A Hamiltonian replica exchange molecular dynamics (MD) method for the study of folding, based on the analysis of the stabilization determinants of proteins

Study of Correlated Motions to Detect the Conformational Transitions of the Intrinsically Disordered Sheep Prion Peptide

Intrinsically disordered proteins (IDPs) are known for their random structural changes throughout their sequence based on the environment. The mechanism underlying these structural changes is difficult to explain. All biological processes are known to follow the direction through which they act. A study of the correlated motion can help to understand the direction of the change. Herein, we introduced the multivariate statistical analysis (MSA) technique to study the correlated motion of the peptide. The correlated motion of the sheep prion peptide was studied with the change in the temperature and solvent. These techniques helped to identify the contributing residual motions that helped to form the different secondary structures of the protein and also the triggering factors that drive these sorts of residual motions. The structural details match the experimentally reported data. It was found that the direction of the change of the secondary structure for this peptide shifted from the C-terminal to the N-terminal with an increase in the temperature. It was found that the involvement of the hydrophobic residues present at the C-terminal and the middle residues (residues 12-17) is responsible for forming a β-sheet at the normal temperature. Hydration water was found to play an important role in this change. Insights gained from this study can be used to design strategies for desirable structural changes in the IDPs.

Optimizing Excipient Properties to Prevent Aggregation in Biopharmaceutical Formulations

Excipients are included within protein biotherapeutic solution formulations to improve colloidal and conformational stability but are generally not designed for the specific purpose of preventing aggregation and improving cryoprotection in solution. In this work, we have explored the relationship between the structure and antiaggregation activity of excipients by utilizing coarse-grained molecular dynamics modeling of protein-excipient interaction. We have studied human serum albumin as a model protein, and we report the interaction of 41 excipients (polysorbates, fatty alcohol ethoxylates, fatty acid ethoxylates, phospholipids, glucosides, amino acids, and others) in terms of the reduction of solvent accessible surface area of aggregation-prone regions, proposed as a mechanism of aggregation prevention. Polyoxyethylene sorbitan had the greatest degree of interaction with aggregation-prone regions, decreasing the solvent accessible surface area of APRs by 20.7 nm2 (40.1%). Physicochemical descriptors generated by Mordred are employed to probe the structure-property relationship using partial least-squares regression. A leave-one-out cross-validated model had a root-mean-square error of prediction of 4.1 nm2 and a mean relative error of prediction of 0.077. Generally, longer molecules with a large number of alcohol-terminated PEG units tended to interact more, with qualitatively different protein interactions, wrapping around the protein. Shorter or less ethoxylated compounds tend to form hemimicellar clusters at the protein surface. We propose that an improved design would feature many short chains of 5 to 10 PEG units in many distinct branches and at least some hydrophobic content in the form of medium-length or greater aliphatic chains (i.e., six or more carbon atoms). The combination of molecular dynamics simulation and quantitative modeling is an important first step in an all-purpose protein-independent model for the computer-aided design of stabilizing excipients.

Q-RepEx: A Python pipeline to increase the sampling of empirical valence bond simulations

The exploration of chemical systems occurs on complex energy landscapes. Comprehensively sampling rugged energy landscapes with many local minima is a common problem for molecular dynamics simulations. These multiple local minima trap the dynamic system, preventing efficient sampling. This is a particular challenge for large biochemical systems with many degrees of freedom. Replica exchange molecular dynamics (REMD) is an approach that accelerates the exploration of the conformational space of a system, and thus can be used to enhance the sampling of complex biomolecular processes. In parallel, the empirical valence bond (EVB) approach is a powerful approach for modeling chemical reactivity in biomolecular systems. Here, we present an open-source Python-based tool that interfaces with the Q simulation package, and increases the sampling efficiency of the EVB free energy perturbation/umbrella sampling approach by means of REMD. This approach, Q-RepEx, both decreases the computational cost of the associated REMD-EVB simulations, and opens the door to more efficient studies of biochemical reactivity in systems with significant conformational fluctuations along the chemical reaction coordinate.

Deciphering the QR Code of the CRISPR-Cas9 System: Synergy between Gln768 (Q) and Arg976 (R)

Markov state models (MSMs) and machine learning (ML) algorithms can extrapolate the long-time-scale behavior of large biomolecules from molecular dynamics (MD) trajectories. In this study, an MD-MSM-ML scheme has been applied to probe the large endonuclease (Cas9) in the bacterial adaptive immunity CRISPR-Cas9 system. CRISPR has become a programmable and state-of-the-art powerful genome editing tool that has already revolutionized life sciences. CRISPR-Cas9 is programmed to process specific DNA sequences in the genome. However, human/biomedical applications are compromised by off-target DNA damage. Characterization of Cas9 at the structural and biophysical levels is a prerequisite for the development of efficient and high-fidelity Cas9 variants. The Cas9 wild type and two variants (R63A-R66A-R70A, R69A-R71A-R74A-R78A) are studied herein. The configurational space of Cas9 is provided with a focus on the conformations of the side chains of two residues (Gln768 and Arg976). A model for the synergy between those two residues is proposed. The results are discussed within the context of experimental literature. The results and methodology can be exploited for the study of large biomolecules in general and for the engineering of more efficient and safer Cas9 variants for applications.

Iterative Landmark-Based Umbrella Sampling (ILBUS) Protocol for Sampling of Conformational Space of Biomolecules

Computer simulations of biomolecules such as molecular dynamics often suffer from insufficient sampling. Due to limited computational resources, insufficient sampling prevents obtaining proper equilibrium distributions of observed properties. To deal with this problem, we proposed a simulation protocol for efficient resampling of collected off-equilibrium trajectories. These trajectories are utilized for the initial mapping of the conformational space, which is later properly resampled by the introduced Iterative Landmark-Based Umbrella Sampling (ILBUS) method. Reconstruction of static equilibrium properties is achieved by the multistate Bennett acceptance ratio (MBAR) method, which enables efficient use of simulated data. The ILBUS protocol is geometry-based and does not demand any additional collective variable or a dimensional-reduction technique. The only requirement is a set of suitably spaced reference conformations, which serve as landmarks in the mapped conformational space. Additionally, the ILBUS protocol encompasses an iterative process that optimizes the force constant used in the umbrella sampling simulation. Such tuning is an inherent feature of the protocol and does not need to be performed by the user in advance. Furthermore, even the simulations with suboptimal force constants can be used in estimates by MBAR. We demonstrate the feasibility and the performance of this approach in the study of the conformational landscape of the alanine dipeptide, met-enkephalin, and adenylate kinase.

Fundamental Redesign of the TIGER2hs Kernel to Address Severe Parameter Sensitivity

Replica exchange molecular dynamics simulations are one of the most popular approaches to enhance conformational sampling of molecular systems. Applications range from protein folding to protein-protein or other host-guest interactions, as well as binding free energy calculations. While these methods are computationally expensive, highly accurate results can be obtained. We recently developed TIGER2hs, an improved version of the temperature intervals with global exchange of replicas (TIGER2) algorithm. This method combines the replica-based enhanced sampling in an explicit solvent with a hybrid solvent energy evaluation. During the exchange attempts, bulk water is replaced by an implicit solvent model, allowing sampling with significantly less replicas than parallel tempering (REMD). This enables accurate enhanced sampling calculations with only a fraction of computational resources compared to REMD. Our latest results highlight several issues with sampling imbalance and parameter sensitivity within the original TIGER2 exchange algorithms that affect the overall state populations. A high sensitivity on replica number and maximum temperature is eliminated by changing to a pairwise exchange kernel (PE) without additional sorting. Simulations are controlled by adjusting the average temperature change per exchange ⟨ΔT/χ⟩ to below 30 K to mimic a controlled temperature mixing of replicas similar to REMD. Thus, this parameter provides an applicable property for selecting combinations of replica number and maximum temperature to adjust simulations for best accuracy, with flexible resource investment. This increases the robustness of the method and ensures results in excellent agreement with REMD, as demonstrated for three different peptides.

Improving ligand-ranking of AutoDock Vina by changing the empirical parameters

AutoDock Vina (Vina) achieved a very high docking-success rate, p ^ , but give a rather low correlation coefficient, R , for binding affinity with respect to experiments. This low correlation can be an obstacle for ranking of ligand-binding affinity, which is the main objective of docking simulations. In this context, we evaluated the dependence of Vina R coefficient upon its empirical parameters. R is affected more by changing the gauss2 and rotation than other terms. The docking-success rate p ^ is sensitive to the alterations of the gauss1, gauss2, repulsion, and hydrogen bond parameters. Based on our benchmarks, the parameter set1 has been suggested to be the most optimal. The testing study over 800 complexes indicated that the modified Vina provided higher correlation with experiment R set 1 = 0.556 ± 0.025 compared with R Default = 0.493 ± 0.028 obtained by the original Vina and R Vina 1.2 = 0.503 ± 0.029 by Vina version 1.2. Besides, the modified Vina can be also applied more widely, giving R ≥ 0.500 for 32/48 targets, compared with the default package, giving R ≥ 0.500 for 31/48 targets. In addition, validation calculations for 1036 complexes obtained from version 2019 of PDBbind refined structures showed that the set1 of parameters gave higher correlation coefficient ( R set 1 = 0.617 ± 0.017 ) than the default package ( R Default = 0.543 ± 0.020 ) and Vina version 1.2 ( R Vina 1.2 = 0.540 ± 0.020 ). The version of Vina with set1 of parameters can be downloaded at https://github.com/sontungngo/mvina. The outcomes would enhance the ranking of ligand-binding affinity using Autodock Vina.

Fighting Against Bacterial Lipopolysaccharide-Caused Infections through Molecular Dynamics Simulations: A Review

Lipopolysaccharide (LPS) is the primary component of the outer leaflet of Gram-negative bacterial outer membranes. LPS elicits an overwhelming immune response during infection, which can lead to life-threatening sepsis or septic shock for which no suitable treatment is available so far. As a result of the worldwide expanding multidrug-resistant bacteria, the occurrence and frequency of sepsis are expected to increase; thus, there is an urge to develop novel strategies for treating bacterial infections. In this regard, gaining an in-depth understanding about the ability of LPS to both stimulate the host immune system and interact with several molecules is crucial for fighting against LPS-caused infections and allowing for the rational design of novel antisepsis drugs, vaccines and LPS sequestration and detection methods. Molecular dynamics (MD) simulations, which are understood as being a computational microscope, have proven to be of significant value to understand LPS-related phenomena, driving and optimizing experimental research studies. In this work, a comprehensive review on the methods that can be combined with MD simulations, recently applied in LPS research, is provided. We focus especially on both enhanced sampling methods, which enable the exploration of more complex systems and access to larger time scales, and free energy calculation approaches. Thereby, apart from outlining several strategies for surmounting LPS-caused infections, this work reports the current state-of-the-art of the methods applied with MD simulations for moving a step forward in the development of such strategies.

Effects of Amino Acid Side-Chain Length and Chemical Structure on Anionic Polyglutamic and Polyaspartic Acid Cellulose-Based Polyelectrolyte Brushes

We used atomistic molecular dynamics (MD) simulations to study polyelectrolyte brushes based on anionic α,L-glutamic acid and α,L-aspartic acid grafted on cellulose in the presence of divalent CaCl₂ salt at different concentrations. The motivation is to search for ways to control properties such as sorption capacity and the structural response of the brush to multivalent salts. For this detailed understanding of the role of side-chain length, the chemical structure and their interplay are required. It was found that in the case of glutamic acid oligomers, the longer side chains facilitate attractive interactions with the cellulose surface, which forces the grafted chains to lie down on the surface. The additional methylene group in the side chain enables side-chain rotation, enhancing this effect. On the other hand, the shorter and more restricted side chains of aspartic acid oligomers prevent attractive interactions to a large degree and push the grafted chains away from the surface. The difference in side-chain length also leads to differences in other properties of the brush in divalent salt solutions. At a low grafting density, the longer side chains of glutamic acid allow the adsorbed cations to be spatially distributed inside the brush resulting in a charge inversion. With an increase in grafting density, the difference in the total charge of the aspartic and glutamine brushes disappears, but new structural features appear. The longer sides allow for ion bridging between the grafted chains and the cellulose surface without a significant change in main-chain conformation. This leads to the brush structure being less sensitive to changes in salt concentration.

Simulated tempering with irreversible Gibbs sampling techniques

We present here two novel algorithms for simulated tempering simulations, which break the detailed balance condition (DBC) but satisfy the skewed detailed balance to ensure invariance of the target distribution. The irreversible methods we present here are based on Gibbs sampling and concern breaking DBC at the update scheme of the temperature swaps. We utilize three systems as a test bed for our methods: a Markov chain Monte Carlo simulation on a simple system described by a one-dimensional double well potential, the Ising model, and molecular dynamics simulations on alanine pentapeptide (ALA5). The relaxation times of inverse temperature, magnetic susceptibility, and energy density for the Ising model indicate clear gains in sampling efficiency over conventional Gibbs sampling techniques with DBC and also over the conventionally used simulated tempering with the Metropolis-Hastings (MH) scheme. Simulations on ALA5 with a large number of temperatures indicate distinct gains in mixing times for inverse temperature and consequently the energy of the system compared to conventional MH. With no additional computational overhead, our methods were found to be more efficient alternatives to the conventionally used simulated tempering methods with DBC. Our algorithms should be particularly advantageous in simulations of large systems with many temperature ladders, as our algorithms showed a more favorable constant scaling in Ising spin systems as compared with both reversible and irreversible MH algorithms. In future applications, our irreversible methods can also be easily tailored to utilize a given dynamical variable other than temperature to flatten rugged free energy landscapes.

Influence of Calcium Binding on Conformations and Motions of Anionic Polyamino Acids. Effect of Side Chain Length

Investigation of the effect of CaCl2 salt on conformations of two anionic poly(amino acids) with different side chain lengths, poly-(α-l glutamic acid) (PGA) and poly-(α-l aspartic acid) (PASA), was performed by atomistic molecular dynamics (MD) simulations. The simulations were performed using both unbiased MD and the Hamiltonian replica exchange (HRE) method. The results show that at low CaCl2 concentration adsorption of Ca2+ ions lead to a significant chain size reduction for both PGA and PASA. With the increase in concentration, the chains sizes partially recover due to electrostatic repulsion between the adsorbed Ca2+ ions. Here, the side chain length becomes important. Due to the longer side chain and its ability to distance the charged groups with adsorbed ions from both each other and the backbone, PGA remains longer in the collapsed state as the CaCl2 concentration is increased. The analysis of the distribution of the mineral ions suggests that both poly(amino acids) should induce the formation of mineral with the same structure of the crystal cell.

Role of Oxidized Gly25, Gly29, and Gly33 Residues on the Interactions of Aβ1-42 with Lipid Membranes

Oxidative stress is known to play an important role in the pathogenesis of Alzheimer's disease. Moreover, it is becoming increasingly evident that the plasma membrane of neurons plays a role in modulating the aggregation and toxicity of Alzheimer's amyloid-β peptide (Aβ). In this study, the combined and interdependent effects of oxidation and membrane interactions on the 42 residues long Aβ isoform are investigated using molecular simulations. Hamiltonian replica exchange molecular dynamics simulations are utilized to elucidate the impact of selected oxidized glycine residues of Aβ42 on the interactions of the peptide with a model membrane comprised of 70% POPC, 25% cholesterol, and 5% of the ganglioside GM1. The main findings are that, independent of the oxidation state, Aβ prefers binding to GM1 over POPC, which is further enhanced by the oxidation of Gly29 and Gly33 and reduced the formation of β-sheet. Our results suggest that the differences observed in Aβ42 conformations and its interaction with a lipid bilayer upon oxidation originate from the position of the oxidized Gly residue with respect to the hydrophobic sequence of Aβ42 involving the Gly29-XXX-Gly33-XXX-Gly37 motif and from specific interactions between the peptide and the terminal sugar groups of GM1.

Replica-Based Protein Structure Sampling Methods II: Advanced Hybrid Solvent TIGER2hs

In many cases, native states of proteins may be predicted with sufficient accuracy by molecular dynamics simulations (MDSs) with modern force fields. Enhanced sampling methods based on MDS are applied for exploring the phase space of a protein sequence and to overcome barriers on rough conformational energy landscapes. The minimum free energy state is obtained with sampling algorithms providing sufficient convergence and accuracy. A reliable but computationally very expensive method is replica exchange molecular dynamics, with many modifications to this approach presented in the past. Recently, we demonstrated how our temperature intervals with global exchange of replicas hybrid (TIGER2h) solvent sampling algorithm made a good compromise between efficiency and accuracy. There, all states are sampled under full explicit solvent conditions with a freely chosen number of replicas, whereas an implicit solvent is used during the swap decisions. This hybrid method yielded a much better approximation to the agreement with calculations in an explicit solvent than fully implicit solvent simulations. Here, we present an extension of TIGER2h and add a few layers of explicit water molecules around the peptide for the energy calculations, whereas the dynamics in fully explicit water is maintained. We claim that these water layers better reproduce steric effects, the polarization of the solvent, and the resulting reaction field energy than typical implicit solvent models. By investigating the protein-solvent interactions across comprehensive thermodynamic state ensembles, we found a strong conformational dependence of this reaction field energy. All simulations were performed with nanoscale molecular dynamics on two peptides, the α-helical peptide (AAQAA)₃ and the β-hairpin peptide HP7. A production-ready TIGER2hs implementation is supplied, approaching the accuracy of full explicit solvent sampling at a fraction of computational resources.

From glucose to enantiopure morpholino β-amino acid: a new tool for stabilizing γ-turns in peptides

“Environmentally sustainable” synthesis of a new enantiopure morpholino β-amino acid from glucose: a new tool for exotic peptide architectures.

Replica-Based Protein Structure Sampling Methods: Compromising between Explicit and Implicit Solvents

The structure of a protein is often not completely accessible by experiments. In silico, replica exchange molecular dynamics (REMD) is the standard sampling method for predicting the secondary and tertiary structures from the amino acid sequence, but it is computationally very expensive. Two recent adaptations from REMD, temperature intervals with global exchange of replicas (TIGER2) and TIGER2A, have been tested here in implicit and explicit solvents. Additionally, explicit, implicit, and hybrid solvent REMD are compared. On the basis of the hybrid REMD (REMDh) method, we present a new hybrid TIGER2h algorithm for faster structural sampling, while retaining good accuracy. The implementations of REMDh, TIGER2, TIGER2A, and TIGER2h are provided for nanoscale molecular dynamics (NAMD). All the methods were tested with two model peptides of known structure, (AAQAA)₃ and HP7, with helix and sheet motifs, respectively. The TIGER2 methods and REMDh were also applied to the unknown structure of the collagen type I telopeptides, which represent bigger proteins with some degree of disorder. We present simulations covering more than 180 μs and analyze the performance and convergence of the distributions of states between the particular methods by dihedral principal component and secondary structure analysis.

Replica exchange molecular dynamics study of the amyloid beta (11–40) trimer penetrating a membrane

The transmembrane Aβ_11–40 trimer is investigated for the first time using REMD and FEP.

Unconstrained Enhanced Sampling for Free Energy Calculations of Biomolecules: A Review

Free energy calculations are central to understanding the structure, dynamics and function of biomolecules. Yet insufficient sampling of biomolecular configurations is often regarded as one of the main sources of error. Many enhanced sampling techniques have been developed to address this issue. Notably, enhanced sampling methods based on biasing collective variables (CVs), including the widely used umbrella sampling, adaptive biasing force and metadynamics, have been discussed in a recent excellent review (Abrams and Bussi, Entropy, 2014). Here, we aim to review enhanced sampling methods that do not require predefined system-dependent CVs for biomolecular simulations and as such do not suffer from the hidden energy barrier problem as encountered in the CV-biasing methods. These methods include, but are not limited to, replica exchange/parallel tempering, self-guided molecular/Langevin dynamics, essential energy space random walk and accelerated molecular dynamics. While it is overwhelming to describe all details of each method, we provide a summary of the methods along with the applications and offer our perspectives. We conclude with challenges and prospects of the unconstrained enhanced sampling methods for accurate biomolecular free energy calculations.

Current state of theoretical and experimental studies of the voltage-dependent anion channel (VDAC)

Voltage-dependent anion channel (VDAC), the major channel of the mitochondrial outer membrane provides a controlled pathway for respiratory metabolites in and out of the mitochondria. In spite of the wealth of experimental data from structural, biochemical, and biophysical investigations, the exact mechanisms governing selective ion and metabolite transport, especially the role of titratable charged residues and interactions with soluble cytosolic proteins, remain hotly debated in the field. The computational advances hold a promise to provide a much sought-after solution to many of the scientific disputes around solute and ion transport through VDAC and hence, across the mitochondrial outer membrane. In this review, we examine how Molecular Dynamics, Free Energy, and Brownian Dynamics simulations of the large β-barrel channel, VDAC, advanced our understanding. We will provide a short overview of non-conventional techniques and also discuss examples of how the modeling excursions into VDAC biophysics prospectively aid experimental efforts. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.