Abstract
A hybrid model of cell dynamics is presented. It is illustrated by model examples and applied to study erythropoiesis (red blood cell production). In this approach, cells are considered as discrete objects while intra-cellular proteins and extra-cellular biochemical substances are described with continuous models. Spatial organization of erythropoiesis occurring in specific structures of the bone marrow, called erythroblastic island, is investigated.
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Aispuru GR, Aguirre MV, Aquino-Esperanza JA, Lettieri CN, Juaristi JA, Brandan NC (2008) Erythroid expansion and survival in response to acute anemia stress: the role of EPO receptor, GATA-1, Bcl-xL and caspase-3. Cell Biol Int 32(8):966–978
Anderson ARA, Rejniaka KA, Gerleea P, Quaranta V (2007) Modelling of cancer growth, evolution and invasion: bridging scales and models. Math Model Nat Phenom 2(3):1–29
Bessonov N, Kurbatova P, Volpert V (2010) Particle dynamics modelling of cell populations. Math Model Nat Phenom. JANO9-the 9th international conference on numerical analysis and optimization 5(7):42–47
Bessonov N, Crauste F, Fischer S, Kurbatova P, Volpert V (2011) Application of hybrid models to blood cell production in the bone marrow. Math Model Nat Phenom 6(7):2–12
Bessonov N, Kurbatova P, Volpert V (2013) Pattern formation in hybrid models of cell populations. In: Capasso V et al (eds) Pattern formation in morphogenesis. Springer Proceedings in Mathematics 15, Springer, Berlin, pp 107–119
Chasis JA, Mohandas N (2008) Erythroblastic islands: niches for erythropoiesis. Blood 112(3):470–478
Crauste F, Demin I, Gandrillon O, Volpert V (2010) Mathematical study of feedback control roles and relevance in stress erythropoiesis. J Theor Biol 263:303–316
De Maria R, Testa U, Luchetti L, Zeuner A, Stassi G, Pelosi E, Riccioni R, Felli N, Samoggia P, Peschle C (1999) Apoptotic role of Fas/Fas ligand system in the regulation of erythropoiesis. Blood 93:796–803
Dillon R, Owen M, Painter K (2008) A single-cell-based model of multicellular growth using the immersed boundary method. AMS Contemp Math 466:1–15
Dormann S, Deutsch A (2002) Modeling of self-organized avascular tumor growth with a hybrid cellular automaton. Silico Biol 2:393–406
Fischer S, Kurbatova P, Bessonov N, Gandrillon O, Volpert V, Crauste F (2012) Modelling erythroblastic islands: using a hybrid model to assess the function of central macrophage. J Theor Biol 298:92–106
Gandrillon O (2002) The v-erbA oncogene. Assessing its differentiation-blocking ability using normal chicken erythrocytic progenitor cells. Methods Mol Biol 202:91–107
Gandrillon O, Schmidt U, Beug H, Samarut J (1999) TGF-beta cooperates with TGF-alpha to induce the self-renewal of normal erythrocytic progenitors: evidence for an autocrine mechanism. Embo J 18:2764–2781
Giverso C, Scianna M, Preziosi L, Lo Buono N, Funaro A (2010) Individual cell-based model for in-vitro mesothelial invasion of ovarian cancer. Math Model Nat Phenom 5(1):203–223
Jeon J, Quaranta V, Cummings PT (2010) An off-lattice hybrid discrete-continuum model of tumor growth and invasion. Biophys J 98(1):37–47
Jiang Y, Pjesivac-Grbovic J, Cantrell C, Freyer JP (2005) A multiscale model for avascular tumor growth. Biophys J 289(6):3884–3894
Karttunen M, Vattulainen I, Lukkarinen A (2004) A novel methods in soft matter simulations. Springer, Berlin
Koulnis M, Liu Y, Hallstrom K, Socolovsky M (2011) Negative autoregulation by Fas stabilizes adult erythropoiesis and accelerates its stress response, PLoS One 6(7):e21192
Koury MJ, Bondurant MC (1990) Erythropoietin retards DNA breakdown and prevents programmed death in erythroid progenitor cells. Science 248:378–381
Kurbatova P, Bernard S, Bessonov N, Crauste F, Demin I, Dumontet C, Fischer S, Volpert V (2011) Hybrid model of erythropoiesis and leukemia treatment with cytosine arabinoside. SIAM J App Math 71(6):2246–2268
McDougall SR, Anderson ARA, Chaplain MAJ, Sherratt JA (2002) Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies. Bull Math Biol 64(4):673–702
Ramis-Conde I, Drasdo D, Anderson ARA, Mark A, Chaplain J (2008) Modeling the influence of the E-Cadherin–Catenin pathway in cancer cell invasion: a multiscale approach. Biophys J 95(1):155–165
Rhodes MM, Kopsombut P, Bondurant MC, Price JO, Koury MJ (2008) Adherence to macrophages in erythroblastic islands enhances erythroblast proliferation and increases erythrocyte production by a different mechanism than erythropoietin. Blood 111(3):1700–1708
Rubiolo C, Piazzolla D, Meissl K, Beug H, Huber JC, Kolbus A, Baccarini M (2006) A balance between Raf-1 and Fas expression sets the pace of erythroid differentiation. Blood 108:152–159
Sawyer ST, Jacobs-Helber SM (2000) Unraveling distinct intracellular signals that promote survival and proliferation: study of erythropoietin, stem cell factor, and constitutive signaling in leukemic cells. J Hematother Stem Cell Res 9:21–29
Scianna M, Merks RMH, Preziosi L, Medico E (2009) Individual cell-based models of cell scatter of ARO and MLP-29 cells in response to hepatocyte growth factor. J Theor Biol 260(1):151–160
Stéphanou A, McDougall SR, Anderson ARA, Chaplain MAJ (2005) Mathematical modelling of flow in 2D and 3D vascular networks: applications to anti-angiogenic and chemotherapeutic drug strategies. Math Comput Model 41(10):1137–1156
Tsiftsoglou AS, Vizirianakis IS, Strouboulis J (2009) Erythropoiesis: model systems, molecular regulators, and developmental programs. IUBMB Life 61(8):800–830
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Authors thank Prof. Mark Koury and all members of the INRIA Team DRACULA for fruitful discussions.
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Kurbatova, P., Eymard, N. & Volpert, V. Hybrid Model of Erythropoiesis. Acta Biotheor 61, 305–315 (2013). https://doi.org/10.1007/s10441-013-9188-2
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DOI: https://doi.org/10.1007/s10441-013-9188-2