# How fast can a microscopic creature travel?

I'm trying to figure out how fast my tiny critters from a previous question, Mistraille, can travel. Why? It's not that I'm detail orientated and want to know the exact decimal point of speed they can reach but rather I want to know how much time my victims with open wounds have to prevent the carnivorous Mistraille from infecting them.

Critter Details

• My critter is very very tiny, about the size of plankton and zooplankton (think microns).
• They always travel in a group/swarm and are named after their appearance, a low lying mist or fog back.
• They travel by crawling on the ground, hopping or jumping (on top of each other if necessary) and gliding on proto-wings. (see generic sediment transport image below).
• They normally travel with the direction of the prevailing wind, but can travel against it if necessary.
• They travel with more 'determination' (speed and cohesion) when prey has been smelled. (for the purposes of this question, wind and 'determination' can be ignored as I only need to figure out their basic speed. Wind and 'determination' dynamics are more story orientated).

Victim Details plants or animals with open sores or cuts can be infected by Mistraille and then be eaten from the inside.

If given enough time;

• plants could produce a resin or gummy substance to seal the 'wound'
• plants could send out a signal and the surround plants could uproot themselves to 'run away' with the wind.
• animals and humans could cause the wound to be covered with a seal (gummy plants) to prevent the Mistraille from infecting them.
• animals and humans could 'run away'.

But all of this takes time. How much time do they have? seconds, minutes, hours?

QUESTION

In a lab-based situation with no outside forces helping, How fast could a microscopic critter realistically travel metres to tens of metres?

BONUS

What body characteristics would make them slower/faster?

• Just a cool reference: blogs.bu.edu/biolocomotion/2011/12/10/rockets-in-horse-poop. Effectively, there is a fungus that can shoot it's microscopic spores a good few meters away from itself (using massive amounts of pressure). Richard Hammond likens this movement to dropping a coin into honey saying: the smaller the object being fired, the "thicker" the air becomes. Not the best analogy, but the point is: the smaller/lighter an object is, the harder it becomes to move substantial distances through air, hence why the spore needs such an extreme acceleration to get where it wants to grow. – Harry David Oct 27 '16 at 8:33

# Microscopic Cellular Motility

There are many factors affecting motility of organisms at the microscopic level, but viscosity of the medium and concentration/density of the organism (swarm) seems often to be the greatest factors. Temperature certainly affects microbial motility, and the fastest moving bacteria are found living as thermophiles at high temperature where the rate of everything is higher and in organisms who depend on speed to make their living (eg predators) as opposed to simply moving up a chemotactic gradient looking for food.

As suggested, the best method for determining motility rates for microbial life is the "body length per second" measurement. This normalizes the distance to the organisms relative size and you can begin to see how microbial motility really differs from macroscopic motility. To put it into perspective, Michael Phelps, olympic swimmer, swims 100 meters in about 50 seconds, which is about one body length per second. A sailfish can travel about 30 m/s which equals about 15 body lengths per second. At the microbial level, for example, when E. coli undergoes a chemotactic walk it moves with a speed of roughly 30 um/s, which translates to around 15 of its body lengths every second and an Ovobacter sp. moves at a mind-boggling 1mm/sec (remember it's only ~ 4um) 200 times its body length per second by utilizing almost 400 flagella. Here's a table showing several bacteria and archaea motility measurements.

## Speed Limits

Your microbial organisms will undoubtedly move fastest when gliding or swimming as opposed to crawling or jumping. The molecular basis is that crawling and jumping requires the polymerization of the actin molecule or mobilization of microtubules for movement. This also goes for virulent strains like Listeria that move around inside the victim's cells by taking over the host cell's cytoskeleton. Swimming and gliding, on the other hand, often employ a flagellar rotating mechanism which is happening orders of magnitude faster than polymerization required for running/jumping.

Recent microbial research has provided evidence that suggests that motility may play an emerging, important role where dense communities of microbial life exist where their survival and growth is predicated upon more sophisticated communication (like Quorum Sensing), relative location, and level of cooperation, all of which are subject to motility.

## Size Limits

Another question you might ask is how large can your organisms grow and be able to move through a viscous environment at x um/sec with the amount of force yielded from most bacterial motors? The relation $F=6\pi\eta RV$, known as Stoke's Law, governs the relation of force (F) to velocity (V) in a fluid viscosity η, where R is the radius of the organism moving through the medium. Using the viscosity of air (assuming your world's air is like Earth's), $1.81×10^{−5} Pa.s$, a motor force exerting ~ 5 pN at 50% efficiency, and the average Mistraille size of micrometer-scale plankton, you can play with the size of the organism to get a feel of their relative velocities. Since these microbes prey on other organisms (animals/plants you mention), you might find changing the viscosity to match air, water (inside target's cells), or blood of the victim.

• wow! thanks for such a detailed answer. and thanks for bringing Ovobacter propellens to my attention! – EveryBitHelps Oct 30 '16 at 21:27

It seems that the fastest recorded insect (the Australian Tiger Beetle) was clocked at 2.5 m/s running on its hind legs. These beasties also have vestigial wings, similar to your Mistraille, but cannot fly.

But it seems that the smaller the creature the slower the absolute speed. To compare speeds more accurately one should look at the bodylengths per second. When this raw metrics is taken a Californian mite is the fastest creature at 322 bl/s. Much better than the beetle's 120 bl/s, but only 0.225 m/s is actual speed.

This mite is a much closer likeness to your Mistraille, but I would go even further. The mite is 0.7 mm in length whereas plankton, as you mention, can be as small as 0.002 mm. This would inevitably lead to a further decrease in actual speed, even if their speed relative to their bodylength was impressive. As another reference, fleas which are roughly 2 mm in length travel at about 1.5 m/s when jumping using their explosivly strong hind legs. I would approximate something generous in the region of 0.2 m/s for the Mistraille, under their own propulsion that is.

Other things to take into account:

• The proto-wings may increase this speed
• Being so small and moving in air rather than in water, the Mistraille have an incredible advantage when it comes to accelerating. This includes changing direction and stopping, which would all be performed very rapidly due to their low mass
• The same problem/advantage as a falling flea. During the descent of a "hop" whilst falling and unpowered your small creatures will be subject to a very harsh terminal velocity

I would say that the Mistraille are going to move fastest with the aid of wind, maybe in some combination of running, hopping to catch the with, gliding/falling whilst resting, followed by further running. This might also give them the tumultuous, jerky, mist-like movement you're describing.

The only thing I can think to make them faster is real wings (you could still limit how much they can fly), or large hind legs giving more of a cockroach-like upright run or a bigger flea-like hop.

This is a great article covering several points relevant to your questions on speed/anatomy: http://www.bbc.com/earth/story/20141021-the-fastest-insect-in-the-world

As for how long their prey have, that very much depends on how soon they can detect the presence of a Mistraille cloud. However, assuming a moderately large swarm visible at 100 m, moving at a wind-boosted 2.5 m/s, that gives them 40s. Not long enough to do much other than run really!

Something else you might want to account for when they are wind-aided is their unpredictable course due to gusts and the shifting breeze.

• Excellent thanks. And welcome! great third answer! – EveryBitHelps Oct 26 '16 at 21:39
• I would not relay on some micro wings, when size of creatures are micrometer sizes - they just almost pointless because drag/mass will be higher smaller they are. for 0.1mm and higher yes probably. – MolbOrg Oct 30 '16 at 15:08