Worm Breeder's Gazette 17(1): 52 (October 1, 2001)

These abstracts should not be cited in bibliographies. Material contained herein should be treated as personal communication and should be cited as such only with the consent of the author.

Simulation of bacterial transport in the pharynx

Leon Avery

Department of Molecular Biology, University of Texas Southwestern Medical Center, 6000 Harry Hines Blvd, Dallas, TX 75390-9148

C elegans is a filter-feeder: it takes in liquid with suspended particles (bacteria), then spits out the liquid, while trapping the particles. However, the pharynx lacks any obvious filter. When one analyzes videotaped motions of bacteria in the pharyngeal lumen, they seem to move backward with the liquid during the pharyngeal contraction, as you would expect. However, when the muscle relaxes, the liquid rushes forward and out the mouth, while the bacteria seem to remain where they are. Unfortunately, the relaxation is very fast, only a few milliseconds, so that the detailed motions can't be seen. One can imagine exotic mechanisms by which bacteria are trapped during muscle relaxation (one that seminar audiences often come up with is differential adhesion of bacteria to the walls of the pharyngeal lumen depending on membrane potential). However, I decided to test whether I could simulate the trapping of bacteria by simple hydrodynamic mechanisms.

The simulation incorporates three assumptions. Two are not controversial:

1.       When the diameter of the pharyngeal lumen is less than the diameter of the bacterium, the bacterium is held in place by the lumen walls.

2.       When the diameter of the lumen is greater than the diameter of the bacterium, the bacterium moves with the fluid.

Under these assumptions, there would be no net transport of bacteria if the pharynx contracted simultaneously along its entire length and the relaxation were a simple reverse of the contraction. This is actually a very general result: in a system as small as the nematode pharynx, inertial forces can be ignored, and fluid motions are linearly related to the forces that generate them. Such a system can generate no net change if its motions are described by a single degree of freedom. In fact, analysis of videotapes shows that pharyngeal motions are not synchronized along the entire length of the pharynx: the anterior isthmus begins its contraction and relaxation slightly after the corresponding motions of the corpus. When this slight delay is included in the simulation, bacteria assumed to move at the mean fluid velocity are trapped and transported, but very inefficiently. The volume of the anterior isthmus is much less than that of the corpus, so that its influence is small.

The last assumption that went into the simulation is less obvious, but is plausible given the triradiate shape of the pharyngeal lumen (figure above):

3.       Bacteria are pushed to the center of the pharyngeal lumen when it closes (figure below).

Fluid moves faster than the mean velocity at the center of a tube, because motion near the walls is slowed by friction. The ratio of center to mean flow velocities can be determined by solving the Poisson equation. Solving Poisson's equation for the pharyngeal lumen predicts that the center flow velocity should range from 2.2 to 3.2 times mean velocity, depending on the extent to which the lumen is open. Thus, the third assumption predicts that bacteria will at move 2-3x mean velocity. This increased velocity, it turns out, greatly magnifies the effect of the delayed isthmus motions. The simulated pharynx transports bacteria posteriorly with an efficiency that looks like the real thing.

The simulation, along with a more detailed explanation, is available as a Java applet at http://eatworms.swmed.edu/~leon/pharynx_sim/.

These results suggest that simple hydrodynamics are indeed sufficient to explain the trapping and transport of bacteria within the pharynx. The most direct way to test whether this mechanism is correct would be high-speed videotapes of the motions of particles in the pharyngeal lumen, which, although technically difficult, is probably possible. Until that can be done, there are other predictions that are simpler to test. First, the model predicts that the changes in anterior isthmus motions should have large effects on the transport of bacteria within the corpus. Second, it predicts that the relative timing of the motions of the corpus and anterior isthmus should be critical. (We have had evidence for this for many years: M3, which control the timing of relaxation, is important for efficient transport of bacteria.) Third, it predicts that asymmetric motions of the pharyngeal muscles, which would tend to drive the bacteria off-center, should decrease the efficiency of bacterial transport.