Lecture 20: Physics of Microbial Motility
Today:
Compared to microbes
What’s going on here?
Fish:
Flaps fins once
Keeps moving
Bacteria:
Stops spinning flagella
Instantly comes to a halt
It’s as if the fish is swimming through water, but the bacterium is swimming through honey
But aren’t they swimming in the same water????
Yes, but bacteria have to obey the laws of physics. Let’s take a look.
What is viscosity?
“Thickness” of a fluid → how much internal friction there is between layers of the fluid
(animation from wikipedia)
What is viscosity?
Is there more resistance if you pull faster or slower?
viscous drag from fluid
The more viscous a fluid, the more friction it offers something moving through it.
particle speed
drag force
constant drag coefficient
Which experiences more drag?
fluid
Which experiences more drag?
Drag leads to terminal velocity
Bacteria are effectively swimming at terminal velocity all the time!
What is the drag coefficient?
Use “dimensional analysis”: consider the physical units in the equation, what you think the coefficient should depend on, and how to write the simplest mathematical expression to get the right units
What is the drag coefficient?
Use “dimensional analysis”: consider the physical units in the equation, what you think the coefficient should depend on, and how to write the simplest mathematical expression to get the right units
How does a moving object impact a fluid?
(object velocity)
Fluid flow profile
There is a force required to distort the fluid.
What are the components of this force?
Let’s estimate these effects and then look at what the environment is like when either one dominates
What is the inertial component? (Extremely hand-waving argument)
(object velocity)
Fluid flow profile
What is the viscous component? (Extremely hand-waving argument)
(object velocity)
Fluid flow profile
We found a few slides ago that viscous drag is proportional to the viscosity, particle size, and particle velocity. By Newton’s 3rd law, the viscous force on the fluid is the same!
Viscous vs. inertial fluid forces
(object velocity)
Fluid flow profile
Inertial forces correspond to ballistic flow in response to a pressure difference. Think about turning on a hose or sucking through a straw
Viscous forces correspond to the fluid resisting its own lateral deformations. Think about honey sticking together into thick streams.
How do we characterize a fluid situation as inertial or viscous?
Reynolds number
~human in water:
~bacteria in water:
What viscosity would we need to swim in to experience the world that bacteria do?
Need this to be at least 100,000 times greater than it is for water for the flow to be remotely like it is for bacteria!!!!
Fluid | |
water | 0.01 |
honey | ~1 |
wood rosin | 1-40 |
blackstrap molasses | 100-5,000 |
What viscosity would we need to swim in to experience the world that bacteria do?
Extremely strange fluids that are far beyond our experience
University of Queensland “pitch drop experiment”
Started in October 1930.
How many drops have fallen to date?
“bitumen”: petroleum byproduct
9
High Reynolds number: “our” world
If a fluid starts flowing, after the force that started it flowing stops acting, the flow continues due to the fluid’s inertia:
High Reynolds number: “our” world
Fluid flow is turbulent!
Pressure differences easily drive vortex flows.
Low Reynolds number: world of microbes
Coutanceau (1968)
Low Reynolds number: world of microbes
When driving force of flow stops, there is no inertia. Drag/viscosity kills fluid flow immediately
detergent
Low Reynolds number flow is often described as “deck of cards”-like flow
Here we see three key aspects of low-Reynolds number:
Low Reynolds number flow is reversible
What is the impact of reversible flow for swimming microbes?
Imagine bacteria swam like we do:
?
They couldn’t swim! The reversible nature of low Reynolds number flow would cause them to return to their original position.
What do they do?
Flagella: rigid, rotating corkscrews
25 nm
Flagellum rotates to drive bacteria through water!
How to measure flagellar rotation?
Coat glass with anti-body for flagella
Stick cells
Entire cell bodies of bacteria stuck to glass should rotate
How do flagella propel bacteria?
First look at a rigid rod in viscous, low-Reynolds number environment under two slightly different conditions:
Now think about an oblique rod in a viscous environment
Drag force that cancels gravity
↑ Larger drag force!
Total drag force
Rightward force!
Flagellar rotation
A rotating flagellum is almost like an oblique rod perpetually falling.
Bacterium moves to the right!
Rotation is not “reciprocal” like moving arms back and forth. As long as you spin the flagella, you’ll swim, but you’ll come to a stop immediately upon flagella turning off!
How far will a bacterium “coast”?
?
Less than a millionth of a cell length!!!!
Why swim?
nutrient concentration
Would be good to swim over here!
How?
Swimming toward food
measure concentration here
measure concentration there
Swim toward higher!!
?
~ 3 µm
Would need a shockingly steep gradient to sense a difference at this length scale
What do they do then?
Swimming toward food
nutrient concentration
“Run and tumble”
Results in “biased random walk” behavior
What have we learned?