Short-lived alpha-helical intermediates in the folding of beta-sheet proteins.

Several lines of evidence point strongly toward the importance of highly alpha-helical intermediates in the folding of all globular proteins, regardless of their native structure. However, experimental refolding studies demonstrate no observable alpha-helical intermediate during refolding of some beta-sheet proteins and have dampened enthusiasm for this model of protein folding. In this study, beta-sheet proteins were hypothesized to have potential to form amphiphilic helices at a period of <3.6 residues/turn that matches or exceeds the potential at 3.6 residues/turn. Hypothetically, such potential is the basis for an effective and unidirectional mechanism by which highly alpha-helical intermediates might be rapidly disassembled during folding and potentially accounts for the difficulty in detecting highly alpha-helical intermediates during the folding of some proteins. The presence of this potential was confirmed, indicating that a model entailing ubiquitous formation of alpha-helical intermediates during the folding of globular proteins predicts previously unrecognized features of primary structure. Further, the folding of fatty acid binding protein, a predominantly beta-sheet protein that exhibits no apparent highly alpha-helical intermediate during folding, was dramatically accelerated by 2,2,2-trifluoroethanol, a solvent that stabilizes alpha-helical structure. This observation suggests that formation of an alpha-helix can be a rate-limiting step during folding of a predominantly beta-sheet protein and further supports the role of highly alpha-helical intermediates in the folding of all globular proteins.

Sequence and Structure Based Protein Folding Studies With Implications

As the expression of the genetic blueprint, proteins are at the heart of all biological systems. The ever increasing set of available protein structures has taught us that diversity is the hallmark of their architecture, a fundamental characteristic that enables them to perform the vast array of functionality upon which all of life depends. This diversity, however, is central to one of the most challenging problems in molecular biology: how does a folding polypeptide chain navigate its way through all of the myriad of possible conformations to find its own particular biologically active form? With few overarching structural principles to draw upon that can be applied to all protein architecture, the search for a solution to the protein folding problem has yet to produce an algorithm that can explain and duplicate this fundamental biological process. In this thesis, we take a two-pronged approach for investigating the protein folding process. Our initial statistical studies of the distributions of hydrophobic and hydrophilic residues within α-helices and β-sheets suggest (i) that hydrophobicity plays a critical role in helix and sheet formation; and (ii) that the nucleation of these motifs may result in largely unidirectional growth. Most tellingly, from an examination of the amino acids found in the smallest β-sheets, we do not find any evidence of a β-nucleating code in the primary protein sequence. Complementing these statistical analyses, we have analyzed the structural environments of several ever-widening aspects of protein topology. Our examination of the gaps between strands in the smallest β-sheets reveals a common organizational principle underlying β-formation involving strands separated by large sequential gaps: with very few exceptions, these large gaps fold into single, compact structural modules, bringing the β-strands that are otherwise far apart in the sequence close together in space. We conclude, therefore, that β-nucleation in the smallest sheets results from the co-location of two strands that are either local in sequence, or local in space following prior folding events. A second study of larger β-sheets both corroborates and extends these findings: virtually all large sequential gaps between pairs of β-strands organize themselves into an hierarchical arrangement, creating a bread-crumb model of go-and-come-back structural organization that ultimately juxtaposes two strands of a parental β-structure that are far apart in the sequence in close spatial proximity. In a final study, we have formalized this go-and-come-back notion into the concept of anti-parallel double-strandedness (DS), and measure this property across protein architecture in general. With over 90% of all residues in a large, non-redundant set of protein structures classified as DS, we conclude that DS is a unifying structural principle that underpins all globular proteins. We postulate, moreover, that this one simple principle, anti-parallel double-strandedness, unites protein structure, protein folding and protein evolution.

Stochastic protein folding simulation in the three-dimensional HP-model

We present results from three-dimensional protein folding simulations in the HP-model on ten benchmark problems. The simulations are executed by a simulated annealing-based algorithm with a time-dependent cooling schedule. The neighbourhood relation is determined by the pull-move set. The results provide experimental evidence that the maximum depth D of local minima of the underlying energy landscape can be upper bounded by D < n(2/3). The local search procedure employs the stopping criterion (In/delta)(D/gamma) where m is an estimation of the average number of neighbouring conformations, gamma relates to the mean of non-zero differences of the objective function for neighbouring conformations, and 1-delta is the confidence that a minimum conformation has been found. The bound complies with the results obtained for the ten benchmark problems. (c) 2008 Elsevier Ltd. All rights reserved.

Population-based local search for protein folding simulation in the MJ energy model and cubic lattices

We present experimental results on benchmark problems in 3D cubic lattice structures with the Miyazawa-Jernigan energy function for two local search procedures that utilise the pull-move set: (i) population-based local search (PLS) that traverses the energy landscape with greedy steps towards (potential) local minima followed by upward steps up to a certain level of the objective function; (ii) simulated annealing with a logarithmic cooling schedule (LSA). The parameter settings for PLS are derived from short LSA-runs executed in pre-processing and the procedure utilises tabu lists generated for each member of the population. In terms of the total number of energy function evaluations both methods perform equally well, however. PLS has the potential of being parallelised with an expected speed-up in the region of the population size. Furthermore, both methods require a significant smaller number of function evaluations when compared to Monte Carlo simulations with kink-jump moves. (C) 2009 Elsevier Ltd. All rights reserved.

Approximating the Set of Local Minima in Partial RNA Folding Landscapes

Motivation: We study a stochastic method for approximating the set of local minima in partial RNA folding landscapes associated with a bounded-distance neighbourhood of folding conformations. The conformations are limited to RNA secondary structures without pseudoknots. The method aims at exploring partial energy landscapes pL induced by folding simulations and their underlying neighbourhood relations. It combines an approximation of the number of local optima devised by Garnier and Kallel (2002) with a run-time estimation for identifying sets of local optima established by Reeves and Eremeev (2004).

Results: The method is tested on nine sequences of length between 50 nt and 400 nt, which allows us to compare the results with data generated by RNAsubopt and subsequent barrier tree calculations. On the nine sequences, the method captures on average 92% of local minima with settings designed for a target of 95%. The run-time of the heuristic can be estimated by O(n2D?ln?), where n is the sequence length, ? is the number of local minima in the partial landscape pL under consideration and D is the maximum number of steepest descent steps in attraction basins associated with pL.

General, PDB-based collective variables for protein folding

New, automated forms of data-analysis are required in order to understand the high-dimensional trajectories that are obtained from molecular dynamics simulations on proteins. Dimensionality reduction algorithms are particularly appealing in this regard as they allow one to construct unbiased, low-dimensional representations of the trajectory using only the information encoded in the trajectory. The downside of this approach is that different sets of coordinates are required for each different chemical systems under study precisely because the coordinates are constructed using information from the trajectory. In this paper we show how one can resolve this problem by using the sketch-map algorithm that we recently proposed to construct a low-dimensional representation of the structures contained in the protein data bank (PDB). We show that the resulting coordinates are as useful for analysing trajectory data as coordinates constructed using landmark configurations taken from the trajectory and that these coordinates can thus be used for understanding protein folding across a range of systems.

Metal ions and protein folding: conformational and functional interplay

Dissertation presented to obtain a PhD degree in Biochemistry at Instituto de Tecnologia Química e Biológica, Universidade Nova de Lisboa

Metal ions modulate the folding and stability of the tumor suppressor protein S100A2

Febs Journal (2009)276:1776-1786

A new paradigm for the folding of ribonucleic acids

De récentes découvertes montrent le rôle important que joue l’acide ribonucléique (ARN) au sein des cellules, que ce soit le contrôle de l’expression génétique, la régulation de plusieurs processus homéostasiques, en plus de la transcription et la traduction de l’acide désoxyribonucléique (ADN) en protéine. Si l’on veut comprendre comment la cellule fonctionne, nous devons d’abords comprendre ses composantes et comment ils interagissent, et en particulier chez l’ARN. La fonction d’une molécule est tributaire de sa structure tridimensionnelle (3D). Or, déterminer expérimentalement la structure 3D d’un ARN s’avère fort coûteux. Les méthodes courantes de prédiction par ordinateur de la structure d’un ARN ne tiennent compte que des appariements classiques ou canoniques, similaires à ceux de la fameuse structure en double-hélice de l’ADN. Ici, nous avons amélioré la prédiction de structures d’ARN en tenant compte de tous les types possibles d’appariements, dont ceux dits non-canoniques. Cela est rendu possible dans le contexte d’un nouveau paradigme pour le repliement des ARN, basé sur les motifs cycliques de nucléotides ; des blocs de bases pour la construction des ARN. De plus, nous avons dévelopées de nouvelles métriques pour quantifier la précision des méthodes de prédiction des structures 3D des ARN, vue l’introduction récente de plusieurs de ces méthodes. Enfin, nous avons évalué le pouvoir prédictif des nouvelles techniques de sondage de basse résolution des structures d’ARN.

Protein Folding Simulations: Confinement, External Fields and Sequence Design

The present Thesis looks at the problem of protein folding using Monte Carlo and Langevin simulations, three topics in protein folding have been studied: 1) the effect of confining potential barriers, 2) the effect of a static external field and 3) the design of amino acid sequences which fold in a short time and which have a stable native state (global minimum). Regarding the first topic, we studied the confinement of a small protein of 16 amino acids known as 1NJ0 (PDB code) which has a beta-sheet structure as a native state. The confinement of proteins occurs frequently in the cell environment. Some molecules called Chaperones, present in the cytoplasm, capture the unfolded proteins in their interior and avoid the formation of aggregates and misfolded proteins. This mechanism of confinement mediated by Chaperones is not yet well understood. In the present work we considered two kinds of potential barriers which try to mimic the confinement induced by a Chaperon molecule. The first kind of potential was a purely repulsive barrier whose only effect is to create a cavity where the protein folds up correctly. The second kind of potential was a barrier which includes both attractive and repulsive effects. We performed Wang-Landau simulations to calculate the thermodynamical properties of 1NJ0. From the free energy landscape plot we found that 1NJ0 has two intermediate states in the bulk (without confinement) which are clearly separated from the native and the unfolded states. For the case of the purely repulsive barrier we found that the intermediate states get closer to each other in the free energy landscape plot and eventually they collapse into a single intermediate state. The unfolded state is more compact, compared to that in the bulk, as the size of the barrier decreases. For an attractive barrier modifications of the states (native, unfolded and intermediates) are observed depending on the degree of attraction between the protein and the walls of the barrier. The strength of the attraction is measured by the parameter $\epsilon$. A purely repulsive barrier is obtained for $\epsilon=0$ and a purely attractive barrier for $\epsilon=1$. The states are changed slightly for magnitudes of the attraction up to $\epsilon=0.4$. The disappearance of the intermediate states of 1NJ0 is already observed for $\epsilon =0.6$. A very high attractive barrier ($\epsilon \sim 1.0$) produces a completely denatured state. In the second topic of this Thesis we dealt with the interaction of a protein with an external electric field. We demonstrated by means of computer simulations, specifically by using the Wang-Landau algorithm, that the folded, unfolded, and intermediate states can be modified by means of a field. We have found that an external field can induce several modifications in the thermodynamics of these states: for relatively low magnitudes of the field ($<2.06 \times 10^8$ V/m) no major changes in the states are observed. However, for higher magnitudes than ($6.19 \times 10^8$ V/m) one observes the appearance of a new native state which exhibits a helix-like structure. In contrast, the original native state is a $\beta$-sheet structure. In the new native state all the dipoles in the backbone structure are aligned parallel to the field. The design of amino acid sequences constitutes the third topic of the present work. We have tested the Rate of Convergence criterion proposed by D. Gridnev and M. Garcia ({\it work unpublished}). We applied it to the study of off-lattice models. The Rate of Convergence criterion is used to decide if a certain sequence will fold up correctly within a relatively short time. Before the present work, the common way to decide if a certain sequence was a good/bad folder was by performing the whole dynamics until the sequence got its native state (if it existed), or by studying the curvature of the potential energy surface. There are some difficulties in the last two approaches. In the first approach, performing the complete dynamics for hundreds of sequences is a rather challenging task because of the CPU time needed. In the second approach, calculating the curvature of the potential energy surface is possible only for very smooth surfaces. The Rate of Convergence criterion seems to avoid the previous difficulties. With this criterion one does not need to perform the complete dynamics to find the good and bad sequences. Also, the criterion does not depend on the kind of force field used and therefore it can be used even for very rugged energy surfaces.

Facilitating folding of outer membrane proteins, roles of the periplasmic chaperone Skp and the outer membrane lipoprotein BamD

This thesis describes several important advancements in the understanding of the assembly of outer membrane proteins of Gram-negative bacteria like Escherichia coli. A first study was performed to identify binding regions in the trimeric chaperone Skp for outer membrane proteins. Skp is known to facilitate the passage of unfolded outer membrane proteins (OMPs) through the periplasm to the outer membrane (OM). A gene construct named “synthetic chaperone protein (scp)” gene was used to express a fusion protein (Scp) into the cytoplasm of E. coli. The scp gene was used as a template to design mutants of Scp suitable for structural and functional studies using site-directed spectroscopy. Fluorescence resonance energy transfer (FRET) was used to identify distances in Skp-OmpA complexes that separate regions in Scp and in outer membrane protein A (OmpA) from E. coli. For this study, single cysteine (Cys) mutants and single Cys - single tryptophan (Trp) double mutants of Scp were prepared. For FRET experiments, the cysteines were labeled with the tryptophan fluorescence energy acceptor IAEDANS. Single Trp mutants of OmpA were used as fluorescence energy donors. In the second part of this thesis, the function of BamD and the structure of BamD-Scp complexes were examined. BamD is an essential component of the β-barrel assembly machinery (BAM) complex of the OM of Gram-negative bacteria. Fluorescence spectroscopy was used to probe the interactions of BamD with lipid membranes and to investigate the interactions of BamD with possible partner proteins from the periplasm and from the OM. A range of single cysteine (Cys) and single tryptophan (Trp) mutants of BamD were prepared. A very important conclusion from the extensive FRET study is that the essential lipoprotein BamD interacts and binds to the periplasmic chaperone Skp. BamD contains tetratrico peptide repeat (TPR) motifs that are suggested to serve as docking sites for periplasmic chaperones such as Skp.

El concepto de serie num??rica : un estudio a trav??s del modelo de Pirie y Kieren centrado en el mecanimo 'folding back'

Resumen basado en el de la publicaci??n

Pressure-jump-induced kinetics reveals a hydration dependent folding/unfolding mechanism of ribonuclease A

Pressure-jump (p-jump)-induced relaxation kinetics was used to explore the energy landscape of protein folding/unfolding of Y115W, a fluorescent variant of ribonuclease A. Pressure-jumps of 40MPa amplitude (5ms dead-time) were conducted both to higher (unfolding) and to lower (folding) pressure, in the range from 100 to 500MPa, between 30 and 50°C. Significant deviations from the expected symmetrical protein relaxation kinetics were observed. Whereas downward p-jumps resulted always in single exponential kinetics, the kinetics induced by upward p-jumps were biphasic in the low pressure range and monophasic at higher pressures. The relative amplitude of the slow phase decreased as a function of both pressure and temperature. At 50°C, only the fast phase remained. These results can be interpreted within the framework of a two-dimensional energy surface containing a pressure- and temperature-dependent barrier between two unfolded states differing in the isomeric state of the Asn-113–Pro-114 bond. Analysis of the activation volume of the fast kinetic phase revealed a temperature-dependent shift of the unfolding transition state to a larger volume. The observed compensation of this effect by glycerol offers an explanation for its protein stabilizing effect

Green fluorescent protein as a reporter of prion protein folding

Background: The amino terminal half of the cellular prion protein PrPc is implicated in both the binding of copper ions and the conformational changes that lead to disease but has no defined structure. However, as some structure is likely to exist we have investigated the use of an established protein refolding technology, fusion to green fluorescence protein (GFP), as a method to examine the refolding of the amino terminal domain of mouse prion protein. Results: Fusion proteins of PrPc and GFP were expressed at high level in E. coli and could be purified to near homogeneity as insoluble inclusion bodies. Following denaturation, proteins were diluted into a refolding buffer whereupon GFP fluorescence recovered with time. Using several truncations of PrPc the rate of refolding was shown to depend on the prion sequence expressed. In a variation of the format, direct observation in E. coli, mutations introduced randomly in the PrPc protein sequence that affected folding could be selected directly by recovery of GFP fluorescence. Conclusion: Use of GFP as a measure of refolding of PrPc fusion proteins in vitro and in vivo proved informative. Refolding in vitro suggested a local structure within the amino terminal domain while direct selection via fluorescence showed that as little as one amino acid change could significantly alter folding. These assay formats, not previously used to study PrP folding, may be generally useful for investigating PrPc structure and PrPc-ligand interaction.