Abstract
Cellzilla is a two-dimensional tissue simulation platform for plant modeling utilizing Cellerator arrows. Cellerator describes biochemical interactions with a simplified arrow-based notation; all interactions are input as reactions and are automatically translated to the appropriate differential equations using a computer algebra system. Cells are represented by a polygonal mesh of well-mixed compartments. Cell constituents can interact intercellularly via Cellerator reactions utilizing diffusion, transport, and action at a distance, as well as amongst themselves within a cell. The mesh data structure consists of vertices, edges (vertex pairs), and cells (and optional intercellular wall compartments) as ordered collections of edges. Simulations may be either static, in which cell constituents change with time but cell size and shape remain fixed; or dynamic, where cells can also grow. Growth is controlled by Hookean springs associated with each mesh edge and an outward pointing pressure force. Spring rest length grows at a rate proportional to the extension beyond equilibrium. Cell division occurs when a specified constituent (or cell mass) passes a (random, normally distributed) threshold. The orientation of new cell walls is determined either by Errera's rule, or by a potential model that weighs contributions due to equalizing daughter areas, minimizing wall length, alignment perpendicular to cell extension, and alignment perpendicular to actual growth direction.
Highlights
In recent years, there has been much interest in accurate multiscale models of morphogenesis
Cellzilla has variety of shapes that can be used for basic simulations such as rectangular and hexagonal arrays, as well as circular, semicircular and parabolic templates that can be populated with randomly placed Voronoi centers
The user can supply a template of his or her own consisting either of cell enters or cell walls as described previously
Summary
There has been much interest in accurate multiscale models of morphogenesis. Very few general purpose tools exist at all, and even fewer are specific to plants. L-System based tools, the best known being L-Studio (Karwowski and Prusinkiewicz, 2004), were among the first; they are ideally suited to branching structures because they are based on formal language theory (a grammar based on axioms, a short alphabet, strings derived from that alphabet based on specific production rules that are tuned to branching). L-system rules have been embedded in higher level languages such as C [cpfg, (Prusinkiewicz and Lindenmayer, 1990)] to allow the encoding of models and the description of geometrical and topological relationships. The Virtual Plant’s OpenAlea Platform (Pradal et al, 2008) provides a general-purpose collection of simulation modules that use Python as the primary scripting language and allows L-systems to be incorporated (Boudon et al, 2012)
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