Adding self-renewal in committed erythroid progenitors improves the biological relevance of a mathematical model of erythropoiesis

Journal of Theoretical Biology

Volumn 250, Issue 2, 2008, Pages 322-338

  Crauste, Fabien ^a   Pujo Menjouet, Laurent ^a   Génieys, Stéphane ^a   Molina, Clément ^b   Gandrillon, Olivier ^b  

^a UNIVERSITÉ LYON 1   (France)

^b UNIVERSITÉ LYON 1   (France)

Author keywords

Age structured model; Delay differential equations; Self renewal; Severe anemia; Stress erythropoiesis

Indexed keywords

ANEMIA; APOPTOSIS; COMPARATIVE STUDY; DATA SET; MODELING;

ANEMIA; APOPTOSIS; ARTICLE; CELL COMPARTMENTALIZATION; CELL FUNCTION; ERYTHROID PRECURSOR CELL; ERYTHROPOIESIS; FEEDBACK SYSTEM; MATHEMATICAL MODEL; NEGATIVE FEEDBACK; NONHUMAN; OSCILLATION; POSITIVE FEEDBACK; PRIORITY JOURNAL; STEADY STATE;

MUS;

EID: 37449011452     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2007.09.041     Document Type: Article

References (61)

1. Ackleh A.S., Banks H.T., and Deng K. A finite difference approximation for a coupled system of nonlinear size-structured population. Nonlinear Anal. 50 (2002) 727-748 10.1016/S0362-546X(01)00780-5
2. Ackleh A.S., Deng K., Ito K., and Thibodeaux J. A structured erythropoiesis model with nonlinear cell maturation velocity and hormone decay rate. Math. Biosci. 204 (2006) 21-48 10.1016/j.mbs.2006.08.004
3. Adimy M., and Crauste F. Global stability of a partial differential equation with distributed delay due to cellular replication. Nonlinear Anal. 54 8 (2003) 1469-1491 10.1016/S0362-546X(03)00197-4
4. Adimy M., and Crauste F. Modelling and asymptotic stability of a growth factor-dependent stem cells dynamics model with distributed delay. Discrete Continuous Dynamical Syst. Ser. B 8 1 (2007) 19-38
5. Adimy M., Crauste F., and Pujo-Menjouet L. On the stability of a maturity structured model of cellular proliferation. Discrete Continuous Dynamical Syst. Ser. A 12 3 (2005) 501-522
6. Adimy M., Crauste F., and Ruan S. A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. SIAM J. Appl. Math. 65 4 (2005) 1328-1352
7. Adimy M., Crauste F., and Ruan S. Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases. Bull. Math. Biol. 68 8 (2006) 2321-2351
8. Adimy M., Crauste F., and Ruan S. Periodic oscillations in leukopoiesis models with two delays. J. Theor. Biol. 242 (2006) 288-299 10.1016/j.jtbi.2006.02.020
9. Adimy, M., Crauste, F., El Abdllaoui, A., 2007. Asymptotic behavior of a discrete maturity structured system of hematopoietic stem cells dynamics with several delays. Math. Modelling Nat. Phenom. 1 (2).
10. Adimy M., and Pujo-Menjouet L. Asymptotic behaviour of a singular transport equation modelling cell division. Discrete Continuous Dynamical Syst. Ser. B 3 (2003) 439-456
11. Banks H.T., Cole C.E., Schlosser P.M., and Hien T. Modelling and optimal regulation of erythropoiesis subject to benzene intoxication. Math. Biol. Eng. 1 1 (2004) 15-48
12. Bauer A., Tronche F., Wessely O., Kellendonk C., Reichardt H.M., Steinlein P., Schutz G., and Beug H. The glucocorticoid receptor is required for stress erythropoiesis. Genes Dev. 13 (1999) 2996-3002
13. Bélair J., Mackey M.C., and Mahaffy J.M. Age-structured and two-delay models for erythropoiesis. Math. Biosci. 128 (1995) 317-346 10.1016/0025-5564(94)00078-E
14. Berlin N.I., and Lotz C. Life span of the red blood cell of the rat following acute hemorrhage. Proc. Soc. Exp. Biol. Med. 78 (1951) 788
15. Bernard S., Bélair J., and Mackey M.C. Oscillations in cyclical neutropenia: new evidence based on mathematical modeling. J. Theor. Biol. 223 (2003) 283-298 10.1016/S0022-5193(03)00090-0
16. Bernard S., Pujo-Menjouet L., and Mackey M.C. Analysis of cell kinetics using a cell division marker: mathematical modeling of experimental data. Biophys. J. 84 (2003) 3414-3424
17. Bernard S., Bélair J., and Mackey M.C. Bifurcations in a white-blood-cell production model. C.R. Biol. 327 (2004) 201-210 10.1016/j.crvi.2003.05.005
18. 0 phase in the cell cycle. Cell Tissue Kinet. 19 (1970) 321-334
19. Chappell D., Tilbrook P.A., Bittorf T., Colley S.M., Meyer G.T., and Klinken S.P. Prevention of apoptosis in J2E erythroid cells by erythropoietin: involvement of JAK2 but not MAP kinases. Cell Death Differ. 4 (1997) 105-113
20. Colijn C., and Mackey M.C. A mathematical model of hematopoiesis-I. Periodic chronic myelogenous leukemia. J. Theor. Biol. 237 (2005) 117-132 10.1016/j.jtbi.2005.03.033
21. Colijn C., and Mackey M.C. A mathematical model of hematopoiesis-II. Cyclical neutropenia. J. Theor. Biol. 237 (2005) 133-146 10.1016/j.jtbi.2005.03.034
22. Ferrell J.E. Tripping the switch fantastic: how a protein kinase cascade can convert graded inputs into switch-like outputs. Trends Biochem. Sci. 21 12 (1996) 460-466
23. Ferrell J.E. How responses get more switch-like as you move down a protein kinase cascade. Trends Biochem. Sci. 22 8 (1997) 288-289
24. Gandrillon O. The v-erbA oncogene. Assessing its differentiation-blocking ability using normal chicken erythrocytic progenitor cells. Methods Mol. Biol. 202 (2002) 91-107
25. Gandrillon O., Schmidt U., Beug H., and Samarut J. TGF-beta cooperates with TGF-alpha to induce the self-renewal of normal erythrocytic progenitors: evidence for an autocrine mechanism. EMBO J. 18 (1999) 2764-2781
26. Haurie C., Dale D.C., and Mackey M.C. Cyclical neutropenia and other periodic hematological diseases: a review of mechanisms and mathematical models. Blood 92 (1998) 2629-2640
27. Haurie C., Dale D.C., and Mackey M.C. Occurrence of periodic oscillations in the differential blood counts of congenital, idiopathic and cyclical neutropenic patients before and during treatment with G-CSF. Exp.. Hematol. 27 (1999) 401-409 10.1016/S0301-472X(98)00061-7
28. Koury M.J., and Bondurant M.C. Erythropoietin retards DNA breakdown and prevents programmed death in erythroid progenitor cells. Science 248 (1990) 378-381
29. Krause D.S. Regulation of hematopoietic stem cell fate. Oncogene 21 (2002) 3262-3269
30. Kuang Y. Delay differential equations with applications in population dynamics. Mathematics in Science and Engineering vol. 191 (1993), Academic Press, New York
31. Lajtha, L.G., 1959. On DNA labeling in the study of the dynamics of bone marrow cell populations. In: Stohlman, Jr., F. (Ed.), The Kinetics of Cellular Proliferation. Grune and Stratton. New York, pp. 173-182.
32. Loeffler M., and Wichmann H.E. A comprehensive mathematical model of stem cell proliferation which reproduces most of the published experimental results. Cell Tissue Kinet. 13 (1980) 543-561
33. Loeffler M., Pantel K., Wulff H., and Wichmann H.E. A mathematical model of erythropoiesis in mice and rats. Part 1. Structure of the model. Cell Tissue Kinet. 22 (1989) 13-30
34. Lomb N.R. Least-squares frequency analysis of unequally spaced data. Astrophys. Space Sci. 39 (1976) 447-462
35. Mackey M.C. Unified hypothesis of the origin of aplastic anaemia and periodic hematopoi{dotless}̈esis. Blood 51 (1978) 941-956
36. Mackey, M.C., 1979. Dynamic hematological disorders of stem cell origin. In: Vassileva-Popova, G., Jensen, E.V. (Eds.), Biophysical and Biochemical Information Transfer in Recognition. Plenum Press, New York, pp. 373-409.
37. Mackey, M.C., 1997. Mathematical models of hematopoietic cell replication and control. In: Othmer, H.G., Adler, F.R., Lewis, M.A., Dallon, J.C. (Eds.), The Art of Mathematical Modelling: Case Studies in Ecology, Physiology and Biofluids. Prentice-Hall, Englewood Cliffs, NJ, pp. 149-178.
38. Mackey M.C., and Rudnicki R. Global stability in a delayed partial differential equation describing cellular replication. J. Math. Biol. 33 (1994) 89-109
39. Mackey M.C., and Rudnicki R. A new criterion for the global stability of simultaneous cell replication and maturation processes. J. Math. Biol. 38 (1999) 195-219
40. Mahaffy J.M., Belair J., and Mackey M.C. Hematopoietic model with moving boundary condition and state dependent delay: applications in erythropoiesis. J. Theor. Biol. 190 (1998) 135-146 10.1006/jtbi.1997.0537
41. Mitjavila M.T., Le Couedic J.P., Casadevall N., Navarro S., Villeval J.L., Dubart A., and Vainchenker W. Autocrine stimulation by erythropoietin and autonomous growth of human erythroid leukemic cells in vitro. J. Clin. Invest. 88 3 (1991) 789-797
42. Nagai K., Oue K., and Kawagoe H. Studies on the short-lived reticulocytes by use of the in vitro labeling method. Acta. haematol. Jpn 31 (1968) 967
43. Nagai K., Ishizu K., and Kakishita E. Studies on the erythroblast dynamics based on the production of fetal hemoglobin. Acta Haematol. Jpn. 34 (1971)
44. Pain B., Woods C.M., Saez J., Flickinger T., Raines M., Kung H.J., Peyrol S., Moscovici C., Moscovici G., Jurdic P., Lazarides E., and Samarut J. 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) 37-46 10.1016/0092-8674(91)90405-N
45. Pantel K., Loeffler M., Bungart B., and Wichmann H.E. A mathematical model of erythropoiesis in mice and rats. Part 4. Differences between bone marrow and spleen. Cell Tissue Kinet. 23 (1990) 283-297
46. 0 model of hematopoietic stem cells. SIAM J. Appl. Dynamical Syst. 4 2 (2005) 312-332
47. Pujo-Menjouet L., and Mackey M.C. Contribution to the study of periodic chronic myelogenous leukemia. C.R. Biol. 327 (2004) 235-244 10.1016/j.crvi.2003.05.004
48. Roeder I. Quantitative stem cell biology: computational studies in the hematopoietic system. Curr. Opinion Hematol. 13 (2006) 222-228
49. Roeder I., and Loeffler M. A novel dynamic model of hematopoietic stem cell organization based on the concept of within-tissue plasticity. Exp. Hematol. 30 (2002) 853-861
50. Sakata S., Enoki Y., Tomita S., and Kohzuki H. In vitro erythropoietin assay based on erythroid colony formation in fetal mouse liver cell culture. Br. J. Haematol. 61 2 (1985) 293-302
51. Shampine, L.F., Thompson, S., 2001. Solving DDEs in Matlab. Appl. Numer. Math. 37, 441-458. doi:10.1016/S0168-9274(00)00055-6. 〈http://www.radford.edu/thompson/webddes/〉.
52. Shimada A. The maturation of reticulocytes. II Life-span of red cells originating from stress reticulocytes. Acta Med. Okayama 29 4 (1975) 283-289
53. Starck J., Cohet N., Gonnet C., Sarrazin S., Doubeikovskaia Z., Doubeikovski A., Verger A., Duterque-Coquillaud M., and Morle F. Functional cross-antagonism between transcription factors FLI-1 and EKLF. Mol. Cell Biol. 23 4 (2003) 1390-1402
54. Stohlman F. Humoral regulation of erythropoiesis. VII. Shortened survival of erythrocytes by erythropoietin or severe anemia. Proc. Soc. Exp. Biol. Med. 107 (1961) 884
55. Walter H., Krob E.J., and Ascher G.S. Abnormal membrane surface properties during maturation of rat reticulocytes elicited by bleeding as measured by partition in two-polymer aqueous phases. Br. J. Haematol. 31 2 (1975) 149-157
56. Watt F.M., and Hogan B.L. Out of Eden: stem cells and their niches. Science 287 (2000) 1427-1430
57. Weissman I.L. Stem cells: units of development, units of regeneration, and units in evolution. Cell 100 (2000) 157-168 10.1016/S0092-8674(00)81692-X
58. Wichman H.E., and Loeffler M. Mathematical Modeling of Cell Proliferation (1985), CRC Press, Boca Raton, FL
59. Wichmann H.E., Loeffler M., and Schmitz S. A concept of hemopoietic regulation and its biomathematical realisation. Blood Cells 14 (1985) 411-429
60. Wichmann H.E., Loeffler M., Pantel K., and Wulff H. A mathematical model of erythropoiesis in mice and rats. Part 2. Stimulated erythropoiesis. Cell Tissue Kinet. 22 (1989) 31-49
61. Wulff H., Wichmann H.E., Loeffler M., and Pantel K. A mathematical model of erythropoiesis in mice and rats. Part 3. Suppressed erythropoiesis. Cell Tissue Kinet. 22 (1989) 51-61