Polymer principles and protein folding

Cooperative Unfolding of a Metastable Serpin to a Molten Globule Suggests a Link Between Functional and Folding Energy Landscapes

Alpha-1 antitrypsin (alpha(1)-AT) is a member of the serpin class of protease inhibitors, and folds to a metastable state rather than its thermodynamically most stable native state. Upon cleavage by a target protease, alpha(1)-AT undergoes a dramatic conformational change to a stable form, translocating the bound protease more than 70 A to form an inhibitory protease-serpin complex. Numerous mutagenesis studies on serpins have demonstrated the trade-off between the stability of the metastable state on the one hand and the inhibitory efficiency on the other. Studies of the equilibrium unfolding of serpins provide insight into this connection between structural plasticity and metastability. We studied equilibrium unfolding of wild-type alpha(1)-AT using hydrogen-deuterium/exchange mass spectrometry to characterize the structure and the stability of an equilibrium intermediate that was observed in low concentrations of denaturant in earlier studies. Our results show that the intermediate observed at low concentrations of denaturant has no protection from hydrogen-deuterium exchange, indicating a lack of stable structure. Further, differential scanning calorimetry of alpha(1)-AT at low concentrations of denaturant shows no heat capacity peak during thermal denaturation, indicating that the transition from the intermediate to the unfolded state is not a cooperative first-order-like phase transition.. Our results show that the unfolding of alpha(1)-AT involves a cooperative transition to a molten globule form, followed by a non-cooperative transition to a random-coil form as more guanidine is added. Thus, the entire alpha(1)-AT molecule consists of one cooperative structural unit rather than multiple structural domains with different stabilities. Furthermore, our results together with previous mutagenesis studies suggest a possible link between an equilibrium molten globule and a functional intermediate that may be populated during the protease inhibition.

Why are proteins charged? Networks of charge-charge interactions in proteins measured by charge ladders and capillary electrophoresis

Almost all proteins contain charged amino acids. While the function in catalysis or binding of individual charges in the active site can often be identified, it is less clear how to assign function to charges beyond this region. Are they necessary for solubility? For reasons other than solubility? Can manipulating these charges change the properties of proteins? A combination of capillary electrophoresis (CE) and protein charge ladders makes it possible to study the roles of charged residues on the surface of proteins outside the active site. This method involves chemical modification of those residues to generate a large number of derivatives of the protein that differ in charge. CE separates those derivatives into groups with the same number of modified charged groups. By studying the influence of charge on the properties of proteins using charge ladders, it is possible to estimate the net charge and hydrodynamic radius and to infer the role of charged residues in ligand binding and protein folding.

The protein folding problem: when will it be solved?

The protein folding problem can be viewed as three different problems: defining the thermodynamic folding code; devising a good computational structure prediction algorithm; and answering Levinthal's question regarding the kinetic mechanism of how proteins can fold so quickly. Once regarded as a grand challenge, protein folding has seen much progress in recent years. Folding codes are now being used to successfully design proteins and non-biological foldable polymers; aided by the Critical Assessment of Techniques for Structure Prediction (CASP) competition, protein structure prediction has now become quite good. Even the once-challenging Levinthal puzzle now seems to have an answer--a protein can avoid searching irrelevant conformations and fold quickly by making local independent decisions first, followed by non-local global decisions later.

UV resonance Raman measurements of poly-L-lysine's conformational energy landscapes: dependence on perchlorate concentration and temperature

UV resonance Raman spectroscopy has been used to determine the conformational energy landscape of poly-L-lysine (PLL) in the presence of NaClO4 as a function of temperature. At 1 degree C, in the presence of 0.83 M NaClO4, PLL shows an approximately 86% alpha-helix-like content, which contains alpha-helix and pi-bulge/helix conformations. The high alpha-helix-like content of PLL occurs because of charge screening due to strong ion-pair formation between ClO4- and the lysine side chain -NH3+. As the temperature increases from 1 to 60 degrees C, the alpha-helix and pi-bulge/helix conformations melt into extended conformations (PPII and 2.51-helix). We calculate the Psi Ramachandran angle distribution of the PLL peptide bonds from the UV Raman spectra which allows us to calculate the PLL (un)folding energy landscapes along the Psi reaction coordinate. We observe a basin in the Psi angle conformational space associated with alpha-helix and pi-bulge/helix conformations and another basin for the extended PPII and 2.51-helical conformations.

Protein interfacial pocket engineering via coupled computational filtering and biological focusing criterion

To engineer bio-macromolecular systems, protein-substrate interactions and their configurations need to be understood, harnessed, and utilized. Due to the inherent large numbers of combinatorial configurations and conformational complexity, methods that rely on heuristics or stochastics, such as practical computational filtering (CF) or biological focusing (BF) criterions, when used alone rarely yield insights into these complexes or successes in (re)designing them. Here we use a coupled CF-BF criterion upon an amenable interfacial pocket (IP) of a protein scaffold complexed with its substrate to undergo residue replacement and R-group refinement (R4) to filter out energetically unfavorable residues and R-group conformations, and focus in on those that are evolutionarily favorable. We show that this coupled filtering and focusing can efficiently provide a putative engineered IP candidate and validate it computationally and empirically. The CF-BF criterion may permit holistic understanding of the nuances of existing protein IPs and their scaffolds and facilitate bioengineering efforts to alter substrate specificity. Such approach may contribute to accelerated elucidation of engineering principles of bio-macromolecular systems.

Electrostatics dominate quadruplex stability

Stabilization of nucleic acid structures results from a balance of multiple interactions, including electrostatics, base stacking, hydrophobic interactions, hydrogen bonding, van der Waals forces, etc. Nucleic acid quadruplexes are unusual structures in that their formation is driven by specific binding of metal ions. This unique mode of metal binding, which is tightly coupled to oligonucleotide folding, can engender correspondingly unique solution behavior. In particular, we show that addition of many cosolvents, such as primary aliphatic alcohols, increases the thermal stability of quadruplexes, as determined by melting temperature, Tm, in direct contrast to the response of duplexes to the same admixture of solvents. Thermal stability is observed to increase as the dielectric constant of the composite solvent decreases. This behavior suggests a dominant role for electrostatics in quadruplex formation and stability. Additional studies done with other cosolvents and solutes suggest that, in some cases, other forces may come into play, including the possibility of direct interaction with the quadruplex structure. Nonetheless, many cosolvents and small molecules, such as ethanol, dimethylformamide, and betaine, stabilize the quadruplex conformation in sharp distinction to their destabilization of DNA duplexes.

Novel approach for alpha-helical topology prediction in globular proteins: generation of interhelical restraints

The protein folding problem represents one of the most challenging problems in computational biology. Distance constraints and topology predictions can be highly useful for the folding problem in reducing the conformational space that must be searched by deterministic algorithms to find a protein structure of minimum conformational energy. We present a novel optimization framework for predicting topological contacts and generating interhelical distance restraints between hydrophobic residues in alpha-helical globular proteins. It should be emphasized that since the model does not make assumptions about the form of the helices, it is applicable to all alpha-helical proteins, including helices with kinks and irregular helices. This model aims at enhancing the ASTRO-FOLD protein folding approach of Klepeis and Floudas (Journal of Computational Chemistry 2003;24:191-208), which finds the structure of global minimum conformational energy via a constrained nonlinear optimization problem. The proposed topology prediction model was evaluated on 26 alpha-helical proteins ranging from 2 to 8 helices and 35 to 159 residues, and the best identified average interhelical distances corresponding to the predicted contacts fell below 11 A in all 26 of these systems. Given the positive results of applying the model to several protein systems, the importance of interhelical hydrophobic-to-hydrophobic contacts in determining the folding of alpha-helical globular proteins is highlighted.

Estimation of absolute solvent and solvation shell entropies via permutation reduction

Despite its prominent contribution to the free energy of solvated macromolecules such as proteins or DNA, and although principally contained within molecular dynamics simulations, the entropy of the solvation shell is inaccessible to straightforward application of established entropy estimation methods. The complication is twofold. First, the configurational space density of such systems is too complex for a sufficiently accurate fit. Second, and in contrast to the internal macromolecular dynamics, the configurational space volume explored by the diffusive motion of the solvent molecules is too large to be exhaustively sampled by current simulation techniques. Here, we develop a method to overcome the second problem and to significantly alleviate the first one. We propose to exploit the permutation symmetry of the solvent by transforming the trajectory in a way that renders established estimation methods applicable, such as the quasiharmonic approximation or principal component analysis. Our permutation-reduced approach involves a combinatorial problem, which is solved through its equivalence with the linear assignment problem, for which O(N3) methods exist. From test simulations of dense Lennard-Jones gases, enhanced convergence and improved entropy estimates are obtained. Moreover, our approach renders diffusive systems accessible to improved fit functions.

Explicit factorization of external coordinates in constrained statistical mechanics models

If a macromolecule is described by curvilinear coordinates or rigid constraints are imposed, the equilibrium probability density that must be sampled in Monte Carlo simulations includes the determinants of different mass-metric tensors. In this work, the authors explicitly write the determinant of the mass-metric tensor G and of the reduced mass-metric tensor g, for any molecule, general internal coordinates and arbitrary constraints, as a product of two functions; one depending only on the external coordinates that describe the overall translation and rotation of the system, and the other only on the internal coordinates. This work extends previous results in the literature, proving with full generality that one may integrate out the external coordinates and perform Monte Carlo simulations in the internal conformational space of macromolecules.

Secondary structures in long compact polymers

Compact polymers are self-avoiding random walks that visit every site on a lattice. This polymer model is used widely for studying statistical problems inspired by protein folding. One difficulty with using compact polymers to perform numerical calculations is generating a sufficiently large number of randomly sampled configurations. We present a Monte Carlo algorithm that uniformly samples compact polymer configurations in an efficient manner, allowing investigations of chains much longer than previously studied. Chain configurations generated by the algorithm are used to compute statistics of secondary structures in compact polymers. We determine the fraction of monomers participating in secondary structures, and show that it is self-averaging in the long-chain limit and strictly less than 1. Comparison with results for lattice models of open polymer chains shows that compact chains are significantly more likely to form secondary structure.

Fluorescence correlation spectroscopy shows that monomeric polyglutamine molecules form collapsed structures in aqueous solutions

We have used fluorescence correlation spectroscopy measurements to quantify the hydrodynamic sizes of monomeric polyglutamine as a function of chain length (N) by measuring the scaling of translational diffusion times (tau(D)) for the peptide series (Gly)-(Gln)(N)-Cys-Lys(2) in aqueous solution. We find that tau(D) scales with N as tau(o)N(nu) and therefore ln(tau(D)) = ln(tau(o)) + nuln(N). The values for nu and ln(tau(o)) are 0.32 +/- 0.02 and 3.04 +/- 0.08, respectively. Based on these observations, we conclude that water is a polymeric poor solvent for polyglutamine. Previous studies have shown that monomeric polyglutamine is intrinsically disordered. These observations combined with our fluorescence correlation spectroscopy data suggest that the ensemble for monomeric polyglutamine is made up of a heterogeneous collection of collapsed structures. This result is striking because the preference for collapsed structures arises despite the absence of residues deemed to be hydrophobic in the sequence constructs studied. Working under the assumption that the driving forces for collapse are similar to those for aggregation, we discuss the implications of our results for the thermodynamics and kinetics of polyglutamine aggregation, a process that has been implicated in the molecular mechanism of Huntington's disease.

A backbone-based theory of protein folding

Under physiological conditions, a protein undergoes a spontaneous disorder order transition called "folding." The protein polymer is highly flexible when unfolded but adopts its unique native, three-dimensional structure when folded. Current experimental knowledge comes primarily from thermodynamic measurements in solution or the structures of individual molecules, elucidated by either x-ray crystallography or NMR spectroscopy. From the former, we know the enthalpy, entropy, and free energy differences between the folded and unfolded forms of hundreds of proteins under a variety of solvent/cosolvent conditions. From the latter, we know the structures of approximately 35,000 proteins, which are built on scaffolds of hydrogen-bonded structural elements, alpha-helix and beta-sheet. Anfinsen showed that the amino acid sequence alone is sufficient to determine a protein's structure, but the molecular mechanism responsible for self-assembly remains an open question, probably the most fundamental open question in biochemistry. This perspective is a hybrid: partly review, partly proposal. First, we summarize key ideas regarding protein folding developed over the past half-century and culminating in the current mindset. In this view, the energetics of side-chain interactions dominate the folding process, driving the chain to self-organize under folding conditions. Next, having taken stock, we propose an alternative model that inverts the prevailing side-chain/backbone paradigm. Here, the energetics of backbone hydrogen bonds dominate the folding process, with preorganization in the unfolded state. Then, under folding conditions, the resultant fold is selected from a limited repertoire of structural possibilities, each corresponding to a distinct hydrogen-bonded arrangement of alpha-helices and/or strands of beta-sheet.

A model of local-minima distribution on conformational space and its application to protein structure prediction

A quantitative two-parameter model is developed to describe local energy minima distribution. On a conformational space measured by least-square-fitting root-mean-squared distance (RMSD), the number of local minima in a r RMSD region is proposed to be proportional to exp(-1/r). As part of the model derivations, the minimum RMSD of decoys from the largest cluster, the number of decoys in the largest cluster, and the RMSD distribution of the decoys have inner connections with each other. The model is successfully verified on a 49 helix-packing decoy set and a 30 loop-prediction decoy set, as well as both knowledge-based potential (DFIRE) and physical force-fields (OPLS and CHARMM). One of the model's applications is predicting behaviors of a large amount of decoys (e.g., minimum RMSD of 40,000 decoys) by generating only a small number of decoys (e.g., 500). It may be applied to structure predictions guided by any Lennard-Jones-like potential functions and can be extended to other sampling methods guided by simple energy terms.

Quantitation of the nearest-neighbour effects of amino acid side-chains that restrict conformational freedom of the polypeptide chain using reversed-phase liquid chromatography of synthetic model peptides with L- and D-amino acid substitutions

Side-chain backbone interactions (or "effects") between nearest neighbours may severely restrict the conformations accessible to a polypeptide chain and thus represent the first step in protein folding. We have quantified nearest-neighbour effects (i to i+1) in peptides through reversed-phase liquid chromatography (RP-HPLC) of model synthetic peptides, where L- and D-amino acids were substituted at the N-terminal end of the peptide sequence, adjacent to a L-Leu residue. These nearest-neighbour effects (expressed as the difference in retention times of L- and D-peptide diastereomers at pHs 2 and 7) were frequently dramatic, depending on the type of side-chain adjacent to the L-Leu residue, albeit such effects were independent of mobile phase conditions. No nearest-neighbour effects were observed when residue i is adjacent to a Gly residue. Calculation of minimum energy conformations of selected peptides supported the view that, whether a L- or D-amino acid is substituted adjacent to L-Leu, its orientation relative to this bulky Leu side-chain represents the most energetically favourable configuration. We believe that such energetically favourable, and different, configurations of L- and D-peptide diastereomers affect their respective interactions with a hydrophobic stationary phase, which are thus quantified by different RP-HPLC retention times. Side-chain hydrophilicity/hydrophobicity coefficients were generated in the presence of these nearest-neighbour effects and, despite the relative difference in such coefficients generated from peptides substituted with L- or D-amino acids, the relative difference in hydrophilicity/hydrophobicity between different amino acids in the L- or D-series is maintained. Overall, our results demonstrate that such nearest-neighbour effects can clearly restrict conformational space of an amino acid side-chain in a polypeptide chain.

Exploring the relationship between funneled energy landscapes and two-state protein folding

It should take an astronomical time span for unfolded protein chains to find their native state based on an unguided conformational random search. The experimental observation that folding is fast can be rationalized by assuming that protein energy landscapes are sloped towards the native state minimum, such that rapid folding can proceed from virtually any point in conformational space. Folding transitions often exhibit two-state behavior, involving extensively disordered and highly structured conformers as the only two observable kinetic species. This study employs a simple Brownian dynamics model of "protein particles" moving in a spherically symmetrical potential. As expected, the presence of an overall slope towards the native state minimum is an effective means to speed up folding. However, the two-state nature of the transition is eradicated if a significant energetic bias extends too far into the non-native conformational space. The breakdown of two-state cooperativity under these conditions is caused by a continuous conformational drift of the unfolded proteins. Ideal two-state behavior can only be maintained on surfaces exhibiting large regions that are energetically flat, a result that is supported by other recent data in the literature (Kaya and Chan, Proteins: Struct Funct Genet 2003;52:510-523). Rapid two-state folding requires energy landscapes exhibiting the following features: (i) A large region in conformational space that is energetically flat, thus allowing for a significant degree of random sampling, such that unfolded proteins can retain a random coil structure; (ii) a trapping area that is strongly sloped towards the native state minimum.

Design of random copolymers with statistically controlled monomer sequence distributions via Monte Carlo simulations

We use Monte Carlo simulations to model the formation of random copolymers with tunable monomer sequence distributions. Our scheme is based on the original idea proposed a few years ago by Khokhlov and Khalatur [Physica A 249, 253 (1998); Phys. Rev. Lett. 82, 3456 (1999)], who showed that the distribution of species B in A-B random copolymers can be regulated by (a) adjusting the coil size of a homopolymer A and (b) chemically modifying ("coloring") monomers that reside at (or close to) the periphery of the coil with species B. In contrast to Khokhlov and Khalatur's work, who modeled the polymer modification by performing the coloring instantaneously, we let the chemical coloring reaction progress over time using computer simulations. We show that similar to Khokhlov and Khalatur's work, the blockiness (i.e., number of consecutive monomers) of the B species along the A-B copolymer increases with increasing degree of collapse of the parent homopolymer A. A simple analysis of the A-B monomer sequences in the copolymers reveals that monomer sequence distributions in homopolymers "colored" under collapsed conformations possess certain degrees of self-similarity, while there is no correlation found among the monomer sequence distributions formed by coloring homopolymers with expanded conformations.

Analyses of simulations of three-dimensional lattice proteins in comparison with a simplified statistical mechanical model of protein folding

Folding and unfolding simulations of three-dimensional lattice proteins were analyzed using a simplified statistical mechanical model in which their amino acid sequences and native conformations were incorporated explicitly. Using this statistical mechanical model, under the assumption that only interactions between amino acid residues within a local structure in a native state are considered, the partition function of the system can be calculated for a given native conformation without any adjustable parameter. The simulations were carried out for two different native conformations, for each of which two foldable amino acid sequences were considered. The native and non-native contacts between amino acid residues occurring in the simulations were examined in detail and compared with the results derived from the theoretical model. The equilibrium thermodynamic quantities (free energy, enthalpy, entropy, and the probability of each amino acid residue being in the native state) at various temperatures obtained from the simulations and the theoretical model were also examined in order to characterize the folding processes that depend on the native conformations and the amino acid sequences. Finally, the free energy landscapes were discussed based on these analyses.

Relationships between the folding rate constant and the topological parameters of small two-state proteins based on general random walk model

In this paper, we propose an analytically tractable model of protein folding based on one-dimensional general random walk. A second-order differential equation for the mean folding time of a single protein is constructed which can be used to derive the observed relationship between the folding rate constant and the number of native contacts. The parameters appearing in the model can be determined by fitting the theoretical prediction to the experimental result. In addition, taking into account the fact that the number of native contacts is almost proportional to the relative contact order, we can also explain the observed relationship between the folding rate constant and the relative contact order.

A correlation-based method for the enhancement of scoring functions on funnel-shaped energy landscapes

A correlation-based approach is introduced for enhancing the ability of structure-scoring methods to identify and distinguish native-like conformations. The proposed method relies on a funnel-shaped scoring function that decreases steadily toward the native state. It takes advantage of the idea that the structure from a given ensemble that is closest to the native basin leads to the highest correlation coefficient between a given score and distance to that structure as an approximation of the native state for the entire ensemble. The method is applied successfully to a number of different test cases that demonstrate substantial improvements in the correlation of the score with the distance from the true native state but also result in the selection of more native-like structures compared to the original score.

A physically meaningful method for the comparison of potential energy functions

In the study of the conformational behavior of complex systems, such as proteins, several related statistical measures are commonly used to compare two different potential energy functions. Among them, the Pearson's correlation coefficient r has no units and allows only semiquantitative statements to be made. Those that do have units of energy and whose value may be compared to a physically relevant scale, such as the root-mean-square deviation (RMSD), the mean error of the energies (ER), the standard deviation of the error (SDER) or the mean absolute error (AER), overestimate the distance between potentials. Moreover, their precise statistical meaning is far from clear. In this article, a new measure of the distance between potential energy functions is defined that overcomes the aforementioned difficulties. In addition, its precise physical meaning is discussed, the important issue of its additivity is investigated, and some possible applications are proposed. Finally, two of these applications are illustrated with practical examples: the study of the van der Waals energy, as implemented in CHARMM, in the Trp-Cage protein (PDB code 1L2Y) and the comparison of different levels of the theory in the ab initio study of the Ramachandran map of the model peptide HCO-L-Ala-NH2.

Self-organization versus Watchmaker: Molecular motors and protein translocation

Generation of directional movement at the molecular scale is a phenomenon crucial for biological organization and dynamics. It is traditionally described in mechanistic terms, in consistency with the conventional machine-like image of the cell. The designated and highly specialized protein machines and molecular motors are presumed to bring about most of cellular motion. A review of experimental data suggests, however, that uncritical adherence to mechanistic interpretations may limit the ability of researchers to comprehend and model biology. Specifically, this article illustrates that the interpretation of molecular motors and protein translocation in terms of stochasticity and self-organization appears to provide a more adequate and fruitful conceptual framework for understanding of biological organization at the molecular scale.

Automated use of mutagenesis data in structure prediction

In the absence of experimental structural determination, numerous methods are available to indirectly predict or probe the structure of a target molecule. Genetic modification of a protein sequence is a powerful tool for identifying key residues involved in binding reactions or protein stability. Mutagenesis data is usually incorporated into the modeling process either through manual inspection of model compatibility with empirical data, or through the generation of geometric constraints linking sensitive residues to a binding interface. We present an approach derived from statistical studies of lattice models for introducing mutation information directly into the fitness score. The approach takes into account the phenotype of mutation (neutral or disruptive) and calculates the energy for a given structure over an ensemble of sequences. The structure prediction procedure searches for the optimal conformation where neutral sequences either have no impact or improve stability and disruptive sequences reduce stability relative to wild type. We examine three types of sequence ensembles: information from saturation mutagenesis, scanning mutagenesis, and homologous proteins. Incorporating multiple sequences into a statistical ensemble serves to energetically separate the native state and misfolded structures. As a result, the prediction of structure with a poor force field is sufficiently enhanced by mutational information to improve accuracy. Furthermore, by separating misfolded conformations from the target score, the ensemble energy serves to speed up conformational search algorithms such as Monte Carlo-based methods.

Pressure as a tool to study protein-unfolding/refolding processes: The case of ribonuclease A

This paper gives an overview of the application of high-pressure to study the folding/unfolding processes of proteins using Ribonuclease A as a model protein. A particular focus is the study of pressure-equilibrium unfolding and folding kinetics using variants and the information obtained by comparing these with the wild-type enzyme.

A novel sensitive method for the detection of user-defined compositional bias in biological sequences

MOTIVATION

Most biological sequences contain compositionally biased segments in which one or more residue types are significantly overrepresented. The function and evolution of these segments are poorly understood. Usually, all types of compositionally biased segments are masked and ignored during sequence analysis. However, it has been shown for a number of proteins that biased segments that contain amino acids with similar chemical properties are involved in a variety of molecular functions and human diseases. A detailed large-scale analysis of the functional implications and evolutionary conservation of different compositionally biased segments requires a sensitive method capable of detecting user-specified types of compositional bias.

RESULTS

We present BIAS, a novel sensitive method for the detection of compositionally biased segments composed of a user-specified set of residue types. BIAS uses the discrete scan statistics that provides a highly accurate correction for multiple tests to compute analytical estimates of the significance of each compositionally biased segment. The method can take into account global compositional bias when computing analytical estimates of the significance of local clusters. BIAS is benchmarked against SEG, SAPS and CAST programs. We also use BIAS to show that groups of proteins with the same biological function are significantly associated with particular types of compositionally biased segments.

Free energy landscapes of RNA/RNA complexes: with applications to snRNA complexes in spliceosomes

We develop a statistical mechanical model for RNA/RNA complexes with both intramolecular and intermolecular interactions. As an application of the model, we compute the free energy landscapes, which give the full distribution for all the possible conformations, for U4/U6 and U2/U6 in major spliceosome and U4atac/U6atac and U12/U6atac in minor spliceosome. Different snRNA experiments found contrasting structures, our free energy landscape theory shows why these structures emerge and how they compete with each other. For yeast U2/U6, the model predicts that the two distinct experimental structures, the four-helix junction structure and the helix Ib-containing structure, can actually coexist and specifically compete with each other. In addition, the energy landscapes suggest possible mechanisms for the conformational switches in splicing. For instance, our calculation shows that coaxial stacking is essential for stabilizing the four-helix junction in yeast U2/U6. Therefore, inhibition of the coaxial stacking possibly by protein-binding may activate the conformational switch from the four-helix junction to the helix Ib-containing structure. Moreover, the change of the energy landscape shape gives information about the conformational changes. We find multiple (native-like and misfolded) intermediates formed through base-pairing rearrangements in snRNA complexes. For example, the unfolding of the U2/U6 undergoes a transition to a misfolded state which is functional, while in the unfolding of U12/U6atac, the functional helix Ib is found to be the last one to unfold and is thus the most stable structural component. Furthermore, the energy landscape gives the stabilities of all the possible (functional) intermediates and such information is directly related to splicing efficiency.

A Unified Approach to Conformational Statistics of Classical Polymer and Polypeptide Models

We present a unified method to generate conformational statistics which can be applied to any of the classical discrete-chain polymer models. The proposed method employs the concepts of Fourier transform and generalized convolution for the group of rigid-body motions in order to obtain probability density functions of chain end-to-end distance. In this paper, we demonstrate the proposed method with three different cases: the freely-rotating model, independent energy model, and interdependent pairwise energy model (the last two are also well-known as the Rotational Isomeric State model). As for numerical examples, for simplicity, we assume homogeneous polymer chains. For the freely-rotating model, we verify the proposed method by comparing with well-known closed-form results for mean-squared end-to-end distance. In the interdependent pairwise energy case, we take polypeptide chains such as polyalanine and polyvaline as examples.

An Experimental Investigation of Conformational Fluctuations in Proteins G and L

The B1 domains of streptococcal proteins G and L are structurally similar, but they have different sequences and they fold differently. We have measured their NMR spectra at variable temperature using a range of concentrations of denaturant. Many residues have curved amide proton temperature dependence, indicating that they significantly populate alternative, locally unfolded conformations. The results, therefore, provide a view of the locations of low-lying, locally unfolded conformations. They indicate approximately 4-6 local minima for each protein, all within ca. 2.5 kcal/mol of the native state, implying a locally rough energy landscape. Comparison with folding data for these proteins shows that folding involves most molecules traversing a similar path, once a transition state containing a beta hairpin has been formed, thereby defining a well-populated pathway down the folding funnel. The hairpin that directs the folding pathway differs for the two proteins and remains the most stable part of the folded protein.

Effects of frustration, confinement, and surface interactions on the dimerization of an off-lattice β-barrel protein

We study the effects of confinement, sequence frustration, and surface interactions on the thermodynamics of dimerization of an off-lattice minimalist beta-barrel protein using replica exchange molecular dynamics. We vary the degree of frustration of the protein by tuning the specificity of the hydrophobic interactions and investigate dimerization in confining spheres of different radii. We also investigate surface effects by tethering the first residue of one of the proteins to a uniformly repulsive surface. We find that increasing the confinement and frustration stabilize the dimer, while adding a repulsive surface decreases its stability. Different ensembles of structures, including properly dimerized and various partially dimerized states, are observed at the association transition temperature T(a), depending on the amount of frustration and whether a surface is present. The presence of a surface is predicted to alter the morphology of larger aggregates formed from partially unfolded dimeric conformations.

Antagonism, non-native interactions and non-two-state folding in S6 revealed by double-mutant cycle analysis

When folding to the native state N in the presence of salt, the apparent two-state folder S6 transiently forms a transient off-pathway state C with substantial secondary and tertiary structure. Fifteen double mutant cycles were analysed to compare side-chain interaction energies DeltaDeltaG(int) in C, N and TS (the transition state between N and the denatured state). The kinetic signatures of these destabilizing mutants suggest folding scenarios involving unfolding intermediates and even alternative unfolding pathways. However, restricting the kinetic data to linear parts of the chevron plot allows reliable extrapolation to zero molar denaturant of rate constants of folding, unfolding and misfolding. Side-chain interactions appear to contribute to the stability of C, but in a substantially non-native environment, as shown by changes in the sign of DeltaDeltaG(int) between C and N. Remarkably, there appear to be significant (0.7-2 kcal/mol) antagonistic interactions between the two residues Leu30 and Leu75 in N and TS, which may be linked to subtle structural changes seen in the crystal structures of the mutants. A small number of overlapping residues are involved in these kinds of antagonistic interactions in N, TS and C, suggesting that repulsive interactions are coded into the protein topology whether the protein folds or misfolds. Destabilizing double mutants indicate that apparent two-state folders can be induced to behave in more complex ways provided that the native state is suitably destabilized.

Characterization of the folding landscape of monomeric lactose repressor: quantitative comparison of theory and experiment

Recent theoretical/computational studies based on simplified protein models and experimental investigation have suggested that the native structure of a protein plays a primary role in determining the folding rate and mechanism of relatively small single-domain proteins. Here, we extend the study of the relationship between protein topology and folding mechanism to a larger protein with complex topology, by analyzing the folding process of monomeric lactose repressor (MLAc) computationally by using a Gō-like C(alpha) model. Next, we combine simulation and experimental results (see companion article in this issue) to achieve a comprehensive assessment of the folding landscape of this protein. Remarkably, simulated kinetic and equilibrium analyses show an excellent quantitative agreement with the experimental folding data of this study. The results of this comparison show that a simplified, completely unfrustrated C(alpha) model correctly reproduces the complex folding features of a large multidomain protein with complex topology. The success of this effort underlines the importance of synergistic experimental/theoretical approaches to achieve a broader understanding of the folding landscape.

Kinetics of Loop Formation and Breakage in the Denatured State of Iso-1-cytochrome c

The earliest events in protein folding involve the formation of simple loops. Observing the rates of loop closure under denaturing conditions can provide direct insight into the relative probability and sequence determinants for formation of loops of different sizes. The persistence of these initial contacts is equally important for efficient folding, so measurement of rates of loop breakage under denaturing conditions is also essential. We have used stopped-flow and continuous-flow methods to measure the rates of histidine-heme loop formation and breakage in the denatured state of iso-1-cytochrome c (in the presence of 3 M guanidine HCl). The data indicate that the mechanism for forming loops is a two-step process, the first step being the deprotonation of the histidine, and the second step being the binding of the histidine to the heme. This mechanism makes it possible to extract both the rate constants of formation, k(f), and breakage, k(b), of loops from the pH dependence of the observed rate constant, k(obs). To determine the dependence of k(f) and k(b) on loop size, we have carried out kinetic measurements for seven single surface histidine variants of iso-1-cytochrome c. A scaling factor (the dependence of k(f) on log[loop size]) of approximately -1.8 is observed for loop formation, similar to that observed in other systems. The magnitude of k(b) varies from 30 s(-1) to 300 s(-1), indicating that the stability of different loops varies considerably. The implications of the kinetics of loop formation and breakage in the denatured state for the mechanism of protein folding are discussed.

Prediction of protein thermostability with a direction- and distance-dependent knowledge-based potential

The increasing use of enzymes in industrial processes and the importance of understanding protein folding and stability have led to several attempts to predict and quantify the effect of every possible amino acid exchange (mutation) on the thermostability of proteins. In this article we describe a knowledge-based discrimination function that acts as a fast and reliable guide in protein engineering and optimization. The function used consists of two parts, a pairwise energy function based on a distance- and direction-dependent atomic description of the amino acid environment, and a torsion angle energy function. In a first step a training set of 11 proteins including 646 mutant proteins with experimentally determined thermostability was used to optimize the knowledge-based energy functions. The resulting potential function was then tested using a test mutant database consisting of 918 various point mutations introduced in 27 proteins. The best correlation coefficient obtained for the experimental data and the predicted thermostability for the training set is r = 0.81 (561 data points). A total of 76% of the mutations could be predicted correctly as being either stabilizing or destabilizing. The results for the test set are r = 0.74 (747 data points) and 72%, respectively. The global correlation over the combined data (1308 mutants) obtained is 0.78.

Ligand-induced thermostability in proteins: thermodynamic analysis of ANS-albumin interaction

A comparative thermodynamic study of the interaction of anilinonaphthalene sulfonate (ANS) derivatives with bovine serum albumin (BSA) was performed by using differential scanning calorimetry (DSC) and isothermal titration calorimetry (ITC). The chemically related ligands, 1,8-ANS and 2,6-ANS, present a similar affinity for BSA with different binding energetics. The analysis of the binding driving forces suggests that not only hydrophobic effect but also electrostatic interactions are relevant, even though they have been extensively used as probes for non-polar domains in proteins. Ligand association leads to an increase in protein thermostability, indicating that both dyes interact mainly with native BSA. ITC data show that 1,8-ANS and 2,6-ANS have a moderate affinity for BSA, with an association constant of around 1-9x10(5) M(-1) for the high-affinity site. Ligand binding is disfavoured by conformational entropy. The theoretical model used to simulate DSC data satisfactorily reproduces experimental thermograms, validating this approach as one which provides new insights into the interaction between one or more ligands with a protein. By comparison with 1,8-ANS, 2,6-ANS appears as a more "inert" probe to assess processes which involve conformational changes in proteins.

Conformational detours during folding of a collapsed state

The protein S6 is a useful model to probe the role of partially folded states in the folding process. In the absence of salt, S6 folds from the denatured state D to the native state N without detectable intermediates. High concentrations of sodium sulfate induce the accumulation of a collapsed state C, which is off the direct folding route. However, the mutation VA85 enables S6 to fold from C directly to N through the transition state TS(C). According to the denaturant dependence of this reaction, TS(C) and C are equally compact, but the data are difficult to deconvolute. Therefore, I have measured the heat capacities (DeltaC(p)) for the D-->C and C-->TS(C) transitions. The DeltaC(p)-values suggest that C needs to increase its surface area in order to fold directly to N. This underlines that it is a misfolded state that can only fold by at least partial unfolding. In contrast to the C-state formed by S6 wildtype, the VA85 C-state is just as compact as the native state, and this may be a prerequisite for direct folding. Individual "gatekeeper" residues may thus play a disproportionately large role in guiding proteins through different folding pathways.

Application of tabu search strategy for finding low energy structure of protein

OBJECTIVE

Understanding protein functionality would mean understanding the basics of life. This functionality follows a three-dimensional structure of proteins. Unfortunately till now it is not possible to obtain these structures artificially. This article offers a survey on the use of meta-heuristic methods in context of simplified models of protein folding.

METHODS

Tabu search (TS) strategy is one of the most successful meta-heuristics that has been applied for large number of optimization problems. In the paper, the application of TS for finding low energy conformations of proteins in a simplified lattice model has been proposed.

RESULTS

The algorithm has been extensively tested and the tests showed its good performance. It compares well with the other heuristic approaches.

CONCLUSIONS

The approach presented is competitive as compared with other methods and due to its low computation time can be used as a complementary tool for an analysis of the three-dimensional protein structures.

Direct measurement of protein energy landscape roughness

The energy landscape of proteins is thought to have an intricate, corrugated structure. Such roughness should have important consequences on the folding and binding kinetics of proteins, as well as on their equilibrium fluctuations. So far, no direct measurement of protein energy landscape roughness has been made. Here, we combined a recent theory with single-molecule dynamic force spectroscopy experiments to extract the overall energy scale of roughness epsilon for a complex consisting of the small GTPase Ran and the nuclear transport receptor importin-beta. The results gave epsilon > 5k(B)T, indicating a bumpy energy surface, which is consistent with the ability of importin-beta to accommodate multiple conformations and to interact with different, structurally distinct ligands.

Ion-interaction-capillary zone electrophoresis of cationic proteomic peptide standards

We have employed a novel capillary electrophoresis (CE) approach recently developed in our laboratory, termed ion-interaction-capillary zone electrophoresis (II-CZE), to the resolution of a mixture of 27 synthetic cationic proteomic peptide standards. These peptides were comprised of three groups of nine peptides (with net charges of +1, +2 and +3 for all nine peptides within a group), the hydrophobicity of the nine peptides within a group varying only subtly between adjacent peptides. This bidimensional CE approach achieved excellent resolution of the peptides with high peak capacity by combining the powerful CZE mechanism located in the background electrolyte (BGE) with an hydrophobicity-based mechanism also located in the BGE, the latter consisting of high concentrations (up to 0.4M) of aqueous perfluorinated acids (trifluoroacetic acid, pentafluoropropionic acid and heptafluorobutyric acid). Thus, concomitant with a CZE separation of the three differently charged groups of peptides, there is an hydrophobically-mediated separation of the peptides within these groups effected through interaction of the hydrophobic anions of the perfluorinated acids with hydrophobic amino acid side-chains in the peptides. This methodology is dramatically different from other CE methods that have used complexing agents such as micelles or cyclodextrins in MEKC. Overall, the results presented here demonstrate the value of CE as a peptide separative tool in its own right, including its use for proteomic applications, and not merely as a complementary technique to reversed-phase high-performance liquid chromatography (RP-HPLC).

Water and molecular chaperones act as weak links of protein folding networks: energy landscape and punctuated equilibrium changes point towards a game theory of proteins

Water molecules and molecular chaperones efficiently help the protein folding process. Here we describe their action in the context of the energy and topological networks of proteins. In energy terms water and chaperones were suggested to decrease the activation energy between various local energy minima smoothing the energy landscape, rescuing misfolded proteins from conformational traps and stabilizing their native structure. In kinetic terms water and chaperones may make the punctuated equilibrium of conformational changes less punctuated and help protein relaxation. Finally, water and chaperones may help the convergence of multiple energy landscapes during protein-macromolecule interactions. We also discuss the possibility of the introduction of protein games to narrow the multitude of the energy landscapes when a protein binds to another macromolecule. Both water and chaperones provide a diffuse set of rapidly fluctuating weak links (low affinity and low probability interactions), which allow the generalization of all these statements to a multitude of networks.

Fast tree search for a triangular lattice model of protein folding

Using a triangular lattice model to study the designability of protein folding, we overcame the parity problem of previous cubic lattice model and enumerated all the sequences and compact structures on a simple two-dimensional triangular lattice model of size 4+5+6+5+4. We used two types of amino acids, hydrophobic and polar, to make up the sequences, and achieved 2²³+2¹² different sequences excluding the reverse symmetry sequences. The total string number of distinct compact structures was 219,093, excluding reflection symmetry in the self-avoiding path of length 24 triangular lattice model. Based on this model, we applied a fast search algorithm by constructing a cluster tree. The algorithm decreased the computation by computing the objective energy of non-leaf nodes. The parallel experiments proved that the fast tree search algorithm yielded an exponential speed-up in the model of size 4+5+6+5+4. Designability analysis was performed to understand the search result.

Protein folding pathways from replica exchange simulations and a kinetic network model

We present an approach to the study of protein folding that uses the combined power of replica exchange simulations and a network model for the kinetics. We carry out replica exchange simulations to generate a large ( approximately 10(6)) set of states with an all-atom effective potential function and construct a kinetic model for folding, using an ansatz that allows kinetic transitions between states based on structural similarity. We use this network to perform random walks in the state space and examine the overall network structure. Results are presented for the C-terminal peptide from the B1 domain of protein G. The kinetics is two-state after small temperature perturbations. However, the coil-to-hairpin folding is dominated by pathways that visit metastable helical conformations. We propose possible mechanisms for the alpha-helix/beta-hairpin interconversion.

Recent developments in structural proteomics for protein structure determination

The major challenges in structural proteomics include identifying all the proteins on the genome-wide scale, determining their structure-function relationships, and outlining the precise three-dimensional structures of the proteins. Protein structures are typically determined by experimental approaches such as X-ray crystallography or nuclear magnetic resonance (NMR) spectroscopy. However, the knowledge of three-dimensional space by these techniques is still limited. Thus, computational methods such as comparative and de novo approaches and molecular dynamic simulations are intensively used as alternative tools to predict the three-dimensional structures and dynamic behavior of proteins. This review summarizes recent developments in structural proteomics for protein structure determination; including instrumental methods such as X-ray crystallography and NMR spectroscopy, and computational methods such as comparative and de novo structure prediction and molecular dynamics simulations.

Relevant distance between two different instances of the same potential energy in protein folding

In the context of complex systems and, particularly, of protein folding, a physically meaningful distance is defined which allows to make useful statistical statements about the way in which energy differences are modified when two different instances of the same potential-energy function are used. When the two instances arise from the fact that different algorithms or different approximations are used, the distance herein defined may be used to evaluate the relative accuracy of the two methods. When the difference is due to a change in the free parameters of which the potential depends on, the distance can be used to quantify, in each region of parameter space, the robustness of the modeling to such a change and this, in turn, may be used to assess the significance of a parameters' fit. Both cases are illustrated with a practical example: the study of the Poisson-based solvation energy in the Trp-Cage protein (PDB code 1L2Y).

Molecular dynamics simulation of amyloid beta dimer formation

Recent experiments with amyloid beta (Abeta) peptide indicate that formation of toxic oligomers may be an important contribution to the onset of Alzheimer's disease. The toxicity of Abeta oligomers depends on their structure, which is governed by assembly dynamics. Due to limitations of current experimental techniques, a detailed knowledge of oligomer structure at the atomic level is missing. We introduce a molecular dynamics approach to study Abeta dimer formation. 1), We use discrete molecular dynamics simulations of a coarse-grained model to identify a variety of dimer conformations; and 2), we employ all-atom molecular mechanics simulations to estimate thermodynamic stability of all dimer conformations. Our simulations of a coarse-grained Abeta peptide model predicts 10 different planar beta-strand dimer conformations. We then estimate the free energies of all dimer conformations in all-atom molecular mechanics simulations with explicit water. We compare the free energies of Abeta(1-42) and Abeta(1-40) dimers. We find that 1), dimer conformations have higher free energies compared to their corresponding monomeric states; and 2), the free-energy difference between the Abeta(1-42) and the corresponding Abeta(1-40) dimer conformation is not significant. Our results suggest that Abeta oligomerization is not accompanied by the formation of thermodynamically stable planar beta-strand dimers.

Conformational energy landscape of the acyl pocket loop in acetylcholinesterase: a Monte Carlo-generalized Born model study

The X-ray crystal structure of the reaction product of acetylcholinesterase (AChE) with the inhibitor diisopropylphosphorofluoridate (DFP) showed significant structural displacement in a loop segment of residues 287-290. To understand this conformational selection, a Monte Carlo (MC) simulation study was performed of the energy landscape for the loop segment. A computational strategy was applied by using a combined simulated annealing and room temperature Metropolis sampling approach with solvent polarization modeled by a generalized Born (GB) approximation. Results from thermal annealing reveal a landscape topology of broader basin opening and greater distribution of energies for the displaced loop conformation, while the ensemble average of conformations at 298 K favored a shift in populations toward the native by a free-energy difference in good agreement with the estimated experimental value. Residue motions along a reaction profile of loop conformational reorganization are proposed where Arg-289 is critical in determining electrostatic effects of solvent interaction versus Coulombic charging.

Exact sequence analysis for three-dimensional hydrophobic-polar lattice proteins

We have exactly enumerated all sequences and conformations of hydrophobic-polar (HP) proteins with chains of up to 19 monomers on the simple cubic lattice. For two variants of the HP model, where only two types of monomers are distinguished, we determined and statistically analyzed designing sequences, i.e., sequences that have a nondegenerate ground state. Furthermore we were interested in characteristic thermodynamic properties of HP proteins with designing sequences. In order to be able to perform these exact studies, we applied an efficient enumeration method based on contact sets.

Molecular dynamics simulation links conformation of a pore-flanking region to hyperekplexia-related dysfunction of the inhibitory glycine receptor

Inhibitory glycine receptors mediate rapid synaptic inhibition in mammalian spinal cord and brainstem. The previously identified hyperekplexia mutation GLRA1(P250T), located within the intracellular TM1-2 loop of the GlyR alpha1 subunit, results in altered receptor activation and desensitization. Here, elementary steps of ion channel function of alpha1(250) mutants were resolved and shown to correlate with hydropathy and molar volume of residue alpha1(250). Single-channel recordings and rapid activation kinetic studies using laser pulse photolysis showed reduced conductance but similar open probability of alpha1(P250T) mutant channels. Molecular dynamics simulation of a helix-turn-helix motif representing the intracellular TM1-2 domain revealed alterations in backbone conformation, indicating an increased flexibility in these mutants that paralleled changes in elementary steps of channel function. Thus, the architecture of the TM1-2 loop is a critical determinant of ion channel conductance and receptor desensitization.