Influence of the native topology on the folding barrier for small proteins

The possibility of downhill instead of two-state folding for proteins has been a very controversial topic which arose from recent experimental studies. From the theoretical side, this question has also been accomplished in different ways. Given the experimental observation that a relationship exists between the native structure topology of a protein and the kinetic and thermodynamic properties of its folding process, Gō-type potentials are an appropriate way to approach this problem. In this work, we employ an interaction potential from this family to get a better insight on the topological characteristics of the native state that may somehow determine the presence of a thermodynamic barrier in the folding pathway. The results presented here show that, indeed, the native topology of a small protein has a great influence on its folding behavior, mostly depending on the proportion of local and long range contacts the protein has in its native structure. Furthermore, when all the interactions present contribute in a balanced way, the transition results to be cooperative. Otherwise, the tendency to a downhill folding behavior increases.     

The protein folding transition state: insights from kinetics and thermodynamics

We perform extensive lattice Monte Carlo simulations of protein folding to construct and compare the equilibrium and the kinetic transition state ensembles of a model protein that folds to the native state with two-state kinetics. The kinetic definition of the transition state is based on the folding probability analysis method, and therefore on the selection of conformations with 0.4相似文献   

Probing molecular kinetics with Markov models: metastable states, transition pathways and spectroscopic observables

Markov (state) models (MSMs) have attracted a lot of interest recently as they (1) can probe long-term molecular kinetics based on short-time simulations, (2) offer a way to analyze great amounts of simulation data with relatively little subjectivity of the analyst, (3) provide insight into microscopic quantities such as the ensemble of transition pathways, and (4) allow simulation data to be reconciled with measurement data in a rigorous and explicit way. Here we sketch our current perspective of Markov models and explain in short their theoretical basis and assumptions. We describe transition path theory which allows the entire ensemble of protein folding pathways to be investigated and that combines naturally with Markov models. Experimental observations can be naturally linked to Markov models with the dynamical fingerprint theory, by which experimentally observable timescales can be equipped with an understanding of the structural rearrangement processes that take place at these timescales. The concepts of this paper are illustrated by a simple kinetic model of protein folding.     

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.     

On/off switching on polymer conformation

The manner of folding transition from elongated coil to compact globule of single polymer chain is discussed. Based on theoretical consideration, it is argued the semi-flexible polymer chain exhibits large discrete transition on the level of individual single chains, whereas the transition looks continuous, or cooperative, on the ensemble of chains. As the experimental verification, in the present article thermodynamic and kinetic aspects of folding transition of single giant DNA molecules are described. It is shown that rich variety of nano-ordered structures are obtained from single DNA molecules through suitable setup of the experimental conditions. The stability of such nano-structures generated from single polymer chain is discussed in relation to the ordered compact structure with large number of chains in semi-dilute and concentrated polymer solutions.     

Molecular dynamics study of peptides in implicit water: ab initio folding of beta-hairpin, beta-sheet, and beta beta alpha-motif

In this communication, we have demonstrated that molecular dynamics simulations using a GB implicit solvation model with the all-atom based force field (CHARMM19) can describe the spontaneous folding of small peptides in aqueous solution. The native structures of peptides with various structural motifs (beta-hairpin, beta-sheet, and betabetaalpha-moiety) were successfully predicted within reasonable time scales by MD simulations at moderately elevated temperatures. It is expected that the present simulations provide further insight into mechanism/pathways of the peptide folding.     

Molecular dynamics with the united-residue model of polypeptide chains. II. Langevin and Berendsen-bath dynamics and tests on model alpha-helical systems

The implementation of molecular dynamics (MD) with our physics-based protein united-residue (UNRES) force field, described in the accompanying paper, was extended to Langevin dynamics. The equations of motion are integrated by using a simplified stochastic velocity Verlet algorithm. To compare the results to those with all-atom simulations with implicit solvent in which no explicit stochastic and friction forces are present, we alternatively introduced the Berendsen thermostat. Test simulations on the Ala(10) polypeptide demonstrated that the average kinetic energy is stable with about a 5 fs time step. To determine the correspondence between the UNRES time step and the time step of all-atom molecular dynamics, all-atom simulations with the AMBER 99 force field and explicit solvent and also with implicit solvent taken into account within the framework of the generalized Born/surface area (GBSA) model were carried out on the unblocked Ala(10) polypeptide. We found that the UNRES time scale is 4 times longer than that of all-atom MD simulations because the degrees of freedom corresponding to the fastest motions in UNRES are averaged out. When the reduction of the computational cost for evaluation of the UNRES energy function is also taken into account, UNRES (with hydration included implicitly in the side chain-side chain interaction potential) offers about at least a 4000-fold speed up of computations relative to all-atom simulations with explicit solvent and at least a 65-fold speed up relative to all-atom simulations with implicit solvent. To carry out an initial full-blown test of the UNRES/MD approach, we ran Berendsen-bath and Langevin dynamics simulations of the 46-residue B-domain of staphylococcal protein A. We were able to determine the folding temperature at which all trajectories converged to nativelike structures with both approaches. For comparison, we carried out ab initio folding simulations of this protein at the AMBER 99/GBSA level. The average CPU time for folding protein A by UNRES molecular dynamics was 30 min with a single Alpha processor, compared to about 152 h for all-atom simulations with implicit solvent. It can be concluded that the UNRES/MD approach will enable us to carry out microsecond and, possibly, millisecond simulations of protein folding and, consequently, of the folding process of proteins in real time.     

Foldamer simulations: novel computational methods and applications to poly-phenylacetylene oligomers

We apply several methods to probe the ensemble kinetic and structural properties of a model system of poly-phenylacetylene (pPA) oligomer folding trajectories. The kinetic methods employed included a brute force accounting of conformations, a Markovian state matrix method, and a nonlinear least squares fit to a minimalist kinetic model used to extract the folding time. Each method gave similar measures for the folding time of the 12-mer chain, calculated to be on the order of 7 ns for the complete folding of the chain from an extended conformation. Utilizing both a linear and a nonlinear scaling relationship between the viscosity and the folding time to correct for a low simulation viscosity, we obtain an upper and a lower bound for the approximate folding time within the range 70 ns相似文献   

Conformational selection or induced fit for Brinker and DNA recognition

Brinker is the key target protein of the Drosophila Decapentaplegic morphogen signalling pathway. Brinker is widely expressed and can bind with DNA. NMR spectra suggest that apo-Brinker is intrinsically unstructured and undergoes a folding transition upon DNA-binding. However, the coupled mechanism of binding and folding is poorly understood. Here, we performed molecular dynamics (MD) simulations for both bound and apo-Brinker to study the mechanism. Room-temperature MD simulations suggest that Brinker becomes more rigid and stable upon DNA-binding. Kinetic analysis of high-temperature MD simulations shows that both bound and apo-Brinker unfold via a two-state process. The time scale of tertiary unfolding is significantly different between bound and apo-Brinker. The predicted Φ-values suggest that there are more residues with native-like transition state ensembles (TSEs) for bound Brinker than for apo-Brinker. The average RMSD differences between bound and apo-Brinker and Kolmogorov-Smirnov (KS) test analysis illustrate that Brinker folding upon DNA-binding might obey induced-fit mechanism based on MD simulations. These methods can be used for the research of other biomolecular folding upon ligand-binding.     

Molecular Dynamics Studies of Collapse Stages in the chain folding process of Polyethylene

Althoughtheequilibriumpropertiesofthepolymerhavebeenextensivelystudied,kineticphenomenasuchasthecondensingprocessandcollapsetransitionstillhavemanyunclearaspects,andmucheffortwastakentomakeathoroughinvestigationandstudy.Moleculardynamic(MD)simulationsofthefoldingandcollapseprocessforapolyethylenechainwasrecentlycarriedoutbymanyauthors1'2'3.Itwasreportedthatatwo-stagecollapseprocesswasseenwithouttorsionpotential',andthreestageswerefoundbysimplificationofthecomputationalmodel5.ButthecollaPsesta…     

Understanding the folding rates and folding nuclei of globular proteins

The first part of this paper contains an overview of protein structures, their spontaneous formation ("folding"), and the thermodynamic and kinetic aspects of this phenomenon, as revealed by in vitro experiments. It is stressed that universal features of folding are observed near the point of thermodynamic equilibrium between the native and denatured states of the protein. Here the "two-state" ("denatured state" <--> "native state") transition proceeds without accumulation of metastable intermediates, but includes only the unstable "transition state". This state, which is the most unstable in the folding pathway, and its structured core (a "nucleus") are distinguished by their essential influence on the folding/unfolding kinetics. In the second part of the paper, a theory of protein folding rates and related phenomena is presented. First, it is shown that the protein size determines the range of a protein's folding rates in the vicinity of the point of thermodynamic equilibrium between the native and denatured states of the protein. Then, we present methods for calculating folding and unfolding rates of globular proteins from their sizes, stabilities and either 3D structures or amino acid sequences. Finally, we show that the same theory outlines the location of the protein folding nucleus (i.e., the structured part of the transition state) in reasonable agreement with experimental data.     

Effects of long-range electrostatic forces on simulated protein folding kinetics

Molecular dynamics simulations are a useful tool for characterizing protein folding pathways. There are several methods of treating electrostatic forces in these simulations with varying degrees of physical fidelity and computational efficiency. In this article, we compare the reaction field (RF) algorithm, particle-mesh Ewald (PME), and tapered cutoffs with increasing cutoff radii to address the impact of the electrostatics method employed on the folding kinetics. We quantitatively compare different methods by a correlation of quantitative measures of protein folding kinetics. The results of these comparisons show that for protein folding kinetics, the RF algorithm can quantitatively reproduce the kinetics of the more costly PME algorithm. These results not only assist the selection of appropriate algorithms for future simulations, but also give insight on the role that long-range electrostatic forces have in protein folding.     

Trigger factor slows co-translational folding through kinetic trapping while sterically protecting the nascent chain from aberrant cytosolic interactions

The E. coli chaperone trigger factor (TF) interacts directly with nascent polypeptide chains as they emerge from the ribosome exit tunnel. Small protein domains can fold under the cradle created by TF, but the co-translational folding of larger proteins is slowed down by its presence. Because of the great experimental challenges in achieving high spatial and time resolution, it is not yet known whether or not TF alters the folding properties of small proteins and if the reduced rate of folding of larger proteins is the result of kinetic or thermodynamic effects. We show, by molecular simulations employing a coarse-grained model of a series of ribosome nascent-chain complexes, that TF does not alter significantly the co-translational folding process of a small protein G domain but delays that of a large β-galactosidase domain as a result of kinetic trapping of its unfolded ensemble. We demonstrate that this trapping occurs through a combination of three distinct mechanisms: a decrease in the rate of structural rearrangements within the nascent chain, an increase in the effective exit tunnel length due to folding outside the cradle, and entanglement of the nascent chain with TF. We present evidence that this TF-induced trapping represents a trade-off between promoting co-translational folding and sterically shielding the nascent chain from aberrant cytosolic interactions that could lead to its aggregation or degradation.     

Structural Analysis of a Helical Peptide Unfolding Pathway

The analysis of the folding mechanism in peptides adopting well‐defined secondary structure is fundamental to understand protein folding. Herein, we describe the thermal unfolding of a 15‐mer vascular endothelial growth factor mimicking α‐helical peptide (QK_L10A) through the combination of spectroscopic and computational analyses. In particular, on the basis of the temperature dependencies of QK_L10A H_α chemical shifts we show that the first phase of the thermal helix unfolding, ending at around 320 K, involves mainly the terminal regions. A second phase of the transition, ending at around 333 K, comprises the central helical region of the peptide. The determination of high‐resolution QK_L10A conformational preferences in water at 313 K allowed us to identify, at atomic resolution, one intermediate of the folding–unfolding pathway. Molecular dynamics simulations corroborate experimental observations detecting a stable central helical turn, which represents the most probable site for the helix nucleation in the folding direction. The data presented herein allows us to draw a folding–unfolding picture for the small peptide QK_L10A compatible with the nucleation–propagation model. This study, besides contributing to the basic field of peptide helix folding, is useful to gain an insight into the design of stable helical peptides, which could find applications as molecular scaffolds to target protein–protein interactions.     

Pulling direction as a reaction coordinate for the mechanical unfolding of single molecules

The folding and unfolding kinetics of single molecules, such as proteins or nucleic acids, can be explored by mechanical pulling experiments. Determining intrinsic kinetic information, at zero stretching force, usually requires an extrapolation by fitting a theoretical model. Here, we apply a recent theoretical approach describing molecular rupture in the presence of force to unfolding kinetic data obtained from coarse-grained simulations of ubiquitin. Unfolding rates calculated from simulations over a broad range of stretching forces, for different pulling directions, reveal a remarkable "turnover" from a force-independent process at low force to a force-dependent process at high force, akin to the "roll-over" in unfolding rates sometimes seen in studies using chemical denaturant. While such a turnover in rates is unexpected in one dimension, we demonstrate that it can occur for dynamics in just two dimensions. We relate the turnover to the quality of the pulling direction as a reaction coordinate for the intrinsic folding mechanism. A novel pulling direction, designed to be the most relevant to the intrinsic folding pathway, results in the smallest turnover. Our results are in accord with protein engineering experiments and simulations which indicate that the unfolding mechanism at high force can differ from the intrinsic mechanism. The apparent similarity between extrapolated and intrinsic rates in experiments, unexpected for different unfolding barriers, can be explained if the turnover occurs at low forces.     

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.     

Failure of one-dimensional Smoluchowski diffusion models to describe the duration of conformational rearrangements in floppy, diffusive molecular systems: a case study of polymer cyclization

Motivated by recent experimental efforts to measure the duration of individual folding∕unfolding transitions in proteins and RNA, here we use simulations to study the duration of a simple transition mimicking an elementary step in biopolymer folding: the closure of a loop in a long polymer chain. While the rate of such a transition is well approximated by a one-dimensional Smoluchowski model that views the end-to-end distance dynamics of a polymer chain as diffusion governed by the one-dimensional potential of mean force, the same model fails rather dramatically to describe the duration of such transitions. Instead, the latter timescale is well described by a model where the chain ends diffuse freely, uninfluenced by the average entropic force imposed by the polymer chain. The effective diffusion coefficient then depends on the length scale of the loop closure transition. Our findings suggest that simple one-dimensional models, when applied to estimate the duration of reactive events in complex molecular systems, should be used with caution.     

Elucidation of conformational hysteresis on a giant DNA

The conformational behavior of a giant DNA mediated by condensing agents in the bulk solution has been investigated through experimental and theoretical approaches. Experimentally, a pronounced conformational hysteresis is observed for folding and unfolding processes, by increasing and decreasing the concentration of condensing agent (polyethylene glycol) (PEG), respectively. To elucidate the observed hysteresis, a semiflexible chain model is studied by using Monte Carlo simulations for the coil-globule transition. In the simulations, the hysteresis loop emerges for stiff enough chains, indicating distinct pathways for folding and unfolding processes. Also, our results show that globular state is thermodynamically more stable than coiled state in the hysteresis loop. Our findings suggest that increasing chain stiffness may reduce the chain conformations relevant to the folding pathway, which impedes the folding process.     

Length dependent folding kinetics of phenylacetylene oligomers: structural characterization of a kinetic trap

Using simulation to study the folding kinetics of 20-mer poly-phenylacetylene (pPA) oligomers, we find a long time scale trapped kinetic phase in the cumulative folding time distribution. This is demonstrated using molecular dynamics to simulate an ensemble of over 100 folding trajectories. The simulation data are fit to a four-state kinetic model which includes the typical folded and unfolded states, along with an intermediate state, and most surprisingly, a kinetically trapped state. Topologically diverse conformations reminiscent of alpha helices, beta turns, and sheets in proteins are observed, along with unique structures in the form of knots. The nonhelical conformations are implicated, on the basis of structural correlations to kinetic parameters, to contribute to the trapped kinetic behavior. The strong solvophobic forces which mediate the folding process and produce a stable helical folded state also serve to overstabilize the nonhelical conformations, ultimately trapping them. From our simulations, the folding time is predicted to be on the order of 2.5-12.5 mus in the presence of the trapped kinetic phase. The folding mechanism for these 20-mer chains is compared with the previously reported folding mechanism for the pPA 12-mer chains. A linear scaling relationship between the chain length and the mean first passage time is predicted in the absence of the trapped kinetic phase. We discuss the major implications of this discovery in the design of self-assembling nanostructures.