# Dynamics of Erythroid Progenitors and Erythroleukemia

N. Bessonov; F. Crauste; I. Demin; V. Volpert

Mathematical Modelling of Natural Phenomena (2009)

- Volume: 4, Issue: 3, page 210-232
- ISSN: 0973-5348

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topBessonov, N., et al. "Dynamics of Erythroid Progenitors and Erythroleukemia." Mathematical Modelling of Natural Phenomena 4.3 (2009): 210-232. <http://eudml.org/doc/222310>.

@article{Bessonov2009,

abstract = {
The paper is devoted to mathematical modelling of erythropoiesis,
production of red blood cells in the bone marrow.
We discuss intra-cellular regulatory networks which determine
self-renewal and differentiation of erythroid progenitors.
In the case of excessive self-renewal, immature cells can fill
the bone marrow resulting in the development of leukemia.
We introduce a parameter characterizing the strength of mutation.
Depending on its value, leukemia will or will not develop.
The simplest model of treatment of acute myeloid leukemia with
chemotherapy allows us to determine the conditions of successful
treatment or of its failure. We show
that insufficient treatment can worsen the situation.
In some cases curing may not be possible even
without resistance to treatment.
Modelling presented in this work is based on ordinary differential
equations, reaction-diffusion systems and individual based
approach.
},

author = {Bessonov, N., Crauste, F., Demin, I., Volpert, V.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {erythropoiesis; leukemia; reaction-diffusion systems; cellular
modelling; cellular modelling},

language = {eng},

month = {6},

number = {3},

pages = {210-232},

publisher = {EDP Sciences},

title = {Dynamics of Erythroid Progenitors and Erythroleukemia},

url = {http://eudml.org/doc/222310},

volume = {4},

year = {2009},

}

TY - JOUR

AU - Bessonov, N.

AU - Crauste, F.

AU - Demin, I.

AU - Volpert, V.

TI - Dynamics of Erythroid Progenitors and Erythroleukemia

JO - Mathematical Modelling of Natural Phenomena

DA - 2009/6//

PB - EDP Sciences

VL - 4

IS - 3

SP - 210

EP - 232

AB -
The paper is devoted to mathematical modelling of erythropoiesis,
production of red blood cells in the bone marrow.
We discuss intra-cellular regulatory networks which determine
self-renewal and differentiation of erythroid progenitors.
In the case of excessive self-renewal, immature cells can fill
the bone marrow resulting in the development of leukemia.
We introduce a parameter characterizing the strength of mutation.
Depending on its value, leukemia will or will not develop.
The simplest model of treatment of acute myeloid leukemia with
chemotherapy allows us to determine the conditions of successful
treatment or of its failure. We show
that insufficient treatment can worsen the situation.
In some cases curing may not be possible even
without resistance to treatment.
Modelling presented in this work is based on ordinary differential
equations, reaction-diffusion systems and individual based
approach.

LA - eng

KW - erythropoiesis; leukemia; reaction-diffusion systems; cellular
modelling; cellular modelling

UR - http://eudml.org/doc/222310

ER -

## References

top- M. Adimy, and F. Crauste, Modelling and asymptotic stability of a growth factor-dependent stem cells dynamics model with distributed delay, Discrete Cont. Dyn. Syst. Ser. B 8 (2007), pp. 19–38.
- M. Adimy, F. Crauste, and A. El Abdllaoui, Asymptotic Behavior of a Discrete Maturity Structured System of Hematopoietic Stem Cells Dynamics with Several Delays, Math. Model. Nat. Phenom., 1 (2006), No. 2, pp. 1–22.
- M. Adimy, F. Crauste, and S. Ruan, A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia, SIAM J. Appl. Math., 65 (2005), pp. 1328–1352.
- M. Adimy, F. Crauste, and S. Ruan, Periodic Oscillations in Leukopoiesis Models with Two Delays, J. Theor. Biol., 242 (2006), pp. 288–299.
- M. Adimy, F. Crauste, and S. Ruan, Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases, Bull. Math. Biol., 68 (2006), pp. 2321–2351.
- A.R.A. Anderson, K.A. Rejniak, P. Gerlee, and V. Quaranta, Modelling of Cancer Growth, Evolution and Invasion: Bridging Scales and Models, Math. Model. Nat. Phenom. 2 (2007), pp.1–27.
- A. Bauer, F. Tronche, O. Wessely, C. Kellendonk, H.M. Reichardt, P. Steinlein, G. Schutz, and H. Beug, The glucocorticoid receptor is required for stress erythropoiesis, Genes Dev. 13 (1999), pp. 2996–3002.
- J. Bélair, M.C. Mackey, and J.M. Mahaffy, Age-structured and two delay models for erythropoiesis, Math. Biosci. 128 (1995), pp. 317–346.
- S. Bernard, J. Bélair, and M.C. Mackey, Oscillations in cyclical neutropenia: new evidence based on mathematical modeling, J. Theor. Biol. 223 (2003), pp. 283–298.
- N. Bessonov, L. Pujo-Menjouet, and V. Volpert. Cell modelling of hematopoiesis. Math. Model. Nat. Phenom., 1 (2006), No. 2, pp. 81-103.
- N. Bessonov, I. Demin, L. Pujo-Menjouet, and V. Volpert. A multi-agent model describing self-renewal or differentiation effect of blood cell population. Mathematical and computer modelling, 49 (2009), pp. 2116-2127.
- D. Bonnet, Haematopoietic stem cells, Pathol. 197 (2002), pp. 430–440.
- V. Capasso, and D. Bakstein. An introduction to continuous-time stochastic processes. Birkhauser, Boston, 2005.
- C. Colijn, and M.C. Mackey, A mathematical model of hematopoiesis-I. Periodic chronic myelogenous leukemia, J. Theor. Biol. 237 (2005), pp. 117–132.
- C. Colijn, and M.C. Mackey, A mathematical model of hematopoiesis-II. Cyclical neutropenia, J. Theor. Biol. 237 (2005), pp. 133–146. erythropoiesis
- F. Crauste, L. Pujo-Menjouet, S. Génieys, C. Molina, and O. Gandrillon, Adding self-renewal in committed erythroid progenitors improves the biological relevance of a mathematical model of erythropoiesis, J. Theor. Biol. 250 (2008), pp. 322–338.
- S. Dazy, F. Damiola, N. Parisey, H. Beug, and O. Gandrillon, The MEK-1/ ERKs signalling pathway is differentially involved in the self-renewal of early and late avian erythroid progenitor cells, Oncogene, 22 (2003), pp. 9205–9216.
- R. De Maria, U. Testa, L. Luchetti, A. Zeuner, G. Stassi, E. Pelosi, R. Riccioni, N. Felli, P. Samoggia, and C. Peschle, Apoptotic role of Fas/Fas ligand system in the regulation of erythropoiesis, Blood, 93.3 (1999), pp. 796–803.
- I. Demin, F. Crauste, O. Gandrillon, and V. Volpert, A multi-scale model of erythropoiesis, Journal of Biological Dynamics (in press). DOI: DOI10.180/17513750902777642
- A. Ducrot, and V. Volpert. On a model of leukemia development with a spatial cell distribution. Math. Model. Nat. Phenom., 2 (2007), No. 3, 101-120.
- O. Gandrillon, U. Schmidt, H. Beug, and J. Samarut, TGF-beta cooperates with TGF-alpha to induce the self-renewal of normal erythrocytic progenitors: evidence for an autocrine mechanism, EMBO J. 18 (1999), pp. 2764–2781.
- S. Huang, Y.-P.Guo, G. May, and T. Enver, Bifurcation dynamics in lineage-commitment in bipotent progenitor cells, Dev. biol. 305 (2007), pp. 695–713.
- M.J. Koury, and M.C. Bondurant, Erythropoietin retards DNA breakdown and prevents programmed death in erythroid progenitor cells, Science, 248 (1990), pp. 378–381.
- C. Lacombe, and P. Mayeux, Biology of erythropoietin, Haematologica, 83 (1998), pp. 724–732.
- M. von Lindern, W. Zauner, G. Mellitzer, P. Steinlein, G. Fritsch, K. Huber, B. Löwenberg, and H. Beug, The glucocorticoid receptor cooperates with the erythropoietin receptor and c-Kit to enhance and sustain proliferation of erythroid progenitors in vitro, Blood, 94 (1999), pp. 550–559.
- M.C. Mackey, Unified hypothesis of the origin of aplastic anaemia and periodic hematopoiesis, Blood, 51 (1978), pp. 941–956.
- F.M. Mazzella, C. Alvares, A. Kowal-Vern, and H.R. Schumacher, The acute erythroleukemias, Clin. Lab. Med., 20 (2000), pp. 119–37.
- V. Munugalavadla, and R. Kapur, Role of c-Kit and erythropoietin receptor in erythropoiesis, Critical Reviews in Oncology/Hematology, 54 (2005), pp. 63–75.
- J.D. Murray, Mathematical Biology, Springer, New York, 2004.
- B. Pain, C.M. Woods, J. Saez, T. Flickinger, M. Raines, S. Peyrol, C. Moscovici, M.G. Moscovici, H.J. Kung, P. Jurdic, et al., EGF-R as a hemopoietic growth factor receptor: the c-erbB product is present in normal chicken erythrocytic progenitor cells and controls their self-renewal, Cell, 65 (1991), pp. 37–46.
- J.C. Panetta, W.E. Evans, and M.H. Cheok, Mechanistic mathematical modeling of mercaptopurine effects on cell cycle of human acute lymphoblastic leukemia cells, Br. Journal of Cancer, 94 (2006), pp. 93–100.
- L. Pujo-Menjouet, and M.C. Mackey, Contribution to the study of periodic chronic myelogenous leukemia, C.R. Biol. 327 (2004), pp. 235–244.
- I. Roeder, and I. Glauche, Towards an understanding of lineage specification in hematopoietic stem cells: A mathematical model for the interaction of transcription factors GATA-1 and PU.1, J. Theor. Biol. 241 (2006), pp. 852–865.
- C. Rubiolo, D. Piazzolla, K. Meissl, H. Beug, J.C. Huber, A. Kolbus, and M. Baccarini, A balance between Raf-1 and Fas expression sets the place of erythroid differentiation, Blood, 108 (2006), pp. 152–159.
- J.E. Rubnitz, B. Gibson, and B.O. Smith, Acute myeloid leukemia, Pediatr. Clin. North. Am., 55 (2008), 1, pp. 21–51.
- E. Shochat, S.M. Stemmer, and L. Segel, Human haematopoiesis in steady state and following intense perturbations, Bull. Math. Biol., 64 (2002), pp. 861–886.
- U. Testa, Apoptotic mechanisms in the control of erythropoiesis, Leukemia, 18 (2004), pp. 1176–1199.
- W. Vainchenker, A. Dusa, and S.N. Constantinescu, JAKs in pathologies: Role of Janus kinases in hematopoietic malignancies and immunodeficiencies, Seminars in Cell and Developmental Biology, 19 (2008), pp. 385–393.
- V. Vainstein, Y. Ginosar, M. Shoham, D.O. Ranmar, A. Ianovski, and Z. Agur, The complex effect of granulocyte colony-stimulating factor on human granulopoiesis analyzed by a new physiologically-based mathematical model, J. Theor. Biol., 234 (2005), pp. 311-327.
- V. Vainstein, Y. Ginosar, M. Shoham, A. Ianovski, A. Rabinovich, Y. Kogan, V. Selitser, and Z. Agur, Improving Cancer Therapy by Doxorubicin and Granulocyte Colony-Stimulating Factor: Insights from a Computerized Model of Human Granulopoiesis, Math. Model. Nat. Phenom., Vol. 1, No. 2 (2006), pp. 70–80.
- A. Volpert, Vl. Volpert, Vit. Volpert. Travelling wave solutions of parabolic systems. AMS, Providence, 1994.
- F.M. Watt, and B.L. Hogan, Out of Eden: stem cells and their niches, Science, 287 (2000), pp. 1427–1430.
- I.L. Weissman, Stem cells: units of development, units of regeneration, and units in evolution, Cell 100 (2000), pp. 157–168.

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