Modeling multiple taxis: Tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence

Abstract

We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating). The migrating cells perform nonlinear diffusion and two types of taxis in response to non-diffusing cues: away from proliferating cells and up the gradient of surrounding tissue. Transitions between the two cell subpopulations are influenced by subcellular (receptor binding) dynamics, thus conferring the setting a multiscale character. We prove global existence of weak solutions to a simplified model version and perform numerical simulations for the full setting under several phenotype switching and motility scenarios. We also compare (via simulations) this model with the corresponding haptotaxis-chemotaxis one featuring indirect chemorepellent production and provide a discussion about possible model extensions and mathematical challenges.

A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis

“…The macroscopic system Model (25) features two types of taxis: a repellent, flux-limited pH-taxis of glioma cells moving in the opposite direction of the proton concentration gradient ∇h, and chemotaxis of endothelial cells following the gradient of VEGF. As such, the setting does not fall into any class of models with multiple taxis as reviewed in [59], since each cell population is performing only one type of taxis, but it raises mathematical questions which are at least partially related to those models. The proton production by tumor cells gives the pH-taxis a direct character, while VEGF, the chemotactic cue of ECs, is produced by glioma cells in presence of acidity; at the same time, glioma proliferation is favorably influenced by ECs.…”

Multi-Cue Kinetic Model with Non-Local Sensing for Cell Migration on a Fiber Network with Chemotaxis

“…Among the few examples of multiple-cue analysis, we recall the work proposed by Painter et al (2000), where a macroscopic drift-diffusion model is derived from a space jump process describing the response to multiple chemicals. A review of macroscopic PDEs including multiple-taxis has been recently proposed by Kolbe et al (2021). Looking specifically at the combination of chemotaxis and contact guidance, in Wagle and Tranquillo (2000) one of the first models describing microscopic dynamics is proposed, while, in Azimzade et al (2019), a microscopic double-cue stochastic model was introduced to analyze cell migration and classify tumor associated collagen signatures (TACS).…”

“…A review of macroscopic PDEs including multiple-taxis has been recently proposed by Kolbe et al. ( 2021 ). Looking specifically at the combination of chemotaxis and contact guidance, in Wagle and Tranquillo ( 2000 ) one of the first models describing microscopic dynamics is proposed, while, in Azimzade et al.…”

Multiphase modelling of glioma pseudopalisading under acidosis

“…Indeed, in highly acidic regions cell ion channels and pH-sensing receptors are mostly occupied, thus making cells insensitive to the presence of protons in their environment. As in [11,24,26,27], we call this a repellent pH-tactic behaviour. Similarly, the choice in (3.4) means that there is some intraspecific tissue stress (compression) further accentuated by the interaction between glioma cells and their fibrous environment.…”