Topology-based models and NMR structures in protein folding simulations

Topology-based interaction potentials are simplified models that use the native contacts in the folded structure of a protein to define an energetically unfrustrated folding funnel. They have been widely used to analyze the folding transition and pathways of different proteins through computer simulations. Obviously, they need a reliable, experimentally determined folded structure to define the model interactions. In structures elucidated through NMR spectroscopy, a complex treatment of the raw experimental data usually provides a series of models, a set of different conformations compatible with the available experimental data. Here, we use an efficient coarse-grained simulation technique to independently consider the contact maps from every different NMR model in a protein whose structure has been resolved by the use of NMR spectroscopy. For lambda-Cro repressor, a homodimeric protein, we have analyzed its folding characteristics with a topology-based model. We have focused on the competition between the folding of the individual chains and their binding to form the final quaternary structure. From 20 different NMR models, we find a predominant three-state folding behavior, in agreement with experimental data on the folding pathway for this protein. Individual NMR models, however, show distinct characteristics, which are analyzed both at the level of the interplay between tertiary/quaternary structure formation and also regarding the thermal stability of the tertiary structure of every individual chain.     

Dynamic folding pathway models of the villin headpiece subdomain (HP‐36) structure

We have investigated the folding pathway of the 36‐residue villin headpiece subdomain (HP‐36) by action‐derived molecular dynamics simulations. The folding is initiated by hydrophobic collapse, after which the concurrent formation of full tertiary structure and α‐helical secondary structure is observed. The collapse is observed to be associated with a couple of specific native contacts contrary to the conventional nonspecific hydrophobic collapse model. Stable secondary structure formation after the collapse suggests that the folding of HP‐36 follows neither the framework model nor the diffusion‐collision model. The C‐terminal helix forms first, followed by the N‐terminal helix positioned in its native orientation. The short middle helix is shown to form last. Signs for multiple folding pathways are also observed. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Metal-coupled folding of Cys2His2 zinc-finger

Zinc-fingers, which widely exist in eukaryotic cell and play crucial roles in life processes, depend on the binding of zinc ion for their proper folding. To computationally study the zinc-coupled folding of the zinc-fingers, charge transfer and metal induced protonation/deprotonation effects have to be considered. Here, by attempting to implicitly account for such effects in classical molecular dynamics and performing intensive simulations with explicit solvent for the peptides with and without zinc binding, we investigate the folding of the Cys2His2-type zinc-finger motif and the coupling between the peptide folding and zinc binding. We find that zinc ion not only stabilizes the native structure but also participates in the whole folding process. It binds to the peptide at an early stage of folding and directs or modulates the folding and stabilizations of the component beta-hairpin and alpha-helix. Such a crucial role of zinc binding is mediated by the packing of the conserved hydrophobic residues. We also find that the packing of the hydrophobic residues and the coordination of the native ligands are coupled. Meanwhile, the processes of zinc binding, mis-ligation, ligand exchange, and zinc induced secondary structure conversion as well as the water behavior due to the involvement of zinc ion are characterized. Our results are in good agreement with related experimental observations and provide significant insight into the general mechanisms of the metal cofactor dependent protein folding and other metal-induced conformational changes of biological importance.     

Robustness of atomistic Gō models in predicting native-like folding intermediates

Go? models are exceedingly popular tools in computer simulations of protein folding. These models are native-centric, i.e., they are directly constructed from the protein's native structure. Therefore, it is important to understand up to which extent the atomistic details of the native structure dictate the folding behavior exhibited by Go? models. Here we address this challenge by performing exhaustive discrete molecular dynamics simulations of a Go? potential combined with a full atomistic protein representation. In particular, we investigate the robustness of this particular type of Go? models in predicting the existence of intermediate states in protein folding. We focus on the N47G mutational form of the Spc-SH3 folding domain (x-ray structure) and compare its folding pathway with that of alternative native structures produced in silico. Our methodological strategy comprises equilibrium folding simulations, structural clustering, and principal component analysis.     

Multi-nucleation and vectorial folding pathways of large helix protein

At present we have already had the detailed knowledge of the folding of small model proteins, but a unified picture of how large proteins fold is still absent. We simulated the folding of a large eight-helix-bundle protein with a length of 145 amino acids by using a united-residue protein model. We observed a multiple nucleation folding pathway: the formation of secondary structures was followed by the nucleation of helices at the two terminal parts and also at the middle of the chain, and then the nuclei grew and combined with each other to form the tertiary structure. Surprisingly, we also found a vectorial folding pathway that was shown recently for co-translational folding in the ribosome exit tunnel. Furthermore, we found that all three-helix subunits in the chain can fold into native-like conformations independently, especially those at the two terminal parts and the middle of the chain, which may be responsible for the nucleation's. These results may be helpful to understand the folding mechanism of large repeat helical proteins.     

Rerouting the folding pathway of the Notch ankyrin domain by reshaping the energy landscape

The modular nature of repeat proteins has made them a successful target for protein design. Ankyrin repeat, TPR, and leucine rich repeat domains that have been designed solely on consensus information have been shown to have higher thermostability than their biological counterparts. We have previously shown that we can reshape the energy landscape of a repeat protein by adding multiple C-terminal consensus ankyrin repeats to the five N-terminal repeats of the Notch ankyrin domain. Here we explore how the folding mechanism responds to reshaping of the energy landscape. We have used analogous substitutions of a conserved alanine with glycine in each repeat to determine the distribution of structure in the transition state ensembles of constructs containing one (Nank1-5C1) and two consensus (Nank1-5C2) ankyrin repeats. Whereas folding of the wild-type Notch ankyrin domain is slowed by substitutions in its central repeats, (1) folding of Nank1-5C1 and Nank1-5C2 is slowed by substitutions in the C-terminal repeats. Thus, the addition of C-terminal stabilizing repeats shifts the transition state ensemble toward the C-terminal repeats, rerouting the folding pathway of the ankyrin repeat domain. These findings indicate that, for the Notch ankyrin domain, folding pathways are selected based on local energetics.     

Discrete structure of an RNA folding intermediate revealed by cryo-electron microscopy

RNA folding occurs via a series of transitions between metastable intermediate states. It is unknown whether folding intermediates are discrete structures folding along defined pathways or heterogeneous ensembles folding along broad landscapes. We use cryo-electron microscopy and single-particle image reconstruction to determine the structure of the major folding intermediate of the specificity domain of a ribonuclease P ribozyme. Our results support the existence of a discrete conformation for this folding intermediate.     

Folding Dynamics of 10‐Residue β‐Hairpin Peptide Chignolin

Short peptides that fold into β‐hairpins are ideal model systems for investigating the mechanism of protein folding because their folding process shows dynamics typical of proteins. We performed folding, unfolding, and refolding molecular dynamics simulations (total of 2.7 μs) of the 10‐residue β‐hairpin peptide chignolin, which is the smallest β‐hairpin structure known to be stable in solution. Our results revealed the folding mechanism of chignolin, which comprises three steps. First, the folding begins with hydrophobic assembly. It brings the main chain together; subsequently, a nascent turn structure is formed. The second step is the conversion of the nascent turn into a tight turn structure along with interconversion of the hydrophobic packing and interstrand hydrogen bonds. Finally, the formation of the hydrogen‐bond network and the complete hydrophobic core as well as the arrangement of side‐chain–side‐chain interactions occur at approximately the same time. This three‐step mechanism appropriately interprets the folding process as involving a combination of previous inconsistent explanations of the folding mechanism of the β‐hairpin, that the first event of the folding is formation of hydrogen bonds and the second is that of the hydrophobic core, or vice versa.     

Machine learning algorithms for predicting protein folding rates and stability of mutant proteins: comparison with statistical methods

Machine learning algorithms have wide range of applications in bioinformatics and computational biology such as prediction of protein secondary structures, solvent accessibility, binding site residues in protein complexes, protein folding rates, stability of mutant proteins, and discrimination of proteins based on their structure and function. In this work, we focus on two aspects of predictions: (i) protein folding rates and (ii) stability of proteins upon mutations. We briefly introduce the concepts of protein folding rates and stability along with available databases, features for prediction methods and measures for prediction performance. Subsequently, the development of structure based parameters and their relationship with protein folding rates will be outlined. The structure based parameters are helpful to understand the physical basis for protein folding and stability. Further, basic principles of major machine learning techniques will be mentioned and their applications for predicting protein folding rates and stability of mutant proteins will be illustrated. The machine learning techniques could achieve the highest accuracy of predicting protein folding rates and stability. In essence, statistical methods and machine learning algorithms are complimenting each other for understanding and predicting protein folding rates and the stability of protein mutants. The available online resources on protein folding rates and stability will be listed.     

Carbohydrate–DNA Interactions at G‐Quadruplexes: Folding and Stability Changes by Attaching Sugars at the 5′‐End

Quadruplex DNA structures are attracting an enormous interest in many areas of chemistry, ranging from chemical biology, supramolecular chemistry to nanoscience. We have prepared carbohydrate–DNA conjugates containing the oligonucleotide sequences of G‐quadruplexes (thrombin binding aptamer (TBA) and human telomere (TEL)), measured their thermal stability and studied their structure in solution by using NMR and molecular dynamics. The solution structure of a fucose–TBA conjugate shows stacking interactions between the carbohydrate and the DNA G‐tetrad in addition to hydrogen bonding and hydrophobic contacts. We have also shown that attaching carbohydrates at the 5′‐end of a quadruplex telomeric sequence can alter its folding topology. These results suggest the possibility of modulating the folding of the G‐quadruplex by linking carbohydrates and have clear implications in molecular recognition and the design of new G‐quadruplex ligands.     

The protein folding transition-state ensemble from a Gō-like model

Characterizing the structure of transition states (TS) is a first step towards understanding two-state protein folding mechanisms. However, a direct experimental characterization of these states is challenging and indirect information derived from protein engineering methodologies (?-value analysis) is often difficult to interpret. We present here a theoretical study on the nature of the transition state ensemble for three representative proteins covering the major structural classes using a mean-field C(α)-based Gō-model. We identify that transition state ensembles are dominated by local contacts, indicating that most non-local contacts form only upon crossing the macroscopic folding free energy barrier. We demonstrate that the mean ?-value corresponds to the fraction of stabilization energy gained at the barrier-top in two-state-like systems, and that it depends monotonically on the stability conditions. Furthermore, we show that there is a fundamental connection between small destabilization and large ?-values that in turn depends on the location of the mutated residue in the structure. These results that are in agreement with the recent empirical findings highlight the importance of local energetics in determining folding mechanisms.     

Prediction of protein folding rates from primary sequences using hybrid sequence representation

The ability to predict protein folding rates constitutes an important step in understanding the overall folding mechanisms. Although many of the prediction methods are structure based, successful predictions can also be obtained from the sequence. We developed a novel method called prediction of protein folding rates (PPFR), for the prediction of protein folding rates from protein sequences. PPFR implements a linear regression model for each of the mainstream folding dynamics including two-, multi-, and mixed-state proteins. The proposed method provides predictions characterized by strong correlations with the experimental folding rates, which equal 0.87 for the two- and multistate proteins and 0.82 for the mixed-state proteins, when evaluated with out-of-sample jackknife test. Based on in-sample and out-of-sample tests, the PPFR's predictions are shown to be better than most of other sequence only and structure-based predictors and complementary to the predictions of the most recent sequence-based QRSM method. We show that simultaneous incorporation of several characteristics, including the sequence, physiochemical properties of residues, and predicted secondary structure provides improved quality. This hybridized prediction model was analyzed to reveal the complementary factors that can be used in tandem to predict folding rates. We show that bigger proteins require more time for folding, higher helical and coil content and the presence of Phe, Asn, and Gln may accelerate the folding process, the inclusion of Ile, Val, Thr, and Ser may slow down the folding process, and for the two-state proteins increased beta-strand content may decelerate the folding process. Finally, PPFR provides strong correlation when predicting sequences with low similarity.     

New scenarios of protein folding can occur on the ribosome

Identifying and understanding the differences between protein folding in bulk solution and in the cell is a crucial challenge facing biology. Using Langevin dynamics, we have simulated intact ribosomes containing five different nascent chains arrested at different stages of their synthesis such that each nascent chain can fold and unfold at or near the exit tunnel vestibule. We find that the native state is destabilized close to the ribosome surface due to an increase in unfolded state entropy and a decrease in native state entropy; the former arises because the unfolded ensemble tends to behave as an expanded random coil near the ribosome and a semicompact globule in bulk solution. In addition, the unfolded ensemble of the nascent chain adopts a highly anisotropic shape near the ribosome surface and the cooperativity of the folding-unfolding transition is decreased due to the appearance of partially folded structures that are not populated in bulk solution. The results show, in light of these effects, that with increasing nascent chain length folding rates increase in a linear manner and unfolding rates decrease, with larger and topologically more complex folds being the most highly perturbed by the ribosome. Analysis of folding trajectories, initiated by temperature quench, reveals the transition state ensemble is driven toward compaction and greater native-like structure by interactions with the ribosome surface and exit vestibule. Furthermore, the diversity of folding pathways decreases and the probability increases of initiating folding via the N-terminus on the ribosome. We show that all of these findings are equally applicable to the situation in which protein folding occurs during continuous (non-arrested) translation provided that the time scales of folding and unfolding are much faster than the time scale of monomer addition to the growing nascent chain, which results in a quasi-equilibrium process. These substantial ribosome-induced perturbations to almost all aspects of protein folding indicate that folding scenarios that are distinct from those of bulk solution can occur on the ribosome.     

All-atom structure prediction and folding simulations of a stable protein

We present results from all-atom, fully unrestrained ab initio folding simulations for a stable protein with nontrivial secondary structure elements and a hydrophobic core. The construct, "trpcage", is a 20-residue sequence optimized by the Andersen group at University of Washington and is currently the smallest protein that displays two-state folding properties. Compared over the well-defined regions of the experimental structure, our prediction has a remarkably low 0.97 A Calpha root-mean-square-deviation (rmsd) and 1.4 A for all heavy atoms. The simulated structure family displays additional features that are suggested by experimental data, yet are not evident in the family of NMR-derived structures.     

Importance of native-state topology for determining the folding rate of two-state proteins

Understanding the relationship between amino acid sequences and folding rate of proteins is a challenging task similar to protein folding problem. In this work, we have analyzed the relative importance of protein sequence and structure for predicting the protein folding rates in terms of amino acid properties and contact distances, respectively. We found that the parameters derived with protein sequence (physical-chemical, energetic, and conformational properties of amino acid residues) show very weak correlation (|r| < 0.39) with folding rates of 28 two-state proteins, indicating that the sequence information alone is not sufficient to understand the folding rates of two-state proteins. However, the maximum positive correlation obtained for the properties, number of medium-range contacts, and alpha-helical tendency reveals the importance of local interactions to initiate protein folding. On the other hand, a remarkable correlation (r varies from -0.74 to -0.88) has been obtained between structural parameters (contact order, long-range order, and total contact distance) and protein folding rates. Further, we found that the secondary structure content and solvent accessibility play a marginal role in determining the folding rates of two-state proteins. Multiple regression analysis carried out with the combination of three properties, beta-strand tendency, enthalpy change, and total contact distance improved the correlation to 0.92 with protein folding rates. The relative importance of existing methods along with multiple-regression model proposed in this work will be discussed. Our results demonstrate that the native-state topology is the major determinant for the folding rates of two-state proteins.     

Slow Unfolded-State Structuring in Acyl-CoA Binding Protein Folding Revealed by Simulation and Experiment

Protein folding is a fundamental process in biology, key to understanding many human diseases. Experimentally, proteins often appear to fold via simple two- or three-state mechanisms involving mainly native-state interactions, yet recent network models built from atomistic simulations of small proteins suggest the existence of many possible metastable states and folding pathways. We reconcile these two pictures in a combined experimental and simulation study of acyl-coenzyme A binding protein (ACBP), a two-state folder (folding time ～10 ms) exhibiting residual unfolded-state structure, and a putative early folding intermediate. Using single-molecule FRET in conjunction with side-chain mutagenesis, we first demonstrate that the denatured state of ACBP at near-zero denaturant is unusually compact and enriched in long-range structure that can be perturbed by discrete hydrophobic core mutations. We then employ ultrafast laminar-flow mixing experiments to study the folding kinetics of ACBP on the microsecond time scale. These studies, along with Trp-Cys quenching measurements of unfolded-state dynamics, suggest that unfolded-state structure forms on a surprisingly slow (～100 μs) time scale, and that sequence mutations strikingly perturb both time-resolved and equilibrium smFRET measurements in a similar way. A Markov state model (MSM) of the ACBP folding reaction, constructed from over 30 ms of molecular dynamics trajectory data, predicts a complex network of metastable stables, residual unfolded-state structure, and kinetics consistent with experiment but no well-defined intermediate preceding the main folding barrier. Taken together, these experimental and simulation results suggest that the previously characterized fast kinetic phase is not due to formation of a barrier-limited intermediate but rather to a more heterogeneous and slow acquisition of unfolded-state structure.     

Folding of elongated proteins: conventional or anomalous?

The complexity of the mechanisms by which proteins fold has been shown by many studies to be governed by their native-state topologies. This was manifested in the ability of the native topology-based model to capture folding mechanisms and the success of folding rate predictions based on various topological measures, such as the contact order. However, while the finer details of topological complexity have been thoroughly examined and related to folding kinetics, simpler characteristics of the protein, such as its overall shape, have been largely disregarded. In this study, we investigated the folding of proteins with an unusual elongated geometry that differs substantially from the common globular structure. To study the effect of the elongation degree on the folding kinetics, we used repeat proteins, which become more elongated as they include more repeating units. Some of these have apparently anomalous experimental folding kinetics, with rates that are often less than expected on the basis of rates for globular proteins possessing similar topological complexity. Using experimental folding rates and a larger set of rates obtained from simulations, we have shown that as the protein becomes increasingly elongated, its folding kinetics becomes slower and deviates more from the rate expected on the basis of topology measures fitted for globular proteins. The observed slow kinetics is a result of a more complex pathway in which stable intermediates composed of several consecutive repeats can appear. We thus propose a novel measure, an elongation-sensitive contact order, that takes into account both the extent of elongation and the topological complexity of the protein. This new measure resolves the apparent discrimination between the folding of globular and elongated repeat proteins. Our study extends the current capabilities of folding-rate predictions by unifying the kinetics of repeat and globular proteins.     

Learning the Fastest RNA Folding Path Based on Reinforcement Learning and Monte Carlo Tree Search

RNA molecules participate in many important biological processes, and they need to fold into well-defined secondary and tertiary structures to realize their functions. Like the well-known protein folding problem, there is also an RNA folding problem. The folding problem includes two aspects: structure prediction and folding mechanism. Although the former has been widely studied, the latter is still not well understood. Here we present a deep reinforcement learning algorithms 2dRNA-Fold to study the fastest folding paths of RNA secondary structure. 2dRNA-Fold uses a neural network combined with Monte Carlo tree search to select residue pairing step by step according to a given RNA sequence until the final secondary structure is formed. We apply 2dRNA-Fold to several short RNA molecules and one longer RNA 1Y26 and find that their fastest folding paths show some interesting features. 2dRNA-Fold is further trained using a set of RNA molecules from the dataset bpRNA and is used to predict RNA secondary structure. Since in 2dRNA-Fold the scoring to determine next step is based on possible base pairings, the learned or predicted fastest folding path may not agree with the actual folding paths determined by free energy according to physical laws.