ACTIONS ON EACH INDIVIDUAL

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

5

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).

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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

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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

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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

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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.