Ionic current
An ionic current is an electric current carried by ions, atoms or molecules with a net charge, moving through a solution, a gel, a melt or a solid ionic conductor. In a metal wire the charge is carried by electrons; in salt water it is carried by positive and negative ions drifting in opposite directions, and both contribute to the current. Ionic currents run the nervous system, charge batteries and are the measured quantity in a nanopore, where a voltage drives ions through a single hole a few nanometres wide.
Nanopore currents lie between about a picoampere and a few nanoamperes. A current of 3.1 nA, which a standard model predicts for a pore 5 nm wide in 1 M potassium chloride at 200 mV, corresponds to about nineteen billion ions crossing the membrane every second. No instrument can count those ions one at a time. A molecule that enters the pore keeps tens of thousands of them from crossing during its passage, and that deficit is large enough to measure, which is how nanopores count molecules.
Carriers and conductivity
The conductivity of an electrolyte, σ, is the sum over its kinds of ion of charge × concentration × mobility, where the mobility is the drift speed per unit of electric field. In water at 25 °C a potassium ion drifts at about 7.6 × 10−8 m/s for every volt per metre, and a chloride ion at about 7.9 × 10−8 m/s, so in potassium chloride the two ions carry almost equal shares of the current. That near-equality is why potassium chloride fills salt bridges and nanopore cells alike: it keeps the junctions between solutions from generating voltages of their own.[1] Solutions of potassium chloride are also the international primary standards of electrolytic conductivity.[2]
One-molar potassium chloride, the usual nanopore electrolyte, conducts about 11 S/m at 25 °C, and its conductivity rises by roughly 2% for each degree of warming, because the water becomes less viscous. A cubic nanometre of it holds on average 0.6 potassium ions and 0.6 chloride ions. Each ion drags a shell of water molecules with it. Measured by the size of that shell, potassium and chloride are almost the same, 3.31 and 3.32 Å in radius; sodium is larger at 3.58 Å and lithium, the smallest of the alkali metal ions without its water, is the largest with it, at 3.82 Å.[3]
From wire to water
The current in the external circuit is carried by electrons and the current in the solution by ions, and the handover happens at the electrodes. The usual choice is silver coated with silver chloride. At the electrode where electrons leave the wire, they combine with silver chloride to give silver metal and a chloride ion that enters the solution; at the other electrode, silver takes up a chloride ion from the solution and gives up an electron to the wire. Each electron counted by the amplifier corresponds to one chloride ion released or consumed.[1] The reaction keeps the electrode's potential stable as long as both silver chloride and chloride ions remain, which is why the Ag/AgCl electrode is the standard in electrophysiology and nanopore work.
Ionic current through a pore
A pore obeys Ohm's law over most of its working range. Its resistance is that of a cylinder of electrolyte, 4L/(πσd2) for diameter d and length L, plus the access resistance of the regions where the current converges on each mouth, which J. E. Hall gave in 1975 as 1/(2σd) per side.[4][5] The sum sets the pore conductance. Because both terms scale with the conductivity, the current follows the salt concentration and the temperature of the bath.
| Pore diameter | Membrane thickness | Current | Elementary charges per second |
|---|---|---|---|
| 2 nm | 20 nm | 0.31 nA | 1.9 × 109 |
| 5 nm | 20 nm | 1.7 nA | 1.1 × 1010 |
| 10 nm | 20 nm | 5.9 nA | 3.7 × 1010 |
| 100 nm | 200 nm | 59 nA | 3.7 × 1011 |
| 1 µm | 200 nm | 1.7 µA | 1.0 × 1013 |
| 100 µm | 500 µm | 29 µA | 1.8 × 1014 |
The range explains the instruments. A pore of protein or a solid-state pore a few nanometres wide passes tens of picoamperes to a few nanoamperes, and the changes that matter are a fraction of that, so the amplifiers are built to resolve picoamperes. A biological channel such as alpha-hemolysin carries about 120 pA at 120 mV, or 7.5 × 108 ions a second.[6] The ion channels of nerve and muscle carry single-channel currents of a few picoamperes, which Erwin Neher and Bert Sakmann first recorded in 1976.[7] One picoampere is about 6.2 million elementary charges a second.
Nineteen billion a second
The conversion from current to ions is a division by the elementary charge, 1.602 × 10−19 C.
A solid-state pore 5 nm wide through a membrane 10 nm thick, in 1 M potassium chloride with σ = 11 S/m, has a predicted conductance of 15.5 nS, or 3.1 nA at 200 mV; without the access resistance the same formula would give 4.3 nA.[5] The 3.1 nA is about 1.9 × 1010 charges per second, nineteen every nanosecond, carried by potassium ions moving toward the negative electrode and chloride ions moving the other way.[a] Signal & Noise used the figure for the headline of a feature on the live molecular stream of Molecular Reality Corporation.[8]
The same pore holds a modest crowd. Its volume is about 196 nm3, so at any instant it contains about 120 ions of each kind, some 240 in all. The field inside it, about 1.4 × 107 V/m, drives each ion through the 10 nm channel in roughly ten nanoseconds. A pore 2 nm wide in a sheet one atom thick holds about four ions at a time, and the entire signal of such a pore comes from that space.
Counting ions and counting molecules
Single ions cannot be resolved in a current of this size. At 3.1 nA an ion enters the pore on average every 52 picoseconds, while each takes about ten nanoseconds to cross, so the passages overlap by a factor of about two hundred and merge into a smooth flow. The charge of one ion spread over a 10 µs measurement is a current of 16 fA, a hundredth of the thermal noise of the pore's own resistance in a 10 kHz bandwidth, about 1.6 pA. The flow is also grainy at a level no amplifier can remove: if the crossings were independent, about 19,400 ions would cross in a microsecond with a spread of about 139, a jitter of 0.7%.
Molecules are another matter. A strand of DNA that lowers the current by 0.6 nA for 10 µs keeps about 37,000 elementary charges from crossing, and that deficit stands well clear of the noise.
Every nanopore measurement is a count of ions that did not arrive. The current blockade of a molecule is read as a change in the rate of a flow that is itself far too fast to follow, which is the same bargain the Coulter counter struck with blood cells in the 1950s.
Other ionic currents
A current also flows when salt water is pushed through a channel with charged walls, because the flow carries along the excess of counterions near the walls. This streaming current was known in the nineteenth century. In 2019 groups in Manchester and Paris measured it in slits a few ångströms high between sheets of graphite and boron nitride, and found that a fraction of a volt could raise the pressure-driven flow up to twentyfold; their paper was titled "Molecular streaming and its voltage control in ångström-scale channels".[9] Molecular Reality uses the same two words for something else, molecules passing through sensors and their data passing to the public, and its founder wrote in March 2026 that "Nobody outside the corps calls it molecular streaming yet."[10]
In a cone-shaped pore with charged walls the current can be larger for one polarity than for the other, an effect called ion current rectification. A single conical pore etched in a plastic film and driven by a fluctuating voltage was shown in 2002 to pump potassium ions against their concentration gradient.[11] At low salt concentrations the electric double layer at the walls carries a larger share of the current, and a molecule entering a pore can then raise the current instead of lowering it.[12]
See also
Notes
- ^ The value is a model prediction, not a measurement of any particular pore. Real pores of nominally the same size differ in shape and surface charge, and their measured currents scatter around such predictions.
References
- ^ a b Bard, A. J.; Faulkner, L. R. (2001). Electrochemical Methods: Fundamentals and Applications. 2nd ed. Wiley. ISBN 0-471-04372-9.
- ^ Pratt, K. W.; Koch, W. F.; Wu, Y. C.; Berezansky, P. A. (2001). "Molality-based primary standards of electrolytic conductivity (IUPAC Technical Report)". Pure and Applied Chemistry 73 (11): 1783-1793. doi:10.1351/pac200173111783.
- ^ Nightingale, E. R. (1959). "Phenomenological theory of ion solvation. Effective radii of hydrated ions". Journal of Physical Chemistry 63 (9): 1381-1387. doi:10.1021/j150579a011.
- ^ Hall, J. E. (1975). "Access resistance of a small circular pore". Journal of General Physiology 66 (4): 531-532. doi:10.1085/jgp.66.4.531.
- ^ a b Kowalczyk, S. W.; Grosberg, A. Y.; Rabin, Y.; Dekker, C. (2011). "Modeling the conductance and DNA blockade of solid-state nanopores". Nanotechnology 22 (31): 315101. doi:10.1088/0957-4484/22/31/315101.
- ^ Kasianowicz, J. J.; Brandin, E.; Branton, D.; Deamer, D. W. (1996). "Characterization of individual polynucleotide molecules using a membrane channel". Proceedings of the National Academy of Sciences 93 (24): 13770-13773. doi:10.1073/pnas.93.24.13770.
- ^ Neher, E.; Sakmann, B. (1976). "Single-channel currents recorded from membrane of denervated frog muscle fibres". Nature 260 (5554): 799-802. doi:10.1038/260799a0.
- ^ Lenora Ashgrove (July 29, 2026). "Nineteen Billion Ions a Second, Live on the Internet". Signal & Noise.
- ^ Mouterde, T.; et al. (2019). "Molecular streaming and its voltage control in ångström-scale channels". Nature 567 (7746): 87-90. doi:10.1038/s41586-019-0961-5.
- ^ Kemmishtree (March 28, 2026). "Marching orders". EQBio-OS.
- ^ Siwy, Z.; Fuliński, A. (2002). "Fabrication of a synthetic nanopore ion pump". Physical Review Letters 89 (19): 198103. doi:10.1103/PhysRevLett.89.198103.
- ^ Smeets, R. M. M.; Keyser, U. F.; Krapf, D.; Wu, M.-Y.; Dekker, N. H.; Dekker, C. (2006). "Salt dependence of ion transport and DNA translocation through solid-state nanopores". Nano Letters 6 (1): 89-95. doi:10.1021/nl052107w.