CompuCell3d manual and Tutorial Version 2
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III.B. DynamicsA GGH simulation consists of many attempts to copy cell indices between neighboring pixels. In CompuCell3D the default dynamical algorithm is modified Metropolis dynamics. During each index-copy attempt, we select a target pixel,  , randomly from the cell lattice, and then randomly select one of its neighboring pixels,  , as a source pixel. If they belong to the same generalized cell (i.e., if  ) we do not need copy index. Otherwise the cell containing the source pixel  attempts to occupy the target pixel. Consequently, a successful index copy increases the volume of the source cell and decreases the volume of the target cell by one pixel.
Figure 2. GGH representation of an index-copy attempt for two cells on a 2D square lattice – The “white” pixel (source) attempts to replace the “grey” pixel (target). The probability of accepting the index copy is given by equation . In the modified Metropolis algorithm we evaluate the change in the total effective energy due to the attempted index copy and accept the index-copy attempt with probability:  ,
where  is a parameter representing the effective cell motility (we can think of as the amplitude of cell-membrane fluctuations). Equation is the Boltzmann acceptance function. Users can define other acceptance functions in CompuCell3D. The conversion between MCS and experimental time depends on the average values of . MCS and experimental time are proportional in biologically-meaningful situations (87-90).
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