Modeling Morphogenesis in silico and in vitro: Towards Quantitative, Predictive, Cell-based Modeling

R. M. H. Merks; P. Koolwijk

Mathematical Modelling of Natural Phenomena (2009)

  • Volume: 4, Issue: 4, page 149-171
  • ISSN: 0973-5348

Abstract

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Cell-based, mathematical models help make sense of morphogenesis—i.e. cells organizing into shape and pattern—by capturing cell behavior in simple, purely descriptive models. Cell-based models then predict the tissue-level patterns the cells produce collectively. The first step in a cell-based modeling approach is to isolate sub-processes, e.g. the patterning capabilities of one or a few cell types in cell cultures. Cell-based models can then identify the mechanisms responsible for patterning in vitro. This review discusses two cell culture models of morphogenesis that have been studied using this combined experimental-mathematical approach: chondrogenesis (cartilage patterning) and vasculogenesis (de novo blood vessel growth). In both these systems, radically different models can equally plausibly explain the in vitro patterns. Quantitative descriptions of cell behavior would help choose between alternative models. We will briefly review the experimental methodology (microfluidics technology and traction force microscopy) used to measure responses of individual cells to their micro-environment, including chemical gradients, physical forces and neighboring cells. We conclude by discussing how to include quantitative cell descriptions into a cell-based model: the Cellular Potts model.

How to cite

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Merks, R. M. H., and Koolwijk, P.. "Modeling Morphogenesis in silico and in vitro: Towards Quantitative, Predictive, Cell-based Modeling." Mathematical Modelling of Natural Phenomena 4.4 (2009): 149-171. <http://eudml.org/doc/222289>.

@article{Merks2009,
abstract = { Cell-based, mathematical models help make sense of morphogenesis—i.e. cells organizing into shape and pattern—by capturing cell behavior in simple, purely descriptive models. Cell-based models then predict the tissue-level patterns the cells produce collectively. The first step in a cell-based modeling approach is to isolate sub-processes, e.g. the patterning capabilities of one or a few cell types in cell cultures. Cell-based models can then identify the mechanisms responsible for patterning in vitro. This review discusses two cell culture models of morphogenesis that have been studied using this combined experimental-mathematical approach: chondrogenesis (cartilage patterning) and vasculogenesis (de novo blood vessel growth). In both these systems, radically different models can equally plausibly explain the in vitro patterns. Quantitative descriptions of cell behavior would help choose between alternative models. We will briefly review the experimental methodology (microfluidics technology and traction force microscopy) used to measure responses of individual cells to their micro-environment, including chemical gradients, physical forces and neighboring cells. We conclude by discussing how to include quantitative cell descriptions into a cell-based model: the Cellular Potts model. },
author = {Merks, R. M. H., Koolwijk, P.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {morphogenesis; cell cultures; quantitative biology; cell-based modeling; cellular potts model; vasculogenesis; angiogenesis; chondrogenesis; cellular Potts model},
language = {eng},
month = {7},
number = {4},
pages = {149-171},
publisher = {EDP Sciences},
title = {Modeling Morphogenesis in silico and in vitro: Towards Quantitative, Predictive, Cell-based Modeling},
url = {http://eudml.org/doc/222289},
volume = {4},
year = {2009},
}

TY - JOUR
AU - Merks, R. M. H.
AU - Koolwijk, P.
TI - Modeling Morphogenesis in silico and in vitro: Towards Quantitative, Predictive, Cell-based Modeling
JO - Mathematical Modelling of Natural Phenomena
DA - 2009/7//
PB - EDP Sciences
VL - 4
IS - 4
SP - 149
EP - 171
AB - Cell-based, mathematical models help make sense of morphogenesis—i.e. cells organizing into shape and pattern—by capturing cell behavior in simple, purely descriptive models. Cell-based models then predict the tissue-level patterns the cells produce collectively. The first step in a cell-based modeling approach is to isolate sub-processes, e.g. the patterning capabilities of one or a few cell types in cell cultures. Cell-based models can then identify the mechanisms responsible for patterning in vitro. This review discusses two cell culture models of morphogenesis that have been studied using this combined experimental-mathematical approach: chondrogenesis (cartilage patterning) and vasculogenesis (de novo blood vessel growth). In both these systems, radically different models can equally plausibly explain the in vitro patterns. Quantitative descriptions of cell behavior would help choose between alternative models. We will briefly review the experimental methodology (microfluidics technology and traction force microscopy) used to measure responses of individual cells to their micro-environment, including chemical gradients, physical forces and neighboring cells. We conclude by discussing how to include quantitative cell descriptions into a cell-based model: the Cellular Potts model.
LA - eng
KW - morphogenesis; cell cultures; quantitative biology; cell-based modeling; cellular potts model; vasculogenesis; angiogenesis; chondrogenesis; cellular Potts model
UR - http://eudml.org/doc/222289
ER -

References

top
  1. D. Amarie, J. A. Glazier, S. C. Jacobson. Compact microfluidic structures for generating spatial and temporal gradients. Anal. Chem., 79 (2007), No. 24, 9471–9477.  
  2. D. Ambrosi, A. Gamba, G. Serini. Cell directional persistence and chemotaxis in vascular morphogenesis. B. Math. Biol., 66 (2004), No. 6, 1851–1873.  
  3. A. R. A. Anderson, M. A. J. Chaplain, K. A. Rejniak, editors. Single-Cell-Based Models in Biology and Medicine. Mathematics and Biosciences in Interaction. Birkhaüser, Basel, Switzerland, 2007.  
  4. C. Bakal, J. Aach, G. Church, N. Perrimon. Quantitative morphological signatures define local signaling networks regulating cell morphology. Science, 316 (2007), No. 5832, 1753–1756.  
  5. A. Balter, R. M. H. Merks, N. J. Popławski, M. Swat, J. A. Glazier. The Glazier–Graner–Hogeweg model: Extensions, future directions, and opportunities for further study. In A. R. A. Anderson, M. A. J. Chaplain, K. A. Rejniak, editors, Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interaction, pages 151–167. Birkhaüser, Basel, Switzerland, 2007.  
  6. J. B. Beltman, A. F. M. Maree, J. N. Lynch, M. J. Miller, R. J. de Boer. Lymph node topology dictates T cell migration behavior. J. Exp. Med., 204 (2007), No. 4, 771–780.  
  7. G. W. Brodlan, D. A. Clausi. Embryonic tissue morphogenesis modeled by FEM. J. Biomech. Eng.-T. ASME, 116 (1994), No. 2, 146–155.  
  8. N. Caille, O. Thoumine, Y. Tardy, J.-J. Meister. Contribution of the nucleus to the mechanical properties of endothelial cells. J. Biomech., 35 (2002), No. 2, 177–187.  
  9. R. R. Chen, E. A. Silva, W. W. Yuen, A. A. Brock, C. Fischbach, A. S. Lin, R. E. Guldberg, D. J. Mooney. Integrated approach to designing growth factor delivery systems. FASEB J., 21 (2007), No. 14, 3896–903.  
  10. S. Christley, M. S. Alber, S. A. Newman. Patterns of mesenchymal condensation in a multiscale, discrete stochastic model. PLoS Comput. Biol., 3 (2007), No. 4, e76.  
  11. T. Cickovski, K. Aras, M. S. Alber, J. A. Izaguirre, M. Swat, J. A. Glazier, R. M. H. Merks, T. Glimm, H. G. E. Hentschel, S. A. Newman. From genes to organisms via the cell - a problem-solving environment for multicellular development. Comput. Sci. Eng., 9 (2007), No. 4, 50–60.  
  12. E. H. Davidson. A genomic regulatory network for development. Science, 295 (2002), No. 5560, 1669–1678.  
  13. E. Flenner, F. Marga, A. Neagu, L. Kosztin, G. Forgacs. Relating biophysical properties across scales. Curr. Top. Dev. Biol., 81 (2008), 461–483.  
  14. G. Forgacs, S. A. Newman. Biological physics of the developing embryo. Cambridge University Press, 2005.  
  15. A. Gamba, D. Ambrosi, A. Coniglio, A. de Candia, S. D. Talia, E. Giraudo, G. Serini, L. Preziosi, F. Bussolino. Percolation, morphogenesis, and Burgers dynamics in blood vessels formation. Phys. Rev. Lett., 90 (2003), No. 11, 118101.  
  16. J. A. Glazier, A. Balter, N. J. Popławski. Magnetization to morphogenesis: a brief history of the Glazier-Graner-Hogeweg model. In A. R. A. Anderson, M. A. J. Chaplain, and K. A. Rejniak, editors, Single Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interaction, pages 79–106. Birkhaüser, Basel, Switzerland, 2007.  
  17. J. A. Glazier, F. Graner. Simulation of the differential adhesion driven rearrangement of biological cells. Phys. Rev. E, 47 (1993), No. 3, 2128–2154.  
  18. V. A. Grieneisen, J. Xu, A. F. M. Marée, P. Hogeweg, B. Scheres. Auxin transport is sufficient to generate a maximum and gradient guiding root growth. Nature, 449 (2007), No. 7165, 1008–13.  
  19. D. Guidolin, B. Nico, A. S. Belloni, G. G. Nussdorfer, A. Vacca, D. Ribatti. Morphometry and mathematical modelling of the capillary-like patterns formed in vitro by bone marrow macrophages of patients with multiple myeloma. Leukemia, 21 (2007), No. 10, 2201–3.  
  20. M. S. Hutson, G. W. Brodland, J. Yang, D. Viens. Cell sorting in three dimensions: Topology, fluctuations, and fluidlike instabilities. Phys. Rev. Lett., 101 (2008), No. 14, 4.  
  21. J. Käfer, T. Hayashi, A. F. M. Marée, R. W. Carthew, F. Graner. Cell adhesion and cortex contractility determine cell patterning in the drosophila retina. Proc. Natl. Acad. Sci. U.S.A., 104 (2007), No. 47, 18549–54.  
  22. K. Keren, Z. Pincus, G. M. Allen, E. L. Barnhart, G. Marriott, A. Mogilner, J. A. Theriot. Mechanism of shape determination in motile cells. Nature, 453 (2008), No. 7194.  
  23. M. A. Kiskowski, M. S. Alber, G. L. Thomas, J. A. Glazier, N. B. Bronstein, J. Pu, S. A. Newman. Interplay between activator-inhibitor coupling and cell-matrix adhesion in a cellular automaton model for chondrogenic patterning. Dev. Biol., 271 (2004), No. 2, 372–87.  
  24. D. Manoussaki. A mechanochemical model of angiogenesis and vasculogenesis. ESAIM-Math. Model. Num., 37 (2003), No. 4, 581–599.  
  25. D. Manoussaki, S. R. Lubkin, R. B. Vernon, J. D. Murray. A mechanical model for the formation of vascular networks in vitro. Acta Biotheor., 44 (1996), No. 3-4, 271–282.  
  26. A. F. M. Marée, V. A. Grieneisen, P. Hogeweg. The Cellular Potts Model and biophysical properties of cells, tissues and morphogenesis. In A. R. A. Anderson, M. J. Chaplain, K. A. Rejniak, editors, Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interaction, pages 107–136. Birkhaüser, Basel, Switzerland, 2007.  
  27. A. F. M. Marée, P. Hogeweg. Modelling dictyostelium discoideum morphogenesis: the culmination. B. Math. Biol., 64 (2002), No. 2, 327–353.  
  28. A. F. M. Marée, A. Jilkine, A. Dawes, V. A. Grieneisen, L. Edelstein-Keshet. Polarization and movement of keratocytes: A multiscale modelling approach. B. Math. Biol., 68 (2006), No. 5, 1169–1211.  
  29. R. M. H. Merks, J. A. Glazier. A cell-centered approach to developmental biology. Phys. A, 352 (2005), No. 1, 113–130.  
  30. R. M. H. Merks, S. A. Newman, J. A. Glazier. Cell-oriented modeling of in vitro capillary development. In ACRI 2004: Sixth International conference on Cellular Automata for Research and Industry, Lect. Notes Comput. Sc., 3305 (2004), 425–434.  
  31. R. M. H. Merks, S. V. Brodsky, M. S. Goligorksy, S. A. Newman, J. A. Glazier. Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling. Dev. Biol., 289 (2006), No. 1, 44–54.  
  32. R. M. H. Merks, J. A. Glazier. Dynamic mechanisms of blood vessel growth. Nonlinearity, 19 (2006), No. 1, C1–C10.  
  33. R. M. H. Merks, E. D. Perryn, A. Shirinifard, J. A. Glazier. Contact-inhibited chemotaxis in de novo and sprouting blood-vessel growth. PLoS Comput. Biol., 4 (2008), No. 9, e1000163.  
  34. P. Namy, J. Ohayon, P. Tracqui. Critical conditions for pattern formation and in vitro tubulogenesis driven by cellular traction fields. J. Theor. Biol., 227 (2004), No. 1, 103–120.  
  35. T. Newman. Modeling multicellular systems using subcellular elements. Math. Biosci. Eng., 2 (2005), No. 3, 613–624.  
  36. E. Palsson. A 3-D model used to explore how cell adhesion and stiffness affect cell sorting and movement in multicellular systems. J. Theor. Biol., 254 (2008), No. 1, 1–13.  
  37. S. Petronis, C. Gretzer, B. Kasemo, J. Gold. Model porous surfaces for systematic studies of material-cell interactions. J. Biomed. Mater. Res. A, 66 (2003), No. 3, 707–21.  
  38. N. J. Popławski, A. Shirinifard, M. Swat, J. A. Glazier. Simulation of single-species bacterial-biofilm growth using the Glazier-Graner-Hogeweg model and the CompuCell3D modeling environment. Math. Biosci. Eng., 5 (2008), No. 2, 355–388.  
  39. C. A. Reinhart-King, M. Dembo, D. A. Hammer. The dynamics and mechanics of endothelial cell spreading. Biophys. J., 89 (2005), No. 1, 676–89.  
  40. C. A. Reinhart-King, M. Dembo, D. A. Hammer. Cell-cell mechanical communication through compliant substrates. Biophys. J., 95 (2008), No. 12, 6044–51.  
  41. K. A. Rejniak. An immersed boundary framework for modelling the growth of individual cells: an application to the early tumour development. J. Theor. Biol., 247 (2007), No. 1, 186–204.  
  42. K. A. Rejniak, A. R. A. Anderson. A computational study of the development of epithelial acini: I. sufficient conditions for the formation of a hollow structure. B. Math. Biol., 70 (2008), No. 3, 677–712.  
  43. J. P. Rieu, A. Upadhyaya, J. A. Glazier, N. B. Ouchi, Y. Sawada. Diffusion and deformations of single hydra cells in cellular aggregates. Biophys. J., 79 (2000), No. 4, 1903–1914.  
  44. S. A. Sandersius, T. J. Newman. Modeling cell rheology with the subcellular element model. Phys. Biol., 5 (2008), No. 1, 015002.  
  45. N. J. Savill, P. Hogeweg. Modelling morphogenesis: from single cells to crawling slugs. J. Theor. Biol., 184 (1997), No. 3, 229–235.  
  46. B. G. Sengers, C. C. V. Donkelaar, C. W. J. Oomens, F. P. T. Baaijens. The local matrix distribution and the functional development of tissue engineered cartilage, a finite element study. Ann. Biomed. Eng., 32 (2004), No. 12, 1718–1727.  
  47. B. G. Sengers, M. Taylor, C. P. Please, R. O. C. Oreffo. Computational modelling of cell spreading and tissue regeneration in porous scaffolds. Biomaterials, 28 (2007), No. 10, 1926–1940.  
  48. G. Serini, D. Ambrosi, E. Giraudo, A. Gamba, L. Preziosi, F. Bussolino. Modeling the early stages of vascular network assembly. EMBO J., 22 (2003), No. 8, 1771–9.  
  49. A. Shamloo, N. Ma, M.-M. Poo, L. L. Sohn, S. C. Heilshorn. Endothelial cell polarization and chemotaxis in a microfluidic device. Lab Chip, 8 (2008), No. 8, 1292–9.  
  50. T. Sun, P. McMinn, S. Coakley, M. Holcombe, R. Smallwood, S. MacNeil. An integrated systems biology approach to understanding the rules of keratinocyte colony formation. J. Roy. Soc. Interface, 4 (2007), No. 17, 1077–1092.  
  51. A. Szabo, E. Mehes, E. Kosa, A. Czirok. Multicellular sprouting in vitro. Biophys. J., 95 (2008), No. 6, 2702–10.  
  52. A. Szabo, E. D. Perryn, A. Czirok. Network formation of tissue cells via preferential attraction to elongated structures. Phys. Rev. Lett., 98 (2007), No. 3, 038102.  
  53. Y. Tsukada, K. Aoki, T. Nakamura, Y. Sakumura, M. Matsuda, S. Ishii. Quantification of local morphodynamics and local GTPase activity by edge evolution tracking. PLoS Comput. Biol., 4 (2008), No. 11, e1000223.  
  54. N. Tymchenko, J. Wallentin, S. Petronis, L. M. Bjursten, B. Kasemo, J. Gold. A novel cell force sensor for quantification of traction during cell spreading and contact guidance. Biophys. J., 93 (2007), No. 1, 335–45.  
  55. A. Vaziri, A. Gopinath. Cell and biomolecular mechanics in silico. Nat. Mater., 7 (2008), No. 1, 15–23.  
  56. D. Walker, J. Southgate, G. Hill, A. Holcombe, D. Hose, S. Wood, S. M. Neil, R. Smallwood. The epitheliome: agent-based modelling of the social behaviour of cells. Biosystems, 76 (2004), No. 1-3, 89–100.  
  57. G. M. Walker, J. Sai, A. Richmond, M. Stremler, C. Y. Chung, J. P. Wikswo. Effects of flow and diffusion on chemotaxis studies in a microfabricated gradient generator. Lab Chip, 5 (2005), No. 6, 611–618.  
  58. Z. Xu, N. Chen, S. C. Shadden, J. E. Marsden, M. M. Kamocka, E. D. Rosen, M. S. Alber. Study of blood flow impact on growth of thrombi using a multiscale model. Soft Matter, 5 (2009), No. 4, 769–779.  
  59. Z. Yin, D. Noren, C. J. Wang, R. Hang, A. Levchenko. Analysis of pairwise cell interactions using an integrated dielectrophoretic-microfluidic system. Mol. Syst. Biol., 4 (2008), 232.  
  60. W. Zeng, G. L. Thomas, J. A. Glazier. Non-turing stripes and spots: a novel mechanism for biological cell clustering. Phys. A, 341 (2004), 482–494.  

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