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Cellular Potts Model with New Principle

03/2020 ~ 07/2020

During the bio project, "Dynamic Response of Cell Under Biaxial Tension", I wondered whether the cellular motion could be modeled.
By doing research, I found that the Cellular Potts model can simulate the cell migration. 
Still, it seemed insufficient because there was no physical principle in the governing equation (Hamiltonian) of the model.
Even though scientists tried to introduce some new equations in Hamiltonian for realistic description, these equations were only empirical equations that did not contain any meaningful principle.

I devised a new concept, cell polarity, and derived the governing equation from the concept.
Cell polarity is a vector quantity, and its definition is as follows:

\[\vec{A} = \sum_{i = 1}^{N}{\vec{c_{i}}}\]

where \(\vec{A}\) is a cell polarity, \(\vec{c_{i}}\) is an unit vector of \(i^{th}\) actin filament whose direction is parallel to the longitudinal direction of the filament, and \(N\) is the number of actin filaments.

Since cell motion is dependent on the actin filaments, cell polarity plays a crucial role in cell motion.
Cell polarity can be affected by an interaction between cells and their shape.
Based on this concept and other scientific principles, I derived the physically meaningful Hamiltonian for Cellular Potts model. 

The final model is presented below.


Where \(T\) is an artificial temperature, \(C_{s}\) is a weight of surface energy term, \(t\) is an initial thickness of cell, \(A_0\) is an initial area of cell, \(C_{a1}\) and \(C_{a2}\) are coefficients of actin polymerization term, \(\gamma\) is the surface tension of cell membrane. The black line represents the polarity of the cell. 
The format of the above program was based on the code of Niculescu et al.

This project is incomplete. Program for multicell is in progress.