Swimming microbes steer themselves into mathematical order

March 4, 2019 by Chris Barncard, University of Wisconsin-Madison
A sheet of tiny swimming organisms that “push” themselves through fluid with, say, flagella, create forces in the liquid that bend the sheet in asymmetric, shrinking folds. Credit: Saverio Spagnolie

Freeing thousands of microorganisms to swim in random directions in an infinite pool of liquid may not sound like a recipe for order, but eventually the swarm will go with its own flow.

Theoretical modeling led by University of Wisconsin–Madison applied mathematician Saverio Spagnolie shows that the forces generated by different kinds of tiny swimmers will sweep them all up in predictable ways.

"When each individual particle experiences the flows created by all the other particles, it's known that really surprising effects can naturally emerge," says Spagnolie. "The flows and orientations of the swimmers become coherent on a length scale much longer than any individual particle, resulting in huge flocks of organisms swimming in the same direction and, perhaps unintentionally, working together."

The movement of crowds of things too small to easily see—like and filaments inside responsible for cell-division—is critically important to research in materials science, engineering and biochemistry.

By simulating the interactions of large groups of particles which each create a flow, Spagnolie and Arthur Evans of UW–Madison, University of Michigan physicist Christopher Miles and mathematician Michael Shelley of the Flatiron Institute and New York University found that when the particles are confined to a thin sheet and allowed to expand into an empty , the collective motion can be described by equations already used in entirely different classical problems in . The group published its findings today in the journal Physical Review Letters.

"If you're solving for the trajectory of 10,000 or 100 or even 10 things bouncing around, it's hard to see what's going on. You can lose sight of deep structure," says Spagnolie, whose work is supported by the National Science Foundation. "But if there are enough particles, they can be seen themselves as a type of active fluid, with equations describing the velocity and density of a local group of particles—just like how we think about deriving equations to describe flowing water or air."

When a computer simulation of a sheet of swimming particles (yellow marks their highest concentration, blue empty liquid) is nudged into action, the forces and flows bend, disperse and gather the organisms in what looks like coherent flocks. Credit: Saverio Spagnolie

The researchers worked out the relevant equations for particles that move by various means—swimmers that actively push or pull themselves through fluid, and types (like microtubules inside a cell) that push or pull themselves through molecular means without active appendages like flagella—and goosed them into motion.

"From that perturbation there's this explosion of motion," Spagnolie says. "And then we watch how the different forces play out on different types of particles."

While a tight colony of pulling swimmers, for example, stretches itself out in a line perpendicular to the direction they're headed, a colony of pushers stretches quickly in the direction of motion, and then bends on itself over and over in a cascade of shrinking folds.

"That these individuals can group together passively due to their fluid interactions alone, and that this results in large-scale events and effects they can't achieve as independent particles, is relevant to many biological functions—like nutrient mixing and bacterial resistance to antibiotics in bacterial swarms and biofilms," Spagnolie says.

The researchers believe their theoretical description of the rapid growth of active sheets—which unexpectedly resembled well-known equations like those used to describe the movement of fluids trapped between plates or dispersed through soil—will be of use to others working at the point where fluids interact with miniature movers like bacteria and microtubules.

"This is one of the first theoretical considerations of concentrated invading a bulk fluid," Spagnolie says. "The hope is that this will be a case of theory leading experiment, offering predictions that can be validated or invalidated by researchers who are very much on the edge of carrying such an experiment out."

Explore further: High-angle helix helps bacteria swim

More information: Rafael D. Schulman et al. Droplets Capped with an Elastic Film Can Be Round, Elliptical, or Nearly Square, Physical Review Letters (2018). DOI: 10.1103/PhysRevLett.121.248004

Related Stories

High-angle helix helps bacteria swim

August 13, 2013

(Phys.org) —A high-angle helix helps microorganisms like sperm and bacteria swim through mucus and other viscoelastic fluids, according to a new study by researchers from Brown University and the University of Wisconsin. ...

Physicists experimentally verify 40-year-old fluid equations

August 27, 2018

For decades, researchers have been using equations derived in the mid-1970s for a variety of fluid applications involving inks, foams, and bubbles, among other uses. These fundamental fluid equations describe how much force ...

Researchers explain emergence of bacterial vortex

June 23, 2014

When a bunch of B. subtilis bacteria are confined within a droplet of water, a very strange thing happens. The chaotic motion of all those individual swimmers spontaneously organizes into a swirling vortex, with bacteria ...

Tiny 'racetracks' show how bacteria get organized

July 13, 2016

As the world prepares to watch the Summer Olympics' track and field events in Rio, it will come as no surprise that the runners in each race travel in the same direction around the track. But new research shows that if those ...

Squished cells could shape design of synthetic materials

May 4, 2016

Life is flexible. All living cells are basically squishy balloons full of water, proteins and DNA, surrounded by oily membranes. Those membranes stand up to significant amounts of stretching and bending, but only recently ...

Recommended for you

Coffee-based colloids for direct solar absorption

March 22, 2019

Solar energy is one of the most promising resources to help reduce fossil fuel consumption and mitigate greenhouse gas emissions to power a sustainable future. Devices presently in use to convert solar energy into thermal ...

Physicists reveal why matter dominates universe

March 21, 2019

Physicists in the College of Arts and Sciences at Syracuse University have confirmed that matter and antimatter decay differently for elementary particles containing charmed quarks.

ATLAS experiment observes light scattering off light

March 20, 2019

Light-by-light scattering is a very rare phenomenon in which two photons interact, producing another pair of photons. This process was among the earliest predictions of quantum electrodynamics (QED), the quantum theory of ...

How heavy elements come about in the universe

March 19, 2019

Heavy elements are produced during stellar explosion or on the surfaces of neutron stars through the capture of hydrogen nuclei (protons). This occurs at extremely high temperatures, but at relatively low energies. An international ...

0 comments

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.