Optimized particle-mesh Ewald/multiple-time step integration for molecular dynamics simulations

Predicting the DNA sequence dependence of nanopore ion current using atomic-resolution Brownian dynamics

It has become possible to distinguish DNA molecules of different nucleotide sequences by measuring ion current passing through a narrow pore containing DNA. To assist experimentalists in interpreting the results of such measurements and to improve the DNA sequence detection method, we have developed a computational approach that has both the atomic-scale accuracy and the computational efficiency required to predict DNA sequence-specific differences in the nanopore ion current. In our Brownian dynamics method, the interaction between the ions and DNA is described by three-dimensional potential of mean force maps determined to a 0.03 nm resolution from all-atom molecular dynamics simulations. While this atomic-resolution Brownian dynamics method produces results with orders of magnitude less computational effort than all-atom molecular dynamics requires, we show here that the ion distributions and ion currents predicted by the two methods agree. Finally, using our Brownian dynamics method, we find that a small change in the sequence of DNA within a pore can cause a large change in the ion current, and validate this result with all-atom molecular dynamics.

Optimization of the molecular dynamics method for simulations of DNA and ion transport through biological nanopores

Molecular dynamics (MD) simulations have become a standard method for the rational design and interpretation of experimental studies of DNA translocation through nanopores. The MD method, however, offers a multitude of algorithms, parameters, and other protocol choices that can affect the accuracy of the resulting data as well as computational efficiency. In this chapter, we examine the most popular choices offered by the MD method, seeking an optimal set of parameters that enable the most computationally efficient and accurate simulations of DNA and ion transport through biological nanopores. In particular, we examine the influence of short-range cutoff, integration timestep and force field parameters on the temperature and concentration dependence of bulk ion conductivity, ion pairing, ion solvation energy, DNA structure, DNA-ion interactions, and the ionic current through a nanopore.

Nanopore analysis of individual RNA/antibiotic complexes

Nanopores in thin solid-state membranes are used to rapidly analyze individual RNA/drug complexes. The interactions of a truncated A-site RNA model of the prokaryotic ribosome with aminoglycoside antibiotics are characterized by passing individual molecules through a 3-3.5 nm diameter pore fabricated in a 8-10 nm thick silicon nitride membrane. Complexes of the A-site RNA with aminoglycosides can be distinguished from unbound A-site based on the ion current signatures produced as they pass through the nanopores. Counting the fraction of free and drug-bound molecules affords label-free drug-RNA binding isotherms consistent with literature reports and with data generated using independent fluorescence-based assays. Our measurements are supported by molecular dynamics simulations, which illustrate the relationship between the ionic current and complexation of the A-site RNA with paramomycin, a prototypical aminoglycoside antibiotic.

Atoms-to-microns model for small solute transport through sticky nanochannels

Modeling the transport of solutes through fluidic systems that have adsorbing surfaces is challenging due to the range of length and time scales involved. The components of such systems typically have dimensions from hundreds of nanometres to microns, whereas adsorption of solutes is sensitive to the atomic-scale structure of the solutes and surfaces. Here, we describe an atomic-resolution Brownian dynamics method for modeling the transport of solutes through sticky nanofluidic channels. Our method can fully recreate the results of all-atom molecular dynamics simulations at a fraction of the computational cost of the latter, which makes simulations of micron-size channels at a millisecond time scale possible without losing information about the atomic-scale features of the system. We demonstrate the capability of our method by simulating the rise and fall of solute concentration in sub-micron-long sticky nanochannels, showing that the atomic-scale features of the channels' surfaces have a dramatic effect on the kinetics of solute transport in and out of the channels. We expect our method to find applications in design and optimization of micro and nanofluidic systems for solute-specific transport and to complement existing approaches to modeling lab-on-a-chip devices by providing atomic scale information at a low computational cost.

Characterizing and controlling the motion of ssDNA in a solid-state nanopore

Sequencing DNA in a synthetic solid-state nanopore is potentially a low-cost and high-throughput method. Essential to the nanopore-based DNA sequencing method is the ability to control the motion of a single-stranded DNA (ssDNA) molecule at single-base resolution. Experimental studies showed that the average translocation speed of DNA driven by a biasing electric field can be affected by ionic concentration, solvent viscosity, or temperature. Even though it is possible to slow down the average translocation speed, instantaneous motion of DNA is too diffusive to allow each DNA base to stay in front of a sensor site for its measurement. Using extensive all-atom molecular dynamics simulations, we study the diffusion constant, friction coefficient, electrophoretic mobility, and effective charge of ssDNA in a solid-state nanopore. Simulation results show that the spatial fluctuation of ssDNA in 1 ns is comparable to the spacing between neighboring nucleotides in ssDNA, which makes the sensing of a DNA base very difficult. We demonstrate that the recently proposed DNA transistor could potentially solve this problem by electrically trapping ssDNA inside the DNA transistor and ratcheting ssDNA base-by-base in a biasing electric field. When increasing the biasing electric field, we observed that the translocation of ssDNA changes from ratcheting to steady-sliding. The simulated translocation of ssDNA in the DNA transistor was theoretically characterized using Fokker-Planck analysis.

Lipid bilayer coated Al(2)O(3) nanopore sensors: towards a hybrid biological solid-state nanopore

Solid-state nanopore sensors are highly versatile platforms for the rapid, label-free electrical detection and analysis of single molecules, applicable to next generation DNA sequencing. The versatility of this technology allows for both large scale device integration and interfacing with biological systems. Here we report on the development of a hybrid biological solid-state nanopore platform that incorporates a highly mobile lipid bilayer on a single solid-state Al(2)O(3) nanopore sensor, for the potential reconstitution of ion channels and biological nanopores. Such a system seeks to combine the superior electrical, thermal, and mechanical stability of Al(2)O(3) solid-state nanopores with the chemical specificity of biological nanopores. Bilayers on Al(2)O(3) exhibit higher diffusivity than those formed on TiO(2) and SiO(2) substrates, attributed to the presence of a thick hydration layer on Al(2)O(3), a key requirement to preserving the biological functionality of reconstituted membrane proteins. Molecular dynamics simulations demonstrate that the electrostatic repulsion between the dipole of the DOPC headgroup and the positively charged Al(2)O(3) surface may be responsible for the enhanced thickness of this hydration layer. Lipid bilayer coated Al(2)O(3) nanopore sensors exhibit excellent electrical properties and enhanced mechanical stability (GΩ seals for over 50 h), making this technology ideal for use in ion channel electrophysiology, the screening of ion channel active drugs and future integration with biological nanopores such as α-hemolysin and MspA for rapid single molecule DNA sequencing. This technology can find broad application in bio-nanotechnology.

Dual chaperone role of the C-terminal propeptide in folding and oligomerization of the pore-forming toxin aerolysin

Throughout evolution, one of the most ancient forms of aggression between cells or organisms has been the production of proteins or peptides affecting the permeability of the target cell membrane. This class of virulence factors includes the largest family of bacterial toxins, the pore-forming toxins (PFTs). PFTs are bistable structures that can exist in a soluble and a transmembrane state. It is unclear what drives biosynthetic folding towards the soluble state, a requirement that is essential to protect the PFT-producing cell. Here we have investigated the folding of aerolysin, produced by the human pathogen Aeromonas hydrophila, and more specifically the role of the C-terminal propeptide (CTP). By combining the predictive power of computational techniques with experimental validation using both structural and functional approaches, we show that the CTP prevents aggregation during biosynthetic folding. We identified specific residues that mediate binding of the CTP to the toxin. We show that the CTP is crucial for the control of the aerolysin activity, since it protects individual subunits from aggregation within the bacterium and later controls assembly of the quaternary pore-forming complex at the surface of the target host cell. The CTP is the first example of a C-terminal chain-linked chaperone with dual function.

Many pathogenic bacteria produce proteins, called pore-forming toxins, designed to perforate the plasma membrane of target cells thus perturbing host cell integrity and functionality. It is, however, important that these toxins do not form pores in the producing bacterium. To prevent this, bacteria initially produce them in a soluble state. After being secreted by the bacterium, the toxin subsequently acquires – often through a multimerization step– the ability to insert into the membrane. Here we were interested in the mechanisms ensuring that the toxin initially folds into the soluble state. Using as an example aerolysin from the human pathogen Aeromonas hydrophila, we show that the bacterium produces the toxin with a C-terminal extension of about 45 amino acids that promotes the folding of the protein into the soluble state. We find that by mutating or removing this extension, the protein folds poorly or not at all. Addition of the peptide in trans however lead to partial recovery of activity suggesting that this extension promotes folding, and being intramolecular thus results in a very high effective concentration. In addition to this chaperone role for correctly folding the monomeric form of the toxin, the C-terminal peptide is also crucial for controlling the folding of the quaternary structure of the mature pore complex at the surface of the target host cell.

Separating instability from aggregation propensity in γS-crystallin variants

Molecular dynamics (MD) simulations, circular dichroism (CD), and dynamic light scattering (DLS) measurements were used to investigate the aggregation propensity of the eye-lens protein γS-crystallin. The wild-type protein was investigated along with the cataract-related G18V variant and the symmetry-related G106V variant. The MD simulations suggest that local sequence differences result in dramatic differences in dynamics and hydration between these two apparently similar point mutations. This finding is supported by the experimental measurements, which show that although both variants appear to be mostly folded at room temperature, both display increased aggregation propensity. Although the disease-related G18V variant is not the most strongly destabilized, it aggregates more readily than either the wild-type or the G106V variant. These results indicate that γS-crystallin provides an excellent model system for investigating the role of dynamics and hydration in aggregation by locally unfolded proteins.

Control of Nanoscale Environment to Improve Stability of Immobilized Proteins on Diamond Surfaces

Immunoassays for detection of bacterial pathogens rely on the selectivity and stability of bio-recognition elements such as antibodies tethered to sensor surfaces. The search for novel surfaces that improve the stability of biomolecules and assay performance has been pursued for a long time. However, the anticipated improvements in stability have not been realized in practice under physiological conditions because the surface functionalization layers on commonly used substrates, silica and gold, are themselves unstable on time scales of days. In this paper, we show that covalent linking of antibodies to diamond surfaces leads to substantial improvements in biological activity of proteins as measured by the ability to selectively capture cells of the pathogenic bacterium Escherichia coli O157:H7 even after exposure to buffer solutions at 37 °C for extended periods of time, approaching 2 weeks. Our results from ELISA, XPS, fluorescence microscopy, and MD simulations suggest that by using highly stable surface chemistry and controlling the nanoscale organization of the antibodies on the surface, it is possible to achieve significant improvements in biological activity and stability. Our findings can be easily extended to functionalization of micro and nanodimensional sensors and structures of biomedical diagnostic and therapeutic interest.

Rectification of the current in alpha-hemolysin pore depends on the cation type: the alkali series probed by MD simulations and experiments

A striking feature of the alpha-hemolysin channel-a prime candidate for biotechnological applications-is the dependence of its ionic conductance on the magnitude and direction of the applied bias. Through a combination of lipid bilayer single-channel recording and molecular dynamics (MD) simulations, we characterized the current-voltage relationship of alpha-hemolysin for all alkali chloride salts at neutral pH. The rectification of the ionic current was found to depend on the type of cations and increase from Li(+) to Cs(+). Analysis of the MD trajectories yielded a simple quantitative model that related the ionic current to the electrostatic potential, the concentration and effective mobility of ions in the channel. MD simulations reveal that the major contribution to the current asymmetry and rectification properties originates from the cationic contribution to the current that is significantly reduced in a cationic dependent way when the membrane polarity is reversed. The variation of chloride current was found to be less important. We report that the differential affinity of cations for the charged residues positioned at the channel's end modulates the number of ions inside the channel stem thus affecting the current properties. Through direct comparison of simulation and experiment, this study evaluates the accuracy of the MD method for prediction of the asymmetric, voltage dependent conductances of a membrane channel.

Modeling Pressure-Driven Transport of Proteins through a Nanochannel

Reducing the size of a nanofluidic channel not only creates new opportunities for high-precision manipulation of biological macromolecules, but also makes the performance of the entire nanofluidic system more susceptible to undesirable interactions between the transported biomolecules and the walls of the channel. In this manuscript, we report molecular dynamics simulations of a pressure-driven flow through a silica nanochannel that characterized, with atomic resolution, adsorption of a model protein to its surface. Although the simulated adsorption of the proteins was found to be nonspecific, it had a dramatic effect on the rate of the protein transport. To determine the relative strength of the protein-silica interactions in different adsorbed states, we simulated flow-induced desorption of the proteins from the silica surface. Our analysis of the protein conformations in the adsorbed states did not reveal any simple dependence of the adsorption strength on the size and composition of the protein-silica contact, suggesting that the heterogeneity of the silica surface may be a important factor.

Control and reversal of the electrophoretic force on DNA in a charged nanopore

Electric field driven transport of DNA through solid-state nanopores is the key process in nanopore-based DNA sequencing that promises dramatic reduction of genome sequencing costs. A major hurdle in the development of this sequencing method is that DNA transport through the nanopores occurs too quickly for the DNA sequence to be detected. By means of all-atom molecular dynamics simulations, we demonstrate that the velocity of DNA transport through a nanopore can be controlled by the charge state of the nanopore surface. In particular, we show that the charge density of the nanopore surface controls the magnitude and/or direction of the electro-osmotic flow through the nanopore and thereby can significantly reduce or even reverse the effective electrophoretic force on DNA. Our work suggests a physical mechanism to control DNA transport in a nanopore by chemical, electrical or electrochemical modification of the nanopore surface.

The effect of calcium on the conformation of cobalamin transporter BtuB

BtuB is a beta-barrel membrane protein that facilitates transport of cobalamin (vitamin B12) from the extracellular medium across the outer membrane of Escherichia coli. It is thought that binding of B12 to BtuB alters the conformation of its periplasm-exposed N-terminal residues (the TonB box), which enables subsequent binding of a TonB protein and leads to eventual uptake of B12 into the cytoplasm. Structural studies determined the location of the B12 binding site at the top of the BtuB's beta-barrel, surrounded by extracellular loops. However, the structure of the loops was found to depend on the method used to obtain the protein crystals, which-among other factors-differed in calcium concentration. Experimentally, calcium concentration was found to modulate the binding of the B12 substrate to BtuB. In this study, we investigate the effect of calcium ions on the conformation of the extracellular loops of BtuB and their possible role in B12 binding. Using all-atom molecular dynamics, we simulate conformational fluctuations of several X-ray structures of BtuB in the presence and absence of calcium ions. These simulations demonstrate that calcium ions can stabilize the conformation of loops 3-4, 5-6, and 15-16, and thereby prevent occlusion of the binding site. Furthermore, binding of calcium ions to extracellular loops of BtuB was found to enhance correlated motions in the BtuB structure, which is expected to promote signal transduction. Finally, we characterize conformation dynamics of the TonB box in different X-ray structures and find an interesting correlation between the stability of the TonB box structure and calcium binding.

Deciphering ionic current signatures of DNA transport through a nanopore

Within just a decade from the pioneering work demonstrating the utility of nanopores for molecular sensing, nanopores have emerged as versatile systems for single-molecule manipulation and analysis. In a typical setup, a gradient of the electrostatic potential captures charged solutes from the solution and forces them to move through a single nanopore, across an otherwise impermeable membrane. The ionic current blockades resulting from the presence of a solute in a nanopore can reveal the type of the solute, for example, the nucleotide makeup of a DNA strand. Despite great success, the microscopic mechanisms underlying the functionality of such stochastic sensors remain largely unknown, as it is not currently possible to characterize the microscopic conformations of single biomolecules directly in a nanopore and thereby unequivocally establish the causal relationship between the observables and the microscopic events. Such a relationship can be determined using molecular dynamics-a computational method that can accurately predict the time evolution of a molecular system starting from a given microscopic state. This article describes recent applications of this method to the process of DNA transport through biological and synthetic nanopores.

Three-dimensional molecular theory of solvation coupled with molecular dynamics in Amber

We present the three-dimensional molecular theory of solvation (also known as 3D-RISM) coupled with molecular dynamics (MD) simulation by contracting solvent degrees of freedom, accelerated by extrapolating solvent-induced forces and applying them in large multi-time steps (up to 20 fs) to enable simulation of large biomolecules. The method has been implemented in the Amber molecular modeling package, and is illustrated here on alanine dipeptide and protein G.

Electric and Electrophoretic Inversion of the DNA Charge in Multivalent Electrolytes

Counterion-induced inversion of the DNA charge was characterized through extensive molecular dynamics simulations. We observed reversal of the DNA motion in an external electric field upon increasing the concentration of trivalent or quadrivalent counterions. In the case of a divalent electrolyte, inversion of the DNA's electric charge was observed at high concentrations of the electrolyte but not reversal of the DNA' electrophoretic motion. We demonstrate that inversion of the DNA's electrophoretic mobility results from a complex interplay of electrostatics and hydrodynamics.

Ionic current flow through ZnO nanotubes

The control of ionic current (electrolyte) flow through zinc oxide (ZnO) nanotubes is investigated. We studied a structure operating like a field effect transistor with a tunable ionic flow. The main investigation tool used was molecular dynamics simulation. We complemented the molecular dynamics simulation with the site binding method in order to study the effect of the double layer on the ionic current flowing through the nanotube. We achieved this by considering the electrolyte solution as a virtual semiconductor wire. The double layer capacitance and surface charge of the inner walls of the ZnO nanotube have been calculated. The results indicate that ZnO nanotubes can be tuned to operate as ion selectors. ZnO nanotubes exhibit enhanced functionality with characteristics similar to those of the nanopore membrane.

Structure, dynamics, and ion conductance of the phospholamban pentamer

A 52-residue membrane protein, phospholamban (PLN) is an inhibitor of an adenosine-5'-triphosphate-driven calcium pump, the Ca2+-ATPase. Although the inhibition of Ca2+-ATPase involves PLN monomers, in a lipid bilayer membrane, PLN monomers form stable pentamers of unknown biological function. The recent NMR structure of a PLN pentamer depicts cytoplasmic helices extending normal to the bilayer in what is known as the bellflower conformation. The structure shows transmembrane helices forming a hydrophobic pore 4 A in diameter, which is reminiscent of earlier reports of possible ion conductance through PLN pentamers. However, recent FRET measurements suggested an alternative structure for the PLN pentamer, known as the pinwheel model, which features a narrower transmembrane pore and cytoplasmic helices that lie against the bilayer. Here, we report on structural dynamics and conductance properties of the PLN pentamers from all-atom (AA) and coarse-grained (CG) molecular dynamics simulations. Our AA simulations of the bellflower model demonstrate that in a lipid bilayer membrane or a detergent micelle, the cytoplasmic helices undergo large structural fluctuations, whereas the transmembrane pore shrinks and becomes asymmetric. Similar asymmetry of the transmembrane region was observed in the AA simulations of the pinwheel model; the cytoplasmic helices remained in contact with the bilayer. Using the CG approach, structural dynamics of both models were investigated on a microsecond timescale. The cytoplasmic helices of the CG bellflower model were observed to fall against the bilayer, whereas in the CG pinwheel model the conformation of the cytoplasmic helices remained stable. Using steered molecular dynamics simulations, we investigated the feasibility of ion conductance through the pore of the bellflower model. The resulting approximate potentials of mean force indicate that the PLN pentamer is unlikely to function as an ion channel.

Analyzing the forces binding a restriction endonuclease to DNA using a synthetic nanopore

Restriction endonucleases are used prevalently in recombinant DNA technology because they bind so stably to a specific target sequence and, in the presence of cofactors, cleave double-helical DNA specifically at a target sequence at a high rate. Using synthetic nanopores along with molecular dynamics (MD), we have analyzed with atomic resolution how a prototypical restriction endonuclease, EcoRI, binds to the DNA target sequence--GAATTC--in the absence of a Mg(2+) ion cofactor. We have previously shown that there is a voltage threshold for permeation of DNA bound to restriction enzymes through a nanopore that is associated with a nanonewton force required to rupture the complex. By introducing mutations in the DNA, we now show that this threshold depends on the recognition sequence and scales linearly with the dissociation energy, independent of the pore geometry. To predict the effect of mutation in a base pair on the free energy of dissociation, MD is used to qualitatively rank the stability of bonds in the EcoRI-DNA complex. We find that the second base in the target sequence exhibits the strongest binding to the protein, followed by the third and first bases, with even the flanking sequence affecting the binding, corroborating our experiments.

Microscopic mechanics of hairpin DNA translocation through synthetic nanopores

Nanoscale pores have proved useful as a means to assay DNA and are actively being developed as the basis of genome sequencing methods. Hairpin DNA (hpDNA), having both double-helical and overhanging coil portions, can be trapped in a nanopore, giving ample time to execute a sequence measurement. In this article, we provide a detailed account of hpDNA interaction with a synthetic nanopore obtained through extensive all-atom molecular dynamics simulations. For synthetic pores with minimum diameters from 1.3 to 2.2 nm, we find that hpDNA can translocate by three modes: unzipping of the double helix and--in two distinct orientations--stretching/distortion of the double helix. Furthermore, each of these modes can be selected by an appropriate choice of the pore size and voltage applied transverse to the membrane. We demonstrate that the presence of hpDNA can dramatically alter the distribution of ions within the pore, substantially affecting the ionic current through it. In experiments and simulations, the ionic current relative to that in the absence of DNA can drop below 10% and rise beyond 200%. Simulations associate the former with the double helix occupying the constriction and the latter with accumulation of DNA that has passed through the constriction.

Strain softening in stretched DNA

The microscopic mechanics of DNA stretching was characterized using extensive molecular dynamics simulations. By employing an anisotropic pressure-control method, realistic force-extension dependences of effectively infinite DNA molecules were obtained. A coexistence of B and S DNA domains was observed during the overstretching transition. The simulations revealed that strain softening may occur in the process of stretching torsionally constrained DNA. The latter observation was qualitatively reconciled with available experimental data using a random-field Ising model.

In meso crystal structure and docking simulations suggest an alternative proteoglycan binding site in the OpcA outer membrane adhesin

OpcA is an integral outer membrane adhesin protein from Neisseria meningitidis, the causative agent of meningococcal meningitis and septicemia. It binds to sialic acid (SA)-containing polysaccharides on the surface of epithelial cells. The crystal structure of OpcA showed that the protein adopts a 10-stranded beta-barrel structure, with five extensive loop regions on the extracellular side of the membrane. These form a crevice structure, lined with basic residues, which was hypothesized to act as the binding site for polysaccharide ligands. In the current study, a distinctly different OpcA structure has been obtained using crystals grown from a lipidic mesophase. Comparison of the two structures shows that the largest loop (L2), which closes over the end of the beta-barrel in the original crystal form, adopts a much more extended structure by reaching outward and away from the protein. The difference in conformation may be attributable to the absence of zinc ions from the crystallization conditions for the in meso crystal form: in the original structure, two zinc ions were bound to the external loops. Molecular dynamics (MD) simulations performed on the two OpcA models in a lipid bilayer environment demonstrated pronounced loop mobility. These observations support the view that the loop regions of OpcA are capable of a high degree of conformational flexibility. The original binding site for polysaccharide is not present in the in meso crystal form, and is disrupted during MD simulations. Docking analysis suggests a putative alternative location for the SA ligand in the new crystal form of OpcA.

Structure refinement of the OpcA adhesin using molecular dynamics

OpcA from Neisseria meningitidis, the causative agent of meningococcal meningitis and septicemia, is an integral outer membrane protein that facilitates meningococcal adhesion through binding the proteoglycan receptors of susceptible cells. Two structures of OpcA have been determined by x-ray diffraction to 2 A resolution, revealing dramatically different conformations in the extracellular loops--the protein domain implicated in proteoglycan binding. In the first structure, a positively charged crevice formed by loops 1 and 2 was identified as the site for binding proteoglycans, whereas in the second structure the crevice was not evident as loops 1 and 2 adopted different conformations. To reconcile these results, molecular-dynamics simulations were carried out on both structures embedded in a solvated lipid bilayer membrane. Free of crystal contacts and crystallization agents, the loops were observed to undergo large structural transformations, suggesting that the conformation of the loops in either x-ray structure is affected by crystallization. Subsequent simulations of both structures in their crystal lattices confirmed this conclusion. Based on our molecular-dynamics trajectories, we propose a model for OpcA that combines stable structural features of the available x-ray structures. In this model, all five extracellular loops of OpcA have stable secondary structures. The loops form a funnel that leads to the base of the beta-barrel and that includes Tyr-169 on its exposed surface, which has been implicated in proteoglycan binding.

How directional translocation is regulated in a DNA helicase motor

PcrA helicase from Bacillus stearothermophilus is one of the smallest motor proteins structurally known in full atomic detail. It translocates progressively from the 3' end to the 5' end of single-stranded DNA utilizing the free energy from ATP hydrolysis. The similarities in structure and reaction pathway between PcrA helicase and F1-ATPase suggest a similar mechanochemical mechanism at work in both systems. Previous studies of PcrA translocation demonstrated a domain stepping mechanism in which, during one ATP hydrolysis cycle, the pulling together and pushing apart of two translocation domains is synchronized with alternating mobilities of the individual domains such that PcrA moves unidirectionally along single-stranded DNA. To substantiate this translocation mechanism, this study applies molecular dynamics simulations, elastic network theory, and multiple sequence alignment to analyze the system. The analysis provides further evidence that directional translocation of PcrA is regulated allosterically through synchronization of ATP hydrolysis and domain mobilities. We identify a set of essential residues coevolutionarily coupled in related helicases that should be involved in the allosteric regulation of these motor proteins.

Exploring transmembrane transport through alpha-hemolysin with grid-steered molecular dynamics

The transport of biomolecules across cell boundaries is central to cellular function. While structures of many membrane channels are known, the permeation mechanism is known only for a select few. Molecular dynamics (MD) is a computational method that can provide an accurate description of permeation events at the atomic level, which is required for understanding the transport mechanism. However, due to the relatively short time scales accessible to this method, it is of limited utility. Here, we present a method for all-atom simulation of electric field-driven transport of large solutes through membrane channels, which in tens of nanoseconds can provide a realistic account of a permeation event that would require a millisecond simulation using conventional MD. In this method, the average distribution of the electrostatic potential in a membrane channel under a transmembrane bias of interest is determined first from an all-atom MD simulation. This electrostatic potential, defined on a grid, is subsequently applied to a charged solute to steer its permeation through the membrane channel. We apply this method to investigate permeation of DNA strands, DNA hairpins, and alpha-helical peptides through alpha-hemolysin. To test the accuracy of the method, we computed the relative permeation rates of DNA strands having different sequences and global orientations. The results of the G-SMD simulations were found to be in good agreement in experiment.

Construction of 3D models of the CYP11B family as a tool to predict ligand binding characteristics

Aldosterone is synthesised by aldosterone synthase (CYP11B2). CYP11B2 has a highly homologous isoform, steroid 11beta-hydroxylase (CYP11B1), which is responsible for the biosynthesis of aldosterone precursors and glucocorticoids. To investigate aldosterone biosynthesis and facilitate the search for selective CYP11B2 inhibitors, we constructed three-dimensional models for CYP11B1 and CYP11B2 for both human and rat. The models were constructed based on the crystal structure of Pseudomonas Putida CYP101 and Oryctolagus Cuniculus CYP2C5. Small steric active site differences between the isoforms were found to be the most important determinants for the regioselective steroid synthesis. A possible explanation for these steric differences for the selective synthesis of aldosterone by CYP11B2 is presented. The activities of the known CYP11B inhibitors metyrapone, R-etomidate, R-fadrazole and S-fadrazole were determined using assays of V79MZ cells that express human CYP11B1 and CYP11B2, respectively. By investigating the inhibitors in the human CYP11B models using molecular docking and molecular dynamics simulations we were able to predict a similar trend in potency for the inhibitors as found in the in vitro assays. Importantly, based on the docking and dynamics simulations it is possible to understand the enantioselectivity of the human enzymes for the inhibitor fadrazole, the R-enantiomer being selective for CYP11B2 and the S-enantiomer being selective for CYP11B1.

A multiple time step algorithm compatible with a large number of distance classes and an arbitrary distance dependence of the time step size for the fast evaluation of nonbonded interactions in molecular simulations

A new algorithm is introduced to perform the multiple time step integration of the equations of motion for a molecular system, based on the splitting of the nonbonded interactions into a series of distance classes. The interactions between particle pairs in successive classes are updated at a progressively decreasing frequency. Unlike previous multiple time-stepping schemes relying on distance classes, the present algorithm sorts interacting particle pairs by their next update times rather than by their update frequencies. For this reason, the proposed scheme is extremely flexible with respect to the number of classes that can be employed (up to hundred or more) and the distance dependence of the relative time step size (arbitrary integer function of the distance). It can also easily be adapted to classes defined based on a criterion other than the interparticle distance (e.g., interaction magnitude). Different variants of the algorithm are tested in terms of accuracy and efficiency for simulations of a pure water system (6167 molecules) under truncated-octahedral periodic boundary conditions, and compared to the twin-range method standardly used with GROMOS96 (short- and long-range cutoff distances of 0.8 and 1.4 nm, pair list and intermediate-range interactions updated every five steps). In particular, multiple time-stepping schemes with an accuracy comparable to that of the twin-range method can be designed, that permit to increase the effective (long-range) cutoff distance from 1.4 to 3.0 nm with a performance loss of only about a factor 2. This result is quite encouraging, considering the benefits of doubling the cutoff radius in the context of (bio-)molecular simulations.

Adaptive time stepping in biomolecular dynamics

We present an adaptive time stepping scheme based on the extrapolative method of Barth and Schlick [LN, J. Chem. Phys. 109, 1633 (1998)] to numerically integrate the Langevin equation with a molecular-dynamics potential. This approach allows us to use (on average) a time step for the strong nonbonded force integration corresponding to half the period of the fastest bond oscillation, without compromising the slow degrees of freedom in the problem. We show with simple examples how the dynamic step size stabilizes integration operators, and discuss some of the limitations of such stability. The method introduced uses a slightly more accurate inner integrator than LN to accommodate the larger steps. The adaptive time step approach reproduces temporal features of the bovine pancreatic trypsin inhibitor (BPTI) test system (similar to the one used in the original introduction of LN) compared to short-time integrators, but with energies that are shifted with respect to both LN, and traditional stochastic versions of Verlet. Although the introduction of longer steps has the effect of systematically heating the bonded components of the potential, the temporal fluctuations of the slow degrees of freedom are reproduced accurately. The purpose of this paper is to display a mechanism by which the resonance traditionally associated with using time steps corresponding to half the period of oscillations in molecular dynamics can be avoided. This has theoretical utility in terms of designing numerical integration schemes--the key point is that by factoring a propagator so that time steps are not constant one can recover stability with an overall (average) time step at a resonance frequency. There are, of course, limitations to this approach associated with the complicated, nonlinear nature of the molecular-dynamics (MD) potential (i.e., it is not as straightforward as the linear test problem we use to motivate the method). While the basic notion remains in the full Newtonian problem, it is easier to see the effects when damping is considered to be physical--that is, we do not view our method as a perturbation of Newtonian dynamics, we associate the damping with the environment, for example, a water bath (with gamma approximately 90 ps(-1)) [Zagrovic and Pande, J. Comp. Chem. 24, 1432 (2003)]. All stochastic approaches to MD are stabilized by large physical damping, but here, we are really using it only to show that the resonance frequency can be obtained. Another simplifying assumption used in this paper is "heavy" hydrogen (we take the hydrogen mass to be 10 amu)--the view here is that we are interested primarily in the slowest degrees of freedom, and this approach has effects similar to bond freezing and united atom treatments of hydrogen. So from the point of view of biomolecular applications, the method described here is best suited to studies in which water is not explicit (so that damping in the problem can really be viewed as environmental interaction), and the interest is in slow dynamics where the effects of hydrogen are neglectable. There are a number of parameters in the LN method and the one derived here, and we cannot in a short paper address all adjustments, so our primary goal as a first pass is to show that stability can be recovered for a set of numerically forced (and hence artificial) bond oscillations, and compare stability to fixed-step methods.

Detecting SNPs using a synthetic nanopore

We have discovered a voltage threshold for permeation through a synthetic nanopore of dsDNA bound to a restriction enzyme that depends on the sequence. Molecular dynamic simulations reveal that the threshold is associated with a nanonewton force required to rupture the DNA-protein complex. A single mutation in the recognition site for the restriction enzyme, i.e., a single nucleotide polymorphism (SNP), can easily be detected as a change in the threshold voltage. Consequently, by measuring the threshold voltage in a synthetic nanopore, it may be possible to discriminate between two variants of the same gene (alleles) that differ in one base.

Langevin stabilization of molecular-dynamics simulations of polymers by means of quasisymplectic algorithms

Algorithms for the numerical integration of Langevin equations are compared in detail from the point of view of their accuracy, numerical efficiency, and stability to assess them as potential candidates for molecular-dynamics simulations of polymeric systems. Some algorithms are symplectic in the deterministic frictionless limit and prove to stabilize long time-step integrators. They are tested against other popular algorithms. The optimal algorithm depends on the main goal: accuracy or efficiency. The former depends on the observable of interest. A recently developed quasisymplectic algorithm with great accuracy in the position evaluation exhibits better overall accuracy and stability than the other ones. On the other hand, the well-known BrunGer-Brooks-Karplus [Chem. Phys. Lett. 105, 495 (1982)] algorithm is found to be faster with limited accuracy loss but less stable. It is also found that using higher-order algorithms does not necessarily improve the accuracy. Moreover, they usually require more force evaluations per single step, thus leading to poorer performances.

Structure-based model of the stepping motor of PcrA helicase

DNA helicases are ubiquitous molecular motors involved in cellular DNA metabolism. They move along single-stranded DNA (ssDNA) and separate duplex DNA into its component strands, utilizing the free energy from ATP hydrolysis. The PcrA helicase from Bacillus stearothermophilus translocates as a monomer progressively from the 3' end to the 5' end of ssDNA and is one of the smallest motor proteins structurally known in full atomic detail. Using high-resolution crystal structures of the PcrA-DNA complex, we performed nanosecond molecular dynamics simulations and derived potential energy profiles governing individual domain movement of the PcrA helicase along ssDNA. Based on these profiles, the millisecond translocation of the helicase along ssDNA was described through Langevin dynamics. The calculations support a domain stepping mechanism of PcrA helicase, in which, during one ATP hydrolysis cycle, the pulling together and pushing apart of domains 2A and 1A are synchronized with alternating mobilities of the individual domains in such a fashion that PcrA moves unidirectionally along ssDNA. By combining short timescale (nanoseconds) molecular dynamics and long timescale (milliseconds) stochastic-dynamics descriptions, our study suggests a structure-based mechanism of the ATP-powered unidirectional movement of PcrA helicase.

Gaussian split Ewald: A fast Ewald mesh method for molecular simulation

Gaussian split Ewald (GSE) is a versatile Ewald mesh method that is fast and accurate when used with both real-space and k-space Poisson solvers. While real-space methods are known to be asymptotically superior to k-space methods in terms of both computational cost and parallelization efficiency, k-space methods such as smooth particle-mesh Ewald (SPME) have thus far remained dominant because they have been more efficient than existing real-space methods for simulations of typical systems in the size range of current practical interest. Real-space GSE, however, is approximately a factor of 2 faster than previously described real-space Ewald methods for the level of force accuracy typically required in biomolecular simulations, and is competitive with leading k-space methods even for systems of moderate size. Alternatively, GSE may be combined with a k-space Poisson solver, providing a conveniently tunable k-space method that performs comparably to SPME. The GSE method follows naturally from a uniform framework that we introduce to concisely describe the differences between existing Ewald mesh methods.

Interface connections of a transmembrane voltage sensor

Voltage-sensitive ion channels open and close in response to changes in transmembrane (TM) potential caused by the motion of the S4 voltage sensors. These sensors are alpha-helices that include four or more positively charged amino acids, most commonly arginine. The so-called paddle model, based on the high-resolution structure of the KvAP K+ channel [Jiang, et al. (2003) Nature 423, 33-41], posits that the S4 sensors move within the membrane bilayer in response to TM voltage changes. Direct exposure of S4 sensors to lipid is contrary to the classical expectation that the dielectric contrast between the membrane hydrocarbon core and water presents an insurmountable energetic penalty to burial of electric charges. Nevertheless, recent experiments have shown that a helix with the sequence of KvAP S4 can be inserted across the endoplasmic reticulum membrane. To reconcile this result with the classical energetics argument, we have carried out a molecular dynamics simulation of an isolated TM S4 helix in a lipid bilayer. The simulation reveals a stabilizing hydrogen-bonded network of water and lipid phosphates around the arginines that reduces the effective thickness of the bilayer hydrocarbon core to approximately 10 A in the vicinity of the helix. It suggests that bilayer phospholipids can adapt locally to strongly perturbing protein elements, causing the phospholipids to become a structural extension of the protein.

Imaging alpha-hemolysin with molecular dynamics: ionic conductance, osmotic permeability, and the electrostatic potential map

alpha-Hemolysin of Staphylococcus aureus is a self-assembling toxin that forms a water-filled transmembrane channel upon oligomerization in a lipid membrane. Apart from being one of the best-studied toxins of bacterial origin, alpha-hemolysin is the principal component in several biotechnological applications, including systems for controlled delivery of small solutes across lipid membranes, stochastic sensors for small solutes, and an alternative to conventional technology for DNA sequencing. Through large-scale molecular dynamics simulations, we studied the permeability of the alpha-hemolysin/lipid bilayer complex for water and ions. The studied system, composed of approximately 300,000 atoms, included one copy of the protein, a patch of a DPPC lipid bilayer, and a 1 M water solution of KCl. Monitoring the fluctuations of the pore structure revealed an asymmetric, on average, cross section of the alpha-hemolysin stem. Applying external electrostatic fields produced a transmembrane ionic current; repeating simulations at several voltage biases yielded a current/voltage curve of alpha-hemolysin and a set of electrostatic potential maps. The selectivity of alpha-hemolysin to Cl(-) was found to depend on the direction and the magnitude of the applied voltage bias. The results of our simulations are in excellent quantitative agreement with available experimental data. Analyzing trajectories of all water molecule, we computed the alpha-hemolysin's osmotic permeability for water as well as its electroosmotic effect, and characterized the permeability of its seven side channels. The side channels were found to connect seven His-144 residues surrounding the stem of the protein to the bulk solution; the protonation of these residues was observed to affect the ion conductance, suggesting the seven His-144 to comprise the pH sensor that gates conductance of the alpha-hemolysin channel.

MDSIMAID: Automatic parameter optimization in fast electrostatic algorithms

MDSIMAID is a recommender system that optimizes parallel Particle Mesh Ewald (PME) and both sequential and parallel multigrid (MG) summation fast electrostatic solvers. MDSIMAID optimizes the running time or parallel scalability of these methods within a given error tolerance. MDSIMAID performs a run time constrained search on the parameter space of each method starting from semiempirical performance models. Recommended parameters are presented to the user. MDSIMAID's optimization of MG leads to configurations that are up to 14 times faster or 17 times more accurate than published recommendations. Optimization of PME can improve its parallel scalability, making it run twice as fast in parallel in our tests. MDSIMAID and its Python source code are accessible through a Web portal located at http://mdsimaid.cse.nd.edu.

Insights into the molecular mechanism of rotation in the Fo sector of ATP synthase

F(1)F(o)-ATP synthase is a ubiquitous membrane protein complex that efficiently converts a cell's transmembrane proton gradient into chemical energy stored as ATP. The protein is made of two molecular motors, F(o) and F(1), which are coupled by a central stalk. The membrane unit, F(o), converts the transmembrane electrochemical potential into mechanical rotation of a rotor in F(o) and the physically connected central stalk. Based on available data of individual components, we have built an all-atom model of F(o) and investigated through molecular dynamics simulations and mathematical modeling the mechanism of torque generation in F(o). The mechanism that emerged generates the torque at the interface of the a- and c-subunits of F(o) through side groups aSer-206, aArg-210, and aAsn-214 of the a-subunit and side groups cAsp-61 of the c-subunits. The mechanism couples protonation/deprotonation of two cAsp-61 side groups, juxtaposed to the a-subunit at any moment in time, to rotations of individual c-subunit helices as well as rotation of the entire c-subunit. The aArg-210 side group orients the cAsp-61 side groups and, thereby, establishes proton transfer via aSer-206 and aAsn-214 to proton half-channels, while preventing direct proton transfer between the half-channels. A mathematical model proves the feasibility of torque generation by the stated mechanism against loads typical during ATP synthesis; the essential model characteristics, e.g., helix and subunit rotation and associated friction constants, have been tested and furnished by steered molecular dynamics simulations.

Microscopic Kinetics of DNA Translocation through synthetic nanopores

We have previously demonstrated that a nanometer-diameter pore in a nanometer-thick metal-oxide-semiconductor-compatible membrane can be used as a molecular sensor for detecting DNA. The prospects for using this type of device for sequencing DNA are avidly being pursued. The key attribute of the sensor is the electric field-induced (voltage-driven) translocation of the DNA molecule in an electrolytic solution across the membrane through the nanopore. To complement ongoing experimental studies developing such pores and measuring signals in response to the presence of DNA, we conducted molecular dynamics simulations of DNA translocation through the nanopore. A typical simulated system included a patch of a silicon nitride membrane dividing water solution of potassium chloride into two compartments connected by the nanopore. External electrical fields induced capturing of the DNA molecules by the pore from the solution and subsequent translocation. Molecular dynamics simulations suggest that 20-basepair segments of double-stranded DNA can transit a nanopore of 2.2 x 2.6 nm(2) cross section in a few microseconds at typical electrical fields. Hydrophobic interactions between DNA bases and the pore surface can slow down translocation of single-stranded DNA and might favor unzipping of double-stranded DNA inside the pore. DNA occluding the pore mouth blocks the electrolytic current through the pore; these current blockades were found to have the same magnitude as the blockade observed when DNA transits the pore. The feasibility of using molecular dynamics simulations to relate the level of the blocked ionic current to the sequence of DNA was investigated.

Kinetics of cytochrome C folding: atomically detailed simulations

The vast range of time scales (from nanoseconds to seconds) during protein folding is a challenge for experiments and computations. To make concrete predictions on folding mechanisms, atomically detailed simulations of protein folding, using potentials derived from chemical physics principles, are desired. However, due to their computational complexity, straightforward molecular dynamics simulations of protein folding are impossible today. An alternative algorithm is used that makes it possible to compute approximate atomically detailed long time trajectories (the Stochastic Difference Equation in Length). This algorithm is used to compute 26 atomically detailed folding trajectories of cytochrome c (a millisecond process). The early collapse of the protein chain (with marginal formation of secondary structure), and the earlier formation of the N and C helices (compare to the 60's helix) are consistent with the experiment. The existence of an energy barrier upon entry to the molten globule is examined as well. In addition to (favorable) comparison to experiments, we show that non-native contacts drive the formation of the molten globule. In contrast to popular folding models, the non-native contacts do not form off-pathway kinetic traps in cytochrome c.

Inherent speedup limitations in multiple time step/particle mesh Ewald algorithms

Multiple time step (MTS) algorithms present an effective integration approach to reduce the computational cost of dynamics simulations. By using force splitting to allow larger time steps for the more slowly varying force components, computational savings can be realized. The Particle-Mesh-Ewald (PME) method has been independently devised to provide an effective and efficient treatment of the long-range electrostatics interactions. Here we examine the performance of a combined MTS/PME algorithm previously developed for AMBER on a large polymerase beta/DNA complex containing 40,673 atoms. Our goal is to carefully combine the robust features of the Langevin/MTS (LN) methodology implemented in CHARMM-which uses position rather than velocity Verlet with stochasticity to make possible outer time steps of 150 fs-with the PME formulation. The developed MTS/PME integrator removes fast terms from the reciprocal-space Ewald component by using switch functions. We analyze the advantages and limitations of the resulting scheme by comparing performance to the single time step leapfrog Verlet integrator currently used in AMBER by evaluating different time-step protocols using three assessors for accuracy, speedup, and stability, all applied to long (i.e., nanosecond) simulations to ensure proper energy conservation. We also examine the performance of the algorithm on a parallel, distributed shared-memory computer (SGI Origin 2000 with 8 300-MHz R12000 processors). Good energy conservation and stability behavior can be demonstrated, for Newtonian protocols with outer time steps of up to 8 fs and Langevin protocols with outer time steps of up to 16 fs. Still, we emphasize the inherent limitations imposed by the incorporation of MTS methods into the PME formulation that may not be widely appreciated. Namely, the limiting factor on the largest outer time-step size, and hence speedup, is an intramolecular cancellation error inherent to PME. This error stems from the excluded-nonbonded correction term contained in the reciprocal-space component. This cancellation error varies in time and introduces artificial frequencies to the governing dynamics motion. Unfortunately, we find that this numerical PME error cannot be easily eliminated by refining the PME parameters (grid resolution and/or order of interpolating polynomial). We suggest that methods other than PME for fast electrostatics may allow users to reap the full advantages from MTS algorithms.