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Stochasticity and Determinism in Models of Hematopoiesis

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A Systems Biology Approach to Blood

Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 844))

Abstract

This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader’s use.

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References

  1. Whichard ZL, Sarkar CA, Kimmel M, Corey SJ. Hematopoiesis and its disorders: a systems biology approach. Blood. 2010;115(12):2339–47.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  2. Snijder B, Pelkmans L. Origins of regulated cell-to-cell variability. Nat Rev Mol Cell Biol. 2011;12(2):119–25.

    Article  CAS  PubMed  Google Scholar 

  3. Pelkmans L. Using cell-to-cell variability-a new era in molecular biology. Science. 2012;336(6080):425–6.

    Article  CAS  PubMed  Google Scholar 

  4. Raue A, Becker V, Klingmüller U, Timmer J. Identifiability and observability analysis for experimental design in nonlinear dynamical models. Chaos. 2010;20(4):045105.

    Article  CAS  PubMed  Google Scholar 

  5. Laurent M, Deschatrette J, Wolfrom Claire M. Unmasking chaotic attributes in time series of living cell populations. PLoS ONE. 2010;5(2):e9346.

    Article  PubMed Central  PubMed  Google Scholar 

  6. Kimmel M, Darzynkiewicz Z, Arino O, Traganos F. Analysis of a cell cycle model based on unequal division of metabolic constituents to daughter cells during cytokinesis. J Theor Biol. 1984;110(4):637–64.

    Article  CAS  PubMed  Google Scholar 

  7. Schroeder T. Long-term single-cell imaging of mammalian stem cells. Nat Methods. 2011;8(4):S30–5.

    Article  CAS  PubMed  Google Scholar 

  8. Takizawa H, Boettcher S, Manz MG. Demand-adapted regulation of early hematopoiesis in infection and inflammation. Blood. 2012;119(13):2991–3002.

    Article  CAS  PubMed  Google Scholar 

  9. Ogawa M. Stochastic model revisited. Int J Hematol. 1999;69(1):2.

    CAS  PubMed  Google Scholar 

  10. Abkowitz JL, Catlin SN, Guttorp P. Evidence that hematopoiesis may be a stochastic process in vivo. Nat Med. 1996;2(2):190–7.

    Article  CAS  PubMed  Google Scholar 

  11. Brock A, Chang H, Huang S. Non-genetic heterogeneity—a mutation-independent driving force for the somatic evolution of tumours. Nat Rev Genet. 2009;10(5):336–42.

    Article  CAS  PubMed  Google Scholar 

  12. Cohen Ariel A, et al. Dynamic proteomics of individual cancer cells in response to a drug. Science. 2008;322(5907):1511–6.

    Article  Google Scholar 

  13. Sigal A, et al. Variability and memory of protein levels in human cells. Nature. 2006;444(7119):643–6.

    Article  CAS  PubMed  Google Scholar 

  14. Webb GF. Random transitions, size control, and inheritance in cell population dynamics. Math Biosci. 1987;85(1):71–91.

    Article  Google Scholar 

  15. Arino O, Kimmel M. Asymptotic analysis of a cell cycle model based on unequal division. SIAM J Appl Math. 1987;47(1):128–45.

    Article  Google Scholar 

  16. Tyson JJ, Hannsgen KB. Cell growth and division: a deterministic/probabilistic model of the cell cycle. J Math Biol. 1986;23(2):231–46.

    Article  CAS  PubMed  Google Scholar 

  17. Harnevo LE, Agur Z. Drug resistance as a dynamic process in a model for multistep gene amplification under various levels of selection stringency. Cancer Chemother Pharmacol. 1992;30(6):469–76.

    Article  CAS  PubMed  Google Scholar 

  18. Kimmel M, Axelrod DE. Mathematical models of gene amplification with applications to cellular drug resistance and tumorigenicity. Genetics. 1990;125(3):633–44.

    CAS  PubMed Central  PubMed  Google Scholar 

  19. Gupta PB, Fillmore CM, Jiang G, Shapira SD, Tao K, Kuperwasser C, Lander ES. Stochastic state transitions give rise to phenotypic equilibrium in populations of cancer cells. Cell. 2011;146(4):633–44.

    Article  CAS  PubMed  Google Scholar 

  20. Chang HH, Hemberg M, Barahona M, Ingber DE, Huang S. Transcriptome-wide noise controls lineage choice in mammalian progenitor cells. Nature. 2008;453(7194):544–7.

    Article  CAS  PubMed  Google Scholar 

  21. Laslo P, Spooner CJ, Warmflash A, Lancki DW, Lee H-J, Sciammas R, Gantner BN, Dinner AR, Singh H. Multilineage transcriptional priming and determination of alternate hematopoietic cell fates. Cell. 2006;126(4):755–66.

    Article  CAS  PubMed  Google Scholar 

  22. Muzzey D, van Oudenaarden A. When it comes to decisions, myeloid progenitors crave positive feedback. Cell. 2006;126(4):650–2.

    Article  CAS  PubMed  Google Scholar 

  23. Loose M, Swiers G, Patient R. Transcriptional networks regulating hematopoietic cell fate decisions. Curr Opin Hematol. 2007;14(4):307–14.

    Article  CAS  PubMed  Google Scholar 

  24. Raser JM, O’Shea EK. Noise in gene expression: origins, consequences, and control. Science. 2005;309(5743):2010–13.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  25. Elowitz MB, Levine AJ, Siggia ED, Swain PS. Stochastic gene expression in a single cell. Sci Sig. 2002;297(5584):1183.

    CAS  Google Scholar 

  26. Lipniacki T, Paszek P, Marciniak-Czochra A, Brasier AR, Kimmel M. Transcriptional stochasticity in gene expression. J Theor Biol. 2006;238(2):348–67.

    Article  CAS  PubMed  Google Scholar 

  27. Samoilov MS, Price G, Arkin AP. From fluctuations to phnotypes: the physiology of noise. Sci Signal. 2006;2006(366):re17.

    Google Scholar 

  28. Tieu KS, Tieu RS, Martinez-Agosto JA, Sehl ME. Stem cell niche dynamics: from homeostasis to carcinogenesis. Stem Cells Int. 2012;2012:9.

    Article  Google Scholar 

  29. Roeder I, Horn M, Glauche I, Hochhaus A, Mueller Martin C, Loeffler M. Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications. Nat Med. 2006;12(10):1181–4.

    Article  CAS  PubMed  Google Scholar 

  30. Uguz A, Coskun M, Yuzbey S, Kizilors A, Karadogan I, Gura A, Yoldas B, Oygur N, Yegin O. Apoptosis of cord blood neutrophils and their response to colony-stimulating factors. Am J Perinatol. 2003;19(08):427–34.

    Article  Google Scholar 

  31. Lajtha LG, Pozzi LV, Schofield R, Fox M. Kinetic properties of haemopoietic stem cells. Cell Prolif. 1969;2(1):39–49.

    Article  Google Scholar 

  32. Haurie C, Dale DC, Mackey MC. Cyclical neutropenia and other periodic hematological disorders: a review of mechanisms and mathematical models. Blood. 1998;92(8):2629–40.

    CAS  PubMed  Google Scholar 

  33. Wazewska-Czyzewska M, Lasota A. Mathematical models of the red cell system. Mat Stos. 1976;6:25–40.

    Google Scholar 

  34. Lo W-C, Chou C-S, Gokoffski KK, Wan FY-M, Lander AD, Calof AL, Nie Q. Feedback regulation in multistage cell lineages. Math Biosci Eng. 2009;6(1):59.

    Article  PubMed Central  PubMed  Google Scholar 

  35. Arino, Ovide, and Marek Kimmel. “Stability analysis of models of cell production systems.” Mathematical Modelling 1986;7(9):1269-1300.

    Google Scholar 

  36. Marciniak-Czochra A, Stiehl T, Ho AD, Jäger W, Wagner W. Modeling of asymmetric cell division in hematopoietic stem cells-regulation of self-renewal is essential for efficient repopulation. Stem Cells Dev. 2009;18(3):377–86.

    Article  CAS  PubMed  Google Scholar 

  37. Nakata Y, Getto P, Marciniak-Czochra A, Alarcón T. Stability analysis of multi-compartment models for cell production systems. J Biol Dyn. 2012;6(Supp. 1):2–18.

    Article  PubMed  Google Scholar 

  38. Getto P, Marciniak-Czochra A, Nakata Y, Vivanco M. dM. Global dynamics of two-compartment models for cell production systems with regulatory mechanisms. Math Biosci. 2013;245:258–68.

    Article  PubMed  Google Scholar 

  39. Stiehl T, Marciniak-Czochra A. Characterization of stem cells using mathematical models of multistage cell lineages. Math Comput Model. 2011;53(7):1505–17.

    Article  Google Scholar 

  40. Marciniak-Czochra A, Stiehl T, Wagner W. Modeling of replicative senescence in hematopoietic development. Aging. 2009;1(8):723.

    CAS  PubMed Central  PubMed  Google Scholar 

  41. Lander AD, Gokoffski KK, Wan FYM, Nie Q, Calof AL. Cell lineages and the logic of proliferative control. PLoS Biol. 2009;7(1):e1000015.

    Article  PubMed Central  Google Scholar 

  42. Foley C, Mackey MC. Dynamic hematological disease: a review. J Math Biol. 2009;58(1-2):285–322.

    Article  PubMed  Google Scholar 

  43. Bernard S, Bélair J, Mackey MC. Oscillations in cyclical neutropenia: new evidence based on mathematical modeling. J Theor Biol. 2003;223(3):283–98.

    Article  PubMed  Google Scholar 

  44. Stiehl T, Ho AD, Marciniak-Czochra A. The impact of CD34 + cell dose on engraftment after stem cell transplantations: personalized estimates based on mathematical modeling. Bone Marrow Transp. 2014;49:30–7.

    Article  CAS  Google Scholar 

  45. Stiehl T, Marciniak-Czochra A. Mathematical modelling of leukemogenesis and cancer stem cell dynamics. Math Mod Natural Phenomena. 2012;7:166–202.

    Article  Google Scholar 

  46. Stiehl T, Baran N, Ho AD, Marciniak-Czochra A. Clonal selection and therapy resistance in acute leukemias: mathematical modelling explains different proliferation patterns at diagnosis and relapse. J R Soc Interface. 2014;11:20140079. http://dx.doi.org/10.1098/rsif.2014.0079.

  47. Walenda T, Stiehl T, Braun H, Froebel J, Ho AD, Schroeder T, Goecke T, Germing U, Marciniak-Czochra A, Wagner W. Feedback signals in myelodysplastic syndromes: increased self-renewal of the malignant clone suppresses normal hematopoiesis. PLoS Comput Biol. 2014;10(4):e1003599.

    Google Scholar 

  48. Kim PS, Lee PP. Levy Doron. A PDE model for imatinib-treated chronic myelogenous leukemia. Bull Math Biol. 2008;70(7):1994–2016.

    Article  PubMed  Google Scholar 

  49. Al-Hajj M, Clarke MF. Self-renewal and solid tumor stem cells. Oncogene. 2004;23(43):7274–82.

    Article  CAS  PubMed  Google Scholar 

  50. Moore KA, Lemischka IR. Stem cells and their niches. Science. 2006;311(5769):1880–5.

    Article  CAS  PubMed  Google Scholar 

  51. Lord BI. Biology of the haemopoietic stem cell. In: Stem cells. 1997. pp. 401–22.

    Google Scholar 

  52. Uchida N, Fleming WH, Alpern EJ, Weissman IL. Heterogeneity of hematopoietic stem cells. Curr Opin Immunol. 1993;5(2):177–84.

    Article  CAS  PubMed  Google Scholar 

  53. Doumic M, Marciniak-Czochra A, Perthame B, Zubelli JP. A structured population model of cell differentiation. SIAM J Appl Math. 2011;71(6):1918–40.

    Article  Google Scholar 

  54. Gwiazda P, Jamróz G, Marciniak-Czochra A. Models of discrete and continuous cell differentiation in the framework of transport equation. SIAM J Math Anal. 2012;44(2):1103–33.

    Article  Google Scholar 

  55. Arino O, Kimmel M. Comparison of approaches to modeling of cell population dynamics. SIAM J Appl Math. 1993;53(5):1480–504.

    Article  Google Scholar 

  56. Haccou P, Jagers P, Vatutin VA. Branching processes: variation, growth, and extinction of populations. Vol. 5. Cambridge: Cambridge University Press; 2005.

    Google Scholar 

  57. Kimmel M, Corey S. Stochastic hypothesis of transition from inborn neutropenia to AML: interactions of cell population dynamics and population genetics. Front Oncol. 2013;3:89.

    Article  PubMed Central  PubMed  Google Scholar 

  58. Glaubach T, Corey SJ. From famine to feast: sending out the clones. Blood. 2012;119(22):5063–4.

    Article  CAS  PubMed  Google Scholar 

  59. Dong F, Van Paassen M, Van Buitenen C, Hoefsloot LH, Lowenberg B, Touw IP. A point mutation in the granulocyte colony-stimulating factor receptor (G-CSF-R) gene in a case of acute myeloid leukemia results in the overexpression of a novel G-CSF-R isoform. Blood. 1995;85(4):902–11.

    CAS  PubMed  Google Scholar 

  60. Donadieu J, Leblanc T, Bader Meunier B, Barkaoui M, Fenneteau O, Bertrand Y, Maier-Redelsperger M, et al. Analysis of risk factors for myelodysplasias, leukemias and death from infection among patients with congenital neutropenia. Experience of the French Severe Chronic Neutropenia Study Group. Haematologica. 2005;90(1):45–53.

    PubMed  Google Scholar 

  61. Rosenberg PS, Alter BP, Bolyard AA, Bonilla MA, Boxer LA, Cham B, Fier C, et al. The incidence of leukemia and mortality from sepsis in patients with severe congenital neutropenia receiving long-term G-CSF therapy. Blood. 2006;107(12):4628–35.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  62. Germeshausen M, Skokowa J, Ballmaier M, Zeidler C, Welte K. G-CSF receptor mutations in patients with congenital neutropenia. Curr Opin Hematol. 2008;15(4):332–7.

    Article  CAS  PubMed  Google Scholar 

  63. Beekman R, Touw IP. G-CSF and its receptor in myeloid malignancy. Blood. 2010;115(25):5131–6.

    Article  CAS  PubMed  Google Scholar 

  64. Beekman R, Valkhof MG, Sanders MA, van Strien PMH, Haanstra JR, Broeders L, Geertsma-Kleinekoort WM, et al. Sequential gain of mutations in severe congenital neutropenia progressing to acute myeloid leukemia. Blood. 2012;119(22):5071–7.

    Article  CAS  PubMed  Google Scholar 

  65. Rosenberg PS, Zeidler C, Bolyard AA, Alter BP, Bonilla MA, Boxer LA, Dror Y, et al. Stable long‐term risk of leukaemia in patients with severe congenital neutropenia maintained on G-CSF therapy. Br J Haematol. 2010;150(2):196–9.

    CAS  PubMed Central  PubMed  Google Scholar 

  66. Kimmel M, Axelrod DE. Branching processes in biology. Springer New York;2002.

    Google Scholar 

  67. Schroeder T. Asymmetric cell division in normal and malignant hematopoietic precursor cells. Cell Stem Cell. 2007;1(5):479–81.

    Article  CAS  PubMed  Google Scholar 

  68. Wu M, Kwon HY, Rattis F, Blum J, Zhao C, Ashkenazi R, Jackson TL, Gaiano N, Oliver T, Reya T. Imaging hematopoietic precursor division in real time. Cell Stem Cell. 2007;1(5):541–54.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  69. Gardner TS, Cantor CR, Collins JJ. Construction of a genetic toggle switch in Escherichia coli. Nature. 2000;403(6767):339–42.

    Article  CAS  PubMed  Google Scholar 

  70. Vose JM, Armitage JO. Clinical applications of hematopoietic growth factors. J Clin Oncol. 1995;13(4):1023–35.

    CAS  PubMed  Google Scholar 

  71. Awaya N, Uchida H, Miyakawa Y, Kinjo K, Matsushita H, Nakajima H, Ikeda Y, Kizaki M. Novel variant isoform of G-CSF receptor involved in induction of proliferation of FDCP‐2 cells: relevance to the pathogenesis of myelodysplastic syndrome. J Cell Physiol. 2002;191(3):327–35.

    Article  CAS  PubMed  Google Scholar 

  72. Loinger A, Lipshtat A, Balaban NQ, Biham O. Stochastic simulations of genetic switch systems. Phys Rev E. 2007;75(2):021904.

    Article  Google Scholar 

  73. Laslo P, Pongubala JMR, Lancki DW, Singh H. Gene regulatory networks directing myeloid and lymphoid cell fates within the immune system. Semin Immunol. 2008;20(4):228–35.

    Article  CAS  PubMed  Google Scholar 

  74. Michaels JL, Naudot V, Liebovitch LS. Dynamic stabilization in the PU1-GATA1 circuit using a model with time-dependent kinetic change. Bull Math Biol. 2011;73(9):2132–51.

    Article  PubMed  Google Scholar 

  75. Jaruszewicz J, Zuk PJ, Lipniacki T. Type of noise defines global attractors in bistable molecular regulatory systems. J Theor Biol. 2013;317:140–51.

    Article  PubMed Central  PubMed  Google Scholar 

  76. Traulsen A, Pacheco JM, Luzzatto L, Dingli D. Somatic mutations and the hierarchy of hematopoiesis. Bioessays. 2010;32(11):1003–8.

    Article  CAS  PubMed  Google Scholar 

  77. Wilson A, Laurenti E, Oser G, van der Wath RC, Blanco-Bose W, Jaworski M, Offner S, et al. Hematopoietic stem cells reversibly switch from dormancy to self-renewal during homeostasis and repair. Cell. 2008;135(6):1118–29.

    Article  CAS  PubMed  Google Scholar 

  78. Becker V, Schilling M, Bachmann J, Baumann U, Raue A, Maiwald T, Timmer J, Klingmuller U. Covering a broad dynamic range: information processing at the erythropoietin receptor. Sci Signal. 2010;328(5984):1404.

    CAS  Google Scholar 

  79. Moolgavkar SH, Knudson AG. Mutation and cancer: a model for human carcinogenesis. J Natl Cancer Inst. 1981;66(6):1037–52.

    CAS  PubMed  Google Scholar 

  80. Radivoyevitch T, et al. Quantitative modeling of chronic myeloid leukemia: insights from radiobiology. Blood. 2012;119(19):4363–71.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  81. Ley TJ, et al. Genomic and epigenomic landscapes of adult de novo acute myeloid leukemia. N Engl J Med. 2013;368(22):2059–74.

    Article  Google Scholar 

  82. Bozic I, Antal T, Ohtsuki H, Carter H, Kim D, Chen S, Karchin R, Kinzler KW, Vogelstein B, Nowak MA. Accumulation of driver and passenger mutations during tumor progression. Proc Natl Acad Sci U S A. 2010;107(43):18545–50.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  83. Tomasetti C, Vogelstein B, Parmigiani G. Half or more of the somatic mutations in cancers of self-renewing tissues originate prior to tumor initiation. Proc Natl Acad Sci U S A. 2013;110(6):1999–2004.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  84. Sehl M, Zhou H, Sinsheimer JS, Lange KL. Extinction models for cancer stem cell therapy. Math Biosci. 2011;234(2):132–46.

    Article  PubMed Central  PubMed  Google Scholar 

  85. Parkin B, Ouillette P, Li Y, Keller J, Lam C, Roulston D, Li C, Shedden K, Malek SN. Clonal evolution and devolution after chemotherapy in adult acute myelogenous leukemia. Blood. 2013;121(2):369–77.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  86. Peixoto D, Dingli D, Pacheco JM. Modelling hematopoiesis in health and disease. Math Comput Model. 2011;53(7):1546–57.

    Article  Google Scholar 

  87. Morrison SJ, Kimble J. Asymmetric and symmetric stem-cell divisions in development and cancer. Nature. 2006;441(7097):1068–74.

    Article  CAS  PubMed  Google Scholar 

  88. Molofsky AV, Pardal R, Morrison SJ. Diverse mechanisms regulate stem cell self-renewal. Curr Opin Cell Biol. 2004;16(6):700–7.

    Article  CAS  PubMed  Google Scholar 

  89. Shenghui H, Nakada D, Morrison SJ. Mechanisms of stem cell self-renewal. Annu Rev Cell Dev. 2009;25:377–406.

    Article  Google Scholar 

  90. Huang S. Systems biology of stem cells: three useful perspectives to help overcome the paradigm of linear pathways. Philos Trans R Soc Lond B Biol Sci. 2011;366(1575):2247–59.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  91. Bertolusso R, Kimmel M. Modeling spatial effects in early carcinogenesis: stochastic versus deterministic reaction-diffusion systems. Math Model Nat Phenom. 2012;7(1):245–60.

    Article  Google Scholar 

  92. Marciniak-Czochra A, Kimmel M. Reaction-difusion model of early carcinogenesis: the effects of influx of mutated cells. Math Model Nat Phenom. 2008;3(7):90–114.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics and Bioengineering, Rice University, 2102 Duncan Hall, 6100 Main St., 77005, Houston, TX, USA

    Marek Kimmel

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  1. Marek Kimmel
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Editors and Affiliations

  1. Departments of Pediatrics and Cell & Molecular Biology, Northwestern University Feinberg School of Medicine and Lurie Children’s Hospital of Chicago, Chicago, Illinois, USA

    Seth Joel Corey

  2. Department of Statistics, Rice University, Houston, Texas, USA

    Marek Kimmel

  3. Northwestern University Comprehensive Cancer Center, Evanston, Illinois, USA

    Joshua N. Leonard

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Kimmel, M. (2014). Stochasticity and Determinism in Models of Hematopoiesis. In: Corey, S., Kimmel, M., Leonard, J. (eds) A Systems Biology Approach to Blood. Advances in Experimental Medicine and Biology, vol 844. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2095-2_7

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