosen benchmarks as THB proteins potentially thermostable in the native folds. Folding simulation experiments with MD establish that the designed sequences are rapid in the folding of individual helices, but not in the evolution of tertiary structure; energetic cum topological frustrations remain but could be the artifacts of the starting conformations that were chosen in the THBs in the folding simulations. Overall, a practical high-throughput approach for de novo protein design has been developed that may have fruitful application for any type of tertiary structure.     

Local structure-based sequence profile database for local and global protein structure predictions

MOTIVATION: A large body of evidence suggests that protein structural information is frequently encoded in local sequences-sequence-structure relationships derived from local structure/sequence analyses could significantly enhance the capacities of protein structure prediction methods. In this paper, the prediction capacity of a database (LSBSP2) that organizes local sequence-structure relationships encoded in local structures with two consecutive secondary structure elements is tested with two computational procedures for protein structure prediction. The goal is twofold: to test the folding hypothesis that local structures are determined by local sequences, and to enhance our capacity in predicting protein structures from their amino acid sequences. RESULTS: The LSBSP2 database contains a large set of sequence profiles derived from exhaustive pair-wise structural alignments for local structures with two consecutive secondary structure elements. One computational procedure makes use of the PSI-BLAST alignment program to predict local structures for testing sequence fragments by matching the testing sequence fragments onto the sequence profiles in the LSBSP2 database. The results show that 54% of the test sequence fragments were predicted with local structures that match closely with their native local structures. The other computational procedure is a filter system that is capable of removing false positives as possible from a set of PSI-BLAST hits. An assessment with a large set of non-redundant protein structures shows that the PSI-BLAST + filter system improves the prediction specificity by up to two-fold over the prediction specificity of the PSI-BLAST program for distantly related protein pairs. Tests with the two computational procedures above demonstrate that local sequence-structure relationships can indeed enhance our capacity in protein structure prediction. The results also indicate that local sequences encoded with strong local structure propensities play an important role in determining the native state folding topology.     

Denatured-state energy landscapes of a protein structural database reveal the energetic determinants of a framework model for folding

Position-specific denatured-state thermodynamics were determined for a database of human proteins by use of an ensemble-based model of protein structure. The results of modeling denatured protein in this manner reveal important sequence-dependent thermodynamic properties in the denatured ensembles as well as fundamental differences between the denatured and native ensembles in overall thermodynamic character. The generality and robustness of these results were validated by performing fold-recognition experiments, whereby sequences were matched with their respective folds based on amino acid propensities for the different energetic environments in the protein, as determined through cluster analysis. Correlation analysis between structure and energetic information revealed that sequence segments destined for β-sheet in the final native fold are energetically more predisposed to a broader repertoire of states than are sequence segments destined for α-helix. These results suggest that within the subensemble of mostly unstructured states, the energy landscapes are dominated by states in which parts of helices adopt structure, whereas structure formation for sequences destined for β-strand is far less probable. These results support a framework model of folding, which suggests that, in general, the denatured state has evolutionarily evolved to avoid low-energy conformations in sequences that ultimately adopt β-strand. Instead, the denatured state evolved so that sequence segments that ultimately adopt α-helix and coil will have a high intrinsic structure formation capability, thus serving as potential nucleation sites.     

Exploring local and non-local interactions for protein stability by structural motif engineering

In order to probe the relative contribution of local and non-local interactions to the thermodynamic stability of proteins, we have devised an experimental approach based on a combination of motif engineering and sequence shuffling. Candidate chain segments in an immunoglobulin V(L) domain were identified whose conformation is proposed to be dominated by non-local interactions. Locally interacting structural motifs of a different conformation were then constructed as replacements, by introducing motif consensus sequences. We find that all nine replacements we constructed systematically reduce the folding cooperativity. By comparing this destabilising effect with the folding transitions of shuffled sequences for three of these motifs, we estimate the contribution of local, native interactions to the free energy of folding. Our results suggest that local and non-local interactions contribute to stability by an approximately equal amount, but that local interactions stabilise by increasing the resistance to denaturation while non-local interactions increase folding cooperativity. The systematic loss of stability by sequence shuffling in these host-guest experiments suggests that the designed interactions indeed are present in the native state, thus consensus sequence engineering may be a useful tool in structure design, but non-local interactions must be taken into account for global stability engineering. Statistical approaches are powerful tools for engineering protein structure and stability, but an analysis based on local sequence propensities alone does not adequately represent the balance of sequence and context in protein structures.     

枯草芽孢杆菌同义密码子使用偏性对蛋白质折叠速率的影响

目前,有关同义密码子使用偏性对蛋白质折叠的影响研究中,样本蛋白均来源于不同的物种。考虑到同义密码子使用偏性的物种差异性,选取枯草杆菌的核蛋白为研究对象。首先,将每条核蛋白按二级结构截取为α螺旋片段、β折叠片段和无规卷曲（α-β混合）片段,并计算其蛋白质折叠速率。然后,整理每个片段相应的核酸序列信息,计算其同义密码子使用度。在此基础上,分析枯草芽孢杆菌核蛋白的同义密码子使用偏性与蛋白质折叠速率的相关性。发现对于不同二级结构的肽链片段,都有部分密码子的使用偏性与其对应的肽链折叠速率显著相关。进一步分析发现,与肽链片段折叠速率显著相关的密码子绝大部分为枯草杆菌全序列或核蛋白序列的每一组同义密码子中使用度最高的密码子。结果表明,在蛋白质的折叠过程中,枯草芽孢杆菌的同义密码子使用偏性起着重要作用。     

Circular dichroism of reduced and oxidized recombinant human epidermal growth factor.

To further elucidate the role of the disulfide bonds in determining the protein folding of recombinant human epidermal growth factor (r-HuEGF) we studied the structure of reduced and oxidized r-HuEGF using circular dichroism (CD). The far UV CD spectrum of reduced r-HuEGF in 10 mM sodium phosphate pH 3.0 is very different from that of the oxidized molecule. The spectrum of the reduced molecule consists of a plateau from 225 to 200 nm, consistent with the presence of alpha-helix, beta-sheet, and unordered structure. The addition of the alpha-helix inducer trifluoroethanol to the reduced molecule resulted in an enhancement of alpha-helix, at the apparent expense of beta-sheet, while the oxidized molecule was unaffected by the presence of this reagent. Secondary structure predictions based on the amino acid sequence of EGF correlate most closely with the structure of the reduced molecule. From these results, it appears that the r-HuEGF has a more regular secondary structure in the absence of the disulfide bonds than in their presence. This suggests that the folding of EGF occurs by destroying the regular secondary structure that was present in the reduced state, and that the structure of the native molecule is dictated largely by disulfide bonding.     

A tale of two secondary structure elements: when a beta-hairpin becomes an alpha-helix.

In this work, we have analyzed the relative importance of secondary versus tertiary interactions in stabilizing and guiding protein folding. For this purpose, we have designed four different mutants to replace the alpha-helix of the GB1 domain by a sequence with strong beta-hairpin propensity in isolation. In particular, we have chosen the sequence of the second beta-hairpin of the GB1 domain, which populates the native conformation in aqueous solution to a significant extent. The resulting protein has roughly 30 % of its sequence duplicated and maintains the 3D-structure of the wild-type protein, but with lower stability (up to -5 kcal/mol). The loss of intrinsic helix stability accounts for about 80 % of the decrease in free energy, illustrating the importance of local interactions in protein stability. Interestingly enough, all the mutant proteins, included the one with the duplicated beta-hairpin sequence, fold with similar rates as the GB1 domain. Essentially, it is the nature of the rate-limiting step in the folding reaction that determines whether a particular interaction will speed up, or not, the folding rates. While local contacts are important in determining protein stability, residues involved in tertiary contacts in combination with the topology of the native fold, seem to be responsible for the specificity of protein structures. Proteins with non-native secondary structure tendencies can adopt stable folds and be as efficient in folding as those proteins with native-like propensities.     

Simulating protein folding initiation sites using an alpha‐carbon‐only knowledge‐based force field

Protein folding is a hierarchical process where structure forms locally first, then globally. Some short sequence segments initiate folding through strong structural preferences that are independent of their three‐dimensional context in proteins. We have constructed a knowledge‐based force field in which the energy functions are conditional on local sequence patterns, as expressed in the hidden Markov model for local structure (HMMSTR). Carbon‐alpha force field (CALF) builds sequence specific statistical potentials based on database frequencies for α‐carbon virtual bond opening and dihedral angles, pair‐wise contacts and hydrogen bond donor‐acceptor pairs, and simulates folding via Brownian dynamics. We introduce hydrogen bond donor and acceptor potentials as α‐carbon probability fields that are conditional on the predicted local sequence. Constant temperature simulations were carried out using 27 peptides selected as putative folding initiation sites, each 12 residues in length, representing several different local structure motifs. Each 0.6 μs trajectory was clustered based on structure. Simulation convergence or representativeness was assessed by subdividing trajectories and comparing clusters. For 21 of the 27 sequences, the largest cluster made up more than half of the total trajectory. Of these 21 sequences, 14 had cluster centers that were at most 2.6 Å root mean square deviation (RMSD) from their native structure in the corresponding full‐length protein. To assess the adequacy of the energy function on nonlocal interactions, 11 full length native structures were relaxed using Brownian dynamics simulations. Equilibrated structures deviated from their native states but retained their overall topology and compactness. A simple potential that folds proteins locally and stabilizes proteins globally may enable a more realistic understanding of hierarchical folding pathways. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Evidence that microRNA precursors, unlike other non-coding RNAs, have lower folding free energies than random sequences

MOTIVATION: Most non-coding RNAs are characterized by a specific secondary and tertiary structure that determines their function. Here, we investigate the folding energy of the secondary structure of non-coding RNA sequences, such as microRNA precursors, transfer RNAs and ribosomal RNAs in several eukaryotic taxa. Statistical biases are assessed by a randomization test, in which the predicted minimum free energy of folding is compared with values obtained for structures inferred from randomly shuffling the original sequences. RESULTS: In contrast with transfer RNAs and ribosomal RNAs, the majority of the microRNA sequences clearly exhibit a folding free energy that is considerably lower than that for shuffled sequences, indicating a high tendency in the sequence towards a stable secondary structure. A possible usage of this statistical test in the framework of the detection of genuine miRNA sequences is discussed.     

How the Sequence of a Gene Specifies Structural Symmetry in Proteins

Internal symmetry is commonly observed in the majority of fundamental protein folds. Meanwhile, sufficient evidence suggests that nascent polypeptide chains of proteins have the potential to start the co-translational folding process and this process allows mRNA to contain additional information on protein structure. In this paper, we study the relationship between gene sequences and protein structures from the viewpoint of symmetry to explore how gene sequences code for structural symmetry in proteins. We found that, for a set of two-fold symmetric proteins from left-handed beta-helix fold, intragenic symmetry always exists in their corresponding gene sequences. Meanwhile, codon usage bias and local mRNA structure might be involved in modulating translation speed for the formation of structural symmetry: a major decrease of local codon usage bias in the middle of the codon sequence can be identified as a common feature; and major or consecutive decreases in local mRNA folding energy near the boundaries of the symmetric substructures can also be observed. The results suggest that gene duplication and fusion may be an evolutionarily conserved process for this protein fold. In addition, the usage of rare codons and the formation of higher order of secondary structure near the boundaries of symmetric substructures might have coevolved as conserved mechanisms to slow down translation elongation and to facilitate effective folding of symmetric substructures. These findings provide valuable insights into our understanding of the mechanisms of translation and its evolution, as well as the design of proteins via symmetric modules.     

A Folding Zone in the Ribosomal Exit Tunnel for Kv1.3 Helix Formation

Although it is now clear that protein secondary structure can be acquired early, while the nascent peptide resides within the ribosomal exit tunnel, the principles governing folding of native polytopic proteins have not yet been elucidated. We now report an extensive investigation of native Kv1.3, a voltage-gated K⁺ channel, including transmembrane and linker segments synthesized in sequence. These native segments form helices vectorially (N- to C-terminus) only in a permissive vestibule located in the last 20 Å of the tunnel. Native linker sequences similarly fold in this vestibule. Finally, secondary structure acquired in the ribosome is retained in the translocon. These findings emerge from accessibility studies of a diversity of native transmembrane and linker sequences and may therefore be applicable to protein biogenesis in general.     

The hydrogen exchange core and protein folding.

A database of hydrogen-deuterium exchange results has been compiled for proteins for which there are published rates of out-exchange in the native state, protection against exchange during folding, and out-exchange in partially folded forms. The question of whether the slow exchange core is the folding core (Woodward C, 1993, Trends Biochem Sci 18:359-360) is reexamined in a detailed comparison of the specific amide protons (NHs) and the elements of secondary structure on which they are located. For each pulsed exchange or competition experiment, probe NHs are shown explicitly; the large number and broad distribution of probe NHs support the validity of comparing out-exchange with pulsed-exchange/competition experiments. There is a strong tendency for the same elements of secondary structure to carry NHs most protected in the native state, NHs first protected during folding, and NHs most protected in partially folded species. There is not a one-to-one correspondence of individual NHs. Proteins for which there are published data for native state out-exchange and theta values are also reviewed. The elements of secondary structure containing the slowest exchanging NHs in native proteins tend to contain side chains with high theta values or be connected to a turn/loop with high theta values. A definition for a protein core is proposed, and the implications for protein folding are discussed. Apparently, during folding and in the native state, nonlocal interactions between core sequences are favored more than other possible nonlocal interactions. Other studies of partially folded bovine pancreatic trypsin inhibitor (Barbar E, Barany G, Woodward C, 1995, Biochemistry 34:11423-11434; Barber E, Hare M, Daragan V, Barany G, Woodward C, 1998, Biochemistry 37:7822-7833), suggest that developing cores have site-specific energy barriers between microstates, one disordered, and the other(s) more ordered.     

Non-native interactions play an effective role in protein folding dynamics

Systematic Monte Carlo simulations of simple lattice models show that the final stage of protein folding is an ordered process where native contacts get locked (i.e., the residues come into contact and remain in contact for the duration of the folding process) in a well‐defined order. The detailed study of the folding dynamics of protein‐like sequences designed as to exhibit different contact energy distributions, as well as different degrees of sequence optimization (i.e., participation of non‐native interactions in the folding process), reveals significant differences in the corresponding locking scenarios—the collection of native contacts and their average locking times, which are largely ascribable to the dynamics of non‐native contacts. Furthermore, strong evidence for a positive role played by non‐native contacts at an early folding stage was also found. Interestingly, for topologically simple target structures, a positive interplay between native and non‐native contacts is observed also toward the end of the folding process, suggesting that non‐native contacts may indeed affect the overall folding process. For target models exhibiting clear two‐state kinetics, the relation between the nucleation mechanism of folding and the locking scenario is investigated. Our results suggest that the stabilization of the folding transition state can be achieved through the establishment of a very small network of native contacts that are the first to lock during the folding process.     

Computer simulations of protein folding by targeted molecular dynamics

We have performed 128 folding and 45 unfolding molecular dynamics runs of chymotrypsin inhibitor 2 (CI2) with an implicit solvation model for a total simulation time of 0.4 microseconds. Folding requires that the three-dimensional structure of the native state is known. It was simulated at 300 K by supplementing the force field with a harmonic restraint which acts on the root-mean-square deviation and allows to decrease the distance to the target conformation. High temperature and/or the harmonic restraint were used to induce unfolding. Of the 62 folding simulations started from random conformations, 31 reached the native structure, while the success rate was 83% for the 66 trajectories which began from conformations unfolded by high-temperature dynamics. A funnel-like energy landscape is observed for unfolding at 475 K, while the unfolding runs at 300 K and 375 K as well as most of the folding trajectories have an almost flat energy landscape for conformations with less than about 50% of native contacts formed. The sequence of events, i.e., secondary and tertiary structure formation, is similar in all folding and unfolding simulations, despite the diversity of the pathways. Previous unfolding simulations of CI2 performed with different force fields showed a similar sequence of events. These results suggest that the topology of the native state plays an important role in the folding process.     

mRNA的序列、结构以及翻译速率与蛋白质结构的关系

mRNA所包含的核苷酸序列通过三联体密码子决定了蛋白质的氨基酸序列。但是, 由于对氨基酸同义密码使用频率上的差异, 密码子与反密码子相互作用效率上的不同, 以及密码子上下文关系和mRNA 不同区域二级结构上的差异, 造成了核糖体对mRNA 不同区域翻译速度上的差异, 加之共翻译折叠的作用, 使得mRNA 的序列和结构影响着蛋白质空间结构的形成。