Skip to content

Research at St Andrews

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

Research output: Contribution to journalArticle



Niklas Kolbe, Nikolaos Sfakianakis, Christian Stinner, Christina Surulescu, Jonas Lenz

School/Research organisations


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.


Original languageEnglish
JournalArXiv e-prints
Publication statusSubmitted - 4 May 2020

    Research areas

  • math.AP, q-bio.CB, 35Q92 (Primary), 92C17, 92C50 (Secondary)

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model

    Giesselmann, J., Kolbe, N., Lukáčová-Medvidová, M. & Sfakianakis, N., Dec 2018, In : Discrete and Continuous Dynamical Systems - Series B. 23, 10, p. 4397-4431 35 p.

    Research output: Contribution to journalArticle

  2. Modelling cell-cell collision and adhesion with the Filament Based Lamellipodium Model

    Sfakianakis, N., Peurichard, D., Brunk, A. & Schmeiser, C., 28 Nov 2018, In : BIOMATH. 7, 2, 14 p., 1811097.

    Research output: Contribution to journalArticle

  3. Stability, convergence, and sensitivity analysis of the FBLM and the corresponding FEM

    Sfakianakis, N. & Brunk, A., Nov 2018, In : Bulletin of Mathematical Biology. 80, 11, p. 2789-2827 39 p.

    Research output: Contribution to journalArticle

  4. Energy intake functions and energy budgets of ectotherms and endotherms derived from their ontogenetic growth in body mass and timing of sexual maturation

    Werner, J., Sfakianakis, N., Rendall, A. D. & Griebeler, E. M., 7 May 2018, In : Journal of Theoretical Biology. 444, p. 83-92 10 p.

    Research output: Contribution to journalArticle

Related by journal

  1. Coupled differentiation and division of embryonic stem cells inferred from clonal snapshots

    Ruske, L. J., Kursawe, J., Tsakiridis, A., Wilson, V., Fletcher, A. G., Blythe, R. A. & Schumacher, L. J., 27 Apr 2020, In : ArXiv e-prints.

    Research output: Contribution to journalArticle

  2. Understanding the stochastic partial differential equation approach to smoothing

    Miller, D. L., Glennie, R. & Seaton, A. E., 21 Jan 2020, In : ArXiv e-prints.

    Research output: Contribution to journalArticle

  3. Demonstrating a non-reciprocal optical resonator for unlimited time-bandwidth performance

    Cardea, I., Grassani, D., Fabbri, S. J., Upham, J., Boyd, R. W., Altug, H., Schulz, S. A., Tsakmakidis, K. L. & Brès, C-S., 20 Mar 2019, (Submitted) In : ArXiv e-prints.

    Research output: Contribution to journalArticle

ID: 267788117