Experimental and Computational Investigation of Probiotic‐Induced Tumor–Immune Dynamics in a 4T1 Murine Breast Cancer Model

ABSTRACT

Probiotics have recently attracted considerable attention as potential adjunctive therapies for breast cancer (BC) due to their immunomodulatory and anti‐tumor properties. Here, the therapeutic effects of Bacillus coagulans (B.C) and Bifidobacterium bifidum (B.B) are investigated in a 4T1 murine mammary carcinoma model. To analyze tumor progression and immune response under probiotic intervention, we integrate in vivo observations with a nonlinear spatiotemporal tumor–immune framework. The resulting reaction–diffusion system is solved using a high‐order Legendre–Gauss–Lobatto (LGL) spectral collocation method within an Arbitrary Lagrangian–Eulerian (ALE) moving‐boundary formulation. Both strains significantly reduced tumor volume () and improved survival, with B. coagulans showing stronger enhancement of and nitric oxide (NO) production. The calibrated simulations reproduced the observed tumor regression kinetics and revealed that, post‐treatment, probiotic‐driven immune activation shifts the dynamics toward a locally asymptotically stable tumor‐free state, while exposing a bistable structure in which initial states within the basin of a second, stable, tumor‐persistent equilibrium converge to that persistent state. Integrating high‐order spectral analysis with nonlinear tumor–immune modeling provides a numerically stable, biologically grounded framework for studying probiotic‐mediated cancer immunotherapy, moving‐boundary tumor dynamics, and the conditions separating tumor eradication from persistence.