lesson 9.3. - enzymatic kinetics, microbial kinetics and

SECTION II: KINETICS AND BIOREACTOR DESIGN:

LESSON 9.3. - Enzymatic kinetics, microbial kinetics and metabolic

stoichiometry – Models and Metabolic Stoichiometry

JAVIER CALZADA FUNES

Biotechnology Department, Biosciences School

UNIVERSIDAD FRANCISCO DE VITORIA

KINETICS AND METABOLIC STOICHIOMETRY

AIMS FOR TODAY’S LESSON

1.- KINDS OF MODELS

Using concepts as “segregation” and “structure”.

2.- MALTHUS MODEL and its prediction capability.

3.- LOGISTIC EQUATION and its prediction capability.

4.- MONOD EQUATION and its prediction capability.

5.- OTHER MODELS

Models


Malthus Logistic Equation Monod Other models

1. KINETIC MODELS

A model is a simplified representation of a biological phenomenon,

designed to facilitate predictions and calculations that can be

expressed in mathematical form

A model is an approximation to a real phenomenon

"All models are wrong but useful“

Modeling involves an agreement between the reliability, degree

of complexity and the effort required to produce the model.

Models



1. KINETIC MODELS

MODELS NON STRUCTURED STRUCTURED

NON

SEGREGATED

Cell population considered

as a whole:

average individual and

one single component

Description of a

Average cell whose

different components

vary along time

SEGREGATED

Cell population

(distribution of any

characteristic),


Multicomponent

description within a una

cell population,

heterogeneity from one cell

to another cell

Models



1. KINETIC MODELS

Structured Model considering a large network of enzymatic

reactions within the cell.

Totally Segregated Model considering that every cell in the

culture is different in both size and metabolic state.

Models



1. KINETIC MODELS

Balanced Growth cell growth Is defined as a function of a

limiting component, which controls its rate of limiting substrate,

while the other components are in adequate concentrations and

not limiting growth..

Average Cell cells within a population are equal and behave in

the same way.

Models




NON

SEGREGATED


as a whole:



Description of a

Average cell whose


vary along time

SEGREGATED

Cell population


characteristic),


Multicomponent


cell population,


to another cell

1. KINETIC MODELS

Balanced

Growth

Balanced

Growth

Avera

ge c

ell

Avera

ge c

ell

Models



1. KINETIC MODELS

Real case Growth of cells in the system is

segregated and structured very complex to

describe.

Simplest case cell population is considered as a

non-segregated and unstructured system.

Models




NON

SEGREGATED


as a whole:



Description of a

Average cell whose


vary along time

SEGREGATED

Cell population


characteristic),


Multicomponent


cell population,


to another cell

1. KINETIC MODELS

Models



1. KINETIC MODELS

1. Non structured Nor Segregated models

2. Structured but Non Segregated

3. Non structured but Segregated.

Models



1. KINETIC MODELS


Growth Models.

Models describing both growth and substrate uptake.

Models describing growth, substrate uptake and product generation.


3. Non structured but Segregated.

Models



1. KINETIC MODELS


Growth Models.




Cell Models

Metabolic Models

Chemically Structured Models

3. Non structured but Segregated

Models



1. KINETIC MODELS


Growth Models.




Cell Models

Metabolic Models

Chemically Structured Models.


Filamentous microorganisms

Mixed culture

Models



1. KINETIC MODELS


Growth Models.



MAIN CHARACTERISTICS:

• Black box: what happens inside the cells?

• Non structured

• Homogeneously distributed population Non segregated.

• Great simplification of the reality.

• Useful for technological purposes.

• Can be applied under different situations.

Models



1. KINETIC MODELS


Growth Models.



MAIN EXAMPLES:

• Malthus Law.

• Logistic Equation

• Monod equation


1.- MALTHUS MODEL

2.- LOGISTIC EQUATION

3.- MONOD EQUATION

4.- OTHER MODELS


1.- MALTHUS MODEL

Malthus


Models Logistic Equation Monod Other models

2. MALTHUS MODEL


Growth Models.

• Describing one single process

• Simple equations only considering [X]

])([][

Xfrdt

Xd

CellsSubstrate Cells

Malthus



2. MALTHUS MODEL

Valid only to describe the exponential growth stage.

Unable to describe the stationary phase.

)··exp(][][

])([][

0 tXXXdt

Xd

Xfdt

Xd


Growth Models.

Malthus



2. MALTHUS MODEL


Growth Models.

latlat

lat

lat

ttXXXdt

Xdtt

XXdt

Xdtt

XXtt

XXt

··exp·][

0][

0

][][

][][0

0

0

0

0

Malthus



2. MALTHUS MODEL


Growth Models.

0

2000

4000

6000

8000

10000

12000

14000

16000

0 1 2 3 4 5 6 7 8

N (

cfu

)

Time (h)


1.- MALTHUS MODEL


3.- MONOD EQUATION

4.- OTHER MODELS

Logistic Equation


Malthus Models Monod Other models

3. LOGISTIC EQUATION


Growth Models.

• Describing one single process

• Simple equations only considering [X]

])([][

Xfrdt

Xd

CellsSubstrate Cells

Logistic Equation





Growth Models.

)·exp(1·1

)··exp(

1·][

])([][

max

0

0

max

tX

X

tXX

X

XX

dt

Xd

Xfdt

Xd

Logistic Equation





Growth Models.

It predicts exponential and stationary phase,

but it does not consider the influence of the substrate (limiting nutrient).

)·exp(1·1

)··exp(

max

0

0

tX

X

tXX

Logistic Equation




])·[exp(1·1

])·[·exp(;1··

][

0][

0

][][

][][0

max

0

0

max

0

0

0

lat

latlat

lat

lat

ttX

X

ttXX

X

XX

dt

Xdtt

XXdt

Xdtt

XXtt

XXt


Growth Models.

Logistic Equation





Growth Models.

N (

cfu

)

Time (h)


1.- MALTHUS MODEL


3.- MONOD EQUATION

4.- OTHER MODELS


3.- MONOD EQUATION


Models Malthus Logistic Equation Other models Monod

4. MONOD DEQUATION


Growth Models.

Predicts specific growth rate according to substrate concentration

Under limiting substrate conditions.

Hyperbolic kinetics ≈ Michaelis-Menten kinetics for an enzymatic process

XSK

SXS

dt

Xd

SXfdt

Xd

S

m ··

·][

)],([][



4. MONOD DEQUATION


Growth Models.

= specific growth rate for a particular substrate concentration

m = maximum = specific growth rate for a particular substrate

concentration

S = substrate concentration

Ks = saturation constant ([S] for = 1/2 de m)

XSK

S

dt

Xd

S

m ··][



4. MONOD DEQUATION


Growth Models.

XSKdt

XdSK

Xdt

XdSK

XSK

SXS

dt

Xd

S

mS

mS

S

m

··][

·][

··

·][

Malthus

M'Kendrick y Pai


1.- MALTHUS MODEL


3.- MONOD EQUATION

4.- OTHER MODELS


4.- OTHER MODELS

Other Models


Models Malthus Logistic Equation Monod

5. OTHER MODELS


Growth Models.




Cell Models

Metabolic Models




Mixed culture

Other Models



5. OTHER MODELS


Cell Models

BIOMASS 1

BIOMASS 2

Carbon

Nitrogen

Oxygen

Products

Biomass

SUBSTRATES CELLS PRODUCTS

Maintenance

Other Models



5. OTHER MODELS


Cell Models

Model of Wiliams (1967)

Two compartment:

Synthetic section (K): RNA + small biomolecules.

Genetic-Structural section (G): DNA + proteins

Hypothesis

Cell Division G section doubling its size

Reaction Scheme

S K + G

2

Other Models



5. OTHER MODELS


Cell Models


Reaction Scheme

S K + G

2 GK S k = r 11

G K k = r 22

Substrate Catalytic agent

1

Other Models



5. OTHER MODELS


Cell Models


Reaction Scheme

S K + G

2

1

GK S k = r 11

G K k = r 22

21211 ;; rr

dt

Gdrr

dt

Kdr

dt

Sd

Other Models



5. OTHER MODELS


Growth Models.




Cell Models

Metabolic Models




Mixed culture

Other Models



5. OTHER MODELS



Mixed culture

Other Models



5. OTHER MODELS


SEGREGATION based on a property distribution function

Cellular age: difficult to measure and to relate to composition

Biomass: filamentous fungi.

Other Models



5. OTHER MODELS



Hifa

(Micelio)

Bud

Branching

Unicellular

Filamentous

Fission and Budding

Mycelium

Other Models



5. OTHER MODELS



Growth

r yema

) ( Branching frequency

f


ANY QUESTION?

SECTION II: KINETICS AND BIOREACTOR DESIGN:

LESSON 9.3. - Enzymatic kinetics, microbial kinetics and metabolic

stoichiometry – Models and Metabolic Stoichiometry

JAVIER CALZADA FUNES

Biotechnology Department, Biosciences School

UNIVERSIDAD FRANCISCO DE VITORIA

lesson 9.3. - enzymatic kinetics, microbial kinetics and

Documents