Hybrid MD-Nernst Planck model of α-hemolysin conductance properties

Non-isothermal flow of an electrolyte in a charged nanochannel

Electrokinetic flows are generally analyzed, assuming isothermal conditions even though such situations are hard to be achieved in practice. In this paper, the flow of a symmetric electrolyte in a charged nanochannel subjected to an axial temperature gradient is investigated using molecular dynamics simulations. We analyze the relative contribution of the Soret effect, the thermoelectric effect, and the double layer potential in the electrical double layer for various surface charges and temperature gradients. We find the flow driven by thermal gradient is analogous to electroosmotic flow. The thermophoretic motion of the electrolyte is significant for negative surface charge than the positive surface charge. The vibrational spectrum of graphene is calculated to delineate the effect of the surface charge polarity on the observed thermophoretic motion of the electrolyte. A unique structure of interfacial water layer is observed for the positive and negative surface charges. We attribute the presence of these structures to the differences in water-carbon interactions existing for various surface charge polarity. For an applied thermal gradient in the range 2.6 K nm-1 to 8 K nm-1, we observe a continuous net flow with average velocities reaching up to 9.4 m s-1 inside the channel for a negative surface charge of -0.101 C m-2. The results indicate that in a charged graphene-based nanochannel, temperature gradients can be employed to induce streaming current, depending on the relative influence of the Soret effect and the double layer potential.

Ionic transport through a protein nanopore: a Coarse-Grained Molecular Dynamics Study

The MARTINI coarse-grained (CG) force field is used to test the ability of CG models to simulate ionic transport through protein nanopores. The ionic conductivity of CG ions in solution was computed and compared with experimental results. Next, we studied the electrostatic behavior of a solvated CG lipid bilayer in salt solution under an external electric field. We showed this approach correctly describes the experimental conditions under a potential bias. Finally, we performed CG molecular dynamics simulations of the ionic transport through a protein nanopore (α-hemolysin) inserted in a lipid bilayer, under different electric fields, for 2-3 microseconds. The resulting I - V curve is qualitatively consistent with experiments, although the computed current is one order of magnitude smaller. Current saturation was observed for potential biases over ±350 mV. We also discuss the time to reach a stationary regime and the role of the protein flexibility in our CG simulations.

Size-dependent interaction of a 3-arm star poly(ethylene glycol) with two biological nanopores

We use two pore-forming proteins, alpha-hemolysin and aerolysin, to compare the polymer size-dependence of ionic current block by two types of ethyleneglycol polymers: 1) linear and 2) 3-arm star poly(ethylene glycol), both applied as a polydisperse mixture of average mass 1kDa under high salt conditions. The results demonstrate that monomer size sensitivity, as known for linear PEGs, is conserved for the star polymers with only subtle differences in the dependence of the residual conductance on monomer number. To explain this absence of a dominant effect of polymer architecture, we propose that PEG adsorbs to the inner pore wall in a collapsed, salted-out state, likely due to the effect of hydrophobic residues in the pore wall on the availability of water for hydration.

Molecular dynamics simulation of water permeation through the alpha-hemolysin channel

The alpha-hemolysin (AHL) nanochannel is a non-selective channel that allows for uncontrolled transport of small molecules across membranes leading to cell death. Although it is a bacterial toxin, it has promising applications, ranging from drug delivery systems to nano-sensing devices. This study focuses on the transport of water molecules through an AHL nanochannel using molecular dynamics (MD) simulations. Our results show that AHL can quickly transport water across membranes. The first-passage time approach was used to estimate the diffusion coefficient and the mean exit time. To study the energetics of transport, the potential of mean force (PMF) of a water molecule along the AHL nanochannel was calculated. The results show that the energy barriers of water permeation across a nanopore are always positive along the channel and the values are close to thermal energy (kBT). These findings suggest that the observed quick permeation of water is due to small energy barriers and a hydrophobic inner channel surface resulting in smaller friction. We speculate that these physical mechanisms are important in how AHL causes cell death.

Optimization of 3D Poisson-Nernst-Planck model for fast evaluation of diverse protein channels

We show the accuracy and applicability of our fast algorithmic implementation of a three-dimensional Poisson-Nernst-Planck (3D-PNP) flow model for characterizing different protein channels. Due to its high computational efficiency, our model can predict the full current-voltage characteristics of a channel within minutes, based on the experimental 3D structure of the channel or its computational model structure. Compared with other methods, such as Brownian dynamics, which currently needs a few weeks of the computational time, or even much more demanding molecular dynamics modeling, 3D-PNP is the only available method for a function-based evaluation of very numerous tentative structural channel models. Flow model tests of our algorithm and its optimal parametrization are provided for five native channels whose experimental structures are available in the protein data bank (PDB) in an open conductive state, and whose experimental current-voltage characteristics have been published. The channels represent very different geometric and structural properties, which makes it the widest test to date of the accuracy of 3D-PNP on real channels. We test whether the channel conductance, rectification, and charge selectivity obtained from the flow model, could be sufficiently sensitive to single-point mutations, related to unsignificant changes in the channel structure. Our results show that the classical 3D-PNP model, under proper parametrization, is able to achieve a qualitative agreement with experimental data for a majority of the tested characteristics and channels, including channels with narrow and irregular conductivity pores. We propose that although the standard PNP model cannot provide insight into complex physical phenomena due to its intrinsic limitations, its semiquantitative agreement is achievable for rectification and selectivity at a level sufficient for the bioinformatical purpose of selecting the best structural models with a great advantage of a very short computational time.

The role of Lys147 in the interaction between MPSA-gold nanoparticles and the α-hemolysin nanopore

Single channel recordings were used to determine the effect of direct electrostatic interactions between sulfonate-coated gold nanoparticles and the constriction of the Staphylococcus aureus α-hemolysin protein channel on the ionic current amplitude. We provide evidence that Lys147 of α-hemolysin can interact with the sulfonate groups at the nanoparticle surface, and these interactions can reversibly block 100% of the residual ionic current. Lys147 is normally involved in a salt bridge with Glu111. The capture of a nanoparticle leads to a partial current block at neutral pH values, but protonation of Glu111 at pH 2.8 results in a full current block when the nanoparticle is captured. At pH 2.8, we suggest that Lys147 is free to engage in electrostatic interactions with sulfonates at the nanoparticle surface. To verify our results, we engineered a mutation in the α-hemolysin protein, where Glu111 is substituted by Ala (E111A), thus removing Glu111-Lys147 interactions and facilitating Lys147-sulfonate electrostatic interactions. This mutation leads to a 100% current block at pH 2.8 and a 92% block at pH 8.0, showing that electrostatic interactions are formed between the nanopore and the nanoparticle surface. Besides demonstrating the effect of electrostatic interactions on cross channel ionic current, this work offers a novel approach to controlling open and closed states of the α-hemolysin nanopore as a function of external gears.

Assessment of Common Simulation Protocols for Simulations of Nanopores, Membrane Proteins, and Channels

Molecular dynamics (MD) simulation has become a common technique to study biological systems. Transport of small molecules through carbon nanotubes and membrane proteins has been an intensely studied topic, and MD simulations have been able to provide valuable predictions, many of which have later been experimentally proven. Simulations of such systems pose challenges, and unexpected problems in commonly used protocols and methods have been found in the past few years. The two main reasons why some were not found before are that most of these newly discovered errors do not lead to unstable simulations. Furthermore, some of them manifest themselves only after relatively long simulation times. We assessed the reliability of the most common simulations protocols by MD and stochastic dynamics (SD) or Langevin dynamics, simulations of an alpha hemolysin nanochannel embedded in a palmitoyloleoylphosphatidylcholine (POPC) lipid bilayer. Our findings are that (a) reaction field electrostatics should not be used in simulations of such systems, (b) local thermostats should be preferred over global ones since the latter may lead to an unphysical temperature distribution,

Testing the applicability of Nernst-Planck theory in ion channels: comparisons with Brownian dynamics simulations

The macroscopic Nernst-Planck (NP) theory has often been used for predicting ion channel currents in recent years, but the validity of this theory at the microscopic scale has not been tested. In this study we systematically tested the ability of the NP theory to accurately predict channel currents by combining and comparing the results with those of Brownian dynamics (BD) simulations. To thoroughly test the theory in a range of situations, calculations were made in a series of simplified cylindrical channels with radii ranging from 3 to 15 Å, in a more complex 'catenary' channel, and in a realistic model of the mechanosensitive channel MscS. The extensive tests indicate that the NP equation is applicable in narrow ion channels provided that accurate concentrations and potentials can be input as the currents obtained from the combination of BD and NP match well with those obtained directly from BD simulations, although some discrepancies are seen when the ion concentrations are not radially uniform. This finding opens a door to utilising the results of microscopic simulations in continuum theory, something that is likely to be useful in the investigation of a range of biophysical and nano-scale applications and should stimulate further studies in this direction.

Ion selectivity of alpha-hemolysin with beta-cyclodextrin adapter. II. Multi-ion effects studied with grand canonical Monte Carlo/Brownian dynamics simulations

In a previous study of ion selectivity of alpha-hemolysin (alphaHL) in complex with beta-cyclodextrin (betaCD) adapter, we calculated the potential of mean force (PMF) and characterized the self-diffusion coefficients of isolated K(+) and Cl(-) ions using molecular dynamics simulations (Y. Luo et al., "Ion Selectivity of alpha-Hemolysin with beta-Cyclodextrin Adapter: I. Single Ion Potential of Mean Force and Diffusion Coefficient"). In the present effort, these results pertaining to single isolated ions in the wide aqueous pore are extended to take into account multi-ion effects. The grand canonical Monte Carlo/Brownian dynamics (GCMC/BD) algorithm is used to simulate ion currents through the wild-type alphaHL ion channel, as well as two engineered alphaHL mutants, with and without the cyclic oligosaccaride betaCD lodged in the lumen of the pore. The GCMC/BD current-voltage curves agree well with experimental results and show that betaCD increases the anion selectivity of alphaHL. Comparisons between multi-ion PMFs from GCMC/BD simulations and single-ion PMFs demonstrate that multi-ion effects and pore shape are crucial for explaining this behavior. It is concluded that the narrow betaCD adapter increases the anion selectivity of alphaHL because it reduces the pore radius locally, which decreases the ionic screening and the dielectric shielding of the strong electrostatic field induced by a nearby ring of positively charged alphaHL side chains.

Continuum electrostatic calculations of the pKa of ionizable residues in an ion channel: dynamic vs. static input structure

We have computed the pK(a)'s of the ionizable residues of a protein ion channel, the Staphylococcus aureus toxin alpha-hemolysin, by using two types of input structures, namely the crystal structure of the heptameric alpha-hemolysin and a set of over four hundred snapshots from a 4.38 ns Molecular Dynamics simulation of the protein inserted in a phospholipid planar bilayer. The comparison of the dynamic picture provided by the Molecular Simulation with the static one based on the X-ray crystal structure of the protein embedded in a lipid membrane allows analyzing the influence of the fluctuations in the protein structure on its ionization properties. We find that the use of the dynamic structure provides interesting information about the sensitivity of the computed pK(a) of a given residue to small changes in the local structure. The calculated pK(a) are consistent with previous indirect estimations obtained from single-channel conductance and selectivity measurements.

Ion flux through membrane channels--an enhanced algorithm for the Poisson-Nernst-Planck model

A novel algorithmic scheme for numerical solution of the 3D Poisson-Nernst-Planck model is proposed. The algorithmic improvements are universal and independent of the detailed physical model. They include three major steps: an adjustable gradient-based step value, an adjustable relaxation coefficient, and an optimized segmentation of the modeled space. The enhanced algorithm significantly accelerates the speed of computation and reduces the computational demands. The theoretical model was tested on a regular artificial channel and validated on a real protein channel-alpha-hemolysin, proving its efficiency.

Model-based prediction of the alpha-hemolysin structure in the hexameric state

The alpha-hemolysin toxin self-assembles in lipid bilayers to form water-filled pores. In recent years, alpha-hemolysin has received great attention, mainly due to its possible usage as a sensing element. We measured the ion currents through single alpha-hemolysin channels and confirmed the presence of two different subpopulations of channels with conductance levels of 465 +/- 30 pS and 280 +/- 30 pS. Different oligomerization states could be responsible for these two conductances. In fact, a heptameric structure of the channel was revealed by x-ray crystallography, whereas atomic force microscopy revealed a hexameric structure. Due to the low resolution of atomic force microscopy the atomic details of the hexameric structure are still unknown, and are here predicted by computational methods. Several possible structures of the hexameric channel were defined, and were simulated by molecular dynamics. The conductances of these channel models were computed by a numerical method based on the Poisson-Nernst-Planck electrodiffusion theory, and the values were compared to experimental data. In this way, we identified a model of the alpha-hemolysin hexameric state with conductance characteristics consistent with the experimental data. Since the oligomerization state of the channel may affect its behavior as a molecular sensor, knowing the atomic structure of the hexameric state will be useful for biotechnological applications of alpha-hemolysin.

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.