Detailed folding structures of kappa-conotoxin RIIIJ and its mutageneses obtained from 2-dimensional HP model

Kappa-conotoxin RIIIJ is a conopeptide to inhibit voltage-gated potassium channels, however, its detailed folding structures have yet to be studied. With the advance in computing power, it is possible to use the HP model to analyze all its possible folding structures. In this study, the amino acid sequences of kappa-conotoxin RIIIJ and its four mutageneses were converted into ten HP sequences according to the normalized hydrophobicity index. All 282 429 536 481 possible folding structures in each HP sequence were found using the 2-dimensional HP model, and the detailed folding structures at native state were studied. The results showed that kappa-conotoxin RIIIJ had 180 and 90 folding structures at their native state with minimal energy of -9 and -10 at pH 2 and pH 7; its mutagenesis (6-8) TPP - > SLN increased the numbers of the folding structures to 456 and 564 at pH 2 and pH 7; whereas its mutageneses (6-11) TPPKKH - > SLNLRL, (9- 11) KKH - > LRL, and (10-11) KH - > RL decreased the numbers of the folding structures to 60, 30 and 90 at both pH levels, respectively. Thereafter, the normalized hydrophobicity index was employed to distinguish those native states, and attempts were made to explain the effect of mutageneses on potassium channels in terms of the number of folding structures and numerical native states.     

Analysis on folding of misgurin using two-dimensional HP model

Misgurin is an antimicrobial peptide from the loach, while the hydrophobic-polar (HP) model is a way to study the folding conformations and native states in peptide and protein although several amino acids cannot be classified either hydrophobic or polar. Practically, the HP model requires extremely intensive computations, thus it has yet to be used widely. In this study, we use the two-dimensional HP model to analyze all possible folding conformations and native states of misgurin with conversion of natural amino acids according to the normalized amino acid hydrophobicity index as well as the shortest benchmark HP sequence. The results show that the conversion of misgurin into HP sequence with glycine as hydrophobic amino acid at pH 2 has 1212 folding conformations with the same native state of minimal energy -6; the conversion of glycine as polar amino acid at pH 2 has 13,386 folding conformations with three native states of minimal energy -5; the conversion of glycine as hydrophobic amino acid at pH 7 has 2538 folding conformations with three native states of minimal energy -5; and the conversion of glycine as polar amino acid at pH 7 has 12,852 folding conformations with three native states of minimal energy -4. Those native states can be ranked according to the normalized amino acid hydrophobicity index. The detailed discussions suggest two ways to modify misgurin.     

Alternatively folded states of an immunoglobulin

Well-defined, non-native protein structures of low stability have been increasingly observed as intermediates in protein folding or as equilibrium structures populated under specific solvent conditions. These intermediate structures, frequently referred to as molten globule states, are characterized by the presence of secondary structure, a lack of significant tertiary contacts, increased hydrophobicity and partial specific volume as compared to native structures, and low cooperativity in thermal unfolding. The present study demonstrates that under acidic conditions (pH less than 3) the antibody MAK33 can assume a folded stable conformation. This A-state is characterized by a high degree of secondary structure, increased hydrophobicity, a native-like maximum wavelength of fluorescence emission, and a tendency toward slow aggregation. A prominent feature of this low-pH conformation is the stability against denaturant and thermal unfolding that is manifested in highly cooperative reversible phase transitions indicative of the existence of well-defined tertiary contacts. These thermodynamic results are corroborated by the kinetics of folding from the completely unfolded chain to the alternatively folded state at pH 2. The given data suggest that MAK33 at pH 2 adopts a cooperative structure that differs from the native immunoglobulin fold at pH 7. This alternatively folded state exhibits certain characteristics of the molten globule but differs distinctly from it by its extraordinary structural stability that is characteristic for native protein structures.     

The Effect of pH and Heat Pre-Treatments on the Physicochemical and Emulsifying Properties of β-lactoglobulin

The overall goal of this research was to investigate structure-function mechanisms associated the emulsifying properties β-lactoglobulin (β-LG). Specifically the physicochemical (i.e., surface charge and hydrophobicity, size and interfacial tension) and emulsifying (i.e., emulsification activity (EAI) and stability indices (ESI)) properties of β-LG were investigated in response to changes in pH (3.0, 5.0 and 7.0) and heat pre-treatment conditions (25, 55 and 85 °C). Hydrophobicity was found to be greatest at pH 5.0/85 °C, whereas at all conditions it was significantly lower. Surface charge on β-LG was found to be neutral at?~?pH 3.9, regardless of conditions. Aggregate size was also found to be highest at pH 5.0/85 °C (avg. hydrodynamic radii of ~714 nm), corresponding to a reduced net surface charge and high hydrophobicity. Little size dependence of aggregates was observed at pH 3.0 regardless to the temperature pre-treatments (radii ~120 nm). In contrast, at pH 7.0 slight temperature dependence was apparent, where treatments at 25, 55 and 85 °C led to radii of 412.8, 307.2 and 232.3 nm, respectively. Overall, the addition of β-LG to a canola oil–water system resulted in a decline in interfacial tension from ~28 mN/m to ~18 mN/m, however the effect of pH/temperature conditions was minimal. EAI was found to be highest when β-LG solutions displayed high surface charge combined with moderate hydrophobicity. In contrast, ESI was higher under conditions where β-LG solutions remained in a native (25 °C) or fully denatured state (85 °C) versus one in where partially unravelling may be occurring (55 °C).     

Low folding cooperativity of HP35 revealed by single-molecule force spectroscopy and molecular dynamics simulation

Some small proteins, such as HP35, fold at submicrosecond timescale with low folding cooperativity. Although these proteins have been extensively investigated, still relatively little is known about their folding mechanism. Here, using single-molecule force spectroscopy and steered molecule dynamics simulation, we study the unfolding of HP35 under external force. Our results show that HP35 unfolds at extremely low forces without a well-defined unfolding transition state. Subsequently, we probe the structure of unfolded HP35 using the persistence length obtained in the force spectroscopy. We found that the persistence length of unfolded HP35 is around 0.72 nm, >40% longer than typical unstructured proteins, suggesting that there are a significant amount of residual secondary structures in the unfolded HP35. Molecular dynamics simulation further confirmed this finding and revealed that many native contacts are preserved in HP35, even its two ends have been extended up to 8 nm. Our results therefore suggest that retaining a significant amount of secondary structures in the unfolded state of HP35 may be an efficient way to reduce the entropic cost for the formation of tertiary structure and increase the folding speed, although the folding cooperativity is compromised. Moreover, we anticipate that the methods we used in this work can be extended to the study of other proteins with complex folding behaviors and even intrinsically disordered ones.     

A Compact Native 24-Residue Supersecondary Structure Derived from the Villin Headpiece Subdomain

Many small proteins fold highly cooperatively in an all-or-none fashion and thus their native states are well protected from thermal fluctuations by an extensive network of interactions across the folded structure. Because protein structures are stabilized by local and nonlocal interactions among distal residues, dissecting individual substructures from the context of folded proteins results in large destabilization and loss of unique three-dimensional structure. Thus, mini-protein substructures can only rarely be derived from natural templates. Here, we describe a compact native 24-residues-long supersecondary structure derived from the hyperstable villin headpiece subdomain consisting of helices 2 and 3 (HP24). Using a combination of experimental techniques, including NMR and small-angle x-ray scattering, as well as all-atom replica exchange molecular-dynamics simulations, we show that a variant with stabilizing substitutions (HP24stab) forms a densely packed and compact conformation. In HP24stab, interactions between helices 2 and 3 are similar to those observed in native folded HP35, and the two helices cooperatively stabilize each other by completing the hydrophobic core lining the central part of HP35. Interestingly, even though the HP24wt fragment shows a more expanded and less structured conformation, NMR and simulations demonstrate a preference for a native-like topology. Thus, the two stabilizing residues in HP24stab shift the energy balance toward the native state, leading to a minimal folding motif.     

Reliable protein folding on complex energy landscapes: the free energy reaction path

A theoretical framework is developed to study the dynamics of protein folding. The key insight is that the search for the native protein conformation is influenced by the rate r at which external parameters, such as temperature, chemical denaturant, or pH, are adjusted to induce folding. A theory based on this insight predicts that 1), proteins with complex energy landscapes can fold reliably to their native state; 2), reliable folding can occur as an equilibrium or out-of-equilibrium process; and 3), reliable folding only occurs when the rate r is below a limiting value, which can be calculated from measurements of the free energy. We test these predictions against numerical simulations of model proteins with a single energy scale.     

Cooperative tertiary interaction network guides RNA folding

Noncoding RNAs form unique 3D structures, which perform many regulatory functions. To understand how RNAs fold uniquely despite a small number of tertiary interaction motifs, we mutated the major tertiary interactions in a group I ribozyme by single-base substitutions. The resulting perturbations to the folding energy landscape were measured using SAXS, ribozyme activity, hydroxyl radical footprinting, and native PAGE. Double- and triple-mutant cycles show that most tertiary interactions have?a small effect on the stability of the native state. Instead, the formation of core and peripheral structural motifs is cooperatively linked in near-native folding intermediates, and this cooperativity depends on the native helix orientation. The emergence of a cooperative interaction network at an early stage of folding suppresses nonnative structures and guides the search for the native state. We suggest that cooperativity in noncoding RNAs arose from natural selection of architectures conducive to forming?a unique, stable fold.     

Kinetics of protein folding: Nucleation mechanism,time scales,and pathways

The kinetics and thermodynamics of protein folding is investigated using low friction Langevin simulation of minimal continuum mode of proteins. We show that the model protein has two characteristic temperatures: (a) T_θ, at which the chain undergoes a collapse transition from an extended conformation; (b) T_f(< T_θ), at which a finite size first-order transition to the folded state takes place. The kinetics of approach to the native state from initially denatured conformations is probed by several novel correlation functions. We find that the overall kinetics of approach to the native conformation occurs via a three-stage multiple pathway mechanism. The initial stage, characterized by a series of local dihedral angle transitions, eventually results in the compaction of the protein. Subsequently, the molecule acquires native-like structures during the second stage of folding. The final stage of folding involves activated transitions from one of the native-like structures to the native conformation. The first two stages are characterized by a multiplicity of pathways while relatively few paths are involved in the final stage. A detailed analysis of the dynamics of individual trajectories reveals a novel picture of protein folding. We find that afraction of the initial population reaches the native conformation without the formation of any detectable intermediates. This pathway is associated with a nucleation mechanism, i.e., once a critical number of tertiary contacts are established then the native state is reached rapidly. The remaining fraction of molecules become trapped in misfolded structures (stabilized by incorrect tertiary contacts). The slow folding involves transitions over barriers from these structures to the native conformation. The theoretical predictions are compared with recent experiments that probe protein folding kinetics by hydrogen exchange labeling technique. © 1995 John Wiley & Sons, Inc.     

The Dominant Folding Route Minimizes Backbone Distortion in SH3

Energetic frustration in protein folding is minimized by evolution to create a smooth and robust energy landscape. As a result the geometry of the native structure provides key constraints that shape protein folding mechanisms. Chain connectivity in particular has been identified as an essential component for realistic behavior of protein folding models. We study the quantitative balance of energetic and geometrical influences on the folding of SH3 in a structure-based model with minimal energetic frustration. A decomposition of the two-dimensional free energy landscape for the folding reaction into relevant energy and entropy contributions reveals that the entropy of the chain is not responsible for the folding mechanism. Instead the preferred folding route through the transition state arises from a cooperative energetic effect. Off-pathway structures are penalized by excess distortion in local backbone configurations and contact pair distances. This energy cost is a new ingredient in the malleable balance of interactions that controls the choice of routes during protein folding.     

Extracting contact energies from protein structures: A study using a simplified model

In this study, we exploited an elementary 2-dimensional square lattice model of HP polymers to test the premise of extracting contact energies from protein structures. Given a set of prespecified energies for H–H, H–P, and P–P contacts, all possible sequences of various lengths were exhaustively enumerated to find sequences that have unique lowest-energy conformations. The lowest-energy structures (or native structures) of such (native) sequences were used to extract contact energies using the Miyazawa-Jernigan procedure and here-defined reference state. The relative magnitudes of the original energies were restored reasonably well, but the extracted contact energies were independent of the absolute magnitudes of the initial energies. We turned to a more detailed characterization of the energy landscapes of the native sequences in light of a new theoretical framework on protein folding. Foldability of such sequences imposes two limits on the absolute value of the prespecified energies: a lower bound entailed by the minimum requirement for thermodynamic stability and an upper bound associated with the entrapment of the chain to local minima. We found that these two limits confine the prespecified energy values to a rather narrow range which, surprisingly, also contains the extracted energies in all the cases examined. These results indicate that the quasi-chemical approximation can be used to connect quantitatively the occurrence of various residue–residue contacts in an ensemble of native structures with the energies of the contacts. More importantly, they suggest that the extracted contact energies do contain information on structural stability and can be used to estimate actual structural energetics. This study also encourages the use of structure-derived contact energies in threading. The finding that there is a rather narrow range of energies that are optimal for folding a sequence also cautions the use of arbitrary energy Hamiltonion in minimal folding models. Proteins 31:299–308, 1998. © 1998 Wiley-Liss, Inc.     

Monte Carlo simulation of protein folding with orientation-dependent monomer–monomer interactions

We present the results of lattice Monte Carlo simulations of protein folding in the framework of a model taking into account (i) the dependence of the energy of interaction of amino-acid residues on their orientation and (ii) the rigidity of the polypeptide chain with respect to the formation of kinks. If the chain is flexible, the final protein structures are predicted to be compact. Increasing the energy cost of creation of kinks is found to favor the formation of flat structures mimicking an ideal antiparallel β sheet. For compact structures, the kinetics of folding exhibit the standard two-phase regime (a rapid collapse to one of the metastable state, followed by slow reconfiguration of the chain to the native structure). For flat structures, the transition to the native state is often gradual. Proteins 29:508–516, 1997. © 1997 Wiley-Liss, Inc.     

Routes are trees: the parsing perspective on protein folding

An important puzzle in structural biology is the question of how proteins are able to fold so quickly into their unique native structures. There is much evidence that protein folding is hierarchic. In that case, folding routes are not linear, but have a tree structure. Trees are commonly used to represent the grammatical structure of natural language sentences, and chart parsing algorithms efficiently search the space of all possible trees for a given input string. Here we show that one such method, the CKY algorithm, can be useful both for providing novel insight into the physical protein folding process, and for computational protein structure prediction. As proof of concept, we apply this algorithm to the HP lattice model of proteins. Our algorithm identifies all direct folding route trees to the native state and allows us to construct a simple model of the folding process. Despite its simplicity, our model provides an account for the fact that folding rates depend only on the topology of the native state but not on sequence composition.     

Conformational states of annexin VI in solution induced by acidic pH

Acidic pH-induced folding of annexin (Anx)VI in solution was investigated in order to study the mechanism of formation of ion channels by the protein in membranes. Using 2-(p-toluidino)naphthalene-6-sulfonic acid as a hydrophobic probe, it was demonstrated that AnxVI exerts a large change in hydrophobicity at acidic pH. Moreover, circular dichroism spectra indicated that the native state of AnxVI changes at acidic pH towards a state characterized by a significant loss of alpha-helix content and appearance of new beta-structures. These changes are reversible upon an increase of pH. It is postulated that the structural folding of AnxVI could explain how a soluble protein may undergo transition into a molecule able to penetrate the membrane hydrophobic region. The physiological significance of these observations is discussed.     

NMR characterization of a peptide model provides evidence for significant structure in the unfolded state of the villin headpiece helical subdomain

The villin headpiece subdomain (HP36) is the smallest naturally occurring protein that folds cooperatively. The protein folds on a microsecond time scale. Its small size and very rapid folding have made it a popular target for biophysical studies of protein folding. Temperature-dependent one-dimensional (1D) NMR studies of the full-length protein together with CD and 1D NMR studies of the 21-residue peptide fragment (HP21) derived from HP36 have shown that there is significant structure in the unfolded state of HP36 and have demonstrated that HP21 is a good model of these interactions. Here, we characterized the model peptide HP21 in detail by two-dimensional NMR. Strongly upfield shifted C(alpha) protons, the magnitude of the 3J(NH,alpha) coupling constants, and the pattern of backbone-backbone and backbone-side chain NOEs indicate that the ensemble of structures populated by HP21 contains alpha-helical structure and native as well as non-native hydrophobic contacts. The hydrogen-bonded secondary structure inferred from the NOEs is, however, not sufficient to confer significant protection against amide H-D exchange. These studies indicate that there is significant secondary structure and hydrophobic clustering in the unfolded state of HP36. The implications for the folding of HP36 are discussed.     

Global optimisation by replica exchange with scaled hybrid Hamiltonians

A global optimisation scheme based on replica-exchange molecular dynamics simulation with scaled hybrid Hamiltonians is presented and applied to fold trpzip2 peptide from extended structures with explicit water model using only eight replicas. The algorithm is shown to be capable of reproducibly optimising the peptide to structures of root mean squared deviations less than 2.5 Å with respect to all heavy atoms of NMR models. Moreover, the large amount of structural data sampled in the optimisation process enables us to provide a possible folding mechanism. The transition state ensemble is characterised by a largely formed turn and a compact packing of tryptophan 2, 4 and 9. The tryptophan 2/11 pair is found to form at a very late stage of the folding process. The first (closest to the turn) and the fourth native backbone hydrogen bonds form earlier and a picture of strict zipping up of hydrogen bonds is not observed. It is demonstrated in the present study that this global optimisation method which integrates structure prediction with approximated conformational samplings may be of help to understand the folding puzzle.     

Structural characteristics of thermostable immunogenic outer membrane protein from Salmonella enterica serovar Typhi

In this work, we explored the acid-induced unfolding pathway of non-porin outer membrane protein (OMP), an immunogenic protein from Salmonella Typhi, by monitoring the conformational changes over a pH range of 1.0–7.0 by circular dichroism, intrinsic fluorescence, ANS binding, acrylamide quenching, and dynamic light scattering. The spectroscopic measurements showed that OMP in its native state at pH 7.0 exists in more stable and compact conformation. In contrast, at pH 2.0, OMP retains substantial amount of secondary structure, disrupted side chain interactions, increased hydrodynamic radii, and nearly four-fold increase in ANS fluorescence with respect to the native state, indicating that MG state exists at pH 2.0. Quenching of tryptophan fluorescence by acrylamide further confirmed the accumulation of a partially unfolded state between native and unfolded state. The effect of pH on the conformation and thermostability of OMP points towards its heat resistance at neutral pH (T _m?~?69 °C at pH 7.0, monitored by change in MRE_{222 nm}). Acid unfolded state was also characterized by the lack of a cooperative thermal transition. All these results suggested that acid-induced unfolded state of OMP at pH 2.0 represented the molten globule state. The chemical denaturation studies with GuHCl and urea as denaturants showed dissimilar results. The chemical unfolding experiments showed that in both far-UV CD and fluorescence measurements, GuHCl is more efficient than urea. GuHCl is characterized by low C _m (~1 M), while urea is characterized by high C _m (~3 M). The fully unfolded states were reached at 2 M GuHCl and 4 M urea concentration, respectively. This study adds to several key considerations of importance in the development of therapeutic agents against typhoid fever for clinical purposes.     

Protein folding in the landscape perspective: Chevron plots and non-arrhenius kinetics

We use two simple models and the energy landscape perspective to study protein folding kinetics. A major challenge has been to use the landscape perspective to interpret experimental data, which requires ensemble averaging over the microscopic trajectories usually observed in such models. Here, because of the simplicity of the model, this can be achieved. The kinetics of protein folding falls into two classes: multiple-exponential and two-state (single-exponential) kinetics. Experiments show that two-state relaxation times have “chevron plot” dependences on denaturant and non-Arrhenius dependences on temperature. We find that HP and HP+ models can account for these behaviors. The HP model often gives bumpy landscapes with many kinetic traps and multiple-exponental behavior, whereas the HP+ model gives more smooth funnels and two-state behavior. Multiple-exponential kinetics often involves fast collapse into kinetic traps and slower barrier climbing out of the traps. Two-state kinetics often involves entropic barriers where conformational searching limits the folding speed. Transition states and activation barriers need not define a single conformation; they can involve a broad ensemble of the conformations searched on the way to the native state. We find that unfolding is not always a direct reversal of the folding process. Proteins 30:2–33, 1998. © 1998 Wiley-Liss, Inc.     

Analyzing the effect of homogeneous frustration in protein folding

The energy landscape theory has been an invaluable theoretical framework in the understanding of biological processes such as protein folding, oligomerization, and functional transitions. According to the theory, the energy landscape of protein folding is funneled toward the native state, a conformational state that is consistent with the principle of minimal frustration. It has been accepted that real proteins are selected through natural evolution, satisfying the minimum frustration criterion. However, there is evidence that a low degree of frustration accelerates folding. We examined the interplay between topological and energetic protein frustration. We employed a C_α structure‐based model for simulations with a controlled nonspecific energetic frustration added to the potential energy function. Thermodynamics and kinetics of a group of 19 proteins are completely characterized as a function of increasing level of energetic frustration. We observed two well‐separated groups of proteins: one group where a little frustration enhances folding rates to an optimal value and another where any energetic frustration slows down folding. Protein energetic frustration regimes and their mechanisms are explained by the role of non‐native contact interactions in different folding scenarios. These findings strongly correlate with the protein free‐energy folding barrier and the absolute contact order parameters. These computational results are corroborated by principal component analysis and partial least square techniques. One simple theoretical model is proposed as a useful tool for experimentalists to predict the limits of improvements in real proteins.Proteins 2013; 81:1727–1737. © 2013 Wiley Periodicals, Inc.