Fluctuation-driven molecular transport through an asymmetric membrane channel

Elastic versus brittle mechanical responses predicted for dimeric cadherin complexes

Cadherins are a superfamily of adhesion proteins involved in a variety of biological processes that include the formation of intercellular contacts, the maintenance of tissue integrity, and the development of neuronal circuits. These transmembrane proteins are characterized by ectodomains composed of a variable number of extracellular cadherin (EC) repeats that are similar but not identical in sequence and fold. E-cadherin, along with desmoglein and desmocollin proteins, are three classical-type cadherins that have slightly curved ectodomains and engage in homophilic and heterophilic interactions through an exchange of conserved tryptophan residues in their N-terminal EC1 repeat. In contrast, clustered protocadherins are straighter than classical cadherins and interact through an antiparallel homophilic binding interface that involves overlapped EC1 to EC4 repeats. Here we present molecular dynamics simulations that model the adhesive domains of these cadherins using available crystal structures, with systems encompassing up to 2.8 million atoms. Simulations of complete classical cadherin ectodomain dimers predict a two-phased elastic response to force in which these complexes first softly unbend and then stiffen to unbind without unfolding. Simulated α, β, and γ clustered protocadherin homodimers lack a two-phased elastic response, are brittle and stiffer than classical cadherins and exhibit complex unbinding pathways that in some cases involve transient intermediates. We propose that these distinct mechanical responses are important for function, with classical cadherin ectodomains acting as molecular shock absorbers and with stiffer clustered protocadherin ectodomains facilitating overlap that favors binding specificity over mechanical resilience. Overall, our simulations provide insights into the molecular mechanics of single cadherin dimers relevant in the formation of cellular junctions essential for tissue function.

Collective mechanical responses of cadherin-based adhesive junctions as predicted by simulations

Cadherin-based adherens junctions and desmosomes help stabilize cell-cell contacts with additional function in mechano-signaling, while clustered protocadherin junctions are responsible for directing neuronal circuits assembly. Structural models for adherens junctions formed by epithelial cadherin (CDH1) proteins indicate that their long, curved ectodomains arrange to form a periodic, two-dimensional lattice stabilized by tip-to-tip trans interactions (across junction) and lateral cis contacts. Less is known about the exact architecture of desmosomes, but desmoglein (DSG) and desmocollin (DSC) cadherin proteins are also thought to form ordered junctions. In contrast, clustered protocadherin (PCDH)-based cell-cell contacts in neuronal tissues are thought to be responsible for self-recognition and avoidance, and structural models for clustered PCDH junctions show a linear arrangement in which their long and straight ectodomains form antiparallel overlapped trans complexes. Here, we report all-atom molecular dynamics simulations testing the mechanics of minimalistic adhesive junctions formed by CDH1, DSG2 coupled to DSC1, and PCDHγB4, with systems encompassing up to 3.7 million atoms. Simulations generally predict a favored shearing pathway for the adherens junction model and a two-phased elastic response to tensile forces for the adhesive adherens junction and the desmosome models. Complexes within these junctions first unbend at low tensile force and then become stiff to unbind without unfolding. However, cis interactions in both the CDH1 and DSG2-DSC1 systems dictate varied mechanical responses of individual dimers within the junctions. Conversely, the clustered protocadherin PCDHγB4 junction lacks a distinct two-phased elastic response. Instead, applied tensile force strains trans interactions directly, as there is little unbending of monomers within the junction. Transient intermediates, influenced by new cis interactions, are observed after the main rupture event. We suggest that these collective, complex mechanical responses mediated by cis contacts facilitate distinct functions in robust cell-cell adhesion for classical cadherins and in self-avoidance signaling for clustered PCDHs.

Super-Arrhenius diffusion in a binary colloidal mixture at low volume fraction: an effect of depletion interaction due to an asymmetric barrier

We report results from the molecular dynamics simulations of a binary colloidal mixture subjected to an external potential barrier along one of the spatial directions at low volume fraction, ϕ = 0.2. The variations in the asymmetry of the external potential barrier do not change the dynamics of the smaller particles, showing Arrhenius diffusion. However, the dynamics of the larger particles shows a crossover from sub-Arrhenius to super-Arrhenius diffusion with the asymmetry in the external potential at the low temperatures and low volume fraction. Super-Arrhenius diffusion is generally observed in the high density systems where the transient cages are present due to dense packing, e.g., supercooled liquids, jammed systems, diffusion through porous membranes, dynamics within the cellular environment, etc. This model can be applied to study the molecular transport across cell membranes, nano-, and micro-channels which are characterized by spatially asymmetric potentials.

Phonon-Induced Ratchet Motion of a Water Nanodroplet on a Supported Black Phosphorene

Phonons are not supposed to carry any physical momentum as lattice vibrational modes; thus, it is believed no mass transport could be induced by phonons. In this Letter, we show that a ratchet motion of a water nanodroplet could be induced on a two-dimensional puckered lattice like black phosphorene (BP) by exciting its flexural phonons through a moving substrate. The water nanodroplet exhibits a forward motion along the armchair or a backward motion along the zigzag directions on a BP lattice that is supported on a substrate possessing a relative armchair or zigzag forward motion with BP. Through the analysis of the structure and vibrational density states of BP, it is found that in-plane lattice displacement asymmetry and the in-plane vibration asymmetry are induced by the excited flexural phonons, which determine the water nanodroplet motion as an anisotropic Brownian motor. Simulations of the nanodroplet motion as functions of the substrate relative motion speed and direction and also the substrate coupling strength with BP are performed. Results of the nanodroplet ratchet motion exhibit good agreement with the theoretical predications from calculating the Brownian motor asymmetry. Our findings reveal a promising mass transport strategy and a further understanding of phonon-related interactions in crystalline solids.

Two-state diffusive mobility of slow and fast transport of water in narrow nanochannels

Transport of water in narrow nanochannels as a single-file chain is involved in various biological activities and nanofluidic applications. However, although the consistent dipole orientation of the water molecules is intensively studied, its effect upon the transport behavior is still unknown. In this Rapid Communication, we find two states of slow and fast transport coexist in the single-file water in the presence of channel defects that break the collective dipole orientation. A low diffusive mobility is found for the dipole orientation inconsistent configurations while mobility approximately two times higher is found for the consistent ones. The two-state diffusion process relies on the different hydrogen bond connections, which possess overlapped structures, enabling a spontaneous transition. The slow state is insensitive to the increased defect number while the fast state is reduced accordingly. The two states exhibit different lifetime and temperature dependences that demonstrate a possibility for manipulation. Our result implies the possibility of two-state diffusion process of water in nanofluid phenomena due to the common presence of defects in nanochannels.

Glycerol transport through the aquaglyceroporin GlpF: bridging dynamics and kinetics with atomic simulation

The aquaglyceroporin GlpF is a member of the aquaporin family. It selectively conducts small molecules, such as glycerol, across the cell membrane under a concentration gradient of the substrate. Atomistic molecular dynamics (MD) simulation would provide great insight into the substrate transport mechanism of GlpF and membrane channels alike. Ideally, non-equilibrium simulations under various concentration gradients of glycerol are desired to emulate the transportation in cells, but this kind of simulation is difficult due to a complicated system setup and high computational cost. Here, we present a new strategy to extract non-equilibrium kinetic information from equilibrium MD simulation. We first performed long-time (totally 22.5 μs) multi-copy equilibrium MD simulations of glycerol conduction through GlpF. Tens of times the spontaneous permeation of glycerol through GlpF was observed, allowing us to elucidate the detailed mechanism of the stereoselectivity for glycerol. Then we employed Markov state model (MSM) analysis of the MD trajectories to identify the intermediate states during glycerol transport and calculate the inter-state transition rate constants. Based on the results of MSM analysis, we built the kinetic models of glycerol transport and calculated the glycerol fluxes under various concentration gradients by solving the master equations. The results agree well with the experimental measurement at a certain glycerol concentration, and provide holistic information on the glycerol conduction capacity of GlpF. Our work demonstrates that long-time atomistic MD simulations can now bridge the microscopic dynamics and the kinetic description of substance transport through membrane channels, hopefully facilitating the engineering of new selective channels for various molecules.

Experimental evidence of symmetry breaking of transition-path times

While thermal rates of state transitions in classical systems have been studied for almost a century, associated transition-path times have only recently received attention. Uphill and downhill transition paths between states at different free energies should be statistically indistinguishable. Here, we systematically investigate transition-path-time symmetry and report evidence of its breakdown on the molecular- and meso-scale out of equilibrium. In automated Brownian dynamics experiments, we establish first-passage-time symmetries of colloids driven by femtoNewton forces in holographically-created optical landscapes confined within microchannels. Conversely, we show that transitions which couple in a path-dependent manner to fluctuating forces exhibit asymmetry. We reproduce this asymmetry in folding transitions of DNA-hairpins driven out of equilibrium and suggest a topological mechanism of symmetry breakdown. Our results are relevant to measurements that capture a single coordinate in a multidimensional free energy landscape, as encountered in electrophysiology and single-molecule fluorescence experiments.

Filling of Irregular Channels with Round Cross-Section: Modeling Aspects to Study the Properties of Porous Materials

The filling of channels in porous media with particles of a material can be interpreted in a first approximation as a packing of spheres in cylindrical recipients. Numerous studies on micro- and nanoscopic scales show that they are, as a rule, not ideal cylinders. In this paper, the channels, which have an irregular shape and a circular cross-section, as well as the packing algorithms are investigated. Five patterns of channel shapes are detected to represent any irregular porous structures. A novel heuristic packing algorithm for monosized spheres and different irregularities is proposed. It begins with an initial configuration based on an fcc unit cell and the subsequent densification of the obtained structure by shaking and gravity procedures. A verification of the algorithm was carried out for nine sinusoidal axisymmetric channels with different D_min/D_max ratio by MATLAB^® simulations, reaching a packing fraction of at least 0.67 (for sphere diameters of 5%D_min or less), superior to a random close packing density. The maximum packing fraction was 73.01% for a channel with a ratio of D_min/D_max = 0.1 and a sphere size of 5%D_min. For sphere diameters of 50%D_min or larger, it was possible to increase the packing factor after applying shaking and gravity movements.

Nanochannels as molecular check valves

A molecular check valve is a nanomachine that enables unidirectional molecular transport. In this work, we report a novel molecular check valve fabricated by asymmetric modification of a silica nanoporous membrane (SNM) consisting of parallel nanochannels with a diameter of 2-3 nm. Asymmetric modification refers to the thermal deposition of hydrophobic polydimethylsiloxane (PDMS) only on one side of the SNM to generate hydrophobic nanoorifices. Such an asymmetric nanostructure, designated as PDMS-SNM, could synergistically exert a hydrophobic force on the molecules by PDMS nanoorifices and an electrostatic force by naked silica nanochannels, resulting in unidirectional molecular transport under specific circumstances. Typically, only positively charged molecules were able to transport across the PDMS-SNM from the PDMS nanoorifice side, while backward transport from the other side was prohibited. In the former case, positively charged molecules were subject to electrostatic attraction from naked silica channels, which could exceed the hydrophobic rejection from PDMS nanoorifices to pull the molecule across the PDMS-SNM. However, in the latter case the electrostatic attraction is no longer a driving force to overcome the hydrophobic rejection from PDMS nanoorifices to promote the molecular transport. On the other hand, the PDMS-SNM based molecular check valve can be shut down to prevent any molecular transport from either side of the PDMS-SNM under certain conditions, such as a high salt concentration or an appropriate pH (e.g., pH 3). We believe that it could be applied to convert natural fluctuation energy into directed motion, as well as to prevent backward transport in batteries and fuel cells.

Active translocation of a semiflexible polymer assisted by an ATP-based molecular motor

In this work we study the assisted translocation of a polymer across a membrane nanopore, inside which a molecular motor exerts a force fuelled by the hydrolysis of ATP molecules. In our model the motor switches to its active state for a fixed amount of time, while it waits for an ATP molecule which triggers the motor, during an exponentially distributed time lapse. The polymer is modelled as a beads-springs chain with both excluded volume and bending contributions, and moves in a stochastic three dimensional environment modelled with a Langevin dynamics at a fixed temperature. The resulting dynamics shows a Michaelis-Menten translocation velocity that depends on the chain flexibility. The scaling behavior of the mean translocation time with the polymer length for different bending values is also investigated.

Nonequilibrium steady states in a closed inhomogeneous asymmetric exclusion process with generic particle nonconservation

We study the totally asymmetric exclusion process (TASEP) on a nonuniform one-dimensional ring consisting of two segments having unequal hopping rates, or defects. We allow weak particle nonconservation via Langmuir kinetics (LK), which are parametrized by generic unequal attachment and detachment rates. For an extended defect, in the thermodynamic limit the system generically displays inhomogeneous density profiles in the steady state-the faster segment is either in a phase with spatially varying density having no density discontinuity, or a phase with a discontinuous density changes. Nonequilibrium phase transitions between the above phases are controlled by the inhomogeneity and LK. The slower segment displays only macroscopically uniform bulk density profiles in the steady states, reminiscent of the maximal current phase of TASEP but with a bulk density generally different from half. With a point defect, there are spatially uniform low- and high-density phases as well, in addition to the inhomogeneous density profiles observed for an extended defect. In all the cases, it is argued that the mean particle density in the steady state is controlled only by the ratio of the LK attachment and detachment rates.

Anomalous Dynamical Behavior of Freestanding Graphene Membranes

We report subnanometer, high-bandwidth measurements of the out-of-plane (vertical) motion of atoms in freestanding graphene using scanning tunneling microscopy. By tracking the vertical position over a long time period, a 1000-fold increase in the ability to measure space-time dynamics of atomically thin membranes is achieved over the current state-of-the-art imaging technologies. We observe that the vertical motion of a graphene membrane exhibits rare long-scale excursions characterized by both anomalous mean-squared displacements and Cauchy-Lorentz power law jump distributions.

Carbon Nanomembranes

Carbon nanomembranes (CNMs) are synthetic 2D carbon sheets with tailored physical or chemical properties. These depend on the structure, molecular composition, and surroundings on either side. Due to their molecular thickness, they can be regarded as "interfaces without bulk" separating regions of different gaseous, liquid, or solid components and controlling the materials exchange between them. Here, a universal scheme for the fabrication of 1 nm-thick, mechanically stable, functional CNMs is presented. CNMs can be further modified, for example perforated by ion bombardment or chemically functionalized by the binding of other molecules onto the surfaces. The underlying physical and chemical mechanisms are described, and examples are presented for the engineering of complex surface architectures, e.g., nanopatterns of proteins, fluorescent dyes, or polymer brushes. A simple transfer procedure allows CNMs to be placed on various support structures, which makes them available for diverse applications: supports for electron and X-ray microscopy, nanolithography, nanosieves, Janus nanomembranes, polymer carpets, complex layered structures, functionalization of graphene, novel nanoelectronic and nanomechanical devices. To close, the potential of CNMs in filtration and sensorics is discussed. Based on tests for the separation of gas molecules, it is argued that ballistic membranes may play a prominent role in future efforts of materials separation.

Enhancement of Water Evaporation on Solid Surfaces with Nanoscale Hydrophobic-Hydrophilic Patterns

Using molecular dynamics simulations, we show that the evaporation of nanoscale water on hydrophobic-hydrophilic patterned surfaces is unexpectedly faster than that on any surfaces with uniform wettability. The key to this phenomenon is that, on the patterned surface, the evaporation rate from the hydrophilic region only slightly decreases due to the correspondingly increased water thickness; meanwhile, a considerable number of water molecules evaporate from the hydrophobic region despite the lack of water film. Most of the evaporated water from the hydrophobic region originates from the hydrophilic region by diffusing across the contact lines. Further analysis shows that the evaporation rate from the hydrophobic region is approximately proportional to the total length of the contact lines.

Phase coexistence and particle nonconservation in a closed asymmetric exclusion process with inhomogeneities

We construct a one-dimensional totally asymmetric simple exclusion process (TASEP) on a ring with two segments having unequal hopping rates, coupled to particle nonconserving Langmuir kinetics (LK) characterized by equal attachment and detachment rates. In the steady state, in the limit of competing LK and TASEP, the model is always found in states of phase coexistence. We uncover a nonequilibrium phase transition between a three-phase and a two-phase coexistence in the faster segment, controlled by the underlying inhomogeneity configurations and LK. The model is always found to be half-filled on average in the steady state, regardless of the hopping rates and the attachment-detachment rate.

Active polymer translocation in the three-dimensional domain

In this work we study the translocation process of a polymer through a nanochannel where a time dependent force is acting. Two conceptually different types of driving are used: a deterministic sinusoidal one and a random telegraph noise force. The mean translocation time presents interesting resonant minima as a function of the frequency of the external driving. For the computed sizes, the translocation time scales with the polymer length according to a power law with the same exponent for almost all the frequencies of the two driving forces. The dependence of the translocation time with the polymer rigidity, which accounts for the persistence length of the molecule, shows a different low frequency dependence for the two drivings.

Nonequilibrium steady states in asymmetric exclusion processes on a ring with bottlenecks

Generic inhomogeneous steady states in an asymmetric exclusion process on a ring with a pair of point bottlenecks are studied. We show that, due to an underlying universal feature, measurements of coarse-grained steady-state densities in this model resolve the bottleneck structures only partially. Unexpectedly, it displays localization-delocalization transitions and confinement of delocalized domain walls, controlled by the interplay between particle number conservation and bottleneck competition for moderate particle densities.

Adiabatically driven Brownian pumps

We investigate a Brownian pump which, being powered by a flashing ratchet mechanism, produces net particle transport through a membrane. The extension of the Parrondo's approach developed for reversible Brownian motors [Parrondo, Phys. Rev. E 57, 7297 (1998)] to adiabatically driven pumps is given. We demonstrate that the pumping mechanism becomes especially efficient when the time variation of the potential occurs adiabatically fast or adiabatically slow, in perfect analogy with adiabatically driven Brownian motors which exhibit high efficiency [Rozenbaum et al., Phys. Rev. E 85, 041116 (2012)]. At the same time, the efficiency of the pumping mechanism is shown to be less than that of Brownian motors due to fluctuations of the number of particles in the membrane.

Enhanced permeation of single-file water molecules across a noncylindrical nanochannel

We utilize molecular dynamics simulations to study the effect of noncylindrical shapes of a nanochannel (which are inspired from the shape of real biological water nanochannels) on the permeation of single-file water molecules across the nanochannel. Compared with the cylindrical shape that has been tremendously adopted in the literature, the noncylindrical shapes play a crucial role in enhancing water permeation. Remarkably, the maximal enhancement ratio reaches a value of 6.28 (enhancement behavior). Meanwhile, the enhancement becomes saturated when the volume of the noncylindrical shape continues to increase (saturation behavior). The analysis of average diffusivity of water molecules helps to reveal the mechanism underlying the two behaviors whereas Poiseuille's law fails to explain them. These results pave a way for designing high-flow nanochannels and provide insight into water permeation across biological water nanochannels.

A kinetic Monte Carlo approach to investigate antibiotic translocation through bacterial porins

Many relevant biological processes take place on time scales not reachable by standard all-atom computer simulations. The translocation of antibiotics through non-specific bacterial porins is an example. Microscopic effects compete to determine penetration routes and, consequently, free energy barriers to be overcome. Since bacteria can develop resistance to treatment also by reducing their antibiotic permeability, to understand the microscopic aspects of antibiotic translocation is an important step to rationalize drug design. Here, to investigate the translocation we propose a complete numerical model that combines the diffusion-controlled rate theory and a kinetic Monte Carlo scheme based on both experimental data and microscopically well-founded all-atom simulations. Within our model, an antibiotic translocating through an hour-glass-shaped channel can be described as a molecule moving on a potential of mean force featuring several affinity sites and a high central barrier. The implications of our results for the characterization of antibiotic translocation at in vivo concentrations are discussed. The presence of an affinity site close to the mouth of the channel seems to favor the translocation of antibiotics, the affinity site acting as a particle reservoir. Possible connections between results and the appearance of mutations in clinical strains are also outlined.

Self-adjusted sustaining oscillation of confined water chain in carbon nanotubes

We show by molecular dynamics and first principle calculations that a water chain confined in carbon nanotubes can self-adjust into regular oscillation with remarkably lower entropy from random thermal motion with higher entropy at room temperature. The turning between the two phases is triggered by the water orientation fluttering into or from the energy optimum configuration of the chain. The findings are expected to be helpful in creation of self-sustaining nanoelectromechanical systems driven by ambient energy.

Biotechnical and other applications of nanoporous membranes

Recent advances mean that arrays of nearly uniform cylindrical, conical and pyramidal shaped pores can be produced in several types of substrates. Surface modification of nanopore surfaces can give unique mass transport characteristics that have recently been explored for biomolecule separation, detection and purification. Recent interest has focused on the use of nanoporous membranes for mass transfer diodes that act analogous to solid-state devices based on electron conduction. Asymmetric pores such as conical pores can show superior performance characteristics compared to traditional cylindrical pores in ion rectification. However, many phenomena for membranes with asymmetric pores still remain to be exploited in biomolecular separation, biosensing, microfluidics, logic gates, and energy harvesting and storage.

Fluxes of non-interacting and strongly repelling particles through a single conical channel: Analytical results and their numerical tests

Using a diffusion model of particle dynamics in the channel, we study entropic effects in channel-facilitated transport. We derive general expressions for the fluxes of non-interacting particles and particles that strongly repel each other through the channel of varying cross section area, assuming that the transport is driven by the difference in particle concentrations on the two sides of the membrane. For a special case of a right truncated cone expanding in the left-to-right direction, we show how the fluxes depend on the geometric parameters of the channel and on the particle concentrations. For non-interacting particles the flux is direction-independent in the sense that inversion of the concentration difference leads to the inversion of the direction of the flux without changing its magnitude. This symmetry is broken for repelling particles: The flux in the left-to-right direction exceeds its right-to-left counterpart. Our theoretical predictions are supported by three-dimensional Brownian dynamics simulations.

Effect of charge on water filling/emptying transitions of nanochannel

The effect of external charge on distribution properties of water molecules confined inside the single-walled carbon nanotube (SWNT) with modified carbon-water interactions is investigated by the molecular dynamics simulations. It is found that when a single external charge (of value +1.0e) is in the middle region of the SWNT, the nanotube is filled by the single-file water chain. Sharp transitions between empty (closed) and filled (open) states occur once the charge moves out the middle region. Simulation results indicate that filling and emptying kinetics depend sensitively on the position of external charge. These findings are helpful to understand the mechanism of charge-dependent gating of hydrophobic nanotubes.

Brownian pump in nonlinear diffusive media

A Brownian pump in nonlinear diffusive media is investigated in the presence of an unbiased external force. The pumping system is embedded in a finite region and bounded by two particle reservoirs. In the adiabatic limit, we obtain the analytical expressions of the current and the pumping capacity as a function of temperature for normal diffusion, subdiffusion, and superdiffusion. It is found that important anomalies are detected in comparison with the normal diffusion case. The superdiffusive regime, compared with the normal one, exhibits an opposite current for low temperatures. In the subdiffusive regime, the current may become forbidden for low temperatures and negative for high temperatures.

Effect of interactions on molecular fluxes and fluctuations in the transport across membrane channels

Transport of molecules across membrane channels is investigated theoretically using exactly solvable one-dimensional discrete-state stochastic models. An interaction between molecules and membrane pores is modeled via a set of binding sites with different energies. It is shown that the interaction potential strongly influences the particle currents as well as fluctuations in the number of translocated molecules. For small concentration gradients, the attractive sites lead to largest currents and fluctuations, while the repulsive interactions yield the largest fluxes and dispersions for large concentration gradients. Interaction energies that lead to maximal currents and maximal fluctuations are the same only for locally symmetric potentials, where transition states are equally distant from the neighboring binding sites, while they differ for the locally asymmetric potentials. The conditions for the most optimal translocation transport with maximal current and minimal dispersion are discussed. It is argued that, in this case, the interaction strength is independent of local symmetry of the potential of mean forces. In addition, the effect of the global asymmetry of the interaction potential is investigated, and it is shown that it also strongly affects the particle translocation dynamics. These phenomena can be explained by analyzing the details of the particle entering and leaving the binding sites in the channel.

On achieving experimental accuracy from molecular dynamics simulations of flexible molecules: aqueous glycerol

The rotational isomeric states (RIS) of glycerol at infinite dilution have been characterized in the aqueous phase via a 1 micros conventional molecular dynamics (MD) simulation, a 40 ns enhanced sampling replica exchange molecular dynamics (REMD) simulation, and a reevaluation of the experimental NMR data. The MD and REMD simulations employed the GLYCAM06/AMBER force field with explicit treatment of solvation. The shorter time scale of the REMD sampling method gave rise to RIS and theoretical scalar 3J(HH) coupling constants that were comparable to those from the much longer traditional MD simulation. The 3J(HH) coupling constants computed from the MD methods were in excellent agreement with those observed experimentally. Despite the agreement between the computed and the experimental J-values, there were variations between the rotamer populations computed directly from the MD data and those derived from the experimental NMR data. The experimentally derived populations were determined utilizing limiting J-values from an analysis of NMR data from substituted ethane molecules and may not be completely appropriate for application in more complex molecules, such as glycerol. Here, new limiting J-values have been derived via a combined MD and quantum mechanical approach and were used to decompose the experimental 3J(HH) coupling constants into population distributions for the glycerol RIS.

Water permeation across nanochannels with defects

Defects are common in fabricated nanochannels. In this paper, water permeation across a single-walled carbon nanotube with defects was studied using molecular dynamics simulations. It is found that the impact on water permeation is negligible when the density of the defects is small, while a significant reduction in water permeation is observed when the density of the defects is high. These findings should be helpful in both understanding water permeation across nanochannels and designing efficient artificial nanochannel.

Brownian pump powered by a white-noise flashing ratchet

A Brownian pump of particles powered by a stochastic flashing ratchet mechanism is studied. The pumping device is embedded in a finite region and bounded by particle reservoirs. In the steady state, we exactly calculate the spatial density profile, the concentration ratio between both reservoirs and the particle flux. We propose a simulation framework for the consistent evaluation of such observable quantities.

Directed molecular transport in an oscillating channel with randomness

Stability of directed transport and molecular separation in a symmetric channel is analyzed. The original mechanism is based on harmonic spatial oscillations of the channel, under which the system exhibits multiple regimes of a directed transport. The particles may be forced to move with different velocities and directions as the amplitude and/or frequency of the oscillations are adjusted to a proper resonance. The advantage of this mechanism in contrast to the ratchet systems is that the average particle velocity is larger than the velocity of the growing of the width of the particle spatial distribution. We have studied the stability of the directed transport with regard to random impacts to the channel parameters and oscillation frequency. Here we present the results of the simulations which show that the ability of the combined longitudinally and transversally vibrating randomized dynamic channel to perform directed molecular transport remains resilient to quite intensive random channel structure fluctuations (50-60%) and relatively strong random impacts to its oscillations (15-20%).

Ion transport and selectivity in nanopores with spatially inhomogeneous fixed charge distributions

Polymeric nanopores with fixed charges show ionic selectivity when immersed in aqueous electrolyte solutions. The understanding of the electrical interaction between these charges and the mobile ions confined in the inside nanopore solution is the key issue in the design of potential applications. The authors have theoretically described the effects that spatially inhomogeneous fixed charge distributions exert on the ionic transport and selectivity properties of the nanopore. A comprehensive set of one-dimensional distributions including the skin, core, cluster, and asymmetric cases are analyzed on the basis of the Nernst-Planck equations. Current-voltage curves, nanopore potentials, and transport numbers are calculated for the above distributions and compared with those obtained for a homogeneously charged nanopore with the same average fixed charge concentration. The authors have discussed if an appropriate design of the spatial fixed charge inhomogeneity can lead to an enhancement of the transport and selectivity with respect to the homogeneous nanopore case. Finally, they have compared the theoretical predictions with relevant experimental data.

Tunable non-equilibrium gating of flexible DNA nanochannels in response to transport flux

Biological nanochannels made from proteins play a central role in cellular signalling. The rapid emergence of DNA nanotechnology in recent years has opened up the possibility of making similar nanochannels from DNA. Building on previous work on switchable DNA nanocompartment, we have constructed complex DNA nanosystems to investigate the gating behaviour of these nanochannels. Here we show that DNA nanochannels can be gated by stress exerted by permeating solute particles at non-equilibrium states due to the high flexibility of the nanochannels. This novel gating mechanism results in tunable ratchet-like transport of solute particles through the nanochannels. A simple model that couples non-equilibrium channel gating with transport flux can quantitatively explain a number of the phenomena we observe. With only one set of model parameters, we can reproduce diverse gating behaviours, modulated by an inherent gating threshold. This work could lead to the development of new devices based on DNA nanochannels.

Geometry-induced asymmetric diffusion

Past work has shown that ions can pass through a membrane more readily in one direction than the other. We demonstrate here in a model and an experiment that for a mixture of small and large particles such asymmetric diffusion can arise solely from an asymmetry in the geometry of the pores of the membrane. Our deterministic simulation considers a two-dimensional gas of elastic disks of two sizes diffusing through a membrane, and our laboratory experiment examines the diffusion of glass beads of two sizes through a metal membrane. In both experiment and simulation, the membrane is permeable only to the smaller particles, and the asymmetric pores lead to an asymmetry in the diffusion rates of these particles. The presence of even a small percentage of large particles can clog a membrane, preventing passage of the small particles in one direction while permitting free flow of the small particles in the other direction. The purely geometric kinetic constraints may play a role in common biological contexts such as membrane ion channels.

On the use of local diffusion models for path ensemble averaging in potential of mean force computations

We use a constant velocity steered molecular dynamics (SMD) simulation of the stretching of deca-alanine in vacuum to demonstrate a technique that can be used to create a surrogate processes approximation (SPA) using the time series that come out of SMD simulations. In this article, the surrogate processes are constructed by first estimating a sequence of local parametric diffusion models along a SMD trajectory and then a single global model is constructed by piecing the local models together through smoothing splines (estimation is made computationally feasible by likelihood function approximations). The SPAs are then "bootstrapped" in order to obtain a plausible range of work values associated with a particular SMD realization. This information is then used to assist in estimating a potential of mean force constructed by appealing to the Jarzynski equality. When this procedure is repeated for a small number of SMD paths, it is shown that the global models appear to come from a single family of closely related diffusion processes. Possible techniques for exploiting this observation are also briefly discussed. The findings of this paper have potential relevance to computationally expensive computer simulations and experimental works involving optical tweezers where it is difficult to collect a large number of samples, but possible to sample accurately and frequently in time.

Electrostatic gating of a nanometer water channel

Water permeation across a single-walled carbon nanotube (SWNT) under the influence of a mobile external charge has been studied with molecular dynamics simulations. This designed nanopore shows an excellent on-off gating behavior by a single external charge (of value +1.0e): it is both sensitive to the available charge signal when it is close (less than a critical distance of 0.85 A or about half the size of a water molecule) and effectively resistant to charge noise, i.e., the effect on the flow and net flux across the channel is found to be negligible when the charge is >0.85 A away from the wall of the nanopore. This critical distance can be estimated from the interaction balance for the water molecule in the SWNT closest to the imposed charge with its neighboring water molecules and with the charge. The flow and net flux decay exponentially with respect to the difference between these two interaction energies when the charge gets closer to the wall of the SWNT and reaches a very small value once the charge crosses the wall, suggesting a dominating effect on the permeation properties from local water molecules near the external charge. These findings might have biological implications because membrane water channels share a similar single-file water chain inside these nanoscale channels.

Channel-facilitated molecular transport across membranes: attraction, repulsion, and asymmetry

Transport of molecules across membrane channels is investigated theoretically using exactly solvable discrete stochastic site-binding models. It is shown that the interaction potential between molecules and the channel has a strong effect on translocation dynamics. The presence of attractive binding sites in the pore accelerates the particle current for small concentrations outside the membrane, while for large concentrations, surprisingly, repulsive binding sites yield the most optimal transport. In addition, the asymmetry of the interaction potential also strongly influences the channel transport. The mechanism underlying these phenomena is discussed using the details of particle dynamics at the binding sites.

Molecular dynamics simulation of ratchet motion in an asymmetric nanochannel

The persistence of ratchet effects, i.e., nonzero mass flux under a zero-mean time-dependent drive, when many-body interactions are present, is studied via molecular dynamics (MD) simulations of a simple liquid flowing in an asymmetric nanopore. The results show that (i) ratchet effects persist under many-body density correlations induced by the forcing; (ii) two distinct linear responses (flux proportional to the drive amplitude) appear under strong loads. One regime has the same conductivity of linear response theory up to a forcing of about 10 kT, while the second displays a smaller conductivity, the difference in responses is due to geometric effects alone. (iii) Langevin simulations based on a naive mapping of the many-body equilibrium bulk diffusivity, D, onto the damping rate, gamma are also found to yield two distinct linear responses. However, in both regimes, the flux is significantly smaller than the one of MD simulations.

Mechanism of Ion Permeation in a Model Channel: Free Energy Surface and Dynamics of K+Ion Transport in an Anion-Doped Carbon Nanotube

The mechanism of the ion permeation is investigated for an anion-doped carbon nanotube, as a model of the K+ channel, by analyzing the free energy surface and the dynamics of the ion permeation through the model channel. It is found that the main rate-determining step is how an ion enters the channel. The entrance of the ion is mostly blocked by a water molecule located at this entrance. Only about 10% of K+ ions which reach the mouth of the channel can really enter the channel. The rejection rate sensitively depends on the location of this water molecule, which is easily controlled by the charge of the carbon nanotube; for example, the maximum permeation is obtained when the anion charge is at a certain value, -5.4e in the present model. At this charge, the facile translocation of the ion inside the channel is also induced due to the number of fluctuations of the ions inside the channel. Therefore, the so-called "Newton's balls", a toy model, combined with a simple ion diffusion model for explaining the fast ion permeation should be modified. The present analysis thus suggests that there exists an optimum combination of the length and the charge of the carbon nanotube for the most efficient ion permeation.

Bulk-driven nonequilibrium phase transitions in a mesoscopic ring

We study a periodic one-dimensional exclusion process composed of a driven and a diffusive part. In a mesoscopic limit where both dynamics compete we identify bulk-driven phase transitions. We employ mean-field theory complemented by Monte Carlo simulations to characterize the emerging nonequilibrium steady states. Monte Carlo simulations reveal interesting correlation effects that we explain phenomenologically.

Molecular transport through channels and pores: effects of in-channel interactions and blocking

Facilitated translocation of molecules through channels and pores is of fundamental importance for transmembrane transport in biological systems. Several such systems have specific binding sites inside the channel, but a clear understanding of how the interaction between channel and molecules affects the flow is still missing. We present a generic analytical treatment of the problem that relates molecular flow to the first passage time across and the number of particles inside the channel. Both quantities depend in different ways on the channel properties. For the idealized case of noninteracting molecules, we find an increased flow whenever there is a binding site in the channel, despite an increased first passage time. In the more realistic case that molecules may block the channel, we find an increase of flow only up to a certain threshold value of the binding strength and a dependence on the sign of the concentration gradient, i.e., asymmetric transport. The optimal binding strength in that case is analyzed. In all cases the reason for transport facilitation is an increased occupation probability of a particle inside the channel that overcomes any increase in the first passage time because of binding.

High resolution crystal structures and molecular dynamics studies reveal substrate binding in the porin Omp32

The porin Omp32 is the major outer membrane protein of the bacterium Delftia acidovorans. The crystal structures of the strongly anion-selective porin alone and in complex with the substrate malate were solved at 1.5 and 1.45 A resolution, respectively, and revealed a malate-binding motif adjacent to the channel constriction zone. Binding is mediated by interaction with a cluster of two arginine residues and two threonines. This binding site is specific for Omp32 and reflects the physiological adaptation of the organism to organic acids. Structural studies are combined with a 7-ns unbiased molecular dynamics simulation of the trimeric channel in a model membrane. Molecular dynamics trajectories show how malate ions are efficiently captured from the surrounding bulk solution by the electrostatic potential of the channel, translocated to the binding site region, and immobilized in the constriction zone. In accordance with these results, conductance measurements with Omp32 inserted in planar lipid membranes revealed binding of malate. The anion-selective channel Omp32 is the first reported example of a porin with a 16-stranded beta-barrel and proven substrate specificity. This finding suggests a new view on the correlation of porin structure with substrate binding in specific channels.