Deciphering population-level response under spatial drug heterogeneity on microhabitat structures

Bacteria and cancer cells live in a spatially heterogeneous environment, where migration shapes the microhabitat structures critical for colonization and metastasis. The interplay between growth, migration, and microhabitat structure complicates the prediction of population responses to drugs, such as clearance or sustained growth, posing a longstanding challenge. Here, we disentangle growth-migration dynamics and identify that population decline is determined by two decoupled terms: a spatial growth variation term and a microhabitat structure term. Notably, the microhabitat structure term can be interpreted as a dynamic-related centrality measure. For fixed spatial drug arrangements, we show that interpreting these centralities reveals how different network structures, even with identical edge densities, microhabitat numbers, and spatial heterogeneity, can lead to distinct population-level responses. Increasing edge density shifts the population response from growth to clearance, supporting an inversed centrality-connectivity relationship, and mirroring the effects of higher migration rates. Furthermore, we derive a sufficient condition for robust population decline across various spatial growth rate arrangements, regardless of spatial-temporal fluctuations induced by drugs. Additionally, we demonstrate that varying the maximum growth-to-death ratio, determined by drug-bacteria interactions, can lead to distinct population decline profiles and a minimal decline phase emerges. These findings address key challenges in predicting population-level responses and provide insights into divergent clinical outcomes under identical drug dosages. This work may offer a new method of interpreting treatment dynamics and potential approaches for optimizing spatially explicit drug dosing strategies.