Summary
Cells of the embryonic vertebrate limb in high-density culture undergo chondrogenic pattern formation, which results in the formation of regularly spaced “islands” of cartilage analogous to the cartilage primordia of the developing limb skeleton. In this chapter a discrete, multiscale agent-based stochastic model is described, which is based on an extended cell representation coupled with biologically motivated reaction-diffusion processes and cell-matrix adhesion, for studying the behavior of limb bud precartilage mesenchymal cells. The model is calibrated using experimental data, and the sensitivity of key parameters is studied.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alber, M., Kiskowski, M., Glazier, J., Jiang, Y.: On cellular automaton approaches to modeling biological cells. In: Rosenthal, J., Gilliam, D. (eds.) Mathematical Systems Theory in Biology, Communication, and Finance, volume 134, 1–39. Springer-Verlag, New York (2003).
Belov, A.P., Giles, J.D.: Dynamical model of buoyant cyanobacteria. Hydrobiologia, 349, 87–97 (1997).
Chaturvedi, R., Huang, C., Kazmierczak, B., Schneider, T., Izaguirre, J.A., Glimm, T., Hentschel, H.G.E., Glazier, J.A., Newman, S.A., Alber, M.S.: On multiscale approaches to three-dimensional modelling of morphogenesis. J. R. Soc. Interface, 2, 237–253 (2005).
Christley, S., Alber, M.S., Newman, S.A.: Patterns of mesenchymal condensation in a multiscale, discrete stochastic model. PLoS Comput. Biol., in press.
Cui, C.: Dynamics of cell movement and tissue motion in gastrulation and micromass cell culture. Ph.D. thesis, Indiana University, Bloomington, IN, (2005).
Deutsch, A.: Orientation-induced pattern formation: swarm dynamics in a lattice-gas automaton model. Int. J. Bifurc. Chaos, 6, 1735–1752 (1996).
Downie, S., Newman, S.: Morphogenetic differences between fore and hind limb precartilage mesenchyme: Relation to mechanisms of skeletal pattern formation. Dev. Biol., 162, 195–208 (1994).
Downie, S., Newman, S.: Different roles for fibronectin in the generation of fore and hind limb precartilage condensations. Dev. Biol., 172, 519–530 (1995).
Ede, D., Flint, O., Wilby, O., Colquhoun, P.: The development of precartilage condensations in limb bud mesenchyme in vivo and in vitro. In: Ede, D., Hinchliffe, J., Balls, M. (eds.) Vertebrate Limb and Somite Morphogenesis, 161–179. Cambridge University Press, Cambridge (1977).
Ermentrout, G.B., Edelstein-Keshet, L.: Cellular automata approaches to biological modeling. J. Theor. Biol., 160, 97–133 (1993).
Forgacs, G., Newman, S.: Biological Physics of the Developing Embryo. Cambridge University Press (2005).
Frenz, D., Jaikaria, N., Newman, S.: The mechanism of precartilage mesenchymal condensation: A major role for interaction of the cell surface with the amino-terminal heparin-binding domain of fibronectin. Dev. Biol., 136, 97–103 (1989).
Glazier, J.A., Graner, F.: Simulation of the differential adhesion driven rearrangement of biological cells. Phys. Rev. E, 47, 2128–2154 (1993).
Hall, B.K., Miyake, T.: All for one and one for all: Condensations and the initiation of skeletal development. BioEssays, 22, 138–147 (2000).
Holmes, L.B., Trelstad, R.L.: Cell polarity in precartilage mouse limb mesenchyme cells. Dev. Biol., 78, 511–520 (1980).
Izaguirre, J.A., Chaturvedi, R., Huang, C., Cickovski, T., Coffand, J., Thomas, G., Forgacs, G., Alber, M., Hentschel, G., Newman, S.A., Glazier, J.A.: COMPUCELL, a multi-model framework for simulation of morphogenesis. Bioinformatics, 20, 1129–1137 (2004).
Jones, D.S., Sleeandhoopesman, B.D.: Differential Equations and Mathematical Biology. CRC Press, Boca Raton, FL, (2003).
Kiskowski, M., Alber, M., Thomas, G., Glazier, J.A. Bronstein, N.B., Pu, J., Newman, S.A.: Interplay between activator-inhibitor coupling and cell-matrix adhesion in a cellular automaton model for chondrogenic patterning. Dev. Biol., 271, 372–387 (2004).
Lander, A., Nie, Q., Wan, F.: Do morphogen gradients arise by diffusion? Dev. Cell, 2, 785–796 (2002).
Leonard, C., Fuld, H., Frenz, D., Downie, S.A., Massagué, J., Newman, S.A.: Role of transforming growth factor-β in chondrogenic pattern formation in the embryonic limb: Stimulation of mesenchymal condensation and fibronectin gene expression by exogenenous TGF-β and evidence for endogenous TGF-β-like activity. Dev. Biol., 145, 99–109 (1991).
Luo, Y., Kostetskii, I., Radice, G.: N-cadherin is not essential for limb mesenchymal chondrogenesis. Dev. Dyn., 232, 336–344 (2005).
Maree, A., Hogeweg, P.: How amoeboids self-organize into a fruiting body: Multicellular coordination in Dictyostelium discoideum. Proc. Nat. Acad. Sci. USA, 98, 3879–3883 (2001).
Miura, T., Komori, M., Shiota, K.: A novel method for analysis of the periodicity of chondrogenic patterns in limb bud cell culture: Correlation of in vitro pattern formation with theoretical models. Anat. Embryol., 201, 419–428 (2000).
Miura, T., Shiota, K.: Extracellular matrix environment influences chondrogenic pattern formation in limb bud micromass culture: Experimental verification of theoretical models. Anal. Rec., 258, 100–107 (2000).
Miura, T., Shiota, K.: TGFβ2 acts as an ‘‘activator’’ molecule in reaction-diffusion model and is involved in cell sorting phenomenon in mouse limb micromass culture. Dev. Dyn., 217, 241–249 (2000).
Miura, T., Shiota, K., Morriss-Kay, G., Maini, P.K.: Mixed-mode pattern in Doublefootmutant mouse limb-Turing reaction-diffusion model on a growing domain during limb development. J. Theor. Biol. (in press) doi:10.1016/j.jtbi.2005.10.016, (2005).
Moftah, M., Downie, S., Bronstein, N.B, Mezemtseva, N., Pu, J., Maher, P.A., Newman, S.A.: Ectodermal FGFs induce perinodular inhibition of limb chondrogenesis in vitro and in vivo via FGF receptor 2. Dev. Biol., 249, 270–282 (2002).
Murray, J.: Mathematical Biology. Springer-Verlag, New York (2003).
Newman, S.: Sticky fingers: Hox genes and cell adhesion in vertebrate development. BioEssays, 18, 171–174 (1996).
Newman, S., Frisch, H.: Dynamics of skeletal pattern formation in developing chick limb. Science, 205, 662–668 (1979).
Newman, S., Tomasek, J.: Morphogenesis of connective tissues. In: Comper, W.D. (ed.) Extracellular Matrix Molecular Components and Interactions, volume 2, 335–369. Harwood Academic Publishers, Amsterdam (1996).
Panikov, N.S.: Microbial Growth Kinetics. Springer, New York, (1995).
Scott, E.M., Rattray, E.A.S., Prosser, J.I., Killham, K., Glover, L.A., Lynch, J.M., Bazin, M.J.: A mathematical model for dispersal of bacterial inoculants colonizing the wheat rhizosphere. Soil Biol. Biochem., 27, 1307–1318 (1995).
Sozinova, O., Jiang, Y., Kaiser, D., Alber, M.: A three-dimensional model of fruiting body formation. Proc. Natl. Acad. Sci. USA, 103(46), 17255–17259 (2006).
Sozinova, O., Jiang, Y., Kaiser, D., Alber, M.: A three-dimensional model of myxobacterial aggregation by contact-mediated interactions. Proc. Nat. Acad. Sci. USA, 102, 11308–11312 (2005).
Turing, A.: The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 237, 37–72 (1952).
Walker, D.C., Hill, G., Wood, S.M., Smallwood, R.H., Southgate, J.: Agent-based computational modeling of wounded epithelial cell monolayers. IEEE Transactions on Nanobioscience, 3, 153–163 (2004).
Wanner, O.: Modelling of biofilms. Biofouling, 10, 31–41 (1996).
Widelitz, R., Jiang, T., Murray, B., Chuong, C.: Adhesion molecules in skeletogenesis: II. Neural cell adhesion molecules mediate precartilaginous mesenchymal condensations and enhance chondrogenesis. J. Cell. Physiol., 156, 399–411 (1993).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 springer
About this chapter
Cite this chapter
Christley, S., Newman, S., Alber, M. (2007). Agent-Based Model for Developmental Pattern Formation with Multiscale Dynamics and Varying Cell Geometry. In: Deutsch, A., Brusch, L., Byrne, H., Vries, G.d., Herzel, H. (eds) Mathematical Modeling of Biological Systems, Volume I. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4558-8_13
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4558-8_13
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4557-1
Online ISBN: 978-0-8176-4558-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)