Nineteen Billion Ions a Second, Live on the Internet

Three point one nanoamps is a small current. A phone charging over USB draws about two amps, more than six hundred million times as much. Counted in charges, though, 3.1 nA is a crowd. Since 2019 the elementary charge has been fixed by definition at exactly 1.602176634 × 10⁻¹⁹ coulomb, so one coulomb is about 6.2415 billion billion elementary charges, and 3.1 nA is about 1.94 × 10¹⁰ charges a second. In salt water the charges ride on ions, and in potassium chloride every ion carries exactly one, so about nineteen billion ions cross the pore each second. That is nineteen every nanosecond.

The number comes from a model that is simple enough to check by hand. Take a cylindrical hole 5 nm wide through a membrane 10 nm thick, fill it with 1 M potassium chloride, whose conductivity is about 11 S/m at room temperature, and put 200 mV across it. The cylinder alone has a resistance of about 46 MΩ, which would pass 4.3 nA. Ions also have to funnel into the hole from the open liquid on each side, and that access resistance adds about 1/(σd), or 18 MΩ here. With both terms the conductance comes to 15.5 nS and the current to 3.1 nA.

Access resistance has an unusually short pedigree. It comes from a two-page paper by J. E. Hall in the Journal of General Physiology in 1975, written about channels in biological membranes. In 2011 Kowalczyk and colleagues tested the combined expression, G = σ[4L/(πd²) + 1/d]⁻¹, against solid-state pores. As a membrane gets thinner the first term vanishes, and the pore conductance ends up depending only on the width of the mouth.

At any instant the 5 nm cylinder holds about 236 ions. A 2 nm hole in a membrane one nanometer thick, the scale of the thinnest pores, holds about four.

Potassium chloride is the field's default salt for a reason that shows up in the traffic. Its two ions move at almost the same speed in an electric field, 7.6 and 7.9 × 10⁻⁸ m² per volt-second, so each carries about half of the current, potassium a little under half and chloride a little over, in opposite directions. Of the nineteen billion, roughly 9.5 billion are potassium ions heading one way and 9.9 billion are chloride ions heading the other.

The bench behind the browser

Molecular Reality Corporation, a small company that builds nanopore instruments, streams this kind of current from its lab bench in the US Southwest to a page on its website. From June 13 the stream was the company's home page, and since June 29 it has been the default view of a new front page. The amplifier is a four-channel, USB-powered patch-clamp unit made by the Italian firm Elements. The company calls it the EDR4, and the page's status line carries the unit's serial number, e4-00044.

Two camera panes over the trace are labeled Microscope and Fluidics. The vertical axis is a logarithmic slider that runs from plus or minus 10 fA to plus or minus 600 nA, almost eight decades; in charges per second, the bottom of the scale is 62,000 and the top is 3.7 trillion. A spike detector marks dips in the trace, with a threshold that defaults to 3.8 standard deviations, and a chat overlay called LabChat runs along the bottom.

The pore on the stream is a macropore. The lab's provisions list, behind a button marked Prov, gives it as a "200 um laser-drilled pore" in a "d2600 style cell: delrin/teflon combo with luer locks and potted electrode." A hole 200 µm wide is 40,000 times wider than the model's 5 nm pore and has 1.6 billion times its cross-section. It belongs to the size range of the apertures Wallace Coulter used to count blood cells. For a sphere much smaller than the aperture, the fractional rise in resistance is roughly d³/(D²L), the particle's diameter cubed over the square of the aperture's diameter times its length (DeBlois and Bean, 1970). The provisions list does not give the thickness of the membrane, but if the hole were as long as it is wide, a 10 µm cell would raise its resistance by about one part in 8,000, and a 1 µm bacterium by about one part in 8 million. At this size, the dips worth looking for come from cells and particles several micrometers across.

The first sample on the list is tap water, entered as a "Baseline conductivity standard."

What carries the current in the wires

Ions stop at the electrodes. Most nanopore cells use electrodes of silver coated with silver chloride, and at their surfaces the current changes carriers: at one electrode, silver and a chloride ion from the solution become silver chloride and release an electron into the wire, and at the other the reaction runs backward. One formula unit of silver chloride is made or unmade for every elementary charge, which is one more reason the field likes potassium chloride: the salt supplies the chloride the electrodes consume. At 3.1 nA, an hour of recording builds about 17 nanograms of silver chloride on one electrode and strips the same amount from the other.

From current to ions

The conversion from current to charges does not depend on the pore. One nanoamp is 6.24 billion elementary charges a second, so any reading on the stream's trace can be turned into charge traffic with a single multiplication. Turning charges into ions takes the chemistry of the sample.

Tap water carries a few millimoles per liter of mixed salts, mostly calcium, magnesium, sodium, bicarbonate, chloride and sulfate. Calcium, magnesium and sulfate carry two charges apiece, so a nanoamp of tap water is somewhat fewer than 6.24 billion ions a second. Tap water's conductivity is also a hundred or more times lower than that of 1 M potassium chloride, which is why the same hole passes far less current with it. Conductivity also climbs by about 2 percent for each degree Celsius, and a bench that warms by 5 °C over an afternoon reads about 10 percent more current through the same hole.

Salt concentration changes more than the count. Any charged surface in salt water gathers a thin cloud of oppositely charged ions, and the thickness of that cloud, the Debye length, is about 0.3 nm in 1 M potassium chloride and about 4 nm in tap water. In a 5 nm pore filled with tap water the clouds from opposite walls would nearly meet, and current carried along the charged walls would rival the current through the middle. In a hole 200 µm wide the walls are too far apart to matter.

The floor under the noise

Counting sets a limit that no electronics can remove. If ions cross independently, the number that crosses in a fixed interval fluctuates by about its own square root. At 3.1 nA about 97,000 charges cross in five microseconds, give or take about 311, a jitter of 0.3 percent before any amplifier is involved; in one microsecond it is 19,400 give or take 139, or 0.7 percent.

The amplifier adds noise of its own. A resistive-feedback amplifier turns current into voltage through a feedback resistor, and the resistor's own thermal noise falls as its resistance rises: about 128 fA per root hertz for 1 MΩ, about 4 fA for 1 GΩ. Over a 10 kHz bandwidth the 1 MΩ resistor alone contributes 12.8 pA of noise. The amplifiers descend from biology. Erwin Neher and Bert Sakmann developed the patch clamp in the 1970s to record the current through a single ion channel in a cell membrane, a few picoamps, and shared the 1991 Nobel Prize in Physiology or Medicine for it. Two picoamps through one channel is about 12 million ions a second.

The part of the amplifier's noise caused by capacitance at its input grows faster than the bandwidth: doubling the bandwidth multiplies it by 2 to the power 1.5, about 2.8. Nanopore traces are filtered for that reason, and filtering is the reason short events get smeared.

What a molecule looks like

A molecule in a pore shows up as a shortfall. It takes room the ions would have used, and the current drops while it is inside. In the model pore a DNA double helix would block about a fifth of the current, roughly 0.6 nA, and over ten microseconds that is about 37,000 charges that did not cross. Coulter's counters registered blood cells the same way, with the depth of the dip tracking the volume of what passed.

Eighteen streams, several of air

The stream's archive lists eighteen recorded streams. The first ones are recordings of air, named air-test-10, air-test-11, air-test-12, air-test-20, air-test-24, air-test-25 and air-test-99, among others. Recording air is a standard first check: with no liquid there is no ionic path, so what the amplifier reports is its own floor of leakage, pickup and noise.

Later entries move on to water. A recording begun on June 16 under the title "What-a-Day-for-a-Daystream" lists tap water, the 200-micron laser-drilled pore and a flow cell called "08-delrin-ptfe-demonpore2600-style"; it was never finished, and the archive does not list it. The archive's water recordings are titled "airbubbletest-tap-wter," "tapwater-test-2" and "tapwatertest," and one, from June 28, is "Crazy pet time." A synthetic "golden-test-stream" exists to test the archive's viewer. The recordings run from about one minute to 24 minutes.

What the browser receives

Between the bench and the browser sits a relay. The amplifier reports over USB to a small program on a laptop, which passes the readings to a server, and the server sends browsers packets of summaries rather than the raw samples: a half-second preview of up to 256 points, 32 bars with a minimum, maximum and mean apiece, and features computed on the fly, including the baseline, the RMS noise, the event rate and the mean current. The page's status line gives a display rate of 20 Hz and a tick of 60 Hz.

Each packet also carries four numbers for a video game built on the same data, Maxine's Quest: danger, mana, spawn rate and stability, each between 0 and 1. A quiet pore reads danger near 0 and mana near 1. An active one reads danger about 0.75 and mana about 0.15.

A hundred hours

The front page carries a promise for the summer: "This is going to be 100 hours of molecular streaming in 100 days to start feeding our nanopore world model." When nothing is running, the stream page says "Next stream coming soon, check back for live molecular data."