Lecture 20: Chemotaxis
Today:
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!
Simpler example of tilted rod
↑ Larger drag force!
Total drag force
Rightward component!
Flagellar rotation
A rotating flagellum is almost like an oblique rod perpetually falling.
Bacterium moves to the right!
Shouldn’t there be an off-axis component of motion?
2 things:
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?
By swimming, they change a concentration gradient in space to a concentration change in time!
Swimming toward food
nutrient concentration
“Run and tumble”
Results in “biased random walk” behavior
Run and tumble
Berg, E. coli in motion (2004)
10 µm
Runs
(~1 second on average)
Tumbles
(~0.1 seconds on average)
How does E. coli find food with this strategy?
Run and tumble
Berg, E. coli in motion (2004)
10 µm
Runs
(~1 second on average)
Tumbles
(~0.1 seconds on average)
Questions to answer:
Uniform concentration of nutrients
Time
Tumble freq. (1/sec)
1
nutrient concentration
This is just like our diffusion example from week 1!
In the absence of a concentration gradient, cells will move around like this, without any overall direction.
Changing concentration of nutrients
Time
Tumble freq. (1/sec)
1
nutrient concentration
Increase in [nutrient]
Cells sense time changes in concentration
An experiment to measure E. coli response to changing nutrients
Observe cells in the presence of aspartate and “photo-caged” aspartate
An experiment to measure E. coli response to changing nutrients
Observe cells in the presence of aspartate and “photo-caged” aspartate
E. coli cells shift their tumbling rate in response to a time change in nutrient concentration
(Rate of change of flagellum direction, related to tumbling frequency!)
E. coli cells adapt after a concentration shift
Sensory Adaptation
Couple concentration derivative sensing to tumbling frequency → swim toward food!
While swimming perpendicular to the gradient, concentration is not changing in time. Start tumbling!
Concentration is increasing in time while swimming in this direction → tumbling unlikely.
Eventually the cell will tumble again.
Etc . . .
flow
flow
Low attractant
High attractant
Couple concentration derivative sensing to tumbling frequency → swim toward food!
While swimming perpendicular to the gradient, concentration is not changing in time. Start tumbling!
Concentration is increasing in time while swimming in this direction → tumbling unlikely.
Eventually the cell will tumble again.
Etc . . .
How do they do this?!?!
How do bacteria sense food?
A
Y
cell membrane
CheY protein
CheA kinase
attractant
flagellum
flagellar motor
spins counter-clockwise (swimming)
(inactive)
CheW receptor
How do bacteria sense food?
A
Z
Y
Y
P
cell membrane
CheY protein
CheA kinase
attractant
flagellum
flagellar motor
spins counter-clockwise (swimming)
CheA activates!
Y
P
spins clockwise (tumbling)!
(inactive)
CheZ phosphatase
At a steady-state concentration, the opposing action of CheA and CheZ lead to a steady-state YP concentration and hence a constant probability of tumbling.
CheW receptor
Why does CW spinning lead to tumbling?
We saw last time that on the length scale of a bacterium, viscous drag from the fluid overwhelms inertia, so the cell comes to a stop immediately upon flagellar rotation stopping.
For the same reason, when the cell stops swimming, it will not randomly spin around to reorient itself. It must actively change its direction.
Why does CW spinning lead to tumbling?
Under normal swimming, there is a flagellar bunch. When they all rotate counter-clockwise, the cell move forward.
If one goes clockwise, it will break the bunch breaks and the cell turns.
The tumbling frequency increases with higher [Yp]
A
Z
Y
Y
P
active CheA
spins counter-clockwise (swimming)
Y
P
spins clockwise (tumbling)!
A
inactive CheA
Measuring flagellar bias as a function of Yp concentration
CheY
GFP
Inducible promoter
CheY has a fluorescent label.
Can’t distinguish between CheY and CheYP, but authors assume that if concentration of CheY goes up via induction, then CheYP will increase proportionally
Flagella labeled with nano-scale bead for optical imaging.
Authors can now observe CheY and flagella activity and correlate them. But how do they know the CheY concentration?
Measuring [CheY-GFP] with fluorescence correlation spectroscopy (FCS)
Y
GFP
Y
GFP
Time
GFP Int.
GFP
Y
If molecules diffuse slowly, this will be long and the signal will be correlated with itself over long time scales
If concentration is low, there will tend to be 0-1 molecules in the volume at a time, leading to high correlation at short time scales
Observing flagellar rotation at different CheY concentrations
CheY concentration
Directly observe flagellar rotation direction
Flagella switch to CW at ~3 µM CheY-P!
How do bacteria sense food?
A
Z
Y
Y
P
cell membrane
CheY protein
CheA kinase
attractant
flagellum
flagellar motor
spins counter-clockwise (swimming)
CheA activates!
Y
P
spins clockwise (tumbling)!
(inactive)
CheZ phosphatase
How does CheA become less active in the presence of nutrients/attractants?
CheW receptor
Attractants increase [YP] by lowering CheA activity
(log(C))
A
A
A
Receptor clustering leads to cooperative binding
More attractant, less CheA activity, less tumbling!
How do cells adapt?
How do cells adapt?
How do cells adapt?
K
A
4 methylation sites
How do cells adapt?
K
A
CH3
4 methylation sites
Each time the receptor complex is methylated, it becomes more active → more attractant is needed to prevent tumbling
How do cells adapt?
K
Each time the receptor complex is methylated, it becomes more active → more attractant is needed to prevent tumbling
A
CH3
4 methylation sites
CH3
How do cells adapt?
K
A
CH3
4 methylation sites
CH3
Each time the receptor complex is methylated, it becomes more active → more attractant is needed to prevent tumbling
CH3
How do cells adapt?
K
Each time the receptor complex is methylated, it becomes more active → more attractant is needed to prevent tumbling
A
CH3
4 methylation sites
CH3
CH3
CH3
How do cells adapt?
A
CH3
CH3
CH3
CH3
CheR
CheB
The CheR enzyme adds methyl groups to the receptor complex
The CheB enzyme removes methyl groups from the receptor complex
The key for adaptation is that in its active conformation, i.e. more methyl groups, CheA also phosphorylates CheB to cause it to remove methyl groups!
P
This competition is always happening, even without sensing any attractant
How do cells adapt?
A
CH3
CH3
CH3
CH3
CheR
CheB
Y
P
P
cause tumbling
reduce CheA activity
CheB not reducing activity as much
CheR still going at the same rate
Separation of time scales leads to adaptation time
A
CH3
CheR
Y
Y
P
Phosphorylation reaction + diffusion to flagellar motor: ~microseconds to milliseconds
Methylation reaction: very flow, ~seconds to minutes
Separation of time scales leads to adaptation time
fast phosphorylation response
slow methylation adaptation
E. coli cells sense temporal changes in concentration!
Z
Y
Y
P
A
CH3
CheR
CH3
CheB
P
Tumbling
Adaptation
Coupling time derivative sensing to swimming converts a temporal response circuit into a spatial one!!!
While swimming perpendicular to the gradient, concentration is not changing in time. Start tumbling!
Concentration is increasing in time while swimming in this direction → tumbling unlikely.
Eventually the cell will tumble again.
Etc . . .
How do they do this?!?!
What have we learned?
Almost every area of science is necessary to understand bacterial chemotaxis!!
Physics: swimming/tumbling, concentration sensing
Genetics: molecular pathways
Biochemistry: time scales of phosphorylation and methylation reactions; conformational changes of receptors, etc
Z
Y
Y
P
A
CheR
CheB
P
Y
Y
P
Together a fundamental problem in biology!!!