Scope

Cellular geometry

1,2,3 dimensional description of shape and location of membrane bound cellular structures, filaments, points.

1. explicit surfaces (polygonal tesselations), identify volumes by adjacency and interior points.
2. implicit surfaces, identify surfaces by isosurfaces (e.g. f(x,y,z) == 0).
   1. volume sampled distance maps (e.g. level sets).
   2. inside-outside functions (e.g. R-Functions, f(x,y,z)<0).
3. geometric primatives (e.g. spheres) with constructive solid geometry (i.e. union, intersection, difference).

molecular localization

1. nonuniform continuous field of molecular concentration.
2. discrete molecular locations

biological process localization

• no localization, possible when operating on well-stirred pools (current SBML)
• compartmental localization, mapped uniformly to geometric domains associated with a compartment.
• sub-domain localization through spatially varying kinetic parameters

Overall Approach

Geometric Definition

compartmental dimension and domain dimension.