A mathematical model describing the tip-stalk regulation in angiogenesis

Autores

Dandara Lorrayne do Nascimento Center for Technological Education of Minas Gerais (CEFET-MG). Graduate Program in Mathematical and Computational Modeling https://orcid.org/0000-0003-1169-1575
Ana Paula Alves Federal University of Minas Gerais (UFMG). Graduate Program in Physics. State University of Minas Gerais (UEMG) https://orcid.org/0000-0003-0594-8215
Leonardo Ferreira Calazans Center for Technological Education of Minas Gerais (CEFET-MG). Graduate Program in Mathematical and Computational Modeling https://orcid.org/0000-0003-3320-3587
Ubirajara Agero Federal University of Minas Gerais (UFMG). Graduate Program in Physics https://orcid.org/0000-0002-4987-9031
Allbens P. F. Atman Center for Technological Education of Minas Gerais (CEFET-MG). Graduate Program in Mathematical and Computational Modeling. National Institute of Science and Technology - Complex Systems – INCT https://orcid.org/0000-0002-7614-2721

Palavras-chave:

Angiogenesis, Physiological Angiogenesis, Pathological Angiogenesis, Protein Dynamics, Mathematical Modeling

Resumo

Angiogenesis is the process of new blood vessel growth from existing vessels, involving extensive cell signaling. Under normal conditions, new vessels are robust and organized, with a balance among angiogenesis factors. In abnormal conditions, such as tumor development, vessels are stunted and tangled due to an imbalance of these factors. Pathological angiogenesis stimulates rapid vessel growth to feed the oxygen and nutriente starved tumor. Inhibiting angiogenesis can cause side effects like hypertension, thrombosis, and fatigue. To better understand this process, significant effort has gone into studying signaling pathways, contributing to drug development for diseases like cancer. This study presents a mathematical model describing angiogenesis on a microscopic scale, comparing its results with experimental data on vascular network topology. The model, implemented in MatLab®, uses ordinary differential equations to represent cell behavior. Results show that altering VEGF (Vascular Endothelial Growth Factor) disrupts system balance, impacting angiogenesis and possibly explaining differences in network topology seen experimentally.

Biografia do Autor

Dandara Lorrayne do Nascimento, Center for Technological Education of Minas Gerais (CEFET-MG). Graduate Program in Mathematical and Computational Modeling

Doctoral student in Mathematical and Computational Modeling at the Federal Center for Technological Education of Minas Gerais (CEFET-MG) and Master's in Mathematical and Computational Modeling from CEFET-MG (2021). Graduated in Mathematics from the Federal Institute of Minas Gerais (IFMG) Campus Formiga (2018). She was a scientific initiation scholarship holder in the area of mathematical modeling (A mathematical model for angiogenesis in solid tumors), a CAPES scholarship holder in the Institutional Teaching Initiation Scholarship Program (PIBID), and a scholarship holder in a research, development, and innovation (RDI) project in partnership with the private sector and Embrapii (Brazilian Company of Industrial Research and Innovation) in the area of intelligent systems. Currently, she is a permanent EBTT Mathematics professor at the Federal Institute of Southeast Minas Gerais - Campus Bom Sucesso. She was a professor at the Federal Institute of Minas Gerais - IFMG Campus Arcos, working in the Mechanical Engineering, Postgraduate Program in Teaching (EaD), and Occupational Safety (EaD) courses. She has experience as a producer of educational materials for Distance Education and as a teacher in Distance Education courses.

Ana Paula Alves, Federal University of Minas Gerais (UFMG). Graduate Program in Physics. State University of Minas Gerais (UEMG)

Holds a Bachelor's degree in Physics from the Federal University of Minas Gerais (2008), a Master's degree in Physics from the Federal University of Minas Gerais (2011), and a Ph.D. in Physics from the Federal University of Minas Gerais (2018). Has a strong interest in obtaining quantitative parameters to describe Biological Systems. Experienced in the area of Experimental Physics, primarily focusing on the following topics: statistical characterization of vascular networks forming during embryonic development, application of Defocusing Microscopy to analyze mechanical properties of the cell membrane under different treatments, and quantitative image analysis of the contractility dynamics of cardiomyocytes under various treatments. Works with interdisciplinary topics involving multivariate statistical analysis of angular deformation and residual temporal curing degree in curved polymeric composites. Currently, she is a professor at the State University of Minas Gerais and coordinator of the Physics Teaching Program at the Academic Unit of Passos.

Leonardo Ferreira Calazans, Center for Technological Education of Minas Gerais (CEFET-MG). Graduate Program in Mathematical and Computational Modeling

Has a degree in Physics from the Federal University of Minas Gerais (2009) and a master's degree in Mathematical and Computational Modeling from the Federal Center for Technological Education of Minas Gerais (2014) and a Ph.D. in Physics from the Federal University of Minas Gerais (2020). Worked with numerical methods for nonlinear optimization applied to quantum information problems. Has experience in Statistical Mechanics and Non-equilibrium Thermodynamics, Stochastic Processes, and Monte Carlo simulation. Programs in C and Python. Currently, is doing postdoctoral research on the properties of granular materials through molecular dynamics simulation.

Ubirajara Agero, Federal University of Minas Gerais (UFMG). Graduate Program in Physics

Holds a bachelor's degree in Physics from the Federal University of Minas Gerais (1995), a master's degree in Physics from the Federal University of Minas Gerais (1998), a PhD in Physics from the Federal University of Minas Gerais (2003), and completed postdoctoral studies at Indiana University, USA (2006-2008) and the Polytechnic University of Turin, Italy (2018-2019). Currently, he is an associate professor at the Federal University of Minas Gerais. He has experience in the field of Biological Systems Physics, with a focus on the following topics: defocusing microscopy, phagocytosis, macrophages, and embryonic development.

Allbens P. F. Atman , Center for Technological Education of Minas Gerais (CEFET-MG). Graduate Program in Mathematical and Computational Modeling. National Institute of Science and Technology - Complex Systems – INCT

Bachelor of Physics (UFMG-1996), Master of Physics (UFMG-1998), Doctor of Science (UFMG-2002), Post-Doctorate (Université de Paris VI - Pierre et Marie Curie - 2002/2004), Post-Doctorate (UFMG-2004/2005). Currently holds the position of Associate Professor IV at the Federal Center for Technological Education of Minas Gerais (CEFET-MG). Member of the National Institute of Science and Technology - Complex Systems, he was a Visiting Professor (PMMH/ESPCI: 2008, "Chair Total" - 2013) and one of the awardees in the "Research in Paris" project (Paris City Hall-2010) at the École Superieure de Physique et Chimie (ESPCI). Leader of the Complex Systems Study Group in the Physics Department at CEFET-MG, he has interdisciplinary interests in areas such as Statistical Physics, Mechanics, Elasticity and Rheology, Plasma Physics, Econophysics, Non-Extensive Statistical Mechanics, Epidemiology, and Biologically Motivated Problems, collaborating with dozens of researchers in these fields. He has experience in supervising undergraduate research, master's and doctoral students, and has produced scholarly work on the following topics: fractals, roughness, simulation, cellular automata, percolation, self-organized criticality, granular materials, elasticity, rheology, mathematical modeling, econophysics, epidemic propagation, and computational methods in physics.

Referências

Alves, A., Mesquita, O., Gómez-Gardeñes, J., & Agero, U. (2018). Graph analysis of cell clusters forming vascular networks. Royal Society Open Science, 5(3), 171592.

Andersson, E. R., Sandberg, R., & Lendahl, U. (2011). Notch signaling. Development, 138(17), 3593–3612.

Apte, R. S., Chen, D. S., & Ferrara, N. (2019). VEGF in signaling and disease. Cell, 176(6), 1248–1264.

Beatus, P., & Lendahl, U. (1998). Notch and neurogenesis. Journal of Neuroscience Research, 54(2), 125–136.

Bhadada, S. V., Goyal, B. R., & Patel, M. M. (2011). Angiogenic targets for potential disorders. Fundamental & Clinical Pharmacology, 25(1), 29–47.

Boareto, M., Jolly, M. K., Ben-Jacob, E., & Onuchic, J. N. (2015a). Jagged mediates differences in normal and tumor angiogenesis by affecting tip-stalk fate decision. Proceedings of the National Academy of Sciences, 112(29), E3836–E3844.

Boareto, M., Jolly, M. K., Lu, M., Onuchic, J. N., Clementi, C., & Ben-Jacob, E. (2015b). Jagged–Delta asymmetry in Notch signaling can give rise to a sender/receiver hybrid phenotype. Proceedings of the National Academy of Sciences, 112(5), E402–E409.

Boareto, M., Jolly, M. K., Goldman, A., Pietilä, M., Mani, S., Sengupta, S., Ben-Jacob, E., Levine, H., & Onuchic, J. N. (2016). Notch-Jagged signalling can give rise to clusters of cells exhibiting a hybrid epithelial/mesenchymal phenotype. Journal of the Royal Society Interface, 13(118).

Bocci, F., Onuchic, J. N., & Jolly, M. K. (2020). Understanding the principles of pattern formation driven by Notch signaling by integrating experiments and theoretical models. Frontiers in Physiology, 11, 929.

Cheng, W. K., Oon, C. E., Kaur, G., Sainson, R. C., & Li, J.-L. (2022). Downregulation of manic fringe impedes angiogenesis and cell migration of renal carcinoma. Microvascular Research, 142, 104341.

Chen, S., Tang, C., Chie, M., Tsai, Y. F. C., Lu, Y., Chen, W., Lai, C., Wei, C., Tai, H., Chou, W., & Wang, S. (2019). Resistin facilitates VEGF-A dependent angiogenesis by inhibiting miR-16-5p in human chondrosarcoma cells. Cell Death & Disease, 10(31).

De Palma, M., Biziato, D., & Petrova, T. V. (2017). Microenvironmental regulation of tumour angiogenesis. Nature Reviews Cancer, 17(8), 457–474.

Domingues, J. S. (2010). Modelo matemático e computacional do surgimento da angiogênese em tumores e sua conexão com as células-tronco (Dissertação de mestrado, Centro Federal de Educação Tecnológica de Minas Gerais). Belo Horizonte, Brasil.

Flournoy, J., Ashkanani, S., & Chen, Y. (2022). Mechanical regulation of signal transduction in angiogenesis. Frontiers in Cell and Developmental Biology, 10, 1069783.

Folkman, J. (1984). In biology of endothelial cells, Developments in Cardiovascular Medicine (27).

Fouladzadeh, A., Dorraki, M., Min, K., Cockshell, M., Thompson, E., Verjans, J., & Abbott, D. (2021). The development of tumour vascular networks. Communications Biology, 4(1), 1111.

Fragoso, C. R., Ferreira, T. F., & Marques, D. M. (2009). Modelagem Ecológica em Ecossistemas Aquáticos. Oficina de Textos.

Freire, R. M. (2007). Modelagem matemática para a simulação de estratégias de controle biológico da mosca-do-mediterrâneo C. capitata (Diptera: Tephritidae) em plantações de citrus: Utilização de variáveis temporais e espaciais (Dissertação de mestrado, Universidade Estadual Paulista). Rio Claro, Brasil.

Funahashi, Y., Hernandez, S. L., Das, I., Ahn, A., Huang, J., Vorontchikhina, M., Sharma, A., Kanamaru, E., Borisenko, V., & DeSilva, D. M. (2008). A Notch1 ectodomain construct inhibits endothelial notch signaling, tumor growth, and angiogenesis. Cancer Research, 68(12), 4727–4735.

Geindreau, M., Bruchard, M., & Vegran, F. (2022). Role of cytokines and chemokines in angiogenesis in a tumor context. Cancers, 14(10), 2446.

Geudens, I., & Gerhardt, H. (2011). Coordinating cell behaviour during blood vessel formation. Development, 138(21), 4569–4583.

Huang, Y., & Nan, G. (2019). Oxidative stress induced angiogenesis. Journal of Clinical Neuroscience, 63, 13–16.

Jain, R. K. (2005). Normalization of tumor vasculature. Science, 307(5706), 58–62.

Jarriault, S., Brou, C., Logeat, F., Schroeter, E. H., Kopan, R., & Israel, A. (1995). Signalling downstream of activated mammalian Notch. Nature, 377, 355–358.

Kargozar, S., Baino, F., Hamzehlou, S., Hamblin, M. R., & Mozafari, M. (2020). Nanotechnology for angiogenesis: Opportunities and challenges. Chemical Society Reviews, 49(12), 5008–5057.

Kumar, S., Srivastav, R. K., Wilkes, D. W., Ross, T., Kim, S., Kowalski, J., Chatla, S.,

Zhang, Q., Nayak, A., Guha, M., Fuchs, S. Y., Thomas, C., & Chakrabarti, R. (2019). Estrogen dependent DLL1 mediated Notch signaling promotes luminal breast cancer. Oncogene, 38(1), 2092–2107.

Leite, N. M. G. (2009). Modelagem matemática para a conexão entre células-tronco e câncer (Dissertação de mestrado, Centro Federal de Educação Tecnológica de Minas Gerais). Belo Horizonte, Brasil.

Liao, B., & Oates, A. C. (2017). Delta-Notch signalling in segmentation. Arthropod Structure & Development 46 (3) 429–447.

Li, L., Krantz, I. D., Deng, Y., Genin, A., Banta, A. B., Collins, C. C., Qi, M., Trask, B. J., Kuo, W. L., & Cochran, J. (1997). Alagille syndrome is caused by mutations in human JAGGED1, which encodes a ligand for NOTCH1. Nature Genetics, 16(3), 243–251.

LoPilato, R. K., Kroeger, H., Mohan, S. K., Lauderdale, J. D., Grimsey, N., &

Haltiwanger, R. S. (2023). Two Notch1 Ofucose sites have opposing functions in mouse retinal angiogenesis. Glycobiology, 33(8), 661-672.

Lugano, R., Ramachandran, M., & Dimberg, A. (2020). Tumor angiogenesis. Cellular and Molecular Life Sciences, 77(9), 1745–1770.

Mercurio, A. M. (2019). VEGF/neuropilin signaling in cancer stem cells. International Journal of Molecular Sciences, 20(3), 1–12.

Moreira, E. A., & Ramos, R. (2021). Potencial antineoplásico dos fitocanabinóides. Revista Multidisciplinar em Saúde, 2(4), 137–137.

Mukherji, S. K. (2010). Bevacizumab (Avastin). American Journal of Neuroradiology, 31(2), 235–236.

Nascimento, D. L. (2021). Modelo matemático para a angiogênese baseado na dinâmica das vias de sinalização Notch e VEGF (Mestrado em Modelagem Matemática e Computacional). Centro Federal de Educação Tecnológica de Minas Gerais.

Nunes, D. N., Dias-Neto, E., Cardó-Vila, M., Edwards, J. K., Dobroff, A. S., Giordano, R. J., ... Pasqualini, R. (2015). Synchronous down-modulation of mir-17 family members is an early causative event in the retinal angiogenic switch. Proceedings of the National Academy of Sciences, 1–6.

Ozel, I., Duerig, I., Domnich, M., Lang, S., Pylaeva, E., & Jablonska, J. (2022). The good, the bad, and the ugly: Neutrophils, angiogenesis, and cancer. Cancers, 14(3), 536.

Patel, N. S., Li, J.-L., Generali, D., Poulsom, R., Cranston, D. W., & Harris, A. L. (2005).

Up-regulation of Delta-like 4 ligand in human tumor vasculature and the role of basal expression in endothelial cell function. Cancer Research, 65(19), 8690–8697.

Phng, L., & Gerhardt, H. (2009). Angiogenesis. Developmental Cell, 16(2), 196–208.

Polacheck, W. J., Kutys, M. L., Yang, J., Eyckmans, J., Wu, Y., Vasavada, H., Hirschi, K. K., & Chen, C. S. (2017). A non-canonical Notch complex regulates adherens junctions and vascular barrier function. Nature, 552(7684), 258–262.

Qing, X., Xu, W., Liu, S., Chen, Z., Ye, C., & Zhang, Y. (2022). Molecular characteristics, clinical significance, and cancer immune interactions of angiogenesis associated genes in gastric cancer. Frontiers in Immunology, 13, 843077.

Qi, S., Deng, S., Lian, Z., & Yu, K. (2022). Novel drugs with high efficacy against tumor angiogenesis. International Journal of Molecular Sciences, 23(13), 6934.

Reiche, F. V., Bacal, F., & Mano, M. S. (2009). Inibidores da angiogênese e seus efeitos cardiovasculares no paciente com câncer: Importância do manejo multidisciplinar. Revista da Sociedade de Cardiologia do Estado de São Paulo, 19(4), 572–583.

Ross, D. A., & Kadesch, T. (2001). The Notch intracellular domain can function as a coactivator for LEF-1. Molecular and Cellular Biology, 21(22), 7537–7544.

Sarin, A., & Marcel, N. (2017). The Notch1-autophagy interaction: Regulating self-eating for survival. Autophagy, 13(2), 446–447.

Sayama, H. (2015). Introduction to the modeling and analysis of complex systems. Open SUNY Textbooks.

Scianna, M., Bell, C., & Preziosi, L. (2013). A review of mathematical models for the formation of vascular networks. Journal of Theoretical Biology, 333, 174–209.

Shibuya, M. (2011). Vascular endothelial growth factor (VEGF) and its receptor (VEGFR) signaling in angiogenesis: A crucial target for anti-and pro-angiogenic therapies. Genes & Cancer, 2(12), 1097–1105.

Siebel, C., & Lendahl, U. (2017). Notch signaling in development, tissue homeostasis, and disease. Physiological Reviews, 97, 1235–1294.

Silva, G. M. F. (2012). Células-tronco e surgimento de tumores (Dissertação de mestrado, Centro Federal de Educação Tecnológica de Minas Gerais). Belo Horizonte, Brasil.

Siveen, K. S., Prabhu, K., Krishnankutty, R., Kuttikrishnan, S., Tsakou, M., Alali, F. Q., Dermime, S., Mohammad, R. M., & Uddin, S. (2017). Vascular endothelial growth factor (VEGF) signaling in tumour vascularization. Current Vascular Pharmacology, 15(7), 339–351.

Troost, T., Binshtok, U., Sprinzak, D., & Klein, T. (2023). Cis-inhibition suppresses basal Notch signaling during sensory organ precursor selection. Proceedings of the National Academy of Sciences, 120(23), e2214535120.

Thurston, G., & Kitajewski, J. (2008). VEGF and delta-notch: Interacting signalling pathways in tumour angiogenesis. British Journal of Cancer, 99(8), 1204–1209.

Wang, Z., Li, Y., Banerjee, S., & Sarkar, F. H. (2009). Emerging role of Notch in stem cells and cancer. Cancer Letters, 279(1), 8–12.

Xiu, M. X., & Liu, Y. M. (2019). The role of oncogenic Notch2 signaling in cancer. American Journal of Cancer Research, 9(5), 837–854.

Zhou, B., Lin, W., Long, Y., Yang, Y., Zhang, H., Wu, K., & Chu, Q. (2022). Notch signaling pathway: Architecture, disease, and therapeutics. Signal Transduction and Targeted Therapy, 7(1), 95.