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.     

Free-energy landscape of glycerol permeation through aquaglyceroporin GlpF determined from steered molecular dynamics simulations

The free-energy landscape of glycerol permeation through the aquaglyceroporin GlpF has been estimated in the literature by the nonequilibrium method of steered molecular dynamics (SMD) simulations and by the equilibrium method of adaptive biasing force (ABF) simulations. However, the ABF results qualitatively disagree with the SMD results that were based on the Jarzynski equality (JE) relating the equilibrium free-energy difference to the nonequilibrium work of the irreversible pulling experiments. In this paper, I present a new SMD study of the glycerol permeation through GlpF to explore the free-energy profile of glycerol along the permeation channel. Instead of the JE in terms of thermodynamic work, I use the fluctuation-dissipation theorem (FDT) of Brownian dynamics (BD), in terms of mechanical work, for extracting the free-energy difference from the nonequilibrium work of irreversible pulling experiments. The results of this new SMD-BD-FDT study are in agreement with the experimental data and with the ABF results.     

Conformational free energy of alkylsilanes by nonequilibrium-pulling Monte Carlo simulation

The stationary phase in supercritical fluid chromatography includes alkylsilanes, bearing typically 18-carbon alkane chains, bonded to silica. The silanes are in contact with supercritical carbon dioxide. Interaction of the stationary phase with analytes from the mobile phase depends on conformation of the silanes, whether they form a collapsed layer between the silica and the carbon dioxide or are extended into the carbon dioxide. Although equilibrium conformation of alkylsilanes can be determined by equilibrium Monte Carlo (MC) simulation, that is hampered by slow relaxation of the chains. An alternative is to pull alkylsilanes from collapsed to extended conformations, then calculate free energy change from the Jarzynski equality. This work compares conformational results from equilibrium MC simulation to free energies from nonequilibrium pulling simulations. Because both equilibrium and nonequilibrium simulations are faster for shorter silanes, this work also compares results from 8-carbon and 18-carbon silanes. Free energies from nonequilibrium pulling predict that alkylsilanes tend to bend over and form a layer between silica and carbon dioxide. Results from equilibrium simulations are qualitatively consistent with results from nonequilibrium pulling. Longer-chain silanes have greater tendency to extend slightly into the carbon dioxide.     

Protein-protein interaction investigated by steered molecular dynamics: the TCR-pMHC complex

We present a novel steered molecular dynamics scheme to induce the dissociation of large protein-protein complexes. We apply this scheme to study the interaction of a T cell receptor (TCR) with a major histocompatibility complex (MHC) presenting a peptide (p). Two TCR-pMHC complexes are considered, which only differ by the mutation of a single amino acid on the peptide; one is a strong agonist that produces T cell activation in vivo, while the other is an antagonist. We investigate the interaction mechanism from a large number of unbinding trajectories by analyzing van der Waals and electrostatic interactions and by computing energy changes in proteins and solvent. In addition, dissociation potentials of mean force are calculated with the Jarzynski identity, using an averaging method developed for our steering scheme. We analyze the convergence of the Jarzynski exponential average, which is hampered by the large amount of dissipative work involved and the complexity of the system. The resulting dissociation free energies largely underestimate experimental values, but the simulations are able to clearly differentiate between wild-type and mutated TCR-pMHC and give insights into the dissociation mechanism.     

Evaluation of protein–ligand affinity prediction using steered molecular dynamics simulations

In computational drug design, ranking a series of compound analogs in a manner that is consistent with experimental affinities remains a challenge. In this study, we evaluated the prediction of protein–ligand binding affinities using steered molecular dynamics simulations. First, we investigated the appropriate conditions for accurate predictions in these simulations. A conic harmonic restraint was applied to the system for efficient sampling of work values on the ligand unbinding pathway. We found that pulling velocity significantly influenced affinity predictions, but that the number of collectable trajectories was less influential. We identified the appropriate pulling velocity and collectable trajectories for binding affinity predictions as 1.25 Å/ns and 100, respectively, and these parameters were used to evaluate three target proteins (FK506 binding protein, trypsin, and cyclin-dependent kinase 2). For these proteins using our parameters, the accuracy of affinity prediction was higher and more stable when Jarzynski’s equality was employed compared with the second-order cumulant expansion equation of Jarzynski’s equality. Our results showed that steered molecular dynamics simulations are effective for predicting the rank order of ligands; thus, they are a potential tool for compound selection in hit-to-lead and lead optimization processes.     

Mechanistic insights into the physiological functions of cell adhesion proteins using single molecule force spectroscopy

Intercellular adhesion molecules play an important role in regulating several cellular processes such as a proliferation, migration and differentiation. They also play an important role in regulating solute diffusion across monolayers of cells. The adhesion characteristics of several intercellular adhesion molecules have been studied using various biochemical assays. However, the advent of single molecule force spectroscopy as a powerful tool to analyze the kinetics and strength of protein interactions has provided us with an opportunity to investigate these interactions at the level of a single molecule. The study of interactions involving intercellular adhesion molecules has gained importance because of the fact that qualitative and quantitative changes in these proteins are associated with several disease processes. In this review, we focus on the basic principles, data acquisition and analysis in single molecule force spectroscopy experiments. Furthermore, we discuss the correlation between results obtained using single molecule force experiments and the physiological functions of the proteins in the context of intercellular adhesion molecules. Finally, we summarize some of the diseases associated with changes in intercellular adhesion molecules.     

Free energy of formation of clusters of sulphuric acid and water molecules determined by guided disassembly

We evaluate the grand potential of a cluster of two molecular species, equivalent to its free energy of formation from a binary vapour phase, using a non-equilibrium molecular dynamics technique where guide particles, each tethered to a molecule by a harmonic force, move apart to disassemble a cluster into its components. The mechanical work performed in an ensemble of trajectories is analysed using the Jarzynski equality to obtain a free energy of disassembly, a contribution to the cluster grand potential. We study clusters of sulphuric acid and water at 300 K, using a classical interaction scheme, and contrast two modes of guided disassembly. In one, the cluster is broken apart through simple pulling by the guide particles, but we find the trajectories tend to be mechanically irreversible. In the second approach, the guide motion and strength of tethering are modified in a way that prises the cluster apart, a procedure that seems more reversible. We construct a surface representing the cluster grand potential, and identify a critical cluster for droplet nucleation under given vapour conditions. We compare the equilibrium populations of clusters with calculations reported by Henschel et al. [J. Phys. Chem. A 2014;118:2599] based on optimised quantum chemical structures.     

Observing structure,function and assembly of single proteins by AFM

Single molecule experiments provide insight into the individuality of biological macromolecules, their unique function, reaction pathways, trajectories and molecular interactions. The exceptional signal-to-noise ratio of the atomic force microscope allows individual proteins to be imaged under physiologically relevant conditions at a lateral resolution of 0.5–1 nm and a vertical resolution of 0.1–0.2 nm. Recently, it has become possible to observe single molecule events using this technique. This capability is reviewed on various water-soluble and membrane proteins. Examples of the observation of function, variability, and assembly of single proteins are discussed. Statistical analysis is important to extend conclusions derived from single molecule experiments to protein species. Such approaches allow the classification of protein conformations and movements. Recent developments of probe microscopy techniques allow simultaneous measurement of multiple signals on individual macromolecules, and greatly extend the range of experiments possible for probing biological systems at the molecular level. Biologists exploring molecular mechanisms will benefit from a burgeoning of scanning probe microscopes and of their future combination with molecular biological experiments.     

Velocity-dependent mechanical unfolding of bacteriorhodopsin is governed by a dynamic interaction network

Bacteriorhodopsin is a model system for membrane proteins. This seven transmembrane helical protein is embedded within a membrane structure called purple membrane. Its structural stability against mechanical stress was recently investigated by atomic force microscopy experiments, in which single proteins were extracted from the purple membrane. Here, we study this process by all-atom molecular dynamics simulations, in which single bacteriorhodopsin molecules were extracted and unfolded from an atomistic purple membrane model. In our simulations, key features from the experiments like force profiles and location of key residues that resist mechanical unfolding were reproduced. These key residues were seen to be stabilized by a dynamic network of intramolecular interactions. Further, the unfolding pathway was found to be velocity-dependent. Simulations in which the mechanical stress was released during unfolding revealed relaxation motions that allowed characterization of the nonequilibrium processes during fast extraction.     

Monomeric class I molecules mediate TCR/CD3 epsilon/CD8 interaction on the surface of T cells.

Both CD8 and the TCR bind to MHC class I molecules during physiologic T cell activation. It has been shown that for optimal T cell activation to occur, CD8 must be able to bind the same class I molecule that is bound by the TCR. However, no direct evidence for the class I-dependent association of CD8 and the TCR has been demonstrated. Using fluorescence resonance energy transfer, we show directly that a single class I molecule causes TCR/CD8 interaction by serving as a docking molecule for both CD8 and the TCR. Furthermore, we show that CD3epsilon is brought into close proximity with CD8 upon TCR/CD8 association. These interactions are not dependent on the phosphorylation events characteristic of T cell activation. Thus, MHC class I molecules, by binding to both CD8 and the TCR, mediate the reorganization of T cell membrane components to promote cellular activation.     

Kinetic Theory Model for Ion Movement through Biological Membranes: I. Field-Dependent Conductances in the Presence of Solution Symmetry

A model for ion movement through specialized sites in the plasma membrane is presented and analyzed using techniques from nonequilibrium kinetic theory. It is assumed that ions traversing these specialized regions interact with membrane molecules through central conservative forces. The membrane molecules are approximated as massive spherical scattering centers so that ionic fractional energy losses per collision are much less than one. Equations for steady-state membrane ionic currents and conductances as functions of externally applied electric field strength are derived and numerically analyzed, under the restriction of identical solutions on each size of the membrane and constant electric fields within the membrane. The analysis is carried through for a number of idealized ion-membrane molecule central force interactions. For any interaction leading to a velocity-dependent ion-membrane molecule collision frequency, the membrane chord conductance is a function of the externally applied electric field. Interactions leading to a collision frequency that is an increasing (decreasing) function of ionic velocity are characterized by chord conductances that are decreasing (increasing) functions of field strength. For ion-neutral molecule interactions, the conductance is such a rapidly decreasing function of field strength that the slope conductance becomes negative for all field strengths above a certain value.     

Transition state of the rate-limiting step of heat denaturation of Cry3A delta-endotoxin

Heat denaturation of Cry3A delta-endotoxin from Bacillus thuringiensis var. tenebrionis and its 55 kDa fragment was studied by differential scanning microcalorimetry at low pH. Analysis of the calorimetric data has shown that denaturation of Cry3A delta-endotoxin is a nonequilibrium process at heating rates from 0. 125 to 2 K/min. This means that the stability of delta-endotoxin (the apparent temperature of denaturation Tm) under these conditions is under kinetic control rather than under thermodynamic control. It has been shown that heat denaturation of this protein is a one-step kinetic process. The enthalpy of the process and its activation energy were measured as functions of temperature. The data obtained allow confirmation of the fact that the conformation of delta-endotoxin at the transition state only slightly differs from its native conformation with respect to compactness and extent of hydration. The comparison of the activation energy for intact delta-endotoxin and the 55 kDa fragment showed that the transition of the molecule to a transition state does not cause any changes in the conformation of three N-terminal alpha-helices. Complete removal of the N-terminal domain of delta-endotoxin and 40 amino acids from the C-terminus beta-sheet domain III causes an irreversible loss of the tertiary structure. Thus, during protein folding the nucleation core determining protein stability does not involve its three initial alpha-helices but may include the remaining alpha-helices of the N-terminal domain. The functional significance of peculiarities of structure arrangement of the delta-endotoxin molecule is discussed.     

JIP1 regulates the directionality of APP axonal transport by coordinating kinesin and dynein motors

Regulation of the opposing kinesin and dynein motors that drive axonal transport is essential to maintain neuronal homeostasis. Here, we examine coordination of motor activity by the scaffolding protein JNK-interacting protein 1 (JIP1), which we find is required for long-range anterograde and retrograde amyloid precursor protein (APP) motility in axons. We identify novel interactions between JIP1 and kinesin heavy chain (KHC) that relieve KHC autoinhibition, activating motor function in single molecule assays. The direct binding of the dynactin subunit p150^Glued to JIP1 competitively inhibits KHC activation in vitro and disrupts the transport of APP in neurons. Together, these experiments support a model whereby JIP1 coordinates APP transport by switching between anterograde and retrograde motile complexes. We find that mutations in the JNK-dependent phosphorylation site S421 in JIP1 alter both KHC activation in vitro and the directionality of APP transport in neurons. Thus phosphorylation of S421 of JIP1 serves as a molecular switch to regulate the direction of APP transport in neurons.     

An investigation of the role of the copper in galactose oxidase.

Galactose oxidase is a metalloenzyme containing a single copper atom per molecule. The mechanism of action of galactose oxidase is studied in this paper by investigating substrate specificity and activation by peroxidase, and probing the copper site by electron spin resonance (ESR) spectroscopy. Line-shape simulation of ESR spectra are also reported and a comparison is made between observed and simulated spectra for galactose oxidase. A comparison is also reported for the enzyme from various commercial sources and enzyme isolated from a fungus in this laboratory. The results of this investigation suggest that the copper is in an environment of four in-plane nitrogens with axial symmetry.     

A human vitamin D receptor mutant activated by cholecalciferol

The human vitamin D receptor (hVDR) is a member of the nuclear receptor superfamily, involved in calcium and phosphate homeostasis; hence implicated in a number of diseases, such as Rickets and Osteoporosis. This receptor binds 1α,25-dihydroxyvitamin D(3) (also referred to as 1,25(OH)(2)D(3)) and other known ligands, such as lithocholic acid. Specific interactions between the receptor and ligand are crucial for the function and activation of this receptor, as implied by the single point mutation, H305Q, causing symptoms of Type II Rickets. In this work, further understanding of the significant and essential interactions between the ligand and the receptor was deciphered, through a combination of rational and random mutagenesis. A hVDR mutant, H305F, was engineered with increased sensitivity towards lithocholic acid, with an EC(50) value of 10 μM and 40±14 fold activation in mammalian cell assays, while maintaining wild-type activity with 1,25(OH)(2)D(3). Furthermore, via random mutagenesis, a hVDR mutant, H305F/H397Y, was discovered to bind a novel small molecule, cholecalciferol, a precursor in the 1α,25-dihydroxyvitamin D(3) biosynthetic pathway, which does not activate wild-type hVDR. This variant, H305F/H397Y, binds and activates in response to cholecalciferol concentrations as low as 100 nM, with an EC(50) value of 300 nM and 70±11 fold activation in mammalian cell assays. In silico docking analysis of the variant displays a dramatic conformational shift of cholecalciferol in the ligand binding pocket in comparison to the docked analysis of cholecalciferol with wild-type hVDR. This shift is hypothesized to be due to the introduction of two bulkier residues, suggesting that the addition of these bulkier residues introduces molecular interactions between the ligand and receptor, leading to activation with cholecalciferol.     

Three-dimensional molecular modeling with single molecule FRET

Single molecule fluorescence energy transfer experiments enable investigations of macromolecular conformation and folding by the introduction of fluorescent dyes at specific sites in the macromolecule. Multiple such experiments can be performed with different labeling site combinations in order to map complex conformational changes or interactions between multiple molecules. Distances that are derived from such experiments can be used for determination of the fluorophore positions by triangulation. When combined with a known structure of the macromolecule(s) to which the fluorophores are attached, a three-dimensional model of the system can be determined. However, care has to be taken to properly derive distance from fluorescence energy transfer efficiency and to recognize the systematic or random errors for this relationship. Here we review the experimental and computational methods used for three-dimensional modeling based on single molecule fluorescence resonance transfer, and describe recent progress in pushing the limits of this approach to macromolecular complexes.     

A toolbox for generating single‐stranded DNA in optical tweezers experiments

Essential genomic transactions such as DNA‐damage repair and DNA replication take place on single‐stranded DNA (ssDNA) or require specific single‐stranded/double‐stranded DNA (ssDNA/dsDNA) junctions (SDSJ). A significant challenge in single‐molecule studies of DNA–protein interactions using optical trapping is the design and generation of appropriate DNA templates. In contrast to dsDNA, only a limited toolbox is available for the generation of ssDNA constructs for optical tweezers experiments. Here, we present several kinds of DNA templates suitable for single‐molecule experiments requiring segments of ssDNA of several kilobases in length. These different biotinylated dsDNA templates can be tethered between optically trapped microspheres and can, by the subsequent use of force‐induced DNA melting, be converted into partial or complete ssDNA molecules. We systematically investigated the time scale and efficiency of force‐induced melting at different ionic strengths for DNA molecules of different sequences and lengths. Furthermore, we quantified the impact of microspheres of different sizes on the lifetime of ssDNA tethers in optical tweezers experiments. Together, these experiments provide deeper insights into the variables that impact the production of ssDNA for single molecules studies and represent a starting point for further optimization of DNA templates that permit the investigation of protein binding and kinetics on ssDNA. © 2013 Wiley Periodicals, Inc. Biopolymers 99:611–620, 2013.