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Lecture 20: Chemotaxis

Today:

  • Review bacterial swimming
  • Examine the dynamics of bacteria finding food
  • Connect swimming to cellular protein circuits that control swimming
  • Understand how cells sense changes in nutrient concentration over time, not concentration itself
  • See how that becomes a way to find food by coupling the sensing to swimming

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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!

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Simpler example of tilted rod

 

 

 

↑ Larger drag force!

Total drag force

Rightward component!

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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:

  1. Cancelled by components on the other side of the flagellum
  2. Flagellum spinning quickly, so over time the off-axis components cancel each other, but the rightward component is constant

 

 

 

 

 

 

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Why swim?

nutrient concentration

Would be good to swim over here!

How?

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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!

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Swimming toward food

nutrient concentration

“Run and tumble”

  1. Swim straight for a while
  2. If you sense conditions are getting worse, stop swimming to randomly re-orient yourself
  3. Swim straight for a while
  4. Repeat

Results in “biased random walk” behavior

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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?

  • Every so often E. coli stops swimming and tumbles
  • E. coli monitors food concentration in time
  • If concentration is higher than it was in the past, E. coli reduces the probability of initiating a tumble (reverse is true for chemical repellents)
  • Cells sense the rate of change of concentration or its time derivative, not the concentration itself

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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:

  • How does E. coli measure changes in concentration?
    • E. coli is sensitive to 5 orders of magnitude range of attractant concentrations!!!
  • How does E. coli tumble?
  • What are the dynamics of this motion?
  • What is the underlying biological mechanism for this behavior?

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Uniform concentration of nutrients

Time

Tumble freq. (1/sec)

1

nutrient concentration

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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.

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Changing concentration of nutrients

Time

Tumble freq. (1/sec)

1

nutrient concentration

Increase in [nutrient]

Cells sense time changes in concentration

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An experiment to measure E. coli response to changing nutrients

Observe cells in the presence of aspartate and “photo-caged” aspartate

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An experiment to measure E. coli response to changing nutrients

Observe cells in the presence of aspartate and “photo-caged” aspartate

 

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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!)

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E. coli cells adapt after a concentration shift

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Sensory Adaptation

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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 . . .

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flow

flow

Low attractant

High attractant

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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?!?!

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How do bacteria sense food?

A

Y

cell membrane

CheY protein

CheA kinase

attractant

flagellum

flagellar motor

spins counter-clockwise (swimming)

(inactive)

CheW receptor

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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

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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.

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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.

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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

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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?

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Measuring [CheY-GFP] with fluorescence correlation spectroscopy (FCS)

Y

GFP

Y

GFP

  1. Collect fluorescence from diffraction-limited volume with a confocal microscope
  2. Observe the intensity of fluorescence over time
  3. Analyze the signal correlation
  4. Can measure fluorophore concentration and diffusion at the single-molecule level!

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

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Observing flagellar rotation at different CheY concentrations

  1. Induce different levels of CheY-GFP
  2. Observe CheY-GFP concentration with GFP FCS
  3. Directly observe flagellar rotation direction via red light scattered off nano-bead-labeled flagellum

CheY concentration

Directly observe flagellar rotation direction

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Flagella switch to CW at ~3 µM CheY-P!

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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

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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!

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How do cells adapt?

 

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How do cells adapt?

 

 

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How do cells adapt?

K

 

A

4 methylation sites

 

 

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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

 

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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

 

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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

 

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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

 

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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

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How do cells adapt?

A

CH3

CH3

CH3

CH3

CheR

CheB

Y

  1. CheA is active, resulting in more frequent tumbling
  2. Attractant binds
  3. CheA becomes less active, leading to swimming/running
  4. CheB not removing CH3 at the same rate
  5. CheR still adding at the same rate
  6. CheA activity increases, returning to the original rate of tumbling

P

P

cause tumbling

reduce CheA activity

CheB not reducing activity as much

CheR still going at the same rate

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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

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Separation of time scales leads to adaptation time

fast phosphorylation response

slow methylation adaptation

E. coli cells sense temporal changes in concentration!

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Z

Y

Y

P

A

CH3

CheR

CH3

CheB

P

Tumbling

Adaptation

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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?!?!

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What have we learned?

  • E. coli find food by performing a biased random walk toward higher nutrient concentrations (reverse with repellents)
  • The achieve this by sensing changes in concentration over time and coupling that to running-tumbling, converting time change sensing to space change sensing!
  • The time change sensing is achieved through separation of time scales: response happens fast via phosphorylation; adaptation happens slowly via methylation

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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!!!