Proteins In Explicit Solvent Research Articles

Molecular Dynamics-Assisted Interpretation of Experimentally Determined Intrinsically Disordered Protein Conformational Components: The Case of Human α-Synuclein.

Mass spectrometry and single molecule force microscopy are two experimental approaches able to provide structural information on intrinsically disordered proteins (IDPs). These techniques allow the dissection of conformational ensembles in their main components, although at a low-resolution level. In this work, we interpret the results emerging from these experimental approaches on human alpha synuclein (AS) by analyzing a previously published 73 μs-long molecular-dynamics (MD) simulation of the protein in explicit solvent. We further compare MD-based predictions of single molecule Förster resonance energy transfer (smFRET) data of AS in solution with experimental data. The combined theoretical and experimental data provide a description of AS main conformational ensemble, shedding light into its intramolecular interactions and overall structural compactness. This analysis could be easily transferred to other IDPs.

Substrate specificity of the phenolic acid decarboxylase from Lactobacillus plantarum and related bacteria analyzed by molecular dynamics and docking

The phenolic acid decarboxylase (PAD) is a 44 kDa homodimeric, thermolabile and acid-resistant enzyme that some bacteria have developed as a detoxification system against phenolic acids produced by plants. It seems that the specificity of the PAD for their different substrates may be determined by an initial binding of the substrate to a cavity located in the vicinity of the active site. In order to test this hypothesis, PAD structures from Lactobacillus plantarum and 10 phylogenetically related bacteria were modeled and used for blind docking assays with p-coumaric acid as well as with 3 p-coumaric analogs and 42 property-matched decoys, to evaluate both the efficiency as the specificity with which the substrate can bind to the cavity. We show that both the efficiency and the specificity are low with raw models (not optimized) of the protein structures, but they are significantly increased when an equilibrium molecular dynamics simulation of the model of the protein in explicit solvent is previously conducted to the docking assay. The docking results showed that the binding efficiencies for the cis and trans conformations of the p-coumaric acid are different and suggest that the affinity of this substrate in the PADs from different bacteria may depend on the presence of charged amino acid residues in the cavity.

Sampling conformational space of intrinsically disordered proteins in explicit solvent: Comparison between well-tempered ensemble approach and solute tempering method

Intrinsically disordered proteins (IDPs) are a class of proteins that expected to be largely unstructured under physiological conditions. Due to their heterogeneous nature, experimental characterization of IDP is challenging. Temperature replica exchange molecular dynamics (T-REMD) is a widely used enhanced sampling method to probe structural characteristics of these proteins. However, its application has been hindered due to its tremendous computational cost, especially when simulating large systems in explicit solvent. Two methods, parallel tempering well-tempered ensemble (PT-WTE) and replica exchange with solute tempering (REST), have been proposed to alleviate the computational expense of T-REMD. In this work, we select three different IDP systems to compare the sampling characteristics and efficiencies of the two methods Both the two methods could efficiently sample the conformational space of IDP and yield highly consistent results for all the three IDPs. The efficiencies of the two methods: are compatible, with about 5–6 times better than the plain T-REMD. Besides, the advantages and disadvantages of each method are also discussed. Specially, the PT-WTE method could provide temperature dependent data of the system which could not be achieved by REST, while the REST method could readily be used to a part of the system, which is quite efficient to simulate some biological processes.

Efficient Geometry Optimization of Large Molecular Systems in Solution Using the Fragment Molecular Orbital Method.

The analytic gradient is derived for the frozen domain formulation of the fragment molecular orbital (FMO) method combined with the polarizable continuum model. The accuracy is tested in comparison to full FMO calculations for a representative set of systems in terms of the gradient accuracy, protein-ligand binding energies, and optimized structures. The frozen domain method reproduced geometries optimized with full FMO within 0.03-0.09 Å in terms of reduced mean square deviations, whereas a single-point gradient calculation is accelerated by the factor of 38 (Trp-cage protein in explicit solvent, PDB: 1L2Y ) and 12 (crambin, PDB: 1CRN ). The method is applied to a geometry optimization of the K-Ras protein-ligand complex (4Q03) using two domain definitions, and the optimized structures are consistent with experiment. Pair interaction analysis is used to identify residues important in binding the ligand.

Simulation of coupled folding and binding of an intrinsically disordered protein in explicit solvent with metadynamics

The C-terminal domain of measles virus nucleoprotein is an intrinsically disordered protein that could bind to the X domain (XD) of phosphoprotein P to exert its physiological function. Experiments reveal that the minimal binding unit is a 21-residue α-helical molecular recognition element (α-MoRE-MeV), which adopts a fully helical conformation upon binding to XD. Due to currently limited computing power, direct simulation of this coupled folding and binding process with atomic force field in explicit solvent cannot be achieved. In this work, two advanced sampling methods, metadynamics and parallel tempering, are combined to characterize the free energy surface of this process and investigate the underlying mechanism. Starting from an unbound and partially folded state of α-MoRE-MeV, multiple folding and binding events are observed during the simulation and the energy landscape was well estimated. The results demonstrate that the isolated α-MoRE-MeV resembles a molten globule and rapidly interconverts between random coil and multiple partially helical states in solution. The coupled folding and binding process occurs through the induced fit mechanism, with the residual helical conformations providing the initial binding sites. Upon binding, α-MoRE-MeV can easily fold into helical conformation without obvious energy barriers. Two mechanisms, namely, the system tending to adopt the structure in which the free energy of isolated α-MoRE-MeV is the minimum, and the binding energy of α-MoRE-MeV to its partner protein XD tending to the minimum, jointly dominate the coupled folding and binding process. With the advanced sampling approach, more IDP systems could be simulated and common mechanisms concerning the coupled folding and binding process could be investigated in the future.

Reduction of All-Atom Protein Folding Dynamics to One-Dimensional Diffusion.

Theoretical models have often modeled protein folding dynamics as diffusion on a low-dimensional free energy surface, a remarkable simplification. However, the accuracy of such an approximation and the number of dimensions required were not clear. For all-atom folding simulations of ten small proteins in explicit solvent we show that the folding dynamics can indeed be accurately described as diffusion on just a single coordinate, the fraction of native contacts (Q). The diffusion models reproduce both folding rates, and finer details such as transition-path durations and diffusive propagators. The Q-averaged diffusion coefficients decrease with chain length, as anticipated from energy landscape theory. Although the Q-diffusion model does not capture transition-path durations for the protein NuG2, we show that this can be accomplished by designing an improved coordinate Qopt. Overall, one-dimensional diffusion on a suitable coordinate turns out to be a remarkably faithful model for the dynamics of the proteins considered.

Folding Atomistic Proteins in Explicit Solvent Using Simulated Tempering.

Following a previous report on a coarse-grained protein model in implicit solvent, we applied simulated tempering (ST) with on-the-fly Helmholtz free energy (weight factors) determination to the folding or aggregation of seven proteins with the CHARMM, OPLS, and AMBER protein, and the SPC and TIP3P water force fields. For efficiency and reliability, we also performed replica exchange molecular dynamics (REMD) simulations on the alanine di- and deca-peptide, and the dimer of the Aβ16-22 Alzheimer's fragment, and used experimental data and previous simulation results on the chignolin, beta3s, Trp-cage, and WW domain peptides of 10-37 amino acids. The sampling with ST is found to be more efficient than with REMD for a much lower CPU cost. Starting from unfolded or extended conformations, the WW domain and the Trp-cage peptide fold to their NMR structures with a backbone RMSD of 2.0 and 1 Å. Remarkably, the ST simulation explores transient non-native topologies for Trp-cage that have been rarely discussed by other simulations. Our ST simulations also show that the CHARMM22* force field has limitations in describing accurately the beta3s peptide. Taken together, these results open the door to the study of the configurations of single proteins, protein aggregates, and any molecular systems at atomic details in explicit solvent using a single normal CPU. They also demonstrate that our ST scheme can be used with any force field ranging from quantum mechanics to coarse-grain and atomistic.

Targeting Electrostatic Interactions in Accelerated Molecular Dynamics with Application to Protein Partial Unfolding

Accelerated molecular dynamics (aMD) is a promising sampling method to generate an ensemble of conformations and to explore the free energy landscape of proteins in explicit solvent. Its success resides in its ability to reduce barriers in the dihedral and the total potential energy space. However, aMD simulations of large proteins can generate large fluctuations of the dihedral and total potential energy with little conformational changes in the protein structure. To facilitate wider conformational sampling of large proteins in explicit solvent, we developed a direct intrasolute electrostatic interactions accelerated MD (DISEI-aMD) approach. This method aims to reduce energy barriers within rapidly changing electrostatic interactions between solute atoms at short-range distances. It also results in improved reconstruction quality of the original statistical ensemble of the system. Recently, we characterized a pH-dependent partial unfolding of diphtheria toxin translocation domain (T-domain) using microsecond long MD simulations. In this work, we focus on the study of conformational changes of a low-pH T-domain model in explicit solvent using DISEI-aMD. On the basis of the simulations of the low-pH T-domain model, we show that the proposed sampling method accelerates conformational rearrangement significantly faster than multiple standard aMD simulations and microsecond long conventional MD simulations.

Finite-size effect on the charging free energy of protein in explicit solvent.

The finite-size effect in periodic system is examined for the charging free energy of protein in explicit solvent over a variety of charged states. The key to the finite-size correction is the self-energy, which is defined as the interaction energy of the solute with its own periodic images and the neutralizing background. By employing the thermodynamic-integration method with systematically varied sizes of the unit cell of molecular dynamics (MD) simulations, we show for ubiquitin that the self-energy corrects the finite-size effect on the charging free energy within 1 kcal/mol at total charges of -5e, -1e, neutral, and +1e and within 5 kcal/mol even for a highly charged state with +8e. We then sought the additional correction from the solvation effect using the numerical solution to the Poisson equation of the protein with implicit solvent. This correction reduces the cell-size dependence of the charging free energy at +8e to 3 kcal/mol and is well expressed as the self-energy divided by the dielectric constant of solvent water.

Constant pH molecular dynamics of proteins in explicit solvent with proton tautomerism

pH is a ubiquitous regulator of biological activity, including protein-folding, protein-protein interactions, and enzymatic activity. Existing constant pH molecular dynamics (CPHMD) models that were developed to address questions related to the pH-dependent properties of proteins are largely based on implicit solvent models. However, implicit solvent models are known to underestimate the desolvation energy of buried charged residues, increasing the error associated with predictions that involve internal ionizable residue that are important in processes like hydrogen transport and electron transfer. Furthermore, discrete water and ions cannot be modeled in implicit solvent, which are important in systems like membrane proteins and ion channels. We report on an explicit solvent constant pH molecular dynamics framework based on multi-site λ-dynamics (CPHMD(MSλD)). In the CPHMD(MSλD) framework, we performed seamless alchemical transitions between protonation and tautomeric states using multi-site λ-dynamics, and designed novel biasing potentials to ensure that the physical end-states are predominantly sampled. We show that explicit solvent CPHMD(MSλD) simulations model realistic pH-dependent properties of proteins such as the Hen-Egg White Lysozyme (HEWL), binding domain of 2-oxoglutarate dehydrogenase (BBL) and N-terminal domain of ribosomal protein L9 (NTL9), and the pKa predictions are in excellent agreement with experimental values, with a RMSE ranging from 0.72 to 0.84 pKa units. With the recent development of the explicit solvent CPHMD(MSλD) framework for nucleic acids, accurate modeling of pH-dependent properties of both major class of biomolecules-proteins and nucleic acids is now possible.

A hybrid MD-kMC algorithm for folding proteins in explicit solvent

We present a novel hybrid MD-kMC algorithm that is capable of efficiently folding proteins in explicit solvent. We apply this algorithm to the folding of a small protein, Trp-Cage. Different kMC move sets that capture different possible rate limiting steps are implemented. The first uses secondary structure formation as a relevant rate event (a combination of dihedral rotations and hydrogen-bonding formation and breakage). The second uses tertiary structure formation events through formation of contacts via translational moves. Both methods fold the protein, but via different mechanisms and with different folding kinetics. The first method leads to folding via a structured helical state, with kinetics fit by a single exponential. The second method leads to folding via a collapsed loop, with kinetics poorly fit by single or double exponentials. In both cases, folding times are faster than experimentally reported values, The secondary and tertiary move sets are integrated in a third MD-kMC implementation, which now leads to folding of the protein via both pathways, with single and double-exponential fits to the rates, and to folding rates in good agreement with experimental values. The competition between secondary and tertiary structure leads to a longer search for the helix-rich intermediate in the case of the first pathway, and to the emergence of a kinetically trapped long-lived molten-globule collapsed state in the case of the second pathway. The algorithm presented not only captures experimentally observed folding intermediates and kinetics, but yields insights into the relative roles of local and global interactions in determining folding mechanisms and rates.

Knotting a Protein in Explicit Solvent

Recently, experiments have confirmed that trefoil knotted proteins can fold spontaneously, consistent with predictions from simulations of simplified protein models. These simulations suggest folding the knot involves threading the protein terminal across a twisted loop via a slipknot configuration. Here, we report unbiased all-atom explicit-solvent simulations of the knotting dynamics of a protein. In simulations totaling 40 μs, we find that 5 out of 15 simulations reach the knotted native state when initiated from unknotted, slipknotted intermediates. The completed threading events had durations of 0.1–2 μs. Comparison of explicit-solvent to structure-based simulations shows that similar native contacts are responsible for threading the slipknot through the loop; however, competition between native and non-native salt bridges during threading results in increased energetic roughness. Overall, these simulations support a slipknotting mechanism for proteins with complex topology, and help verify that simp...

Knotting a Protein in Explicit Solvent

Recently, experiments have confirmed that trefoil knotted proteins can fold spontaneously, consistent with predictions from simulations of simplified protein models. These simulations suggest folding the knot involves threading the protein terminal across a twisted loop via a slipknot configuration. Here, we report unbiased all-atom explicit-solvent simulations of the knotting dynamics of a protein. In simulations totaling 40 μs, we find that 5 out of 15 simulations reach the knotted native state when initiated from unknotted, slipknotted intermediates. The completed threading events had durations of 0.1–2 μs. Comparison of explicit-solvent to structure-based simulations shows that similar native contacts are responsible for threading the slipknot through the loop; however, competition between native and non-native salt bridges during threading results in increased energetic roughness. Overall, these simulations support a slipknotting mechanism for proteins with complex topology, and help verify that simplified models are useful tools for studying knotted proteins.

A Hamiltonian Replica Exchange Molecular Dynamics (MD) Method for the Study of Folding, Based on the Analysis of the Stabilization Determinants of Proteins

Herein, we present a novel Hamiltonian replica exchange protocol for classical molecular dynamics simulations of protein folding/unfolding. The scheme starts from the analysis of the energy-networks responsible for the stabilization of the folded conformation, by means of the energy-decomposition approach. In this framework, the compact energetic map of the native state is generated by a preliminary short molecular dynamics (MD) simulation of the protein in explicit solvent. This map is simplified by means of an eigenvalue decomposition. The highest components of the eigenvector associated with the lowest eigenvalue indicate which sites, named “hot spots”, are likely to be responsible for the stability and correct folding of the protein. In the Hamiltonian replica exchange protocol, we use modified force-field parameters to treat the interparticle non-bonded potentials of the hot spots within the protein and between protein and solvent atoms, leaving unperturbed those relative to all other residues, as well as solvent-solvent interactions. We show that it is possible to reversibly simulate the folding/unfolding behavior of two test proteins, namely Villin HeadPiece HP35 (35 residues) and Protein A (62 residues), using a limited number of replicas. We next discuss possible implications for the study of folding mechanisms via all atom simulations.

Correction for Zhang and Ma, Folding helical proteins in explicit solvent using dihedral-biased tempering

Correction for Zhang and Ma, Folding helical proteins in explicit solvent using dihedral-biased tempering

Folding helical proteins in explicit solvent using dihedral-biased tempering

Using a single-trajectory-based tempering method with a high-temperature dihedral bias, we repeatedly folded four helical proteins [α(3)D (PDB ID: 2A3D, 73 residues), α(3)W (1LQ7, 67 residues), Fap1-NR(α) (2KUB, 81 residues) and S-836 (2JUA, 102 residues)] and some of the mutants in explicit solvent within several microseconds. The lowest root-mean-square deviations of backbone atoms from the experimentally determined structures were 1.9, 1.4, 1.0, and 2.1Å, respectively. Cluster analyses of folding trajectories showed the native conformation usually occupied the most populated cluster. The simulation protocol can be applied to large-scale simulations of other helical proteins on commonly accessible computing platforms.

Velocity-scaling optimized replica exchange molecular dynamics of proteins in a hybrid explicit/implicit solvent

We propose a scheme for replica exchange molecular dynamics of proteins in explicit solvent that minimizes the number of required replicas using velocity rescaling. Our approach relies on a hybrid method where the protein evolves at each temperature in an explicit solvent, but replica exchange moves utilize an implicit solvent term. The two terms are coupled through the velocity rescaling. We test the efficiency of this approach for a common test case, the trp-cage protein.

A Free-Energy Landscape for Coupled Folding and Binding of an Intrinsically Disordered Protein in Explicit Solvent from Detailed All-Atom Computations

The N-terminal repressor domain of neural restrictive silencer factor (NRSF) is an intrinsically disordered protein (IDP) that binds to the paired amphipathic helix (PAH) domain of mSin3. An NMR experiment revealed that the minimal binding unit of NRSF is a 15-residue segment that adopts a helical structure upon binding to a cleft of mSin3. We computed a free-energy landscape of this system by an enhanced conformational sampling method, all-atom multicanonical molecular dynamics. The simulation started from a configuration where the NRSF segment was fully disordered and distant from mSin3 in explicit solvent. In the absence of mSin3, the disordered NRSF segment thermally fluctuated between hairpins, helices, and bent structures. In the presence of mSin3, the segment bound to mSin3 by adopting the structures involved in the isolated state, and non-native and native complexes were formed. The free-energy landscape comprised three superclusters, and free-energy barriers separated the superclusters. The native complex was located at the center of the lowest free-energy cluster. When NRSF landed in the largest supercluster, the generated non-native complex moved on the landscape to fold into the native complex, by increasing the interfacial hydrophobic contacts and the helix content. When NRSF landed in other superclusters, the non-native complex overcame the free-energy barriers between the various segment orientations in the binding cleft of mSin3. Both population-shift and induced-fit (or induced-folding) mechanisms work cooperatively in the coupled folding and binding. The diverse structural adaptability of NRSF may be related to the hub properties of the IDP.

Application of biasing-potential replica exchange simulations for loop modeling and refinement of proteins in explicit solvent

Comparative protein modeling of a target protein based on sequence similarity to a protein with known structure is widely used to provide structural models of proteins. Frequently, the quality of the target- template sequence alignment is non-uniform along the sequence: parts can be modeled with a high confidence, whereas other parts differ strongly from the template. In principle, molecular dynamics (MD) simulations can be used to refine protein model structures and also to model loops in homology modeled protein structures, but it is limited by the currently accessible simulation time scales. In the current work we have used a recently developed biasing potential replica exchange (BP-Rex) MD [1] method to refine and to model loops in homology modeled protein structure at atomic resolution including explicit solvent. In standard Rex MD [2] simulations several replicas of a system are run in parallel at different temperatures allowing exchanges at preset time intervals. In a BP-Rex MD simulation replicas are controlled by various levels of a biasing potential to reduce the energy barriers associated with peptide backbone dihedral transitions. The method requires much fewer replicas for efficient sampling compared with standard temperature Rex MD. Starting from incorrect loop conformations this BP-Rex MD method samples the correct loop conformations as dominant conformations in all the cases. Application of BP-Rex MD to several protein loops indicates improved conformational sampling of backbone dihedral angle of loop residues compared to conventional MD simulations. BP-Rex MD refinement simulations on several test cases starting from decoy structures deviating significantly from the native structure resulted in final structures in much closer agreement with experiment compared to conventional MD simulations [3].

Ab initio simulation of a 57‐residue protein in explicit solvent reproduces the native conformation in the lowest free‐energy cluster

An enhanced conformational sampling method, multicanonical molecular dynamics (McMD), was applied to the ab intio folding of the 57-residue first repeat of human glutamyl- prolyl-tRNA synthetase (EPRS-R1) in explicit solvent. The simulation started from a fully extended structure of EPRS-R1 and did not utilize prior structural knowledge. A canonical ensemble, which is a conformational ensemble thermodynamically probable at an arbitrary temperature, was constructed by reweighting the sampled structures. Conformational clusters were obtained from the canonical ensemble at 300 K, and the largest cluster (i.e., the lowest free-energy cluster), which contained 34% of the structures in the ensemble, was characterized by the highest similarity to the NMR structure relative to all alternative clusters. This lowest free-energy cluster included native-like structures composed of two anti-parallel α-helices. The canonical ensemble at 300 K also showed that a short Gly-containing segment, which adopts an α-helix in the native structure, has a tendency to be structurally disordered. Atomic-level analyses demonstrated clearly that inter-residue hydrophobic interactions drive the helix formation of the Gly-containing segment, and that increasing the hydrophobic contacts accompanies exclusion of water molecules from the vicinity of this segment. This study has shown, for the first time, that the free-energy landscape of a structurally well-ordered protein of about 60 residues is obtainable with an all atom model in explicit water without prior structural knowledge.