The Coulter Counter

In Intermediate Physics for Medicine and Biology, Russ Hobbie and I often include applications of important topics in the homework problems. One such problem, new in Chapter 6 of the 5th edition, is an analysis of a Coulter counter.

Problem 23. The Coulter counter or resistive pulse technique is used to count and size particles in a wide variety of applications (Kubitschek 1969; DeBlois and Bean 1970), including the automated counting of blood cells. The cells being counted are assumed to be nonconducting and immersed in a conducting fluid. The fluid is made to flow through a narrow channel. When a suspended particle enters the channel there is a change in resistance. Assume a long channel of radius b with no end effects.

(a) What is the resistance of pure fluid of resistivity ρ = 1/σ in a segment of channel of length 2a?

(b) A cylindrical non-conducting cell of radius a and length 2a is in the channel. Its axis and the axis of the channel coincide. What is the resistance of a segment of channel of length 2a? Ignore end effects.

(c) Show that the resistance change (the difference between these two results) is proportional to the volume of the cell, V=2πa³, and inversely proportional to b⁴.

In the August issue of Physics Today is an article about extending the Coulter counter to sequencing DNA. Murugappan Muthukumar, Calin Plesa, and Cees Dekker write

In the 1940s Wallace Coulter set about finding a way to quickly count blood cells, which at the time was a slow and inefficient process. His approach was to pass cells, one by one, through a small hole connecting to compartments filled with electrolyte solution. Simultaneously, he applied a voltage across the compartment and measured the ionic current passed through the hole. As a cell passed through the hole, it would partially block the flow of electric charges, and the current would drop by an amount proportional to the volume of the cell….Coulter’s technique worked out wonderfully and revolutionized cell counting.

Then, the authors describe how this method can be used to sequence DNA.

The last two decades have seen a renaissance of the Coulter counter concept. The principle remains essentially the same, but nanopores—holes with a diameter of merely a few nanometers—have shrunk the length scale from that of single cells to that of single molecules. When DNA molecules are added to one side of the pore and an electric field is applied, the resulting electrophoretic force on the negatively charged DNA can pull the molecule through the pore in a head-to-tail fashion, leading to an observable blockade in the ionic current…

In the 1990s several research groups … began probing whether the different bases on a DNA strand might block measurably different amounts of ionic current as they pass through a nanopore. If so, the pattern of current generated by a DNA strand threaded through a nanopore might provide a linear readout of the strand’s base sequence… Although significant challenges remain to turn that vision into a practical reality, the goal appears to be within reach.

The authors then describe more details about the technique. Some use transmembrane proteins like the membrane channels described in Chapter 9 of IPMB. Others use tiny holes drilled into sheets of silicon nitride. Still others use a hybrid of these two.

Clearly the method will not work unless the DNA is a single strand. Wanunu (2012) discusses the molecular dynamics involved in unzipping a double strand to obtain two single strands, one of which can then be threaded through the pore to do the sequencing. The nanopores must be very narrow if you are to have any chance of distinguishing different bases attached to the DNA backbone.

Russ and I had no idea about these modern uses of the Coulter counter when we added the homework problem. This new application of the Coulter idea shows how a strong understanding of the fundamentals of physics as applied to medicine and biology can allow one to quickly move to the forefront of cutting-edge new technologies.