Reconstructing potential energy functions from simulated force-induced unbinding processes

Quantitative Prediction of Dissociation Rates of PYK2 Ligands Using Umbrella Sampling and Milestoning

We used umbrella sampling and the milestoning simulation method to study the dissociation of multiple ligands from protein kinase PYK2. The activation barriers obtained from the potential of mean force of the umbrella sampling simulations correlated well with the experimental dissociation rates. Using the zero-temperature string method, we obtained optimized paths along the free-energy surfaces for milestoning simulations of three ligands with a similar structure. The milestoning simulations gave an absolute dissociation rate within 2 orders of magnitude of the experimental value for two ligands but at least 3 orders of magnitude too high for the third. Despite the similarity in their structures, the ligands took different pathways to exit from the binding site of PYK2, making contact with different sets of residues. In addition, the protein experienced different conformational changes for dissociation of the three ligands.

Polymer mechanochemistry: from single molecule to bulk material

The field of polymer mechanochemistry has experienced a renaissance over the past decades, primarily propelled by the rapid development of force-sensitive molecular units (i.e., mechanophores) and principles governing the reactivity of polymer networks for mechanochemical transduction or material strengthening. In addition to fundamental guidelines for converting mechanical energy input into chemical output, there has also been increasing focus on engineering applications of polymer mechanochemistry for specific functions, mechanically adaptive material systems, and smart devices. These endeavors are made possible by multidisciplinary approaches involving the development of multifunctional mechanophores for mechanoresponsive polymer systems, mechanochemical catalysis and synthesis, three-dimensional (3D) printed mechanochromic materials, reasonable design of polymer network topology, and computational modeling. The aim of this minireview is to provide a summary of recent advancements in covalent polymer mechanochemistry. We specifically focus on productive mechanophores, mechanical remodeling of polymeric materials, and the development of theoretical concepts.

15 Years of molecular simulation of drug-binding kinetics

INTRODUCTION

Drug-binding kinetics has been increasingly recognized as an important factor to be considered in drug discovery. Long residence time could prolong the action of some drugs while produce toxicity on others. Early evaluation of the binding kinetics of drug candidates could reduce attrition rate late in the drug discovery process. Computational prediction of drug-binding kinetics is useful as compounds can be evaluated even before they are made. However, simulation of drug-binding kinetics is a challenging problem because of the long-time scale involved. Nevertheless, significant progress has been made.

AREAS COVERED

This review illustrates the rapid evolution of qualitative to quantitative molecular dynamics-based methods that have been developed over the last 15 years.

EXPERT OPINION

The development of new methods based on molecular dynamics simulations now enables computation of absolute association/dissociation rate constants. Cheaper methods capable of identifying candidates with fast or slow binding kinetics, or rank-ordering rate constants are also available. Together, these methods have generated useful insights into the molecular mechanisms of drug-binding kinetics, and the design of drug candidates with therapeutically favorable kinetics. Although predicting absolute rate constants is still expensive and challenging, rapid improvement is expected in the coming years with the continuing refinement of current technologies, development of new methodologies, and the utilization of machine learning.

MPED: Quantifying Point Cloud Distortion Based on Multiscale Potential Energy Discrepancy

In this article, we propose a new distortion quantification method for point clouds, the multiscale potential energy discrepancy (MPED). Currently, there is a lack of effective distortion quantification for a variety of point cloud perception tasks. Specifically, in human vision tasks, a distortion quantification method is used to predict human subjective scores and optimize the selection of human perception task parameters, such as dense point cloud compression and enhancement. In machine vision tasks, a distortion quantification method usually serves as loss function to guide the training of deep neural networks for unsupervised learning tasks (e.g., sparse point cloud reconstruction, completion, and upsampling). Therefore, an effective distortion quantification should be differentiable, distortion discriminable, and have low computational complexity. However, current distortion quantification cannot satisfy all three conditions. To fill this gap, we propose a new point cloud feature description method, the point potential energy (PPE), inspired by classical physics. We regard the point clouds are systems that have potential energy and the distortion can change the total potential energy. By evaluating various neighborhood sizes, the proposed MPED achieves global-local tradeoffs, capturing distortion in a multiscale fashion. We further theoretically show that classical Chamfer distance is a special case of our MPED. Extensive experiments show that the proposed MPED is superior to current methods on both human and machine perception tasks. Our code is available at https://github.com/Qi-Yangsjtu/MPED.

Seeding the multi-dimensional nonequilibrium pulling for Hamiltonian variation: indirect nonequilibrium free energy simulations at QM levels

The combination of free energy simulations in the alchemical and configurational spaces provides a feasible route to access the thermodynamic profiles under a computationally demanding target Hamiltonian. Normally, due to the significant differences between the computational cost of ab initio quantum mechanics (QM) calculations and those of semi-empirical quantum mechanics (SQM) and molecular mechanics (MM), this indirect method could be used to obtain the QM thermodynamics by combining the SQM or MM results and the SQM-to-QM or MM-to-QM corrections. In our previous work, a multi-dimensional nonequilibrium pulling framework for Hamiltonian variations was introduced based on bidirectional pulling and bidirectional reweighting. The method performs nonequilibrium free energy simulations in the configurational space to obtain the thermodynamic profile along the conformational change pathway under a selected computationally efficient Hamiltonian, and uses the nonequilibrium alchemical method to correct or perturb the thermodynamic profile to that under the target Hamiltonian. The BAR-based method is designed to achieve the best generality and transferability and thus leads to modest (∼20 fold) speedup. In this work, we explore the possibility of further accelerating the nonequilibrium free energy simulation by employing unidirectional pulling and using the selection criterion to obtain the initial configurations used to initiate nonequilibrium trajectories following the idea of adaptive steered molecular dynamics (ASMD). A single initial condition is used to seed the whole multi-dimensional nonequilibrium free energy simulation and the sampling is performed fully in the nonequilibrium ensemble. Introducing very short ps-length equilibrium sampling to grab more initial seeds could also be helpful. The ASMD scheme estimates the free energy difference with the unidirectional exponential average (EXP), but it does not follow exactly the requirements of the EXP estimator. Another deficiency of the seeding simulation is the inherently sequential or serial pulling due to the inter-segment dependency, which triggers some problems in the parallelizability of the simulation. Numerical tests are performed to grasp some insights and guidelines for using this selection-criterion-based ASMD scheme. The presented selection-criterion-based multi-dimensional ASMD scheme follows the same perturbation network of the BAR-based method, and thus could be used in various Hamiltonian-variation cases.

Simulation of protein pulling dynamics on second time scale with boxed molecular dynamics

We demonstrate how recently developed Boxed Molecular Dynamics (BXD) and kinetics [D. V. Shalashilin et al., J. Chem. Phys. 137, 165102 (2012)] can provide a kinetic description of protein pulling experiments, allowing for a connection to be made between experiment and the atomistic protein structure. BXD theory applied to atomic force microscopy unfolding is similar in spirit to the kinetic two-state model [A. Noy and R. W. Friddle, Methods 60, 142 (2013)] but with some differences. First, BXD uses a large number of boxes, and therefore, it is not a two-state model. Second, BXD rate coefficients are obtained from atomistic molecular dynamics simulations. BXD can describe the dependence of the pulling force on pulling speed. Similar to Shalashilin et al. [J. Chem. Phys. 137, 165102 (2012)], we show that BXD is able to model the experiment at a very long time scale up to seconds, which is way out of reach for standard molecular dynamics.

Boron rich nanotube drug carrier system is suited for boron neutron capture therapy

Boron neutron capture therapy (BNCT) is a two-step therapeutic process that utilizes Boron-10 in combination with low energy neutrons to effectively eliminate targeted cells. This therapy is primarily used for difficult to treat head and neck carcinomas; recent advances have expanded this method to cover a broader range of carcinomas. However, it still remains an unconventional therapy where one of the barriers for widespread adoption is the adequate delivery of Boron-10 to target cells. In an effort to address this issue, we examined a unique nanoparticle drug delivery system based on a highly stable and modular proteinaceous nanotube. Initially, we confirmed and structurally analyzed ortho-carborane binding into the cavities of the nanotube. The high ratio of Boron to proteinaceous mass and excellent thermal stability suggest the nanotube system as a suitable candidate for drug delivery into cancer cells. The full physicochemical characterization of the nanotube then allowed for further mechanistic molecular dynamic studies of the ortho-carborane uptake and calculations of corresponding energy profiles. Visualization of the binding event highlighted the protein dynamics and the importance of the interhelical channel formation to allow movement of the boron cluster into the nanotube. Additionally, cell assays showed that the nanotube can penetrate outer membranes of cancer cells followed by localization around the cells' nuclei. This work uses an integrative approach combining experimental data from structural, molecular dynamics simulations and biological experiments to thoroughly present an alternative drug delivery device for BNCT which offers additional benefits over current delivery methods.

Molecular dynamics simulations of ortho-carborane nano-diamond storage within the nonpolar channel cavities of a right-handed coiled-coil tetrabrachion nanotube

Molecular dynamics simulations have been performed on a complex in which clusters of boron in the form of molecules of the nanodiamond ortho-carborane ( C 2 B 10 H 12 ) have been inserted into the four large nonpolar cavities of a nanotube of the right-handed coiled-coil ( R H C C ) t e t r a b r a c h i o n . The techniques of multi-configurational thermodynamic integration, steered molecular dynamics and umbrella sampling have been combined to investigate the energetics of storage of ortho-carborane in the cavities and to map out the free energy landscape of the RHCC - t e t r a b r a c h i o n - o r t h o - c a r b o r a n e complex along the central channel and along directions transverse to the central channel. The purpose of the study was to explore potential pathways for the diffusion of ortho-carborane between the cavities and the solvent and to assess the stability of the complex as a possible drug delivery system for boron neutron capture therapy (BNCT). The investigation reveals a complex free energy landscape with a multitude of peaks and valleys, all of which can be related to specific architectural elements of the RHCC - n a n o t u b e , and the activation barriers for ortho-carborane capture and release support the requirements for rapid cargo uptake coupled with tight binding to the cavities.

Analytical Method Using a Scaled Hypersphere Search for High-Dimensional Metadynamics Simulations

Metadynamics (MTD) is one of the most effective methods for calculating the free energy surface and finding rare events. Nevertheless, numerous studies using MTD have been carried out using 3D or lower dimensional collective variables (CVs), as higher dimensional CVs require costly computational resources and the obtained results are too complex to understand the important events. The latter issue can be conveniently solved by utilizing the free energy reaction network (FERN), which is a graph structure consisting of edges of minimum free energy paths (MFEPs), nodes of equation (EQ) points, and transition state (TS) points. In the present article, a new method for exploring FERNs on high-dimensional CVs using MTD and the scaled hypersphere search (SHS) method is described. A test calculation based on the MTD-SHS simulation of met-enkephalin in explicit water with 7 CVs was conducted. As a result, 889 EQ points and 1805 TS points were found. The MTD-SHS approach can find MFEPs exhaustively; therefore, the FERNs can be estimated without any a priori knowledge of the EQ and TS points.

BAR-based multi-dimensional nonequilibrium pulling for indirect construction of QM/MM free energy landscapes: from semi-empirical to ab initio

The indirect method for the construction of quantum mechanics (QM)/molecular mechanics (MM) free energy landscapes provides a cheaper alternative for free energy simulations at the QM level. The indirect method features a direct calculation of the free energy profile with a computationally efficient but less accurate Hamiltonian (i.e. low-level Hamiltonian) and a low-level-to-high-level correction. In the thermodynamic cycle, the direct low-level calculation along the physically meaningful reaction coordinate is corrected via the alchemical method, which is often achieved with perturbation-based techniques. In our previous work, a multi-dimensional nonequilibrium pulling framework is proposed for the indirect construction of QM/MM free energy landscapes. Previously, we focused on obtaining semi-empirical QM (SQM) results indirectly from direct MM simulations and MM to SQM corrections. In this work, we apply this method to obtain results under ab initio QM Hamiltonians by combining direct SQM results and SQM to QM corrections. A series of SQM and QM Hamiltonians are benchmarked. It is observed that PM6 achieves the best performance among the low-level Hamiltonians. Therefore, we recommend using PM6 as the low-level theory in the indirect free energy simulation. Considering its higher similarity to the high-level Hamiltonians, PM6 corrected with the bond charge correction could be more accurate than the existing AM1-BCC model. Another central result in the current work is a basic protocol of choosing the strength of restraints and an appropriate time step in nonequilibrium free energy simulation at the stiff spring limit. We provide theoretical derivations to emphasize the importance of using a sufficiently large force constant and choosing an appropriate time step. It is worth noting that a general rule of thumb for choosing the time step, according to our derivation, is that a time step of 1 fs or smaller should be used, as long as the stiff spring approximation is employed, even in simulations with constraints on bonds involving hydrogen atoms.

Energetics of Storage and Diffusion of Water and Cyclo-Octasulfur for a Nonpolar Cavity of RHCC Tetrabrachion by Molecular Dynamics Simulations

Tetrabrachion forms the key component of the S-layer of Staphylothermus marinus. Molecular dynamics simulations have been used to study the energetics of occupancy of cavity 3 of the right-handed coiled-coil stalk of tetrabrachion by both water molecules and cyclooctasulfur S₈ crowns, as well as to determine possible pathways and free energy barriers for the diffusion of both water and cyclooctasulfur through the peptide walls of RHCC tetrabrachion between cavity 3 and bulk solvent. Calculations of the transfer free energy from solvent to cavity show that clusters of six, seven and eight water molecules are marginally stable in cavity 3, but that occupancy of the cavity by a cyclooctasulfur ring is favoured significantly over water clusters of all sizes. Thermal activation simulations at T = 400K revealed that water molecules diffusing through the wall pass through a sequence of metastable configurations where they are temporarily immobilized by forming networks of hydrogen bonds with specific wall residues. Calculations of the free energy of these metastable configurations using multi-configurational thermodynamic integration yielded a free energy profile with a principal free energy maximum ∆G~50 kJ/mol and a slight activation asymmetry in favour of the direction from cavity to solvent. Potential exit pathways for cyclooctasulfur were investigated with the methods of steered molecular dynamics and umbrella sampling. The cyclooctasulfur was steered through a gap in the tetrabrachion wall along a linear path from cavity 3 into the solvent and the resulting trajectory was subdivided into 22 sampling windows. The free energy profile created for the trajectory by umbrella sampling showed a sharp principal maximum as a function of the reaction coordinate with asymmetric free energy barriers ∆G_exit~220 kJ/mol and ∆G_entrance~100 kJ/mol for cavity exit and entrance, respectively.

Simulated (Un)Binding of Arachidonic Acid in the Cyclooxygenase site of Prostaglandin H2 Synthase-1

Molecular dynamics simulations with external forces are employed to study the unbinding and binding of arachidonic acid (AA) in the cyclooxygenase (COX) site of prostaglandin H2 synthase-1. Simulations with AA inside the COX binding channel reveal sequences of concerted bond rotations in the fatty acid alkyl chain which obviate the need for gross conformational changes in the protein and substrate during unbinding and binding. The all-cis structure of AA, with double bonds separated by two single bonds, facilitates easy access to the COX channel and correct positioning inside the active site for the COX chemistry to occur. Two derivatives of AA, one with a cis double bond changed to a trans configuration and the other with a double bond reduced to a single bond, are also studied. In both cases the concertedness of bond rotations in the fatty acid chain is diminished and larger forces are required to move the fatty acid inside the COX channel. Important motions of residues near the mouth of the COX channel are found and analyzed. In particular, a conformational “switch” involving Arg83, Glu524 and Arg120 is seen to mediate the movement of the substrate from the membrane to the channel.

Single-Molecule Force Spectroscopy: Experiments, Analysis, and Simulations

The mechanical properties of cells and of subcellular components are important to obtain a mechanistic molecular understanding of biological processes. The quantification of mechanical resistance of cells and biomolecules using biophysical methods matured thanks to the development of nanotechnologies such as optical and magnetic tweezers, the biomembrane force probe, and atomic force microscopy (AFM). The quantitative nature of force spectroscopy measurements has converted AFM into a valuable tool in biophysics. Force spectroscopy allows the determination of the forces required to unfold protein domains and to disrupt individual receptor/ligand bonds. Molecular simulations as a computational microscope allow investigation of similar biological processes with an atomistic detail. In this chapter, we first provide a step-by-step protocol of force spectroscopy experiments using AFM, including sample preparation, measurements, and analysis and interpretation of the resulting dynamic force spectrum in terms of available theories. Next, we present the background for molecular dynamics (MD) simulations focusing on steered molecular dynamics (SMD) and the importance of bridging computational tools with experimental techniques.

Mechanobiology: protein refolding under force

The application of direct force to a protein enables to probe wide regions of its energy surface through conformational transitions as unfolding, extending, recoiling, collapsing, and refolding. While unfolding under force typically displayed a two-state behavior, refolding under force, from highly extended unfolded states, displayed a more complex behavior. The first recording of protein refolding at a force quench step displayed an initial rapid elastic recoil, followed by a plateau phase at some extension, concluding with a collapse to a final state, at which refolding occurred. These findings stirred a lively discussion, which led to further experimental and theoretical investigation of this behavior. It was demonstrated that the polymeric chain of the unfolded protein is required to fully collapse to a globular conformation for the maturation of native structure. This behavior was modeled using one-dimensional free energy landscape over the end-to-end length reaction coordinate, the collective measured variable. However, at low forces, conformational space is not well captured by such models, and using two-dimensional energy surfaces provides further insight into the dynamics of this process. This work reviews the main concepts of protein refolding under constant force, which is essential for understanding how mechanotransducing proteins operate in vivo.

Perspective: Mechanochemistry of biological and synthetic molecules

Coupling of mechanical forces and chemical transformations is central to the biophysics of molecular machines, polymer chemistry, fracture mechanics, tribology, and other disciplines. As a consequence, the same physical principles and theoretical models should be applicable in all of those fields; in fact, similar models have been invoked (and often repeatedly reinvented) to describe, for example, cell adhesion, dry and wet friction, propagation of cracks, and action of molecular motors. This perspective offers a unified view of these phenomena, described in terms of chemical kinetics with rates of elementary steps that are force dependent. The central question is then to describe how the rate of a chemical transformation (and its other measurable properties such as the transition path) depends on the applied force. I will describe physical models used to answer this question and compare them with experimental measurements, which employ single-molecule force spectroscopy and which become increasingly common. Multidimensionality of the underlying molecular energy landscapes and the ensuing frequent misalignment between chemical and mechanical coordinates result in a number of distinct scenarios, each showing a nontrivial force dependence of the reaction rate. I will discuss these scenarios, their commonness (or its lack), and the prospects for their experimental validation. Finally, I will discuss open issues in the field.

Molecular Dynamics Simulation of Bismuth Telluride Exfoliation Mechanisms in Different Ionic Liquid Solvents

Bismuth telluride (Bi₂Te₃) is a well-known thermoelectric material with potential applications in several different emerging technologies. The bulk structure is composed of stacks of quintuple sheets (with weak interactions between neighboring sheets), and the performance of the material can be significantly enhanced if exfoliated into two-dimensional nanosheets. In this study, eight different imidazolium-based ionic liquids are evaluated as solvents for the exfoliation and dispersion of Bi₂Te₃ at temperatures ranging from 350 to 550 K. Three distinct exfoliation mechanisms are evaluated (pulling, shearing, and peeling) using steered molecular dynamics simulations, and we predict that the peeling mechanism is thermodynamically the most favorable route. Furthermore, the [Tf₂N^-]-based ionic liquids are particularly effective at enhancing the exfoliation, and this performance can be correlated to the unique molecular-level solvation structures developed at the Bi₂Te₃ surfaces. This information helps provide insight into the molecular origins of exfoliation and solvation involving Bi₂Te₃ (and possibly other layered chalcogenide materials) and ionic liquid solvents.

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.

Nanoscale Engineering of Designer Cellulosomes

Biocatalysts showcase the upper limit obtainable for high-speed molecular processing and transformation. Efforts to engineer functionality in synthetic nanostructured materials are guided by the increasing knowledge of evolving architectures, which enable controlled molecular motion and precise molecular recognition. The cellulosome is a biological nanomachine, which, as a fundamental component of the plant-digestion machinery from bacterial cells, has a key potential role in the successful development of environmentally-friendly processes to produce biofuels and fine chemicals from the breakdown of biomass waste. Here, the progress toward so-called "designer cellulosomes", which provide an elegant alternative to enzyme cocktails for lignocellulose breakdown, is reviewed. Particular attention is paid to rational design via computational modeling coupled with nanoscale characterization and engineering tools. Remaining challenges and potential routes to industrial application are put forward.

Bayesian Uncertainty Quantification for Bond Energies and Mobilities Using Path Integral Analysis

Dynamic single-molecule force spectroscopy is often used to distort bonds. The resulting responses, in the form of rupture forces, work applied, and trajectories of displacements, are used to reconstruct bond potentials. Such approaches often rely on simple parameterizations of one-dimensional bond potentials, assumptions on equilibrium starting states, and/or large amounts of trajectory data. Parametric approaches typically fail at inferring complicated bond potentials with multiple minima, while piecewise estimation may not guarantee smooth results with the appropriate behavior at large distances. Existing techniques, particularly those based on work theorems, also do not address spatial variations in the diffusivity that may arise from spatially inhomogeneous coupling to other degrees of freedom in the macromolecule. To address these challenges, we develop a comprehensive empirical Bayesian approach that incorporates data and regularization terms directly into a path integral. All experimental and statistical parameters in our method are estimated directly from the data. Upon testing our method on simulated data, our regularized approach requires less data and allows simultaneous inference of both complex bond potentials and diffusivity profiles. Crucially, we show that the accuracy of the reconstructed bond potential is sensitive to the spatially varying diffusivity and accurate reconstruction can be expected only when both are simultaneously inferred. Moreover, after providing a means for self-consistently choosing regularization parameters from data, we derive posterior probability distributions, allowing for uncertainty quantification.

A comparison of four different conformations adopted by human telomeric G-quadruplex using computer simulations

The telomeric G-quadruplexes for their unique structural features are considered as potential anticancer drug targets. These, however, exhibit structural polymorphism as different topology types for the intra-molecular G-quadruplexes from human telomeric G-rich sequences have been reported based on NMR spectroscopy and X-ray crystallography. These techniques provide detailed atomic-level information about the molecule but relative conformational stability of the different topologies remains unsolved. Therefore, to understand the conformational preference, we have carried out quantum chemical calculations on G-quartets; used all-atom molecular dynamics (MD) simulations and steered molecular dynamics (SMD) simulations to characterize the four human telomeric G-quadruplex topologies based on its G-tetrad core-types, viz., parallel, anti-parallel, mixed-(3 + 1)-form1 and mixed-(3 + 1)-form2. We have also studied a non-telomeric sequence along with these telomeric forms giving a comparison between the two G-rich forms. The structural properties such as base pairing, stacking geometry and backbone conformations have been analyzed. The quantum calculations indicate that presence of a sodium ion inside the G-tetrad plane or two potassium ions on both sides of the plane give it an overall planarity which is much needed for good stacking to form a helix. MD simulations indicate that capping of the G-tetrad core by the TTA loops keep the terminal guanine bases away from water. The SMD simulations along with equilibrium MD studies indicate that the parallel and non-telomeric forms are comparatively less stable. We could come to the conclusion that the anti-parallel form and also the mixed-(3 + 1)-form1 topology are most likely to represent the major conformation., 2016. © 2015 Wiley Periodicals, Inc. Biopolymers 105: 83-99, 2016.

Communication: Does force spectroscopy of biomolecules probe their intrinsic dynamic properties?

In single-molecule pulling experiments, the molecule of interest is attached to a much larger object such as an atomic force microscope tip or a micrometer sized bead. The measured dynamics of molecular transitions is therefore affected by the hydrodynamic drag on the pulling instrument itself. By considering the transitions within the combined system (the molecule and the instrument), it is shown here that two distinct physical regimes exist: when the intrinsic stiffness of the molecule is greater than that of the linker connecting the molecule to the pulling setup then the pulling experiment probes the intrinsic dynamics of the molecule with only relatively small (and quantifiable) corrections resulting from the pulling setup. In contrast, when the stiffness of the linker exceeds that of the molecule, the molecular transition in question involves concerted motion of the molecule and the pulling setup and the hydrodynamic drag on the pulling instrument becomes the dominant source of friction along the molecular reaction coordinate. An analytical formula interpolating between these two cases is further derived. These results explain recent conflicting observations where some single-molecule pulling measurements report anomalously low diffusion coefficients along molecular reaction coordinates while others do not.

Estimation of the free energy of adsorption of a polypeptide on amorphous SiO2 from molecular dynamics simulations and force spectroscopy experiments

Estimating the free energy of adsorption of materials-binding peptides is fundamental to quantify their interactions across bio/inorganic interfaces, but is difficult to achieve both experimentally and theoretically. We employ a combination of molecular dynamics (MD) simulations and dynamical force-spectroscopy experiments based on atomic force microscopy (AFM) to estimate the free energy of adsorption ΔGads of a (GCRL) tetrapeptide on amorphous SiO2 in pure water. The results of both equilibrium, advanced sampling MD and non-equilibrium, steered MD are compared with those of two different approaches used to extract ΔGads from the dependence of experimentally measured adhesion forces on the applied AFM loading rates. In order to obtain unambiguous peak forces and bond loading rates from steered MD trajectories, we have developed a novel numerical protocol based on a piecewise-harmonic fit of the adhesion work profile along each trajectory. The interpretation of the experiments has required a thorough quantitative characterization of the elastic properties of polyethylene glycol linker molecules used to tether (GCRL)15 polypeptides to AFM cantilevers, and of the polypeptide itself. All obtained ΔGads values fall within a relatively narrow window between -5 and -9 kcal mol(-1), but can be associated with large relative error bars of more than 50%. Among the different approaches compared, Replica Exchange with Solute Tempering simulations augmented with MetaDynamics (RESTMetaD) and fitting of dynamic force spectroscopy experiments with the model of Friddle and De Yoreo lead to the most reliable ΔGads estimates.

Modeling, molecular dynamics, and docking assessment of transcription factor rho: a potential drug target in Brucella melitensis 16M

The zoonotic disease brucellosis, a chronic condition in humans affecting renal and cardiac systems and causing osteoarthritis, is caused by Brucella, a genus of Gram-negative, facultative, intracellular pathogens. The mode of transmission and the virulence of the pathogens are still enigmatic. Transcription regulatory elements, such as rho proteins, play an important role in the termination of transcription and/or the selection of genes in Brucella. Adverse effects of the transcription inhibitors play a key role in the non-successive transcription challenges faced by the pathogens. In the investigation presented here, we computationally predicted the transcription termination factor rho (TtFRho) inhibitors against Brucella melitensis 16M via a structure-based method. In view the unknown nature of its crystal structure, we constructed a robust three-dimensional homology model of TtFRho’s structure by comparative modeling with the crystal structure of the Escherichia coli TtFRho (Protein Data Bank ID: 1PVO) as a template in MODELLER (v 9.10). The modeled structure was optimized by applying a molecular dynamics simulation for 2 ns with the CHARMM (Chemistry at HARvard Macromolecular Mechanics) 27 force field in NAMD (NAnoscale Molecular Dynamics program; v 2.9) and then evaluated by calculating the stereochemical quality of the protein. The flexible docking for the interaction phenomenon of the template consists of ligand-related inhibitor molecules from the ZINC (ZINC Is Not Commercial) database using a structure-based virtual screening strategy against minimized TtFRho. Docking simulations revealed two inhibitors compounds – ZINC24934545 and ZINC72319544 – that showed high binding affinity among 2,829 drug analogs that bind with key active-site residues; these residues are considered for protein-ligand binding and unbinding pathways via steered molecular dynamics simulations. Arg215 in the model plays an important role in the stability of the protein-ligand complex via a hydrogen bonding interaction by aromatic-π contacts, and the ADMET (absorption, distribution, metabolism, and excretion) analysis of best leads indicate nontoxic in nature with good potential for drug development.

Calculating binding free energies for protein-carbohydrate complexes

A variety of computational techniques may be applied to compute theoretical binding free energies for protein-carbohydrate complexes. Elucidation of the intermolecular interactions, as well as the thermodynamic effects, that contribute to the relative strength of receptor binding can shed light on biomolecular recognition, and the resulting initiation or inhibition of a biological process. Three types of free energy methods are discussed here, including MM-PB/GBSA, thermodynamic integration, and a non-equilibrium alternative utilizing SMD. Throughout this chapter, the well-known concanavalin A lectin is employed as a model system to demonstrate the application of these methods to the special case of carbohydrate binding.

Characterization of unfolding mechanism of human lamin A Ig fold by single-molecule force spectroscopy-implications in EDMD

A- and B-type lamins are intermediate filament proteins constituting the nuclear lamina underneath the nuclear envelope thereby conferring proper shape and mechanical rigidity to the nucleus. Lamin proteins are also shown to be related diversely to basic nuclear processes. More than 400 mutations in human lamin A protein alone have been reported to produce at least 11 different disease conditions jointly termed as laminopathies. These mutations in lamin A are scattered throughout its helical rod domain, as well as the C-terminal domain containing the conserved Ig-fold region. The commonality of phenotypes in all these diseases is characterized by misshapen nuclei of the affected tissues which might stem from altered rigidity of the supporting lamina hence lamins. Here we have focused on autosomal dominant Emery-Dreifuss Muscular Dystrophy, one such laminopathy where R453W is the causative mutation located in the Ig domain of lamin A. We have investigated by single-molecule force spectroscopy how a stretching mechanical perturbation senses the destabilizing effect of the mutation in the lamin A Ig domain and compared the mechanoelastic properties of the mutant R453W with that of the wild-type in conjunction with steered molecular dynamics. Furthermore, we have shown the interaction of Ig domain with emerin, another key player and interacting partner in the pathogenesis of EDMD, is disrupted in the R453W mutant. This altered mechanoresistance of Ig domain itself and consequent uncoupling of lamin A-emerin interaction might underlie the altered mechanotransduction properties of EDMD affected nuclei.

On the improvement of free-energy calculation from steered molecular dynamics simulations using adaptive stochastic perturbation protocols

The potential of mean force (PMF) calculation in single molecule manipulation experiments performed via the steered molecular dynamics (SMD) technique is a computationally very demanding task because the analyzed system has to be perturbed very slowly to be kept close to equilibrium. Faster perturbations, far from equilibrium, increase dissipation and move the average work away from the underlying free energy profile, and thus introduce a bias into the PMF estimate. The Jarzynski equality offers a way to overcome the bias problem by being able to produce an exact estimate of the free energy difference, regardless of the perturbation regime. However, with a limited number of samples and high dissipation the Jarzynski equality also introduces a bias. In our previous work, based on the Brownian motion formalism, we introduced three stochastic perturbation protocols aimed at improving the PMF calculation with the Jarzynski equality in single molecule manipulation experiments and analogous computer simulations. This paper describes the PMF reconstruction results based on full-atom molecular dynamics simulations, obtained with those three protocols. We also want to show that the protocols are applicable with the second-order cumulant expansion formula. Our protocols offer a very noticeable improvement over the simple constant velocity pulling. They are able to produce an acceptable estimate of PMF with a significantly reduced bias, even with very fast perturbation regimes. Therefore, the protocols can be adopted as practical and efficient tools for the analysis of mechanical properties of biological molecules.

Effect of mutation at the interface of Trp-repressor dimeric protein: a steered molecular dynamics simulation

The strength of key interfacial contacts that stabilize protein-protein interactions have been studied by computer simulation. Experimentally, changes in the interface are evaluated by generating specific mutations at one or more points of the protein structure. Here, such an evaluation is performed by means of steered molecular dynamics and use of a dimeric model of tryptophan repressor and in-silico mutants as a test case. Analysis of four particular cases shows that, in principle, it is possible to distinguish between wild-type and mutant forms by examination of the total energy and force-extension profiles. In particular, detailed atomic level structural analysis indicates that specific mutations at the interface of the dimeric model (positions 19 and 39) alter interactions that appear in the wild-type form of tryptophan repressor, reducing the energy and force required to separate both subunits.

Pulling-spring modulation as a method for improving the potential-of-mean-force reconstruction in single-molecule manipulation experiments

The free-energy calculation is usually limited to close to equilibrium perturbation regimes because faster perturbations introduce a bias into the estimate. The Jarzynski equality offers a solution to this problem by directly connecting the free-energy difference and the external work, regardless how far from equilibrium that work may be. However, a limited sampling coupled to the fast perturbation introduces a slowly converging bias into the Jarzynski free-energy estimate also. In this paper we present two perturbation protocols devised with the intention to overcome the convergence issues of the Jarzynski-based potential of mean force estimation in the single-molecule, constant velocity manipulation experiments. The protocols are designed to improve the convergence issues by increasing the variation of the external work through the modulation of the spring used to pull a molecule. Of the two methods, the one which continuously changes the amplitude of the spring stiffness offers an excellent reconstruction and requires less than one tenth of the samples required by the normal, constant spring pulling to produce the same quality of the reconstruction.

Delineation of the unbinding pathway of α-conotoxin ImI from the α7 nicotinic acetylcholine receptor

α-Conotoxins potently and specifically inhibit isoforms of nicotinic acetylcholine receptors (nAChRs) and are used as molecular probes and as drugs or drug leads. Interactions occurring during binding and unbinding events are linked to binding kinetics, and knowledge of these interactions could help in the development of α-conotoxins as drugs. Here, the unbinding process for the prototypical α-conotoxin ImI/α7-nAChR system was investigated theoretically, and three exit routes were identified using random accelerated molecular dynamics simulations. The route involving the smallest conformation perturbation was further divided into three subpathways, which were studied using steered molecular dynamics simulations. Of the three subpathways, two had better experimental support and lower potential of mean force, indicating that they might be sampled more frequently. Additionally, these subpathways were supported by previous experimental studies. Several pairwise interactions, including a cation-π interaction and charge and hydrogen bond interactions, were identified as potentially playing important roles in the unbinding event.

Protein high-force pulling simulations yield low-force results

All-atom explicit-solvent molecular dynamics simulations are used to pull with extremely large constant force (750–3000 pN) on three small proteins. The introduction of a nondimensional timescale permits direct comparison of unfolding across all forces. A crossover force of approximately 1100 pN divides unfolding dynamics into two regimes. At higher forces, residues sequentially unfold from the pulling end while maintaining the remainder of the protein force-free. Measurements of hydrodynamic viscous stresses are made easy by the high speeds of unfolding. Using an exact low-Reynolds-number scaling, these measurements can be extrapolated to provide, for the first time, an estimate of the hydrodynamic force on low-force unfolding. Below 1100 pN, but surprisingly still at extremely large applied force, intermediate states and cooperative unfoldings as seen at much lower forces are observed. The force-insensitive persistence of these structures indicates that decomposition into unfolded fragments requires a large fluctuation. This finding suggests how proteins are constructed to resist transient high force. The progression of helix and sheet unfolding is also found to be insensitive to force. The force-insensitivity of key aspects of unfolding opens the possibility that numerical simulations can be accelerated by high applied force while still maintaining critical features of unfolding.

Dissecting DNA-histone interactions in the nucleosome by molecular dynamics simulations of DNA unwrapping

The nucleosome complex of DNA wrapped around a histone protein octamer organizes the genome of eukaryotes and regulates the access of protein factors to the DNA. We performed molecular dynamics simulations of the nucleosome in explicit water to study the dynamics of its histone-DNA interactions. A high-resolution histone-DNA interaction map was derived that revealed a five-nucleotide periodicity, in which the two DNA strands of the double helix made alternating contacts. On the 100-ns timescale, the histone tails mostly maintained their initial positions relative to the DNA, and the spontaneous unwrapping of DNA was limited to 1-2 basepairs. In steered molecular dynamics simulations, external forces were applied to the linker DNA to investigate the unwrapping pathway of the nucleosomal DNA. In comparison with a nucleosome without the unstructured N-terminal histone tails, the following findings were obtained: 1), Two main barriers during unwrapping were identified at DNA position ±70 and ±45 basepairs relative to the central DNA basepair at the dyad axis. 2), DNA interactions of the histone H3 N-terminus and the histone H2A C-terminus opposed the initiation of unwrapping. 3), The N-terminal tails of H2A, H2B, and H4 counteracted the unwrapping process at later stages and were essential determinants of nucleosome dynamics. Our detailed analysis of DNA-histone interactions revealed molecular mechanisms for modulating access to nucleosomal DNA via conformational rearrangements of its structure.

Computational investigation of the effect of thermal perturbation on the mechanical unfolding of titin I27

The emergence of single-molecule force measurement experiments has facilitated a better understanding of protein folding pathways and the thermodynamics involved. Computational methods such as steered molecular dynamics (SMD) simulations are helpful in providing atomistic level information on the unfolding pathways. Recent experimental studies have showed that combinations of single-molecule experiments with traditional methods such as chemical and/or thermal denaturation yield additional insights into the folding phenomenon. In this study, we report results from extensive computations (a total of about 60 SMD simulations with a total length of about 0.4 μs) that address the effect of thermal perturbation on the mechanical stability of the I27 domain of the protein titin. A wide range of temperatures (280-340 K) were considered for the pulling, which was done at both constant velocity and constant force using SMD simulations. Good agreement with experimental data, such as for the trends in changes in average force and the maximum force with respect to the temperature, was obtained. This study identifies two competing pathways for the mechanical unfolding of I27, and illustrates the significance of combining various techniques to examine protein folding.

Force-induced lysozyme--HyHEL5 antibody dissociation and its analysis by means of a cooperative binding model

Dynamic force spectroscopy probes the kinetic properties of molecules interacting with each other such as antibody-antigen, receptor-ligand, etc. In this article, a statistical model for the dissociation of such cooperative systems is presented. The partner molecules are assumed to be linked by a number of relatively weak bonds that can be grouped together into cooperative units. Single bonds are assumed to open and close statistically. Our model was used to analyze molecular recognition experiments of single receptor-ligand pairs in which the two molecules are brought into contact using an atomic force microscope, which leads to the formation of a strong and specific bond. Then a prescribed time-dependent force is applied to the complex and the statistical distribution of forces needed to pull the molecules completely apart is measured. This quantity is also calculated from our model. Furthermore, its dependence on the model parameters, such as binding free energy, number of bonds and groups, number of cooperative elementary bonds and degree of cooperativity within a group, influence of the force on the binding free energy, and the rate of change of the pulling force, is determined.

Complex molecular assemblies at hand via interactive simulations

Studying complex molecular assemblies interactively is becoming an increasingly appealing approach to molecular modeling. Here we focus on interactive molecular dynamics (IMD) as a textbook example for interactive simulation methods. Such simulations can be useful in exploring and generating hypotheses about the structural and mechanical aspects of biomolecular interactions. For the first time, we carry out low-resolution coarse-grain IMD simulations. Such simplified modeling methods currently appear to be more suitable for interactive experiments and represent a well-balanced compromise between an important gain in computational speed versus a moderate loss in modeling accuracy compared to higher resolution all-atom simulations. This is particularly useful for initial exploration and hypothesis development for rare molecular interaction events. We evaluate which applications are currently feasible using molecular assemblies from 1900 to over 300,000 particles. Three biochemical systems are discussed: the guanylate kinase (GK) enzyme, the outer membrane protease T and the soluble N-ethylmaleimide-sensitive factor attachment protein receptors complex involved in membrane fusion. We induce large conformational changes, carry out interactive docking experiments, probe lipid-protein interactions and are able to sense the mechanical properties of a molecular model. Furthermore, such interactive simulations facilitate exploration of modeling parameters for method improvement. For the purpose of these simulations, we have developed a freely available software library called MDDriver. It uses the IMD protocol from NAMD and facilitates the implementation and application of interactive simulations. With MDDriver it becomes very easy to render any particle-based molecular simulation engine interactive. Here we use its implementation in the Gromacs software as an example.

Mechanical unfolding of bacterial flagellar filament protein by molecular dynamics simulation

Bacterial flagellum is a nano-scale motility device constructed by self-assembly. During construction of the cell-exterior filament (the 'propeller'), subunit proteins (called flagellin) are thought to be exported through the hollow flagellum to the growing filament tip in an unfolded state. To gain insight into the unfolded state preceding any force-spectroscopy experiments on flagellin, we employed force-probe molecular dynamics simulations. Two schemes to attain an unfolded state suitable for efficient transport were examined: (i) stretching flagellin along its length; (ii) unzipping flagellin from its adjacently placed termini. Atomic-level unfolding pathways and the mechanical efforts involved under each scheme were obtained for the four-domain flagellin from S. typhimurium. Flagellin appeared stiffer and required larger unfolding forces when stretched as the relative sliding of beta-strands require the breaking of multiple hydrogen bonds at once. In contrast, unzipping requires lower unfolding forces as it mainly involves unraveling beta-sheets by breaking hydrogen bonds one by one.

Analyzing single-molecule manipulation experiments

Single-molecule manipulation studies can provide quantitative information about the physical properties of complex biological molecules without ensemble artifacts obscuring the measurements. We demonstrate computational techniques which aim at more fully utilizing the wealth of information contained in noisy experimental time series. The "noise" comes from multiple sources e.g., inherent thermal motion, instrument measurement error, etc. The primary focus of this paper is a methodology that uses time domain based methods to extract the effective molecular friction from single-molecule pulling data. We studied molecules composed of eight tandem repeat titin I27 domains, but the modeling approaches have applicability to other single-molecule mechanical studies. The merits and challenges associated with applying such a computational approach to existing single-molecule manipulation data are also discussed.

CHARMM: the biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.