Elementary steps in protein folding.

The mechanism of protein folding is under intense theoretical and experimental investigation. From stopped-flow mixing experiments we have detailed knowledge of processes slower than about 1 ms, but until recently little was known about folding and unfolding reactions on the microsecond to nanosecond time scale. The use of novel techniques allowed to explore the elementary steps in protein folding, such as intrachain diffusion and formation of alpha-helices, beta-hairpins and loop structures. This brief review discusses the time scales of these early elementary events which are crucial for the understanding of how proteins fold.     

Using motion planning to study protein folding pathways.

We present a framework for studying protein folding pathways and potential landscapes which is based on techniques recently developed in the robotics motion planning community. Our focus in this work is to study the protein folding mechanism assuming we know the native fold. That is, instead of performing fold prediction, we aim to study issues related to the folding process, such as the formation of secondary and tertiary structure, and the dependence of the folding pathway on the initial denatured conformation. Our work uses probabilistic roadmap (PRM) motion planning techniques which have proven successful for problems involving high-dimensional configuration spaces. A strength of these methods is their efficiency in rapidly covering the planning space without becoming trapped in local minima. We have applied our PRM technique to several small proteins (~60 residues) and validated the pathways computed by comparing the secondary structure formation order on our paths to known hydrogen exchange experimental results. An advantage of the PRM framework over other simulation methods is that it enables one to easily and efficiently compute folding pathways from any denatured starting state to the (known) native fold. This aspect makes our approach ideal for studying global properties of the protein's potential landscape, most of which are difficult to simulate and study with other methods. For example, in the proteins we study, the folding pathways starting from different denatured states sometimes share common portions when they are close to the native fold, and moreover, the formation order of the secondary structure appears largely independent of the starting denatured conformation. Another feature of our technique is that the distribution of the sampled conformations is correlated with the formation of secondary structure and, in particular, appears to differentiate situations in which secondary structure clearly forms first and those in which the tertiary structure is obtained more directly. Overall, our results applying PRM techniques are very encouraging and indicate the promise of our approach for studying proteins for which experimental results are not available.     

New structural insights into the refolding of ribonuclease T1 as seen by time-resolved Fourier-transform infrared spectroscopy

To get new structural insights into different phases of the renaturation of ribonuclease T1 (RNase T1), the refolding of the thermally unfolded protein was initiated by rapid temperature jumps and detected by time-resolved Fourier-transform infrared spectroscopy. The characteristic spectral changes monitoring the formation of secondary structure and tertiary contacts were followed on a time scale of 10(-3) to 10(3) seconds permitting the characterization of medium and slow folding reactions. Additionally, structural information on the folding events that occurred within the experimental dead time was indirectly accessed by comparative analysis of kinetic and steady-state refolding data. At slightly destabilizing refolding temperatures of 45 degrees C, which is close to the unfolding transition region, no specific secondary or tertiary structure is formed within 180 ms. After this delay all infrared markers bands diagnostic for individual structural elements indicate a strongly cooperative and relatively fast folding, which is not complicated by the accumulation of intermediates. At strongly native folding temperatures of 20 degrees C, a folding species of RNase T1 is detected within the dead time, which already possesses significant amounts of antiparallel beta-sheets, turn structures, and to some degree tertiary contacts. The early formed secondary structure is supposed to comprise the core region of the five-stranded beta-sheet. Despite these nativelike characteristics the subsequent refolding events are strongly heterogeneous and slow. The refolding under strongly native conditions is completed by an extremely slow formation or rearrangement of a locally restricted beta-sheet region accompanied by the further consolidation of turns and denser backbone packing. It is proposed that these late events comprise the final packing of strand 1 (residues 40-42) of the five-stranded beta-sheet against the rest of this beta-sheet system within an otherwise nativelike environment. This conclusion was supported by the comparison of refolding of RNase T1 and its variant W59Y RNase T1 that enabled the assignment of these very late events to the trans-->cis isomerization reaction of the prolyl peptide bond preceding Pro-39.     

Dynamics of protein folding: probing the kinetic network of folding-unfolding transitions with experiment and theory

The problem of spontaneous folding of amino acid chains into highly organized, biologically functional three-dimensional protein structures continues to challenge the modern science. Understanding how proteins fold requires characterization of the underlying energy landscapes as well as the dynamics of the polypeptide chains in all stages of the folding process. In recent years, important advances toward these goals have been achieved owing to the rapidly growing interdisciplinary interest and significant progress in both experimental techniques and theoretical methods. Improvements in the experimental time resolution led to determination of the timescales of the important elementary events in folding, such as formation of secondary structure and tertiary contacts. Sensitive single molecule methods made possible probing the distributions of the unfolded and folded states and following the folding reaction of individual protein molecules. Discovery of proteins that fold in microseconds opened the possibility of atomic-level theoretical simulations of folding and their direct comparisons with experimental data, as well as of direct experimental observation of the barrier-less folding transition. The ultra-fast folding also brought new questions, concerning the intrinsic limits of the folding rates and experimental signatures of barrier-less "downhill" folding. These problems will require novel approaches for even more detailed experimental investigations of the folding dynamics as well as for the analysis of the folding kinetic data. For theoretical simulations of folding, a main challenge is how to extract the relevant information from overwhelmingly detailed atomistic trajectories. New theoretical methods have been devised to allow a systematic approach towards a quantitative analysis of the kinetic network of folding-unfolding transitions between various configuration states of a protein, revealing the transition states and the associated folding pathways at multiple levels, from atomistic to coarse-grained representations. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.     

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.     

Probing the Effects of Local Frustration in the Folding of a Multidomain Protein

Our current knowledge of protein folding is primarily based on experimental data obtained from isolated domains. In fact, because of their complexity, multidomain proteins have been elusive to the experimental characterization. Thus, the folding of a domain in isolation is generally assumed to resemble what should be observed for more complex structural architectures. Here we compared the folding mechanism of a protein domain in isolation and in the context of its supramodular multidomain structure. By carrying out an extensive mutational analysis we illustrate that while the early events of folding are malleable and influenced by the absence/presence of the neighboring structures, the late events appear to be more robust. These effects may be explained by analyzing the local frustration patterns of the domain, providing critical support for the funneled energy landscape theory of protein folding, and highlighting the role of protein frustration in sculpting the early events of the reaction.     

From helix-coil transitions to protein folding

An evolution of procedures to simulate protein structure and folding pathways is described. From an initial focus on the helix-coil transition and on hydrogen-bonding and hydrophobic interactions, our original attempts to determine protein structure and folding pathways were based on an experimental approach. Experiments on the oxidative folding of reduced bovine pancreatic ribonuclease A (RNase A) led to a mechanism by which the molecule folded to the native structure by a minimum of four different pathways. The experiments with RNase A were followed by development of a molecular mechanics approach, first, making use of global optimization procedures and then with molecular dynamics (MD), evolving from an all-atom to a united-residue model. This hierarchical MD approach facilitated probing of the folding trajectory to longer time scales than with all-atom MD, and hence led to the determination of complete folding trajectories, thus far for a protein containing as many as 75 amino acid residues. With increasing refinement of the computational procedures, the computed results are coming closer to experimental observations, providing an understanding as to how physics directs the folding process.     

Kinetics analysis methods for approximate folding landscapes

MOTIVATION: Protein motions play an essential role in many biochemical processes. Lab studies often quantify these motions in terms of their kinetics such as the speed at which a protein folds or the population of certain interesting states like the native state. Kinetic metrics give quantifiable measurements of the folding process that can be compared across a group of proteins such as a wild-type protein and its mutants. RESULTS: We present two new techniques, map-based master equation solution and map-based Monte Carlo simulation, to study protein kinetics through folding rates and population kinetics from approximate folding landscapes, models called maps. From these two new techniques, interesting metrics that describe the folding process, such as reaction coordinates, can also be studied. In this article we focus on two metrics, formation of helices and structure formation around tryptophan residues. These two metrics are often studied in the lab through circular dichroism (CD) spectra analysis and tryptophan fluorescence experiments, respectively. The approximated landscape models we use here are the maps of protein conformations and their associated transitions that we have presented and validated previously. In contrast to other methods such as the traditional master equation and Monte Carlo simulation, our techniques are both fast and can easily be computed for full-length detailed protein models. We validate our map-based kinetics techniques by comparing folding rates to known experimental results. We also look in depth at the population kinetics, helix formation and structure near tryptophan residues for a variety of proteins. AVAILABILITY: We invite the community to help us enrich our publicly available database of motions and kinetics analysis by submitting to our server: http://parasol.tamu.edu/foldingserver/.     

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.     

Predicting protein folding pathways

A structured folding pathway, which is a time ordered sequence of folding events, plays an important role in the protein folding process and hence, in the conformational search. Pathway prediction, thus gives more insight into the folding process and is a valuable guiding tool to search the conformation space. In this paper, we propose a novel 'unfolding' approach to predict the folding pathway. We apply graph-based methods on a weighted secondary structure graph of a protein to predict the sequence of unfolding events. When viewed in reverse this yields the folding pathway. We demonstrate the success of our approach on several proteins whose pathway is partially known.     

Characterization of the temperature- and pressure-induced inverse and reentrant transition of the minimum elastin-like polypeptide GVG(VPGVG) by DSC, PPC, CD, and FT-IR spectroscopy

We investigated the temperature- and pressure-dependent structure and phase behavior of a solvated oligopeptide, GVG(VPGVG), which serves as a minimalistic elastin-like model system, over a large region of the thermodynamic phase field, ranging from 2 to 120°C and from ambient pressure up to ~10 kbar, applying various spectroscopic (CD, FT-IR) and thermodynamic (DSC, PPC) measurements. We find that this octapeptide behaves as a two-state system which undergoes the well-known inverse-temperature folding transition occurring at T ≈ 36°C, and, in addition, a slow trend reversal at higher temperatures, finally leading to a reentrant unfolding close to the boiling point of water. Furthermore, the pressure-dependence of the folding/unfolding transition was studied to yield a more complete picture of the p, T-stability diagram of the system. A molecular-level picture of these processes, in particular on the role of water for the folding and unfolding events of the peptide, presented with the help of molecular-dynamics simulations, is presented in a companion article in this issue.     

Prediction of folding mechanisms for Ig-like beta sandwich proteins based on inter-residue average distance statistics methods

To understand the folding mechanism of a protein is one of the goals in bioinformatics study. Nowadays, it is enigmatic and difficult to extract folding information from amino acid sequence using standard bioinformatics techniques or even experimental protocols which can be time consuming. To overcome these problems, we aim to extract the initial folding unit for titin protein (Ig and fnIII domains) by means of inter-residue average distance statistics, Average Distance Map (ADM) and contact frequency analysis (F-value). TI I27 and TNfn3 domains are used to represent the Ig-domain and fnIII-domain, respectively. Beta-strands 2, 3, 5, and 6 are significant for the initial folding processes of TI I27. The central strands of TNfn3 were predicted as a primary folding segment. Known 3D structure and unknown 3D structure domains were investigated by structure or non-structure based multiple sequence alignment, respectively, to learn the conserved hydrophobic residues and predicted compact region relevant to evolution. Our results show good correspondence to experimental data, phi-value and protection factor from H-D exchange experiments. The significance of conserved hydrophobic residues near F-value peaks for structural stability using hydrophobic packing is confirmed. Our prediction methods once again could extract a folding mechanism only knowing the amino acid sequence.     

On prediction of folding nuclei in globular proteins

The approach described in this paper on the prediction of folding nuclei in globular proteins with known three dimensional structures is based on a search of the lowest saddle points through the barrier separating the unfolded state from the native structure on the free-energy landscape of protein chain. This search is performed by a dynamic programming method. Comparison of theoretical results with experimental data on the folding nuclei of two dozen of proteins shows that our model provides good phi value predictions for proteins whose structures have been determined by X-ray analysis, with a less limited success for proteins whose structures have been determined by NMR techniques only. Consideration of a full ensemble of transition states results in more successful prediction than consideration of only the transition states with the minimal free energy. In conclusion we have predicted the localization of folding nuclei for three dimensional protein structures for which kinetics of folding is studied now but the localization of folding nuclei is still unknown.     

Snapshots of protein folding problem: implications of folding and misfolding studies

Deciphering the code that determines the three-dimensional structure of proteins and the ability to predict the final folded form of a protein is still elusive to molecular biophysists. In the case of several proteins a similar tertiary structure is not accompanied by any significant sequence similarity. The question now remains whether a code beyond the genetic code that describes the arrangement of the amino acid within a three dimensional protein structure. The available data undoubtedly demonstrates that the redundancy of this code must be tremendous. Several techniques such as nuclear magnetic resonance spectroscopy and laser detection techniques, coupled with fast initiation of the folding reaction, can now probe the folding events in milliseconds or even faster and provide highly relevant information. The thermodynamic analysis of the folding process and of kinetic intermediates opens whole new avenue of understanding. Breaking the protein folding code would enable scientists to look at a gene whose function is unknown and predict the three-dimensional structure of the protein it encodes. This would give them a very good idea of what the gene does. In this review we hope to bring together the information available about protein folding with particular emphasis on folding intermediate(s). Additionally, the practical consequences of the solution of the protein folding problem in medicine and biotechnology are also discussed.     

First principles prediction of protein folding rates

Experimental studies have demonstrated that many small, single-domain proteins fold via simple two-state kinetics. We present a first principles approach for predicting these experimentally determined folding rates. Our approach is based on a nucleation-condensation folding mechanism, where the rate-limiting step is a random, diffusive search for the native tertiary topology. To estimate the rates of folding for various proteins via this mechanism, we first determine the probability of randomly sampling a conformation with the native fold topology. Next, we convert these probabilities into folding rates by estimating the rate that a protein samples different topologies during diffusive folding. This topology-sampling rate is calculated using the Einstein diffusion equation in conjunction with an experimentally determined intra-protein diffusion constant. We have applied our prediction method to the 21 topologically distinct small proteins for which two-state rate data is available. For the 18 beta-sheet and mixed alpha-beta native proteins, we predict folding rates within an average factor of 4, even though the experimental rates vary by a factor of approximately 4 x 10(4). Interestingly, the experimental folding rates for the three four-helix bundle proteins are significantly underestimated by this approach, suggesting that proteins with significant helical content may fold by a faster, alternative mechanism. This method can be applied to any protein for which the structure is known and hence can be used to predict the folding rates of many proteins prior to experiment.     

Piecewise All-Atom SMD Simulations Reveal Key Secondary Structures in Luciferase Unfolding Pathway

Although the folding of single-domain proteins is well characterized theoretically and experimentally, the folding of large multidomain proteins is less well known. Firefly luciferase, a 550 residue three-domain protein, has been commonly used as a substrate to study chaperone reactions and as a model system for the study of folding of long polypeptide chains, including related phenomena such as cotranslational folding. Despite being characterized by various experimental techniques, the atomic-level contributions of various secondary structures of luciferase to its fold’s mechanical stability remain unknown. Here, we developed a piecewise approach for all-atom steered molecular dynamics simulations to examine specific secondary structures that resist mechanical unfolding while minimizing the amount of computational resources required by the large water box of standard all-atom steered molecular dynamics simulations. We validated the robustness of this approach with a small NI3C protein and used our approach to elucidate the specific secondary structures that provide the largest contributions to luciferase mechanostability. In doing so, we show that piecewise all-atom steered molecular dynamics simulations can provide novel atomic resolution details regarding mechanostability and can serve as a platform for novel mutagenesis studies as well as a point for comparison with high-resolution force spectroscopy experiments.     

Computer simulation of the folding-unfolding transition of island-model proteins--folding pathway, transition process, and fluctuations

Monte Carlo computer simulations were performed to elucidate the dynamic aspects of the folding and unfolding transitions of island-model protein. Five different types of model proteins were designed, according to characteristics of backbone structure. The computer simulations clearly show that the unfolding and folding transitions are all-or-none processes between the N-and U-states. They are typical Poisson processes. From the Arrhenius plots of rate constants, the activation enthalpies of folding and unfolding were determined. In addition, the folding pathways were determined along the reaction coordinate. Formations of several local structures along a polypeptide chain are almost simultaneous, but the most probable time sequence of events exists at the moment of transition. That is the most probable folding pathway. The unfolding pathway was found to be just the reverse process of the most probable folding pathway. The relationship between the fluctuations in each equilibrium state and the transition process was considered. In contrast to the theory of absolute reaction rate, the transient states are widely distributed along the reaction coordinate. From analysis of the “transient process,” we tried to determine the critical states from which the transient process starts. As a result, we found that the unfolding transition occurs at the stage near the N-state. During the U-state, large joined blocks rarely appear, but they appear in the transient process towards the N-state. However, the “branch point” between the N- and U-states lies near the N-state, and joined blocks tend to unfold prior to passing over the branch point. We concluded that the stability of later folding intermediates is important for selection of the folding pathway, while preferential selection of an early folding intermediate is important in acceleration of the folding rate. The effects of intrachain cross-linking and peptide fragment binding on the rate constants were examined by using computer simulations of model proteins. In general, a small-sized loop formed by cross-linking accelerates the folding rate and a large-sized loop contributes much to the stabilization of the native conformation. We also found that peptide fragment binding contributes little to the acceleration of the folding rate of the residual protein.     

The unfolded state of the villin headpiece helical subdomain: computational studies of the role of locally stabilized structure

The 36 residue villin headpiece helical subdomain (HP36) is one of the fastest cooperatively folding proteins, folding on the microsecond timescale. HP36's simple three helix topology, fast folding and small size have made it an attractive model system for computational and experimental studies of protein folding. Recent experimental studies have explored the denatured state of HP36 using fragment analysis coupled with relatively low-resolution spectroscopic techniques. These studies have shown that there is apparently only a small tendency to form locally stabilized secondary structure. Here, we complement the experimental studies by using replica exchange molecular dynamics with explicit solvent to investigate the structural features of these peptide models of unfolded HP36. To ensure convergence, two sets of simulations for each fragment were performed with different initial structures, and simulations were continued until these generated very similar final ensembles. These simulations reveal low populations of native-like structure and early folding events that cannot be resolved by experiment. For each fragment, calculated J-coupling constants and helical propensities are in good agreement with experimental trends. HP-1, corresponding to residues 41 to 53 and including the first alpha-helix, contains the highest helical population. HP-3, corresponding to residues 62 through 75 and including the third alpha-helix, contains a small population of helical turn residing at the N terminus while HP-2, corresponding to residues 52 through 61 and including the second alpha-helix, formed little to no structure in isolation. Overall, HP-1 was the only fragment to adopt a native-like conformation, but the low population suggests that formation of significant structure only occurs after formation of specific tertiary interactions.     

The construction of new proteins: V. A template-assembled synthetic protein (TASP) containing both a 4-helix bundle and beta-barrel-like structure

The construction of a template-assembled synthetic protein (TASP) designed to contain both a 4-helix bundle and a beta-barrel as two folding "domains" is described. For the de novo design of proteins, amphiphilic helices (alpha) and beta-sheets (beta) are covalently attached to a template peptide (T) carrying functional side chains suitably oriented to promote intramolecular folding of the secondary structure blocks into a characteristic packing arrangement, i.e., T8-(4 alpha)(4 beta). The design of this new macromolecule was assisted by computer modeling, which suggested a low-energy conformation with tight hydrophobic packing of the secondary structure subunits. Solid-phase synthesis of the "two-domain" TASP molecule was achieved using orthogonal protection techniques. The solution properties as well as circular dichroism (CD) and infrared spectroscopy (IR) data under various experimental conditions are consistent with the folded conformation suggested by modeling.