And three is a crowd....

Figure 1: Phone booth stuffing

Figure 1 is an image from the 1950's fad of "Phone Booth Stuffing". The Guinness book of world records reports N=27. We had been doing something similar - stuffing DNA into nanopores. Actually DNA exists in nature in a very compacted state. We carry about 3 meters of DNA in each of our cells but all of this is contained in a cell nucleus about 6 microns in diameter. This is nicely illustrated in Figure 2 showing a "DNA spill" from a ruptured E. Coli cell.  Multiple DNA strands interacting in a confined environment is encountered in various other situations e.g. the packaging of DNA in phages and the movement of DNA through the pores of a gel during electrophoresis.  How DNA behaves in crowded environments is therefore a subject of some interest.

Figure 2: A DNA spill from E.Coli

It is actually not difficult to stuff many DNA molecules into a nanopore, the hard part is to keep count of how many got in! Figure 3 shows an experimental set up where this can be done in a controlled way. We use nanocapillaries with diameters in the range 20 - 200 nm that can be made very cheaply using a commercial pipette puller. The inside of the capillary is kept at a positive voltage relative to the bath. A DNA coated polystyrene bead held in a Laser Optical Trap is very gently moved towards the nanopore. As the bead approaches the pore, DNA is yanked into the pore by the strong electric field at the entrance region. The capture of each DNA strand is observable as a change in the force acting on the bead (measurable through its displacement in the optical trap) as well as through a change in the measured current. A typical data set is shown in Figure 4 where we "see" N=1,2,3,4,5, .... DNA being yanked into the pore. 

Figure 3: Experimental
set up 

Figure 4: The sequential capture of DNA
strands in the nanopore

The data from such an experiment is shown in Figure 5. It is seen that the force on the bead is proportional to the applied voltage, which is expected. However, the force is not proportional to the number of DNA molecules occupying the pore. In fact, the force per DNA strand is observed to decrease with the number of DNA strands occupying the pore. 

Figure 5: The force scales linearly with
the applied voltage but not with the number
of DNA strands in the pore. 

The explanation for this behavior lies in the hydrodynamic coupling between the individual DNA strands. When the electric field is switched on, the negatively charged DNA moves in a direction opposite to the field. Simultaneously, there is a gush of electroosmotic flow in the direction of the applied field driven by the positively charged counter-ions that surround the DNA as well as the capillary wall. This flow creates a hydrodynamic drag that slows the DNA down. Adding more DNA to the pore increases this electroosmotic flow as each DNA acts as an "electroosmotic pump". Thus, even though the electric force on an individual DNA is not changed by the presence of neighbors, the hydrodynamic drag is. This idea can be transformed into a scaling law according to which the force per strand is a linear function of ln N / ln (R/a) where R is the pore radius and a is the DNA radius. It is shown that the experimental data is in accord with this scaling law. 

REFERENCES

1. Laohakunakorn N., Ghosal S., Otto O., Misiunas K. & Keyser U. "DNA Interactions in Crowded Nanopores" Nano Letters (2013), 13 (6), 2798–2802