# Difference between revisions of "A high-throughput capillary assay for bacterial chemotaxis"

Zach Wissner-Gross (March 2, 2009)

## Information

A high-throughput capillary assay for bacterial chemotaxis

Russell Bainer, Heungwon Park, and Phillipe Cluzel

Journal of Microbiological Methods, 2003, 55, 315-319

## Soft matter keywords

E. coli, chemotaxis, capillary

## Summary

A methods paper, this article is relatively straightforward. The authors use a 96-well plate to perform a high-throughput assay for bacterial chemotaxis by setting up an array of gradients of L-aspartate (a chemoattractant). They establish these gradients using capillary tubes: first they dipped the tubes into motility medium either with or without the L-aspartate. They then sealed the tubes from above with wax, and finally they resuspended the tubes in 96-well plates inoculated with various concentrations of bacteria (E. coli). After 40 minutes, the capillaries were removed, along with any bacteria that had migrated into them. Cell density in the capillaries was determined by monitoring changes in the optical densities of the solutions in the capillaries over the course of several hours (Figure 1).

Figure 1: Bacterial growth, as measured by optical density, over time given different initial bacterial concentrations.

The authors' results matched those found in previous low-throughput experiments. In short, they found the expected logarithmic relationship between cell concentration and the "lag time" before the number of cells that migrated into the capillaries began to saturate their environment. Capillaries containing 10 mM L-aspartate were found to attract 15 times as many bacteria as capillaries lacking the L-aspartate (Figure 2). But again, while this result was simply being verified in this paper, the focus here was on the throughput of the experiment.

Figure 2: Temporal lag between solutions with and without L-aspartate. Bacteria preferred capillaries with the attractant by a factor of 15.

## Soft matter discussion

As I stated in the summary, this article is rather straightforward, serving as a methods paper rather than going into physical detail. However, one point that I found intriguing was how the gradient of chemoattractant is established and how it is affected by the geometry of the setup.

First, let's verify that the gradients are even maintained throughout the bacterial inoculation. From class, we know that the height $H$ of a capillary water column will be

$H=2\cos\theta_E\frac{\kappa^{-2}}{R}$

where $\theta_E$ is the contact angle, $\kappa^{-1}$ is the capillary length, and $R$ is the radius of the column. Since $\kappa^{-1}$ is on the order of a few millimeters, and in this experiment $R$ is 0.5 mm, we would expect $H$ to be a few millimeters or centimeters at most. From Figure 3, reproduced from the paper, we can see that the capillary tubes widen rather suddenly, so that their narrow necks are probably only a few millimeters in length. Thus, we can assume that the bacteria are exposed to a column of mobile media several millimeters in length.

The diffusion constant $D$ for L-aspartate in water is likely on the order of $10^{-6}$ cm$^2$/s, and the inoculation takes place over a time $\tau$ of 40 minutes, or 2400 seconds. Thus, the characteristic diffusion length $d$ the L-aspartate will travel during the inoculation is

$d=\sqrt{D\tau}=\sqrt{(10^{-6})(2400)}=0.5\text{ mm}$

Since $d$ is significantly less than the height of the columns, the gradients of chemoattractant should be more or less maintained throughout the experiment, as desired.

Furthermore, the authors cite previous work showing that thinner capillaries result in a greater ratio $R$ between the number of cells that migrate toward the attractant and those that migrate into capillaries without the attractant. Why might this be the case? Since the capillary tubes widen after only a few millimeters, it seems unlikely that the total height of the column would significantly change by altering the width at the capillary's neck.

Instead, I believe that diffusion is occurring more rapidly for the wider tubes due to the increased cross-sectional area at the capillary tip. Thus, more attractant is leaking out into the bath of E. coli, so relatively more bacteria will stay out in the solution. The gradient will also degrade more quickly over time for wider tubes. Thus, while we might expect more bacteria to migrate into a wider tube, we would expect a narrower tube to be more selective, resulting in a higher value of $R$. I would be very curious to see future results that determine the scaling of selectivity with tube radius or other geometrical features of this assay.