On the stability of the cell size distribution

Diekmann, Odo; Heijmans, H.J.A.M.; Thieme, Horst R.

doi:10.1007/bf00277748

Cited by 193 publications

(218 citation statements)

References 17 publications

(13 reference statements)

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“…Simulations showed that constant and quadratic forms of growth achieved balanced time-invariant growth states using equal and unequal partitioning. Under conditions of linear growth and equal partitioning, however, the population distribution appeared to have a periodic behaviour, a special case originally predicted in theory by Diekmann et al (1984) described as a 'multiplication machine'. In all the remaining cases, unequal division resulted in balanced growth being achieved faster and with broader distribution.…”

Section: Nð0 Tþ ¼ 0 ð6þmentioning

confidence: 81%

Modelling of Mammalian Cells and Cell Culture Processes

Sidoli¹,

Mantalaris

Asprey³

2004

Cytotechnology

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Mammalian cell cultures represent the major source for a number of very high-value biopharmaceutical products, including monoclonal antibodies (MAbs), viral vaccines, and hormones. These products are produced in relatively small quantities due to the highly specialised culture conditions and their susceptibility to either reduced productivity or cell death as a result of slight deviations in the culture conditions. The use of mathematical relationships to characterise distinct parts of the physiological behaviour of mammalian cells and the systematic integration of this information into a coherent, predictive model, which can be used for simulation, optimisation, and control purposes would contribute to efforts to increase productivity and control product quality. Models can also aid in the understanding and elucidation of underlying mechanisms and highlight the lack of accuracy or descriptive ability in parts of the model where experimental and simulated data cannot be reconciled. This paper reviews developments in the modelling of mammalian cell cultures in the last decade and proposes a future direction -the incorporation of genomic, proteomic, and metabolomic data, taking advantage of recent developments in these disciplines and thus improving model fidelity. Furthermore, with mammalian cell technology dependent on experiments for information, model-based experiment design is formally introduced, which when applied can result in the acquisition of more informative data from fewer experiments. This represents only part of a broader framework for model building and validation, which consists of three distinct stages: theoretical model assessment, model discrimination, and model precision, which provides a systematic strategy from assessing the identifiability and distinguishability of a set of competing models to improving the parameter precision of a final validated model. NomenclatureC ij -component i concentration in jth model compartment; R ijk -transport rate of component i into or out of compartment j from the kth source or sink compartment; N in -number of source compartments; N outnumber of sink compartments; r ijl -reaction rate of component i in compartment j in the lth i-generating or i-consuming reaction; N gen -number of reactions generating component i; N con -number of reactions consuming component i; -specific growth rate; app max -apparent maximum specific growth rate; K dspecific death rate; N v -viable cell number; N t -total cell number; D -dilution rate; -parameter; 0 -parameter; -parameter; m -cell mass; m 0 -mass of a dividing cell; t -time; N -cell number; r -single cell growth rate; S -nutrient concentration; s -nutrient concentration vector; À -cell transition rate; ppartition probability density function; Y -yield coefficient; f (m) -the division probability density function; B -coefficient for the beta distribution incorporating the gamma function; x max -vector of maximum XPS 120742 (CYTO) -ms-code CYTO853 -product element 5254543 -23 September 2004 -Newgen

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Section: Nð0 Tþ ¼ 0 ð6þmentioning

confidence: 81%

Modelling of Mammalian Cells and Cell Culture Processes

Sidoli¹,

Mantalaris

Asprey³

2004

Cytotechnology

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“…Another immediate consequence of (13) Let P be defined by (8) and denote by A b a the differential operator −(gN ) − μN restricted to the domain…”

Section: Formulation Of the Resultsmentioning

confidence: 99%

“…We note that due to (8) and the domain of definition of P , the function Ff is locally integrable on [a, 1) for any f ∈ L ∞ [a, 1]. The following lemma gathers some properties of the operator F .…”

Section: Proposition 1 the Operator B Has An Eigenvector W Which Satimentioning

confidence: 99%

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Asynchronous Exponential Growth of a General Structured Population Model

2011

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We consider a class of structured cell population models described by a first order partial differential equation perturbed by a general birth operator which describes in a unified way a wide class of birth phenomena ranging from cell division to the McKendrick model. Using the theory of positive stochastic semigroups we establish new criteria for an asynchronous exponential growth of solutions to such equations.

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“…Models that do distinguish between growth in biomass and growth in cell number must include separate mechanisms for describing cell growth and fission. Such size-structured models were first developed by Sinko and Streifer [22,23], Bell [3] and Bell and Anderson [4] and were later modified and investigated extensively by Diekmann et al [7,8] and Metz and Diekmann [17].…”

Section: Introductionmentioning

confidence: 99%

A size-structured model of bacterial growth and reproduction

Ellermeyer

Pilyugin

2012

Journal of Biological Dynamics

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We consider a size-structured bacterial population model in which the rate of cell growth is both size-and time-dependent and the average per capita reproduction rate is specified as a model parameter. It is shown that the model admits classical solutions. The population-level and distribution-level behaviours of these solutions are then determined in terms of the model parameters. The distribution-level behaviour is found to be different from that found in similar models of bacterial population dynamics. Rather than convergence to a stable size distribution, we find that size distributions repeat in cycles. This phenomenon is observed in similar models only under special assumptions on the functional form of the size-dependent growth rate factor. Our main results are illustrated with examples, and we also provide an introductory study of the bacterial growth in a chemostat within the framework of our model.

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On the stability of the cell size distribution

Cited by 193 publications

References 17 publications

Modelling of Mammalian Cells and Cell Culture Processes

Modelling of Mammalian Cells and Cell Culture Processes

Asynchronous Exponential Growth of a General Structured Population Model

A size-structured model of bacterial growth and reproduction

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