Biology Reference
In-Depth Information
Cellular Potts Models
Cellular Potts models
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are not explicitly mechanical. Initially invented for modelling
entirely physical systems such as magnetic domains in metals, such models treat the 'field'
on which cells exist as a grid consisting of a large number of 'cells', or 'boxes' as they will
be called here to minimize the confusion between the 'cells' of the computer grid (to which
'Cellular Potts' refers) and the living cells of an epithelium. Each box has many attributes, one
of which, still called 'spin' in homage to the physical roots of the model, is the identity of the
biological cell to which the box belongs. Boxes are much smaller than cells, so many adjacent
boxes carry the same value for their spin attribute (
Figure 26.7
). Each box is also associated
with a number of other values that represent biological parameters of the system, such as
adhesion energies, departures from an idea cellular area, surface tension, concentration of
morphogens, and so on.
Within the model, all of the parameters of the box, in relation to those of its neighbours (for
example, is a neighbouring box part of the same cell or is it across a cell-cell boundary) are
treated like the different energy terms (kinetic, potential) of a physical system and are
brought together to make a Hamiltonian, a sort of sum of the 'energies', for each box. At
each step of the simulation, the program running the simulation makes a
random
choice of
box to examine, and calculates its Hamiltonian. The value of the Hamiltonian is used to deter-
mine the probability of the system updating a box to change its spin term to the spin term of
one of its neighbours; such an update would correspond to one cell relinquishing the box and
a part of its neighbour advancing. This done, the computer chooses another random box and
repeats the process. Essentially, the system evolves to minimize its Hamiltonians by
FIGURE 26.7
Representation of biological cells by a Cellular Potts Model. The field is represented by a grid of
boxes (the 'cells' in the phrase 'Cellular Potts'), each being much smaller than a biological cell.
