Workshops/Workshop11/Materials/AbbasHowTo

Parameter Selection Steps

spatial and temporal parameters

1 voxel/pixel corresponds to ..... micron
- spatial resolution depends on questions that you are trying to answer, cell behaviors and processes in the simulation. In general, to recapitulate geometrical shape of cells, you need to use larger cells.
- examples
  - 4x4 cells cannot recapitulate quasi-hexagonal packing of epithelial cells. (4x4 vs 10x10)
  - tumor (3x3x3)
  - invagination (10x10)
1 step (Monte Carlo step, MCS) corresponds to .... seconds
- Time-scales is determined by the processes in the simulation that you have least control on them. For example, to simulate growth of motile cells, at least three time-dependent processes are involved: 1)Growth 2)division 3)motility. You can grow and divide GGH cells at an arbitrary rate. However GGH cells do not move more than 0.1 voxel per MCS for typical parameter setting. Thus cell motility is the key limiting process which you have least control on it. You have to set the time scale of your simulations to match experimentally measured motility and then adjust growth rates and cell cycles.
- CPU-usage optimization: The goal is to simulate the development of simulated tissues using less CPU-time. For example, if simulated cells are moving 0.01 voxel per MCS, you need 10 times more CPU-time to simulate the same amount of development that you can simulate when motility is 0.1 pixel/MCS (optimal). The ratio of (accepted copy attempts)/(total valid attempts) is success rate which is another measure of simulation efficiency. For example, cell sorting simulations running at 0.1 success rate are very efficient. You can always achieve success rate of close to 1 by increasing fluctuation amplitude (temperature), but high temperature will fragment and kill them! So you have to find an optimal temperature to achieve the highest success rate possible without introducing artifacts.
- examples
  - in vitro endothelial cells (ECs) move at about 1 micron per min and divide every 18 hours. To simulate this in vitro growth. First we choose the spatial resolution, for example, length of 1 pixel represents 3 micron. In a simulation running at optimal temperature simulated ECs move at 0.1 pixel/MCS. Using spatial scale of simulation, we can convert pixel/MCS to micron/MCS which for this simulation is 0.3 micron/MCS. Equating 1 micron/min and 0.3 micron/MCS gives us the relationship between MCS and min: 1 MCS = 0.3 min ~ 20 sec.Then we set simulated cell cycle to 3240 MCS and increase target volume of ECs to reach doubling volume after every 3240 MCS.
  - tumor
  - cell sorting
  - epithelium
  - invagination
  - Angiogenesis

Adhesion parameters

step 1: choosing parameters based on known adhesion mechanisms (tight-junction, cadherin-mediated, focal, ...)
- start with the strongest adhesion and assign an arbitrary negative number. Choose less negative numbers to represent weaker adhesions. To represent repulsion use positive numbers.
step 2: converting morphological information (e.g. cell sorting, preferential cell arrangements) to equations
- For example, in cell sorting experiments the hierarchy of adhesion strengths depend on the type of cell sorting.
  - 2-way surface tension for N and C cell types:
    - two cell types mix -> surface tension between two types is zero or negative
    - two cell types do not mix -> surface tension between two cell types is positive
step 3: choosing parameters based on desired configuration changes/cell rearrangements (Drawing technique)
- - Wetting condition (3-way surface tension)
  - Drawing technique

Diffusion parameters

Unit conversion
- example: oxygen diffusion ~ 2x10^{(-5) cm}2/sec
  - (using above time and spatial scale) 2x10^{(-5) cm}2/sec * (pixel/3*10^{(-4) cm)}2 * (20 sec/MCS) = 4400 pixel^2/MCS
- CC3D similar to SBW does not have native amount unit.
Useful length scales
- penetration lengths
  - no decay or uptake ~
  - decay or uptake ~
which PDE solver to use ...
- Transient Solvers (FlexibleDiffusionSolverFE) vs Stationary Solver (FFT/spectral methods)
  - compare diffusion coefficient of diffusive field ( ) to diffusion coefficient of cells( )
    - if : FlexibleDiffusionSolverFE
    - if : StationaryDiffusionSolver
    - if : advection-diffusion