The Innate Growth Bistability of Antibiotic-Resistant Bacteria - - PowerPoint PPT Presentation

The Innate Growth Bistability

• f 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 𝑢 = 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

• 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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The poor stay poor, and the rich get rich that’s how it goes and everybody knows. – Leonard Cohen, “Everybody knows”

• 2. Ingredients of the model

Ingredient 1: diffusion of Cm into the cell

Cm enters the cell passively, by

• diffusion. Rate:

𝐾influx = 𝜆( Cm ext − Cm int) Here, 𝜆 is the cell’s permeability for Cm.

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Ingredient 2: Inactivation of Cm by the CAT protein.

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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:

𝐾CAT = 𝑊

max

Cm int Cm int + 𝐿m

𝑊

max 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 int

We already assumed:

𝐾influx = 𝜆( Cm ext − Cm int)

𝐾CAT = 𝑊

max

Cm int Cm int + 𝐿m

Dynamics of Cm int:

𝑒 Cm int 𝑒𝑢 = 𝐾influx − 𝐾CAT

The equilibrium concentration of

Cm int is such that: 𝐾influx = 𝐾CAT

𝐃𝐃 𝐣𝐣𝐣

𝐾CAT 𝐾CAT 𝜆 Cm ext

Result: threshold-linear response

Parameters: (Vmax/𝜆) and 𝐿m

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/𝐽50 .

Without Cm: 𝜇0 = 𝛿 Rb total. With Cm: 𝜇 = 𝛿 Rb free. So:

𝜇0 𝜇 = 1 + Cm int 𝐽50

. (Full disclosure: I’m cheating a little, because Rb total depends

• n 𝜇… 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:

𝐹 ∝ 𝜇.

• Empirically:

𝑊

max = 𝑊

𝜇 𝜇0

• Remember:

no regulation.

• How come??

Naive expectation contradicts finding

Typical model of gene expression would be: 𝑒𝑑 𝑒𝑢 = 𝛽 − 𝜇 𝑑 Expected equilibrium: 𝑑∗ = 𝛽 𝜇 . Therefore, naively one would expect 𝑑 to decrease with 𝜇. 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: 𝑒𝑁 𝑒𝑢 = 𝛿𝜚R𝑁, 𝑁 𝑢 ∝ e𝛿𝜚R𝑢 So, growth rate: 𝜇 = 𝛿𝜚R.

?

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

𝐾influx = 𝜆 Cm ext − Cm int (1) 𝐾CAT = 𝑊

max Cm int Cm int+𝐿m

(2) 𝐾influx = 𝐾CAT

𝜇0 𝜇 = 1 + Cm int /𝐽50

(4) 𝑊

max = 𝑊 𝜇 𝜇0

(3) From these equations, 𝜇/𝜇0 can be calculated as a function of Cm ext. The behavior is affected by two dimensionless parameters:

𝜍 ≡

𝑊 𝜆 𝐿m , and 𝜏 ≡ 𝐽50/𝐿m.

• 3. Predictions and verification

Model prediction

If the resistance efficacy 𝜍 is above a critical value 𝜍C, the solution has two stable branches. Growth bistability! Remember that 𝜍 ≡

𝑊 𝜆 𝐿m.

Therefore, we can manipulate 𝜍 by simply changing the promoter driving CAT.

Cm ext

Experimental results

Fit of the model to these data fixes the remaining parameters.

Varying the value of 𝑊

All parameters were fixed by previous slide, except 𝑊

0,

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!