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
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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
KINETICS AND METABOLIC STOICHIOMETRY
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
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Logistic Equation Monod Other 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),
one single component
Multicomponent
description within a una
cell population,
heterogeneity from one cell
to another cell
Models
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Logistic Equation Monod Other 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
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Logistic Equation Monod Other 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
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Logistic Equation Monod Other 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),
one single component
Multicomponent
description within a una
cell population,
heterogeneity from one cell
to another cell
1. KINETIC MODELS
Balanced
Growth
Balanced
Growth
Avera
ge c
ell
Avera
ge c
ell
Models
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Logistic Equation Monod Other 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
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Logistic Equation Monod Other 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),
one single component
Multicomponent
description within a una
cell population,
heterogeneity from one cell
to another cell
1. KINETIC MODELS
Models
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Logistic Equation Monod Other models
1. KINETIC MODELS
1. Non structured Nor Segregated models
2. Structured but Non Segregated
3. Non structured but Segregated.
Models
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Logistic Equation Monod Other models
1. KINETIC MODELS
1. Non structured Nor Segregated models
Growth Models.
Models describing both growth and substrate uptake.
Models describing growth, substrate uptake and product generation.
2. Structured but Non Segregated
3. Non structured but Segregated.
Models
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Logistic Equation Monod Other models
1. KINETIC MODELS
1. Non structured Nor Segregated models
Growth Models.
Models describing both growth and substrate uptake.
Models describing growth, substrate uptake and product generation.
2. Structured but Non Segregated
Cell Models
Metabolic Models
Chemically Structured Models
3. Non structured but Segregated
Models
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Logistic Equation Monod Other models
1. KINETIC MODELS
1. Non structured Nor Segregated models
Growth Models.
Models describing both growth and substrate uptake.
Models describing growth, substrate uptake and product generation.
2. Structured but Non Segregated
Cell Models
Metabolic Models
Chemically Structured Models.
3. Non structured but Segregated
Filamentous microorganisms
Mixed culture
Models
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Logistic Equation Monod Other models
1. KINETIC MODELS
1. Non structured Nor Segregated models
Growth Models.
Models describing both growth and substrate uptake.
Models describing growth, substrate uptake and product generation.
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
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Logistic Equation Monod Other models
1. KINETIC MODELS
1. Non structured Nor Segregated models
Growth Models.
Models describing both growth and substrate uptake.
Models describing growth, substrate uptake and product generation.
MAIN EXAMPLES:
• Malthus Law.
• Logistic Equation
• Monod equation
KINETICS AND METABOLIC STOICHIOMETRY
1.- MALTHUS MODEL
2.- LOGISTIC EQUATION
3.- MONOD EQUATION
4.- OTHER MODELS
KINETICS AND METABOLIC STOICHIOMETRY
1.- MALTHUS MODEL
Malthus
KINETICS AND METABOLIC STOICHIOMETRY
Models Logistic Equation Monod Other models
2. MALTHUS MODEL
1. Non structured Nor Segregated models
Growth Models.
• Describing one single process
• Simple equations only considering [X]
])([][
Xfrdt
Xd
CellsSubstrate Cells
Malthus
KINETICS AND METABOLIC STOICHIOMETRY
Models Logistic Equation Monod Other models
2. MALTHUS MODEL
Valid only to describe the exponential growth stage.
Unable to describe the stationary phase.
)··exp(][][
])([][
0 tXXXdt
Xd
Xfdt
Xd
1. Non structured Nor Segregated models
Growth Models.
Malthus
KINETICS AND METABOLIC STOICHIOMETRY
Models Logistic Equation Monod Other models
2. MALTHUS MODEL
1. Non structured Nor Segregated models
Growth Models.
latlat
lat
lat
ttXXXdt
Xdtt
XXdt
Xdtt
XXtt
XXt
··exp·][
0][
0
][][
][][0
0
0
0
0
Malthus
KINETICS AND METABOLIC STOICHIOMETRY
Models Logistic Equation Monod Other models
2. MALTHUS MODEL
1. Non structured Nor Segregated models
Growth Models.
0
2000
4000
6000
8000
10000
12000
14000
16000
0 1 2 3 4 5 6 7 8
N (
cfu
)
Time (h)
KINETICS AND METABOLIC STOICHIOMETRY
1.- MALTHUS MODEL
2.- LOGISTIC EQUATION
3.- MONOD EQUATION
4.- OTHER MODELS
KINETICS AND METABOLIC STOICHIOMETRY
2.- LOGISTIC EQUATION
Logistic Equation
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Models Monod Other models
3. LOGISTIC EQUATION
1. Non structured Nor Segregated models
Growth Models.
• Describing one single process
• Simple equations only considering [X]
])([][
Xfrdt
Xd
CellsSubstrate Cells
Logistic Equation
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Models Monod Other models
3. LOGISTIC EQUATION
1. Non structured Nor Segregated models
Growth Models.
)·exp(1·1
)··exp(
1·][
])([][
max
0
0
max
tX
X
tXX
X
XX
dt
Xd
Xfdt
Xd
Logistic Equation
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Models Monod Other models
3. LOGISTIC EQUATION
1. Non structured Nor Segregated models
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
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Models Monod Other models
3. 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
1. Non structured Nor Segregated models
Growth Models.
Logistic Equation
KINETICS AND METABOLIC STOICHIOMETRY
Malthus Models Monod Other models
3. LOGISTIC EQUATION
1. Non structured Nor Segregated models
Growth Models.
N (
cfu
)
Time (h)
KINETICS AND METABOLIC STOICHIOMETRY
1.- MALTHUS MODEL
2.- LOGISTIC EQUATION
3.- MONOD EQUATION
4.- OTHER MODELS
KINETICS AND METABOLIC STOICHIOMETRY
3.- MONOD EQUATION
KINETICS AND METABOLIC STOICHIOMETRY
Models Malthus Logistic Equation Other models Monod
4. MONOD DEQUATION
1. Non structured Nor Segregated models
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 ··
·][
)],([][
KINETICS AND METABOLIC STOICHIOMETRY
Models Malthus Logistic Equation Other models Monod
4. MONOD DEQUATION
1. Non structured Nor Segregated models
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 ··][
KINETICS AND METABOLIC STOICHIOMETRY
Models Malthus Logistic Equation Other models Monod
4. MONOD DEQUATION
1. Non structured Nor Segregated models
Growth Models.
XSKdt
XdSK
Xdt
XdSK
XSK
SXS
dt
Xd
S
mS
mS
S
m
··][
·][
··
·][
Malthus
M'Kendrick y Pai
KINETICS AND METABOLIC STOICHIOMETRY
1.- MALTHUS MODEL
2.- LOGISTIC EQUATION
3.- MONOD EQUATION
4.- OTHER MODELS
KINETICS AND METABOLIC STOICHIOMETRY
4.- OTHER MODELS
Other Models
KINETICS AND METABOLIC STOICHIOMETRY
Models Malthus Logistic Equation Monod
5. OTHER MODELS
1. Non structured Nor Segregated models
Growth Models.
Models describing both growth and substrate uptake.
Models describing growth, substrate uptake and product generation.
2. Structured but Non Segregated
Cell Models
Metabolic Models
Chemically Structured Models.
3. Non structured but Segregated
Filamentous microorganisms
Mixed culture
Other Models
KINETICS AND METABOLIC STOICHIOMETRY
Models Malthus Logistic Equation Monod
5. OTHER MODELS
2. Structured but Non Segregated
Cell Models
BIOMASS 1
BIOMASS 2
Carbon
Nitrogen
Oxygen
Products
Biomass
SUBSTRATES CELLS PRODUCTS
Maintenance
Other Models
KINETICS AND METABOLIC STOICHIOMETRY
Models Malthus Logistic Equation Monod
5. OTHER MODELS
2. Structured but Non Segregated
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
KINETICS AND METABOLIC STOICHIOMETRY
Models Malthus Logistic Equation Monod
5. OTHER MODELS
2. Structured but Non Segregated
Cell Models
Model of Wiliams (1967)
Reaction Scheme
S K + G
2 GK S k = r 11
G K k = r 22
Substrate Catalytic agent
1
Other Models
KINETICS AND METABOLIC STOICHIOMETRY
Models Malthus Logistic Equation Monod
5. OTHER MODELS
2. Structured but Non Segregated
Cell Models
Model of Wiliams (1967)
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
KINETICS AND METABOLIC STOICHIOMETRY
Models Malthus Logistic Equation Monod
5. OTHER MODELS
1. Non structured Nor Segregated models
Growth Models.
Models describing both growth and substrate uptake.
Models describing growth, substrate uptake and product generation.
2. Structured but Non Segregated
Cell Models
Metabolic Models
Chemically Structured Models.
3. Non structured but Segregated
Filamentous microorganisms
Mixed culture
Other Models
KINETICS AND METABOLIC STOICHIOMETRY
Models Malthus Logistic Equation Monod
5. OTHER MODELS
3. Non structured but Segregated
Filamentous microorganisms
Mixed culture
Other Models
KINETICS AND METABOLIC STOICHIOMETRY
Models Malthus Logistic Equation Monod
5. OTHER MODELS
3. Non structured but Segregated
SEGREGATION based on a property distribution function
Cellular age: difficult to measure and to relate to composition
Biomass: filamentous fungi.
Other Models
KINETICS AND METABOLIC STOICHIOMETRY
Models Malthus Logistic Equation Monod
5. OTHER MODELS
3. Non structured but Segregated
Filamentous microorganisms
Hifa
(Micelio)
Bud
Branching
Unicellular
Filamentous
Fission and Budding
Mycelium
Other Models
KINETICS AND METABOLIC STOICHIOMETRY
Models Malthus Logistic Equation Monod
5. OTHER MODELS
3. Non structured but Segregated
Filamentous microorganisms
Growth
r yema
) ( Branching frequency
f
KINETICS AND METABOLIC STOICHIOMETRY
ANY QUESTION?
SECTION II: KINETICS AND BIOREACTOR DESIGN:
LESSON 9.3. - Enzymatic kinetics, microbial kinetics and metabolic
stoichiometry – Models and Metabolic Stoichiometry