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1.  Using cellzilla for plant growth simulations at the cellular level 
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.
doi:10.3389/fpls.2013.00408
PMCID: PMC3797531  PMID: 24137172
mathematical model; computational model; software; meristem; cellerator; cellzilla; wuschel; clavata
2.  MathSBML: a package for manipulating SBML-based biological models 
Bioinformatics (Oxford, England)  2004;20(16):2829-2831.
Summary: MathSBML is a Mathematica package designed for manipulating Systems Biology Markup Language (SBML) models. It converts SBML models into Mathematica data structures and provides a platform for manipulating and evaluating these models. Once a model is read by MathSBML, it is fully compatible with standard Mathematica functions such as NDSolve (a differential-algebraic equations solver). MathSBML also provides an application programming interface for viewing, manipulating, running numerical simulations; exporting SBML models; and converting SBML models in to other formats, such as XPP, HTML and FORTRAN. By accessing the full breadth of Mathematica functionality, MathSBML is fully extensible to SBML models of any size or complexity.
Availability: Open Source (LGPL) at http://www.sbml.org and http://www.sf.net/projects/sbml.
doi:10.1093/bioinformatics/bth271
PMCID: PMC1409765  PMID: 15087311

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