Constructing mathematical models from small data sets: Cell-viability model of melanoma under inhibition by MAZ-51

¹ Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa
² Department of Physiology, University of Pretoria, South Africa
³ Department of Anatomy, University of Pretoria, South Africa

^* Corresponding author: roumen.anguelov@up.ac.za

Received: 3 May 2025
Accepted: 20 November 2025

Abstract

The synthetic indolinone derivative MAZ-51 is a selective inhibitor of vascular endothelial growth factor receptor 3 (VEGFR-3), a tyrosine kinase receptor essential for lymphangiogenesis and tumor progression. By competing with adenosine triphosphate (ATP) for VEGFR-3 binding, MAZ-51 blocks VEGF-C activity, thereby suppressing melanoma cell proliferation and promoting apoptosis. In this study, we employ mathematical modelling to quantify the inhibitory effects of MAZ-51 on the growth of B16-F10 melanoma cells. Cell viability is modeled as a function of both treatment duration and inhibitor concentration, providing a dynamic framework for assessing therapeutic efficacy. Our approach addresses a central challenge in mathematical biology: developing models that remain interpretable and predictive despite limited and variable data. By integrating biological insight with experimental data, we derive a parsimonious model that avoids overparameterization and yields biologically meaningful parameters. The model allows straightforward computation of pharmacological measures such as the half-maximal inhibitory concentration (IC₅₀) and provides deeper insight into the growth rate reduction of melanoma cells under VEGFR-3 inhibition. This work highlights the utility of mathematical modelling in elucidating drug action mechanisms and in quantitatively evaluating targeted cancer therapies.