Basic rules of microbial growth Basic rules of microbial growth

Basic rules of microbial growth Basic rules of microbial growth

Fermentation up stream and down stream processes

E.coli Vibrio cholerae

Saccharomyces cerevisiae

Mucor circenelloides Aszexuális gombanövekedés

Basic rules of microbial growth Basic rules of microbial growth

1=X₀*2⁰

2=X₀*2¹

4=X₀*2²

n=1

n=2

n=3

Binary dividing microorganisms

8=X₀*2³

16=X₀*2⁴

n=3

n=4

n:no of new generations

. .

X=X₀2ⁿ

t g

n = t No of generations

Generációs idő - doubling time generation time

N, x

Cell number pc/ml

Cell mass: dw mg/ml, g/l,kg/m³

Basic rules of microbial growth Basic rules of microbial growth

n 0

t t

0 2 x 2

x

x =

=

x dt .

dx = µ

µ: specific growth rate

x dt .

dx = µ

Specific growth rate

Basic rules of microbial growth Basic rules of microbial growth

dt dx x

≡ 1

µ ^h

x dt .

dx = µ . N

dt

dN = ν

e t

x

x = ^µ N = N e ^{ν t}

Jacques Monod

Basic rules of microbial growth Basic rules of microbial growth

Specific proliferation rate Spec. Doubling rate

t 0 e x

x = ^µ N = N ₀ e ^{ν t}

Relation between µ and tg:

= ln µ 2

t

x ∞

t 0 e x

x = ^µ

Basic rules of microbial growth Basic rules of microbial growth

t

In reality

x

x

LAG

PHASE

ACCELERA TING

GROWTH

EXPONEN- TIAL

PHASE

Basic rules of microbial growth Basic rules of microbial growth

x

t

PHASE

GROWTH

PHASE DECLINING PHASE

x

t dx

x x

g

cot α = µ

Basic rules of microbial growth Basic rules of microbial growth

µ t

t

dt

dx

WHAT IS THE REASON OF THE EXISTENCE OD DECLINING PHASE?

1. NUTRIENT LIMITATION

2. TOXIC METABOLIT PRODUCT(S) 3. LACK OF SPACE

MONOD- model

µ µ

Basic rules of microbial growth Basic rules of microbial growth

S K

S

S

max +

µ

=

µ ^µ

²

Κ

S

S

KRITICAL SUBSTRATE CONCENTRATION LIMITING SUBSTRATE

µ µ

Κ

S

S

N-source

~ ~

µ µ

Κ

S

S

C-Source

~ ~

FERM.TIME FERM.TIME

WHICH S WILL BE LIMITING

???

Basic rules of microbial growth Basic rules of microbial growth

NOTION OF THE LIMITING SUBSTRATE

µ

µ µ

Κ

S

S

VITAMINe -source

~ ~

µ

Κ

S

S

O

~ ~

Κ

S

S

Κ

S

S

FERM.TIME

FERM.TIME

tgα=K_S/µ_max

1/ µ

1/S 1/µ

LINEWEAVER-BURK

tgα=1/µ_max

S/ µ

K

/ µ

HANES v. LANGMUIR

S K

S S

µ µ= +µ max max

1 *

1 1 1

µ µ = + µ

max max Ks * S

Basic rules of microbial growth Basic rules of microbial growth

-1/K

1/S K

S

µ

µ /S µ

tg α =-K

µ

/K

µ µ = max KS − µ S

EADIE-HOFSTEE

dt dS x

1 dt dx x

1 S

x dS Y

dx

s /

x

=

∆

= ∆

−

=

dx = µ

=

YIELD COEFF:

i s

/ x i

-Y

vagy

dS Y dx

i

=

−

=

FOR THE LIMITING S

EXTENSION

Basic rules of microbial growth Basic rules of microbial growth

dt x

r

= dx = µ

S x K

S Y

1 dt

r dS

S x K

S dt

r dx

S S

/ x S

S x

µ +

−

=

=

µ +

=

=

ALWAYS TRUE:

In the exponential and declining phase:

MONOD-model

Differential equation Can be solved

x

x

µ Y vagy -Y dt µ

dx

∆x

dx = = = = − =

Basic rules of microbial growth Basic rules of microbial growth

i x/s

S x S

x i

-Y vagy

Q Y µ µ

µ dt

dS dt

∆S

∆x dS

dx

i

=

−

=

=

=

=

Utilization of C/en source

S S

S = ∆

+ ∆

∆

∆ S = ∆ S _c + ∆ S _E

What for?

incorporation energy production

Basic rules of microbial growth Basic rules of microbial growth

x x

x

E C

+ ∆

= ∆

∆

Yield of incorp. carbon Energy yield Overall yield

Y Y

YY Y

1 Y

1 Y 1

C C

C

E

= −

= −

Y 1 Y

1 Y

1

E C

x/s

+

=

=

2 ∆ x

α α

∆ S

C-content of the cell mass C-content of the substráate 0,46-0,5 50%

2 1 C

c

S Y x

α

= α

∆ =

∆

Material balance for the incorporated carbon

Basic rules of microbial growth Basic rules of microbial growth

2

S

α

∆

2 1

1

2 1

2 1

E

Y .

. Y Y

. Y

Y α − α

= α α −

α α α

=

Some cases from the product one can estimate the energy production and consumption

Assimilated Dissimilated EtOH yeast, sugar

AcOH A.aceti, alcohol

NADH !!!

Glükonsav A.suboxydans, glucose

Basic rules of microbial growth Basic rules of microbial growth

Assimilated Dissimilated

Strain cult. media ratio of cult. media

% %

Streptococcus faecalis

anaerobic growth complett 2 98 Saccharomyces cerevisiae complett

aerobic growth 10 90

anaerobic growth 2 98

Aerobacter cloaceae minimal 55 45

1,2,3,

∆ S = ∆ S _c + ∆ S _E

?

Cell growth Maintenance of viability Cell motion

Osmotic work

Basic rules of microbial growth Basic rules of microbial growth

Osmotic work

Mantenance of orderness

thermodynamics II.law resyntheses

Y x

S

x

S S

E

E g m

= =

+

∆

∆

∆

∆ ∆

dS

dt Y

dx dt

x

= − 1 = − µ Y

dt dS dt

dS Y

dt

dS

E x E

+ µ =

=

 

 





dS dt

x Y

g = µ dS

dt ^m = mx

1 1

Y Y

m

E EG

= +

µ

!!!

Basic rules of microbial growth Basic rules of microbial growth

dt = Y _EG

dt = mx

µ x µ Y

x

Y mx

E EG

= +

1 1

Y Y

m

E EG

= +

µ

modell

1 1

Y Y

m

E EG

= +

µ

specific maintenance coefficient

g/gh =h

1 1 1

Y Y Y

m

x s / c EG

= + +

µ

For the overall yield:

1

Basic rules of microbial growth Basic rules of microbial growth

Y _{x s /} Y _c Y _EG µ

m µ 1 1

Y

+ Y

1 Y

1

µ m

1 1

Y

+ Y

S s

/

Y µ

= µ

m

µ

Y 1 Y

1

EG C

S µ+







 +

= µ

ATP-yield

Y x ATP

Y

ATP

Y

x s ATP s

= ∆ = ′

∆

/ /

′ =

Y

MY

g/mol

g/mol

mol/mol

( ) ( )

m Y

1 Y

1

ATP ATP

ATP

ATP max

ATP ATP

m g

+ µ

=

∆ +

∆

=

∆

10,5 g/mol

Q

Y Y m

ATP ATP

= µ = µ +

(8,3-32)

Basic rules of microbial growth Basic rules of microbial growth

culture specific mentenance

conditions coefficients

m m_ATP Aerobacter cloaceae aerobic, glucose 0,094 14 Saccharomyces cerevisiae anaerobic glucose 0,036 0,52

+ 0,1 mol/dm³ NaCl Saccharomyces cerevisiae anaerobic, glucose

+1,0 mol/dm³ NaCl 0,360 2,2 Penicillium chrysogenum aerobic 0.,022 3,2 Lactobacillus casei aeroic, glucose 0,135 1,5

O

P

„P/O ratio”

mol/gatom

NADH + H⁺ + 1/2O₂ + 3 ADP + 3 H₃PO₄ NAD⁺ + 3 ATP + 4 H₂O

3/1=3

Basic rules of microbial growth Basic rules of microbial growth

x Y P

S

Y P

x p s

p

∆

= ∆

∆

= ∆

Q x S

. H x

. H Y x

Y

S x

kcal

H

∆

= ∆

∆

∆ +

∆

∆

−

= ∆

=

HEAT PROD. YIELD ENTHALPY OF

CELL MASS

ENTHALPY OF SUBSTRATE

METABOLIC

HEAT PRODUCTION

Basic rules of microbial growth Basic rules of microbial growth

HEAT PROD. YIELD

CELL MASS

x x/S

S

x/S S

x kcal

H

∆H Y ∆H

Y .∆∆S/∆

∆H x/ ∆/

.

∆H

∆x/∆S Y

Y = −

+

∆

= −

=

IF THERE IS NO SIGNIFICANT EXTRACELLULAR PRODUCTION

RQ respiration quotient

2 2

O CO 2

2

2 2

q q dt

dO dt dCO O

CO = =

∆

∆

Basic rules of microbial growth Basic rules of microbial growth

C

H

O

+ 6O

6CO

+ 6 H

O

2C₂H₅OH + 6 O₂ 4 CO₂ + 6 H₂O RQ_max =4/6= 0,67

C

H

O

+ CO

2 CH₃OH + 3 O₂ 2 CO₂ + 4H₂O C₂H₂O₄ + ½ O₂ 2CO₂ + H₂O

RQ_max =

RQ_max =2/3= 0,67 RQ_max =2/ ½ = 4

∞

x x

P P x P

GAEDEN:production types

Primary products Secondary products

Growth associated Mixed type Non growth associated

µ

µ

µ

µ

µ

µ

KINETICS OF PRODUCT FORMATION

LUEDEKING – PIRET MODEL r dP

dt

dx

dt x x

dP dt

P

P x

= = +

= = +

α β

µ αµ β

1

µ_P

tgφ=α

III.

µ_X β

tgφ=α φ

φ β

III.

I II.

I: α> α> α> α> 0 és ββββ = 0 GROWTH

ASSOC.

II: αααα = 0 és β> β> β> β> 0 NONGROWTH

ASSOC

III: α> α> α> α> 0 és β> β> β> β> 0 MIXED TYPE