2016/06/23 by Martín López‐García, Lopez-Garcia, Martin, Maria Nowicka +9
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Angiogenesis and VEGF in Cancer #Biomolecules (q-bio.BM) #FOS: Biological sciences #HER2/EGFR in Cancer Research #Mathematical Biology Tumor Growth #Subcellular Processes (q-bio.SC)
paper · pdf · doi:10.48550/arxiv.1606.07269
openalex publication_date 2016/06/23 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
Vascular endothelial growth factor receptors (VEGFRs) are receptor tyrosine\nkinases (RTKs) that regulate proliferation, migration, angiogenesis and\nvascular permeability of endothelial cells. VEGFR1 and VEGFR2 bind vascular\nendothelial growth factors (VEGFs), inducing receptor dimerisation and\nactivation, characterised by phosphorylation of tyrosine residues in their\ncytoplasmic domain. Although experimental evidence suggests that RTK signalling\noccurs both on the plasma membrane and intra-cellularly, and reveals the role\nof endocytosis in RTK signal transduction, we still lack knowledge of VEGFR\nphosphorylation-site use and of the spatiotemporal regulation of VEGFR\nsignalling. In this paper, we introduce four stochastic mathematical models to\nstudy the binding kinetics of vascular endothelial growth factor VEGF-A to\nVEGFR1 and VEGFR2, and phosphorylation. The formation of phosphorylated dimers\non the cell surface is a two-step process: diffusive transport and binding. The\nfirst two of our models only consider VEGFR2, which allows us to introduce new\nstochastic descriptors making use of a matrix-analytic approach. The two\nremaining models describe the competition of VEGFR1 and VEGFR2 for ligand\navailability, and are analysed making use of Gillespie simulations and the van\nKampen approximation. Under the hypothesis that bound phosphorylated receptor\ndimers are the signalling units, we study the time to reach a threshold number\nof such complexes. Our results indicate that the presence of VEGFR1 does not\nonly affect the timescale to reach a given signalling threshold, but it also\naffects the maximum attainable threshold. This result is consistent with the\nconjectured role of VEGFR1 as a decoy receptor, that prevents VEGF-A binding to\nVEGFR2, and thus, VEGFR2 attaining suitable phosphorylation levels. We identify\nan optimum range of ligand concentration for sustained dimer phosphorylation.\n