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. 9µ M 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 The poor stay poor, and the rich get rich that’s how it goes and everybody knows. 1 – Leonard Cohen, “Everybody knows” • We expect a funny kind of 3 positive feedback loop. • Positive feedback can lead 2 to bistability. • At the end of this lecture, you should be able to 4 understand this model, and why it explains growth bistability.
2. Ingredients of the model
Ingredient 1: diffusion of Cm into the cell Cm enters the cell passively, by diffusion. Rate: 1 𝐾 influx = 𝜆 ( Cm ext − Cm int ) 3 Here, 𝜆 is the cell’s permeability for Cm. 2 4
Ingredient 2: Inactivation of Cm by the CAT protein. 1 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: Cm int 𝐾 CAT = 𝑊 max Cm int + 𝐿 m 𝑊 max depends on the concentration of the enzyme CAT.
Ingredient 1+ ingredient 2: What is Cm int as a function of Cm ext ? A 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: 𝐾 influx = 𝜆 ( Cm ext − Cm int ) Cm int 𝜆 Cm ext 𝐾 CAT = 𝑊 max Cm int + 𝐿 m 𝐾 CAT Dynamics of Cm int : d Cm int = 𝐾 influx − 𝐾 CAT 𝐾 CAT d 𝑢 The equilibrium concentration of Cm int is such that: 𝐾 influx = 𝐾 CAT 𝐃𝐃 𝐣𝐣𝐣
Result: threshold-linear response Effective parameters: (V max / 𝜆 ) and 𝐿 m
Ingredient 3: Effect of Cm on growth rate 1 3 2 4
Ingredient 3: Effect of Cm on growth rate Binding reaction: Cm + Rb ↔ Cm ⋅ Rb. Rb free 𝐽 50 1 Rb total = 𝐽 50 + Cm int = 1+ Cm int / 𝐽 50 . Equilibrium: Without Cm: 𝜇 0 = 𝛿 Rb total . 𝜇 = 𝛿 Rb free . With Cm: 𝜇 0 Cm int 𝜇 = 1 + . So: 𝐽 50 (Full disclosure: I’m cheating a little, because Rb total depends on 𝜇 … Luckily, linearity remains in a more careful derivation.)
Ingredient 4: Effect of growth rate on CAT expression 1 3 2 4
Effect of growth rate on expression of unregulated genes • Empirically: 𝐹 ∝ 𝜇 . • Empirically: 𝜇 𝑊 max = 𝑊 0 𝜇 0 • Remember: no regulation. • How come??
Naively, one would expect an opposite trend! 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 = 𝛿𝜚 R 𝑁 , 𝑁 𝑢 ∝ e 𝛿𝜚 R 𝑢 So, growth rate: 𝜇 = 𝛿𝜚 R .
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 𝐾 influx = 𝜆 Cm ext − Cm int (1) Cm int 𝐾 CAT = 𝑊 Cm int +𝐿 m (2) max 𝐾 influx = 𝐾 CAT 𝜇 0 𝜇 = 1 + Cm int / 𝐽 50 (4) 𝜇 𝑊 max = 𝑊 𝜇 0 (3) 0 From these equations, 𝜇 / 𝜇 0 can be calculated as a function of Cm ext . The behavior is affected by two dimensionless parameters: 𝑊 0 𝜍 ≡ 𝜆 𝐿 m , and 𝜏 ≡ 𝐽 50 / 𝐿 m .
3. Predictions and verification
Model prediction If the resistance efficacy 𝜍 is above a critical value 𝜍 C , the solution has two stable branches. Growth bistability! 𝑊 0 Remember that 𝜍 ≡ 𝜆 𝐿 m . Therefore, we can manipulate 𝜍 by simply Cm ext changing the promoter driving CAT.
Experimental results Fit of the model to these data fixes the remaining parameters.
Varying the value of 𝑊 0 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.)
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