We recently released our __nanopore size calculator__ to make your life a little easier. It's important to know what it's doing behind the scenes so you can be confident in the results it gives you. Here's how we did it.

When calculating the size of a nanopore from its measured conductance, one usually assumes the pore has a cylindrical geometry. The open-pore conductance *G*, using a cylindrical model, is expressed as[1]

where *s* is the solution conductivity, *L* is the membrane thickness or effective pore length (more on this below). Pore diameter *d* can then be calculated:

where

This expression is valid when surface effects can be ignored and requires that surface charge be maximally screened. This is practically achieved when operating in very high salt concentration, such as 3.6M LiCl.

The error in the calculated pore diameter can be calculated using standard error propagation techniques as

In practice, when care is taken to measure *G* and *s*, the error in the pore length is the dominant source of error when calculating the pore diameter.

Most of this calculation is done for you by the NNi Nanopore Fabrication Software, but below, we go into some detail on how to improve your size estimate once you have translocated some biomolecules like DNA.

## Measuring the Input Parameters

*G *and *s* can be readily obtained as follows:

An I-V curve from -200 mV to +200 mV, comprised of at least 11 equally spaced voltage steps and fitting the data to a straight line, assuming the pore has an ohmic response, to extract the conductance from the slope.

Note: The current must be measured once the capacitive current has decayed so a wait of 1-2s is advisable between voltage change and current reading

A carefully calibrated conductivity meter to measure the solution conductivity

*s*. 3.6 M LiCl pH 8 should have a conductivity of approximately 16.5 S/m. Or, simply read the conductivity off of the appropriate fabrication or conditioning solution.

The accuracy of the calculated pore diameter is often dominated by the accuracy in the value used for pore length. Using the nominal membrane thickness for the pore length can lead to significant error if the pore deviates from a cylindrical geometry. To avoid using more complicated models, the deviation from a cylindrical geometry is lumped into an effective pore length. This correction is particularly important when using pores in membranes thicker than 10 nm.

The effective pore length can be estimated from the conductance blockade data produced by the single-file passage of long, linear dsDNA. To first order, if the polymer spans a distance longer than the pore length, the conductance blockage of a single unfolded fragment of dsDNA in the pore can be expressed as:

where the diameter of double-stranded DNA is taken to be 2.2 nm. Accordingly, the effective pore length can be calculated as:

Care should be taken in interpreting this value. It is not necessarily a physical quantity, but rather the effective length of a cylinder that would produce the same blockage. This distinction is important, in that the model presupposes a cylindrical pore and then calculates physical parameters of that cylinder that match experimental observation, rather than actually indicating the assumed geometry. In practice, this assumption is reasonable for small aspect ratio pores (*d *< *L*), [2–4] but begins to break down as pore size becomes larger and blockage depth becomes less sensitive to membrane thickness. As such, we suggest care when using this blockage model for pores with a large aspect ratio. In fact, for large aspect ratio pores (*d *> *L*), the pore length can be assumed to be the full membrane thickness.

Below we suggest a protocol using our nanopore fabrication software to obtain data to minimize the error in the calculated pore diameter, for small aspect ratio pores (*d *< *L*):

Fabricate a nanopore using your Spark-E2, entering the nominal thickness of the membrane for pore length. Note that conditioning in 3.6M LiCl pH 8 is an effective way to shield surface effects to obtain a more accurate size reading. See our

__workflow guide__for some simple tutorials on using the system.Run 2kbp or 5kbp dsDNA through pore in 3.6M LiCl pH 8 at 200 mV as described in the Workflow Guide. Perform recording at full bandwidth making sure that all events are fully resolved by the response time of your system. Truncated events will result in the measurement of a lower value. After ~100 translocations (the more the better), extract the mean from the fit to the distribution of blockage amplitude for the single-file events only.

Use the measured mean to calculate the effective pore length following Equation (5).

Flush clean 3.6 M LiCl pH8 in fluidic cartridge to remove DNA.

Perform I-V curve to measure the open pore conductance. Note that the open pore conductance should not have changed by more than 1 nS.

Using

*L*and*G*values from Steps 3 and 5 respectively, re-calculate pore size using Equation (2). The newly calculated, more accurate pore size should be slightly smaller than the initially calculated pore size, if the effective membrane thickness is thinner than the nominal membrane thickness.If the difference between the new accurate pore size and the desired pore size for your experiment is > 1nm, and accuracy is important, condition with the Fabrication Software to desired pore size while entering the new effective pore thickness in the software. Note that if the pore needs to be enlarged significantly, Steps 2-6 may need to be redone as the effective shape of the pore will be changed upon enlargement.

Performing this protocol for 10 chips of a given batch of membranes should provide a distribution of effective pore thicknesses for this batch of chips. From this distribution, the mean and the standard deviation can be used to generate pores of a desired size more accurately and with a known uncertainty, and without having to run this calibration protocol every time. Finally, if an accuracy <1 nm is crucial to the project, running an internal calibrator such as 2kbp or 5kbp dsDNA before or during the experiments should be considered.[5]

In support of the assumptions made above for nanopores fabricated by controlled breakdown, TEM images of pores <30 nm in diameter in SiN membranes <30 nm in thickness have shown circular openings[3,4]. DNA translocation data have also confirmed the accuracy of the calculated pore size with <±1nm using the above method [2].

We hope you find this a useful tool for your research. P.S. Ask Kyle why we recommend 3.6M LiCl some time.

__Previous Topic: Characterizing a nanopore electrically __

## References

[1] Kowalczyk, S. W.; Grosberg, A. Y.; Rabin, Y.; Dekker, C. Modeling the Conductance and DNA Blockade of Solid-State Nanopores. *Nanotechnology* **2011**, *22* (31), 315101. __https://doi.org/10.1088/0957-4484/22/31/315101__.

[2] Briggs, K.; Kwok, H.; Tabard-Cossa, V. Automated Fabrication of 2-Nm Solid-State Nanopores for Nucleic Acid Analysis. *Small ***2014**, *10* (10), 2077–2086. __https://doi.org/10.1002/smll.201303602__.

[3] Carlsen, A. T.; Briggs, K.; Hall, A. R.; Tabard-Cossa, V. Solid-State Nanopore Localization by Controlled Breakdown of Selectively Thinned Membranes. *Nanotechnology* **2017**, *28* (8), 085304. __https://doi.org/10.1088/1361-6528/aa564d__.

[4] Kwok, H.; Briggs, K.; Tabard-Cossa, V. Nanopore Fabrication by Controlled Dielectric Breakdown. *PLoS One* **2014**, *9* (3), e92880. __https://doi.org/10.1371/journal.pone.0092880__.

[5] Charron, M.; Briggs, K.; King, S.; Waugh, M.; Tabard-Cossa, V. Precise DNA Concentration Measurements with Nanopores by Controlled Counting. *Anal. Chem.* **2019**, *91* (19), 12228–12237. __https://doi.org/10.1021/acs.analchem.9b01900__.