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Electrophoresis

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From Molecupedia, the encyclopedia of very small things
Motion of charged particles through a fluid under an electric field

Electrophoresis is the movement of charged particles or molecules through a fluid under an electric field. In a given medium the velocity is proportional to the field, v = μE, and the constant μ is the electrophoretic mobility. Electrophoresis sorts proteins and DNA in gels and capillaries, which made it the reading step of DNA sequencing for decades, and in a nanopore it is the force that draws a molecule to the pore and pulls it through.

Textbooks credit Ferdinand Friedrich Reuss, who worked in Moscow in 1807. The earliest known observation is Gautherot's, in 1801.[1]

Mobility

A charged particle in a field feels the force qE, and the drag of the liquid balances it at a terminal speed. The double layer complicates the balance, because the cloud of counterions around a particle moves the other way and drags liquid with it. Henry's solution of 1931 gives the mobility of a sphere of radius a as

μ=2εrε0ζ3ηf(κa),

where ζ is the zeta potential, η the viscosity, κ the inverse of the Debye length and f a function that rises from 1 for a particle much smaller than the double layer to 3/2 for a particle much larger.[2] The large-particle limit is the Smoluchowski equation, μ = εrε0ζ/η, the same expression that gives the speed of electroosmotic flow at a wall.

In water at 25 °C a potassium ion has a mobility of about 7.6 × 10−8 m2/(V s) and a chloride ion 7.9 × 10−8.[3] Double-stranded DNA moves at 3.75 × 10−8 m2/(V s) in a common buffer, Tris-acetate-EDTA, and at 4.5 × 10−8 in Tris-borate-EDTA, and in free solution that value does not depend on length from about 400 base pairs up to the 48,500 of lambda phage DNA.[4] Charge and friction both grow in proportion to length, so their ratio stays put, and a mixture of fragments cannot be sorted by length in an open solution.[5]

The charge itself is smaller than the chemistry suggests. Each base pair has two phosphates, a bare charge of 2 e per 0.34 nm, but counterions condense on the helix until the spacing of the remaining charges reaches the Bjerrum length of 0.71 nm. The uncondensed fraction is 0.17 nm divided by 0.71 nm, a quarter, so the effective charge is about 0.48 e per base pair.[6] The force measured on a DNA molecule held in a solid-state pore with optical tweezers corresponds to 0.50 e per base pair.[7]

Gels and capillaries

Arne Tiselius described in 1937 an apparatus in which a boundary between a protein solution and a buffer moves under a field, and he applied it to the proteins of blood serum.[8] He received the Nobel Prize in Chemistry in 1948 "for his research on electrophoresis and adsorption analysis, especially for his discoveries concerning the complex nature of the serum proteins".[9]

Supporting the liquid in a gel turned the method into a bench tool. Oliver Smithies separated serum proteins in starch gel in 1955, and Raymond and Weintraub proposed polyacrylamide four years later.[10][11] A gel is a mesh, and long molecules thread through it more slowly than short ones, so DNA fragments emerge in order of length. Proteins differ in charge and shape, but a wide variety of them bind the same mass of sodium dodecyl sulfate per gram, and a gel run with that detergent then sorts them by size.[12] Ulrich Laemmli's paper of 1970, titled for the cleavage of structural proteins during the assembly of the head of bacteriophage T4, describes the gel system that laboratories still call by his name, and Nature's 2014 survey of the most-cited papers ranked it second.[13][14]

Frederick Sanger's method of 1977 for sequencing DNA terminates new copies of a strand at each position of a chosen base, and the copies are sorted by length on a gel.[15] Pulsed fields, which alternate between directions, separated whole yeast chromosomes in 1984.[16] Jorgenson and Lukacs ran the separation in open glass capillaries in 1981.[17]

In nanopores

Cross-section of two chambers of salt solution, cis above and trans below, separated by a membrane with one pore, with an Ag/AgCl electrode in each chamber and a DNA strand entering the pore from cis
With the electrode on the cis side negative, DNA, which is negatively charged, moves through the pore from cis to trans. Not to scale.

A gel is many pores at once, and a nanopore is one pore with a single molecule at a time. In a nanopore cell the whole voltage is dropped across a hole a few nanometers wide, so the field is strong inside the pore and falls with the square of the distance outside it. A molecule whose drift in that field beats its diffusion is captured, and the distance at which the two balance is the capture radius, which for DNA reaches micrometers from the pore; see Capture rate (nanopore) and Translocation (nanopore). The polarity decides the direction: with the negative electrode on the cis side, DNA moves from cis to trans.

Molecules other than DNA are harder to drive. Proteins, in the words of a study of 2024, "unlike DNA, do not have a uniform charge", and the electrophoretic force cannot in general be used to translocate or linearize them.[18] The electroosmotic flow of the pore can then decide the direction, as it did for avidin in silicon nitride pores.

Molecular Reality Corporation puts the physics into one sentence of its guide: "The electric field across the membrane drags charged molecules toward the pore, the way a drain pulls leaves toward the grate. DNA, which carries a negative charge, feels a steady tug toward the positive side."[19]

See also

References

  1. ^ Biscombe, C. J. C. (2017). "The discovery of electrokinetic phenomena: setting the record straight". Angewandte Chemie International Edition 56 (30): 8338-8340. doi:10.1002/anie.201608536. PMID 27902877.
  2. ^ Henry, D. C. (1931). "The cataphoresis of suspended particles. Part I. The equation of cataphoresis". Proceedings of the Royal Society of London A 133 (821): 106-129. doi:10.1098/rspa.1931.0133.
  3. ^ Bard, A. J.; Faulkner, L. R. (2001). Electrochemical Methods: Fundamentals and Applications. 2nd ed. Wiley. ISBN 0-471-04372-9.
  4. ^ Stellwagen, N. C.; Gelfi, C.; Righetti, P. G. (1997). "The free solution mobility of DNA". Biopolymers 42 (6): 687-703. PMID 9358733.
  5. ^ Viovy, J.-L. (2000). "Electrophoresis of DNA and other polyelectrolytes: physical mechanisms". Reviews of Modern Physics 72 (3): 813-872. doi:10.1103/RevModPhys.72.813.
  6. ^ Manning, G. S. (1969). "Limiting laws and counterion condensation in polyelectrolyte solutions I. Colligative properties". The Journal of Chemical Physics 51 (3): 924-933. doi:10.1063/1.1672157.
  7. ^ Keyser, U. F.; et al. (2006). "Direct force measurements on DNA in a solid-state nanopore". Nature Physics 2 (7): 473-477. doi:10.1038/nphys344.
  8. ^ Tiselius, A. (1937). "A new apparatus for electrophoretic analysis of colloidal mixtures". Transactions of the Faraday Society 33: 524-531. doi:10.1039/TF9373300524.
  9. ^ "Arne Tiselius: Facts". NobelPrize.org. Nobel Prize Outreach. Retrieved October 25, 2026.
  10. ^ Smithies, O. (1955). "Zone electrophoresis in starch gels: group variations in the serum proteins of normal human adults". Biochemical Journal 61 (4): 629-641. doi:10.1042/bj0610629.
  11. ^ Raymond, S.; Weintraub, L. (1959). "Acrylamide gel as a supporting medium for zone electrophoresis". Science 130 (3377): 711. doi:10.1126/science.130.3377.711.
  12. ^ Reynolds, J. A.; Tanford, C. (1970). "Binding of dodecyl sulfate to proteins at high binding ratios. Possible implications for the state of proteins in biological membranes". Proceedings of the National Academy of Sciences 66 (3): 1002-1007. doi:10.1073/pnas.66.3.1002.
  13. ^ Laemmli, U. K. (1970). "Cleavage of structural proteins during the assembly of the head of bacteriophage T4". Nature 227 (5259): 680-685. doi:10.1038/227680a0.
  14. ^ Van Noorden, R.; Maher, B.; Nuzzo, R. (2014). "The top 100 papers". Nature 514 (7524): 550-553. doi:10.1038/514550a.
  15. ^ Sanger, F.; Nicklen, S.; Coulson, A. R. (1977). "DNA sequencing with chain-terminating inhibitors". Proceedings of the National Academy of Sciences 74 (12): 5463-5467. doi:10.1073/pnas.74.12.5463.
  16. ^ Schwartz, D. C.; Cantor, C. R. (1984). "Separation of yeast chromosome-sized DNAs by pulsed field gradient gel electrophoresis". Cell 37 (1): 67-75. doi:10.1016/0092-8674(84)90301-5.
  17. ^ Jorgenson, J. W.; Lukacs, K. D. (1981). "Zone electrophoresis in open-tubular glass capillaries". Analytical Chemistry 53 (8): 1298-1302. doi:10.1021/ac00231a037.
  18. ^ Sauciuc, A.; et al. (2024). "Translocation of linearized full-length proteins through an engineered nanopore under opposing electrophoretic force". Nature Biotechnology 42 (8): 1275-1281. doi:10.1038/s41587-023-01954-x.
  19. ^ "Keltar's Field Guide to Molecular Reality". Molecular Reality Corporation. August 2026.
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