CPM Flashcards
Describe the voting rule CA in terms of energy/hamiltonian
What physical model is being described by the asynchronous voting rule?
Ising model of ferromagnets
Guess J for the following final lattice state
J>0: ferromagnetic behaviour, spins try to align with eachother.
Guess J for the following final lattice state
J<0: antiferromagnetic behaviour, spins try to be less aligned
How does CPM differ from the Ising model?
It allows for multiple states, not just binary
What main biological problem is described with CPM?
Cell sorting.
Differential adhesion hypothesis: Cell sort out due to differences in adhesion between cells
different interfacial tensions between different pairs of cells
Cells make and break connections to one another
Strongest connections are kept with highest probability
What values of J are needed to obtain cell sorting?
What values of J are needed to obtain the following final pattern?
What pattern will be observed for the following J values?
Cell sorting
What J values do you need to obtain no cell adhesion?
Describe the following results from a CPM simulation?
A simple CPM simulation (one in which J represents adhesion energy only) does not replicate experimental results. This is because actual biological cells have surface tension and the simulation does not consider the difference in surface tension between ecto and mesoderm (ecto»meso). For this to be acounted J needs to be defined as contact energy which includes adhesion as well as surface tension. Thus minimizing energy would mean minimizing surface tension as well. As surface tension of ectoderm is much higher it will eventually be placed inside the tissue.
what is the formula for cell-cell surface tension between two cell types in terms of contact energies?
what is the formula for surface tension of a cell with its medium in terms of contact energies?
How is CPM computationally implemented?
Metropolis dynamics/Monte Carlo steps: instead of all different positions on the lattice being considered synchronously at the same time, random points (MC samples) are being taken asynchronously instead. In addition as only neighbouriong positions are allowed to switch cell id only those neighbouring points are being considered.
What do sigma.tau and x_vec represent in the CPM mathemaical formulation
sigma: “cell id”
tau: cell type
x_vec: position on lattice
What do lambda(A), “a” and “A” represent in the mathematical formalization of the CPM?
lambda(A): elasticity
a: cell area
A: optimal cell area
