The Innate Growth Bistability
of Antibiotic-Resistant Bacteria
Rutger Hermsen
1. Introduction
Antibiotic-resistant bacteria: a major health concern
World Health Organization (2014):
“This serious threat is no longer a prediction for the future, it is
happening right now in every region of the world and has the
potential to affect anyone, of any age, in any country. Antibiotic
resistance (…) is now a major threat to public health”
Today, we will discuss the following paper
Growth bistability observed in resistant cells
Growth of E. coli bacteria
carrying an unregulated
resistance gene (CAT),
in sub-lethal antibiotic
concentration (0.9µM
chloramphenicol).
Cm added at time 𝑡 = 0.
Halted cells resume growth after Cm is removed
Medium with lower Cm
concentration (0.1 µM)
is flown in after 24 h.
After some time, the cells
resume growth.
Conclusions from movie clip
Spontaneous formation of two subpopulations:
• Some bacteria grow just fine.
• Other bacteria completely stop growing
• The non-growing cells are not dead: they resume
growth after chloramphenicol is removed.
Actually… predicted by a quantitative model
The poor stay poor,
and the rich get rich
that’s how it goes
and everybody knows.
– Leonard Cohen, “Everybody knows”
• We expect a funny kind of
positive feedback loop.
• Positive feedback can lead
to bistability.
• At the end of this lecture,
you should be able to
understand this model,
and why it explains growth
bistability.
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2. Ingredients of the model
Ingredient 1: diffusion of Cm into the cell
Cm enters the cell passively, by
diffusion. Rate:
𝐽influx = 𝜅( Cm
ext
− Cm
1
int )
Here, 𝜅 is the cell’s permeability
for Cm.
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2
4
Ingredient 2:
Inactivation of Cm by the CAT protein.
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3
2
4
Chloramphenicol (Cm) vs CAT
Cm: A prototypical broad-band antibiotic.
Bacteriostatic drug; works by binding to the 50S ribosomal
subunit, preventing protein chain elongation.
CAT (Cm acetyltransferase):
Covalently attaches acetyl group
to chloramphenicol, preventing
it from binding to ribosomes.
Ingredient 2:
Inactivation of Cm by the CAT protein.
Assume standard Michaelis-Menten kinetics:
𝐽CAT = 𝑉max
Cm int
Cm int + 𝐾m
𝑉max depends on the
concentration of the
enzyme CAT.
Cm
int
as a function of Cm
ext :
Dutch analogy
As long as the capacity of the
wind mill exceeds the leakage
into the polder, the water level
in the polder stays low.
?
If the leakage exceeds the
capacity of the wind mill, the
polder floods.
The equilibrium value of Cm
We already assumed:
𝐽influx = 𝜅( Cm
𝐽CAT = 𝑉max
int
− Cm
Cm int
Cm int + 𝐾m
Dynamics of Cm
𝑑 Cm
𝑑𝑡
ext
int )
int :
= 𝐽influx − 𝐽CAT
The equilibrium concentration of
Cm int is such that:
𝐽influx = 𝐽CAT
𝜅 Cm
ext
int
𝐽CAT
𝐽CAT
𝐂𝐂
𝐢𝐢𝐢
Result: threshold-linear response
Parameters: (Vmax /𝜅) and 𝐾m
Ingredient 3: Effect of Cm on growth rate
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Ingredient 3: Effect of Cm on growth rate
Binding reaction: Cm + Rb ↔ Cm ⋅ Rb.
Equilibrium:
Rb free
Rb total
=
1
.
1+ Cm int /𝐼50
Without Cm: 𝜆0 = 𝛾 Rb
With Cm:
So:
𝜆0
𝜆
=1+
𝜆 = 𝛾 Rb
Cm int
.
𝐼50
total .
free .
(Full disclosure: I’m cheating
a little, because Rb total depends
on 𝜆… Luckily, linearity remains
in a more careful derivation.)
Ingredient 4: Effect of growth rate on CAT expression
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Effect of growth rate on expression of unregulated genes
• Empirically:
𝐸 ∝ 𝜆.
• Empirically:
𝑉max = 𝑉0
𝜆
𝜆0
• Remember:
no regulation.
• How come??
Naive expectation contradicts finding
Typical model of gene expression would be:
𝑑𝑐
=𝛼−𝜆𝑐
𝑑𝑡
Expected equilibrium:
𝛼
∗
𝑐 = .
𝜆
Therefore, naively one would expect 𝑐 to decrease with
𝜆. The opposite is found!
The answer:
Ribosome concentration increases with growth rate,
if nutrient quality is varied
This can be understood:
faster growth requires a larger
rate of protein synthesis.
?
Protein mass:
𝑑𝑀
= 𝛾𝜙R 𝑀,
𝑑𝑡
𝑀 𝑡 ∝ e𝛾𝜙R 𝑡
So, growth rate:
𝜆 = 𝛾𝜙R .
Ribosome concentration decreases with growth rate,
if Cm is varied instead
Remember: Cm inhibits ribosomes.
Interpretation: The cell perceives
interference by Cm as a Rb
shortage, and responds by
synthesizing more of them.
?
Plausible regulation:
Un-regulated genes respond differently to
nutrient changes and antibiotic changes.
Interpretation:
Given a fixed cell density, if the
cell invests in a large
concentration of ribosomes
(up to 50% of protein mass!),
this must lead to a reduced
concentration of other proteins.
Proteome partitioning
Better nutrient
Growth rate increases
Growth rate decreases
Putting everything together
𝐽influx = 𝜅 Cm
ext
− Cm
𝐽CAT = 𝑉max
Cm int
Cm int +𝐾m
𝜆0
𝜆
int /𝐼50
𝐽influx = 𝐽CAT
= 1 + Cm
𝑉max = 𝑉0
𝜆
𝜆0
int
(1)
(2)
(4)
(3)
From these equations, 𝜆/𝜆0 can be calculated
as a function of Cm ext .
The behavior is affected by two dimensionless
parameters:
𝜌≡
𝑉0
,
𝜅 𝐾m
and
𝜎 ≡ 𝐼50 /𝐾m .
3. Predictions and verification
Model prediction
If the resistance efficacy 𝜌
is above a critical value 𝜌C ,
the solution has two stable
branches.
Growth bistability!
Remember that 𝜌 ≡
Cm
ext
𝑉0
.
𝜅 𝐾m
Therefore, we can
manipulate 𝜌 by simply
changing the promoter
driving CAT.
Experimental results
Fit of the model to these data
fixes the remaining parameters.
Varying the value of 𝑉0
All parameters were fixed
by previous slide, except 𝑉0 ,
which can be measured
independently.
Excellent fits result.
4. Discussion & conclusions
Discussion & Conclusions
• Strains with unregulated resistance genes can show bistable
growth when exposed to the drug. (We showed this for
chloramphenicol, tetracycline, and minocycline.)
• No specific regulation required, no molecular cooperativity
required.
• Cannot be understood from “local” genetic circuits; the result of
global constraints and the organization of bacterial growth
control.
• Calls into question basic notions of drug resistance, such as
MIC, which is based on bulk measurements instead of behavior
at the single-cell level.
• Growth bistability can have effects on drug-drug interactions.
E.g., cells that do not grow are not killed by ampicillin. (Blocks
cell wall synthesis.)
Thanks!