Dimensionality of Collective Variables for Describing Conformational Changes of a Multi-Domain Protein

GENESIS 2.1: High-Performance Molecular Dynamics Software for Enhanced Sampling and Free-Energy Calculations for Atomistic, Coarse-Grained, and Quantum Mechanics/Molecular Mechanics Models

GENeralized-Ensemble SImulation System (GENESIS) is a molecular dynamics (MD) software developed to simulate the conformational dynamics of a single biomolecule, as well as molecular interactions in large biomolecular assemblies and between multiple biomolecules in cellular environments. To achieve the latter purpose, the earlier versions of GENESIS emphasized high performance in atomistic MD simulations on massively parallel supercomputers, with or without graphics processing units (GPUs). Here, we implemented multiscale MD simulations that include atomistic, coarse-grained, and hybrid quantum mechanics/molecular mechanics (QM/MM) calculations. They demonstrate high performance and are integrated with enhanced conformational sampling algorithms and free-energy calculations without using external programs except for the QM programs. In this article, we review new functions, molecular models, and other essential features in GENESIS version 2.1 and discuss ongoing developments for future releases.

Computational Analysis of Activation of Dimerized Epidermal Growth Factor Receptor Kinase Using the String Method and Markov State Model

Epidermal growth factor receptor (EGFR) activation is accompanied by dimerization. During the activation of the intracellular kinase domain, two EGFR kinases form an asymmetric dimer, and one side of the dimer (receiver) is activated. Using the string method and Markov state model (MSM), we performed a computational analysis of the structural changes in the activation of the EGFR dimer in this study. The string method reveals the minimum free-energy pathway (MFEP) from the inactive to active structure. The MSM was constructed from numerous trajectories of molecular dynamics simulations around the MFEP, which revealed the free-energy map of structural changes. In the activation of the receiver kinase, the unfolding of the activation loop (A-loop) is followed by the rearrangement of the C-helix, as observed in other kinases. However, unlike other kinases, the free-energy map of EGFR at the asymmetric dimer showed that the active state yielded the highest stability and revealed how interactions at the dimer interface induced receiver activation. As the H-helix of the activator approaches the C-helix of the receiver during activation, the A-loop unfolds. Subsequently, L782 of the receiver enters the pocket between the G- and H-helices of the activator, leading to a rearrangement of the hydrophobic residues around L782 of the receiver, which constitutes a structural rearrangement of the C-helix of the receiver from an outward to an inner position. The MSM analysis revealed long-time scale trajectories via kinetic Monte Carlo.

Surface-Accelerated String Method for Locating Minimum Free Energy Paths

We present a surface-accelerated string method (SASM) to efficiently optimize low-dimensional reaction pathways from the sampling performed with expensive quantum mechanical/molecular mechanical (QM/MM) Hamiltonians. The SASM accelerates the convergence of the path using the aggregate sampling obtained from the current and previous string iterations, whereas approaches like the string method in collective variables (SMCV) or the modified string method in collective variables (MSMCV) update the path only from the sampling obtained from the current iteration. Furthermore, the SASM decouples the number of images used to perform sampling from the number of synthetic images used to represent the path. The path is optimized on the current best estimate of the free energy surface obtained from all available sampling, and the proposed set of new simulations is not restricted to being located along the optimized path. Instead, the umbrella potential placement is chosen to extend the range of the free energy surface and improve the quality of the free energy estimates near the path. In this manner, the SASM is shown to improve the exploration for a minimum free energy pathway in regions where the free energy surface is relatively flat. Furthermore, it improves the quality of the free energy profile when the string is discretized with too few images. We compare the SASM, SMCV, and MSMCV using 3 QM/MM applications: a ribozyme methyltransferase reaction using 2 reaction coordinates, the 2'-O-transphosphorylation reaction of Hammerhead ribozyme using 3 reaction coordinates, and a tautomeric reaction in B-DNA using 5 reaction coordinates. We show that SASM converges the paths using roughly 3 times less sampling than the SMCV and MSMCV methods. All three algorithms have been implemented in the FE-ToolKit package made freely available.

Tackling Hysteresis in Conformational Sampling: How to Be Forgetful with MEMENTO

The structure of proteins has long been recognized to hold the key to understanding and engineering their function, and rapid advances in structural biology and protein structure prediction are now supplying researchers with an ever-increasing wealth of structural information. Most of the time, however, structures can only be determined in free energy minima, one at a time. While conformational flexibility may thus be inferred from static end-state structures, their interconversion mechanisms─a central ambition of structural biology─are often beyond the scope of direct experimentation. Given the dynamical nature of the processes in question, many studies have attempted to explore conformational transitions using molecular dynamics (MD). However, ensuring proper convergence and reversibility in the predicted transitions is extremely challenging. In particular, a commonly used technique to map out a path from a starting to a target conformation called steered MD (SMD) can suffer from starting-state dependence (hysteresis) when combined with techniques such as umbrella sampling (US) to compute the free energy profile of a transition. Here, we study this problem in detail on conformational changes of increasing complexity. We also present a new, history-independent approach that we term "MEMENTO" (Morphing End states by Modelling Ensembles with iNdependent TOpologies) to generate paths that alleviate hysteresis in the construction of conformational free energy profiles. MEMENTO utilizes template-based structure modelling to restore physically reasonable protein conformations based on coordinate interpolation (morphing) as an ensemble of plausible intermediates, from which a smooth path is picked. We compare SMD and MEMENTO on well-characterized test cases (the toy peptide deca-alanine and the enzyme adenylate kinase) before discussing its use in more complicated systems (the kinase P38α and the bacterial leucine transporter LeuT). Our work shows that for all but the simplest systems SMD paths should not in general be used to seed umbrella sampling or related techniques, unless the paths are validated by consistent results from biased runs in opposite directions. MEMENTO, on the other hand, performs well as a flexible tool to generate intermediate structures for umbrella sampling. We also demonstrate that extended end-state sampling combined with MEMENTO can aid the discovery of collective variables on a case-by-case basis.

Peptide Dynamics and Metadynamics: Leveraging Enhanced Sampling Molecular Dynamics to Robustly Model Long-Timescale Transitions

Molecular dynamics simulations can in theory reveal the thermodynamics and kinetics of peptide conformational transitions at atomic-level resolution. However, even with modern computing power, they are limited in the timescales they can sample, which is especially problematic for peptides that are fully or partially disordered. Here, we discuss how the enhanced sampling methods accelerated molecular dynamics (aMD) and metadynamics can be leveraged in a complementary fashion to quickly explore conformational space and then robustly quantify the underlying free energy landscape. We apply these methods to two peptides that have an intrinsically disordered nature, the histone H3 and H4 N-terminal tails, and use metadynamics to compute the free energy landscape along collective variables discerned from aMD simulations. Results show that these peptides are largely disordered, with a slight preference for α-helical structures.

Structural and energetic analysis of metastable intermediate states in the E1P-E2P transition of Ca2+-ATPase

Ion pumps (or P-type ATPases) are membrane proteins, which transport ions through biological membranes against a concentration gradient, a function essential for many biological processes, such as muscle contraction, neurotransmission, and metabolism. Molecular mechanisms underlying active ion transport by ion pumps have been investigated by biochemical experiments and high-resolution structure analyses. Here, the transition of sarcoplasmic reticulum Ca²⁺-ATPase upon dissociation of Ca²⁺ is investigated using atomistic molecular dynamics simulations. We find intermediate structures along the pathway are stabilized by transient interactions between A- and P-domains as well as lipid molecules in the transmembrane helices.

Sarcoplasmic reticulum (SR) Ca²⁺-ATPase transports two Ca²⁺ ions from the cytoplasm to the SR lumen against a large concentration gradient. X-ray crystallography has revealed the atomic structures of the protein before and after the dissociation of Ca²⁺, while biochemical studies have suggested the existence of intermediate states in the transition between E1P⋅ADP⋅2Ca²⁺ and E2P. Here, we explore the pathway and free energy profile of the transition using atomistic molecular dynamics simulations with the mean-force string method and umbrella sampling. The simulations suggest that a series of structural changes accompany the ordered dissociation of ADP, the A-domain rotation, and the rearrangement of the transmembrane (TM) helices. The luminal gate then opens to release Ca²⁺ ions toward the SR lumen. Intermediate structures on the pathway are stabilized by transient sidechain interactions between the A- and P-domains. Lipid molecules between TM helices play a key role in the stabilization. Free energy profiles of the transition assuming different protonation states suggest rapid exchanges between Ca²⁺ ions and protons when the Ca²⁺ ions are released toward the SR lumen.

Exploring the Minimum-Energy Pathways and Free-Energy Profiles of Enzymatic Reactions with QM/MM Calculations

Understanding molecular mechanisms of enzymatic reactions is of vital importance in biochemistry and biophysics. Here, we introduce new functions of hybrid quantum mechanical/molecular mechanical (QM/MM) calculations in the GENESIS program to compute the minimum-energy pathways (MEPs) and free-energy profiles of enzymatic reactions. For this purpose, an interface in GENESIS is developed to utilize a highly parallel electronic structure program, QSimulate-QM (https://qsimulate.com), calling it as a shared library from GENESIS. Second, algorithms to search the MEP are implemented, combining the string method (E et al. J. Chem. Phys. 2007, 126, 164103) with the energy minimization of the buffer MM region. The method implemented in GENESIS is applied to an enzyme, triosephosphate isomerase, which converts dihyroxyacetone phosphate to glyceraldehyde 3-phosphate in four proton-transfer processes. QM/MM-molecular dynamics simulations show performances of greater than 1 ns/day with the density functional tight binding (DFTB), and 10-30 ps/day with the hybrid density functional theory, B3LYP-D3. These performances allow us to compute not only MEP but also the potential of mean force (PMF) of the enzymatic reactions using the QM/MM calculations. The barrier height obtained as 13 kcal mol-1 with B3LYP-D3 in the QM/MM calculation is in agreement with the experimental results. The impact of conformational sampling in PMF calculations and the level of electronic structure calculations (DFTB vs B3LYP-D3) suggests reliable computational protocols for enzymatic reactions without high computational costs.

Coarse-Grained Modeling of Multiple Pathways in Conformational Transitions of Multi-Domain Proteins

Large-scale conformational transitions in multi-domain proteins are often essential for their functions. To investigate the transitions, it is necessary to explore multiple potential pathways, which involve different intermediate structures. Here, we present a multi-basin (MB) coarse-grained (CG) structure-based Go̅ model for describing transitions in proteins with more than two moving domains. This model is an extension of our dual-basin Go̅ model in which system-dependent parameters are determined systematically using the multistate Bennett acceptance ratio method. In the MB Go̅ model for multi-domain proteins, we assume that intermediate structures may have partial inter-domain native contacts. This approach allows us to search multiple transition pathways that involve distinct intermediate structures using the CG molecular dynamics (MD) simulations. We apply this scheme to an enzyme, adenylate kinase (AdK), which has three major domains and can move along two different pathways. Using the optimized mixing parameters for each pathway, AdK shows frequent transitions between the Open, Closed, and the intermediate basins and samples a wide variety of conformations within each basin. The explored multiple transition pathways could be compared with experimental data and examined in more detail by atomistic MD simulations.

Increasing the Sampling Efficiency of Protein Conformational Change by Combining a Modified Replica Exchange Molecular Dynamics and Normal Mode Analysis

Understanding conformational change at an atomic level is significant when determining a protein functional mechanism. Replica exchange molecular dynamics (REMD) is a widely used enhanced sampling method to explore protein conformational space. However, REMD with an explicit solvent model requires huge computational resources, immensely limiting its application. In this study, a variation of parallel tempering metadynamics (PTMetaD) with the omission of solvent-solvent interactions in exchange attempts and the use of low-frequency modes calculated by normal-mode analysis (NMA) as collective variables (CVs), namely ossPTMetaD, is proposed with the aim to accelerate MD simulations simultaneously in temperature and geometrical spaces. For testing the performance of ossPTMetaD, five protein systems with diverse biological functions and motion patterns were selected, including large-scale domain motion (AdK), flap movement (HIV-1 protease and BACE1), and DFG-motif flip in kinases (p38α and c-Abl). The simulation results showed that ossPTMetaD requires much fewer numbers of replicas than temperature REMD (T-REMD) with a reduction of ∼70% to achieve a similar exchange ratio. Although it does not obey the detailed balance condition, ossPTMetaD provides consistent results with T-REMD and experimental data. The high accessibility of the large conformational change of protein systems by ossPTMetaD, especially in simulating the very challenging DFG-motif flip of protein kinases, demonstrated its high efficiency and robustness in the characterization of the large-scale protein conformational change pathway and associated free energy profile.

Free Energy Analysis of a Conformational Change of Heme ABC Transporter BhuUV-T

The heme ATP-binding cassette (ABC) transporter BhuUV-T of bacterial pathogen Burkholderia cenocepacia is required to transport heme across the inner cell membrane. The current hypothesis is that the binding of two ATPs to the nucleotide-binding domains of the transporter drives the initial steps of the transport cycle in which the empty transport sites are reoriented from the cytosol to the periplasm. Molecular details are missing because the structure of a key occluded intermediate remains hypothetical. Here we perform molecular simulations to analyze the free energy surface (FES) of the first step of the reorientation, namely the transition from an open inward-facing (IF) transport site to an occluded (Occ) conformation. We have modeled the latter structure in silico in a previous study. A simple annealing procedure removes residual bias originating from non-equilibrium targeted molecular dynamics. The calculated FES reveals the role of the ATPs in inducing the IF → Occ conformational change and validates the modeled Occ conformation.

Exploring Conformational Change of Adenylate Kinase by Replica Exchange Molecular Dynamic Simulation

Replica exchange molecular dynamics (REMD) simulation is a popular enhanced sampling method that is widely used for exploring the atomic mechanism of protein conformational change. However, the requirement of huge computational resources for REMD, especially with the explicit solvent model, largely limits its application. In this study, the availability and efficiency of a variant of velocity-scaling REMD (vsREMD) was assessed with adenylate kinase as an example. Although vsREMD achieved results consistent with those from conventional REMD and experimental studies, the number of replicas required for vsREMD (30) was much less than that for conventional REMD (80) to achieve a similar acceptance rate (∼0.2), demonstrating high efficiency of vsREMD to characterize the protein conformational change and associated free-energy profile. Thus, vsREMD is a highly efficient approach for studying the large-scale conformational change of protein systems.

Large-Scale Biomolecular Conformational Transitions Explored by a Combined Elastic Network Model and Enhanced Sampling Molecular Dynamics

Biomolecules often undergo large-scale conformational transitions when carrying out their functions. However, it is still challenging for conventional molecular dynamics simulations to provide adequate structural dynamics information to interpret associated mechanisms. Here, we present a combined elastic network model and enhanced sampling-based strategy (iterANM-IaMD) by adopting iterANM to construct initial conformation space and enhanced sampling IaMD to explore the free energy landscape along specific large-scale conformational transitions. We applied this strategy to three functionally and structurally distinct proteins (adenylate kinase, calmodulin, and p38α kinase), which undergo striking conformational change upon ligand binding. The simulation results for both free and ligand-bound proteins show qualitative and quantitative agreement with existing studies, suggesting iterANM-IaMD as an accurate and efficient tool to investigate structural dynamics involved in complicated biological processes. Our work also provides insights into the relationship between the dynamics and functionality of biomolecules.

Molecular recognition of ubiquitin and Lys63-linked diubiquitin by STAM2 UIM-SH3 dual domain: the effect of its linker length and flexibility

Multidomain proteins represent a broad spectrum of the protein landscape and are involved in various interactions. They could be considered as modular building blocks assembled in distinct fashion and connected by linkers of varying lengths and sequences. Due to their intrinsic flexibility, these linkers provide proteins a subtle way to modulate interactions and explore a wide range of conformational space. In the present study, we are seeking to understand the effect of the flexibility and dynamics of the linker involved in the STAM2 UIM-SH3 dual domain protein with respect to molecular recognition. We have engineered several constructs of UIM-SH3 with different length linkers or domain deletion. By means of SAXS and NMR experiments, we have shown that the modification of the linker modifies the flexibility and the dynamics of UIM-SH3. Indeed, the global tumbling of both the UIM and SH3 domain is different but not independent from each other while the length of the linker has an impact on the ps-ns time scale dynamics of the respective domains. Finally, the modification of the flexibility and dynamics of the linker has a drastic effect on the interaction of UIM-SH3 with Lys63-linked diubiquitin with a roughly eight-time weaker dissociation constant.

Replica-Exchange Umbrella Sampling Combined with Gaussian Accelerated Molecular Dynamics for Free-Energy Calculation of Biomolecules

We have developed an enhanced conformational sampling method combining replica-exchange umbrella sampling (REUS) with Gaussian accelerated molecular dynamics (GaMD). REUS enhances the sampling along predefined reaction coordinates, while GaMD accelerates the conformational dynamics by adding a boost potential to the system energy. The method, which we call GaREUS (Gaussian accelerated replica-exchange umbrella sampling), enhances the sampling more efficiently than REUS or GaMD, while the computational resource for GaREUS is the same as that required for REUS. The two-step reweighting procedure using the multistate Bennett acceptance ratio method and the cumulant expansion for the exponential average is applied to the simulation trajectories for obtaining the unbiased free-energy landscapes. We apply GaREUS to the calculations of free-energy landscapes for three different cases: conformational equilibria of N-glycan, folding of chignolin, and conformational change of adenyl kinase. We show that GaREUS speeds up the convergences of free-energy calculations using the same amount of computational resources as REUS. The free-energy landscapes reweighted from the trajectories of GaREUS agree with previously reported ones. GaREUS is applicable to free-energy calculations of various biomolecular dynamics and functions with reasonable computational costs.

Replica-Exchange Methods for Biomolecular Simulations

In this study, a replica-exchange method was developed to overcome conformational sampling difficulties in computer simulations of spin glass or other systems with rugged free-energy landscapes. This method was then applied to the protein-folding problem in combination with molecular dynamics (MD) simulation. Owing to its simplicity and sampling efficiency, the replica-exchange method has been applied to many other biological problems and has been continuously improved. The method has often been combined with other sampling techniques, such as umbrella sampling, free-energy perturbation, metadynamics, and Gaussian accelerated MD (GaMD). In this chapter, we first summarize the original replica-exchange molecular dynamics (REMD) method and discuss how new algorithms related to the original method are implemented to add new features. Heterogeneous and flexible structures of an N-glycan in a solution are simulated as an example of applications by REMD, replica exchange with solute tempering, and GaMD. The sampling efficiency of these methods on the N-glycan system and the convergence of the free-energy changes are compared. REMD simulation protocols and trajectory analysis using the GENESIS software are provided to facilitate the practical use of advanced simulation methods.

Exploring Configuration Space and Path Space of Biomolecules Using Enhanced Sampling Techniques-Searching for Mechanism and Kinetics of Biomolecular Functions

To understand functions of biomolecules such as proteins, not only structures but their conformational change and kinetics need to be characterized, but its atomistic details are hard to obtain both experimentally and computationally. Here, we review our recent computational studies using novel enhanced sampling techniques for conformational sampling of biomolecules and calculations of their kinetics. For efficiently characterizing the free energy landscape of a biomolecule, we introduce the multiscale enhanced sampling method, which uses a combined system of atomistic and coarse-grained models. Based on the idea of Hamiltonian replica exchange, we can recover the statistical properties of the atomistic model without any biases. We next introduce the string method as a path search method to calculate the minimum free energy pathways along a multidimensional curve in high dimensional space. Finally we introduce novel methods to calculate kinetics of biomolecules based on the ideas of path sampling: one is the Onsager⁻Machlup action method, and the other is the weighted ensemble method. Some applications of the above methods to biomolecular systems are also discussed and illustrated.

Role of Extracellular Loops and Membrane Lipids for Ligand Recognition in the Neuronal Adenosine Receptor Type 2A: An Enhanced Sampling Simulation Study

Human G-protein coupled receptors (GPCRs) are important targets for pharmaceutical intervention against neurological diseases. Here, we use molecular simulation to investigate the key step in ligand recognition governed by the extracellular domains in the neuronal adenosine receptor type 2A (hA_2AR), a target for neuroprotective compounds. The ligand is the high-affinity antagonist (4-(2-(7-amino-2-(furan-2-yl)-[1,2,4]triazolo[1,5-a][1,3,5]triazin-5-ylamino)ethyl)phenol), embedded in a neuronal membrane mimic environment. Free energy calculations, based on well-tempered metadynamics, reproduce the experimentally measured binding affinity. The results are consistent with the available mutagenesis studies. The calculations identify a vestibular binding site, where lipids molecules can actively participate to stabilize ligand binding. Bioinformatic analyses suggest that such vestibular binding site and, in particular, the second extracellular loop, might drive the ligand toward the orthosteric binding pocket, possibly by allosteric modulation. Taken together, these findings point to a fundamental role of the interaction between extracellular loops and membrane lipids for ligands’ molecular recognition and ligand design in hA_2AR.

Scaling oscillatory platform frequency reveals recurrence of intermittent postural attractor states

The study of postural control has been dominated by experiments on the maintenance of quiet upright standing balance on flat stationary support surfaces that reveal only limited modes of potential configurations of balance stability/instability. Here we examine the self-organization properties of postural coordination as revealed in a dynamic balance task with a moving platform. We scaled a control parameter (platform frequency) to investigate the evolving nature of the coupled oscillator dynamics between center of mass (CoM) and platform. Recurrent map measures were used to reveal whether episodic postural control strategies exist that can be scaled by systematically changing the magnitude of platform motion. The findings showed that at higher platform frequencies (1.2 Hz), the CoM-Platform coupling was less deterministic than lower platform frequencies and evolved to intermittent postural control strategies that oscillated between periodic-chaotic transitions to maintain upright postural balance. Collectively, the recurrence map measures indicated that quasi-static postural attractor states were progressively emerging to the changing task constraints of platform frequency in the maintenance of postural stability. It appears that several dynamic modes of intermittent coupling in postural control can interchangeably co-exist and are expressed as a function of the control parameter of platform frequency.

Energetics and conformational pathways of functional rotation in the multidrug transporter AcrB

The multidrug transporter AcrB transports a broad range of drugs out of the cell by means of the proton-motive force. The asymmetric crystal structure of trimeric AcrB suggests a functionally rotating mechanism for drug transport. Despite various supportive forms of evidence from biochemical and simulation studies for this mechanism, the link between the functional rotation and proton translocation across the membrane remains elusive. Here, calculating the minimum free energy pathway of the functional rotation for the complete AcrB trimer, we describe the structural and energetic basis behind the coupling between the functional rotation and the proton translocation at atomic resolution. Free energy calculations show that protonation of Asp408 in the transmembrane portion of the drug-bound protomer drives the functional rotation. The conformational pathway identifies vertical shear motions among several transmembrane helices, which regulate alternate access of water in the transmembrane as well as peristaltic motions that pump drugs in the periplasm.

GENESIS 1.1: A hybrid-parallel molecular dynamics simulator with enhanced sampling algorithms on multiple computational platforms

GENeralized-Ensemble SImulation System (GENESIS) is a software package for molecular dynamics (MD) simulation of biological systems. It is designed to extend limitations in system size and accessible time scale by adopting highly parallelized schemes and enhanced conformational sampling algorithms. In this new version, GENESIS 1.1, new functions and advanced algorithms have been added. The all-atom and coarse-grained potential energy functions used in AMBER and GROMACS packages now become available in addition to CHARMM energy functions. The performance of MD simulations has been greatly improved by further optimization, multiple time-step integration, and hybrid (CPU + GPU) computing. The string method and replica-exchange umbrella sampling with flexible collective variable choice are used for finding the minimum free-energy pathway and obtaining free-energy profiles for conformational changes of a macromolecule. These new features increase the usefulness and power of GENESIS for modeling and simulation in biological research. © 2017 Wiley Periodicals, Inc.

Rich Dynamics Underlying Solution Reactions Revealed by Sampling and Data Mining of Reactive Trajectories

Efficient sampling in both configuration and trajectory spaces, combined with mechanism analyses via data mining, allows a systematic investigation of the thermodynamics, kinetics, and molecular-detailed dynamics of chemical reactions in solution. Through a Bayesian learning algorithm, the reaction coordinate(s) of a (retro-)Claisen rearrangement in bulk water was variationally optimized. The bond formation/breakage was found to couple with intramolecular charge separation and dipole change, and significant dynamic solvent effects manifest, leading to the "in-water" acceleration of Claisen rearrangement. In addition, the vibrational modes of the reactant and the solvation states are significantly coupled to the reaction dynamics, leading to heterogeneous and oscillatory reaction paths. The calculated reaction rate is well interpreted by the Kramers' theory with a diffusion term accounting for solvent-solute interactions. These findings demonstrated that the reaction mechanisms can be complicated in homogeneous solutions since the solvent-solute interactions can profoundly influence the reaction dynamics and the energy transfer process.

Neural Network and Nearest Neighbor Algorithms for Enhancing Sampling of Molecular Dynamics

The free energy calculations of complex chemical and biological systems with molecular dynamics (MD) are inefficient due to multiple local minima separated by high-energy barriers. The minima can be escaped using an enhanced sampling method such as metadynamics, which apply bias (i.e., importance sampling) along a set of collective variables (CV), but the maximum number of CVs (or dimensions) is severely limited. We propose a high-dimensional bias potential method (NN2B) based on two machine learning algorithms: the nearest neighbor density estimator (NNDE) and the artificial neural network (ANN) for the bias potential approximation. The bias potential is constructed iteratively from short biased MD simulations accounting for correlation among CVs. Our method is capable of achieving ergodic sampling and calculating free energy of polypeptides with up to 8-dimensional bias potential.

Acidity Constant (pKa ) Calculation of Large Solvated Dye Molecules: Evaluation of Two Advanced Molecular Dynamics Methods

pH‐Sensitive dyes are increasingly applied on polymer substrates for the creation of novel sensor materials. Recently, these dye molecules were modified to form a covalent bond with the polymer host. This had a large influence on the pH‐sensitive properties, in particular on the acidity constant (pK_a). Obtaining molecular control over the factors that influence the pK_a value is mandatory for the future intelligent design of sensor materials. Herein, we show that advanced molecular dynamics (MD) methods have reached the level at which the pK_a values of large solvated dye molecules can be predicted with high accuracy. Two MD methods were used in this work: steered or restrained MD and the insertion/deletion scheme. Both were first calibrated on a set of phenol derivatives and afterwards applied to the dye molecule bromothymol blue. Excellent agreement with experimental values was obtained, which opens perspectives for using these methods for designing dye molecules.

Enhanced conformational sampling technique provides an energy landscape view of large-scale protein conformational transitions

A novel in silico approach (NMA–ITS) is introduced to rapidly and effectively sample the configuration space and give quantitative data for exploring the conformational changes of proteins.