Naoki Sato, Kaoru Sato, and Masakazu Toyoshima

Supplementary data

Analysis and modeling of the inverted bioconvection in Chlamydomonas reinhardtii: Emergence of plumes from the layer of accumulated cells

Naoki Sato, Kaoru Sato, and Masakazu Toyoshima

Contents

Supplementary Document S1. Simulation of plume formation

Supplementary Document S1: Simulation of plume formation

Note that Cell2 is in Mode 1, and Cell3 is in Mode 2. Scripts for CompuCell3D follow.

1. Software: CompuCell3D version 3.7.4

2. Simulation in 2D square lattice (800 px × 800 px) with x axis directing to the right and y axis directing to the top.

3. Two types of cells: Cell2 and Cell3. Cell volume = 25, cell surface = 20, Neighboring order = 4.

4. Cell2 emerges in the emerging region Em(x = odd number, 790 ≦ y ≦ 795) every 100 frames with the probability at 0.5.

5. Direction of the movement of Cell2 is determined every 10 frames with a vector pointing to the random point on the half circle below it. The force is 100 (internally defined unit) irrespective of the direction.

6. The cells accumulate at the bottom of the space with time.

7. If a Cell2 becomes the neighbor of n Cell2, then it becomes Cell3 with the probability p. At the same time, all neighboring Cell2 also become Cell3 with the probability at 0.5. The formation of Cell3 normally occurs within the cell layer at the bottom.

8. Direction of the movement of Cell3: the x component of the movement is determined randomly within [-50, 50] every 10 frames, whereas the y component is kept at 100 (upward).

9. Although Cell3 can move independently, the neighboring relationship with other Cell3 may be kept for some duration within the crowded cell layer.

10. If a Cell3 loses all neighbors, it becomes Cell2 which begins to move downward.

11. If a Cell3 attains the region above y ≧ 790, it disappears.

12. A repulsive force at 30 is acting between two Cell2. A weak attractive force at 10 is acting between two Cell3 or between a Cell3 and a Cell2.

13. The simulation is run with varying p and n.

The actual scripts for the simulation are shown on the following pages.

Chlamy.py

import sys

from os import environ

from os import getcwd

import string

sys.path.append(environ["PYTHON_MODULE_PATH"])

import CompuCellSetup

sim,simthread = CompuCellSetup.getCoreSimulationObjects()

# add extra attributes here

CompuCellSetup.initializeSimulationObjects(sim,simthread)

# Definitions of additional Python-managed fields go here

#Add Python steppables here

steppableRegistry=CompuCellSetup.getSteppableRegistry()

from ChlamySteppables import ChlamySteppable

steppableInstance=ChlamySteppable(sim,_frequency=10)

steppableRegistry.registerSteppable(steppableInstance)

CompuCellSetup.mainLoop(sim,simthread,steppableRegistry)

Chlamy.xml

<Potts>

</Potts>

</Plugin>

</Plugin>

</Plugin>

</Plugin>

</CompuCell3D>

ChlamySteppables.py

from PySteppables import *

import CompuCell

import sys

from random import uniform

from math import *

#List of conditions

p = [0.005,0.005,0.005,0.005,0.005,0.005,0.005,0.005]

n = [ 6, 6, 6, 6, 6, 6, 6, 6]

#Number of steps for each simulation

s = 80000

#Total steps

S = len(p)*s

class ChlamySteppable(SteppableBasePy):

def __init__(self,_simulator,_frequency=10):

SteppableBasePy.__init__(self,_simulator,_frequency)

def start(self):

# any code in the start function runs before MCS=0

self.changeNumberOfWorkNodes(8)

self.setMaxMCS(S+1)

def step(self,mcs):

#type here the code that will run every _frequency MCS

#when all simulations end

if mcs==S:

self.cellField[200:600,200:600,0] = self.newCell(self.CELL1)

#for normal steps

else:

#Reset screen for each start of simulation

if mcs%s==0:

for cell in self.cellList:

self.deleteCell(cell)

#Create Cells

if mcs%100==0:

for i in range(self.dim.x):

if uniform(0.0,1.0)<0.5:

self.cellField[i*10:i*10+5,self.dim.y-10:self.dim.y-5,0] = self.newCell(self.CELL2)

#Set speed of cells

for cell in self.cellList:

if cell.type==self.CELL2:

theta=uniform(0.0,1.0)*pi

cell.lambdaVecX=cos(theta)*100

cell.lambdaVecY=sin(theta)*100

elif cell.type==self.CELL3:

cell.lambdaVecX=100*uniform(-0.5,0.5)

cell.lambdaVecY=-100

#Cell2 to Cell3

for cell in self.cellListByType(self.CELL2):

counter=0

for neighbor , commonSurfaceArea in self.getCellNeighborDataList(cell):

counter+=1

if counter == n[int(mcs/s)]:

if uniform(0.0,1.0) < p[int(mcs/s)]:

cell.type=self.CELL3

for neighbor , commonSurfaceArea in self.getCellNeighborDataList(cell):

if neighbor and self.attemptFetchingCellById(neighbor.id).type==self.CELL2:

if uniform(0.0,1.0)<0.50:

self.attemptFetchingCellById(neighbor.id).type=self.CELL3

break

#Cell3 to Cell2

for cell in self.cellListByType(self.CELL3):

if cell.yCOM>self.dim.y-10:

self.deleteCell(cell)

else:

for neighbor , commonSurfaceArea in self.getCellNeighborDataList(cell):

if neighbor and self.attemptFetchingCellById(neighbor.id).type==3:

break

else:

cell.type=self.CELL2

def finish(self):

# Finish Function gets called after the last MCS

pass

Chlamy.cc3d

<XMLScript Type="XMLScript">Simulation/Chlamy.xml</XMLScript>

<PythonScript Type="PythonScript">Simulation/Chlamy.py</PythonScript>

<Resource Type="Python">Simulation/ChlamySteppables.py</Resource>

</Simulation>