# FocalPointPlasticity Plugin¶

FocalPointPlasticity puts constraints on the distance between cells’ center of masses. A key feature of this plugin is that the list of “focal point plasticity neighbors” can change as the simulation evolves and user has to specifies the maximum number of “focal point plasticity neighbors” a given cell can have. Let’s look at relatively simple CC3DML syntax of FocalPointPlasticityPlugin (see Demos/PluginDemos/FocalPointPlasticity/FocalPointPlasticity example and we will show more complex examples later):

<Plugin Name="FocalPointPlasticity">
<Parameters Type1="Condensing" Type2="NonCondensing">
<Lambda>10.0</Lambda>
<ActivationEnergy>-50.0</ActivationEnergy>
<TargetDistance>7</TargetDistance>
<MaxDistance>20.0</MaxDistance>
<MaxNumberOfJunctions>2</MaxNumberOfJunctions>
</Parameters>

<Parameters Type1="Condensing" Type2="Condensing">
<Lambda>10.0</Lambda>
<ActivationEnergy>-50.0</ActivationEnergy>
<TargetDistance>7</TargetDistance>
<MaxDistance>20.0</MaxDistance>
<MaxNumberOfJunctions>2</MaxNumberOfJunctions>
</Parameters>
<NeighborOrder>1</NeighborOrder>
</Plugin>


Parameters section describes properties of links between cells. MaxNumberOfJunctions, ActivationEnergy, MaxDistance and NeighborOrder are responsible for establishing connections between cells. CC3D constantly monitors pixel copies and during pixel copy between two neighboring cells/subcells it checks if those cells are already participating in focal point plasticity constraint. If they are not, CC3D will check if connection can be made (e.g. Condensing cells can have up to two connections with Condensing cells and up to 2 connections with NonCondensing cells – see first line of Parameters section and MaxNumberOfJunctions tag). The NeighborOrder parameter determines the pixel vicinity of the pixel that is about to be overwritten which CC3D will scan in search of the new link between cells. NeighborOrder 1 (which is default value if you do not specify this parameter) means that only nearest pixel neighbors will be visited. The ActivationEnergy parameter is added to overall energy in order to increase the odds of pixel copy which would lead to new connection.

Once cells are linked the energy calculation is carried out according to the formula:

\begin{eqnarray} E = \sum_{i,j,cell\ neighbors}\lambda_{ij}\left ( l_{ij}-L_{ij} \right )^2 \end{eqnarray}

where $$l_{ij}$$ is a distance between center of masses of cells i and j and $$L_{ij}$$ is a target length corresponding to $$l_{ij}$$.

$$\lambda_{ij}$$ and $$L_{ij}$$ between different cell types are specified using Lambda and TargetDistance tags. The MaxDistance determines the distance between cells’ center of masses past which the link between those cells break. When the link breaks, then in order for the two cells to reconnect they would need to come in contact again. However it is usually more likely that there will be other cells in the vicinity of separated cells so it is more likely to establish new link than restore broken one.

The above example was one of the simplest examples of use of FocalPointPlasticity. A more complicated one involves compartmental cells. In this case each cell has separate “internal” list of links between cells belonging to the same cluster and another list between cells belonging to different clusters. The energy contributions from both lists are summed up and everything that we have said when discussing example above applies to compartmental cells. Sample syntax of the FocalPointPlasticity plugin which includes compartmental cells is shown below. We use InternalParameters tag/section to describe links between cells of the same cluster (see Demos/PluginDemos/FocalPointPlasticity/FocalPointPlasticityCompartments example):

<Plugin Name="FocalPointPlasticity">

<Parameters Type1="Top" Type2="Top">
<Lambda>10.0</Lambda>
<ActivationEnergy>-50.0</ActivationEnergy>
<TargetDistance>7</TargetDistance>
<MaxDistance>20.0</MaxDistance>
<MaxNumberOfJunctions NeighborOrder="1">1</MaxNumberOfJunctions>
</Parameters>

<Parameters Type1="Bottom" Type2="Bottom">
<Lambda>10.0</Lambda>
<ActivationEnergy>-50.0</ActivationEnergy>
<TargetDistance>7</TargetDistance>
<MaxDistance>20.0</MaxDistance>
<MaxNumberOfJunctions NeighborOrder="1">1</MaxNumberOfJunctions>
</Parameters>

<InternalParameters Type1="Top" Type2="Center">
<Lambda>10.0</Lambda>
<ActivationEnergy>-50.0</ActivationEnergy>
<TargetDistance>7</TargetDistance>
<MaxDistance>20.0</MaxDistance>
<MaxNumberOfJunctions>1</MaxNumberOfJunctions>
</InternalParameters>

<InternalParameters Type1="Bottom" Type2="Center">
<Lambda>10.0</Lambda>
<ActivationEnergy>-50.0</ActivationEnergy>
<TargetDistance>7</TargetDistance>
<MaxDistance>20.0</MaxDistance>
<MaxNumberOfJunctions>1</MaxNumberOfJunctions>
</InternalParameters>

<NeighborOrder>1</NeighborOrder>

</Plugin>


We can also specify link constituent law and change it to different form that “spring relation”. To do this we use the following syntax inside FocalPointPlasticity CC3DML plugin:

<LinkConstituentLaw>
<!--The following variables lare defined by default: Lambda,Length,TargetLength-->

<Variable Name='LambdaExtra' Value='1.0'/>
<Formula>LambdaExtra*Lambda*(Length-TargetLength)^2</Formula>



By default CC3D defines 3 variables (Lambda, Length, TargetLength) which correspond to $$\lambda_{ij}$$ , $$l_{ij}$$ and $$L_{ij}$$ from the formula above. We can also define extra variables in the CC3DML (e.g. LambdaExtra). The actual link constituent law obeys muParser syntax convention. Once link constituent law is defined it is applied to all focal point plasticity links. The example demonstrating the use of custom link constituent law can be found in Demos/PluginDemos/FocalPointPlasticityCustom.

Sometimes it is necessary to modify link parameters individually for every cell pair. In this case we would manipulate FocalPointPlasticity links using Python scripting. Example Demos/PluginDemos/FocalPointPlasticity/FocalPointPlasticityCompartments demonstrates exactly this situation. You still need to include CC3DML section as the one shown above for compartmental cells, because we need to tell CC3D how to link cells. The only notable difference is that in the CC3DML we have to include <Local/> tag to signal that we will set link parameters (Lambda, TargetDistance, MaxDistance) individually for each cell pair:

<Plugin Name="FocalPointPlasticity">
<Local/>
<Parameters Type1="Top" Type2="Top">
<Lambda>10.0</Lambda>
<ActivationEnergy>-50.0</ActivationEnergy>
<TargetDistance>7</TargetDistance>
<MaxDistance>20.0</MaxDistance>
<MaxNumberOfJunctions NeighborOrder="1">1</MaxNumberOfJunctions>
</Parameters>
...
</Plugin>


Python steppable where we manipulate cell-cell focal point plasticity link properties is shown below:

class FocalPointPlasticityCompartmentsParams(SteppablePy):
def __init__(self, _simulator, _frequency=10):
SteppablePy.__init__(self, _frequency)
self.simulator = _simulator
self.focalPointPlasticityPlugin = CompuCell.getFocalPointPlasticityPlugin()
self.inventory = self.simulator.getPotts().getCellInventory()
self.cellList = CellList(self.inventory)

def step(self, mcs):
for cell in self.cellList:
for fppd in InternalFocalPointPlasticityDataList(self.focalPointPlasticityPlugin, cell):
0.0, 0.0, 0.0)


The syntax to change focal point plasticity parameters (or as here internal parameters) is as follows:

setFocalPointPlasticityParameters(cell1, cell2, lambda, targetDistance, maxDistance)

setInternalFocalPointPlasticityParameters(cell1, cell2, lambda, targetDistance, maxDistance)


Similarly, to inspect current values of the focal point plasticity parameters we would use the following Python construct:

for cell in self.cellList:
for fppd in InternalFocalPointPlasticityDataList(self.focalPointPlasticityPlugin, cell):


For non-internal parameters we simply use FocalPointPlasticityDataList instead of InternalFocalPointPlasticityDataList .

Examples Demos/PluginDemos/FocalPointPlasticity… show in relatively simple way how to use FocalPointPlasticity plugin. Those examples also contain useful comments.

Note

When using FocalPointPlasticity Plugin from Mitosis module one might need to break or create focal point plasticity links. To do so FocalPointPlasticity Plugin provides 4 convenience functions which can be invoked from the Python level:

deleteFocalPointPlasticityLink(cell1, cell2)