From cells to populations: multi-scale quantitative approaches to antimicrobial resistance

Antimicrobial resistance (AMR) is a critical global health challenge that is increasingly being addressed through quantitative and systems-level approaches. Beyond evolutionary genetics and mutational adaptation, bacterial survival under antibiotics also reflects physiological state transitions and metabolic constraints. We review mathematical models across scales, from population-level approaches to dose optimization, multidrug therapy, community effects, and global epistasis to cellular frameworks based on proteome partitioning and resource allocation. These coarse-grained models reveal how metabolic constraints shape antibiotic action, genetically encoded resistance, and non-genetic tolerance or persistence, particularly for ribosome inhibitors and increasingly for other bacteriostatic and bactericidal drugs. They also identify nonlinear behaviors, including bistability, threshold effects, and regime-dependent resistance strategies. Despite the substantial gap between laboratory models and clinical application, this multiscale framework clarifies the interplay among bacterial metabolism, population dynamics, and antibiotic action. We discuss the achievements and limitations of current approaches and the challenges that must be overcome for clinical translation.