Multiscale simulations of protein folding: application to formation of secondary structures

A multiscale simulation method of protein folding is proposed, using atomic representation of protein and solvent, combing genetic algorithms to determine the key protein structures from a global view, with molecular dynamic simulations to reveal the local folding pathways, thus providing an integrated landscape of protein folding. The method is found to be superior to previously investigated global search algorithms or dynamic simulations alone. For secondary structure formation of a selected peptide, RN24, the structures and dynamics produced by this method agree well with corresponding experimental results. Three most populated conformations are observed, including hairpin, β-sheet and α-helix. The energetic barriers separating these three structures are comparable to the kinetic energy of the atoms of the peptide, implying that the transition between these states can be easily triggered by kinetic perturbations, mainly through electrostatic interactions between charged atoms. Transitions between α-helix and β-sheet should jump over at least two energy barriers and may stay in the energetic trap of hairpin. It is proposed that the structure of proteins should be jointly governed by thermodynamic and dynamic factors; free energy is not the exclusive dominant for stability of proteins.     

Efficient sampling of RNA secondary structures from the Boltzmann ensemble of low-energy

We adapt here a surprising technique, the boustrophedon method, to speed up the sampling of RNA secondary structures from the Boltzmann low-energy ensemble. This technique is simple and its implementation straight-forward, as it only requires a permutation in the order of some operations already performed in the stochastic traceback stage of these algorithms. It nevertheless greatly improves their worst-case complexity from to , for n the size of the original sequence. Moreover the average-case complexity of the generation is shown to be improved from to in an Boltzmann-weighted homopolymer model based on the Nussinov–Jacobson free-energy model. These results are extended to the more realistic Turner free-energy model through experiments performed on both structured (Drosophilia melanogaster mRNA 5S) and hybrid (Staphylococcus aureus RNAIII) RNA sequences, using a boustrophedon modified version of the popular software UnaFold. This improvement allows for the sampling of greater and more significant sets of structures in a given time.      

Ab initio folding of extended α‐helix: A theoretical study about the role of electrostatic polarization in the folding of helical structures

In this work, we report the ab initio folding of three different extended helical peptides namely 2khk, N36, and C34 through conventional molecular dynamics simulation at room temperature using implicit solvation model. Employing adaptive hydrogen bond specific charge (AHBC) scheme to account for the polarization effect of hydrogen bonds established during the simulation, the effective folding of the three extended helices were observed with best backbone RMSDs in comparison to the experimental structures over the helical region determined to be 1.30 Å for 2khk, 0.73 Å for N36 and 0.72 Å for C34. In this study, 2khk will be used as a benchmark case serving as a means to compare the ability of polarized (AHBC) and nonpolarized force field in the folding of an extended helix. Analyses conducted revealed the ability of the AHBC scheme in effectively folding the extended helix by promoting helix growth through the stabilization of backbone hydrogen bonds upon formation during the folding process. Similar observations were also noted when AHBC scheme was employed during the folding of C34 and N36. However, under Amber03 force field, helical structures formed during the folding of 2khk was not accompanied by stabilization thus highlighting the importance of electrostatic polarization in the folding of helical structures. Proteins 2013. © 2013 Wiley Periodicals, Inc.     

Elastic properties of proteins: insight on the folding process and evolutionary selection of native structures

We carry out a theoretical study of the vibrational and relaxation properties of naturally occurring proteins with the purpose of characterizing both the folding and equilibrium thermodynamics. By means of a suitable model, we provide a full characterization of the spectrum and eigenmodes of vibration at various temperatures by merely exploiting the knowledge of the protein native structure. It is shown that the rate at which perturbations decay at the folding transition correlates well with experimental folding rates. This validation is carried out on a list of about 30 two-state folders. Furthermore, the qualitative analysis of residues mean square displacements (shown to reproduce crystallographic data accurately) provides a reliable and statistically accurate method to identify crucial folding sites/contacts. This novel strategy is validated against clinical data for human immunodeficiency virus type 1 (HIV-1) protease. Finally, we compare the spectra and eigenmodes of vibration of natural proteins against randomly generated compact structures and regular random graphs. The comparison reveals a distinctive enhanced flexibility of natural structures accompanied by slow relaxation times at the folding temperature. The fact that these properties are connected intimately to the presence and assembly of secondary motifs hints at the special criteria adopted by evolution in the selection of viable folds.     

Translational standby sites: how ribosomes may deal with the rapid folding kinetics of mRNA

We have previously shown that stable base-pairing at a translational initiation site in Escherichia coli can inhibit translation by competing with the binding of ribosomes. When the base-pairing is not too strong, this competition is won by the ribosomes, resulting in efficient translation from a structured ribosome binding site (RBS). We now re-examine these results in the light of RNA folding kinetics and find that the window during which a folded RBS is open is generally much too short to recruit a 30S ribosomal subunit from the cytoplasm. We argue that to achieve efficient expression, a 30S subunit must already be in contact with the mRNA while this is still folded, to shift into place as soon as the structure opens. Single-stranded regions flanking the structure may constitute a standby site, to which the 30S subunit can attach non-specifically. We propose a steady-state kinetic model for the early steps of translational initiation and use this to examine various quantitative aspects of standby binding. The kinetic model provides an explanation of why the earlier equilibrium competition model predicted implausibly high 30S-mRNA affinities. Because all RNA is structured to some degree, standby binding is probably a general feature of translational initiation.     

Modeling the role of disulfide bonds in protein folding: Entropic barriers and pathways

The role of disulfide bonds in directing protein folding is studied using lattice models. We find that the stability and the specificity of the disulfide bond interactions play quite different roles in the folding process: Under some conditions, the stability decreases the overall rate of folding; the specificity, however, by yielding a simpler connectivity of intermediates, always increases the rate of folding. This conclusion is intimately related to the selection mechanism entailed by entropic driving forces, such as the loop formation probability, and entropic barriers separating the native and the many native-like metastable states. The folding time is found to be a minimum for a certain range of the effective disulfide bond interaction. Examination of a model, which allows for the formation of disulfide bonded intermediates, suggests that folding proceeds via a threestage multiple pathways kinetics. We show that there are pathways to the native state involving only native-like intermediates, as well as those that are mediated by nonnative intermediates. These findings are interpreted in terms of the appropriate energy landscape describing the barriers connecting low energy conformations. The consistency of our conclusions with several experimental studies is also discussed. © 1995 Wiley-Liss, Inc.     

Principles of RNA compaction: insights from the equilibrium folding pathway of the P4-P6 RNA domain in monovalent cations

Counterions are required for RNA folding, and divalent metal ions such as Mg(2+) are often critical. To dissect the role of counterions, we have compared global and local folding of wild-type and mutant variants of P4-P6 RNA derived from the Tetrahymena group I ribozyme in monovalent and in divalent metal ions. A remarkably simple picture of the folding thermodynamics emerges. The equilibrium folding pathway in monovalent ions displays two phases. In the first phase, RNA molecules that are initially in an extended conformation enforced by charge-charge repulsion are relaxed by electrostatic screening to a state with increased flexibility but without formation of long-range tertiary contacts. At higher concentrations of monovalent ions, a state that is nearly identical to the native folded state in the presence of Mg(2+) is formed, with tertiary contacts that involve base and backbone interactions but without the subset of interactions that involve specific divalent metal ion-binding sites. The folding model derived from these and previous results provides a robust framework for understanding the equilibrium and kinetic folding of RNA.     

Reinvestigating the codon and amino acid usage of S. cerevisiae genome: a new insight from protein secondary structure analysis

Biased usage of synonymous codons has been elucidated under the perspective of cellular tRNA abundance for quite a long time now. Taking advantage of publicly available gene expression data for Saccharomyces cerevisiae, a systematic analysis of the codon and amino acid usages in two different coding regions corresponding to the regular (helix and strand) as well as the irregular (coil) protein secondary structures, have been performed. Our analyses suggest that apart from tRNA abundance, mRNA folding stability is another major evolutionary force in shaping the codon and amino acid usage differences between the highly and lowly expressed genes in S. cerevisiae genome and surprisingly it depends on the coding regions corresponding to the secondary structures of the encoded proteins. This is obviously a new paradigm in understanding the codon usage in S. cerevisiae. Differential amino acid usage between highly and lowly expressed genes in the regions coding for the irregular protein secondary structure in S. cerevisiae is expounded by the stability of the mRNA folded structure. Irrespective of the protein secondary structural type, the highly expressed genes always tend to encode cheaper amino acids in order to reduce the overall biosynthetic cost of production of the corresponding protein. This study supports the hypothesis that the tRNA abundance is a consequence of and not a reason for the biased usage of amino acid between highly and lowly expressed genes.     

The fastest global events in RNA folding: electrostatic relaxation and tertiary collapse of the Tetrahymena ribozyme

Large RNAs can collapse into compact conformations well before the stable formation of the tertiary contacts that define their final folds. This study identifies likely physical mechanisms driving these early compaction events in RNA folding. We have employed time-resolved small-angle X-ray scattering to monitor the fastest global shape changes of the Tetrahymena ribozyme under different ionic conditions and with RNA mutations that remove long-range tertiary contacts. A partial collapse in each of the folding time-courses occurs within tens of milliseconds with either monovalent or divalent cations. Combined with comparison to predictions from structural models, this observation suggests a relaxation of the RNA to a more compact but denatured conformational ensemble in response to enhanced electrostatic screening at higher ionic concentrations. Further, the results provide evidence against counterion-correlation-mediated attraction between RNA double helices, a recently proposed model for early collapse. A previous study revealed a second 100 ms phase of collapse to a globular state. Surprisingly, we find that progression to this second early folding intermediate requires RNA sequence motifs that eventually mediate native long-range tertiary interactions, even though these regions of the RNA were observed to be solvent-accessible in previous footprinting studies under similar conditions. These results help delineate an analogy between the early conformational changes in RNA folding and the "burst phase" changes and molten globule formation in protein folding.     

Apparent local stability of the secondary structure of Azotobacter vinelandii holoflavodoxin II as probed by hydrogen exchange: implications for redox potential regulation and flavodoxin folding.

As a first step to determine the folding pathway of a protein with an alpha/beta doubly wound topology, the 1H, 13C, and 15N backbone chemical shifts of Azotobacter vinelandii holoflavodoxin II (179 residues) have been determined using multidimensional NMR spectroscopy. Its secondary structure is shown to contain a five-stranded parallel beta-sheet (beta2-beta1-beta3-beta4-beta5) and five alpha-helices. Exchange rates for the individual amide protons of holoflavodoxin were determined using the hydrogen exchange method. The amide protons of 65 residues distributed throughout the structure of holoflavodoxin exchange slowly at pH* 6.2 [kex < 10(-5) s(-1)] and can be used as probes in future folding studies. Measured exchange rates relate to apparent local free energies for transient opening. We propose that the amide protons in the core of holoflavodoxin only exchange by global unfolding of the apo state of the protein. The results obtained are discussed with respect to their implications for flavodoxin folding and for modulation of the flavin redox potential by the apoprotein. We do not find any evidence that A. vinelandii holoflavodoxin II is divided into two subdomains based on its amide proton exchange rates, as opposed to what is found for the structurally but not sequentially homologous alpha/beta doubly wound protein Che Y.     

Redesigning the type II' β‐turn in green fluorescent protein to type I': Implications for folding kinetics and stability

Both Type I' and Type II' β‐turns have the same sense of the β‐turn twist that is compatible with the β‐sheet twist. They occur predominantly in two residue β‐hairpins, but the occurrence of Type I' β‐turns is two times higher than Type II' β‐turns. This suggests that Type I' β‐turns may be more stable than Type II' β‐turns, and Type I' β‐turn sequence and structure can be more favorable for protein folding than Type II' β‐turns. Here, we redesigned the native Type II' β‐turn in GFP to Type I' β‐turn, and investigated its effect on protein folding and stability. The Type I' β‐turns were designed based on the statistical analysis of residues in natural Type I' β‐turns. The substitution of the native “GD” sequence of i+1 and i+2 residues with Type I' preferred “(N/D)G” sequence motif increased the folding rate by 50% and slightly improved the thermodynamic stability. Despite the enhancement of in vitro refolding kinetics and stability of the redesigned mutants, they showed poor soluble expression level compared to wild type. To overcome this problem, i and i + 3 residues of the designed Type I' β‐turn were further engineered. The mutation of Thr to Lys at i + 3 could restore the in vivo soluble expression of the Type I' mutant. This study indicates that Type II' β‐turns in natural β‐hairpins can be further optimized by converting the sequence to Type I'. Proteins 2014; 82:2812–2822. © 2014 Wiley Periodicals, Inc.