CelleratorNetwork Cellzilla2D Home

Description

Needs["Cellzilla2D`"];

Return Value

CelleratorNetwork[tissue, options] returns a cellerator reaction network expanded to a cellular template.

tissue is any Cellzilla2D tissue object.

Options

"Reactions"->network is any cellerator network, e.g., the input to xlr8r's interpret function. The entire set of reactions is assumed to occur in every cell in the template. Reactions are "expanded" to the network by adding indices, e.g., a reaction such as A→B becomes {A[1]→B[1], A[2]→B[2], ...} etc

"Diffusion"-> {{X,βx}, {Y,βY}, ...} - is a list of species/penetrability pairs for each species that is assumed to diffuse between cells.

Each pair {X, βX} represents a species name followed by a penetrability coefficient.

Penetrabilities are converted to diffusion rates by accounting for the areas of the cells and the relative length of the connections. The resulting differential equation for xpecies Xi in cell i with area Aiis

which in turn is represented by a set of Cellerator reactions

Any of the pairs {X, βX} can instead be expressed as a triplet {X, βX, fX}, where fX is the head of a function of two indices fx[i,j] in which case

The triplet format allows one to specify different penetrabilities in different regions of the tissue defined by cell number.

If either of the options "Area" or "Edge" is specified then the values of the area and edge lengths will be replaced with the corresponding dynamic variable names. If either is specified the other must also be specified or a unique name will be automatically generated. These options must be specified if the simulations will include changing cell areas or edge lengths.

"Verbose"→True - set to False to suppress messages.

"Area"→None - specify a dynamic variable name to use for the area of the cell. The value of this option must be a symbol.

"Edge"→None - specify a dynamic variable name to use for the edges. The value of this option must be a symbol.

Example

[ Download Example as Zipped Mathematica Notebook ]

Implementation Notes

See Also



[2012-12-08]