Analysis of persistence thresholds for a nonlocal PDE--ODE model of bacterial persister cells
Chongming Li, Tyler Meadows, Troy Day
TLDR
This paper analyzes a PDE-ODE model to identify a sharp parameter threshold for bacterial persister cell persistence, independent of internal structure.
Key contributions
- Analyzes a nonlocal PDE-ODE model describing epigenetic inheritance in bacterial persister cells.
- Establishes mathematical well-posedness, including existence, uniqueness, and nonnegativity of solutions.
- Identifies a sharp parameter threshold that determines colony extinction or persistence.
- Demonstrates this critical persistence threshold is independent of the internal community structure.
Why it matters
This study provides a robust mathematical framework for understanding bacterial persister cells, which are critical for antibiotic resistance. Identifying a sharp persistence threshold helps predict colony survival and informs strategies against resistant infections.
Original Abstract
Within many bacterial colonies, persister cells exist as a subpopulation that is tolerant to antibiotics and other stressors, yet not genetically distinct from the rest of the colony. A recent study has proposed epigenetic inheritance as a mechanism that leads to the presence of persister cells. We analyze a nonlocal PDE--ODE model introduced in that study to describe the epigenetic inheritance process and establish its mathematical well-posedness, including existence, uniqueness, and nonnegativity of solutions. We identify a sharp parameter threshold delineating extinction from persistence of the colony: below this threshold the washout equilibrium is globally asymptotically stable, while above it a unique positive equilibrium exists and the population is weakly persistent. Notably, this threshold is independent of the internal community structure.
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