Phenotypic plasticity trade-offs in an age-structured model of bacterial growth under stress

TL;DR

Under a more realistic configuration of periodic stress, the results indicate that optimal population growth can only be achieved through fine-tuning simultaneously both the induction of the stress response and the repair efficiency of the damage caused by the antibiotic.

Abstract

Under low concentrations of antibiotics causing DNA damage, \textit{Escherichia coli} bacteria can trigger stochastically a stress response known as the SOS response. While the expression of this stress response can make individual cells transiently able to overcome antibiotic treatment, it can also delay cell division, thus impacting the whole population's ability to grow and survive. In order to study the trade-offs that emerge from this phenomenon, we propose a bi-type age-structured population model that captures the phenotypic plasticity observed in the stress response. Individuals can belong to two types: either a fast-dividing but prone to death ``vulnerable'' type, or a slow-dividing but ``tolerant'' type. We study the survival probability of the population issued from a single cell as well as the population growth rate in constant and periodic environments. We show that the sensitivity of these two different notions of fitness with respect to the parameters describing the phenotypic plasticity differs between the stochastic approach (survival probability) and the deterministic approach (population growth rate). Moreover, under a more realistic configuration of periodic stress, our results indicate that optimal population growth can only be achieved through fine-tuning simultaneously both the induction of the stress response and the repair efficiency of the damage caused by the antibiotic.

Figures (8)

• Figure 1: Schematic representation of the cell division mechanism and age.
• Figure 2: Form of $q$ as function of $\alpha$ in the case of division times following a Gamma distribution of parameters $(a_0, b_0)$ (Example \ref{['ex:gammaBeta0']}). Note that $q$ is always an increasing function of $\alpha$.
• Figure 3: Laplace transforms of division times of type 0 ($\xi_0$, blue dashed line) and type 1 ($\xi_1$, red solid line), and the translation $(1-p)\xi_0(\cdot + \alpha)$ (blue solid line). When $\gamma = 0$, the population growth rate is the largest value of $\lambda$ at which one of the two latter functions (solid lines) pass through $1/2$.
• Figure 4: Illustration of Propositions \ref{['prop:dgamma']} and \ref{['prop:dlambdaGamma_equiv']}.
• Figure 5: Parabolic curves defined by \ref{['eq:pi0']} (red) and \ref{['eq:pi1']} (blue) for $p = 0.6$. In the first case we have $\gamma = 0.3 < 1/2$ and $q = 0.4$. In the second case we have $\gamma = 0.6 > 1/2$ and $q = 0.4$. In the third case we have $\gamma = 0.6$ and $q = 0.02$, so the condition \ref{['eq:extinctionCondition']} is violated and the only intersection in the unit square is (1,1).

Theorems & Definitions (65)

• Definition 2.2
• Lemma 2.3
• proof
• Remark 2.5
• Definition 3.1
• Theorem 3.2
• Remark 3.3
• Remark 3.4
• Example 3.5: Gamma distributed inter-division times
• Theorem 3.6