Chapter 4 Cell Topology, Geometry, and Morphogenesis in Proliferating Epithelia

Gibson, William T; Gibson, Matthew C.

doi:10.1016/s0070-2153(09)89004-2

Cited by 83 publications

(112 citation statements)

References 90 publications

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“…The spatial network is a Voronoi graph obtained by a Delaunay triangulation of random points on a sphere (to avoid distortions due to edge effects) (SI Materials and Methods). The average connectivity is six, with a unimodal distribution; nodes with fewer than four or more than eight connections are rare (27). Individual cells occupy the nodes of a network of size 1,000.…”

Section: Methodsmentioning

confidence: 99%

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Heterogeneity for IGF-II production maintained by public goods dynamics in neuroendocrine pancreatic cancer

Archetti

Ferraro

Christofori

2015

Proc. Natl. Acad. Sci. U.S.A.

147

218

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The extensive intratumor heterogeneity revealed by sequencing cancer genomes is an essential determinant of tumor progression, diagnosis, and treatment. What maintains heterogeneity remains an open question because competition within a tumor leads to a strong selection for the fittest subclone. Cancer cells also cooperate by sharing molecules with paracrine effects, such as growth factors, and heterogeneity can be maintained if subclones depend on each other for survival. Without strict interdependence between subclones, however, nonproducer cells can free-ride on the growth factors produced by neighboring producer cells, a collective action problem known in game theory as the "tragedy of the commons," which has been observed in microbial cell populations. Here, we report that similar dynamics occur in cancer cell populations. Neuroendocrine pancreatic cancer (insulinoma) cells that do not produce insulin-like growth factor II (IGF-II) grow slowly in pure cultures but have a proliferation advantage in mixed cultures, where they can use the IGF-II provided by producer cells. We show that, as predicted by evolutionary game theory, producer cells do not go extinct because IGF-II acts as a nonlinear public good, creating negative frequency-dependent selection that leads to a stable coexistence of the two cell types. Intratumor cell heterogeneity can therefore be maintained even without strict interdependence between cell subclones. Reducing the amount of growth factors available within a tumor may lead to a reduction in growth followed by a new equilibrium, which may explain relapse in therapies that target growth factors.game theory | tumor | evolution

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Section: Methodsmentioning

confidence: 99%

“…5A and SI Materials and Methods). Voronoi graphs resemble the distributions of polygons in cell tissues (27) rather than regular lattices (in which all nodes have the same number of neighbors) or a scale-free network (which is not planar), which are the two topologies generally used in the study of cooperation in social networks (25,26).…”

Section: Significancementioning

confidence: 99%

Heterogeneity for IGF-II production maintained by public goods dynamics in neuroendocrine pancreatic cancer

Archetti

Ferraro

Christofori

2015

Proc. Natl. Acad. Sci. U.S.A.

147

218

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“…While regular lattices neglect the importance of variation in connectivity, scale-free networks are not appropriate if players are distributed on a planar network. The distribution of cells in biological tissues resembles a Voronoi diagram [Lewis 1928, Honda 1978, Gibson & Gibson 2009, Csikász-Nagy et al 2013] rather than a regular lattice or a scale-free network.…”

Section: Voronoi Networkmentioning

confidence: 99%

“…A Voronoi network is defined as a group of such node-joining segments [ Figure 1]. The average connectivity of Voronoi networks is 6, with a unimodal distribution in which fewer than 4 or more than 8 connections are very rare -similar to what is observed in biological samples, both within and among species [Lewis 1928, Gibson & Gibson 2009, Csikász-Nagy et al 2013.…”

Section: Voronoi Networkmentioning

confidence: 99%

Cooperation among cancer cells as public goods games on Voronoi networks

Archetti

2016

Journal of Theoretical Biology

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Cancer cells produce growth factors that diffuse and sustain tumor proliferation, a form of cooperation among cancer cells that can be studied using mathematical models of public goods in the framework of evolutionary game theory. Cell populations, however, form heterogeneous networks that cannot be described by regular lattices or scale-free networks, the types of graphs generally used in the study of cooperation. To describe the dynamics of growth factor production in populations of cancer cells, I study public goods games on Voronoi networks, using a range of non-linear benefits that account for the known properties of growth factors, and different types of diffusion gradients. The results are surprisingly similar to those obtained on regular graphs and different from results on scale-free networks, revealing that network heterogeneity per se does not promote cooperation when public goods diffuse beyond one-step neighbours. The exact shape of the diffusion gradient is not crucial, however, whereas the type of non-linear benefit is an essential determinant of the dynamics. Public goods games on Voronoi networks can shed light on intra-tumor heterogeneity, the evolution of resistance to therapies that target growth factors, and new types of cell therapy.

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“…To translate anatomical descriptions of metazoan morphology into topological analogies, the external shape of an organism is modeled by smooth closed surfaces. The connectivity of an epithelial layer during epithelial morphogenesis is ensured by the system of specialized intercellular contacts that integrate cells into a morphological and functional entity (Kolega 1986;Zallen 2007;Gibson and Gibson 2009). The appearance of the epithelial tissue was one of the most significant innovations in the early metazoan evolution; the steps involved were specializations of intercellular contact complexes and extracellular matrices.…”

Section: Blastulation: Orientable Surfacementioning

confidence: 99%

Topological Invariance of Biological Development

2013

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A topological inevitability of early developmental events through the use of classical topological concepts is discussed. Topological dynamics of forms and maps in embryo development are presented. Forms of a developing organism such as cell sets and closed surfaces are topological objects. Maps (or mathematical functions) are additional topological constructions in these objects and include polarization, singularities and curvature. Topological visualization allows us to analyze relationships that link local morphogenetic processes and integral developmental structures and also to find stable spatio-temporal topological characteristics that are invariant for a taxonomic group. The application of topological principles reveals a topological imperative: certain topological rules define and direct embryogenesis. A topological stability of embryonic morphogenesis is proposed and a topological scenario of developmental and evolutionary transformations is presented.

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Chapter 4 Cell Topology, Geometry, and Morphogenesis in Proliferating Epithelia

Cited by 83 publications

References 90 publications

Heterogeneity for IGF-II production maintained by public goods dynamics in neuroendocrine pancreatic cancer

Heterogeneity for IGF-II production maintained by public goods dynamics in neuroendocrine pancreatic cancer

Cooperation among cancer cells as public goods games on Voronoi networks

Topological Invariance of Biological Development

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