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
1|Page
Victor Pieternella Summary Basic Cell Factory Design.docx BPE22306
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
1|Page
Victor Pieternella Summary Basic Cell Factory Design.docx BPE22306
