Abstract
Morphogenesis, the shaping of an organism, is a complex biological process accomplished through an well organized interplay between growth, differentiation and cell movement.It is still today one of the major outstanding problems in the biological sciences. Pattern formation has been well-addressed in the literature with the development of many mathematical models including the famous reaction-diffusion ones. We here take a different approach, introducing a controlled cellular automaton in order to model the signal molecules, known as growth factors, that convey information from one cell to another during an organism's development and help maintain the viability of the adult. This control represents extracellular structures that have been associated with the regulation of stem cell proliferation and are called fractones. In this paper we introduce two co-evolving automata, one describing the perturbed diffusion of growth factors and one accounting for the rules of basic cellular functions (proliferation, differentiation, migration and apoptosis). Fractones are introduced as an external input to control the shaping of multi-cellular organisms; we analyze their influence on the emerging shape. We illustrate our theory with 2 and 3 dimensional simulations. This work presents the foundation upon which to develop cellular automata as a tool to simulate the morphodynamics in embryonic development.
Highlights
An important question in biology is how the developing embryo is organized on a cellular level to grow into a specific morphology
Growth occurs through mitosis of individual cells, the splitting of one mother cell into two new daughter cells, and it is only through repeated acts of mitosis over time that a cell mass can form
We focus on four principal cell functions which influence the development and viability of cellular masses: Proliferation; Differentiation; Migration and Apoptosis
Summary
An important question in biology is how the developing embryo is organized on a cellular level to grow into a specific morphology (shape). While some influencing factors have been identified (forces between cells [5, 19] and growth factors detected by the cells through receptors on the cell surface [24]), it is still uncertain how the embryo organizes and directs cellular growth. In his pioneering work on mathematical modeling of morphogenesis [22], Alan Turing introduced his well-known intercellular reaction-diffusion process. In the model presented here we consider specialized extra-cellular matrix structures, which have been named fractones [15], as a refined
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