Hybridized distance- and contact-based hierarchical structure modeling for folding soluble and membrane proteins

Crystallography and NMR system (CNS) is currently a widely used method for fragment-free ab initio protein folding from inter-residue distance or contact maps. Despite its widespread use in protein structure prediction, CNS is a decade-old macromolecular structure determination system that was originally developed for solving macromolecular geometry from experimental restraints as opposed to predictive modeling driven by interaction map data. As such, the adaptation of the CNS experimental structure determination protocol for ab initio protein folding is intrinsically anomalous that may undermine the folding accuracy of computational protein structure prediction. In this paper, we propose a new CNS-free hierarchical structure modeling method called DConStruct for folding both soluble and membrane proteins driven by distance and contact information. Rigorous experimental validation shows that DConStruct attains much better reconstruction accuracy than CNS when tested with the same input contact map at varying contact thresholds. The hierarchical modeling with iterative self-correction employed in DConStruct scales at a much higher degree of folding accuracy than CNS with the increase in contact thresholds, ultimately approaching near-optimal reconstruction accuracy at higher-thresholded contact maps. The folding accuracy of DConStruct can be further improved by exploiting distance-based hybrid interaction maps at tri-level thresholding, as demonstrated by the better performance of our method in folding free modeling targets from the 12th and 13th rounds of the Critical Assessment of techniques for protein Structure Prediction (CASP) experiments compared to popular CNS- and fragment-based approaches and energy-minimization protocols, some of which even using much finer-grained distance maps than ours. Additional large-scale benchmarking shows that DConStruct can significantly improve the folding accuracy of membrane proteins compared to a CNS-based approach. These results collectively demonstrate the feasibility of greatly improving the accuracy of ab initio protein folding by optimally exploiting the information encoded in inter-residue interaction maps beyond what is possible by CNS.     

Entropy-driven folding of an RNA helical junction: an isothermal titration calorimetric analysis of the hammerhead ribozyme

Helical junctions are extremely common motifs in naturally occurring RNAs, but little is known about the thermodynamics that drive their folding. Studies of junction folding face several challenges: non-two-state folding behavior, superposition of secondary and tertiary structural energetics, and drastically opposing enthalpic and entropic contributions to folding. Here we describe a thermodynamic dissection of the folding of the hammerhead ribozyme, a three-way RNA helical junction, by using isothermal titration calorimetry of bimolecular RNA constructs. By using this method, we show that tertiary folding of the hammerhead core occurs with a highly unfavorable enthalpy change, and is therefore entropically driven. Furthermore, the enthalpies and heat capacities of core folding are the same whether supported by monovalent or divalent ions. These properties appear to be general to the core sequence of bimolecular hammerhead constructs. We present a model for the ion-induced folding of the hammerhead core that is similar to those advanced for the folding of much larger RNAs, involving ion-induced collapse to a structured, non-native state accompanied by rearrangement of core residues to produce the native fold. In agreement with previous enzymological and structural studies, our thermodynamic data suggest that the hammerhead structure is stabilized in vitro predominantly by diffusely bound ions. Our approach addresses several significant challenges that accompany the study of junction folding, and should prove useful in defining the thermodynamic determinants of stability in these important RNA motifs.     

Polar and nonpolar atomic environments in the protein core: Implications for folding and binding

Hydrophobic interactions are believed to play an important role in protein folding and stability. Semi-empirical attempts to estimate these interactions are usually based on a model of solvation, whose contribution to the stability of proteins is assumed to be proportional to the surface area buried upon folding. Here we propose an extension of this idea by defining an environment free energy that characterizes the environment of each atom of the protein, including solvent, polar or nonpolar atoms of the same protein or of another molecule that interacts with the protein. In our model, the difference of this environment free energy between the folded state and the unfolded (extended) state of a protein is shown to be proportional to the area buried by nonpolar atoms upon folding. General properties of this environment free energy are derived from statistical studies on a database of 82 well-refined protein structures. This free energy is shown to be able to discriminate misfolded from correct structural models, to provide an estimate of the stabilization due to oligomerization, and to predict the stability of mutants in which hydrophobic residues have been substituted by site-directed mutagenesis, provided that no large structural modifications occur. © 1994 Wiley-Liss, Inc.     

Active Cage Mechanism of Chaperonin-Assisted Protein Folding Demonstrated at Single-Molecule Level

The cylindrical chaperonin GroEL and its lid-shaped cofactor GroES of Escherichia coli have an essential role in assisting protein folding by transiently encapsulating non-native substrate in an ATP-regulated mechanism. It remains controversial whether the chaperonin system functions solely as an infinite dilution chamber, preventing off-pathway aggregation, or actively enhances folding kinetics by modulating the folding energy landscape. Here we developed single-molecule approaches to distinguish between passive and active chaperonin mechanisms. Using low protein concentrations (100 pM) to exclude aggregation, we measured the spontaneous and GroEL/ES-assisted folding of double-mutant maltose binding protein (DM-MBP) by single-pair fluorescence resonance energy transfer and fluorescence correlation spectroscopy. We find that GroEL/ES accelerates folding of DM-MBP up to 8-fold over the spontaneous folding rate. Accelerated folding is achieved by encapsulation of folding intermediate in the GroEL/ES cage, independent of repetitive cycles of protein binding and release from GroEL. Moreover, photoinduced electron transfer experiments provided direct physical evidence that the confining environment of the chaperonin restricts polypeptide chain dynamics. This effect is mediated by the net-negatively charged wall of the GroEL/ES cavity, as shown using the GroEL mutant EL(KKK2) in which the net-negative charge is removed. EL(KKK2)/ES functions as a passive cage in which folding occurs at the slow spontaneous rate. Taken together our findings suggest that protein encapsulation can accelerate folding by entropically destabilizing folding intermediates, in strong support of an active chaperonin mechanism in the folding of some proteins. Accelerated folding is biologically significant as it adjusts folding rates relative to the speed of protein synthesis.     

How long does it take to equilibrate the unfolded state of a protein?

How long does it take to equilibrate the unfolded state of a protein? The answer to this question has important implications for our understanding of why many small proteins fold with two state kinetics. When the equilibration within the unfolded state U is much faster than the folding, the folding kinetics will be two state even if there are many folding pathways with different barriers. Yet the mean first passage times (MFPTs) between different regions of the unfolded state can be much longer than the folding time. This seems to imply that the equilibration within U is much slower than the folding. In this communication we resolve this paradox. We present a formula for estimating the time to equilibrate the unfolded state of a protein. We also present a formula for the MFPT to any state within U, which is proportional to the average lifetime of that state divided by the state population. This relation is valid when the equilibration within U is very fast as compared with folding as it often is for small proteins. To illustrate the concepts, we apply the formulas to estimate the time to equilibrate the unfolded state of Trp-cage and MFPTs within the unfolded state based on a Markov State Model using an ultra-long 208 microsecond trajectory of the miniprotein to parameterize the model. The time to equilibrate the unfolded state of Trp-cage is ∼100 ns while the typical MFPTs within U are tens of microseconds or longer.     

Temperature-dependent folding pathways of Pin1 WW domain: an all-atom molecular dynamics simulation of a Gō model

We study the folding thermodynamics and kinetics of the Pin1 WW domain, a three-stranded beta-sheet protein, by using all-atom (except nonpolar hydrogens) discontinuous molecular dynamics simulations at various temperatures with a Gō model. The protein exhibits a two-state folding kinetics near the folding transition temperature. A good agreement between our simulations and the experimental measurements by the Gruebele group has been found, and the simulation sheds new insights into the structure of transition state, which is hard to be straightforwardly captured in experiments. The simulation also reveals that the folding pathways at approximately the transition temperature and at low temperatures are much different, and an intermediate state at a low temperature is predicted. The transition state of this small beta-protein at its folding transition temperature has a well-established hairpin 1 made of beta1 and beta2 strands while its low-temperature kinetic intermediate has a formed hairpin 2 composed of beta2 and beta3 strands. Theoretical results are compared with other simulation results as well as available experimental data. This study confirms that specific side-chain packing in an all-atom Gō model can yield a reasonable prediction of specific folding kinetics for a given protein. Different folding behaviors at different temperatures are interpreted in terms of the interplay of entropy and enthalpy in folding process.     

Reduction of the endoplasmic reticulum accompanies the oxidative damage of diabetes mellitus

The endoplasmic reticulum (ER), similary to other subcompartments of the eukaryotic cell possesses a relatively oxidizing environment. The special milieu of ER lumen is important for many ER-specific processes (redox protein folding, glycoprotein synthesis, quality control of secreted proteins, antigen presentation, etc.). Despite of the vital importance of redox regulation in the ER, we have a surprisingly fragmented knowledge about the mechanisms responsible for the ER redox balance. Moreover, new observations on disulfide bridge synthesis and on glutathione functions urge us to revise our recent theories based on many indirect and in vitro results. We have also very little information about the effects of different pathological conditions on the thiol metabolism and redox folding in the ER. Examining the role of molecular chaperones in the cellular pathology of diabetes mellitus we found that the ER redox environment shifted to a more reducing state, which was followed by changes of the thiol metabolism and structural-functional changes of the protein machinery involved in the redox folding process in diabetes. The possible consequences of these unexpected changes are also discussed.     

Role of unfolded state heterogeneity and en-route ruggedness in protein folding kinetics

In order to improve our understanding of the physical bases of protein folding, there is a compelling need for better connections between experimental and computational approaches. This work addresses the role of unfolded state conformational heterogeneity and en-route intermediates, as an aid for planning and interpreting protein folding experiments. The expected kinetics were modeled for different types of energy landscapes, including multiple parallel folding routes, preferential paths dominated by one primary folding route, and distributed paths with a wide spectrum of microscopic folding rate constants. In the presence of one or more preferential routes, conformational exchange among unfolded state populations slows down the observed rates for native protein formation. We find this to be a general phenomenon, taking place even when unfolded conformations interconvert much faster than the "escape" rate constants to folding. Dramatic kinetic deceleration is expected in the presence of an increasing number of folding-incompetent unfolded conformations. This argues for the existence of parallel folding paths involving several folding-competent unfolded conformations, during the early stages of protein folding. Deviations from single-exponential behavior are observed for unfolded conformations exchanging at comparable rates or more slowly than folding events. Analysis of the effect of en-route (on-path) intermediate formation and landscape ruggedness on folding kinetics leads to the following unexpected conclusions: (1) intermediates, which often retard native state formation, may in some cases accelerate folding, and (2) rugged landscapes, usually associated with stretched exponentials, display single-exponential behavior in the presence of late high-friction paths.     

How RNA folds.

We describe the RNA folding problem and contrast it with the much more difficult protein folding problem. RNA has four similar monomer units, whereas proteins have 20 very different residues. The folding of RNA is hierarchical in that secondary structure is much more stable than tertiary folding. In RNA the two levels of folding (secondary and tertiary) can be experimentally separated by the presence or absence of Mg2+. Secondary structure can be predicted successfully from experimental thermodynamic data on secondary structure elements: helices, loops, and bulges. Tertiary interactions can then be added without much distortion of the secondary structure. These observations suggest a folding algorithm to predict the structure of an RNA from its sequence. However, to solve the RNA folding problem one needs thermodynamic data on tertiary structure interactions, and identification and characterization of metal-ion binding sites. These data, together with force versus extension measurements on single RNA molecules, should provide the information necessary to test and refine the proposed algorithm.     

Contact order dependent protein folding rates: kinetic consequences of a cooperative interplay between favorable nonlocal interactions and local conformational preferences

Physical mechanisms underlying the empirical correlation between relative contact order (CO) and folding rate among naturally occurring small single-domain proteins are investigated by evaluating postulated interaction schemes for a set of three-dimensional 27mer lattice protein models with 97 different CO values. Many-body interactions are constructed such that contact energies become more favorable when short chain segments sequentially adjacent to the contacting residues adopt native-like conformations. At a given interaction strength, this scheme leads to folding rates that are logarithmically well correlated with CO (correlation coefficient r = 0.914) and span more than 2.5 orders of magnitude, whereas folding rates of the corresponding Gō models with additive contact energies have much less logarithmic correlation with CO and span only approximately one order of magnitude. The present protein chain models also exhibit calorimetric cooperativity and linear chevron plots similar to that observed experimentally for proteins with apparent simple two-state folding/unfolding kinetics. Thus, our findings suggest that CO-dependent folding rates of real proteins may arise partly from a significant positive coupling between nonlocal contact favorabilities and local conformational preferences.     

In vitro studies of membrane protein folding.

The study of membrane protein folding is a new and challenging research field. Consequently, there are few direct studies on the in vitro folding of membrane proteins. This review covers work aimed at understanding folding mechanisms and the intermolecular forces that drive the folding of integral membrane proteins. We discuss the kinetic and thermodynamic studies that have been undertaken. Our review also draws on closely related research, mainly from purification studies of functional membrane proteins, and gives an overview of some of the successful methods. A brief survey is also given of the large body of mutagenesis and fragment work on membrane proteins, as this too has relevance to the folding problem. It is noticeable that the choice of solubilizing detergents and lipids can determine the success of the method, and indeed it appears that particular lipid properties can be used to control the rate and efficiency of folding. This has important ramifications for much in vitro folding work in that it aids our understanding of how to obtain and handle folded, functional protein. With this in mind, we also cover some relevant properties of model, lipid-bilayer systems.     

Prediction of the initial folding sites and the entire folding processes for Ig-like beta-sandwich proteins

Describing the whole story of protein folding is currently the main enigmatic problem in molecular bioinformatics study. Protein folding mechanisms have been intensively investigated with experimental as well as simulation techniques. Since a protein folds into its specific 3D structure from a unique amino acid sequence, it is interesting to extract as much information as possible from the amino acid sequence of a protein. Analyses based on inter-residue average distance statistics and a coarse-grained Gō-model simulation were conducted on Ig and FN3 domains of a titin protein to decode the folding mechanisms from their sequence data and native structure data, respectively. The central region of all domains was predicted to be an initial folding unit, that is, stable in an early state of folding. This common feature coincides well with the experimental results and underscores the significance of the β-sandwich proteins' common structure, namely, the key strands for folding and the Greek-key motif, which is located in the central region. We confirmed that our sequence-based techniques were able to predict the initial folding event just next to the denatured state and that a 3D-based Gō-model simulation can be used to investigate the whole process of protein folding.     

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.     

Rapid folding of calcium-free subtilisin by a stabilized pro-domain mutant.

In vitro folding of mature subtilisin is extremely slow. The isolated pro-domain greatly accelerates in vitro folding of subtilisin in a bimolecular reaction whose product is a tight complex between folded subtilisin and folded pro-domain. In our studies of subtilisin, we are trying to answer two basic questions: why does subtilisin fold slowly without the pro-domain and what does the pro-domain do to accelerate the folding rate? To address these general questions, we are trying to characterize all the rate constants governing individual steps in the bimolecular folding reaction of pro-domain with subtilisin. Here, we report the results of a series of in vitro folding experiments using an engineered pro-domain mutant which is independently stable (proR9) and two calcium-free subtilisin mutants. The bimolecular folding reaction of subtilisin and proR9 occurs in two steps: an initial binding of proR9 to unfolded subtilisin, followed by isomerization of the initial complex into the native complex. The central findings are as follows. First, the independently stable proR9 folds subtilisin much faster than the predominantly unfolded wild-type pro-domain. Second, at micromolar concentrations of proR9, the subtilisin folding reaction becomes limited by the rate at which prolines in the unfolded state can isomerize to their native conformation. The simpliest mechanism which closely describes the data includes two denatured forms of subtilisin, which form the initial complex with proR9 at the same rate but which isomerize to the fully folded complex at much different rates. In this model, 77% of the subtilisin isomerizes to the native form slowly and the remaining 23% isomerizes more rapidly (1.5 s-1). The slow-folding population may be unfolded subtilisin with the trans form of proline 168, which must isomerize to the cis form during refolding. Third, in the absence of proline isomerization, the rate of subtilisin folding is rapid and at [proR9] 3 s-1. The implications of these results concerning why subtilisin folds slowly without the pro-domain are discussed.     

Does mRNA structure contain genetic information for regulating co-translational protein folding?

Currently many facets of genetic information are illdefined.In particular,how protein folding is genetically regulated has been a long-standing issue for genetics and protein biology.And a generic mechanistic model with supports of genomic data is still lacking.Recent technological advances have enabled much needed genome-wide experiments.While putting the effect of codon optimality on debate,these studies have supplied mounting evidence suggesting a role of mRNA structure in the regulation of protein folding by modulating translational elongation rate.In conjunctions with previous theories,this mechanistic model of protein folding guided by mRNA structure shall expand our understandings of genetic information and offer new insights into various biomedical puzzles.     

Intermediates in the refolding of ribonuclease at subzero temperatures. 1. Monitoring by nitrotyrosine absorbance

Derivatives of ribonuclease A in which tyrosines-73, -76, and -115 were nitrated have been synthesized, purified to homogeneity, and characterized by NMR, isoelectric points, absorbance spectra, and catalytic activity. The positions of their reversible thermal unfolding transitions were determined in 35% methanol at pH* 3.0 and 6.0. In the present study the kinetics of the refolding of these nitrotyrosine derivatives were measured at -15 degrees C at pH* 3.0 and 6.0 by using a cryosolvent composed of 35% aqueous methanol. The rates of folding of different regions of the molecule were determined by using the nitrotyrosines as environmentally sensitive probes. Multiphasic kinetics were observed for the refolding of the nitro-Tyr-115, -73, and -76 derivatives. The native environment about Tyr-115 was formed more rapidly than that about Tyr-73 and -76, and the native environment about both these tyrosines was attained much sooner than the native state itself, as judged by other probes. The results indicate that different regions of the molecule attain their native environments at different rates. This observation shows that the folding pathway must involve partially folded intermediate states.     

Expanding to fill the gap: a possible role for inert biopolymers in regulating the extent of the 'macromolecular crowding' effect

We discuss the potential for inert biopolymers existing in cells to play a role in regulating the macromolecular crowding effect via their ability to undergo shape changing structural transitions. We have explored this possibility by the use of theory and experiment. The theoretical component utilized Monte-Carlo based simulations to examine the folding of a hypothetical protein in a concentrated environment of hard spheres which are themselves capable of reversible expansion and contraction. The experimental component of the study involved examination of the effect of different sized crowding agents on the thermally induced denaturation of cytochrome c [in phosphate buffered saline solution containing 1.0M guanidinium hydrochloride at pH 7.0]. On the basis of our findings we suggest that in a crowded solution environment the presence of a non-reactive polymer capable of reversible expansion/contraction via folding and unfolding may alter the excluded volume component of the solution. This ability would confer on the non-reactive polymer a novel role in influencing other processes in solution affected by macromolecular crowding.     

Context-Dependent Energetics of Loop Extensions in a Family of Tandem-Repeat Proteins

Consensus-designed tetratricopeptide repeat proteins are highly stable, modular proteins that are strikingly amenable to rational engineering. They therefore have tremendous potential as building blocks for biomaterials and biomedicine. Here, we explore the possibility of extending the loops between repeats to enable further diversification, and we investigate how this modification affects stability and folding cooperativity. We find that extending a single loop by up to 25 residues does not disrupt the overall protein structure, but, strikingly, the effect on stability is highly context-dependent: in a two-repeat array, destabilization is relatively small and can be accounted for purely in entropic terms, whereas extending a loop in the middle of a large array is much more costly because of weakening of the interaction between the repeats. Our findings provide important and, to our knowledge, new insights that increase our understanding of the structure, folding, and function of natural repeat proteins and the design of artificial repeat proteins in biotechnology.     

Matching simulation and experiment: a new simplified model for simulating protein folding.

Simulations of simplified protein folding models have provided much insight into solving the protein folding problem. We propose here a new off-lattice bead model, capable of simulating several different fold classes of small proteins. We present the sequence for an alpha/beta protein resembling the IgG-binding proteins L and G. The thermodynamics of the folding process for this model are characterized using the multiple multihistogram method combined with constant-temperature Langevin simulations. The folding is shown to be highly cooperative, with chain collapse nearly accompanying folding. Two parallel folding pathways are shown to exist on the folding free energy landscape. One pathway contains an intermediate--similar to experiments on protein G, and one pathway contains no intermediates-similar to experiments on protein L. The folding kinetics are characterized by tabulating mean-first passage times, and we show that the onset of glasslike kinetics occurs at much lower temperatures than the folding temperature. This model is expected to be useful in many future contexts: investigating questions of the role of local versus nonlocal interactions in various fold classes, addressing the effect of sequence mutations affecting secondary structure propensities, and providing a computationally feasible model for studying the role of solvation forces in protein folding.     

Using stochastic roadmap simulation to predict experimental quantities in protein folding kinetics: folding rates and phi-values.

This paper presents a new method for studying protein folding kinetics. It uses the recently introduced Stochastic Roadmap Simulation (SRS) method to estimate the transition state ensemble (TSE) and predict the rates and the Phi-values for protein folding. The new method was tested on 16 proteins, whose rates and Phi-values have been determined experimentally. Comparison with experimental data shows that our method estimates the TSE much more accurately than an existing method based on dynamic programming. This improvement leads to better folding-rate predictions. We also compute the mean first passage time of the unfolded states and show that the computed values correlate with experimentally determined folding rates. The results on Phi-value predictions are mixed, possibly due to the simple energy model used in the tests. This is the first time that results obtained from SRS have been compared against a substantial amount of experimental data. The results further validate the SRS method and indicate its potential as a general tool for studying protein folding kinetics.