Bacteria have busy social lives. You might get a glimpse of this the next time you take a shower. The slimy discolored patches that form on bath tiles and on the inside of shower curtains are the mega-cities of the bacterial world. If you zoom into these patches of grime, you’ll find bustling microcosms that are teeming with life at a different scale.

That we can see these microbial communities with our naked eye is testament to the scale of their achievement. Perhaps the most spectacular examples are the giant mats of bacteria that lend life to the Grand Prismatic Spring in Yellowstone National Park. These macroscopic structures are just as impressive as our cities that are visible from outer space. Microbes have colonized practically all moist surfaces on earth, from the inside of our mouths (they’re responsible for dental plaque) to hot vents at the bottom of the ocean. And it all started from small beginnings.

The first wave of bacterial settlers that arrived on your shower curtain were few and far apart. They would try to hold on using the molecular adhesion between themselves and the shower curtain. Those that couldn’t get a grip were flushed down the drain plug.

Bacteria have an adaptation that serves them well in such tricky situations. It’s a sort of multi-purpose prong, technically known as a type IV pilus (plural: pili). These wonderful filament-like structures extend out from the bacteria, and grab on to the surface like a suction cup on a bathroom tile. What happens next is straight out of science fiction.

Once these settlers have their ‘feet’ firmly planted on the ground, the next step is to build a home. They begin to excrete a polymer substance, forming a grid that locks them into place. Many different microbes can co-inhabit these homes, from bacteria and archaea to protozoa, fungi and algae. Each species performs a specialized metabolic function, neatly occupying a niche in this city. Together these interlocked communities, or biofilms, are the beginnings of a thriving multicultural microbial civilization.

Why do bacteria congregate into cities? It’s basically for the same reasons that we do. By collecting together in large numbers, they can more effectively share resources. The grid offers them protection from antibiotic enemies, and helps them share resources. Some biofilms even have their own utilities and telephone system (that’s right, bacteria can talk). These grids have water channels running through them, which the bacteria use to share nutrients and send signals to each other.

But as city dwellers are well aware, moving to the grid comes with its disadvantages. The bacteria pay a price in mobility – their cities have no public transportation. It’s hard enough for bacteria to move in water, and being embedded in an organic glue makes matters considerably worse. Their winding propellers, the bacteria flagella, are of little use here.

However, the bacteria have a clever way out. Their pili (the hair like appendages pictured above) are more than just suction cups. They can also work like a grappling hook. The bacteria shoots them out to hook onto the surface, and then reels itself in. By repeating this motion, it can slowly crawl across the biofilm in a lengthwise motion that biologists delightfully refer to as twitching.

Here’s a video that shows bacteria (Pseudomonas aeruginosa) twitching along a surface as they keep dividing:

and a slowed down version of the same process:

You can see that the motion is jerky, because the bacteria are using their pili to pull themselves forwards or backwards. This crawling strategy was widely accepted as the explanation for how bacteria move in a biofilm.

But there were always some pieces that didn’t quite fit. Scientists knew that bacteria can sometimes make sharp turns, but they never quite understood how. The grappling hooks are mostly in the front and back of the bacteria, and aren’t much use for turning.

In an innovative solution to this problem, some bacteria instead use their pili like a walking stick. Rather than pulling themselves forward, they prop themselves up from the ground, stand upright and flop over. By repeating this motion, they can walk across the terrain. You can watch this strategy at work:

These walkers are not as energy-efficient as the crawlers, but they can move faster and are more meandering, both good ideas if you want to quickly explore new territory.

And a recent paper published by scientists from UCLA and University of Houston adds a new twist to the story. Fan Jin and colleagues describe an experiment where they track the motion of the bacteria Pseudomonas aeruginosa, the star of the twitching videos shown above.

They recorded videos of these bacteria moving under a microscope, and used software to track the positions of the two ends on their rod-shaped body. This process looked something like this:

Near the end of the video, you can see the bacteria make sideways leaps.

By analyzing this motion over many steps of the bacteria, they discovered a consistent pattern to the data. The following figure from the paper shows the horizontal and vertical position of the bacteria, as it crawls along the surface.

From the data, they worked out the speeds of the leading and trailing ends of this bacteria. You can see this plotted as the blue skyline in the figures above. What it shows is that the bacteria are constantly switching between short, furiously fast bursts of motion, and slower, more methodical crawls.

These two motions are quantitatively very different. The scientists found that although the bacteria spend only about 1/20 or 5% of their time in these leaps, they move 20 times faster than their normal crawling pace. Put the two together, and it means that the bacteria cover just as much distance leaping as they do crawling.

This tracking video from the paper shows this sudden move in action:

How do the bacteria manage to propel themselves through these considerable distances? The researchers realized that the bacteria must be using their pili as a slingshot. They use one pilus to tether themselves to the surface, like an anchor. By trying to pull the bacteria forward, the other pili become stretched like taut rubber bands. And as the bacteria severs its anchor, the rubber bands uncoil and it shoots out like a pellet from a slingshot. As it slides away, it can skid to one side like a car that’s taking a turn too quickly. This is the mechanism behind the sudden turns.

But there’s still a puzzle remaining, and it has to do with the physics of the small. In my previous post I talked about how bacteria move in a world of a low Reynolds number. What this means is that a bacteria feels its environment to be thick and viscous, robbing it of its tendency to maintain its speed (inertia). If you try to fling a bacteria forward, it should immediately come to a dead stop. So how are these slingshotting bacteria managing to coast through the slime? The solution comes from the physics of ketchup.

Let’s start with pouring honey out of a bottle. It doesn’t matter much if you squeeze the bottle or not. That’s because honey is a Newtonian fluid, meaning that its viscosity (or syrupy-ness) is independent of how much force you apply. You can’t rush such fluids, they’ll just stubbornly keep doing what they’re going to do.

On the other hand, there are some strange fluids like quicksand. These thicken up if you squeeze them, a fact used as a gag in countless hollywood films (quicksand had its heyday in the 1960s, when 3% of all films showed someone sinking in mud, sand or clay!)

Such fluids in which the viscosity increases with the applied force are known as shear thickening fluids. Silly putty has this property, as does cornstarch mixed with water, much to the amusement of kids everywhere.

And then there are fluids whose viscosity decreases as you squeeze them. These are the shear thinning fluids. This is like ketchup, that flows when you squeeze or shake the bottle, but won’t flow off your burger. Paints work on the same principle. They will flow across the canvas when applied with the force of a brush, but won’t drip when left alone.

And biofilms fall into this latter class of fluids. In the case of our bacteria, the researchers estimate that force of the slingshot is enough to lower the viscosity of the surrounding goo by three-fold.

By launching themselves forward, the bacteria are taking advantage of this quirk of physics to effectively slice through the slime. This is in contrast to the strategy adopted by the stomach bacteria Helicobacter pylori, that solves the problem using chemical engineering. H. pylori lives in the mucus lining of our stomachs, an alarmingly inhospitable environment for a life form. To help it move, it releases a chemical that thins out the surrounding mucus.

These bacterial communities are the results of countless failed experiments in the annals of evolution. In the game of life, success follows a seemingly endless line of heavy losses and incremental gains. And yet, from our shower curtains to the linings of our stomach, these microbes have arrived at strikingly clever solutions to the problem of getting around in a sticky situation.

References

Jin F, Conrad JC, Gibiansky ML, & Wong GC (2011). Bacteria use type-IV pili to slingshot on surfaces. Proceedings of the National Academy of Sciences of the United States of America PMID: 21768344

Gibiansky ML, Conrad JC, Jin F, Gordon VD, Motto DA, Mathewson MA, Stopka WG, Zelasko DC, Shrout JD, & Wong GC (2010). Bacteria use type IV pili to walk upright and detach from surfaces. Science (New York, N.Y.), 330 (6001) PMID: 20929769

Image References
All images link to the source, except those taken from the paper.

Whereas the rigid universe is notable for its strict adherence to a few basic principles, the squishy universe is a different beast altogether.

I was recently out paddling, and noticed that as you move the paddle through water, tiny whirlpools begin to develop along its sides. The whirlpools grow in size, become self-sustaining, and break off and float away. Eventually they die out, as they lose their energy to the fluid around them.

You could also watch the spirals and vortices created by rising smoke. Or notice the strange shapes made by the wind as it sweeps through the clouds. It’s as if fluids have a life of their own, often wondrous and beautiful, and other times surprising and counter-intuitive.

But the motion of fluids is notoriously hard to predict. It’s so difficult that if you can solve the equations of fluid flow, there are people willing to offer you a million dollars. The difficulty comes from a mathematical property of the equations known as non-linearity. Simply put, a non-linear system is one where a small change can lead to a large effect. The same thing that makes these equations difficult to solve is also what makes fluids surprising and interesting. It’s why the weather is so hard to predict – tiny changes in local temperatures and pressures can have a large effect.

At this point, most reasonable people would throw their arms up in despair. But physicists are an unreasonably persistent bunch, and when faced with an equation that they can’t solve, they try to get some insight by looking at what happens at extremes. For example, thick and syrupy fluids like glycerine behave in a surprisingly orderly fashion. Take a look at this video (watch through to the end, it’s worth it).

I bet you’ve never seen a fluid do that before. So what’s going on here? And what does this have to do with swimming sperm?

Let’s take a step back. Picture a flowing river. If there is an obstruction to the water’s path, like a rock jutting out of the surface, the water will move around it and swirl back upstream. Behind the rock, the water remains relatively calm. What you get is a spot on a moving river where the water is remarkably still. These calm spots are called eddies, and kayakers treat them as parking spots on the river.

But fluids don’t always behave like this. If you replace all the water in a river with a viscous fluid like glycerine, there won’t be any eddies. The syrup will simply follow the contours of the rock and smoothly flow around it.

In one case we have smooth, orderly flow, and in the other case we have eddies and turbulent flow. The question arises, is there any way to know what kind of flow will result in a given situation? This question was answered by the physicist Osborne Reynolds in 1883, and he answered it in style.

Here is Reynolds’ elegant experiment. He sent fluid flowing through a thin pipe (analogous to the river), and injected colored dye in a small section of the flow. He watched the dye flow down the tube, and could plainly see whether the flow was smooth or disorderly. By tweaking the parameters in this experiment, he was able to discover the conditions that ensure an orderly flow.

What he found is that there is one simple, magic number that can predict what is going to happen. It neatly ties together all the different physical quantities involved. It’s been named Reynolds number (Re for short), and is given by

These are all quantities that you can directly measure. The viscosity of a fluid is a measure of how slowly it flows. Thick and syrupy fluids like honey and corn syrup have a high viscosity, gases like air have a very low viscosity, and water is somewhere in between. The length in the above equation is a length that describes the object that you are studying (say the width of the rock). Reynolds used the diameter of the pipe. And the speed is that of the fluid.

The Reynolds number has the nice property of being dimensionless, meaning that the number is the same in whatever system of units you choose to measure the above quantities (dimension-full quantities are things like speed, which you could measure in km/h or mph). What Reynolds found is that as this number exceeds 2000, you suddenly get turbulent flow. In fact, this week’s issue of Science magazine mentions a new experiment that verifies this surprising result, and puts the turning point at Re = 2040. (The specifics of this number has to do with a fluid moving through a cylindrical tube with smooth walls. In a different situations, the number will change, but the principle is the same. There is a sudden jump from order to turbulence.)

The above figure gives you an idea of what happens as you increase Reynolds number. Here’s an analogy. The low Reynolds number world is like a collectivist ideal, where water moves along uniformly like soldiers marching in step. The high Reynolds number world is the individualist nightmare, where everyone looks out for themselves. Think of a march versus a mob.

We can arrive at this number from another route. There are two fundamentally different type of forces that act on an object immersed in a fluid. The first kind are inertial forces. This is like the push you give to the water when you take a stroke while swimming. Inertia is what allows water particles to keep moving undisturbed. On the other hand, you have viscous forces which measure the tendency for the fluid to smooth out any irregularities. To use the above analogy, inertial forces reflect the individuality of bits of fluid, and viscous forces are like a communist government enforcing conformity. And when you take the ratio of these forces, you get back the Reynolds number.

This number is of immense importance to aeronautical engineers and to biologists interested in locomotion.

Let’s say you want to simulate the effect of wind on a new wing design. You build a scale model in the lab that is one tenth the size of the actual wing.

But remember how the Reynolds number is defined.

If you shrink the size of the wing by a factor of 10, you have to increase the windspeed by the same amount in order to keep the number fixed. The key point is that systems with the same Reynolds number have essentially the same nature of flow. If you didn’t account for this, your wing would be quite a disaster.

How would a biologist use this idea? Well, nature presents us with organisms that cover an incredible range of sizes, from the tiniest microbes to the blue whales. Here is a table of Reynolds numbers across this range.

The list covers 14 orders of magnitude. A whale swims at a huge Reynolds number. This means that inertial forces completely dominate. If it flaps its tail once, it can coast ahead for an incredible distance. Bacteria live at the other extreme. In a delightful paper entitled Life at low Reynolds number, the physicist Edward Purcell calculated that if you a push a bacteria and then let go, it will coast for a distance equal to one tenth the diameter of a hydrogen atom before coming to a stop. And it will do this in 3 millionths of a second. Bacteria clearly inhabit a world where inertia is utterly irrelevant.

Eels and sperms may look similar, but their method of moving is very different, as their Reynolds numbers are far apart. In fact, we can now answer the question, what would it feel like to swim like a sperm or a bacteria? To do this, you have to somehow get down to their Reynolds number. We can’t change our size, but we can shrink our Reynolds number by swimming in a very viscous fluid. Purcell estimated that you would have to submerge yourself in a swimming pool full of molasses, and move your arms at the speed of the hands of a clock. (Don’t try this at home. Swimming in molasses is not a good idea.) Under these conditions, if you managed to cover a few meters in a few weeks, then you qualify as a low Reynolds number swimmer.

This clearly isn’t a hospitable environment for denizens of our Middle World. But yet this is the scale of the task that microbes face simply to get around.

Except, it’s even harder. Remember the youtube video of the colored dye swirling in the glycerine? The reason that the colors come back to where they start is because at low Reynolds number, flow is reversible. Because inertial forces are so small, certain terms drop out of the complicated fluid flow equations. The equations simplify considerably, and not only are they now solvable, they don’t depend on time any more. If you took the youtube video and played it backwards, you wouldn’t be able to tell the difference.

But this reversibility has a surprising consequence. It means that anything that swims using a repeating flapping motion can’t get anywhere. If it moves forward in one stroke, the other stroke will bring it right back to where it started. Scallops swim by opening their jaws and snapping it shut. In low Reynolds number, scallops can’t get anywhere.

Don’t believe me? See it for yourself. Here’s a rubber band powered toy that paddles forward when in water.

Woohoo! Look at it go. Now, take the same toy and place it in a vat of viscous corn syrup.

The reversibility of the flow ensures that the boat can’t make any progress.

So how, then, do microbes manage to get anywhere? Well, many don’t bother swimming at all, they just let the food drift to them. This is somewhat like a lazy cow that waits for the grass under its mouth to to grow back. But many microbes do swim, and they make use of remarkable adaptations to get around in an environment that is entirely alien to us.

One trick they can use is to deform the shape of their paddle. By cleverly contorting the paddle create more drag on the power stroke than on the recovery stroke, single cell organisms like paramecia break the symmetry of their stroke and thus elude the scallop conundrum. Indeed, this is how the flapping structures known as cilia thrust a cell forward: they flex.

There is an even more ingenious solution that has been hit upon by bacteria, sperm and other cells. Rather than having a cilia, which is essentially a flexible paddle, these cells adopt a different strategy: they use a corkscrew for a propeller. Just as a corkscrew used on a wine bottle converts winding motion into motion along its axis, these organisms spin their helical tails (flagellum) to push themselves forward.

But don’t expect to see human swimmers doing ‘the corkscrew’ anytime soon. This strategy works only at low Reynolds number, where water ‘feels’ as thick as cork, so you can push against it effectively.

And here’s proof. Whereas our rubber band powered stiff paddle couldn’t make any headway in the corn syrup, take a look at what happens if you instead have a helical propeller.

It winds its way into the fluid and inches forwards.

Motion in this viscous world is counter-intuitive and puzzling. By applying science, we can imagine what it must feel like to be very small. And we can work out how to build tiny ships in such a world. But evolution has beaten us to the punchline, and microorganisms have evolved intricate and wonderful structures that pulsate rhythmically and take advantage of the quirks of physics at this scale.

References

Purcell, E. (1977). Life at low Reynolds number American Journal of Physics, 45 (1) DOI: 10.1119/1.10903

Avila K, Moxey D, de Lozar A, Avila M, Barkley D, & Hof B (2011). The onset of turbulence in pipe flow. Science (New York, N.Y.), 333 (6039), 192-6 PMID: 21737736

Reynolds, O. (1883). An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall Be Direct or Sinuous, and of the Law of Resistance in Parallel Channels. Proceedings of the Royal Society of London, 35 (224-226), 84-99 DOI: 10.1098/rspl.1883.0018

In addition to the above papers, I learnt a lot about this subject from the following excellent book, from which many of the figures in this post are taken:
Life in moving fluids: the physical biology of flow by Steven Vogel (1996)

The theme of this post came from reading a following wonderful out-of-print book that I discovered in the basement of Strand bookstore in NYC:
On Size and Life (Scientific American Library) (1983)

Image Credits

Figures from the cited papers or from Life in moving fluids by Steven Vogel are attributed in place.

Slinky by Aaron Steele

Paddle Prints by deanspic

Cartoon of eddies was lifted from Whitewater kayaking: the ultimate guide by Ken Whiting & Kevin Varette

An airfoil wing in a wind tunnel courtesy NASA Langley Research Center

Cilia on a Paramecium courtesy Yellow Tang Moodle

Difference of beating pattern of flagellum and cilia courtesy Wikimedia Commons