Folding Nuclei in Proteins

When a protein folds or unfolds, it passes through many half-folded microstates. Only a few of them can accumulate and be seen experimentally, and this happens only when the folding (or unfolding) occurs far from the point of thermodynamic equilibrium between the native and denatured states. The universal features of folding, though, are observed in the vicinity of the equilibrium point. Here the two-state transition proceeds without any accumulation of metastable intermediates, and only the transition state (folding nucleus) is outlined by its key influence on the folding/unfolding kinetics. This review covers recent experimental and theoretical studies of folding nuclei.     

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Abstract

In response to the criticism by A. Finkelstein (J. Biomol. Struct. Dyn. 20, 311–314, 2002) of our Communication (J. Biomol. Struct. Dyn. 20, 5–6, 2002) several issues are dealt with. Importance of the notion of elementary folding unit, its size and structure, and the necessity of further characterization of the units for the elucidation of the protein folding in vivo are discussed. The criticism (J. Biomol. Struct. Dyn. 20, 311–314, 2002) on the hierarchical protein folding is also briefly addressed.     

Loop Folds in Proteins and Evolutionary Conservation of Folding Nuclei

Abstract

We show that loops of close contacts involving hydrophobic residues are important in protein folding. Contrary to Berezovsky and Trifonov (J. Biomol. Struct. Dyn. 20, 5–6, 2002) the loops important in protein folding usually are much larger in size than 23–31 residues, being instead comparable to the size of the protein for single domain proteins. Additionally what is important are not single loop contacts, but a highly interconnected network of such loop contacts, which provides extra stability to a protein fold and which leads to their conservation in evolution.     

Cunning Simplicity of a Stoichiometry Driven Protein Folding Thesis

Abstract

Mastoparan B (MP-B) is an antimicrobial cationic tetradecapeptide amide isolated from the venom of the hornet Vespa basalis. NMR spectroscopy was used to study the membrane associated structures of MP-B in various model membrane systems such as 120 mM DPC micelles, 200 mM SDS micelles, and 3%(w/v) DMPC/DHPC (1:2) bicelles. In all systems, MP-B has an amphiphilic α-helical structure from Lys² to Leu¹⁴. NOESY experiments performed on MP-B in nondeuterated SDS micelles show that protons in the indole ring of Trp⁹ are in close contact with methylene protons of SDS micelles. T₁ relaxation data and NOE data revealed that the bound form of MP-B may be dominant in SDS micelles. The interactions between MP-B and zwitterionic DPC micelles were much weaker than those between MP-B and anionic SDS micelles. By substitution of Trp⁹ with Ala⁹, the pore-forming activity of MP-B was decreased dramatically. All of these results imply that strong electrostatic interactions between the positively charged Lys residues in MP-B and the anionic phospholipid head groups must be the primary factor for MP-B binding to the cell membrane. Then, insertion of the indole ring of Trp⁹ into the membrane, as well as the amphiphilic α-helical structures of MP-B may allow MP-B to span the lipid bilayer through the C-terminal portion. These structural features are crucial for the potent antibiotic activities of MP-B.     

Sensitivity of the Folding Pathway to the Details of Amino Acid Sequence

Experimental data on the structure of the transition state demonstrate that proteins with the same topology as a rule have similar folding nuclei (the structured formed part of the transition state). In this review discussed are the experimental works showing that the position of folding nuclei is different among proteins with the same topology. These facts emphasize that the folding pathway is sensitive to the details of amino acid sequence.     

Folding rates and low-entropy-loss routes of two-state proteins

We develop a simple model for computing the rates and routes of folding of two-state proteins from the contact maps of their native structures. The model is based on the graph-theoretical concept of effective contact order (ECO). The model predicts that proteins fold by "zipping up" in a sequence of small-loop-closure events, depending on the native chain fold. Using a simple equation, with a few physical rate parameters, we obtain a good correlation with the folding rates of 24 two-state folding proteins. The model rationalizes data from Phi-value analysis that have been interpreted in terms of delocalized or polarized transition states. This model indicates how much of protein folding may take place in parallel, not along a single reaction coordinate or with a single transition state.     

Contact order revisited: influence of protein size on the folding rate

Guided by the recent success of empirical model predicting the folding rates of small two-state folding proteins from the relative contact order (CO) of their native structures, by a theoretical model of protein folding that predicts that logarithm of the folding rate decreases with the protein chain length L as L(2/3), and by the finding that the folding rates of multistate folding proteins strongly correlate with their sizes and have very bad correlation with CO, we reexamined the dependence of folding rate on CO and L in attempt to find a structural parameter that determines folding rates for the totality of proteins. We show that the Abs_CO = CO x L, is able to predict rather accurately folding rates for both two-state and multistate folding proteins, as well as short peptides, and that this Abs_CO scales with the protein chain length as L(0.70 +/- 0.07) for the totality of studied single-domain proteins and peptides.     

On the Prediction of Folding Nuclei in Globular Proteins

An approach to predicting folding nuclei in globular proteins with known three-dimensional structures is proposed. This approach is based on the pinpointing of the lowest saddle points on the barrier between the unfolded state and native structure on the free-energy landscape of a protein chain; the proposed technique uses the dynamic programming method. A comparison of calculation results with experimental data on the folding nuclei of 21 proteins shows that the model provides good Φ value predictions for protein structures determined by X-ray analysis and, less successfully, in structures determined by nuclear magnetic resonance. Consideration of the whole ensemble of transition states provides a better prediction of folding nuclei than consideration of only transition states with lowest free energies. In addition, we predict the location of folding nuclei in three-dimensional structures of some proteins whose folding kinetics is being studied, but there is no experimental evidence concerning their folding nuclei.     

Protein folding: defining a "standard" set of experimental conditions and a preliminary kinetic data set of two-state proteins

Recent years have seen the publication of both empirical and theoretical relationships predicting the rates with which proteins fold. Our ability to test and refine these relationships has been limited, however, by a variety of difficulties associated with the comparison of folding and unfolding rates, thermodynamics, and structure across diverse sets of proteins. These difficulties include the wide, potentially confounding range of experimental conditions and methods employed to date and the difficulty of obtaining correct and complete sequence and structural details for the characterized constructs. The lack of a single approach to data analysis and error estimation, or even of a common set of units and reporting standards, further hinders comparative studies of folding. In an effort to overcome these problems, we define here a "consensus" set of experimental conditions (25 degrees C at pH 7.0, 50 mM buffer), data analysis methods, and data reporting standards that we hope will provide a benchmark for experimental studies. We take the first step in this initiative by describing the folding kinetics of 30 apparently two-state proteins or protein domains under the consensus conditions. The goal of our efforts is to set uniform standards for the experimental community and to initiate an accumulating, self-consistent data set that will aid ongoing efforts to understand the folding process.     

Folding and Misfolding of a PDZ Tandem Repeat

Although the vast majority of the human proteome is represented by multi-domain proteins, the study of multi-domain folding and misfolding is a relatively poorly explored field. The protein Whirlin is a multi-domain scaffolding protein expressed in the inner ear. It is characterized by the presence of tandem repeats of PDZ domains. The first two PDZ domains of Whirlin (PDZ1 and PDZ2 – namely P1P2) are structurally close and separated by a disordered short linker. We recently described the folding mechanism of the P1P2 tandem. The difference in thermodynamic stability of the two domains allowed us to selectively unfold one or both PDZ domains and to pinpoint the accumulation of a misfolded intermediate, which we demonstrated to retain physiological binding activity. In this work, we provide an extensive characterization of the folding and unfolding of P1P2. Based on the observed data, we describe an integrated kinetic analysis that satisfactorily fits the experiments and provides a valuable model to interpret multi-domain folding. The experimental and analytical approaches described in this study may be of general interest for the interpretation of complex multi-domain protein folding kinetics.     

Folding/Unfolding Kinetics of Apomyoglobin

The equilibrium and kinetic folding/unfolding of apomyoglobin (ApoMb) were studied at pH 6.2, 11 °C by recording tryptophan fluorescence. The equilibrium unfolding of ApoMb in the presence of urea was shown to involve accumulation of an intermediate state, which had a higher fluorescence intensity as compared with the native and unfolded states. The folding proceeded through two kinetic phases, a rapid transition from the unfolded to the intermediate state and a slow transition from the intermediate to the native state. The accumulation of the kinetic intermediate state was observed in a wide range of urea concentrations. The intermediate was detected even in the region corresponding to the unfolding limb of the chevron plot. Urea concentration dependence was obtained for the observed folding/unfolding rate. The shape of the dependence was compared with that of two-state proteins characterized by a direct transition from the unfolded to the native state.     

A Comparison of Experimental and Computational Methods for Mapping the Interactions Present in the Transition State for Folding of FKBP12

The folding pathway of FKBP12, a 107 residue / protein, has been characterised in detail using a combination of experimental and computational techniques. FKBP12 follows a two-state model of folding in which only the denatured and native states are significantly populated; no intermediate states are detected. The refolding rate constant in water is 4 s^-1 at 25 °C. Two different experimental strategies were employed for studying the transition state for folding. In the first case, a non-mutagenic approach was used and the unfolding and refolding of the wild-type protein measured as a function of experimental conditions such as temperature, denaturant, ligand and trifluoroethanol (TFE) concentration. These data suggest a compact transition state relative to the unfolded state with some 70% of the surface area buried. The ligand-binding site, whichis mainly formed by two long loops, is largely unstructured in the transition state. TFE experiments suggest that the -helix may be formed in the transition state. The second experimental approach involved using protein engineering techniques with -value analysis. Residue-specific information on the structure and energetics of the transition state can be obtained by this method. 34 mutations were made at sites throughout the protein to probe the extent of secondary and tertiary structure in the transition state. In contrast to some other proteins of this size, no element of structure is fully formed in the transition state, instead, the transition state is similar to that found for smaller, single-domain proteins, such as chymotrypsin inhibitor 2 and the SH3 domainfrom -spectrin. For FKBP12, the central three strands of the -sheet (2, 4 and 5), comprise the most structured region of the transition state. In particular Val 101, which is one of the most highly buried residues and located in the middle of the central -strand,makes approximately 60% of its native interactions. The outer -strands, and the ends of the central -strands are formed to a lesser degree. The short -helix is largely unstructured in the transition state as are the loops. The data are consistent with a nucleation-condensation model of folding, the nucleus of which is formed by side chains within -strands 2, 4 and 5 and the C-terminus of the -helix. These residues are distant in the primary sequence, demonstrating the importance of tertiary interactions in the transition state. High-temperature molecular dynamic simulations on the unfoldingpathway of FKBP12 are in good agreement with the experimental results.     

Cotranslational Folding of Proteins

We suppose that folding of proteins occurs cotranslationally by the following scheme. The polypeptide chains enter the folding sites from protein translocation complexes (ribosome, translocation machinery incorporated in membranes) directionally with the N-terminus and gradually. The chain starts to fold as soon as its N-terminal residue enters the folding site from the translocation complex. The folding process accompanies the translocation of the chain to its folding site and is completed after the C-terminal residue leaves the translocation complex. Proteins fold in sequential stages, by translocation of their polypeptide into folding compartments. At each stage a particular conformation of the N-terminal part of the chain that has emerged from the translocation complex is formed. The formation of both the particular conformations of the N-terminal chain segment at each folding stage and the final native protein conformation at the last stage occurs in a time that does not exceed the duration of the fastest elongation cycle on the ribosome.     

Folding of a small helical protein using hydrogen bonds and hydrophobicity forces

A reduced protein model with five to six atoms per amino acid and five amino acid types is developed and tested on a three-helix-bundle protein, a 46-amino acid fragment from staphylococcal protein A. The model does not rely on the widely used Go approximation, which ignores non-native interactions. We find that the collapse transition is considerably more abrupt for the protein A sequence than for random sequences with the same composition. The chain collapse is found to be at least as fast as helix formation. Energy minimization restricted to the thermodynamically favored topology gives a structure that has a root-mean-square deviation of 1.8 A from the native structure. The sequence-dependent part of our potential is pairwise additive. Our calculations suggest that fine-tuning this potential by parameter optimization is of limited use.     

Non-linear effects of temperature and urea on the thermodynamics and kinetics of folding and unfolding of hisactophilin

Extensive measurements and analysis of thermodynamic stability and kinetics of urea-induced unfolding and folding of hisactophilin are reported for 5-50 degrees C, at pH 6.7. Under these conditions hisactophilin has moderate thermodynamic stability, and equilibrium and kinetic data are well fit by a two-state transition between the native and the denatured states. Equilibrium and kinetic m values decrease with increasing temperature, and decrease with increasing denaturant concentration. The betaF values at different temperatures and urea concentrations are quite constant, however, at about 0.7. This suggests that the transition state for hisactophilin unfolding is native-like and changes little with changing solution conditions, consistent with a narrow free energy profile for the transition state. The activation enthalpy and entropy of unfolding are unusually low for hisactophilin, as is also the case for the corresponding equilibrium parameters. Conventional Arrhenius and Eyring plots for both folding and unfolding are markedly non-linear, but these plots become linear for constant DeltaG/T contours. The Gibbs free energy changes for structural changes in hisactophilin have a non-linear denaturant dependence that is comparable to non-linearities observed for many other proteins. These non-linearities can be fit for many proteins using a variation of the Tanford model, incorporating empirical quadratic denaturant dependencies for Gibbs free energies of transfer of amino acid constituents from water to urea, and changes in fractional solvent accessible surface area of protein constituents based on the known protein structures. Noteworthy exceptions that are not well fit include amyloidogenic proteins and large proteins, which may form intermediates. The model is easily implemented and should be widely applicable to analysis of urea-induced structural transitions in proteins.     

The nature of the free energy barriers to two-state folding

We introduce a simple procedure to analyze the temperature dependence of the folding and unfolding rates of two-state proteins. We start from the simple transition-state-like rate expression: k = D(eff)exp(-DeltaG(TS)/RT), in which upper and lower bounds for the intra-chain effective diffusion coefficient (D(eff)) are obtained empirically using the timescales of elementary processes in protein folding. From the changes in DeltaG(TS) as a function of temperature, we calculate enthalpies and heat capacities of activation, together with the more elusive entropies of activation. We then estimate the conformational entropy of the transition state by extrapolation to the temperature at which the solvation entropy vanishes by cancellation between polar and apolar terms. This approach is based on the convergence temperatures for the entropy of solvating apolar (approximately 385 K) and polar groups (approximately 335 K), the assumption that the structural properties of the transition state are somewhere in between the unfolded and folded states, and the established relationship between observed heat capacity and solvent accessibility.1 To circumvent the lack of structural information about transition states, we use the empirically determined heat capacities of activation as constraints to identify the extreme values of the transition state conformational entropy that are consistent with experiment. The application of this simple approach to six two-state folding proteins for which there is temperature-dependent data available in the literature provides important clues about protein folding. For these six proteins, we obtain an average equilibrium cost in conformational entropy of -4.3 cal x mol(-1)K(-1)per residue, which is in close agreement to previous empirical and computational estimates of the same quantity. Furthermore, we find that all these proteins have a conformationally diverse transition state, with more than half of the conformational entropy of the unfolded state. In agreement with predictions from theory and computer simulations, the transition state signals the change from a regime dominated by loss in conformational entropy to one driven by the gain in stabilization free energy (i.e., including protein interactions and solvation effects). Moreover, the height of the barrier is determined by how much stabilization free energy is realized at that point, which is related to the relative contribution of local versus non-local interactions. A remarkable observation is that the fraction of conformational entropy per residue that is present in the transition state is very similar for the six proteins in this study. Based on this commonality, we propose that the observed change in thermodynamic regime is connected to a change in the pattern of structure formation: from one driven by formation of pairwise interactions to one dominated by coupling of the networks of interactions involved in forming the protein core. In this framework, the barrier to two-state folding is crossed when the folding protein reaches a "critical native density" that allows expulsion of remaining interstitial water and consolidation of the core. The principle of critical native density should be general for all two-state proteins, but can accommodate different folding mechanisms depending on the particularities of the structure and sequence.     

Single-Molecule Force Spectroscopy of Protein Folding

The use of force probes to induce unfolding and refolding of single molecules through the application of mechanical tension, known as single-molecule force spectroscopy (SMFS), has proven to be a powerful tool for studying the dynamics of protein folding. Here we provide an overview of what has been learned about protein folding using SMFS, from small, single-domain proteins to large, multi-domain proteins. We highlight the ability of SMFS to measure the energy landscapes underlying folding, to map complex pathways for native and non-native folding, to probe the mechanisms of chaperones that assist with native folding, to elucidate the effects of the ribosome on co-translational folding, and to monitor the folding of membrane proteins.     

从氨基酸序列预测蛋白质折叠速率

蛋白质折叠速率预测是当今生物物理学最具挑战性的课题之一．近年来,许多科研工作者开展了大量的研究工作来探索折叠速率的决定因素,许多参数和方法被相继提出．但氨基酸残基间的相互作用、氨基酸的序列顺序等信息对折叠速率的影响从未被提及．采用伪氨基酸组成的方法提取氨基酸的序列顺序信息,利用蒙特卡洛方法选择最佳特征因子,建立线性回归模型进行折叠速率预测．该方法能在不需要任何(显示)结构信息的情况下,直接从蛋白质的氨基酸序列出发对折叠速率进行预测．在Jackknife交互检验方法的验证下,对含有99个蛋白质的数据集,发现折叠速率的预测值与实验值有很好的相关性,相关系数能达到0.81,预测误差仅为2.54．这一精度明显优于其他基于序列的方法,充分说明蛋白质的序列顺序信息是影响蛋白质折叠速率的重要因素．     

Chain length is the main determinant of the folding rate for proteins with three-state folding kinetics

We demonstrate that chain length is the main determinant of the folding rate for proteins with the three-state folding kinetics. The logarithm of their folding rate in water (k(f)) strongly anticorrelates with their chain length L (the correlation coefficient being -0.80). At the same time, the chain length has no correlation with the folding rate for two-state folding proteins (the correlation coefficient is -0.07). Another significant difference of these two groups of proteins is a strong anticorrelation between the folding rate and Baker's "relative contact order" for the two-state folders and the complete absence of such correlation for the three-state folders.