Statistical and Mathematical Modeling of Spatiotemporal Dynamics of Stem Cells

  • Walter de Back
  • Thomas Zerjatke
  • Ingo RoederEmail author
Part of the Methods in Molecular Biology book series (MIMB, volume 2017)


Statistical and mathematical modeling are crucial to describe, interpret, compare, and predict the behavior of complex biological systems including the organization of hematopoietic stem and progenitor cells in the bone marrow environment. The current prominence of high-resolution and live-cell imaging data provides an unprecedented opportunity to study the spatiotemporal dynamics of these cells within their stem cell niche and learn more about aberrant, but also unperturbed, normal hematopoiesis. However, this requires careful quantitative statistical analysis of the spatial and temporal behavior of cells and the interaction with their microenvironment. Moreover, such quantification is a prerequisite for the construction of hypothesis-driven mathematical models that can provide mechanistic explanations by generating spatiotemporal dynamics that can be directly compared to experimental observations. Here, we provide a brief overview of statistical methods in analyzing spatial distribution of cells, cell motility, cell shapes, and cellular genealogies. We also describe cell-based modeling formalisms that allow researchers to simulate emergent behavior in a multicellular system based on a set of hypothesized mechanisms. Together, these methods provide a quantitative workflow for the analytic and synthetic study of the spatiotemporal behavior of hematopoietic stem and progenitor cells.

Key words

Statistical modeling Mathematical modeling Spatial statistics Point patterns Cell shape analysis Cell motility Cellular genealogies Cell-based modeling Cellular Potts model Center-based model 



The work presented in this paper is supported by Deutsche Krebshilfe (SyTASC grant number 70111969) and the German Ministry of Education and Research (BMBF) (HaematoOPT grant number 031A424).


  1. 1.
    Krause DS, Scadden DT (2015) A hostel for the hostile: the bone marrow niche in hematologic neoplasms. Haematologica 100(11):1376–1387PubMedPubMedCentralCrossRefGoogle Scholar
  2. 2.
    Krinner A, Roeder I (2014) Quantification and modeling of stem cell–niche interaction. In: A systems biology approach to blood. Springer, pp 11–36Google Scholar
  3. 3.
    Nombela-Arrieta C, Manz MG (2017) Quantification and three-dimensional microanatomical organization of the bone marrow. Blood Adv 1(6):407–416PubMedPubMedCentralCrossRefGoogle Scholar
  4. 4.
    Acar M, Kocherlakota KS, Murphy MM, Peyer JG, Oguro H, Inra CN, Jaiyeola C, Zhao Z, Luby-Phelps K, Morrison SJ (2015) Deep imaging of bone marrow shows non-dividing stem cells are mainly perisinusoidal. Nature 526(7571):126–130PubMedPubMedCentralCrossRefGoogle Scholar
  5. 5.
    Etzrodt M, Endele M, Schroeder T (2014) Quantitative single-cell approaches to stem cell research. Cell Stem Cell 15(5):546–558PubMedCrossRefGoogle Scholar
  6. 6.
    Schroeder T (2011) Long-term single-cell imaging of mammalian stem cells. Nat Methods 8(4s):S30PubMedCrossRefGoogle Scholar
  7. 7.
    Skylaki S, Hilsenbeck O, Schroeder T (2016) Challenges in long-term imaging and quantification of single-cell dynamics. Nat Biotechnol 34(11):1137–1144PubMedCrossRefGoogle Scholar
  8. 8.
    Foster K, Lassailly F, Anjos-Afonso F, Currie E, Rouault-Pierre K, Bonnet D (2015) Different motile behaviors of human hematopoietic stem versus progenitor cells at the osteoblastic niche. Stem Cell Rep 5(5):690–701CrossRefGoogle Scholar
  9. 9.
    Kim S, Lin L, Brown GA, Hosaka K, Scott EW (2017) Extended time-lapse in vivo imaging of tibia bone marrow to visualize dynamic hematopoietic stem cell engraftment. Leukemia 31(7):1582–1592PubMedCrossRefGoogle Scholar
  10. 10.
    Lo Celso C, Lin CP, Scadden DT (2011) In vivo imaging of transplanted hematopoietic stem and progenitor cells in mouse calvarium bone marrow. Nat Protoc 6(1):1–14PubMedCrossRefGoogle Scholar
  11. 11.
    MacLean AL, Smith MA, Liepe J, Sim A, Khorshed R, Rashidi NM, Scherf N, Krinner A, Roeder I, Lo Celso C (2017) Single Cell Phenotyping Reveals Heterogeneity Among Hematopoietic Stem Cells Following Infection. Stem Cells 35(11):2292–2304PubMedCrossRefGoogle Scholar
  12. 12.
    Hilsenbeck O, Schwarzfischer M, Skylaki S, Schauberger B, Hoppe PS, Loeffler D, Kokkaliaris KD, Hastreiter S, Skylaki E, Filipczyk A, Strasser M, Buggenthin F, Feigelman JS, Krumsiek J, van den Berg AJ, Endele M, Etzrodt M, Marr C, Theis FJ, Schroeder T (2016) Software tools for single-cell tracking and quantification of cellular and molecular properties. Nat Biotechnol 34(7):703–706PubMedCrossRefGoogle Scholar
  13. 13.
    Hilsenbeck O, Schwarzfischer M, Loeffler D, Dimopoulos S, Hastreiter S, Marr C, Theis FJ, Schroeder T (2017) fastER: a user-friendly tool for ultrafast and robust cell segmentation in large-scale microscopy. Bioinformatics 33(13):2020–2028PubMedCrossRefGoogle Scholar
  14. 14.
    Molnar C, Jermyn IH, Kato Z, Rahkama V, Östling P, Mikkonen P, Pietiäinen V, Horvath P (2016) Accurate morphology preserving segmentation of overlapping cells based on active contours. Sci Rep 6:32412PubMedPubMedCentralCrossRefGoogle Scholar
  15. 15.
    Sommer C, Straehle C, Koethe U, Hamprecht FA (2011) Ilastik: interactive learning and segmentation toolkit. In: Biomedical imaging: from nano to macro, 2011 IEEE International Symposium on, 2011. IEEE, pp 230–233Google Scholar
  16. 16.
    Pelt DM, Sethian JA (2018) A mixed-scale dense convolutional neural network for image analysis. Proc Natl Acad Sci U S A 115(2):254–259PubMedCrossRefGoogle Scholar
  17. 17.
    Ronneberger O, Fischer P, Brox T (2015) U-net: convolutional networks for biomedical image segmentation. In: International Conference on Medical image computing and computer-assisted intervention. Springer, pp 234–241Google Scholar
  18. 18.
    Meijering E (2012) Cell segmentation: 50 years down the road [life sciences]. IEEE Signal Process Mag 29(5):140–145CrossRefGoogle Scholar
  19. 19.
    Kan A (2017) Machine learning applications in cell image analysis. Immunol Cell Biol 95(6):525–530PubMedCrossRefGoogle Scholar
  20. 20.
    Caicedo JC, Cooper S, Heigwer F, Warchal S, Qiu P, Molnar C, Vasilevich AS, Barry JD, Bansal HS, Kraus O (2017) Data-analysis strategies for image-based cell profiling. Nat Methods 14(9):849–863PubMedCrossRefGoogle Scholar
  21. 21.
    Schindelin J, Arganda-Carreras I, Frise E, Kaynig V, Longair M, Pietzsch T, Preibisch S, Rueden C, Saalfeld S, Schmid B (2012) Fiji: an open-source platform for biological-image analysis. Nat Methods 9(7):676–682PubMedCrossRefGoogle Scholar
  22. 22.
    Carpenter AE, Jones TR, Lamprecht MR, Clarke C, Kang IH, Friman O, Guertin DA, Chang JH, Lindquist RA, Moffat J (2006) CellProfiler: image analysis software for identifying and quantifying cell phenotypes. Genome Biol 7(10):R100PubMedPubMedCentralCrossRefGoogle Scholar
  23. 23.
    Held M, Schmitz MH, Fischer B, Walter T, Neumann B, Olma MH, Peter M, Ellenberg J, Gerlich DW (2010) CellCognition: time-resolved phenotype annotation in high-throughput live cell imaging. Nat Methods 7(9):747–754PubMedCrossRefGoogle Scholar
  24. 24.
    Tinevez J-Y, Perry N, Schindelin J, Hoopes GM, Reynolds GD, Laplantine E, Bednarek SY, Shorte SL, Eliceiri KW (2017) TrackMate: an open and extensible platform for single-particle tracking. Methods 115:80–90PubMedCrossRefGoogle Scholar
  25. 25.
    Wiesmann V, Franz D, Held C, Münzenmayer C, Palmisano R, Wittenberg T (2015) Review of free software tools for image analysis of fluorescence cell micrographs. J Microsc 257(1):39–53PubMedCrossRefGoogle Scholar
  26. 26.
    Nilsson SK, Johnston HM, Coverdale JA (2001) Spatial localization of transplanted hemopoietic stem cells: inferences for the localization of stem cell niches. Blood 97(8):2293–2299PubMedCrossRefGoogle Scholar
  27. 27.
    Gomariz A, Helbling PM, Isringhausen S, Suessbier U, Becker A, Boss A, Nagasawa T, Paul G, Goksel O, Székely G, Stoma S (2018) Quantitative spatial analysis of haematopoiesis-regulating stromal cells in the bone marrow microenvironment by 3D microscopy. Nature communications 9(1):2532.PubMedPubMedCentralCrossRefGoogle Scholar
  28. 28.
    Ripley BD (1976) The second-order analysis of stationary point processes. J Appl Probab 13(2):255–266CrossRefGoogle Scholar
  29. 29.
    Baddeley A (1999) Spatial sampling and censoring. In: Barndorff-Nielsen O, Kendall W, van Lieshout H (eds) Stochastic geometry: likelihood and computation. Chapman and Hall, London, pp 37–78Google Scholar
  30. 30.
    Baddeley A, Rubak E, Turner R (2015) Spatial point patterns: methodology and applications with R. CRC Press, Boca RatonCrossRefGoogle Scholar
  31. 31.
    Cressie N (2015) Statistics for spatial data. Wiley, New YorkGoogle Scholar
  32. 32.
    Gelfand AE, Diggle P, Guttorp P, Fuentes M (2010) Handbook of spatial statistics. CRC Press, Boca RatonCrossRefGoogle Scholar
  33. 33.
    Tranquillo RT, Lauffenburger DA, Zigmond S (1988) A stochastic model for leukocyte random motility and chemotaxis based on receptor binding fluctuations. J Cell Biol 106(2):303–309PubMedCrossRefGoogle Scholar
  34. 34.
    Wu P-H, Giri A, Sun SX, Wirtz D (2014) Three-dimensional cell migration does not follow a random walk. Proc Natl Acad Sci 111(11):3949–3954PubMedCrossRefGoogle Scholar
  35. 35.
    Luzhanskey ID, MacMunn JP, Cohen JD, Barney LE, Jansen LE, Schwartz AD, Peyton S (2017) Anomalous diffusion as a descriptive model of cell migration. bioRxiv:236356Google Scholar
  36. 36.
    Gorelik R, Gautreau A (2014) Quantitative and unbiased analysis of directional persistence in cell migration. Nat Protoc 9(8):1931–1943PubMedCrossRefGoogle Scholar
  37. 37.
    Wu PH, Giri A, Wirtz D (2015) Statistical analysis of cell migration in 3D using the anisotropic persistent random walk model. Nat Protoc 10(3):517–527PubMedPubMedCentralCrossRefGoogle Scholar
  38. 38.
    Dieterich P, Klages R, Preuss R, Schwab A (2008) Anomalous dynamics of cell migration. Proc Natl Acad Sci 105(2):459–463PubMedCrossRefGoogle Scholar
  39. 39.
    Makarava N, Menz S, Theves M, Huisinga W, Beta C, Holschneider M (2014) Quantifying the degree of persistence in random amoeboid motion based on the Hurst exponent of fractional Brownian motion. Phys Rev E 90(4):042703CrossRefGoogle Scholar
  40. 40.
    Masuzzo P, Van Troys M, Ampe C, Martens L (2016) Taking aim at moving targets in computational cell migration. Trends Cell Biol 26(2):88–110PubMedCrossRefGoogle Scholar
  41. 41.
    Sánchez-Corrales YE, Hartley M, van Rooij J, Marée AF, Grieneisen VA (2018) Morphometrics of complex cell shapes: lobe contribution elliptic Fourier analysis (LOCO-EFA). Development. pii: dev156778Google Scholar
  42. 42.
    Pincus Z, Theriot J (2007) Comparison of quantitative methods for cell-shape analysis. J Microsc 227(2):140–156PubMedCrossRefGoogle Scholar
  43. 43.
    Driscoll MK, McCann C, Kopace R, Homan T, Fourkas JT, Parent C, Losert W (2012) Cell shape dynamics: from waves to migration. PLoS Comput Biol 8(3):e1002392PubMedPubMedCentralCrossRefGoogle Scholar
  44. 44.
    Gordonov S, Hwang MK, Wells A, Gertler FB, Lauffenburger DA, Bathe M (2016) Time series modeling of live-cell shape dynamics for image-based phenotypic profiling. Integr Biol 8(1):73–90CrossRefGoogle Scholar
  45. 45.
    Glauche I, Lorenz R, Hasenclever D, Roeder I (2009) A novel view on stem cell development: analysing the shape of cellular genealogies. Cell Prolif 42(2):248–263PubMedCrossRefGoogle Scholar
  46. 46.
    Bach E, Zerjatke T, Herklotz M, Scherf N, Niederwieser D, Roeder I, Pompe T, Cross M, Glauche I (2014) Elucidating functional heterogeneity in hematopoietic progenitor cells: a combined experimental and modeling approach. Exp Hematol 42(9):826–837 e821–817PubMedCrossRefGoogle Scholar
  47. 47.
    Khakhutskyy V, Schwarzfischer M, Hubig N, Plant C, Marr C, Rieger MA, Schroeder T, Theis FJ (2014) Centroid clustering of cellular lineage trees. In: International conference on information technology in bio-and medical informatics. Springer, pp 15–29Google Scholar
  48. 48.
    Stadler T, Skylaki S, DK K, Schroeder T (2018) On the statistical analysis of single cell lineage trees. J Theor Biol 439:160–165PubMedPubMedCentralCrossRefGoogle Scholar
  49. 49.
    Marr C, Strasser M, Schwarzfischer M, Schroeder T, Theis FJ (2012) Multi-scale modeling of GMP differentiation based on single-cell genealogies. FEBS J 279(18):3488–3500PubMedCrossRefGoogle Scholar
  50. 50.
    Nordon RE, Ko K-H, Odell R, Schroeder T (2011) Multi-type branching models to describe cell differentiation programs. J Theor Biol 277(1):7–18PubMedCrossRefGoogle Scholar
  51. 51.
    Strasser MK, Feigelman J, Theis FJ, Marr C (2015) Inference of spatiotemporal effects on cellular state transitions from time-lapse microscopy. BMC Syst Biol 9(1):61PubMedPubMedCentralCrossRefGoogle Scholar
  52. 52.
    Feigelman J, Ganscha S, Hastreiter S, Schwarzfischer M, Filipczyk A, Schroeder T, Theis FJ, Marr C, Claassen M (2016) Analysis of cell lineage trees by exact Bayesian inference identifies negative autoregulation of Nanog in mouse embryonic stem cells. Cell Sys 3(5):480–490.e413CrossRefGoogle Scholar
  53. 53.
    d’Inverno M, Luck M, Luck MM (2004) Understanding agent systems. Springer, BerlinCrossRefGoogle Scholar
  54. 54.
    Krinner A, Roeder I, Loeffler M, Scholz M (2013) Merging concepts-coupling an agent-based model of hematopoietic stem cells with an ODE model of granulopoiesis. BMC Syst Biol 7(1):117PubMedPubMedCentralCrossRefGoogle Scholar
  55. 55.
    Roeder I, Horn M, Glauche I, Hochhaus A, Mueller MC, Loeffler M (2006) Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications. Nat Med 12(10):1181–1184PubMedCrossRefGoogle Scholar
  56. 56.
    Deutsch A, Dormann S (2007) Cellular automaton modeling of biological pattern formation: characterization, applications, and analysis. Springer, BerlinGoogle Scholar
  57. 57.
    Graner F, Glazier JA (1992) Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys Rev Lett 69(13):2013–2016PubMedCrossRefGoogle Scholar
  58. 58.
    Drasdo D (2007) Center-based single-cell models: an approach to multi-cellular organization based on a conceptual analogy to colloidal particles. In: Single-cell-based models in biology and medicine. Springer, pp 171–196Google Scholar
  59. 59.
    Alt S, Ganguly P, Salbreux G (2017) Vertex models: from cell mechanics to tissue morphogenesis. Phil Trans R Soc B 372(1720):20150520PubMedCrossRefGoogle Scholar
  60. 60.
    Fletcher AG, Osterfield M, Baker RE, Shvartsman SY (2014) Vertex models of epithelial morphogenesis. Biophys J 106(11):2291–2304PubMedPubMedCentralCrossRefGoogle Scholar
  61. 61.
    Sandersius SA, Newman TJ (2008) Modeling cell rheology with the subcellular element model. Phys Biol 5(1):015002PubMedCrossRefGoogle Scholar
  62. 62.
    Osborne JM, Fletcher AG, Pitt-Francis JM, Maini PK, Gavaghan DJ (2017) Comparing individual-based approaches to modelling the self-organization of multicellular tissues. PLoS Comput Biol 13(2):e1005387PubMedPubMedCentralCrossRefGoogle Scholar
  63. 63.
    Magno R, Grieneisen VA, Marée AF (2015) The biophysical nature of cells: potential cell behaviours revealed by analytical and computational studies of cell surface mechanics. BMC Biophys 8(1):8PubMedPubMedCentralCrossRefGoogle Scholar
  64. 64.
    Van Liedekerke P, Palm M, Jagiella N, Drasdo D (2015) Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results. Comput Part Mech 2(4):401–444CrossRefGoogle Scholar
  65. 65.
    Tanaka S (2015) Simulation frameworks for morphogenetic problems. Computation 3(2):197–221CrossRefGoogle Scholar
  66. 66.
    Ghaffarizadeh A, Heiland R, Friedman SH, Mumenthaler SM, Macklin P (2018) PhysiCell: an open source physics-based cell simulator for 3-D multicellular systems. PLoS Comput Biol 14(2):e1005991PubMedPubMedCentralCrossRefGoogle Scholar
  67. 67.
    Mirams GR, Arthurs CJ, Bernabeu MO, Bordas R, Cooper J, Corrias A, Davit Y, Dunn S-J, Fletcher AG, Harvey DG (2013) Chaste: an open source C++ library for computational physiology and biology. PLoS Comput Biol 9(3):e1002970PubMedPubMedCentralCrossRefGoogle Scholar
  68. 68.
    Starruß J, de Back W, Brusch L, Deutsch A (2014) Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology. Bioinformatics 30(9):1331–1332PubMedPubMedCentralCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Walter de Back
    • 1
    • 2
  • Thomas Zerjatke
    • 1
  • Ingo Roeder
    • 1
    • 3
    Email author
  1. 1.Carl Gustav Carus Faculty of Medicine, Institute for Medical Informatics and BiometryTU DresdenDresden, SaxonyGermany
  2. 2.Center for Information Services and High Performance ComputingTU DresdenDresden, SaxonyGermany
  3. 3.National Center for Tumor Diseases (NCT), Partner Site DresdenTU DresdenDresden, SaxonyGermany

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