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!!!! DISCLAIMER !!!!

The summary of tools that support spatial modeling/geometries is a preliminary effort and may not be complete/accurate. If anyone has more information or a better understanding of how the spatial/geometry representations work in any of all of the tools presented, please feel free to edit it with the correct information!




  • 1-d, 2-d, 3-d geometries possible.
  • Geometry:
    • Analytic (specify origin, extent, analytic expn for shape)
    • Image-based (construct from segmented image)
  • Boundary conditions: Dirichlet, Neumann, Periodic
  • Membrane diffusion


  • Reaction-Diffusion simulator in 3D space
  • Reaction volume is discretized into a large number of small subvolumes (currently only a cube). State of the system is given by the number of molecules per subvolume
  • Uses SBML to define geometry (annotations added to <compartment>. Every compartment needs a geometry. All compartments are 3D; size ignored)
  • Periodic boundary condn. - for boxes (in x,y,z) and cylinders (y only)


  • Supports only 1st degree PDEs in 1-d (no question of geometry). Specify length; # of spatial grid points
  • BCs: Dirichlet, Neumann, Total Flux
  • Diffusion and advection possible


  • Geometry defined with voxels(?)
  • Pre-defined geometry: created from tomogram images
  • User-defined geometry: specify shape (cube, sphere, ellipsoid); dimension; # of voxels in x,y,z; voxel size
  • For compartments specify 'has Membrane' or 'has Boundary'...
  • Supports membrane diffusion (how?)


  • Simulation events occur on OR around surface of physical object
  • Possible 'geometries' or 'physical objects': ligand release site, box object, polygon list object
    • Ligand release site: spherical. Specify location, diameter, etc.
    • Box object: cube/cuboids (by default, each face perpendicular to one of x,y,z axes). Specify LLF and URB points; closed or open; surface modifiers (permeability, removing surface, tiling surface with stationary molecule, adding active zones to physical objects, color to surface elements)
    • Polygon list object: obtained from 3d reconstruction, objects designed by graphics tools or defined as physical objects. Each surface element - a planar polygon
    • Meta object: aggregation of physical objects
  • Surface regions are defined on object templates (different from surface elements?)
  • Surface permeability (of physical objects) to molecules: transparent, absorptive, reflective
  • Possible geometric transformations on any 'physical object' : translate, rotate, scale
  • Units: um
  • Appears to have only 3-d physical objects,
  • Surfaces are 2-d?
  • Diffusion/Transport of molecules - Brownian motion


  • Geometry: simple 3-d primitives (spheres, boxes) or 2-d triangulated surfaces
  • Cannot create cellular geometries
  • Diffusion : Brownian motion. Particles diffuse within specified geometry (3d or 2d) of cell
  • Diffusing entity (protein, complex, biomolecule) - dimensionless particle
  • The triangles and region commands are used to create geometric objects and membrane boundaries


  • Membranes modeled by surfaces that
    • Are comprised of many 'panels' (for 3-d, panels can be rectangles, triangles, spheres, etc) [panels subvolumes/regions?]
    • Have rules that specify molecular interaction with surface (surface-bound, diffused); all panels in one surface follow same rules


  • 3-D stochastic environment
  • Simulation space divided into 3-D cubic grid of discrete voxels (voxel size specified as input in m^3)
  • System described in SBML
  • 3-D structure of particles specified by 'structure file'
    • Specifies shape & size of simulation space (always a cuboidal space?)
    • Specifies species initial location and quantity
    • If not specified, particles randomly placed in 3-D volume


  • 2-d spatial structures (to simulate nearest-neighbor interactions of molecules)
  • Possible geometries: Square, triangles, hexagon (molecules at nodes (corners) of geometry)
    • Real or toroidal boundaries??


  • 3-D geometry
  • Though there is a 2-d example (?)
  • Appears to be a lattice model, where the lattice itself is the geometry


  • E-Cell Version 4 plans generic representation of space:
    • Support for particle, lattice, and compartment space representations
    • Mixed uses of different spatial representations in a model

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This page was last modified 21:22, 2 December 2009.

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