111Equation Chapter 1 Section 1 CompuCell3d reference Manual Version 4
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- ContactLocalProduct Plugin
Contact EnergyEnergy calculations for the foam simulation are based on the boundary or contact energy between cells (or surface tension, if you prefer). Together with volume constraint contact energy is one of the most commonly used energy terms in the GGH Hamiltonian. In essence it describes how cells "stick" to each other. The explicit formula for the energy is:  ,
where i and j label two neighboring lattice sites ,'s denote cell Ids,'s denote cell types . In the case of foam simulation the total energy of the foam is simply the total boundary length times the surface tension (here defined to be 2J).
In this case, the interaction range is 2, thus only up to second nearest neighbor pixels of a pixel undergoing a change or closer will be used to calculate contact energy change. Foam cells have contact energy per unit area of 3 and Foam and Medium as well as Medium and Medium have contact energy of 0 per unit area. For more information about contact energy calculations see “Introduction to CompuCell3D”
This plugin calculates contact energy based on local (i.e. per cell) cadhering expression levels. This plugin has to be used in conjunction with a steppable that assigns cadherin expression levels to the cell. Such steppables are usually written in Python – see ContactLocalProductExample in Demos directory. We use the following formulas to calculate energy for this plugin: 
By default  .  is a function of cadherins and can be either a simple product  , a product of squared expression levels  or a  .
In the case of the second formula  plays the role of “regular” contact energy between cell and medium.
The syntax of this plugin is as follows: Users need to specify ContactSpecificity (  ) between different cell types ContactFunctionType (by default it is set to Linear - but other allowed key words are Quadratic - and Min - ). EnergyOffset can be set to user specified value using above syntax. NeighborOrder has the same meaning as for “regular” Contact plugin.
Alternatively one can write customized function of the two cadherins and use it instead of the 3 choices given above. To do this, simply use the following syntax: Here we define variable names for cadherins in interacting cells (J1 denotes cadherin for one of the cells and cell2 denotes cadherin for another cell). Then in the Expression tag we give mathematical expression involving the two cadherin levels. The expression syntax has to follow syntax of the muParser - http://muparser.sourceforge.net/mup_features.html#idDef2. Download 0.81 Mb. Share with your friends:
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) and the interaction range (NeighborOrder) of the contact: