Folding Of Trp-cage Research Articles

Collective Variable for Metadynamics Derived From AlphaFold Output.

AlphaFold is a neural network–based tool for the prediction of 3D structures of proteins. In CASP14, a blind structure prediction challenge, it performed significantly better than other competitors, making it the best available structure prediction tool. One of the outputs of AlphaFold is the probability profile of residue–residue distances. This makes it possible to score any conformation of the studied protein to express its compliance with the AlphaFold model. Here, we show how this score can be used to drive protein folding simulation by metadynamics and parallel tempering metadynamics. Using parallel tempering metadynamics, we simulated the folding of a mini-protein Trp-cage and β hairpin and predicted their folding equilibria. We observe the potential of the AlphaFold-based collective variable in applications beyond structure prediction, such as in structure refinement or prediction of the outcome of a mutation.

The Folding of Trp-cage is Regulated by Stochastic Flip of the Side Chain of Tryptophan

Abstract Trp-cage is an artificial 20-residue protein and forms a hydrophobic core at its central cage upon folding. In the present study, the folding of Trp-cage was addressed by parallel cascade selection molecular dynamics (PaCS-MD). Our results of PaCS-MD indicate that flip of the side chain of tryptophan (W6) was correlated with the overall folding. In conclusion, flip of stochastic side chain of W6 regulates the folding into the native or mis-folded states of Trp-cage.

Enhancing Biomolecular Sampling with Reinforcement Learning: A Tree Search Molecular Dynamics Simulation Method.

This paper proposes a novel molecular simulation method, called tree search molecular dynamics (TS-MD), to accelerate the sampling of conformational transition pathways, which require considerable computation. In TS-MD, a tree search algorithm, called upper confidence bounds for trees, which is a type of reinforcement learning algorithm, is applied to sample the transition pathway. By learning from the results of the previous simulations, TS-MD efficiently searches conformational space and avoids being trapped in local stable structures. TS-MD exhibits better performance than parallel cascade selection molecular dynamics, which is one of the state-of-the-art methods, for the folding of miniproteins, Chignolin and Trp-cage, in explicit water.

Enriched Conformational Sampling of DNA and Proteins with a Hybrid Hamiltonian Derived from the Protein Data Bank.

In this article, we present a method for the enhanced molecular dynamics simulation of protein and DNA systems called potential of mean force (PMF)-enriched sampling. The method uses partitions derived from the potentials of mean force, which we determined from DNA and protein structures in the Protein Data Bank (PDB). We define a partition function from a set of PDB-derived PMFs, which efficiently compensates for the error introduced by the assumption of a homogeneous partition function from the PDB datasets. The bias based on the PDB-derived partitions is added in the form of a hybrid Hamiltonian using a renormalization method, which adds the PMF-enriched gradient to the system depending on a linear weighting factor and the underlying force field. We validated the method using simulations of dialanine, the folding of TrpCage, and the conformational sampling of the Dickerson–Drew DNA dodecamer. Our results show the potential for the PMF-enriched simulation technique to enrich the conformational space of biomolecules along their order parameters, while we also observe a considerable speed increase in the sampling by factors ranging from 13.1 to 82. The novel method can effectively be combined with enhanced sampling or coarse-graining methods to enrich conformational sampling with a partition derived from the PDB.

Rapid Folding of Trp-Cage in Ionic Liquid: Implications in Protein Renaturations

Ionic Liquids (ILs) have emerged as ideal solvent media for enzymatic reactions and enhanced protein stability. Studies have also shown the ability of ILs in renaturation of unfolded proteins. Here, we explore the mechanism of protein refolding in ILs by simulating the miniprotein, Trp-cage in varying concentrations of 1-ethyl-3-methylimidazolium tetrafluoroborate ([Emim][BF4]) using all-atom Molecular Dynamics (MD) simulations. Our results show that Trp-cage folded to its native conformation very rapidly in low IL concentrations, while it fails to fold in neat water or high IL concentrations. This rapid folding is attributed to the strong IL ions-water interactions that help in stripping significant amount of water from the unfolded protein surface. Further, the strong electrostatic interactions between IL cations and anions and the specific interaction of [Emim] cations with protein N-terminal residues and [BF4] anions with C-terminal residues facilitate the protein hydrophobic collapse. Interestingly, at higher IL concentrations protein was unable to fold due to significant reduction in the static dielectric constant of the medium that enhanced ion-ion associations.

Adaptive enhanced sampling with a path-variable for the simulation of protein folding and aggregation.

In this article, we present a novel adaptive enhanced sampling molecular dynamics (MD) method for the accelerated simulation of protein folding and aggregation. We introduce a path-variable L based on the un-biased momenta p and displacements dq for the definition of the bias s applied to the system and derive 3 algorithms: general adaptive bias MD, adaptive path-sampling, and a hybrid method which combines the first 2 methodologies. Through the analysis of the correlations between the bias and the un-biased gradient in the system, we find that the hybrid methodology leads to an improved force correlation and acceleration in the sampling of the phase space. We apply our method on SPC/E water, where we find a conservation of the average water structure. We then use our method to sample dialanine and the folding of TrpCage, where we find a good agreement with simulation data reported in the literature. Finally, we apply our methodologies on the initial stages of aggregation of a hexamer of Alzheimer's amyloid β fragment 25-35 (Aβ 25-35) and find that transitions within the hexameric aggregate are dominated by entropic barriers, while we speculate that especially the conformation entropy plays a major role in the formation of the fibril as a rate limiting factor.

Effective Conformational Sampling in Explicit Solvent with Gaussian Biased Accelerated Molecular Dynamics.

In this Article, a user-friendly Gaussian biased accelerated molecular dynamics (GbAMD) method is presented that uses a sum of Gaussians of potential energies as the biased force to accelerate the conformational sampling. The easy parameter setting of GbAMD is demonstrated in a variety of simulation tests for the conformational transitions of proteins with various complexity including the folding of Trpcage, GB1p, and HP35 peptides as well as the functional conformational changes of nCaM and HIV-1 PR proteins. Additionally, the ability of GbAMD in conformational sampling and free-energy evaluation is quantitatively assessed through the comparison of GbAMD simulations on the folding of α-helical Trpcage and β-hairpin GB1p with the accompanying standard dual boost AMD and conventional MD (cMD) simulations. While GbAMD can fold both peptides into their native structures repeatedly in individual trajectories, AMD can only fold Trpcage and cMD fails the folding in both cases. As a result, only GbAMD can quantitatively measure the properties of the equilibrium conformational ensemble of protein folding consistent with experimental data. Also notable is that the structural properties of the indispensable unfolded and transition states in the folding pathways of Trpcage and GB1p characterized by GbAMD simulations are in great agreement with previous simulations on the two peptides. In summary, GbAMD has an effective conformational sampling ability that provides a convenient and effective access for simulating the structural dynamics of biomolecular systems.

How fast fast-folding proteins fold in silico

In reported microcanonical molecular dynamics simulations, fast-folding proteins CLN025 and Trp-cage autonomously folded to experimentally determined native conformations. However, the folding times of these proteins derived from the simulations were more than 4–10 times longer than their experimental values. This article reports autonomous folding of CLN025 and Trp-cage in isobaric–isothermal molecular dynamics simulations with agreements within factors of 0.69–1.75 between simulated and experimental folding times at different temperatures. These results show that CLN025 and Trp-cage can now autonomously fold in silico as fast as in experiments, and suggest that the accuracy of folding simulations for fast-folding proteins begins to overlap with the accuracy of folding experiments. This opens new prospects of developing computer algorithms that can predict both ensembles of conformations and their interconversion rates for a protein from its sequence for artificial intelligence on how and when a protein acts as a receiver, switch, and relay to facilitate various subcellular-to-tissue communications. Then the genetic information that encodes proteins can be better read in the context of intricate biological functions.

A Fast Convergent Simulated Annealing Algorithm for Protein-Folding: Simulated Annealing Outlier FLOODing (SA-OFLOOD) Method

Abstract A Simulated Annealing (SA) algorithm is combined with our recently developed conformational search technique, Outlier FLOODding (OFLOOD) method [J. Comput. Chem. 2015, 36, 97], to avoid a slow convergence in finding a global minimum by the conventional SA (CSA). This method is referred to as SA-OFLOOD and designed for an efficient SA algorithm that robustly detects global minimum states in the protein-folding problems. As a demonstration, SA-OFLOOD was applied to reproduce the folding process of Trp-cage from a fully extended to the native states in implicit solvent. Through the demonstration, SA-OFLOOD successfully predicted the native state of Trp-cage within errors of 0.6 ± 0.2 Å Cα root mean square deviation (RMSD) with only 200 ns simulation time. In contrast, both CSA with sufficiently slow temperature scheduling and canonical MD simulations at room temperature (300 K) failed to find the native state (more than 3.0 Å Cα RMSD), indicating the strength of SA-OFLOOD on the protein-folding problem. As an application to a realistic system, SA-OFLOOD was applied to the folding of Trp-cage in explicit solvent, and the native state was also sampled within Cα RMSD of 1.0 Å through a nanosecond-order simulation time.

Coarse kMC-based replica exchange algorithms for the accelerated simulation of protein folding in explicit solvent.

In this paper, we present a coarse replica exchange molecular dynamics (REMD) approach, based on kinetic Monte Carlo (kMC). The new development significantly can reduce the amount of replicas and the computational cost needed to enhance sampling in protein simulations. We introduce 2 different methods which primarily differ in the exchange scheme between the parallel ensembles. We apply this approach on folding of 2 different β-stranded peptides: the C-terminal β-hairpin fragment of GB1 and TrpZip4. Additionally, we use the new simulation technique to study the folding of TrpCage, a small fast folding α-helical peptide. Subsequently, we apply the new methodology on conformation changes in signaling of the light-oxygen voltage (LOV) sensitive domain from Avena sativa (AsLOV2). Our results agree well with data reported in the literature. In simulations of dialanine, we compare the statistical sampling of the 2 techniques with conventional REMD and analyze their performance. The new techniques can reduce the computational cost of REMD significantly and can be used in enhanced sampling simulations of biomolecules.

Folding and thermodynamic studies of Trp-cage based on polarized force field

Two replica exchange molecular dynamics (REMD) simulations were carried out to study the thermodynamics of a 20-residue Trp-cage folding based on a newly developed polarized protein-specific charge (PPC). Starting from a fully extended conformation, Trp-cage native conformation was successfully sampled using REMD based on a 3-step PPC update. Next, the obtained Trp-cage folded conformation was then used to calculate the PPC in which another REMD was performed to explore the thermodynamic stability of Trp-cage. The theoretical melting temperature T m of ≈325 K was found to be in close agreement with experimental melting temperature, T m of 315 K. This indicates that the PPC was correctly predicting the temperature dependence. The current study provides a direct proof of how electrostatic polarization affects protein folding.

Transition path sampling of protein conformational changes

Conformational changes in proteins often take place on long time scales compared to the molecular timescale. These long time scales, related to high free energy barriers, make such processes difficult to access with a straightforward molecular dynamics approach. The transition path sampling technique has been developed to overcome such timescale differences without assuming a predefined reaction coordinate. We review the transition path sampling methodology with the application of protein conformational change in mind. Using three case studies, based on previous work, we elucidate the strengths and pitfalls of the method. First, the extensive work on the folding of Trp-cage reveals how to sample parallel pathways, how to obtain rate constants, and how to extract reaction coordinates. The second case-study, on the folding of Trpzip4 β-hairpin, illustrates how to treat long-lived intermediates in a conformational change. The final example showcases the light-triggered conformational transition of Photo-active Yellow Protein into its signaling state, highlighting the wealth of insight that can be gathered from a transition path sampling approach, including new hypotheses for reaction mechanisms. We end with an outlook discussing future developments and application of the methodology.

Trp Cage Folding in Confinement

While protein-folding studies are typically performed in bulk solution, the effects of confinement and crowding are poorly understood and in fact may alter the thermodynamics and kinetics of protein folding in a cellular environment. Here we have used all-atom simulations to examine the model Trp-cage mini-protein adsorbed to a purely hydrophobic surface and confined between hydrophobic walls. Replica exchange molecular dynamics simulations were performed to construct the folding free-energy landscape from which meta-stable states not seen in the bulk were indentified. In both cases, these states consist of different conformations of the protein adsorbed to the wall. The intermediates likely affect the free energy barriers to folding. Adsorption of the protein to a hydrophobic wall raises the energy barrier to folding, while lowering the barrier to folding of the confined protein. Although the confined protein is adsorbed to the wall, it appears that confinement stabilizes the α-helix, driving the protein toward the native state. Further, the presence of additional states likely changes the folding mechanism of the protein. Therefore we use multiple state transition path sampling to elucidate the differences between folding of Trp-cage in the bulk and confined between hydrophobic walls. Our simulation results can provide a realistic starting point for experiments on the effect of confinement on the folding behavior in Trp-cage and other small model proteins.

Multiscale Coarse-Graining of the Protein Energy Landscape

A variety of coarse-grained (CG) models exists for simulation of proteins. An outstanding problem is the construction of a CG model with physically accurate conformational energetics rivaling all-atom force fields. In the present work, atomistic simulations of peptide folding and aggregation equilibria are force-matched using multiscale coarse-graining to develop and test a CG interaction potential of general utility for the simulation of proteins of arbitrary sequence. The reduced representation relies on multiple interaction sites to maintain the anisotropic packing and polarity of individual sidechains. CG energy landscapes computed from replica exchange simulations of the folding of Trpzip, Trp-cage and adenylate kinase resemble those of other reduced representations; non-native structures are observed with energies similar to those of the native state. The artifactual stabilization of misfolded states implies that non-native interactions play a deciding role in deviations from ideal funnel-like cooperative folding. The role of surface tension, backbone hydrogen bonding and the smooth pairwise CG landscape is discussed. Ab initio folding aside, the improved treatment of sidechain rotamers results in stability of the native state in constant temperature simulations of Trpzip, Trp-cage, and the open to closed conformational transition of adenylate kinase, illustrating the potential value of the CG force field for simulating protein complexes and transitions between well-defined structural states.

Protein Folding Landscapes for Alpha- and Beta-Miniproteins Using All-Atom Simulations with an Optimized Force-Field

With recent advances in simulation methodology and computer hardware, it has become possible to access physical phenomena occurring on the microsecond timescale with molecular dynamics simulations. Even though most naturally occurring proteins fold on a much slower timescale (milliseconds to seconds), the design of miniproteins (e.g., trpcage, trpzip, beta-hairpin) and proteins (e.g., Villin) which fold close to the protein folding-speed limit (∼ 1 μs) have made feasible direct, high resolution, simulations of protein folding. At the same time, the shortcomings in the current energy functions for proteins are becoming increasingly evident with clear biases in secondary structure preference of different force fields being reflected in which proteins they are able to fold. To be able to compare and complement experimental observations, an ideal force-field would be able to fold different types of secondary structure without additional modifications or inputs.We will present results from extensive replica exchange molecular dynamics simulations for folding of GB1 beta-hairpin and trpcage (representing beta and alpha structures respectively) with a force field based on AMBER ff03 and optimized only to reproduce the helix-coil transition. We obtain converged equilibrium distributions for runs starting from a completely unfolded state and from the native state, with folded populations at room temperature in quantitative agreement with experiment. The folded structures for both the proteins (starting from a completely unfolded structure) have average backbone dRMS from the experimental structures of less than 1 A. Finally, we will present results for the 35-residue protein Villin. Although convergence of equilibrium distributions in this case is not computationally feasible, we nonetheless obtain a folded structure within 1 A dRMS of the native structure, starting from a completely unfolded coil-like conformation.

Key residue-dominated protein folding dynamics

A “key-residue” hypothesis that a few residues’ characteristics contain the essential dynamics of the whole protein is proposed for the study of side-chain relaxation near native states. Molecular dynamics simulation is performed on the folding of Trp-cage, and four key residues are discovered and shown to be highly sensitive to the change of state of the protein away from the native state. Order parameters that characterize the geometrical properties of key residues are shown to form valuable phase plane on which one distinguishes different reaction pathways. Furthermore, one of the key residues, Trp6, is observed to display two reconfiguration processes, in which one is induced by an unconstrained torsion of the side-chain of Trp6, with a rate faster by almost an order of magnitude than the other one described by Kussell’s model. The faster process seems to occur more frequently in our simulation and thus represent a significant mechanism in folding dynamics.