Diffusion of glycerol through Escherichia coli aquaglyceroporin GlpF

The glycerol uptake facilitator, GlpF, a major intrinsic protein found in Escherichia coli, selectively conducts water and glycerol across the inner membrane. The free energy landscape characterizing the assisted transport of glycerol by this homotetrameric aquaglyceroporin has been explored by means of equilibrium molecular dynamics over a timescale spanning 0.12 μs. To overcome the free energy barriers of the conduction pathway, an adaptive biasing force is applied to the glycerol molecule confined in each of the four channels. The results illuminate the critical role played by intramolecular relaxation on the diffusion properties of the permeant. These free energy calculations reveal that glycerol tumbles and isomerizes on a timescale comparable to that spanned by its adaptive-biasing-force-assisted conduction in GlpF. As a result, reorientation and conformational equilibrium of glycerol in GlpF constitute a bottleneck in the molecular simulations of the permeation event. A profile characterizing the position-dependent diffusion of the permeant has been determined, allowing reaction rate theory to be applied for investigating conduction kinetics based on the measured free energy landscape.     

Water and ion permeation in bAQP1 and GlpF channels: a kinetic Monte Carlo study

The kinetic Monte Carlo reaction-path-following technique is applied to determine the lowest-energy water pathway and the coordinating amino acids in bAQP1 and GlpF channels, both treated as rigid. In bAQP1, water molecules pass through the pore between the asparagine-proline-alanine (NPA) and selectivity filter (SF) sites one at a time. The water chain is interrupted at the SF where one water forms three stable hydrogen bonds with protein atoms. In this SF, water's conformation depends on the protonation locus of H182. In GlpF, two water molecules bond simultaneously to the NPA asparagines and pass through the SF in zigzag fashion. No water single-file forms in rigid GlpF. To accommodate a single file of waters requires narrowing the GlpF pore. Our results reveal that in both proteins a proposed bipolar water arrangement is thermally disrupted in the NPA region, especially in the cytoplasmic part of the pore. The equilibrium hydrogen-bonded chain is occasionally interrupted in the hydrophobic zones adjacent to the NPA motifs. The permeation of alkali cations through bAQP1 and GlpF is barred due to a large free-energy barrier in the NPA region as well as a large energy barrier blocking entry from the cytoplasm. Permeation of halides is prevented due to two large energy barriers in the cytoplasmic and periplasmic pores as well as a large free-energy barrier barring entry from the periplasm. Our results, based on modeling charge permeation, support an electrostatic rather than orientational basis for proton exclusion. Binding within the aquaporin pore cannot compensate sufficiently for dehydration of the protonic charge; there is also an electrostatic barrier in the NPA region blocking proton transport. The highly ordered single file of waters, which is drastically interrupted at the SF of bAQP1, may also contribute to proton block.     

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.     

Simulating force-induced conformational transitions in polysaccharides with the SMD replica exchange method

Conventional steered molecular dynamics (SMD) simulations do not readily reproduce equilibrium conditions of atomic force microscopy (AFM) stretch and release measurements of polysaccharides undergoing force-induced conformational transitions because of the gap between the timescales of computer simulations ( approximately 1 mus) and AFM measurements ( approximately 1 s). To circumvent this limitation, we propose using the replica exchange method (REM) to enhance sampling during SMD simulations. By applying REM SMD to a small polysaccharide system and comparing the results with those from AFM stretching experiments, we demonstrate that REM SMD reproduces the experimental results not only qualitatively but quantitatively, approaching near equilibrium conditions of AFM measurements. As tested in this work, hysteresis and computational time of REM SMD simulations of short polysaccharide chains are significantly reduced as compared to regular SMD simulations, making REM SMD an attractive tool for studying forced-induced conformational transitions of small biopolymer systems.     

In silico experiments of single-chain antibody fragment against drugs of abuse

Three sets of in silico experiments have been conducted to elucidate the binding mechanics of two drugs, (+)-methamphetamine (METH) and amphetamine (AMP) to the single-chain variable fragment (scFv) recently engineered from anti-METH monoclonal antibody mAb6H4 (IgG, κlight chain, K_d = 11 nM). The first set of in silico experiments are long time equilibration runs of scFv:drug complexes and of drug-free scFv both in the solution. They demonstrate how the solution structures of scFv deviate from its crystallographic form with or without drug molecules bound to it. They lead to the prediction that the Arrhenius activation barrier is nearly zero for transitions from the dissociated state to the bound state. The second set of in silico experiments are nonequilibrium dynamics of pulling the drug molecules out of the binding pocket of scFv and the equilibration runs for drugs to fall back into the binding pocket. They demonstrate that extra water molecules (in addition to the two crystallographic waters) exist inside the binding pocket, underneath the drug molecules. These extra waters must have been evaporated from the binding pockets during the crystallization process of the in vitro experiments of structural determination. The third set of in silico experiments are nonequilibrium steered molecular dynamics simulations to determine the absolute binding free energies of METH and AMP to scFv. The center of mass of a drug molecule (METH or AMP) is steered (pulled) towards (forward) and away from (reverse) the binding site, sampling forward and reverse pulling paths. Mechanic work is measured along the pulling paths. The work measurements are averaged through the Brownian dynamics fluctuation dissipation theorem to produce the free-energy profiles of the scFv:drug complexes as a function of the drug-scFv separation. These experiments lead to the theoretical prediction of absolute binding energies of METH and AMP that are in agreement with the in vitro experimental results.     

Carbon Nanotube-Encapsulated Drug Penetration Through the Cell Membrane: An Investigation Based on Steered Molecular Dynamics Simulation

Understanding the penetration mechanisms of carbon nanotube (CNTs)-encapsulated drugs through the phospholipid bilayer cell membrane is an important issue for the development of intracellular drug delivery systems. In the present work, steered molecular dynamics (SMD) simulation was used to explore the possibility of penetration of a polar drug, paclitaxel (PTX), encapsulated inside the CNT, through a dipalmitoylphosphatidylcholine bilayer membrane. The interactions between PTX and CNT and between PTX and the confined water molecules inside the CNT had a significant effect on the penetration process of PTX. The results reveal that the presence of a PTX molecule increases the magnitude of the pulling force. The effect of pulling velocity on the penetration mechanism was also investigated by a series of SMD simulations, and it is shown that the pulling velocity had a significant effect on pulling force and the interaction between lipid bilayer and drug molecule.     

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.     

The mechanism of glycerol conduction in aquaglyceroporins.

BACKGROUND: The E. coli glycerol facilitator, GlpF, selectively conducts glycerol and water, excluding ions and charged solutes. The detailed mechanism of the glycerol conduction and its relationship to the characteristic secondary structure of aquaporins and to the NPA motifs in the center of the channel are unknown. RESULTS: Molecular dynamics simulations of GlpF reveal spontaneous glycerol and water conduction driven, on a nanosecond timescale, by thermal fluctuations. The bidirectional conduction, guided and facilitated by the secondary structure, is characterized by breakage and formation of hydrogen bonds for which water and glycerol compete. The conduction involves only very minor changes in the protein structure, and cooperativity between the GlpF monomers is not evident. The two conserved NPA motifs are strictly linked together by several stable hydrogen bonds and their asparagine side chains form hydrogen bonds with the substrates passing the channel in single file. CONCLUSIONS: A complete conduction of glycerol through the GlpF was deduced from molecular dynamics simulations, and key residues facilitating the conduction were identified. The nonhelical parts of the two half-membrane-spanning segments expose carbonyl groups towards the channel interior, establishing a curve-linear pathway. The conformational stability of the NPA motifs is important in the conduction and critical for selectivity. Water and glycerol compete in a random manner for hydrogen bonding sites in the protein, and their translocations in single file are correlated. The suggested conduction mechanism should apply to the whole family.     

Structural determinants of proton blockage in aquaporins

Aquaporins are an important class of membrane channels selective for water and linear polyols but impermeable to ions, including protons. Recent computational studies have revealed that the relay of protons through the water-conduction pathway of aquaporin channels is opposed by a substantial free energy barrier peaking at the signature NPA motifs. Here, free-energy simulations and continuum electrostatic calculations are combined to examine the nature and the magnitude of the contribution of specific structural elements to proton blockage in the bacterial glycerol uptake facilitator, GlpF. Potential of mean-force profiles for both hop and turn steps of structural diffusion in the narrow pore are obtained for artificial variants of the GlpF channel in which coulombic interactions between the pore contents and conserved residues Asn68 and Asn203 at the NPA signature motifs, Arg206 at the selectivity filter, and the peptidic backbone of the two half-helices M3 and M7, which are arranged in head-to-head fashion around the NPA motifs, are turned off selectively. A comparison of these results with electrostatic energy profiles for the translocation of a probe cation throughout the water permeation pathway indicates that the free-energy profile for proton movement inside the narrow pore is dominated by static effects arising from the distribution of charged and polar groups of the channel, whereas dielectric effects contribute primarily to opposing the access of H+ to the pore mouths (desolvation penalty). The single most effective way to abolish the free-energy gradients opposing the movement of H+ around the NPA motif is to turn off the dipole moments of helices M3 and M7. Mutation of either of the two NPA Asn residues to Asp compensates for charge-dipole and dipole-dipole effects opposing the hop and turn steps of structural diffusion, respectively, and dramatically reduces the free energy barrier of proton translocation, suggesting that these single mutants could leak protons.     

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.     

Single-channel water permeabilities of Escherichia coli aquaporins AqpZ and GlpF

From equilibrium molecular dynamics simulations we have determined single-channel water permeabilities for Escherichia coli aquaporin Z (AqpZ) and aquaglyceroporin GlpF with the channels embedded in lipid bilayers. GlpF's osmotic water permeability constant pf exceeds by 2-3 times that of AqpZ and the diffusive permeability constant (pd) of GlpF is found to exceed that of AqpZ 2-9-fold. Achieving complete water selectivity in AqpZ consequently implies lower transport rates overall relative to the less selective, wider channel of GlpF. For AqpZ, the ratio pf/pd congruent with 12 is close to the average number of water molecules in the channel lumen, whereas for GlpF, pf/pd congruent with 4. This implies that single-file structure of the luminal water is more pronounced for AqpZ, the narrower channel of the two. Electrostatics profiles across the pore lumens reveal that AqpZ significantly reinforces water-channel interactions, and weaker water-water interactions in turn suppress water-water correlations relative to GlpF. Consequently, suppressed water-water correlations across the narrow selectivity filter become a key structural determinant for water permeation causing luminal water to permeate slower across AqpZ.     

K+ Block Is the Mechanism of Functional Asymmetry in Bacterial Nav Channels

Crystal structures of several bacterial Na_v channels have been recently published and molecular dynamics simulations of ion permeation through these channels are consistent with many electrophysiological properties of eukaryotic channels. Bacterial Na_v channels have been characterized as functionally asymmetric, and the mechanism of this asymmetry has not been clearly understood. To address this question, we combined non-equilibrium simulation data with two-dimensional equilibrium unperturbed landscapes generated by umbrella sampling and Weighted Histogram Analysis Methods for multiple ions traversing the selectivity filter of bacterial Na_vAb channel. This approach provided new insight into the mechanism of selective ion permeation in bacterial Na_v channels. The non-equilibrium simulations indicate that two or three extracellular K⁺ ions can block the entrance to the selectivity filter of Na_vAb in the presence of applied forces in the inward direction, but not in the outward direction. The block state occurs in an unstable local minimum of the equilibrium unperturbed free-energy landscape of two K⁺ ions that can be ‘locked’ in place by modest applied forces. In contrast to K⁺, three Na⁺ ions move favorably through the selectivity filter together as a unit in a loose “knock-on” mechanism of permeation in both inward and outward directions, and there is no similar local minimum in the two-dimensional free-energy landscape of two Na⁺ ions for a block state. The useful work predicted by the non-equilibrium simulations that is required to break the K⁺ block is equivalent to large applied potentials experimentally measured for two bacterial Na_v channels to induce inward currents of K⁺ ions. These results illustrate how inclusion of non-equilibrium factors in the simulations can provide detailed information about mechanisms of ion selectivity that is missing from mechanisms derived from either crystal structures or equilibrium unperturbed free-energy landscapes.     

Selectivity and conductance among the glycerol and water conducting aquaporin family of channels

The atomic structures of a transmembrane water plus glycerol conducting channel (GlpF), and now of aquaporin Z (AqpZ) from the same species, Escherichia coli, bring the total to three atomic resolution structures in the aquaporin (AQP) family. Members of the AQP family each assemble as tetramers of four channels. Common helical axes support a wider channel in the glycerol plus water channel paradigm, GlpF. Water molecules form a single hydrogen bonded file throughout the 28 A long channel in AqpZ. The basis for absolute exclusion of proton or hydronium ion conductance through the line of water is explored using simulations.     

What makes an aquaporin a glycerol channel? A comparative study of AqpZ and GlpF

The recent availability of high-resolution structures of two structurally highly homologous, but functionally distinct aquaporins from the same species, namely Escherichia coli AqpZ, a pure water channel, and GlpF, a glycerol channel, presents a unique opportunity to understand the mechanism of substrate selectivity in these channels. Comparison of the free energy profile of glycerol conduction through AqpZ and GlpF reveals a much larger barrier in AqpZ (22.8 kcal/mol) than in GlpF (7.3 kcal/mol). In either channel, the highest barrier is located at the selectivity filter. Analysis of substrate-protein interactions suggests that steric restriction of AqpZ is the main contribution to this large barrier. Another important difference is the presence of a deep energy well at the periplasmic vestibule of GlpF, which was not found in AqpZ. The latter difference can be attributed to the more pronounced structural asymmetry of GlpF, which may play a role in attracting glycerol.     

Pulling-speed-dependent force-extension profiles for semiflexible chains

We present theory and simulations to describe nonequilibrium stretching of semiflexible chains that serve as models of DNA molecules. Using a self-consistent dynamical variational approach, we calculate the force-extension curves for worm-like chains as a function of the pulling speed, v(0). Due to nonequilibrium effects the stretching force, which increases with v(0), shows nonmonotonic variations as the persistence length increases. To complement the theoretical calculations we also present Langevin simulation results for extensible worm-like chain models for the dynamics of stretching. The theoretical force-extension predictions compare well with the simulation results. The simulations show that, at high enough pulling speeds, the propagation of tension along the chain conformations transverse to the applied force occurs by the Brochard-Wyart's stem-flower mechanism. The predicted nonequilibrium effects can only be observed in double-stranded DNA at large ( approximately 100 microm/s) pulling speeds.     

Force-based analysis of multidimensional energy landscapes: application of dynamic force spectroscopy and steered molecular dynamics simulations to an antibody fragment-peptide complex

Multidimensional energy landscapes are an intrinsic property of proteins and define their dynamic behavior as well as their response to external stimuli. In order to explore the energy landscape and its implications on the dynamic function of proteins dynamic force spectroscopy and steered molecular dynamics (SMD) simulations have proved to be important tools. In this study, these techniques have been employed to analyze the influence of the direction of the probing forces on the complex of an antibody fragment with its peptide antigen. Using an atomic force microscope, experiments were performed where the attachment points of the 12 amino acid long peptide antigen were varied. These measurements yielded clearly distinguishable basal dissociation rates and potential widths, proving that the direction of the applied force determines the unbinding pathway. Complementary atomistic SMD simulations were performed, which also show that the unbinding pathways of the system are dependent on the pulling direction. However, the main barrier to be crossed was independent of the pulling direction and is represented by a backbone hydrogen bond between Gly^H-H40 of the antibody fragment and Glu^Oε-6_peptide of the peptide. For each pulling direction, the observed barriers can be correlated with the rupture of specific interactions, which stabilize the bound complex. Furthermore, although the SMD simulations were performed at loading rates exceeding the experimental rates by orders of magnitude due to computational limitations, a detailed comparison of the barriers that were overcome in the SMD simulations with the data obtained from the atomic force microscope unbinding experiments show excellent agreement.     

Electrostatic tuning of permeation and selectivity in aquaporin water channels

Water permeation and electrostatic interactions between water and channel are investigated in the Escherichia coli glycerol uptake facilitator GlpF, a member of the aquaporin water channel family, by molecular dynamics simulations. A tetrameric model of the channel embedded in a 16:0/18:1c9-palmitoyloleylphosphatidylethanolamine membrane was used for the simulations. During the simulations, water molecules pass through the channel in single file. The movement of the single file water molecules through the channel is concerted, and we show that it can be described by a continuous-time random-walk model. The integrity of the single file remains intact during the permeation, indicating that a disrupted water chain is unlikely to be the mechanism of proton exclusion in aquaporins. Specific hydrogen bonds between permeating water and protein at the channel center (at two conserved Asp-Pro-Ala "NPA" motifs), together with the protein electrostatic fields enforce a bipolar water configuration inside the channel with dipole inversion at the NPA motifs. At the NPA motifs water-protein electrostatic interactions facilitate this inversion. Furthermore, water-water electrostatic interactions are in all regions inside the channel stronger than water-protein interactions, except near a conserved, positively charged Arg residue. We find that variations of the protein electrostatic field through the channel, owing to preserved structural features, completely explain the bipolar orientation of water. This orientation persists despite water translocation in single file and blocks proton transport. Furthermore, we find that for permeation of a cation, ion-protein electrostatic interactions are more unfavorable at the conserved NPA motifs than at the conserved Arg, suggesting that the major barrier against proton transport in aquaporins is faced at the NPA motifs.     

Theoretical study of enzymatically catalyzed tautomerization of carbon acids in aqueous solution: quantum calculations and steered molecular dynamics simulations

The thermodynamics and kinetics of enzymatically assisted reactions of carbon acids were studied theoretically in this work. Quantum electronic (QE) structure calculations and steered molecular dynamics (SMD) simulations were carried out. Three 3-butenal tautomerization reactions that proceed from the β,γ-unsaturated reactant (R) to the α,β-unsaturated carbon acid product (P) and occur in two elementary steps through an intermediate (I) were studied, ignoring or including the surrounding aqueous medium in the calculations. The Gibbs free energies of activation of the R ? I enolization and I ? P ketonization steps were found to decrease considerably when residues simulating enzymes were introduced into these processes. Although the processes became slightly more favorable thermodynamically when the solution was included in the simulations, they became less favorable kinetically. The results from SMD simulations of these reactions were qualitatively consistent with the values we obtained using QE as well as those found by other authors in similar studies. Our simulations also allowed us to perform a detailed study of these reactions in solution.     

Fosfomycin Permeation through the Outer Membrane Porin OmpF

Fosfomycin is a frequently prescribed drug in the treatment of acute urinary tract infections. It enters the bacterial cytoplasm and inhibits the biosynthesis of peptidoglycans by targeting the MurA enzyme. Despite extensive pharmacological studies and clinical use, the permeability of fosfomycin across the bacterial outer membrane is largely unexplored. Here, we investigate the fosfomycin permeability across the outer membrane of Gram-negative bacteria by electrophysiology experiments as well as by all-atom molecular dynamics simulations including free-energy and applied-field techniques. Notably, in an electrophysiological zero-current assay as well as in the molecular simulations, we found that fosfomycin can rapidly permeate the abundant Escherichia coli porin OmpF. Furthermore, two triple mutants in the constriction region of the porin have been investigated. The permeation rates through these mutants are slightly lower than that of the wild type but fosfomycin can still permeate. Altogether, this work unravels molecular details of fosfomycin permeation through the outer membrane porin OmpF of E. coli and moreover provides hints for understanding the translocation of phosphonic acid antibiotics through other outer membrane pores.     

Modeling loop reorganization free energies of acetylcholinesterase: a comparison of explicit and implicit solvent models

The treatment of hydration effects in protein dynamics simulations varies in model complexity and spans the range from the computationally intensive microscopic evaluation to simple dielectric screening of charge-charge interactions. This paper compares different solvent models applied to the problem of estimating the free-energy difference between two loop conformations in acetylcholinesterase. Molecular dynamics (MD) simulations were used to sample potential energy surfaces of the two basins with solvent treated by means of explicit and implicit methods. Implicit solvent methods studied include the generalized Born (GB) model, atomic solvation potential (ASP), and the distance-dependent dieletric constant. By using the linear response approximation (LRA), the explicit solvent calculations determined a free-energy difference that is in excellent agreement with the experimental estimate, while rescoring the protein conformations with GB or the Poisson equation showed inconsistent and inferior results. While the approach of rescoring conformations from explicit water simulations with implicit solvent models is popular among many applications, it perturbs the energy landscape by changing the solvent contribution to microstates without conformational relaxation, thus leading to non-optimal solvation free energies. Calculations applying MD with a GB solvent model produced results of comparable accuracy as observed with LRA, yet the electrostatic free-energy terms were significantly different due to optimization on a potential energy surface favored by an implicit solvent reaction field. The simpler methods of ASP and the distance-dependent scaling of the dielectric constant both produced considerable distortions in the protein internal free-energy terms and are consequently unreliable.