Whip it, whip it good

by Janie Jones

Have you ever wondered what it’s like to be a sperm?

No, no.  Stay with me here.  This is no joke.  This is your multidisciplinary science lesson for the week.

So, when you are tiny, microscopic organism, or a single cell such as a sperm cell, your swimming reality is not quite same as what we mega-fauna organisms know as the reality of swimming.  We just jump in the water and wiggle a bit and away we go.  But when you are a tiny microscopic life form, though you swim in the same waters as us big’uns, it’s, well, more complicated.
You see, this is where Janie’s brain explodes, because the dreaded world of physics collides with biology.  As Ricky Ricardo would say, “Janie, you got some ‘splaining to do!”  And, I will try, because it’s way cool.
So, fluids have both viscosity and density.  Straight forward.
There is also such a thing as inertia, right?  You all know about inertia, that an object’s inertia resists changes in its “state,” so the whole an-object-in-motion-tends-to-stay-in-motion-and-an-object-at-rest-tends-to-stay-at-rest-unless-acted-upon-by-something-else (or in the physics world, an external force) bit.
Now imagine you are moving through a fluid.  This means you have velocity.   And it would happen that, in a fluid, the ratio of inertial forces to the forces of viscosity is very important.  If you want to know the physics math it’s:

inertial forces/viscous forces=> density x velocity x dimension (such as length of the body traveling through the fluid)/viscosity

This ratio gives you a value known as a Reynolds number.  The important take away fact is that when Reynolds numbers are very small, as in the microscopic world, the forces of viscosity cancel out pretty much everything else.  In fact, the viscosity squared divided by the density is a force.  And when Reynold’s numbers are very low, this is a tremendous amount of force to be reckoned with.
A paper was written on this subject by E. M. Purcell, June 1976.  So to help put things in perspective, in Purcell’s words, we can get an idea of what it might be like to be a microscopic organism swimming at low Reynold’s numbers if we imagine swimming in a pool of molasses and we can only move at the rate of one centimeter per minute.
In our world, if we dive into the water, or do some sort of stroke, our inertia carries us forward a ways.  But, at low Reynolds number inertia has no bearing.  Microscopic organisms do not experience inertia.  Purcell tells us that if we could give a microscopic organism a push, it would come to a stop in 0.6 microseconds and only travel 0.000000000001 meters.
Pretty wild?  Well, while that might seem hard to imagine, low Reynolds numbers play another key role in how microscopic organisms experience physics and motion.  That is, reciprocal motion gets you nowhere.  Literally.
So, think of floating face down in the water and just using your arms to swim.  You hold your arms out in front of you then thrust your arms to the side.  This causes you to move through the water.  You bring them back forward in the reverse motion and repeat the stroke.  The motion is essentially symmetrical and reciprocal.  Your arms travel the same path each time you stroke; they start and end always in the same place, the movement is reversible.  If you have spent any time in the water you know you’ll be much more effective if you tuck your arms in to your body as you bring them forward, but if you use less force as you bring your arms back in the reverse motion, because of inertia, you will still move forward some.
If you are at low Reynold’s number, however, and you try to repeat the this same kind of reversible, symmetrical motion, you simply retrace your movement forward and backward to the exact same spot due to the lack of inertia.
Weird, but true.
So, every wonder why sperm is shaped the way it is?  Because with out the whip-like flagellum, it couldn’t even compete in the fertilization free-swim.

sperm motion

Google Image search sperm+flagella+whip+motion

The flagellum does not move in a reciprocal or symmetrical motion and does not rely on inertia to help it, instead it beats in a wave-like motion.  As you can see from the image, it does not start and stop in the same place with each whip stroke.  Furthermore, the motion changes the orientation of the whole cell.  And, so it can still propel the cell at very low Reynold’s numbers.
If on the other hand, it’s flagellum flapped like a windshield wiper, or your arm in the above swimming example, the lack of inertia would bring the sperm right back to where it started when it reversed the motion.  Not very effective.  This sperm definitely wouldn’t win the egg hunt.
So if you are having problems with sperm motility perhaps your little swimmers didn’t quite get the proper swim lessons.
Bacteria, on the other hand, have different kinds of flagella which are rigid and can’t “whip” the cell forward.  Instead, many bacteria have a corkscrew shaped flagellum that works like a propeller.  Some have corkscrew shaped “bodies” as well, which rotate to help propel the organism with a propeller like effect.  Other bacteria don’t have flagella at all, but instead have multiple cilia, which are more flexible and can promote “whip” like motion.

Well, I hope that wasn’t too dry or boring.  As much as I hate physics math, I still think it’s fascinating conceptually.  Especially when we see it in our every day lives and how it frames our intuitive functioning within the world around us.  But every now and then if we stop and realize that the world we live in isn’t the same world that is experienced by other lifeforms around us, our intuitive feel for every day physics can be thrown out the window.  That’s when physics can really blow your mind.
So, with beach season just around the corner, next time you go for a paddle, perhaps you might spare a moment to think of the microscopic life teaming invisibly all around you and appreciate how amazing biology is that it can compensate for a wide range of physical realities.

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