Lecture 18: Consequences of noise in bacterial gene expression
Today:
In human development, stem cells can go down many paths
Haematopoietic stem cell development
How can you get all these different outcomes from a small group of initially identical cells?
Bacteria go down many different paths in response to stress
Bacillus subtilis
stress
competence
sporulation
motility
metabolic changes
biofilm formation
Vegetative growth
Sometimes referred to as “bet hedging”
What is competence?
+ stress (antibiotics, extreme low nutrients, etc)
soil
B. subtilis lives in the soil
Bacillus
What is competence?
+ stress (antibiotics, extreme low nutrients, etc)
soil
Become competent maybe!
B. subtilis lives in the soil
Competence is a risky strategy
For these reasons, it might be a good strategy for 1) a small proportion of cells to become competent and 2) those cells to stay competent for a short time
How can a cell do this? Take advantage of the noise inherent in gene expression!
Heterogeneous phenotypes in B. subtilis
spore
competence
Under laboratory stress conditions, only 3.6% of cells become competent.
Cells incubated in nutrient-poor conditions
B. subtilis competence is also transient
PcomK
PcomG
How can we understand B. subtilis differentiation into competence?
PcomG-cfp
Small fraction of cells → noise!
Combine these!
This is probably the most math of the semester, so just bear with me!
The B. subtilis competence circuit
ComK is a transcription factor that activates the genes for competence.
High ComK → become competent
The B. subtilis competence circuit
ComK is a transcription factor that activates the genes for competence.
High ComK → become competent
ComK is self-activating
The B. subtilis competence circuit
ComK is a transcription factor that activates the genes for competence.
High ComK → become competent
ComK is self-activating
ComK is one of the few proteins that is actively degraded!
By the MecA-ClpP-ClpC complex.
The B. subtilis competence circuit
ComK is a transcription factor that activates the genes for competence.
High ComK → become competent
ComK is self-activating
ComK is one of the few proteins that is actively degraded!
By the MecA-ClpP-ClpC complex.
ComS competes with ComK for degradation, thereby inhibiting degradation. ComS expressed in all “stressed” cells, not just competent ones.
The B. subtilis competence circuit
ComK is a transcription factor that activates the genes for competence.
High ComK → become competent
ComK is self-activating
ComK is one of the few proteins that is actively degraded!
By the MecA-ClpP-ClpC complex.
ComS competes with ComK for degradation, thereby inhibiting degradation. ComS expressed in all “stressed” cells, not just competent ones.
ComK inhibits ComS!
The B. subtilis competence circuit
1. ComS prevents ComK degradation
2. Which allows ComK to build up to the point of autogeulation
3. But then ComK eventually inhibits comS
4. Stopping the inhibition of ComK degradation!
Leads to transient burst of competence
Let’s see if comK and comS really are anticorrelated in this way.
YFP
P
comS
(competence gene activated by ComK)
Fluorescence trace from cell that becomes competent
Fluorescence trace from sibling cell that does not become competent
Let’s look at a model of this gene circuit. Bear with me!!
B. subtilis competence circuit model
basal production rate
self-activation
What about this complicated degradation dynamics??
Forgive me! It’s a lot of math, so I’ll just write their expression and explain it!
B. subtilis competence circuit model
basal production rate
self-activation
degradation by MecA
degradation by MecA
What kind of dynamics does this model predict???
With 2 bacterial species, we learned a lot looking at the phase plane!
Reviewing phase planes and stability in 2 species
coexistence
bistability
single-species dominance
These equations tell us how the system moves around the phase plane
Are there stable points for ComK and ComS?
Competence phase plane
1
2
3
0
[ComK] (a.u.)
0
2
4
6
[ComS] (a.u.)
high ComK → cell becomes competent
Steady states!
Are they stable or unstable?
Competence phase plane
1
2
3
0
[ComK] (a.u.)
0
2
4
6
[ComS] (a.u.)
high ComK → cell becomes competent
Steady states!
Are they stable or unstable?
Competence phase plane
1
2
3
0
[ComK] (a.u.)
0
2
4
6
[ComS] (a.u.)
high ComK → cell becomes competent
Are they stable or unstable?
This point is stable, but not very stable!
Competence phase plane
1
2
3
0
[ComK] (a.u.)
0
2
4
6
[ComS] (a.u.)
high ComK → cell becomes competent
Are they stable or unstable?
This point is stable, but not very stable!
Say we have a low concentration of ComK and high ComS (turned on with stress).
The system should stay near the stable point (low ComK/no competence)
Competence phase plane
1
2
3
0
[ComK] (a.u.)
0
2
4
6
[ComS] (a.u.)
high ComK → cell becomes competent
Are they stable or unstable?
This point is stable, but not very stable!
What happens if there is a fluctuation in ComS level, preventing degradation of ComK?
Competence phase plane
1
2
3
0
[ComK] (a.u.)
0
2
4
6
[ComS] (a.u.)
high ComK → cell becomes competent
Are they stable or unstable?
This point is stable, but not very stable!
These dynamics take over, causing K to spike and the system to traverse the whole phase plane around the unstable states and back to the stable point!
What happens if there is a fluctuation in ComS level, preventing degradation of ComK?
Add this into the model by incorporating noise!!!
Competence phase plane
1
2
3
0
[ComK] (a.u.)
0
2
4
6
[ComS] (a.u.)
high ComK → cell becomes competent
Are they stable or unstable?
This point is stable, but not very stable!
Add this into the model by incorporating noise!!!
A term that varies randomly in time
These dynamics take over, causing K to spike and the system to traverse the whole phase plane around the unstable states and back to the stable point!
How does this noise term work?
How does this noise term work?
With noise, there is a small, extra term whose value is taken randomly at each time step, adding stochasticity to the solution!
Now no two solutions are the same!
Modeling competence with noise
Many iterations of the model with noise!
Modeling competence with noise
Random fluctuations/noise in ComS!
When ComS exceeds a certain threshold, there is a ComK pulse!
Modeling competence with noise
The vast majority of the time, the system is near the stable state of low ComK, but with a rare noisy ComS spike…
The dynamics of the regulation circuit drive the system to competence!
And the model predicts that feedback between ComK and ComS exit out of competence back to the “vegetative” state
Does this sound familiar?
Neuronal cell culture
Membrane potential
Neuronal action potentials: an excitable system
Prediction: feedback exits competence
ComK
ClpP
ClpC
MecA
ComS
comK
PcomK
comS
PcomS
The authors create a new strain where the feedback is broken!
Prediction: feedback exits competence
ComK
ClpP
ClpC
MecA
ComS
comK
PcomK
comS
PcomS
comS
PcomG
Add a new copy of comS that is activated by ComK
Prediction: feedback exits competence
ComK
ClpP
ClpC
MecA
ComS
comK
PcomK
comS
PcomS
comS
PcomG
This strain cannot exit competence!
B. subtilis competence strategy
PcomG-cfp
Small fraction of cells
Transient
How does B. subtilis achieve this?
PcomG-cfp
Small fraction of cells trying competence?
Use gene noise spikes
Transient time in the competence state?
Feedback w/excitable dynamics
Is competence really initiated by noise?
If it is, then by reducing the cell-to-cell gene expression noise, the dynamics of competence should change.
How do you do that? Create cells that don’t divide. These cells “average” out the noise of several cytoplasms.
ftsW -
DAPI
Long cells still initiate competence
Lengthening cells does reduce noise
2
4
6
8
10
0
1
2
Normalized cell length
Normalized YFP concentration
Experiment
Model
The model predicts a lower probability of entering competence with longer, less noisy cells
simulations
What do we see experimentally?
experiments
Strong evidence that noise initiates competence!
What have we learned?
PcomG-cfp