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Summary Basic Cell Factory Design BPE-22306
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Samenvatting van beide delen van Basic Cell Factory Design (Black Box Model en Metabolic Network Model). Bevat alle formules, inclusief over uitleg hoe ze werken, wat ze doen en waar ze voor gebruikt

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  • 19 oktober 2021
  • 21
  • 2021/2022
  • Samenvatting

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Basic Cell Factory Design BPE-22306
Table of Contents
Black Box Model...................................................................................................................................... 1
Stoichiometry ...................................................................................................................................... 1
General reaction equation: ............................................................................................................. 1
Atom balances: ............................................................................................................................... 1
Electron balance: ............................................................................................................................ 1
Total and Volumetric rates ............................................................................................................. 1
Pirt’s Law ......................................................................................................................................... 2
Luedeking-Piret Law ........................................................................................................................ 2
Luedeking-Piret + Pirt...................................................................................................................... 2
Chemostat ........................................................................................................................................... 3
Mass balance of a Chemostat ......................................................................................................... 3
Rate-limiting Chemostat: Sugar ...................................................................................................... 4
Finding Parameters ..................................................................................................................... 4
Linear Regression .................................................................................................................... 4
Non-linear Regression (solver function in Excel) .................................................................... 5
Rate-limiting Chemostat: Product ................................................................................................... 5
Han-Levenspiel; Kinetic Model ................................................................................................... 5
Finding Parameters ..................................................................................................................... 6
Batch ................................................................................................................................................... 6
Mass balance of a Batch Reactor .................................................................................................... 7
Solving the mass balances .......................................................................................................... 7
Finding parameters ................................................................................................................. 8
Metabolic Network Model ...................................................................................................................... 9
Metabolic network.............................................................................................................................. 9
Metabolic flux ................................................................................................................................. 9
Metabolic reaction equations ......................................................................................................... 9
Reaction linkage types: ............................................................................................................... 9
Reaction branch points ............................................................................................................... 9
Lumping pathways ...................................................................................................................... 9
Solving metabolic mass balances ...................................................................................................... 10
Matrix notation ............................................................................................................................. 10
Solving mass balances with stepwise elimination ........................................................................ 10
Solving mass balances with matrices ............................................................................................ 11




Victor Pieternella Summary Basic Cell Factory Design.docx BPE22306

, Flux Balance Analysis (FBA) ............................................................................................................... 11
FBA constraints ............................................................................................................................. 12
Thermodynamics....................................................................................................................... 12
Circulations ................................................................................................................................... 13
Minimal norm constraint .......................................................................................................... 13
Generalised inverse................................................................................................................... 13
Futile cycles ................................................................................................................................... 13
Statistics ............................................................................................................................................ 14
Redundancy .................................................................................................................................. 14
Statistical test ............................................................................................................................ 14
Statistical test:....................................................................................................................... 15
Variance covariance matrices ............................................................................................... 15
Test function ......................................................................................................................... 15
Chi-square distribution ......................................................................................................... 15
Balancing redundancy relations .................................................................................................... 16
Classifications: ............................................................................................................................... 16
Metabolic Control Analysis ............................................................................................................... 16
Flux Control Coefficient ................................................................................................................ 17
Summation theorem ................................................................................................................. 17
Deviation index ......................................................................................................................... 17
Elasticity ............................................................................................................................................ 18
Determining elasticity coefficients ............................................................................................... 18
Elasticity coefficients from kinetic models ............................................................................... 18
Michaelis-Menten kinetics .................................................................................................... 18
Reversible Michaelis-Menten kinetics (Uni-Uni kinetics) ..................................................... 18
Elasticity coefficients from measured rates.............................................................................. 19
Connectivity theorem ................................................................................................................... 19
Pathways with one intermediate .............................................................................................. 19
Pathways with multiple intermediates .................................................................................... 19




Victor Pieternella Summary Basic Cell Factory Design.docx BPE22306

, Black Box Model
Stoichiometry
General reaction equation:
𝑟𝑠 𝐶𝐻2 𝑂 + 𝑟𝑂 𝑂2 + 𝑟𝐶 𝐶𝑂2 + 𝑟𝑊 𝐻2 𝑂 + 𝑟𝑁 𝑁𝐻3 + 𝑟𝑥 𝐶𝐻2 𝑂0.5 𝑁0.2 (+𝑟𝑃 𝐶𝐻2 𝑂 ) = 0
• Assume CO2 production
• Assume H2O production
• O2 production only for aerobic microbes
• Use C-moles when possible
• Neutral components only (no ions)
• MWX = 0.025 kg Cmol-1

Atom balances:
No product formation:

Components CH2O O2 CO2 H 2O NH3 CH2O0.5N0.2
Atoms rS rO rC rW rN rX unknowns
Carbon 1 0 1 0 0 1 0
Hydrogen 2 0 0 2 3 2 0
Oxygen 1 2 2 1 0 0.5 0
Nitrogen 0 0 0 0 1 0.2 0
4 equations and 6 unknowns → 2 more equations needed:

• Measured rS and rX
• Pirt’s Law and Luedeking-Piret Law

Electron balance:
𝐴𝑡𝑜𝑚 𝑏𝑎𝑙𝑎𝑛𝑐𝑒𝑠: ∑ 𝒏𝒂𝒕𝒐𝒎.𝒊 ∗ 𝒓𝒊 = 𝟎

𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑏𝑎𝑙𝑎𝑛𝑐𝑒: ∑ 𝒏𝒆𝒍𝒆𝒄𝒕𝒓𝒐𝒏𝒔.𝒊 ∗ 𝒓𝒊 = 𝟎

𝐷𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛: 𝜸𝒊 = 𝟒 𝒏𝒊𝑪 + 𝟏 𝒏𝒊𝑯 − 𝟐 𝒏𝒊𝑶 − 𝟑 𝒏𝒊𝑵 [𝑒𝑚𝑜𝑙 (𝐶)𝑚𝑜𝑙 −1 ]
• Electron balance for electron acceptor
• Atom balance for remaining unknowns
• Electron balance links electron acceptor to electron donor and cells

Total and Volumetric rates
Name Symbol Unit
Volumetric rate rL (C)moli m-3 s-1
Total rate ri*VL (C)moli s-1
Specific rate qi (C)moli Cmolx-1 s-1
Cell concentration Cx Cmolx m-3
𝑅𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠: 𝑟𝑠 = −𝑞𝑠 ∗ 𝐶𝑥
𝑟𝑖 = ±𝑞𝑖 ∗ 𝐶𝑥 →→→ 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠: 𝑟𝑝 = +𝑞𝑝 ∗ 𝐶𝑥

𝐶𝑒𝑙𝑙𝑠: 𝑟𝑥 = +𝜇 ∗ 𝐶𝑥 qx = μ



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Victor Pieternella Summary Basic Cell Factory Design.docx BPE22306

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