Comparative energy measurements in single molecule interactions

Single molecule experiments have opened promising new avenues of investigations in biology, but the quantitative interpretation of results remains challenging. In particular, there is a need for a comparison of such experiments with theoretical methods. We experimentally determine the activation free energy for single molecule interactions between two synaptic proteins syntaxin 1A and synaptobrevin 2, using an atomic force microscope and the Jarzynski equality of nonequilibrium thermodynamics. The value obtained is shown to be reasonably consistent with that from single molecule reaction rate theory. The temperature dependence of the spontaneous dissociation lifetime along with different pulling speeds is used to confirm the approach to the adiabatic limit. This comparison of the Jarzynski equality for intermolecular interactions extends the procedure for calculation of activation energies in nonequilibrium processes.     

Effective potentials between gold nano crystals – functional dependence on temperature

A method is presented that allows to combine the effective potential between two nano crystals (NC), the potential of mean force (PMF), as obtained from all-atomistic molecular dynamics simulations with perturbation theory. In this way, a functional dependence of the PMF on temperature is derived, which enables the prediction of the PMF in a wide temperature range. We applied the method to systems of capped gold NCs of different size. They show very good agreement with data from atomistic simulations.     

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.     

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.     

Determining Protein-Induced DNA Bending in Force-Extension Experiments: Theoretical Analysis

Computer simulations were used to investigate the possibility of determining protein-induced DNA bend angles by measuring the extension of a single DNA molecule. Analysis of the equilibrium sets of DNA conformations showed that shortening of DNA extension by a single protein-induced DNA bend can be as large as 35 nm. The shortening has a maximum value at the extending force of ∼0.1 pN. At this force, the DNA extension experiences very large fluctuations that dramatically complicate the measurement. Using Brownian dynamics simulation of a DNA molecule extended by force, we were able to estimate the observation time needed to obtain the desired accuracy of the extension measurement. Also, the simulation revealed large fluctuations of the force, acting on the attached magnetic bead from the stretched DNA molecule.     

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.     

Thermodynamic stability of water molecules in the bacteriorhodopsin proton channel: a molecular dynamics free energy perturbation study.

The proton transfer activity of the light-driven proton pump, bacteriorhodopsin (bR) in the photochemical cycle might imply internal water molecules. The free energy of inserting water molecules in specific sites along the bR transmembrane channel has been calculated using molecular dynamics simulations based on a microscopic model. The existence of internal hydration is related to the free energy change on transfer of a water molecule from bulk solvent into a specific binding site. Thermodynamic integration and perturbation methods were used to calculate free energies of hydration for each hydrated model from molecular dynamics simulations of the creation of water molecules into specific protein-binding sites. A rigorous statistical mechanical formulation allowing the calculation of the free energy of transfer of water molecules from the bulk to a protein cavity is used to estimate the probabilities of occupancy in the putative bR proton channel. The channel contains a region lined primarily by nonpolar side-chains. Nevertheless, the results indicate that the transfer of four water molecules from bulk water to this apparently hydrophobic region is thermodynamically permitted. The column forms a continuous hydrogen-bonded chain over 12 A between a proton donor, Asp 96, and the retinal Schiff base acceptor. The presence of two water molecules in direct hydrogen-bonding association with the Schiff base is found to be strongly favorable thermodynamically. The implications of these results for the mechanism of proton transfer in bR are discussed.     

Insights into the mechanisms of the selectivity filter of Escherichia coli aquaporin Z

Aquaporin Z (AQPZ) is a tetrameric protein that forms water channels in the cell membrane of Escherichia coli. The histidine residue (residue 174) in the selectivity filter (SF) region plays an important role in the transport of water across the membrane. In this work, we perform equilibrium molecular dynamics (MD) simulations to illustrate the gating mechanism of the SF and the influences of residue 174 in two different protonation states: Hsd174 with the proton at Nδ, and Hse174 with the proton at Nε. We calculate the pore radii in the SF region versus the simulation time. We perform steered MD to compute the free-energy profile, i.e., the potential of mean force (PMF) of a water molecule through the SF region. We conduct a quantum mechanics calculation of the binding energy of one water molecule with the residues in the SF region. The hydrogen bonds formed between the side chain of Hsd174 and the side chain of residue 189 (Arg189) play important roles in the selectivity mechanism of AQPZ. The radii of the pores, the hydrogen-bond analysis, and the free energies show that it is easier for water molecules to permeate through the SF region of AQPZ with residue 174 in the Hse state than in the Hsd state.     

Carbinolamine formation and dehydration in a DNA repair enzyme active site

In order to suggest detailed mechanistic hypotheses for the formation and dehydration of a key carbinolamine intermediate in the T4 pyrimidine dimer glycosylase (T4PDG) reaction, we have investigated these reactions using steered molecular dynamics with a coupled quantum mechanics-molecular mechanics potential (QM/MM). We carried out simulations of DNA abasic site carbinolamine formation with and without a water molecule restrained to remain within the active site quantum region. We recovered potentials of mean force (PMF) from thirty replicate reaction trajectories using Jarzynski averaging. We demonstrated feasible pathways involving water, as well as those independent of water participation. The water-independent enzyme-catalyzed reaction had a bias-corrected Jarzynski-average barrier height of approximately (6.5 kcal mol(-1) (27.2 kJ mol(-1)) for the carbinolamine formation reaction and 44.5 kcal mol(-1) (186 kJ mol(-1)) for the reverse reaction at this level of representation. When the proton transfer was facilitated with an intrinsic quantum water, the barrier height was approximately 15 kcal mol(-1) (62.8 kJ mol(-1)) in the forward (formation) reaction and 19 kcal mol(-1) (79.5 kJ mol(-1)) for the reverse. In addition, two modes of unsteered (free dynamics) carbinolamine dehydration were observed: in one, the quantum water participated as an intermediate proton transfer species, and in the other, the active site protonated glutamate hydrogen was directly transferred to the carbinolamine oxygen. Water-independent unforced proton transfer from the protonated active site glutamate carboxyl to the unprotonated N-terminal amine was also observed. In summary, complex proton transfer events, some involving water intermediates, were studied in QM/MM simulations of T4PDG bound to a DNA abasic site. Imine carbinolamine formation was characterized using steered QM/MM molecular dynamics. Dehydration of the carbinolamine intermediate to form the final imine product was observed in free, unsteered, QM/MM dynamics simulations, as was unforced acid-base transfer between the active site carboxylate and the N-terminal amine.     

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.     

Molecular dynamics re-refinement of two different small RNA loop structures using the original NMR data suggest a common structure

Restrained molecular dynamics simulations are a robust, though perhaps underused, tool for the end-stage refinement of biomolecular structures. We demonstrate their utility-using modern simulation protocols, optimized force fields, and inclusion of explicit solvent and mobile counterions-by re-investigating the solution structures of two RNA hairpins that had previously been refined using conventional techniques. The structures, both domain 5 group II intron ribozymes from yeast ai5γ and Pylaiella littoralis, share a nearly identical primary sequence yet the published 3D structures appear quite different. Relatively long restrained MD simulations using the original NMR restraint data identified the presence of a small set of violated distance restraints in one structure and a possibly incorrect trapped bulge nucleotide conformation in the other structure. The removal of problematic distance restraints and the addition of a heating step yielded representative ensembles with very similar 3D structures and much lower pairwise RMSD values. Analysis of ion density during the restrained simulations helped to explain chemical shift perturbation data published previously. These results suggest that restrained MD simulations, with proper caution, can be used to "update" older structures or aid in the refinement of new structures that lack sufficient experimental data to produce a high quality result. Notable cautions include the need for sufficient sampling, awareness of potential force field bias (such as small angle deviations with the current AMBER force fields), and a proper balance between the various restraint weights.     

The catalytic power of ketosteroid isomerase investigated by computer simulation

Ketosteroid isomerase (KSI) catalyzes the isomerization of Delta(5)-3-ketosteroids and Delta(4)-3-ketosteroids at very high rates. Here we examine the principles underlying the catalytic efficiency of KSI by computer simulations using the empirical valence bond method in combination with molecular dynamics free energy perturbation simulations. The simulations reproduce available kinetic and structural data very well and allow us to examine several features of the catalytic mechanism in detail. It is found that about 60% of the rate enhancement is due to stabilization of the negatively charged dienolate intermediate by hydrogen bonding. The critical H-bond between Tyr16 and the intermediate is found to be a normal ionic H-bond with the preferred proton location on the tyrosine residue. The remaining 40% of the catalytic effect originates from a reduction of the reorganization energy of the reaction. The possibility of an active site water molecule occupying the empty cavity adjacent to the catalytic base (Asp40) is also addressed. The existence of such a water molecule could explain how the enzyme manages to maintain a low pK(a) for the general base residue.     

Building a foundation for structure‐based cellulosome design for cellulosic ethanol: Insight into cohesin‐dockerin complexation from computer simulation

The organization and assembly of the cellulosome, an extracellular multienzyme complex produced by anaerobic bacteria, is mediated by the high‐affinity interaction of cohesin domains from scaffolding proteins with dockerins of cellulosomal enzymes. We have performed molecular dynamics simulations and free energy calculations on both the wild type (WT) and D39N mutant of the C. thermocellum Type I cohesin‐dockerin complex in aqueous solution. The D39N mutation has been experimentally demonstrated to disrupt cohesin‐dockerin binding. The present MD simulations indicate that the substitution triggers significant protein flexibility and causes a major change of the hydrogen‐bonding network in the recognition strips—the conserved loop regions previously proposed to be involved in binding—through electrostatic and salt‐bridge interactions between β‐strands 3 and 5 of the cohesin and α‐helix 3 of the dockerin. The mutation‐induced subtle disturbance in the local hydrogen‐bond network is accompanied by conformational rearrangements of the protein side chains and bound water molecules. Additional free energy perturbation calculations of the D39N mutation provide differences in the cohesin‐dockerin binding energy, thus offering a direct, quantitative comparison with experiments. The underlying molecular mechanism of cohesin‐dockerin complexation is further investigated through the free energy profile, that is, potential of mean force (PMF) calculations of WT cohesin‐dockerin complex. The PMF shows a high‐free energy barrier against the dissociation and reveals a stepwise pattern involving both the central β‐sheet interface and its adjacent solvent‐exposed loop/turn regions clustered at both ends of the β‐barrel structure.     

Virtual substitution scan via single‐step free energy perturbation

With the rapid expansion of our computing power, molecular dynamics (MD) simulations ranging from hundreds of nanoseconds to microseconds or even milliseconds have become increasingly common. The majority of these long trajectories are obtained from plain (vanilla) MD simulations, where no enhanced sampling or free energy calculation method is employed. To promote the “recycling” of these trajectories, we developed the Virtual Substitution Scan (VSS) toolkit as a plugin of the open‐source visualization and analysis software VMD. Based on the single‐step free energy perturbation (sFEP) method, VSS enables the user to post‐process a vanilla MD trajectory for a fast free energy scan of substituting aryl hydrogens by small functional groups. Dihedrals of the functional groups are sampled explicitly in VSS, which improves the performance of the calculation and is found particularly important for certain groups. As a proof‐of‐concept demonstration, we employ VSS to compute the solvation free energy change upon substituting the hydrogen of a benzene molecule by 12 small functional groups frequently considered in lead optimization. Additionally, VSS is used to compute the relative binding free energy of four selected ligands of the T4 lysozyme. Overall, the computational cost of VSS is only a fraction of the corresponding multi‐step FEP (mFEP) calculation, while its results agree reasonably well with those of mFEP, indicating that VSS offers a promising tool for rapid free energy scan of small functional group substitutions. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 324–336, 2016.     

The influence of cholesterol on interactions and dynamics of ibuprofen in a lipid bilayer

In this work, molecular dynamics (MD) simulations with atomistic details were performed to examine the influence of the cholesterol on the interactions and the partitioning of the hydrophobic drug ibuprofen in a fully hydrated 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) bilayer. Analysis of MD simulations indicated that ibuprofen molecules prefer to be located in the hydrophobic acyl chain region of DMPC/cholesterol bilayers. This distribution decreases the lateral motion of lipid molecules. The presence of ibuprofen molecules in the bilayers with 0 and 25 mol% cholesterol increases the ordering of hydrocarbon tails of lipids whereas for the bilayers with 50 mol% cholesterol, ibuprofen molecules perturb the flexible chains of DMPC lipids which leads to the reduction of the acyl chain order parameter. The potential of the mean force (PMF) method was used to calculate the free energy profile for the transferring of an ibuprofen molecule from the bulk water into the DMPC/cholesterol membranes. The PMF studies indicated that the presence of 50 mol% cholesterol in the bilayers increases the free energy barrier and slows down the permeation of the ibuprofen drug across the DMPC bilayer. This can be due to the condensing and ordering effects of the cholesterol on the bilayer.     

Changing the Mechanical Unfolding Pathway of FnIII10 by Tuning the Pulling Strength

We investigate the mechanical unfolding of the tenth type III domain from fibronectin (FnIII₁₀) both at constant force and at constant pulling velocity, by all-atom Monte Carlo simulations. We observe both apparent two-state unfolding and several unfolding pathways involving one of three major, mutually exclusive intermediate states. All three major intermediates lack two of seven native β-strands, and share a quite similar extension. The unfolding behavior is found to depend strongly on the pulling conditions. In particular, we observe large variations in the relative frequencies of occurrence for the intermediates. At low constant force or low constant velocity, all three major intermediates occur with a significant frequency. At high constant force or high constant velocity, one of them, with the N- and C-terminal β-strands detached, dominates over the other two. Using the extended Jarzynski equality, we also estimate the equilibrium free-energy landscape, calculated as a function of chain extension. The application of a constant pulling force leads to a free-energy profile with three major local minima. Two of these correspond to the native and fully unfolded states, respectively, whereas the third one can be associated with the major unfolding intermediates.     

Relative binding free energy calculations of inhibitors to two mutants (Glu46----Ala/Gln) of ribonuclease T1 using molecular dynamics/free energy perturbation approaches.

We present free energy perturbation calculations on the complexes of Glu46----Ala46 (E46A) and Glu46----Gln46 (E46Q) mutants of ribonuclease T1 (RNaseT1) with inhibitors 2'-guanosine monophosphate (GMP) and 2'-adenosine monophosphate (AMP) by a thermodynamic perturbation method implemented with molecular dynamics (MD). Using the available crystal structure of the RNaseT1-GMP complex, the structures of E46A-GMP and E46Q-GMP were model built and equilibrated with MD simulations. The structures of E46A-AMP and E46Q-AMP were obtained as a final structure of the GMP----AMP perturbation calculation respectively. The calculated difference in the free energy of binding (delta delta Gbind) was 0.31 kcal/mol for the E46A system and -1.04 kcal/mol for the E46Q system. The resultant free energies are much smaller than the experimental and calculated value of approximately 3 kcal/mol for the native RNaseT1, which suggests that both mutants have greater relative adenine affinities than native RNaseT1. Especially E46Q is calculated to have a larger affinity for adenine than guanine, as we suggested previously from the calculation on the native RNaseT1. Thus, the molecular dynamics/free energy perturbation method may be helpful in protein engineering, directed toward increasing or changing the substrate specificity of enzymes.     

Study of curcumin behavior in two different lipid bilayer models of liposomal curcumin using molecular dynamics simulation

Liposomal formulation of curcumin is an important therapeutic agent for the treatment of various cancers. Despite extensive studies on the biological effects of this formulation in cancer treatment, much remains unknown about curcumin–liposome interactions. Understanding how different lipid bilayers respond to curcumin molecule may help us to design more effective liposomal curcumin. Here, we used molecular dynamics simulation method to investigate the behavior of curcumin in two lipid bilayers commonly used in preparation of liposomal curcumin, namely dipalmitoylphosphatidylcholine (DPPC) and dimyristoylphosphatidylglycerol (DMPG). First, the free energy barriers for translocation of one curcumin molecule from water to the lipid bilayer were determined by using the potential of mean force (PMF). The computed free energy profile exhibits a global minimum at the solvent–headgroup interface (LH region) for both lipid membranes. We also evaluated the free energy difference between the equilibrium position of curcumin in the lipid bilayer and bulk water as the excess chemical potential. Our results show that curcumin has the higher affinity in DMPG compared to DPPC lipid bilayer (?8.39 vs. ?1.69 k_BT) and this is related to more hydrogen bond possibility for curcumin in DMPG lipid membrane. Next, using an unconstrained molecular dynamic simulation with curcumin initially positioned at the center of lipid bilayer, we studied various properties of each lipid bilayer system in the presence of curcumin molecule that was in full agreement with PMF and experimental data. The results of these simulation studies suggest that membrane composition could have a large effect on interaction of curcumin–lipid bilayer.