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minicell_bioproduction_model_v1.py
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minicell_bioproduction_model_v1.py
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### imports ###
import numpy as np
import pandas as pd
from matplotlib import pyplot as plt
from scipy.integrate import odeint
import random as rd
### parameters ###
### E.coli parameters
growth_rate = 0.04
e_max_size = 2
e_min_size = 1
### minicell parameters
minicell_production_rate = 0
m_max_size = 1/5 * e_max_size
m_min_size = 1/5 * e_min_size
######### implementation ###########
### initialisation
cell_count = [1]
minicell_count = []
tmax = 300
time = np.linspace(0,tmax,1000)
tspan = tmax/len(time)
counts = [] # [[[]=cell_count,[]=minicell_count]=t0 , []=cell_count,[]=minicell_count]=t1 , ...]
div = []
mini = []
''' a) exponential growth, constant minicells production'''
minicell_production_rate = 0.03
### functions ###
def minicell_production(cell,t,tspan):
minicell = 0
if cell > e_min_size + m_max_size:
if ((t-tspan)*minicell_production_rate)%1 > (t*minicell_production_rate)%1 :
minicell = m_max_size
cell = cell - minicell
return cell, minicell
### simulation
for t in time:
for i in range(len(cell_count)):
cell_count[i] = round(cell_count[i] + cell_count[i]*growth_rate*tspan,5)
cell_count[i], minicell = minicell_production(cell_count[i],t,tspan)
if minicell > 0:
minicell_count.append(minicell)
mini.append(t)
if cell_count[i] >= 2:
div.append(t)
cell_count[i] = cell_count[i]/2
new_cell = cell_count[i]
cell_count.append(new_cell)
counts.append([cell_count.copy(),minicell_count.copy()])
### plot
plt.figure()
prev = 0
col = 0
for i in range(len(counts)):
if prev < len(counts[i][0]):
style = ["-","--","-."]
prev = len(counts[i][0])
life = time[i:]
plt.plot(life, [l[0][col] for l in counts[i:]], style[col%3], label='cell'+str(prev))
col = col + 1
for t in div:
plt.axvline(x=t, color='lightgrey', linestyle=':')
for t in mini:
plt.axvline(x=t, color='darkgrey', linestyle='--')
plt.ylim([1,2.5])
plt.xlabel("time (m)")
plt.ylabel("size of the bacteria (micron)")
plt.legend()
plt.show()
plt.close()
## counts
final_population = counts[-1]
print("cellule=", len(final_population[0])," minicellule=", len(final_population[1]))
plt.figure()
plt.plot(time,[len(x[0]) for x in counts], label='n of cells')
plt.plot(time,[len(x[1]) for x in counts], label='n of minicells')
plt.legend()
plt.show()
plt.close()
''' b) exponential growth, exponential minicell production'''
minicell_production_rate = 0.02
rate_sum = 0
### functions ###
def minicell_production(cell,t,tspan,rate_sum):
minicell = 0
if cell > e_min_size + m_max_size:
if (rate_sum - (minicell_production_rate*cell*tspan))%1 > rate_sum%1 :
minicell = m_max_size
cell = cell - minicell
return cell, minicell
### simulation
for t in time:
for i in range(len(cell_count)):
cell_count[i] = round(cell_count[i] + cell_count[i]*growth_rate*tspan,5)
if i == 0:
rate_sum = rate_sum + (minicell_production_rate*cell_count[i]*tspan)
cell_count[i], minicell = minicell_production(cell_count[i],t,tspan,rate_sum)
if minicell > 0:
minicell_count.append(minicell)
mini.append(t)
if cell_count[i] >= 2:
div.append(t)
cell_count[i] = cell_count[i]/2
new_cell = cell_count[i]
cell_count.append(new_cell)
counts.append([cell_count.copy(),minicell_count.copy()])
### plot
plt.figure()
prev = 0
col = 0
for i in range(len(counts)):
if prev < len(counts[i][0]):
style = ["-","--","-."]
prev = len(counts[i][0])
life = time[i:]
plt.plot(life, [l[0][col] for l in counts[i:]], style[col%3], label='cell'+str(prev))
col = col + 1
for t in div:
plt.axvline(x=t, color='lightgrey', linestyle=':')
for t in mini:
plt.axvline(x=t, color='darkgrey', linestyle='--')
plt.legend()
plt.ylim([1,2.5])
plt.xlabel("time (m)")
plt.ylabel("size of the bacteria (micron)")
plt.show()
plt.close()
### counts
final_population = counts[-1]
print("cellule=", len(final_population[0])," minicellule=", len(final_population[1]))
plt.figure()
plt.plot(time,[len(x[0]) for x in counts], label='n of cells')
plt.plot(time,[len(x[1]) for x in counts], label='n of minicells')
plt.legend()
plt.show()
plt.close()
''' c) exponential growth, constant minicells '''
minicell_production_rate = 0.03
### functions ###
def minicell_production(cell,tspan):
minicell = 0
if cell > e_min_size + m_max_size:
threshold = minicell_production_rate*tspan*10000
random = rd.randint(1,10000)
if random <= threshold:
minicell = m_max_size
cell = cell - minicell
return cell, minicell
### simulation
for t in time:
for i in range(len(cell_count)):
cell_count[i] = round(cell_count[i] + cell_count[i]*growth_rate*tspan,5)
cell_count[i], minicell = minicell_production(cell_count[i],tspan)
if minicell > 0:
minicell_count.append(minicell)
mini.append(t)
if cell_count[i] >= 2:
div.append(t)
cell_count[i] = cell_count[i]/2
new_cell = cell_count[i]
cell_count.append(new_cell)
counts.append([cell_count.copy(),minicell_count.copy()])
### plot
plt.figure()
prev = 0
col = 0
for i in range(len(counts)):
if prev < len(counts[i][0]):
style = ["-","--","-."]
prev = len(counts[i][0])
life = time[i:]
plt.plot(life, [l[0][col] for l in counts[i:]], style[col%3], label='cell'+str(prev))
col = col + 1
for t in div:
plt.axvline(x=t, color='lightgrey', linestyle=':')
for t in mini:
plt.axvline(x=t, color='darkgrey', linestyle='--')
plt.ylim([1,2.5])
plt.xlabel("time (m)")
plt.ylabel("size of the bacteria (micron)")
plt.legend()
plt.show()
plt.close()
## counts
final_population = counts[-1]
print("cellule=", len(final_population[0])," minicellule=", len(final_population[1]))
plt.figure()
plt.plot(time,[len(x[0]) for x in counts], label='n of cells')
plt.plot(time,[len(x[1]) for x in counts], label='n of minicells')
plt.yscale('log')
plt.legend()
plt.show()
plt.close()
''' d) exponential growth, constant minicells '''
minicell_production_rate = 0.02
## functions ###
def minicell_production(cell,tspan):
minicell = 0
if cell > e_min_size + m_max_size:
threshold = minicell_production_rate*tspan*10000*cell
random = rd.randint(1,10000)
if random <= threshold:
minicell = m_max_size
cell = cell - minicell
return cell, minicell
## simulation
for t in time:
for i in range(len(cell_count)):
cell_count[i] = round(cell_count[i] + cell_count[i]*growth_rate*tspan,5)
cell_count[i], minicell = minicell_production(cell_count[i],tspan)
if minicell > 0:
minicell_count.append(minicell)
mini.append(t)
if cell_count[i] >= 2:
div.append(t)
cell_count[i] = cell_count[i]/2
new_cell = cell_count[i]
cell_count.append(new_cell)
counts.append([cell_count.copy(),minicell_count.copy()])
### plot
plt.figure()
prev = 0
col = 0
for i in range(len(counts)):
if prev < len(counts[i][0]):
style = ["-","--","-."]
prev = len(counts[i][0])
life = time[i:]
plt.plot(life, [l[0][col] for l in counts[i:]], style[col%3], label='cell'+str(prev))
col = col + 1
for t in div:
plt.axvline(x=t, color='lightgrey', linestyle=':')
for t in mini:
plt.axvline(x=t, color='darkgrey', linestyle='--')
plt.ylim([1,2.5])
plt.xlabel("time (m)")
plt.ylabel("size of the bacteria (micron)")
plt.legend()
plt.show()
plt.close()
## counts
final_population = counts[-1]
print("cellule=", len(final_population[0])," minicellule=", len(final_population[1]))
plt.figure()
plt.plot(time,[len(x[0]) for x in counts], label='n of cells')
plt.plot(time,[len(x[1]) for x in counts], label='n of minicells')
plt.yscale('log')
plt.legend()
plt.xlabel('time')
plt.ylabel('count')
plt.show()
plt.close()
# plot ration
plt.figure()
plt.plot(time,[len(x[1])/len(x[0]) for x in counts], label='ratio minicells/cells')
plt.legend()
plt.xlabel('time')
plt.ylabel('ratio')
plt.show()
plt.close()