Temporal changes in the algebraic connectivity of collateral sensitivity maps.

Abstract

e15007 Background: Drug resistance remains one of the greatest challenges in oncology, often limiting the long-term efficacy of cancer therapies. Collateral sensitivity, the phenomenon where resistance to one therapy alters susceptibility to others, offers a potential strategy to overcome treatment failure in cancer. Nevertheless, majority of the studies characterize this phenomenon at endpoints naively assuming complete sampling of the underlying evolutionary mechanisms, agnostic to the evolutionary trajectories. Thus, temporal dynamics of collateral sensitivity and/or how much observational variance due to under sampling exists remains largely unexplored. Methods: We developed a spatial cellular automata model to study temporal dynamics on a latent continuous space. Individual cells occupy a two-dimensional grid and undergo stochastic proliferation, death, and mutation. Each cell carries a continuous genotype vector that maps to multi-drug response phenotypes through a non-linear mapping determining the “fitness” of individual clones allowing selective pressure to shape the evolutionary trajectories. The phenotype values (collateral responses induced by the drug of interest) for each cell were tracked over time and the drug-drug mutual-information matrices were calculated across the population of cells at each timepoint. To characterize the change in drug-drug associations during resistance evolution, we examined the phenotype-covariance network and associated spectral properties of the graph Laplacians. Results: We performed the simulations under different scenarios: drug/no-drug, single/multi -peaked landscape. As expected, the diversity of the genotype space was higher under no-drug condition as opposed to treatment condition. Interestingly however, the fiedler value (algebraic connectivity) of the MI matrices showed a non-linear pattern, initially increasing and subsequently decreasing in the drug treatment setting. In contrast under no drug treatment the fiedler value continued to increase. Conclusions: This framework provides a flexible, quantitative approach to studying collateral sensitivity in continuous tumor phenotypes, moving beyond static or discrete models. By examining temporal changes in algebraic connectivity, we observe distinct patterns under selection and no selection conditions, highlighting that collateral sensitivity maps are not fixed properties but evolve over time. These results suggest that quantifying collateral sensitivity depends on both evolutionary context and sampling of the underlying phenotype space, including factors such as treatment pressure and landscape structure. Overall, this model establishes a foundation for future work aimed at understanding how evolving phenotypic organization impacts multi-drug response and adaptive therapy strategies.