Abstract
Development is a process that needs to be tightly coordinated in both space and time. Cell tracking and lineage tracing have become important experimental techniques in developmental biology and allow us to map the fate of cells and their progeny. A generic feature of developing and homeostatic tissues that these analyses have revealed is that relatively few cells give rise to the bulk of the cells in a tissue; the lineages of most cells come to an end quickly. Computational and theoretical biologists/physicists have, in response, developed a range of modelling approaches, most notably agent-based modelling. These models seem to capture features observed in experiments, but can also become computationally expensive. Here, we develop complementary genealogical models of tissue development that trace the ancestry of cells in a tissue back to their most recent common ancestors. We show that with both bounded and unbounded growth simple, but universal scaling relationships allow us to connect coalescent theory with the fractal growth models extensively used in developmental biology. Using our genealogical perspective, it is possible to study bulk statistical properties of the processes that give rise to tissues of cells, without the need for large-scale simulations.
Highlights
The connection between space and time is fundamental to developmental biology
We will establish a relationship between the exact coalescent [20] and tissue growth models that are inspired by or are related to the classical Eden model [22] (or more general models such as the processes described by the Kardar – Parisi – Zhang (KPZ) equation [23])
The intention of our analysis is fourfold: (i) to demonstrate the direct connection between the space and time dimensions in tissue growth; (ii) to establish that dominant lineages are a natural feature of fractal growth models that is readily captured by a coalescent process; (iii) to determine the scaling factors for coalescent models of biological growth processes and to establish the link to the classical coalescent; and (iv) to show that simple scaling relationships apply to lineage tracing in both unidirectional and unbounded fractal growth systems
Summary
The connection between space and time is fundamental to developmental biology. For over a century, the location of stem cell proliferation and differentiation during development has been known to be well organized and of paramount importance to cell fate decision-making (e.g. Spemann organizer and primitive knots) [1]. Despite the long-established importance of spatial information in understanding tissue development, it was not until relatively recently that widespread understanding of these effects has become possible. More recent experimental work (relying on advanced microscopy [4] with suitable dyes [5] and fluorescence tags [6], etc.) in the context of developmental biology has focused on cell tracking and lineage tracing. These experiments have already given rise to profound new insights. Three-dimensional effects and stochasticity all make lineage tracing and cell-tracking experiments difficult [5,7], . Mathematical or computational models can encapsulate complicated and quantitative mechanistic hypotheses and be used to test systematically which aspects of these hypotheses are borne out by reality
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