, Volume 67, Issue 3, pp 515–530 | Cite as

Revisiting Verhulst and Monod models: analysis of batch and fed-batch cultures

  • Nishikant Shirsat
  • Avesh Mohd
  • Jessica Whelan
  • Niall J. English
  • Brian Glennon
  • Mohamed Al-Rubeai
Original Research


The paper re-evaluates Verhulst and Monod models. It has been claimed that standard logistic equation cannot describe the decline phase of mammalian cells in batch and fed-batch cultures and in some cases it fails to fit somatic growth data. In the present work Verhulst, population-based mechanistic growth model was revisited to describe successfully viable cell density (VCD) in exponential and decline phases of batch and fed-batch cultures of three different CHO cell lines. Verhulst model constants, K, carrying capacity (VCD/ml or μg/ml) and r, intrinsic growth factor (h−1) have physical meaning and they are of biological significance. These two parameters together define the course of growth and productivity and therefore, they are valuable in optimisation of culture media, developing feeding strategies and selection of cell lines for productivity. The Verhulst growth model approach was extended to develop productivity models for batch and fed-batch cultures. All Verhulst models were validated against blind data (R2 > 0.95). Critical examination of theoretical approaches concluded that Monod parameters have no physical meaning. Monod-hybrid (pseudo-mechanistic) batch models were validated against specific growth rates of respective bolus and continuous fed-batch cultures (R2 ≈ 0.90). The reduced form of Monod-hybrid model CL/(KL + CL) describes specific growth rate during metabolic shift (R2 ≈ 0.95). Verhulst substrate-based growth models compared favourably with Monod-hybrid models. Thus, experimental evidence implies that the constants in the Monod-hybrid model may not have physical meaning but they behave similarly to the biological constants in Michaelis–Menten enzyme kinetics, the basis of the Monod growth model.


CHO Verhulst Monod Model constants Metabolic shift 

List of symbols


Carrying capacity for VCD


Carrying capacity, Verhust-population based for VCD


Carrying capacity, Verhust-substrate eased for VCD


Carrying capacity, Verhust for MAb


Intrinsic growth factor


Intrinsic productivity factor


Intrinsic growth factor, Verhulst population based for VCD


Intrinsic growth factor, Verhulst substrate based for VCD


Intrinsic growth factor, Verhulst for MAb


Glucose Monod constant


Glutamine Monod constant


Lactate Monod constant


Ammonia Monod constant


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Nishikant Shirsat
    • 1
  • Avesh Mohd
    • 1
  • Jessica Whelan
    • 1
  • Niall J. English
    • 1
  • Brian Glennon
    • 1
  • Mohamed Al-Rubeai
    • 1
  1. 1.School of Chemical and Bioprocess EngineeringUniversity College DublinBelfield, Dublin 4Ireland

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