Signal-to-noise ratio
The signal-to-noise ratio (SNR) compares the size of a signal with the size of the noise on top of it. Engineers quote it as a ratio of powers, in decibels. Nanopore papers usually quote the ratio of two currents: the depth of an event, ΔI, over the root-mean-square noise of the baseline, σ, in a stated bandwidth. A paper that reports "an SNR of 10" and gives neither the definition nor the bandwidth has told the reader little, because the two definitions differ by a square and the bandwidth can change the noise by a factor of ten.
Definitions
Power goes as the square of amplitude, so the ratio of powers is the square of the ratio of amplitudes. In decibels, SNRdB = 10 log10(Psignal/Pnoise) = 20 log10(Asignal/Anoise). An amplitude ratio of 10 is 20 dB, a ratio of 2 is about 6 dB, and a power ratio of 10, which is 10 dB, is an amplitude ratio of only 3.2.
For an event, the signal is its depth as a fraction of the open-pore current, and the noise is the standard deviation of the current in the filter band with nothing in the pore. Take a pore 5 nm wide through 10 nm of membrane that passes 3.1 nA (see Pore conductance). Double-stranded DNA blocks about 17 percent of that (see Current blockade), which is 0.53 nA. The thermal noise of a 1 MΩ feedback resistor alone is 12.8 pA in a 10 kHz band, so the SNR cannot exceed 41. The amplifier, the capacitance of the pore and its chip, and the flicker noise of the pore all subtract from that figure, and reported values are lower.
What limits it
Four kinds of noise matter. The feedback resistor makes thermal noise, which is white, with a current density of √(4kBT/R): 128 fA/√Hz for 1 MΩ and 4.1 fA/√Hz for 1 GΩ. The current itself makes shot noise, also white, √(2qI), which is 23 fA/√Hz at 1.7 nA. The pore adds flicker, or 1/f, noise, which rises with the square of the current. Last, the voltage noise of the amplifier acting on the capacitance at its input makes capacitive noise, which rises with the 3/2 power of the bandwidth. The white terms grow only as the square root of the bandwidth, so in a fast measurement doubling the bandwidth can raise the noise by nearly three times (23/2 = 2.83). See Nanopore noise and Transimpedance amplifier.
The voltage a user applies helps against some of this and not the rest. Against the white terms the signal rises with the voltage and the noise does not, so the SNR rises in proportion. Against flicker noise it buys nothing, because signal and noise rise together and their ratio stays where it was.
Bandwidth cuts both ways. A narrower filter removes noise, and it also smooths each event, with a rise time of about 0.35 divided by the cutoff frequency, which is 35 µs for a 10 kHz filter. Events shorter than that lose depth, so the SNR of a short event can fall as the filter narrows. The company's whisper in a thunderstorm problem is the case in which the difference between two DNA bases is smaller than the noise of a measurement fast enough to see it.
Thresholds
Software finds an event when the current falls a set number of standard deviations below the baseline (see Event detection (nanopore)), and the number sets the rate of false alarms. The table gives the expected rates for Gaussian noise limited to 10 kHz, which supplies about 20,000 independent samples each second.
| Threshold | Chance per sample | Triggers per second | One every |
|---|---|---|---|
| 3σ | 1.3 × 10−3 | 27 | 37 ms |
| 4σ | 3.2 × 10−5 | 0.63 | 1.6 s |
| 5σ | 2.9 × 10−7 | 0.0057 | 3 minutes |
| 6σ | 9.9 × 10−10 | 0.00002 | 14 hours |
Albert Rose reached a similar number for vision. In 1948, studying how well the eye could see a faint picture, he put the threshold SNR at which a viewer can be sure of a feature at five, with a storage time for the eye of 0.2 s.[1] The figure is still called the Rose criterion in imaging.
Averaging
Averaging N independent measurements of the same quantity improves the SNR by √N. This is the reason for ping-pong sensing, which measures one particle again and again, and for the decimation that brings the MR1 Nanopore Reader's 100 kS/s down to 1 kS/s for its web display, averaging blocks of 100 samples and cutting the white noise by a factor of 10.[2] The company's essay on a world model for nanopore signals says that oversampling shrinks variance as 1/√N. It is the standard deviation that shrinks as 1/√N; the variance shrinks as 1/N.[2]
A 2015 paper reported an SNR above 10 for nucleotides passing a MoS2 pore slowed by an ionic liquid (see Molybdenum disulfide nanopore).[3]
Shannon's capacity formula sets the ceiling that no averaging gets past: a channel of bandwidth B carries at most B log2(1 + SNR) bits a second, with SNR as a ratio of powers.[4] A pore is such a channel, though what its user wants is the identity of a molecule and not a number of bits.
See also
References
- ^ Rose, A. (1948). "The sensitivity performance of the human eye on an absolute scale". Journal of the Optical Society of America 38 (2): 196-208.
- ^ a b "Company records". Molecular Reality Corporation. October 2026.
- ^ Feng, J.; et al. (2015). "Identification of single nucleotides in MoS2 nanopores". Nature Nanotechnology 10 (12): 1070-1076. doi:10.1038/nnano.2015.219.
- ^ Shannon, C. E. (1949). "Communication in the presence of noise". Proceedings of the IRE 37 (1): 10-21. doi:10.1109/JRPROC.1949.232969.