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INDISIM - YEAST An individual-based model to study the behaviour of yeast populations in batch cultures. ACTIONS ON EACH INDIVIDUAL. ACTIONS ON EACH INDIVIDUAL. ACTIONS ON EACH INDIVIDUAL. ACTIONS ON EACH INDIVIDUAL. RANDOM MOTION. RANDOM MOTION. RANDOM MOTION. RANDOM MOTION. - PowerPoint PPT Presentation
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1
INDISIM - YEAST
An individual-based model to study the behaviour of yeast
populations in batch cultures
2
ACTIONS ON EACH INDIVIDUAL
RANDOM MOTION
UPTAKE OF NUTRIENT PARTICLESDEPENDING ON LOCAL ENVIRONMENT (GLUCOSE AND ETHANOL)
AND INDIVIDUAL CHARACTERISTICS (SIZE AND SCARS)
INCREASE OF BIOMASS ACCORDING TO THE METABOLIZED NUTRIENT
PRODUCTION AND EXCRETION OF RESIDUAL PARTICLES (ETHANOL WITH INHIBITORY EFECTS)
BUDDING REPRODUCTION (WITH UNEQUAL DIVISION)
BUDDING PHASE?
CELL DIVISION?
NO
NO
NO
YES
YES
YES
NEW INDIVIDUAL
A
YES
NEW CONFIGURATION OF POPULATION
UNBUDDED PHASE
REQUIREMENTS TO BE VIABLE?
DEATH AND LYSIS
NO
YES
A
ENOUGH NUTRIENT PARTICLES FOR ITS MAINTENANCE ?
UPDATE THE NEW INDIVIDUALCHARACTERISTICS
3
SIMULATION RESULTSThe comparison with experimental data is only qualitative at the present level.
The first simulations results relate to the development of population descriptors and to the development of variability within the population of cells.
The results have been split into two parts:
Global Properties These involve population properties parameters, like the change in concentrations of glucose, of ethanol, number of yeast and of the biomass.
Individual PropertiesWe are concerned with both time evolving and distributions of population parameters, ……. some of which will become directly comparable with experiment when we overcome the question of scaling to real times and energies. Flow cytometric light scattering experiments are capable to probe the properties of individual yeast cells.
4
SIMULATION RESULTS Global Properties
Temporal evolution of nutrient and metabolites in the simulated yeast culture
0
5000000
10000000
15000000
20000000
25000000
30000000
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
Time steps
Nu
mb
er o
f g
luc
os
e p
art
icle
s
0
500000
1000000
1500000
2000000
2500000
3000000
3500000
4000000
4500000
Nu
mb
er o
f et
han
ol p
art
icle
s
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SIMULATION RESULTSGlobal Properties Temporal evolution Thick line: Total biomassThin line: Viable biomass
Log (number of yeast cells)
Evolution of the yeast population: • lag phase (0-40 time step), • exponential phase (40-400 time
step), • linear phase (400–600 time
step), • metabolic slow down (600–1000
time steps),• final phase (1000–1200 time
step).
6
SIMULATION RESULTS
Individual Properties Temporal evolution of the mean biomass of the cell population
0
200
400
600
800
1000
1200
1400
1600
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
Time steps
Me
an
bio
ma
ss
(us
m)
7
SIMULATION RESULTS
Individual Properties Temporal evolution of the average nutrient uptake
0
5
10
15
20
25
30
35
40
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
Time steps
Mea
n n
um
ber
of
glu
cose
par
ticl
es
8
SIMULATION RESULTS
Individual Properties Microscopic population parameters, namely distributions of variables controlled at individual level:
(a) distribution of masses;(b) distribution of genealogical ages; (c) duration of the two periods of the cellular cycle; (d) distribution of masses at the end of each period of the cellular cycle.
These are mainly related to the cellular cycle and reflect the state of the yeast population at given times in the fermentation process.
9
SIMULATION RESULTS
Individual Properties Histograms of the distributions of masses in the simulated yeast culture at
different steps of the simulated evolutionstep = 100 step = 200 step = 300 step = 400
step = 500 step = 600 step = 700 step = 800
step = 900 step = 1000 step = 1100 step = 1200
0%
5%
10%
15%
20%
0%
5%
10%
15%
20%
0 1000 2000 3000
Mass (usm)
0%
5%
10%
15%
20%
0 1000 2000 3000
Mass (usm)
0 1000 2000 3000
Mass (usm)
0 1000 2000 3000
Mass (usm)
10
SIMULATION RESULTS
Individual Properties Histograms of the distributions of genealogical ages of yeast cells in the
simulated yeast culture at different steps of the simulated evolutionstep = 100 step = 200 step = 300 step = 400
step = 500 step = 600 step = 700 step = 800
step = 900 step = 1000 step = 1100 step = 1200
0%
25%
50%
75%
0%
25%
50%
75%
0 5 10 15
Scars
0%
25%
50%
75%
0 5 10 15
Scars
0 5 10 15
Scars
0 5 10 15
Scars
11
SIMULATION RESULTS
Individual Properties
Boxplots of the durations of the unbudded interval (Phase 1) as a function of the genealogical ages of the yeast cells in the simulated yeast culture at different steps of the evolution.
0 5 10 15
Scars
0
50
100
150
Du
rati
on
Ph
ase
1
Step 400
Step 600
0 5 10 15
Scars
0
50
100
150
200
Du
rati
on
Ph
ase
1
Step 700
0 5 10 15
Scars
0
100
200
300
Du
rati
on
Ph
ase
1
12
SIMULATION RESULTS
Individual Properties
Temporal evolution of the 95% confidence intervals for the mean duration of the unbudded interval (Phase 1) of the cells in the simulated yeast culture, using separate plots for daughter and parent cells.
0 100 200 300 400 500 600 700 800 900 1000
Step
0
100
200
300
400
Du
rati
on
Ph
ase
1 fo
r d
aug
hte
r ce
lls
1526
4964
76
123
191
275
336
0 100 200 300 400 500 600 700 800 900 1000
Step
0
100
200
300
400
Du
rati
on
Ph
ase
1 fo
r p
aren
t ce
lls
5 5 8 9 1324
46
81
118 127
13
SIMULATION RESULTS
Individual Properties
Boxplots of the durations of the budding interval (Phase 2) as a function of the genealogical ages of the yeast cells in the simulated yeast culture at different steps of the evolution.
Step 400
0 5 10 15
Scars
0
50
100
150
Du
rati
on
Ph
ase
2
Step 600
0 5 10 15
Scars
0
50
100
150
Du
rati
on
Ph
ase
2
Step 700
0 5 10 15
Scars
0
50
100
150
Du
rati
on
Ph
ase
2
14
SIMULATION RESULTS
Individual Properties
Temporal evolution of the 95% confidence intervals for the mean duration of the budding interval (Phase 2) of the cells in the simulated yeast culture, using separate plots for daughter and parent cells.
0 100 200 300 400 500 600 700 800 900 1000
Step
0
100
200
300
Du
rati
on
Ph
ase
2 fo
r d
aug
ther
ce
lls
3127 32 35
45
68
107
144
216
278
0 100 200 300 400 500 600 700 800 900 1000
Step
0
100
200
300
Du
rati
on
Ph
ase
2 fo
r p
aren
t ce
lls
16 22 21 23 28
49
89
140
187
234
15
SIMULATION RESULTS
Individual Properties Boxplots of the final masses at the end of the unbudded interval (Phase 1),
as a function of the genealogical ages of the yeast cells in the simulated yeast culture, at different steps.
step = 300 step = 400 step = 500
step = 600 step = 700 step = 800
1000
2000
3000
Ma
ss (
usm
)
0 5 10 15
Scars
1000
2000
3000
Ma
ss (
usm
)
0 5 10 15
Scars
0 5 10 15
Scars
16
SIMULATION RESULTS Individual
Properties Boxplots of the final masses for parent and daughter cells at the end of the budding interval (Phase 2), as a function of the genealogical ages of the yeast cells in the simulated yeast culture, at different steps.
step = 300 step = 400 step = 500
step = 600 step = 700 step = 800
1000
2000
3000
Pa
ren
t M
ass
(u
sm
)
0 5 10 15
Scars
1000
2000
3000
Pa
ren
t M
ass
(u
sm
)
0 5 10 15
Scars
0 5 10 15
Scars
step = 300 step = 400 step = 500
step = 600 step = 700 step = 800
0
200
400
600
Dau
gh
ter
Ma
ss (
usm
)
0 5 10 15
Parent scars
0
200
400
600
Dau
gh
ter
Ma
ss (
usm
)
0 5 10 15
Parent scars
0 5 10 15
Parent scars
17
Flow chart of our computer code INDISIM and
a detailed flow chart program step, with the tasks implemented at each time step for
a bacterial study.