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Coulter principle

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Principle of counting and sizing particles by the resistance change they cause in a small aperture
This article is about the measurement principle. For the instruments built on it, see Coulter counter.

The Coulter principle states that a particle suspended in an electrolyte raises the electrical resistance of a small aperture while it passes through, by an amount set mainly by the particle's volume. A current driven through the aperture dips for as long as the particle is inside. Each dip is one particle, its depth measures the volume, and its width measures the time the particle takes to cross.

Cross-section of an aperture between two electrolyte chambers with a particle in it, above a current trace with three dips of different depths
Schematic of the principle. Current flows between two electrodes through one aperture. A particle in the aperture raises the resistance, and the current falls; larger particles give deeper dips.

Wallace H. Coulter demonstrated the effect on October 16, 1948, with a hole burned through a cellophane wrapper, and received a patent for it in 1953. Instruments built on it are called Coulter counters, and the principle still counts and sizes cells in some hematology analyzers and particles in many laboratory instruments.

The link between resistance and volume goes back to James Clerk Maxwell, who worked out in 1873 how a liquid holding a dilute suspension of insulating spheres conducts. Coulter's historian, who was also his technical adviser, reports that Coulter had read of such a method as an engineering student. In the nanopore literature the same measurement is called resistive pulse sensing, the pulses are called current blockades, and the apertures are a few nanometers wide. Molecular Reality Corporation calls itself "a small branch on a seventy year old tree" and puts the difference between a hospital counter and its own instruments down to size.

Principle

Two chambers hold the same electrolyte and are separated by an insulating wall pierced by one aperture. An electrode in each chamber drives a current through the aperture. Because the aperture is the narrowest part of the path, nearly all of the circuit's resistance sits there, and any change in the aperture shows up in the whole circuit. A dilute suspension is drawn through by suction, by pressure or by the electric field itself. A particle that conducts worse than the electrolyte, such as a living cell in saline, a polystyrene bead or a strand of DNA, fills part of the aperture; the resistance rises and the current falls for the microseconds or milliseconds the particle takes to cross.[1][2] Particles that conduct better than the liquid have the opposite effect, which the patent describes alongside the first case.[1]

The 1953 patent states three conditions: the particles must stay suspended without appreciable settling; the fluid and the particles must differ in electrical conductivity, which can be adjusted by adding electrolyte or diluting with distilled water; and the suspension must be dilute enough that a pulse is rarely produced by more than one particle, an overlap the patent calls "masking".[1] It also asks for the aperture to be as short as possible, and for red blood cells it puts the bore at "the order of a thousandth of an inch or less", about 25 µm.[1][a]

Coulter's counters drive the aperture with a constant current and read the voltage pulse. Patch-clamp amplifiers on nanopores usually hold the voltage constant and read the current.[3][4] For small pulses the fractional change is the same either way.

Theory

Pulse height

For a particle much smaller than the aperture, the pulse height is proportional to the particle's volume. Commercial instruments report the result as the diameter of a sphere of equal volume. Beckman Coulter gives the working range of one aperture as 2% to 60% of its diameter, extended to 80% for broad distributions, and notes that noise rises sharply below 2%.[2]

The proportionality is an old result about mixtures. In his Treatise on Electricity and Magnetism, Maxwell derived the conductivity of a medium containing a dilute suspension of spheres. For insulating spheres that fill a fraction φ of the volume, the conductivity of the mixture is that of the liquid multiplied by (1 − φ)/(1 + φ/2), which is 1 − 3φ/2 to first order.[5][6] The 3/2 is the electrical shape factor γ of a sphere. Applied to one particle of volume v in an aperture of cross-sectional area A filled with electrolyte of resistivity ρ, the same bookkeeping gives an excess resistance ΔR=γρv/A2. For a sphere of diameter d in a cylindrical aperture of diameter D this becomes

ΔR≈4ρd3πD4 S(dD),S(dD)=11−0.8 (d/D)3.

The correction S is 1.02 for a sphere 30% as wide as the aperture and 1.11 at half the width, where the field squeezed between particle and wall makes the pulse grow faster than the volume.[6] DeBlois and Bean, who extended the method to submicron pores in 1970, found that their theory agreed with measurements for spheres up to 0.4 of the pore diameter.[7] Dividing by the resistance of the aperture gives the fractional pulse

ΔRR≈d3D2 (L+0.8D) S(dD),

where L is the length of the aperture. In this limit the absolute change ΔR does not depend on L, and the fractional change does. A red blood cell of about 90 µm³ crossing an aperture 100 µm wide and 67 µm long, the dimensions of the first commercial counter, in saline of 1.5 S/m raises a resistance of about 12 kΩ by about 1.5 Ω, a change of 1.2 parts in 10,000.[b][8]

Shape and orientation

Spheres have γ = 3/2. Rods and flat disks have a shape factor that depends on how the particle lies relative to the current, so their pulses vary in height even when the volume is fixed. Golibersuch used the effect in 1973 to watch red blood cells tumble in the flow through an aperture, and a 2017 study applied the same idea to estimate the shape and volume of single proteins in a nanopore.[9][6]

Access resistance

Main article: Access resistance

The 0.8D in the effective length is the resistance of the regions outside each end of the aperture, where the current converges from the whole chamber onto a hole. J. E. Hall's two-page paper of 1975 gave a closed form for it: for a circular hole of diameter D in a thin wall, each side contributes ρ/(2D). The two sides together equal the resistance of a cylinder of the same diameter and a length of πD/4, about 0.8D.[10] The first commercial counter, with L = 0.67D, therefore had more than half of its resistance in these access regions. For a wall of zero thickness the whole resistance is access resistance, and the conductance of the hole becomes σD.[11]

Practical limits

The first limit is coincidence. When two particles are in the sensing zone together they give one larger pulse. Beckman Coulter calls this primary coincidence and corrects counts mathematically when up to one particle in ten is lost; the remedy named in the 1953 patent was dilution.[2][1] The second limit is trajectory. A particle that passes through the middle of the aperture meets a more uniform current density than one that grazes the wall, and particles near the wall give pulses with two peaks, because the current density is highest at the entrance and exit of the aperture; instruments recognize the "M" shape and can discard such pulses.[2]

Beckman Coulter warns that excess current heats the electrolyte, adds noise and can damage the aperture, and gives 800 µA as a typical maximum working current.[2] Conductive particles such as metals can be measured only below the voltage at which their surface barrier breaks down, and porous particles register as the volume of their solid material.[2] Standard apertures run from 10 µm to 2,000 µm across and together cover particles from 0.2 µm to 1,600 µm. Automated hematology analyzers measure cells by electrical impedance, by optical analysis, or by both.[2][12]

Lineage and scale

Maxwell's mixture theory supplied the physics of the pulse, and Coulter supplied the aperture, the counting circuit and the demonstration, which the article on the Coulter counter describes. DeBlois and Bean carried the method down to submicron pores. Biophysicists who recorded currents through single ion channels then recognized the same measurement in a smaller hole still. The table follows the aperture down from a hole burned in cellophane to the narrowest point of a protein channel, and back up to a laser-drilled pore in the company's laboratory.

Apertures and what they detected
Year Aperture or pore Detected Source
1948 A needle-burned hole in a cellophane wrapper; two weeks later a 76 µm hole in 22 µm cellulose acetate film Blood cells, in blood diluted several thousand times, giving pulses of about 1 ms [13]
1956 A 100 µm by 67 µm hole in a ruby or sapphire watch jewel Blood cells [8]
1970 Single submicron pores etched in irradiated plastic sheet Polystyrene spheres 90 nm across; detection limit near 60 nm [7]
1994 The channel of the peptide alamethicin in a lipid bilayer Polyethylene glycol molecules with gyration radii as small as 0.5 to 1.5 nm [14]
1996 The channel of alpha-hemolysin, narrowest at 1.4 nm Single strands of RNA and DNA [4][15]
2001 A single pore ion-beam sculpted in a silicon nitride membrane Single DNA molecules [16]
2015 A glass nanopipette, voltage reversed after each pulse One polystyrene nanoparticle measured thousands of times [17]
2026 A laser-drilled pore listed by the company as 200 µm Phoenix tap water [18]

The 1994 paper opens with the Coulter counter, notes that a capillary 0.45 µm wide had lowered the detection limit to 60 nm particles, and goes on to show that natural channel-forming peptides in a lipid membrane can detect single molecules.[14] Its first author later published an article titled "Ion channels as molecular Coulter counters to probe metabolite transport".[19] In 1996 polynucleotides were driven through an alpha-hemolysin channel, and each passage appeared as a dip in the current lasting from several hundred to several thousand microseconds.[4]

A 100 µm aperture is about 70,000 times wider than the narrowest point of alpha-hemolysin, nearly five orders of magnitude. Across that difference in scale, the link between excluded volume and pulse holds only in part. When the Debye length, about 0.3 nm in 1 M salt, becomes comparable to the pore radius at lower concentrations, surface charge and counterions matter, and a pulse can go up instead of down.[20] In nanopore work the excluded-volume argument above still gives the first estimate of a current blockade, and the access term is written out explicitly in the pore conductance.

The company's guide gives its own reading of the lineage: "Coulter counted cells, the biophysicists threaded DNA, and we are trying to give the whole family mechanical control."[21] The same answer calls the work "a small branch on a seventy year old tree, and the tree is wonderful", and says that pore-based sensing "is older than you might think, and its family tree is noble."[21]

Resolution

In a conventional counter the resolution is limited by the variation in the path each particle takes through the aperture, which Brownian motion sets. A 2015 modification used a nanopipette and programmable hardware that reversed the voltage after each pulse. The same particle went back through the orifice thousands of times, at more than 100 measurements per second, and its mean pulse amplitude was then known well enough to correspond to sub-angstrom size resolution.[17] A 2026 post by the founder of Molecular Reality quotes the paper's own figure, a blocking current "statistically equivalent to resolving particle radii differing by merely 31 pm", and adds that the particles were 250 nm across and that capturing and resampling smaller analytes by reversing the voltage is much harder.[22] The company's posts call the technique ping-ponging; see Ping-pong sensing.

Adjustable apertures

An aperture that can change size during a measurement extends the range of one device. An elastomeric nanometer-scale aperture whose size is set by stretching the membrane was described in 2007 and underlies tunable resistive pulse sensing.[23] Molecular Reality's juxtapore uses two solid surfaces that slide alongside each other, their edges forming the aperture, a design described in US patent 10,908,144.[24][21] The company's guide describes its approach as walking the whole family of pore-based sensing "from the big end toward the small".[21]

Use at Molecular Reality

A post on the company's member site, written in the voice of the persona Thucydides and dated March 29, 2026, opens with the company's verdict on the Coulter brothers: "They should have won a Nobel prize." The post says that Coulter counters are "pore-based devices" and that "the only serious difference is size. The principle is the same." According to the post, the company's data collection starts with pores of micron scale and larger and works down toward the sub-nanometer scale.[25] The company's guide says the technique "still runs in every hospital lab on Earth".[21][dubious · discuss]

In the company's live molecular stream the pore is a laser-drilled hole listed in its lab records as 200 µm across, which sits inside the range of standard Coulter apertures. An EDR4 patch-clamp amplifier records the current at 200 kHz, one measurement every 5 µs.[21][18] The guide explains the choice of test samples this way: at larger pores, ketchup, salsa and tap water "can be watched at the scale of cells and particles, counting what passes, the way Coulter did seventy years ago", while at the nanometer scale they "would clog the doorway instantly". "The road to the small end runs through the big end," it adds, "and the big end loves ketchup."[21]

A dark oval opening with a single red dot and pale specks, seen through a microscope
A laser-drilled pore in dark-field microscopy, from the company's lab inventory, which lists the pore as 200 µm. The dark oval is the opening and the red dot is a laser spot.

In a post of the same date, the founder describes tying knots in a nylon filament and drawing it through a macropore about 2 mm wide, which produced "downward (resistive) spikes" for each knot.[26] DNA knots appear in the same way in solid-state nanopores, as short spikes on the current trace.[27] The demonstration is described in Knot sequencing.

Maxwell appears in the company's story twice. The company's earlier name, demonpore, inc., came from his thought experiment, and a flyer posted in March 2026 adds that "other work by Maxwell inspired the Coulter Counter".[28] The second claim has support in the historical record. Graham reports that as a student of electrical engineering Coulter had read of a method for calculating the resistance of particle suspensions, and cites Maxwell's Treatise for it.[13]

See also

Notes

  1. ^ The patent's account of the pulse is looser than the modern one. In its description of the pulse in Figure 11, variations in particle conductivity change the pulse amplitude, and variations in size change its duration or waveform. It also proposes finding the size of an unknown particle by comparing its current change with that of a particle of known size.[1]
  2. ^ Calculated from the formulas above with γ = 3/2 and S = 1. At the 800 µA that Beckman Coulter gives as a typical maximum working current, the voltage pulse is about 1.2 mV.[2]

References

  1. ^ a b c d e f W. H. Coulter (October 20, 1953). "US2656508A: Means for counting particles suspended in a fluid". Google Patents. Retrieved October 25, 2026.
  2. ^ a b c d e f g h "Coulter Principle Short Course, Chapter 2". Beckman Coulter. Retrieved October 25, 2026.
  3. ^ M. D. Graham (January 9, 2024). "The Coulter Principle: Early Implementations". The Blood Project. Retrieved October 25, 2026.
  4. ^ a b c 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.
  5. ^ Maxwell, J. C. (1873). A Treatise on Electricity and Magnetism, volume 1, chapter IX. Clarendon Press.
  6. ^ a b c Yusko, E. C.; et al. (2017). "Real-time shape approximation and fingerprinting of single proteins using a nanopore (Supplementary Note 2)". Nature Nanotechnology 12 (4): 360-367. doi:10.1038/nnano.2016.267. PMID 27992411.
  7. ^ a b DeBlois, R. W.; Bean, C. P. (1970). "Counting and sizing of submicron particles by the resistive pulse technique". Review of Scientific Instruments 41 (7): 909-916. doi:10.1063/1.1684724.
  8. ^ a b M. D. Graham (November 18, 2020). "The Coulter Principle: For the Good of Humankind, chapter 5, "Promotion"". University of Kentucky. Retrieved October 25, 2026.
  9. ^ Golibersuch, D. C. (1973). "Observation of aspherical particle rotation in Poiseuille flow via the resistance pulse technique. I. Application to human erythrocytes". Biophysical Journal 13 (3): 265-280. doi:10.1016/S0006-3495(73)85984-3.
  10. ^ 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.
  11. ^ 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.
  12. ^ Daves, M.; et al. (2024). "Modern hematology analyzers: beyond the simple blood cells count (with focus on the red blood cells)". Journal of Laboratory and Precision Medicine 9: 4. doi:10.21037/jlpm-23-32.
  13. ^ a b M. D. Graham (November 18, 2020). "The Coulter Principle: For the Good of Humankind, chapter 3, "Invention"". University of Kentucky. Retrieved October 25, 2026.
  14. ^ a b Bezrukov, S. M.; Vodyanoy, I.; Parsegian, V. A. (1994). "Counting polymers moving through a single ion channel". Nature 370 (6487): 279-281. doi:10.1038/370279a0. PMID 7518571.
  15. ^ Song, L.; et al. (1996). "Structure of staphylococcal alpha-hemolysin, a heptameric transmembrane pore". Science 274 (5294): 1859-1866. doi:10.1126/science.274.5294.1859. PMID 8943190.
  16. ^ Li, J.; Stein, D.; McMullan, C.; Branton, D.; Aziz, M. J.; Golovchenko, J. A. (2001). "Ion-beam sculpting at nanometre length scales". Nature 412 (6843): 166-169. doi:10.1038/35084037. PMID 11449268.
  17. ^ a b Edwards, M. A.; German, S. R.; Dick, J. E.; Bard, A. J.; White, H. S. (2015). "High-speed multipass Coulter counter with ultrahigh resolution". ACS Nano 9 (12): 12274-12282. doi:10.1021/acsnano.5b05554. PMID 26549738.
  18. ^ a b "Streams". Molecular Reality Corporation. 2026. Retrieved October 25, 2026.
  19. ^ Bezrukov, S. M. (2000). "Ion channels as molecular Coulter counters to probe metabolite transport". Journal of Membrane Biology 174 (1): 1-13. doi:10.1007/s002320001026. PMID 10741427.
  20. ^ Smeets, R. M. M.; et al. (2006). "Salt dependence of ion transport and DNA translocation through solid-state nanopores". Nano Letters 6 (1): 89-95. doi:10.1021/nl052107w.
  21. ^ a b c d e f g "Keltar's Field Guide to Molecular Reality". Molecular Reality Corporation. August 2026.
  22. ^ Kemmishtree (March 28, 2026). "Molecular Supreme". EQBio-OS.
  23. ^ Sowerby, S. J.; Broom, M. F.; Petersen, G. B. (2007). "Dynamically resizable nanometre-scale apertures for molecular sensing". Sensors and Actuators B: Chemical 123 (1): 325-330. doi:10.1016/j.snb.2006.08.031.
  24. ^ "US10908144B2: Stacks of coaligned nanopores and fabrication and uses thereof". Google Patents. February 2, 2021. Retrieved October 25, 2026.
  25. ^ Thucydides (March 29, 2026). "Bend it like Beckman Coulter". EQBio-OS.
  26. ^ Kemmishtree (March 29, 2026). "Sequencing a string". EQBio-OS.
  27. ^ Plesa, C.; et al. (2016). "Direct observation of DNA knots using a solid-state nanopore". Nature Nanotechnology 11 (12): 1093-1097. doi:10.1038/nnano.2016.153. PMID 27525473.
  28. ^ Kemmishtree (March 28, 2026). "Welcome to my Minds". EQBio-OS.

Further reading

  • Graham, M. D. (2003). "The Coulter principle: Foundation of an industry". JALA: Journal of the Association for Laboratory Automation 8 (6): 72-81. doi:10.1016/S1535-5535-03-00023-6.
  • Graham, M. D. (2013). "The Coulter principle: Imaginary origins". Cytometry Part A 83 (12): 1057-1061. doi:10.1002/cyto.a.22398. PMID 24151220.
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