Engineering & Science
Luedeking-Piret Bioprocess Kinetics: Growth vs. Non-Growth Product Rate
Calculate specific cellular product formation rate q_p = alpha * mu + beta (g product / g DCW / h) and volumetric bioreactor productivity r_p = (alpha * mu + beta) * X (g/(L*h)) across exponential and stationary fermentation phases.
Model fed-batch antibodies, lactic acid, and secondary antibiotics in one kinetic law!
Robert Luedeking and Edgar Piret (1959) showed why fermentation product synthesis rarely stops when cell division slows: microbial and mammalian CHO bioprocesses combine a Growth-Associated yield term alpha * mu (linked directly to primary energy metabolism like ethanol or lactic acid) with a Non-Growth-Associated maintenance/stationary rate beta (dominant in monoclonal antibodies and secondary metabolites like penicillin)!
Combining specific growth rate mu (h^-1) with dry cell weight concentration X (g DCW/L) gives specific productivity q_p = alpha * mu + beta and volumetric bioreactor titer rate r_p = dP / dt = (alpha * mu + beta) * X! In a high-density fed-batch fermentation (alpha = 0.35 g/g, beta = 0.025 g/(g*h), X = 18.0 g/L) growing at mu = 0.20 h^-1, q_p = 0.0950 g/(g*h) and volumetric productivity reaches r_p = 1.710 g/(L*h); shifting to stationary perfusion arrest (mu = 0 h^-1) still sustains r_p = 0.450 g/(L*h) purely from the beta term!
| Bioreactor Phase (alpha = 0.35, beta = 0.025, X = 18 g/L) | Specific Growth Rate mu (h^-1) | Specific Rate qp (g/g/h) | Volumetric Rate rp (g/(L*h)) |
|---|---|---|---|
| Exponential / Fed-Batch Growth | 0.20 h^-1 | 0.0950 | 1.710 g/(L*h) |
| Stationary Production Arrest | 0.00 h^-1 | 0.0250 (= beta) | 0.450 g/(L*h) |
| Invalid Negative Biomass or Growth Rate | Guarded Bioprocess Error | "Invalid Fermentation Inputs" | Requires alpha >= 0, beta >= 0, mu >= 0, X > 0 |
Specific Cellular Product Formation Rate q_p = alpha * mu + beta (g/g/h)
Combines growth-associated coefficient alpha (B2), specific growth rate mu (B4), and non-growth rate beta (B3).
=IF(OR(B2 < 0, B3 < 0, B4 < 0, B5 <= 0), "Invalid Fermentation Inputs", ROUND(B2 * B4 + B3, 4))Volumetric Bioreactor Productivity r_p = (alpha * mu + beta) * X (g/(L*h))
Multiplies specific cellular productivity q_p by dry cell weight biomass concentration X (g/L, cell B5).
=IF(OR(B2 < 0, B3 < 0, B4 < 0, B5 <= 0), "Invalid Fermentation Inputs", ROUND((B2 * B4 + B3) * B5, 3))Try the example
Use the original values or change them to test your understanding.