Unruled Notebook

Fungus eject their spores to the surrounding by different mechanisms. One such mechanism is the squirt gun type where the spore at the front is released by the osmotic turgor pressure from the inside at high speeds to relatively long distances (about 6 feet). Certain fungi like Ascomycota and Zygomycota that grow inside cows, come out in their dung, start this squirting mechanism and throw their spores onto clean plants that are nearby, in the hope that the grazing cow will eat them. Then the birth cycle repeats.

A recent PLOS paper [1] reports the velocities to be as high as 55 miles per hour, claiming such flights as one of the fastest observed in Nature. High speed video camera captured the flight of the spores from fungus. Using the tracking of the spore location from the different camera frames in time, the authors were able to determine both the velocity and acceleration of such flights of multiple spores ejected.There was also some calculations using fluid dynamic models that is explained below.

But before that, here is a great video the authors have made [2] from their experiments

Observe the recoil of the fungus, the initially disc like wake of the mucus behind the spore that changes shapes as it gets left out by the accelerating spore and the almost spherical shape the spore achieve.

In fluid dynamics, such configurations can be simplified as flight of spheres (spores) through a fluid – or the equivalent flow around a stationary sphere. The viscous drag that the fluid (air, in this case) imposes on the spore projectile movement needs to be overcome by an initial force that is ideally equivalent to the pressure difference across the fungus inside and outside (atmospheric pressure). Gravity force in such configuration is negligible when compared to the air viscous drag.

The viscous drag can be calculated from Stokes’ law, which looks simple for laminar flow – i.e. if the spore speed is less such that the Reynolds number calculated using the spore diameter, air speed and viscosity works out to be less than 1, the the drag force is simply where r is the radius of the spore, v its velocity and the viscosity of air. This is the same ‘formula’ we use in high schools to determine sometimes the viscosity of fluids, when the rest of the terms are known. Elsewhere, the famous Millikan’s oil drop experiment to find the electric charge of an electron also used this formula.

Getting back, if the speed is such that this Re number is far greater than one, then one enters an onset of turbulent regime, where the formula for force calculation gets a bit complicated and empirical as well. The fungus spore release studied in this paper [1] is one such instance where the Re is between 1 and 1000, a range where onset of turbulence is inevitable.

The drag force then would look like this

Here the terms account for the transition and turbulence effect. Observe the presence of the density of air, that is arising due to the form drag that manifest only at higher speeds. [some call this inertial drag, but form here implies the the origin of the force due to the shape of the body]. Obviously, in laminar flow the terms drop out and the equation reduce back to Stokes simple formula for laminar flow around spheres.

Once the force is known, it can be used with Newton’s second law, to find the acceleration. When integrated, the equation would give spatial locations, which in the turbulent flow case need to be done using numerical integration (usually, with computers) as the force is a complicated semi-empirical function unyielding for analytical integration.

Sporangiophore ejection mechanism - similar to what is discussed in this note

The spore eventually lands at a location that just cancels out the initial force with the viscous drag along the trajectory – 2 to 3 meters distance away from the cow dung. The paper [1] reports

Launch speeds ranged from 2 to 25 m s⁻¹ and corresponding accelerations of 20,000 to 180,000 g propelled spores over distances of up to 2.5 meters.

Also, the internal pressure required for generating the initial force for the projectile traverse is only about 1 MPa or about 10 atmospheres. From the relevant section of the paper:

The turgor pressures of <1.0 MPa (10 atm) that power these supremely fast movements are no higher than those measured from fungal hyphae [20], suggesting that explosive mechanisms of spore discharge do not require any extraordinary mechanisms of osmolyte accumulation, nor the elaboration of any specialized cell wall structures to maintain this pressure prior to discharge.

Two years back, Bora wrote about the spore release mechanisms discussed at the start of this note. The accompanied picture is from that post. Here is a relevant section for our note:

A fungal spore is a microscopic object. At the small scale (pdf), physics works a little differently – gravity effects are minimal and the air resistance (drag) is the main determinant of maximal distance. Thus, 45 degrees is not neccessarily the optimal angle for achieving the greatest distance.

Frances Trail and Iffa Gaffoor, working with Steven Vogel at Duke University, made some calculations (which I have not seen and I do not think they got published, but I heard them from Dr.Vogel), looking at the shape and size of spore-caps of several species of Pilobolus (they published data on some other shooting fungi, though – you can read the paper here). The optimal angle for maximal distance ranges, in different species, between 9 and 30 degrees, the most common fuzz found on cow dung requiring about 15 degrees. The maximal distance, without wind, is about 6-7 feet. Quite right. Six feet is about as close as cows will come to a cowpie in well managed cattle establishments.

References

[1] Yafetto, L., Carroll, L., Cui, Y., Davis, D., Fischer, M., Henterly, A., Kessler, J., Kilroy, H., Shidler, J., Stolze-Rybczynski, J., Sugawara, Z., & Money, N. (2008). The Fastest Flights in Nature: High-Speed Spore Discharge Mechanisms among Fungi PLoS ONE, 3 (9) DOI: 10.1371/journal.pone.0003237

[2] posted in YouTube by Carl Zimmer from whose blog post I read about this paper