Diffusivity and conductivity of a primitive model electrolyte in a nanopore

Theoretical models for electrochemical impedance spectroscopy and local ζ-potential of unfolded proteins in nanopores

Single solid-state nanopores find increasing use for electrical detection and/or manipulation of macromolecules. These applications exploit the changes in signals due to the geometry and electrical properties of the molecular species found within the nanopore. The sensitivity and resolution of such measurements are also influenced by the geometric and electrical properties of the nanopore. This paper continues the development of an analytical theory to predict the electrochemical impedance spectra of nanopores by including the influence of the presence of an unfolded protein using the variable topology finite Warburg impedance model previously published by the authors. The local excluded volume of, and charges present on, the segment of protein sampled by the nanopore are shown to influence the shape and peak frequency of the electrochemical impedance spectrum. An analytical theory is used to relate the capacitive response of the electrical double layer at the surface of the protein to both the charge density at the protein surface and the more commonly measured zeta potential. Illustrative examples show how the theory predicts that the varying sequential regions of surface charge density and excluded volume dictated by the protein primary structure may allow for an impedance-based approach to identifying unfolded proteins.

Pulsed plasma polymerization for controlling shrinkage and surface composition of nanopores

Solid-state nanopores have emerged as sensors for single molecules and these have been employed to examine the biophysical properties of an increasingly large variety of biomolecules. Herein we describe a novel and facile approach to precisely adjust the pore size, while simultaneously controlling the surface chemical composition of the solid-state nanopores. Specifically, nanopores fabricated using standard ion beam technology are shrunk to the requisite molecular dimensions via the deposition of highly conformal pulsed plasma generated thin polymeric films. The plasma treatment process provides accurate control of the pore size as the conformal film deposition depends linearly on the deposition time. Simultaneously, the pore and channel chemical compositions are controlled by appropriate selection of the gaseous monomer and plasma conditions employed in the deposition of the polymer films. The controlled pore shrinkage is characterized with high resolution AFM, and the film chemistry of the plasma generated polymers is analyzed with FTIR and XPS. The stability and practical utility of this new approach is demonstrated by successful single molecule sensing of double-stranded DNA. The process offers a viable new advance in the fabrication of tailored nanopores, in terms of both the pore size and surface composition, for usage in a wide range of emerging applications.

Determining nanocapillary geometry from electrochemical impedance spectroscopy using a variable topology network circuit model

Solid-state nanopores and nanocapillaries find increasing use in a variety of applications including DNA sequencing, synthetic nanopores, next-generation membranes for water purification, and other nanofluidic structures. This paper develops the use of electrochemical impedance spectroscopy to determine the geometry of nanocapillaries. A network equivalent circuit element is derived to include the effects of the capacitive double layer inside the nanocapillaries as well as the influence of varying nanocapillary radius. This variable topology function is similar to the finite Warburg impedance in certain limits. Analytical expressions for several different nanocapillary shapes are derived. The functions are evaluated to determine how the impedance signals will change with different nanocapillary aspect ratios and different degrees of constriction or inflation at the capillary center. Next, the complex impedance spectrum of a nanocapillary array membrane is measured at varying concentrations of electrolyte to separate the effects of nanocapillary double layer capacitance from those of nanocapillary geometry. The variable topology equivalent circuit element model of the nanocapillary is used in an equivalent circuit model that included contributions from the membrane and the measurement apparatus. The resulting values are consistent with the manufacturer's specified tolerances of the nanocapillary geometry. It is demonstrated that electrochemical impedance spectroscopy can be used as a tool for in situ determination of the geometry of nanocapillaries.

Synthetic nanopores as a test case for ion channel theories: the anomalous mole fraction effect without single filing

The predictions of a theory for the anomalous mole fraction effect (AMFE) are tested experimentally with synthetic nanopores in plastic. The negatively charged synthetic nanopores under consideration are highly cation selective and 50 A in diameter at their smallest point. These pores exhibit an AMFE in mixtures of Ca(2+) and monovalent cations. An AMFE occurs when the conductance through a pore is lower in a mixture of salts than in the pure salts at the same concentration. For ion channels, the textbook interpretation of the AMFE is that multiple ions move through the pore in coordinated, single-file motion. However, because the synthetic nanopores are so wide, their AMFE shows that single filing is not necessary for the AMFE. It is shown that the AMFE in the synthetic nanopores is explained by a theory of preferential ion selectivity. The unique properties of the synthetic nanopores allow us to experimentally confirm several predictions of this theory. These same properties make synthetic nanopores an interesting new platform to test theories of ion channel permeation and selectivity in general.

Anomalous diffusivity and electric conductivity for low concentration electrolytes in nanopores

We apply equilibrium and nonequilibrium molecular dynamics simulations to study the dynamic properties of electrolytes in nanopores. The realistic primitive model and the restrictive primitive model widely used in the statistical mechanics of liquid-state theory are applied to model the electrolytes. The electrolytic ions are immersed in water, treated in this work as either a dielectric continuum ignoring the size of solvent molecules or a macroscopic dielectric continuum (polar property) plus neutral soft spheres, and the aqueous electrolyte is put in a confined space. To simulate a condition mimicking closely processes of practical interest and yet maintaining the simulation computationally manageable, we consider an infinitely long and uncharged cylindrical tube. The equilibrium property of the self-diffusion coefficient D and the nonequilibrium property of electric conductivity sigma are computed in terms of electrolyte concentration, particle size, and cylindrical pore radius. The simulation results for the continuum solvent restrictive primitive model and continuum solvent primitive model show normal behavior for D versus pore radius R at ionic concentration 0.1M -i.e., D decreases with decreasing R -display an R independence of D at a certain threshold concentration and undergo an anomalous increase in D with reducing R at a lower value 0.025 M. The mechanism of the anomaly at the ionic concentration 0.025 M was sought for and interpreted in this work to arise from the energetic and entropic factors. Our simulated data of sigma at this same concentration follow the same trend as D. To delve further into the transport properties, we perform simulation studies for the discrete solvent primitive model and make a detailed analysis of the characteristic of the ion radial density functions. Comparison of the latter functions with those in the continuum solvent primitive model sheds light on the simulated diffusion coefficient within the context of discrete solvent primitive model which is about two orders of magnitude less. This difference in D is naturally attributed to the solvent effect. Similar disparities were reported by others for the discrete and continuum restrictive primitive models.

Model channel ion currents in NaCl-extended simple point charge water solution with applied-field molecular dynamics

Using periodic boundary conditions and a constant applied field, we have simulated current flow through an 8.125-A internal diameter, rigid, atomistic channel with polar walls in a rigid membrane using explicit ions and extended simple point charge water. Channel and bath currents were computed from 10 10-ns trajectories for each of 10 different conditions of concentration and applied voltage. An electric field was applied uniformly throughout the system to all mobile atoms. On average, the resultant net electric field falls primarily across the membrane channel, as expected for two conductive baths separated by a membrane capacitance. The channel is rarely occupied by more than one ion. Current-voltage relations are concentration dependent and superlinear at high concentrations.