Robert S. Eisenberg

Coupling Poisson-Nernst-Planck and density functional theory to calculate ion flux

Ion transport between two baths of fixed ionic concentrations and applied electrostatic (ES) potential is analysed using a one-dimensional drift-diffusion (Poisson–Nernst–Planck, PNP) transport system designed to model biological ion channels. The ions are described as charged, hard spheres with excess chemical potentials computed from equilibrium density functional theory (DFT). The method of Rosenfeld (Rosenfeld Y 1993 J. Chem. Phys. 98 8126) is generalized to calculate the ES excess chemical potential in channels. A numerical algorithm for solving the set of integral–differential PNP/DFT equations is described and used to calculate flux through a calcium-selective ion channel.

Tuning transport properties of nanofluidic devices with local charge inversion.

Nanotubes can selectively conduct ions across membranes to make ionic devices with transport characteristics similar to biological ion channels and semiconductor electron devices. Depending on the surface charge profile of the nanopore, ohmic resistors, rectifiers, and diodes can be made. Here we show that a uniformly charged conical nanopore can have all these transport properties by changing the ion species and their concentrations on each side of the membrane. Moreover, the cation versus anion selectivity of the pores can be changed. We find that polyvalent cations like Ca(2+) and the trivalent cobalt sepulchrate produce localized charge inversion to change the effective pore surface charge profile from negative to positive. These effects are reversible so that the transport and selectivity characteristics of ionic devices can be tuned, much as the gate voltage tunes the properties of a semiconductor.

Charges, currents, and potentials in ionic channels of one conformation.

Flux through an open ionic channel is analyzed with Poisson-Nernst-Planck (PNP) theory. The channel protein is described as an unchanging but nonuniform distribution of permanent charge, the charge distribution observed (in principle) in x-ray diffraction. Appropriate boundary conditions are derived and presented in some generality. Three kinds of charge are present: (a) permanent charge on the atoms of the protein, the charge independent of the electric field; (b) free or mobile charge, carried by ions in the pore as they flux through the channel; and (c) induced (sometimes called polarization) charge, in the pore and protein, created by the electric field, zero when the electric field is zero. The permanent charge produces an offset in potential, a built-in Donnan potential at both ends of the channel pore. The system is completely solved for bathing solutions of two ions. Graphs describe the distribution of potential, concentration, free (i.e., mobile) and induced charge, and the potential energy associated with the concentration of charge, as well as the unidirectional flux as a function of concentration of ions in the bath, for a distribution of permanent charge that is uniform. The model shows surprising complexity, exhibiting some (but not all) of the properties usually attributed to single filing and exchange diffusion. The complexity arises because the arrangement of free and induced charge, and thus of potential and potential energy, varies, sometimes substantially, as conditions change, even though the channel structure and conformation (of permanent charge) is strictly constant. Energy barriers and wells, and the concomitant binding sites and binding phenomena, are outputs of the PNP theory: they are computed, not assumed. They vary in size and location as experimental conditions change, while the conformation of permanent charge remains constant, thus giving the model much of its interesting behavior.

A cation channel in frog lens epithelia responsive to pressure and calcium

SummaryPatch-clamp recording from the apical surface of the epithelium of frog lens reveals a cation-selective channel after pressure (about ±30 mm Hg) is applied to the pipette. The open state of this channel has a conductance of some 50 pS near the resting potential (−56.1±2.3 mV) when 107mm NaCl and 10 HEPES (pH 7.3) is outside the channel. The probability of the channel being open depends strongly on pressure but the current-voltage relation of the open state does not. With minimal Ca2+ (55±2 μm) outside the channel, the current-voltage relation is nonlinear even in symmetrical salt solutions, allowing more current to flow into the cell than out. The channel, in minimal Ca2+ solution, is selective among the monovalent cations in the following sequence K+>Rb+>Cs+>Na+>Li+. The conductance depends monotonically on the mole fraction of K+ when the other ion present is Li+ or Na+. The single-channel current is a saturating function of [K+] when K+ is the permeant ion, for [K+]≤214mm. When [Ca2+]=2mm, the currentvoltage relation is linearized and the channel cannot distinguish Na+ and K+.

Nanoprecipitation-assisted ion current oscillations

Nanoscale pores exhibit transport properties that are not seen in micrometre-scale pores, such as increased ionic concentrations inside the pore relative to the bulk solution, ionic selectivity and ionic rectification. These nanoscale effects are all caused by the presence of permanent surface charges on the walls of the pore. Here we report a new phenomenon in which the addition of small amounts of divalent cations to a buffered monovalent ionic solution results in an oscillating ionic current through a conical nanopore. This behaviour is caused by the transient formation and redissolution of nanoprecipitates, which temporarily block the ionic current through the pore. The frequency and character of ionic current instabilities are regulated by the potential across the membrane and the chemistry of the precipitate. We discuss how oscillating nanopores could be used as model systems for studying nonlinear electrochemical processes and the early stages of crystallization in sub-femtolitre volumes. Such nanopore systems might also form the basis for a stochastic sensor.

Action Potentials without Contraction in Frog Skeletal Muscle Fibers with Disrupted Transverse Tubules

Action potentials, with no accompanying contraction, were recorded from muscle fibers in which the transverse tubular system had been disrupted. The results show that action potentials require an intact transverse tubular system to cause contraction. Furthermore, both the after-depolarization following a single action potential and the slower, late afterpotential following a train of action potentials were absent in this preparation. Therefore, both phenomena must normally involve the transverse tubular system.

Qualitative properties of steady-state Poisson-Nernst-Planck systems: perturbation and simulation study

Poisson--Nernst--Planck (PNP) systems are considered in the case of vanishing permanent charge. A detailed case study, based on natural categories described by system boundary conditions and flux, is carried out via simulation and singular perturbation analysis. Our results confirm the rich structure inherent in these systems. A natural quantity, the quotient of the Debye and characteristic length scales, serves as the singular perturbation parameter. The regions of validity are carefully analyzed by critical comparisons and contrasts between the simulation and the perturbation solution, which can be represented in closed form.

Electrical properties of structural components of the crystalline lens.

The electrical properties of the crystalline lens of the frog eye are measured with stochastic currents applied with a microelectrode near the center of the preparation and potential recorded just under the surface. The stochastic signals are decomposed by Fourier analysis into sinusoidal components, and the impedance is determined from the ratio of mean cross power to input power. The data are fit by an electrical model that includes two paths for current flow: one through the cytoplasm, gap junctions, and outer membrane; the other through inner membranes and the extracellular space between lens fibers. The electrical properties of the structures of the lens which appear as circuit components in the model are determined by the fit to the data. The resistivity of the extracellular space within the lens is comparable to the resistivity of Ringer. The outer membrane has a normal resistance of 5 kohm . cm(2) but large capacitance of 10 muF/cm(2), probably because it represents the properties of several layers of fibers. The inner membranes have properties reminiscent of artificial lipid bilayers: they have high membrane resistance, 2.2 megohm . cm(2), and low specific capacitance, 0.8 muF/cm(2). There is so much membrane within the lens, however, that the sum of the current flow across all the inner membranes is comparable to that across the outer surface.

DIFFUSION AS A CHEMICAL REACTION : STOCHASTIC TRAJECTORIES BETWEEN FIXED CONCENTRATIONS

Stochastic trajectories are described that underly classical diffusion between known concentrations. The description of those experimental boundary conditions requires a phase space using the full Langevin equation, with displacement and velocity as state variables, even if friction entirely dominates the dynamics of diffusion, because the incoming and outgoing trajectories have to be told apart. The conditional flux, probabilities, mean first‐passage times, and contents (of the reaction region) of the four types of trajectories—the trans trajectories LR and RL and the cis trajectories LL and RR—are expressed in terms of solutions of the Fokker–Planck equation in phase space and are explicitly calculated in the Smoluchowski limit of high friction. With these results, diffusion in a region between fixed concentrations can be described exactly as a chemical reaction for any potential function in the region, made of any combination of high or low barriers or wells.

Paralysis of frog skeletal muscle fibres by the calcium antagonist D-600.

The Ca2+ channel blocker D‐600 (methoxyverapamil) paralyses single muscle fibres of the frog: fibres exposed to the drug at 7 degrees C give a single K+ contracture after which they are paralysed, unable to contract in response to electrical stimulation or further applications of K+. Paralysed fibres contract in response to caffeine and have normal resting potentials and action potentials. Fibres treated with D‐600 at 22 degrees C are not paralysed. Paralysed fibres warmed to 22 degrees C recover contractile properties: they twitch and give K+ contractures. Other workers have shown that D‐600 blocks a Ca2+ channel at room temperature; thus, the paralytic action of D‐600 is probably mediated by a different membrane protein, perhaps a different Ca2+ channel from that blocked at room temperature. These results suggest that the binding of D‐600 can disrupt the mechanism coupling electrical potential changes across the T membrane to Ca2+ release from the sarcoplasmic reticulum.