Does buckling instability of the pseudopodium limit how well an amoeba can climb?

The maximum force that a crawling cell can exert on a substrate is a quantity of interest in cell biomechanics. One way of quantifying this force is to allow the cell to crawl against a measurable and adjustable restraining force until the cell is no longer able to move in a direction opposite to the applied force. Fukui et al. (2000) reported on an experiment where amoeboid cells were imaged while they crawled against an artificial gravity field created by a centrifuge. An unexpected observation was that the net applied force on the amoeba did not seem to be the primary factor that limited its ability to climb. Instead, it appeared that the amoeba stalled when it was no longer able to support a pseudopodium against the applied gravity field. The high g-load bend the pseudopodium thereby preventing its attachment to the target point directly ahead of the cell. In this paper we further refine this idea by identifying the bending of the pseudopodium with the onset of elastic instability of a beam under its own weight. It is shown that the principal features of the experiment may be understood through this model and an estimate for the limiting g-load in reasonable accord with the experimental measurements is recovered.