Jump to content
[dismiss]
Molecupedia is a parody encyclopedia written by Molecular Reality Corporation. It is not Wikipedia and is not affiliated with the Wikimedia Foundation. About

Nanopore noise

Page protected
From Molecupedia, the encyclopedia of very small things
Random fluctuations of the ionic current through a nanopore, which limit the signals and events it can resolve

Nanopore noise is the random fluctuation of the ionic current through a nanopore. Together with the bandwidth of the measurement it sets the smallest signal and the shortest event that can be resolved. Several sources contribute, and they dominate at different frequencies. Flicker noise rules the lowest, white thermal noise and shot noise the middle, and at high frequencies the dielectric loss of the chip and the voltage noise of the amplifier acting on the capacitance at its input take over. The last two grow faster than the square root of the bandwidth, so a faster measurement is disproportionately noisier: if the input capacitance dominates, doubling the bandwidth multiplies the noise current by 2.8.[1]

DNA crosses a bare pore in an ultrathin solid-state membrane at 3 to 50 bases a microsecond, so an instrument that read it directly would need megahertz bandwidths and the noise that comes with them.[2] Nanopore sequencing on protein pores slows the DNA with a motor enzyme to a speed at which a bandwidth of a few kilohertz suffices. Noise has also been used as data. In 1972 Katz and Miledi inferred the size of the elementary current at a nerve-muscle synapse from the noise of its response to acetylcholine, four years before single-channel currents were recorded directly (see Patch clamp).[3]

Sources

Thermal noise

Any conductance G at temperature T carries a current noise with a spectral density of 4kBTG, which is independent of frequency. Johnson measured it in 1928 and Nyquist explained it the same year, and it is called Johnson-Nyquist noise.[4][5] Two conductances matter in a nanopore recording: that of the pore, and that of the feedback element of the amplifier. A pore 10 nm wide through a membrane 20 nm thick in 1 M potassium chloride conducts about 30 nS, which passes 5.9 nA at 200 mV and adds 22 fA/√Hz, or 2.2 pA rms in a bandwidth of 10 kHz.[a] A feedback resistor of 1 GΩ adds 4.1 fA/√Hz, which is 0.41 pA in 10 kHz. A resistor of 1 MΩ adds 129 fA/√Hz, which is 12.9 pA in 10 kHz.

Shot noise

Charge arrives in lumps, and a current I made of independent carriers would show a white noise of 2qI, where q is the elementary charge. Schottky described the effect in 1918.[6] For the pore above the formula gives 44 fA/√Hz, twice the thermal value. At 3.1 nA, the current of a 5 nm pore in a membrane 10 nm thick, it gives 32 fA/√Hz, which corresponds to counting about 19,000 charges in a microsecond with a spread of about 140.[b] A 2020 review found the two terms comparable in practice, and both are small beside the others in most recordings.[1]

Flicker noise

At low frequencies the spectral density of the current rises as 1/f. Hooge's empirical relation puts it at SI=αHI2/(Ncf), where Nc is the number of charge carriers in the pore and αH a dimensionless constant.[7] In silicon nitride pores that behave, Smeets and colleagues found αH = 1.1 × 10−4, and that the noise power was inversely proportional to the number of ions in the pore at salt concentrations from 1 mM to 1 M.[8]

Pores do not always behave. Two pores of about 21 nm diameter in the same study differed in 1/f noise power by nearly three orders of magnitude. At a bandwidth of 10 kHz the standard deviation of their currents was 22.6 pA and 78.6 pA, and at 1 kHz it was 3.6 pA and 70.6 pA, so filtering helped the quiet pore and hardly touched the noisy one. Nanobubbles in the pore have been proposed as the cause, and cleaning the surface in piranha solution has lowered the 1/f noise of silicon nitride pores by up to three orders of magnitude.[8][1] Protein pores have a low-frequency noise of their own. The charged residues in the constriction of alpha-hemolysin gain and lose protons, which switches the current between two levels with a relaxation time of about 31 µs and shows as a plateau in the spectrum below about 1 kHz whose height depends on the pH.[1]

Dielectric noise

The membrane chip and its support are imperfect insulators. A capacitor C with a dissipation factor D has a loss conductance of 2πfCD, which by Nyquist's argument carries a thermal noise of 8πkBTDCf. The spectral density rises in proportion to frequency, so the rms noise rises in proportion to the bandwidth. This is dielectric noise, and it dominates from about 2 to 10 kHz. In a Teflon support for a lipid bilayer D is 0.8 to 2 × 10−4 and the capacitance of the thin bilayer sets the noise, which is why the hole in the support is made small.[1]

A silicon chip is lossier. Smeets and colleagues measured a chip capacitance of 368 pF and a loss constant of 0.27 for theirs, and those values give 22.7 pA rms at 10 kHz and 2.3 pA at 1 kHz.[c] A chip on glass with a capacitance below 1 pF, against more than 300 pF for standard silicon chips, removes most of this term.[9]

Input capacitance

The first stage of the amplifier has a voltage noise vn. It appears across the total capacitance at the input, Ctot, which is the sum of the chip, the wiring and the amplifier itself, and drives a current of 2πfCtotvn. The spectral density grows as the square of the frequency and the rms noise as the bandwidth to the power 3/2: Irms=2πCtotvnB3/2/3. The Axopatch 200B has a vn of 3 nV/√Hz. The LMP7721 chip, used in the MR1 Nanopore Reader design, has 6.5 nV/√Hz at 1 kHz.[1][10] Over 10 pF the LMP7721 gives 0.24 pA rms in 10 kHz, and over 50 pF 1.2 pA.[d] At 1 MHz the term is 1,000 times larger than at 10 kHz, 240 pA for the LMP7721 over 10 pF. Balan and colleagues, using chips of 1 to 5 pF and an amplifier whose input capacitance dominated the noise, recorded 117 to 150 pA rms at 1 MHz.[11]

Interference and other sources

Mains hum and its harmonics, radio pickup and vibration add to the list, and the countermeasure is shielding. The bilayer apparatus of the first DNA-in-a-pore experiment sat inside a μ-metal box, and nanopore flow cells and headstages are routinely enclosed in a metal Faraday cage.[12][1] The data sheet of the Axopatch 200B allows 0.005 pA peak to peak at the line frequency and its harmonics, in a headstage with its input open.[13]

Noise against bandwidth

Two log-log plots, the noise power spectrum of a nanopore setup with flicker, thermal, dielectric and capacitive terms, and the rms noise against bandwidth
Left, the calculated current noise spectrum of a silicon-chip setup with the chip capacitance and loss that Smeets and colleagues measured: flicker noise dominates below about 440 Hz, dielectric noise up to about 215 kHz and input-capacitance noise above. Right, the rms noise against bandwidth, with slopes of 1/2, 1 and 3/2. Both panels are calculations.

Each term scales with the bandwidth B in its own way, and the powers add. Flicker noise leaves the rms almost unchanged as B grows, because its power is spread evenly per octave. The white terms rise as B1/2, dielectric noise as B and input-capacitance noise as B3/2. The table gives the terms for a silicon-chip setup built from the figures above.

Calculated rms noise by source and bandwidth, pA
Source Scaling 1 kHz 10 kHz 100 kHz
Pore, 10 nm by 20 nm, thermal B1/2 0.7 2.2 7.0
Feedback resistor, 1 GΩ B1/2 0.13 0.41 1.3
Feedback resistor, 1 MΩ B1/2 4.1 12.9 41
Chip, 368 pF with D = 0.27 B 2.3 22.7 227
Input capacitance, 368 pF, 3 nV/√Hz B3/2 0.13 4.0 127

For comparison, the data sheet of the Axopatch 200B allows at most 0.015 pA rms at 1 kHz and 0.130 pA at 10 kHz in patch mode with the input open. That rises with the bandwidth almost as B, the pattern of capacitive and dielectric noise.[13] At 100 kHz the dielectric noise of the silicon chip, 227 pA, is some 170 times the 1.3 pA of a gigaohm feedback resistor.

Putting the amplifier next to the pore has moved the usable bandwidth from the tens of kilohertz of a patch-clamp amplifier to megahertz. In 2012 Rosenstein and colleagues placed a CMOS preamplifier beside a silicon nitride pore and reached a signal-to-noise ratio above 5 at 1 MHz, resolving DNA signals as brief as 1 µs.[14] In 2016 an amplifier built for the purpose recorded at 10 MHz, with a signal-to-noise ratio above 10 for single-stranded DNA at 5 MHz and transient features as short as 200 ns.[15]

The feedback resistor

A resistive-feedback amplifier has a bandwidth limit of its own. The feedback resistor R and the stray capacitance C across it form a pole at 1/(2πRC), and the larger the resistor the lower the pole. A resistor of 1 GΩ with 0.1 pF across it has its corner at 1.6 kHz. Making the resistor smaller raises the pole and the noise together, which is the trade a designer of a resistive front end makes. The capacitive-feedback design of the Axopatch 200B avoids the choice in patch mode, at the cost of a reset every time the integrated voltage reaches the supply limit.[13] The resistor and capacitor in the schematic of the MR1 Nanopore Reader, 1 MΩ and 2 pF, put the pole of the first stage at 80 kHz. The same 2 pF across 1 GΩ would put it at 80 Hz.

Reducing noise

Most of the measures reduce a capacitance. Coating the chip around the pore with a dielectric such as PDMS thickens the insulation and lowers the chip capacitance, and glass substrates take it below 1 pF. A bilayer support with a hole of 25 µm gave a chip capacitance of 10 to 28 pF, and integrating the amplifier with the pore reduced the total input capacitance to about 4 pF.[1] Low-frequency noise yields to the surface. Hydrophilic coatings such as alumina, cleaning, and a pH far from the isoelectric point of silicon nitride, about 5, all reduce it, and in two-dimensional membranes the noise falls with the area of the suspended film.[1]

Signal against noise

What counts is the signal-to-noise ratio, the current change from a molecule divided by the rms noise at the bandwidth that resolves it.[1] The signal scales with the current through the pore. One alpha-hemolysin channel in 1 M potassium chloride passed 120 pA at 120 mV, against the 5.9 nA of the 10 nm pore above, so a protein pore has to be quieter in proportion.[12] A silicon nitride pore about 1.3 nm wide, driven at 1 V and read at 500 kHz, gave a ratio of 37 for a short strand of DNA, because the high voltage made the signal large while the dielectric and capacitive terms did not grow with it. The protein pore MspA, driven at 180 mV and read at 30 kHz, gave 4. Control of speed alters the comparison more than any quieting of the electronics. The review estimated that if a helicase slowed the strand through MspA to steps that a 200 Hz filter could resolve, the ratio of the same pore would be about 650, more than 160 times higher, because the high-frequency terms are filtered out.[1]

Noise also decides how events are found. A blockade is detected when the current crosses a threshold set at a multiple of the rms noise, and for Gaussian noise a threshold of 3.8 standard deviations is exceeded by chance by 7 samples in 100,000. A trace sampled at 200,000 samples a second would show 14 false crossings every second if each sample were tested alone, so detectors filter first or ask for a run of samples (event detection), and either choice costs time resolution. A sequencer works in this regime. Oxford Nanopore publishes a level table for a pore of its earlier R9.4 generation, giving for each of the 4,096 possible six-base words the mean current, its spread and the noise within a level.[16] The mean levels run from 59 to 120 pA. The noise within a level has a median of 1.6 pA, and the observed level of a given word has a median standard deviation of 2.1 pA. Changing one base of a word moves the expected level by a median of 2.9 pA, and for one change in five by less than 1 pA.[e] For those changes the expected shift is smaller than the noise within a level, and a neural network settles the question by weighing many samples of each base (see basecalling). Current models are trained on data sampled at 5 kHz, and the DNA moves at 400 bases per second, which gives 12.5 samples a base.[17]

At Molecular Reality

The company's guide answers the question of why its trace looks noisy: "Molecules in water dance constantly, and their motion shakes the current. The electronics add their own faint hiss. The membrane itself wobbles." It puts the trade-off in a sentence, "A clean trace is a tradeoff, never a free lunch", and says of the quiet stretches of its stream: "we will not fake noise to entertain you."[18] Signals too faint to separate from the noise are what the company calls the whisper in a thunderstorm problem.[19]

The open design of the MR1 Nanopore Reader gives the arithmetic a concrete case. Its data-acquisition specification lists a noise floor of less than 1.2 pA rms at 10 kHz bandwidth, in a section whose conversion arithmetic assumes a feedback resistor of 1 GΩ, which alone adds 0.41 pA in that bandwidth. The amplifier schematic in the same repository draws a resistor of 1 MΩ, with a capacitor of 2 pF in parallel, between the inverting input and the output of the LMP7721, and that resistor adds 12.9 pA.[20] The repository states its status in one line, "Designed. Simulated. Built and measured: not yet."[21] The stream's amplifier, the EDR4, samples at 200 kHz, one reading every five microseconds, and the guide notes that at the larger pores tested today the currents "run in nanoamps, billionths".[18]

See also

Notes

  1. ^ Conductance G = σ[4L/(πd2) + 1/d]−1 with σ = 10.5 S/m, d = 10 nm and L = 20 nm; T = 300 K. Noise from the pore is taken to be the thermal noise of its conductance. Figures in this article marked as calculated use the same constants and treat the filter as ideal.
  2. ^ The ratio of the two spectral densities is qV/(2kBT), about 3.9 at 200 mV. Ions in a salt solution do not move independently, so the shot-noise formula estimates the size of the effect.
  3. ^ Calculated from the formula with T = 300 K, integrated from zero to the bandwidth. Adding the thermal noise of a 67 MΩ pore (1.6 pA at 10 kHz) and the input-capacitance term described below (4.0 pA) gives 23 pA. Smeets and colleagues recorded a standard deviation of 22.6 pA at 10 kHz from a quiet pore. That pore had its own chip, so the agreement shows the scale of the effect.
  4. ^ Calculated from the formula above.
  5. ^ Calculated from the table: the medians of the columns for the spread of levels and the noise, and the absolute differences between the levels of all words that differ at one position.

References

  1. ^ a b c d e f g h i j k Fragasso, A.; Schmid, S.; Dekker, C. (2020). "Comparing current noise in biological and solid-state nanopores". ACS Nano 14 (2): 1338-1349. doi:10.1021/acsnano.9b09353. PMID 32049492.
  2. ^ Feng, J.; et al. (2015). "Identification of single nucleotides in MoS2 nanopores". Nature Nanotechnology 10 (12): 1070-1076. doi:10.1038/nnano.2015.219. PMID 26389660.
  3. ^ Katz, B.; Miledi, R. (1972). "The statistical nature of the acetylcholine potential and its molecular components". The Journal of Physiology 224 (3): 665-699. doi:10.1113/jphysiol.1972.sp009918. PMID 5071933.
  4. ^ Johnson, J. B. (1928). "Thermal agitation of electricity in conductors". Physical Review 32 (1): 97-109. doi:10.1103/PhysRev.32.97.
  5. ^ Nyquist, H. (1928). "Thermal agitation of electric charge in conductors". Physical Review 32 (1): 110-113. doi:10.1103/PhysRev.32.110.
  6. ^ Schottky, W. (1918). "Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern". Annalen der Physik 362 (23): 541-567. doi:10.1002/andp.19183622304.
  7. ^ Hooge, F. N. (1969). "1/f noise is no surface effect". Physics Letters A 29 (3): 139-140. doi:10.1016/0375-9601(69)90076-0.
  8. ^ a b Smeets, R. M. M.; Keyser, U. F.; Dekker, N. H.; Dekker, C. (2008). "Noise in solid-state nanopores". Proceedings of the National Academy of Sciences 105 (2): 417-421. doi:10.1073/pnas.0705349105. PMID 18184817.
  9. ^ Balan, A.; Chien, C.-C.; Engelke, R.; Drndić, M. (2015). "Suspended solid-state membranes on glass chips with sub 1-pF capacitance for biomolecule sensing applications". Scientific Reports 5: 17775. doi:10.1038/srep17775. PMID 26644307.
  10. ^ "LMP7721 3-femtoampere input bias current precision amplifier". Texas Instruments. 2014. Retrieved October 25, 2026.
  11. ^ Balan, A.; Machielse, B.; Niedzwiecki, D.; Lin, J.; Ong, P.; Engelke, R.; Shepard, K. L.; Drndić, M. (2014). "Improving signal-to-noise performance for DNA translocation in solid-state nanopores at MHz bandwidths". Nano Letters 14 (12): 7215-7220. doi:10.1021/nl504345y. PMID 25418589.
  12. ^ a b 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. PMID 8943010.
  13. ^ a b c "Axon Axopatch 200B Microelectrode Amplifier (data sheet)". Molecular Devices. Retrieved October 25, 2026.
  14. ^ Rosenstein, J. K.; Wanunu, M.; Merchant, C. A.; Drndić, M.; Shepard, K. L. (2012). "Integrated nanopore sensing platform with sub-microsecond temporal resolution". Nature Methods 9 (5): 487-492. doi:10.1038/nmeth.1932. PMID 22426489.
  15. ^ Shekar, S.; Niedzwiecki, D. J.; Chien, C.-C.; Ong, P.; Fleischer, D. A.; Lin, J.; Rosenstein, J. K.; Drndić, M.; Shepard, K. L. (2016). "Measurement of DNA translocation dynamics in a solid-state nanopore at 100 ns temporal resolution". Nano Letters 16 (7): 4483-4489. doi:10.1021/acs.nanolett.6b01661. PMID 27332998.
  16. ^ "kmer_models: legacy_r9.4_180mv_450bps_6mer". GitHub. Oxford Nanopore Technologies. Retrieved October 25, 2026.
  17. ^ "Dorado: decoding Dorado model names". GitHub. Oxford Nanopore Technologies. Retrieved October 25, 2026.
  18. ^ a b "Keltar's Field Guide to Molecular Reality". Molecular Reality Corporation. August 2026.
  19. ^ "Company records". Molecular Reality Corporation. October 2026.
  20. ^ "MR1 Nanopore Reader". GitHub. October 16, 2026.
  21. ^ Dev Okonkwo-Hale (October 17, 2026). "Molecular Reality Open-Sources a Nanopore Reader It Has Not Built Yet". The Picoampere.

Further reading

  • Uram, J. D.; Ke, K.; Mayer, M. (2008). "Noise and bandwidth of current recordings from submicrometer pores and nanopores". ACS Nano 2 (5): 857-872. doi:10.1021/nn700322m.
  • Tabard-Cossa, V.; Trivedi, D.; Wiggin, M.; Jetha, N. N.; Marziali, A. (2007). "Noise analysis and reduction in solid-state nanopores". Nanotechnology 18 (30): 305505. doi:10.1088/0957-4484/18/30/305505.
Retrieved from "https://molecularreality.com/wiki/Nanopore_noise"
Last edited 3 hours ago by Debye Length Enjoyer