Abstract
In recent years, Judah Folkman’s vision of anticancer therapeutics based on inhibiting angiogenesis pathways has begun to be realized. In particular, antibodies sequestering VEGF, and small molecule tyrosine kinase inhibitors targeting VEGF receptors, are now approved for various cancers, alone or in combination with other therapies. More are in the development pipeline, with similar or distinct mechanisms of action. The VEGF system is complex, involving multiple ligands and receptors, along with transport throughout the body via the bloodstream. Predicting outcomes of perturbing this system, either by a single agent or combinations, can be aided by in silico models. Here we discuss the ways in which the above drugs target the VEGF pathway in cancer, and describe the development and implementation of multiscale mathematical models to simulate the action of these drugs in order to predict and compare their likely efficacy for various types of tumors.
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Anderson, A.R. and V. Quaranta, Integrative mathematical oncology. Nat Rev Cancer, 2008. 8(3): p. 227–34.
Arakelyan, L., et al., Multi-scale analysis of angiogenic dynamics and therapy. In Cancer modeling and simulation, ed. L. Preziosi. 2003, LLC (UK): CRC Press. 185–219.
Autiero, M., et al., Role of PlGF in the intra- and intermolecular cross talk between the VEGF receptors Flt1 and Flk1. Nat Med, 2003. 9(7): p. 936–43.
Bais, C., et al., PlGF blockade does not inhibit angiogenesis during primary tumor growth. Cell, 2010. 141(1): p. 166–77.
Barr, M.P., et al., A peptide corresponding to the neuropilin-1-binding site on VEGF(165) induces apoptosis of neuropilin-1-expressing breast tumour cells. Br J Cancer, 2005. 92(2): p. 328–33.
Bauer, A.L., T.L. Jackson, and Y. Jiang, A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis. Biophys J, 2007. 92(9): p. 3105–21.
Bentley, K., H. Gerhardt, and P.A. Bates, Agent-based simulation of notch-mediated tip cell selection in angiogenic sprout initialisation. J Theor Biol, 2008. 250(1): p. 25–36.
Bentley, K., et al., Tipping the balance: robustness of tip cell selection, migration and fusion in angiogenesis. PLoS Comput Biol, 2009. 5(10): e1000549.
Billy, F., et al., A pharmacologically based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy. J Theor Biol, 2009. 260(4): p. 545–62.
Bock, F., et al., Blockade of VEGFR3-signalling specifically inhibits lymphangiogenesis in inflammatory corneal neovascularisation. Graefes Arch Clin Exp Ophthalmol, 2008. 246(1): p. 115–9.
Byrne, H.M., Dissecting cancer through mathematics: from the cell to the animal model. Nat Rev Cancer, 2010. 10(3): p. 221–30.
Chaplain, M.A., S.R. McDougall, and A.R. Anderson, Mathematical modeling of tumor-induced angiogenesis. Annu Rev Biomed Eng, 2006. 8: p. 233–57.
Das, A., et al., A hybrid continuum-discrete modeling approach to predict and control angiogenesis: analysis of combinatorial growth factor and matrix effects on vessel-sprouting morphology. Philos Transact A Math Phys Eng Sci, 2010. 368(1921): p. 2937–60.
Dixelius, J., et al., Ligand-induced vascular endothelial growth factor receptor-3 (VEGFR-3) heterodimerization with VEGFR-2 in primary lymphatic endothelial cells regulates tyrosine phosphorylation sites. J Biol Chem, 2003. 278(42): p. 40973–9.
d’Onofrio, A. and A. Gandolfi, Chemotherapy of vascularised tumours: role of vessel density and the effect of vascular “pruning”. J Theor Biol, 2010. 264(2): p. 253–65.
Dvorak, H.F., Discovery of vascular permeability factor (VPF). Exp Cell Res, 2006. 312(5): p. 522–6.
Edelman, L.B., J.A. Eddy, and N.D. Price, In silico models of cancer. Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 2010. 2(4): p. 438–9.
Ellis, L.M., The role of neuropilins in cancer. Mol Cancer Ther, 2006. 5(5): p. 1099–107.
Ferrara, N., H.P. Gerber, and J. LeCouter, The biology of VEGF and its receptors. Nat Med, 2003. 9(6): p. 669–76.
Ferrara, N., Vascular endothelial growth factor: basic science and clinical progress. Endocr Rev, 2004. 25(4): p. 581–611.
Filion, R.J. and A.S. Popel, A reaction-diffusion model of basic fibroblast growth factor interactions with cell surface receptors. Ann Biomed Eng, 2004. 32(5): p. 645–63.
Fischer, C., et al., Anti-PlGF inhibits growth of VEGF(R)-inhibitor-resistant tumors without affecting healthy vessels. Cell, 2007. 131(3): p. 463–75.
Fischer, C., et al., FLT1 and its ligands VEGFB and PlGF: drug targets for anti-angiogenic therapy? Nat Rev Cancer, 2008. 8(12): p. 942–56.
Folkman, J., Tumor angiogenesis: therapeutic implications. N Engl J Med, 1971. 285(21): p. 1182–6.
Forsten-Williams, K., et al., Control of growth factor networks by heparan sulfate proteoglycans. Ann Biomed Eng, 2008. 36(12): p. 2134–48.
Frieboes, H.B., et al., Three-dimensional multispecies nonlinear tumor growth-II: Tumor invasion and angiogenesis. J Theor Biol, 2010. 264(4): p. 1254–78.
Fukumura, D. and R.K. Jain, Tumor microenvironment abnormalities: causes, consequences, and strategies to normalize. J Cell Biochem, 2007. 101(4): p. 937–49.
Gaur, P., et al., Role of class 3 semaphorins and their receptors in tumor growth and angiogenesis. Clin Cancer Res, 2009. 15(22): p. 6763–70.
Gaur, P., et al., Targeting tumor angiogenesis. Semin Oncol, 2009. 36(2 Suppl 1): p. S12–9.
Geretti, E. and M. Klagsbrun, Neuropilins: novel targets for anti-angiogenesis therapies. Cell Adh Migr, 2007. 1(2): p. 56–61.
Geretti, E., A. Shimizu, and M. Klagsbrun, Neuropilin structure governs VEGF and semaphorin binding and regulates angiogenesis. Angiogenesis, 2008. 11(1): p. 31–9.
Gluzman-Poltorak, Z., et al., Neuropilin-2 is a receptor for the vascular endothelial growth factor (VEGF) forms VEGF-145 and VEGF-165. J Biol Chem, 2000. 275(24): p. 18040–5.
Gordon, M.S., et al., Phase I safety and pharmacokinetic study of recombinant human anti-vascular endothelial growth factor in patients with advanced cancer. J Clin Oncol, 2001. 19(3): p. 843–50.
Gorelik, B., et al., Efficacy of weekly docetaxel and bevacizumab in mesenchymal chondrosarcoma: a new theranostic method combining xenografted biopsies with a mathematical model. Cancer Res, 2008. 68(21): p. 9033–40.
Hattori, K., et al., Placental growth factor reconstitutes hematopoiesis by recruiting VEGFR1(+) stem cells from bone-marrow microenvironment. Nat Med, 2002. 8(8): p. 841–9.
Holash, J., et al., VEGF-Trap: a VEGF blocker with potent antitumor effects. Proc Natl Acad Sci U S A, 2002. 99(17): p. 11393–8.
Hsu, J.Y. and H.A. Wakelee, Monoclonal antibodies targeting vascular endothelial growth factor: current status and future challenges in cancer therapy. BioDrugs, 2009. 23(5): p. 289–304.
Jain, R.K. and B.T. Fenton, Intratumoral lymphatic vessels: a case of mistaken identity or malfunction? J Natl Cancer Inst, 2002. 94(6): p. 417–21.
Jain, H.V., J.E. Nor, and T.L. Jackson, Quantification of endothelial cell-targeted anti-Bcl-2 therapy and its suppression of tumor growth and vascularization. Mol Cancer Ther, 2009. 8(10): p. 2926–36.
Jakobsson, L., K. Bentley, and H. Gerhardt, VEGFRs and Notch: a dynamic collaboration in vascular patterning. Biochem Soc Trans, 2009. 37(Pt 6): p. 1233–6.
Jayson, G.C., et al., Molecular imaging and biological evaluation of HuMV833 anti-VEGF antibody: implications for trial design of antiangiogenic antibodies. J Natl Cancer Inst, 2002. 94(19): p. 1484–93.
Jayson, G.C., et al., Phase I investigation of recombinant anti-human vascular endothelial growth factor antibody in patients with advanced cancer. Eur J Cancer, 2005. 41(4): p. 555–63.
Ji, R.C., Lymphatic endothelial cells, tumor lymphangiogenesis and metastasis: New insights into intratumoral and peritumoral lymphatics. Cancer Metastasis Rev, 2006. 25(4): p. 677–94.
Jimenez, X., et al., A recombinant, fully human, bispecific antibody neutralizes the biological activities mediated by both vascular endothelial growth factor receptors 2 and 3. Mol Cancer Ther, 2005. 4(3): p. 427–34.
Karagiannis, E.D. and A.S. Popel, A theoretical model of type I collagen proteolysis by matrix metalloproteinase (MMP) 2 and membrane type 1 MMP in the presence of tissue inhibitor of metalloproteinase 2. J Biol Chem, 2004. 279(37): p. 39105–14.
Karagiannis, E.D. and A.S. Popel, Distinct modes of collagen type I proteolysis by matrix metalloproteinase (MMP) 2 and membrane type I MMP during the migration of a tip endothelial cell: insights from a computational model. J Theor Biol, 2006. 238(1): p. 124–45.
Kolodkin, A.L., et al., Neuropilin is a semaphorin III receptor. Cell, 1997. 90(4): p. 753–62.
Krupitskaya, Y. and H.A. Wakelee, Ramucirumab, a fully human mAb to the transmembrane signaling tyrosine kinase VEGFR-2 for the potential treatment of cancer. Curr Opin Investig Drugs, 2009. 10(6): p. 597–605.
Kut, C., F. Mac Gabhann, and A.S. Popel, Where is VEGF in the body? A meta-analysis of VEGF distribution in cancer. Br J Cancer, 2007. 97(7): p. 978–85.
Laubenbacher, R., et al., A systems biology view of cancer. Biochim Biophys Acta, 2009. 1796(2): p. 129–39.
Lee, Y.C., The involvement of VEGF in endothelial permeability: a target for anti-inflammatory therapy. Curr Opin Investig Drugs, 2005. 6(11): p. 1124–30.
Leung, D.W., et al., Vascular endothelial growth factor is a secreted angiogenic mitogen. Science, 1989. 246(4935): p. 1306–9.
Levine, H.A., et al., Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma. Bull Math Biol, 2001. 63(5): p. 801–63.
Lockhart, A.C., et al., Phase I study of intravenous vascular endothelial growth factor trap, aflibercept, in patients with advanced solid tumors. J Clin Oncol, 2010. 28(2): p. 207–14.
Lyons, J.M., 3rd, et al., The role of VEGF pathways in human physiologic and pathologic angiogenesis. J Surg Res, 2010. 159(1): p. 517–27.
Mac Gabhann, F. and A.S. Popel, Systems biology of vascular endothelial growth factors. Microcirculation, 2008. 15(8): p. 715–38.
Mac Gabhann, F. and A.S. Popel, Targeting neuropilin-1 to inhibit VEGF signaling in cancer: Comparison of therapeutic approaches. PLoS Comput Biol, 2006. 2(12): p. e180.
Mac Gabhann, F. and A.S. Popel, Dimerization of VEGF receptors and implications for signal transduction: a computational study. Biophys Chem, 2007. 128(2–3): p. 125–39.
Macklin, P., et al., Multiscale modeling and nonlinear simulation of vascular tumour growth. J Math Biol, 2009. 58(4–5): p. 765–98.
Milde, F., M. Bergdorf, and P. Koumoutsakos, A hybrid model for three-dimensional simulations of sprouting angiogenesis. Biophys J, 2008. 95(7): p. 3146–60.
Nagy, J.A., et al., Why are tumour blood vessels abnormal and why is it important to know? Br J Cancer, 2009. 100(6): p. 865–9.
Nagy, J.A., A.M. Dvorak, and H.F. Dvorak, VEGF-A and the induction of pathological angiogenesis. Annu Rev Pathol, 2007. 2: p. 251–75.
Neufeld, G., O. Kessler, and Y. Herzog, The interaction of Neuropilin-1 and Neuropilin-2 with tyrosine-kinase receptors for VEGF. Adv Exp Med Biol, 2002. 515: p. 81–90.
Nilsson, I., et al., VEGF receptor 2/-3 heterodimers detected in situ by proximity ligation on angiogenic sprouts. EMBO J, 2010. 29(8): p. 1377–88.
Nilsson, I., et al., Vascular endothelial growth factor receptor-3 in hypoxia-induced vascular development. Faseb J, 2004. 18(13): p. 1507–15.
Noguera-Troise, I., et al., Blockade of Dll4 inhibits tumour growth by promoting non-productive angiogenesis. Nature, 2006. 444(7122): p. 1032–7.
Owen, M.R., et al.,Angiogenesis and vascular remodelling in normal and cancerous tissues. J Math Biol, 2009. 58(4–5): p. 689–721.
Pan, Q., et al., Neuropilin-1 binds to VEGF121 and regulates endothelial cell migration and sprouting. J Biol Chem, 2007. 282(33): p. 24049–56.
Park, C.S., I.C. Schneider, and J.M. Haugh, Kinetic analysis of platelet-derived growth factor receptor/phosphoinositide 3-kinase/Akt signaling in fibroblasts. J Biol Chem, 2003. 278(39): p. 37064–72.
Peirce, S.M., Computational and mathematical modeling of angiogenesis. Microcirculation, 2008. 15(8): p. 739–51.
Popel, A.S. and P.J. Hunter, Systems biology and Physiome projects. Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 2009. 1: p. 153–8.
Qutub, A.A. and A.S. Popel, Reactive oxygen species regulate hypoxia-inducible factor 1alpha differentially in cancer and ischemia. Mol Cell Biol, 2008. 28(16): p. 5106–19.
Qutub, A.A. and A.S. Popel, Elongation, proliferation & migration differentiate endothelial cell phenotypes and determine capillary sprouting. BMC Syst Biol, 2009. 3: 13.
Qutub, A.A., et al., Multiscale models of angiogenesis. IEEE Eng Med Biol Mag, 2009. 28(2): p. 14–31.
Qutub, A.A., et al., In silico modeling of angiogenesis at multiple scales: From nanoscale to organ system, in Multiscale Modeling of Particle Interactions: Applications in Biology and Nanotechnology, M.R. King and D.J. Gee, Editors. 2010, Wiley. p. 287–320.
Ridgway, J., et al., Inhibition of Dll4 signalling inhibits tumour growth by deregulating angiogenesis. Nature, 2006. 444(7122): p. 1083–7.
Rizzolio, S. and L. Tamagnone, Semaphorin signals on the road to cancer invasion and metastasis. Cell Adh Migr, 2007. 1(2): p. 62–8.
Robinson, C.J. and S.E. Stringer, The splice variants of vascular endothelial growth factor (VEGF) and their receptors. J Cell Sci, 2001. 114(Pt 5): p. 853–65.
Schwartz, J.D., et al., Vascular endothelial growth factor receptor-1 in human cancer: concise review and rationale for development of IMC-18F1 (Human antibody targeting vascular endothelial growth factor receptor-1). Cancer, 2010. 116(4 Suppl): p. 1027–32.
Segerstrom, L., et al., The anti-VEGF antibody bevacizumab potently reduces the growth rate of high-risk neuroblastoma xenografts. Pediatr Res, 2006. 60(5): p. 576–81.
Shibuya, M., Differential roles of vascular endothelial growth factor receptor-1 and receptor-2 in angiogenesis. J Biochem Mol Biol, 2006. 39(5): p. 469–78.
Shibuya, M. and L. Claesson-Welsh, Signal transduction by VEGF receptors in regulation of angiogenesis and lymphangiogenesis. Exp Cell Res, 2006. 312(5): p. 549–60.
Shraga-Heled, N., et al., Neuropilin-1 and neuropilin-2 enhance VEGF121 stimulated signal transduction by the VEGFR-2 receptor. FASEB J, 2007. 21(3): p. 915–26.
Small, A.R., et al., Spatial distribution of VEGF isoforms and chemotactic signals in the vicinity of a tumor. J Theor Biol, 2008. 252(4): p. 593–607.
Soker, S., et al., VEGF165 mediates formation of complexes containing VEGFR-2 and neuropilin-1 that enhance VEGF165-receptor binding. J Cell Biochem, 2002. 85(2): p. 357–68.
Spratlin, J.L., et al., Phase I pharmacologic and biologic study of ramucirumab (IMC-1121B), a fully human immunoglobulin G1 monoclonal antibody targeting the vascular endothelial growth factor receptor-2. J Clin Oncol, 2010. 28(5): p. 780–7.
Stefanini, M.O., et al., A compartment model of VEGF distribution in blood, healthy and diseased tissues. BMC Syst Biol, 2008. 2: 77.
Stefanini, M.O., et al., The increase of plasma vascular endothelial growth factor following the intravenous administration of bevacizumab predicted by a pharmacokinetic model. Cancer Res, 2010. 70(23): 9886–94.
Stefanini, M.O., et al., Computational models of VEGF-associated angiogenic processes in cancer. Math Med Biol, 2011, to appear.
Suchting, S., et al., The Notch ligand Delta-like 4 negatively regulates endothelial tip cell formation and vessel branching. Proc Natl Acad Sci U S A, 2007. 104(9): p. 3225–30.
Sun, S., et al., A deterministic model of growth factor-induced angiogenesis. Bull Math Biol, 2005. 67(2): p. 313–37.
Takahashi, H. and M. Shibuya, The vascular endothelial growth factor (VEGF)/VEGF receptor system and its role under physiological and pathological conditions. Clin Sci (Lond), 2005. 109(3): p. 227–41.
Tammela, T., et al., Blocking VEGFR-3 suppresses angiogenic sprouting and vascular network formation. Nature, 2008. 454(7204): p. 656–60.
Tammela, T. and K. Alitalo, Lymphangiogenesis: Molecular mechanisms and future promise. Cell, 2010. 140(4): p. 460–76.
Tew, W.P., et al., Phase 1 study of aflibercept administered subcutaneously to patients with advanced solid tumors. Clin Cancer Res, 2010. 16(1): p. 358–66.
Van de Veire, S., et al., Further pharmacological and genetic evidence for the efficacy of PlGF inhibition in cancer and eye disease. Cell, 2010. 141(1): p. 178–90.
von Wronski, M.A., et al., Tuftsin binds neuropilin-1 through a sequence similar to that encoded by exon 8 of vascular endothelial growth factor. J Biol Chem, 2006. 281(9): p. 5702–10.
Vempati, P., E.D. Karagiannis, and A.S. Popel, A biochemical model of matrix metalloproteinase 9 activation and inhibition. J Biol Chem, 2007. 282(52): p. 37585–96.
Vempati, P., F. Mac Gabhann, and A.S. Popel, Quantifying the proteolytic release of extracellular matrix-sequestered VEGF with a computational model. PLoS One, 2010. 5(7): e11860.
Witte, L., et al., Monoclonal antibodies targeting the VEGF receptor-2 (Flk1/KDR) as an anti-angiogenic therapeutic strategy. Cancer Metastasis Rev, 1998. 17(2): p. 155–61.
Wu, Y., et al., Anti-vascular endothelial growth factor receptor-1 antagonist antibody as a therapeutic agent for cancer. Clin Cancer Res, 2006. 12(21): p. 6573–84.
Wu, F.T., et al., Modeling of growth factor-receptor systems from molecular-level protein interaction networks to whole-body compartment models. Methods Enzymol, 2009. 467: p. 461–497.
Xu, Y., et al., Neuropilin-2 mediates VEGF-C-induced lymphatic sprouting together with VEGFR3. J Cell Biol, 2010. 188(1): p. 115–30.
Yang, J.C., et al., A randomized trial of bevacizumab, an anti-vascular endothelial growth factor antibody, for metastatic renal cancer. N Engl J Med, 2003. 349(5): p. 427–34.
Youssoufian, H., D.J. Hicklin, and E.K. Rowinsky, Review: monoclonal antibodies to the vascular endothelial growth factor receptor-2 in cancer therapy. Clin Cancer Res, 2007. 13(18 Pt 2): p. 5544s–5548s.
Zhang, F., et al., VEGF-B is dispensable for blood vessel growth but critical for their survival, and VEGF-B targeting inhibits pathological angiogenesis. Proc Natl Acad Sci U S A, 2009. 106(15): p. 6152–7.
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Gabhann, F.M., Stefanini, M.O., Popel, A.S. (2012). Simulating Therapeutics Using Multiscale Models of the VEGF Receptor System in Cancer. In: Jackson, T.L. (eds) Modeling Tumor Vasculature. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0052-3_2
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