# geometries

** !!!! 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!

** !!!! END DISCLAIMER !!!! **

## Contents |

### VCell

- 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

### MesoRD

- 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)

### JSim

- 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

### SmartCell

- 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?)

### MCell

- 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

### ChemCell

- 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

### Smoldyn

- 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

### GridCell

- 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

### StochSim

- 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??

### CompuCell3D

- 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

- 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