Dynamics of Microbial Cell Populations

Tsuchiya, H. M.; Fredrickson, A. G.; Aris, Rutherford

doi:10.1016/s0065-2377(08)60275-6

Cited by 190 publications

(56 citation statements)

References 46 publications

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“…To describe a population of cells consisting of multiple populations with distributed properties within a culture, a PBM model is required. These two model types represent the extremes of the long established microbial model classification spectrum identified by Tsuchiya et al (1966) (Figure 1), which can also be applied to mammalian cell models. In this classification system, a model can be structured or unstructured, segregated or unsegregated, deterministic or stochastic.…”

Section: Mathematical Modelsmentioning

confidence: 99%

“…PBMs have been available since the 1960s and research has been spearheaded by Fredrickson and co-workers (Eakman et al 1966;Tsuchiya et al 1966). Looking beyond the mathematically complex nature of PBMs, the one crucial characterising difference that distinguish them form SCMs is their unmatched ability to account for the corpuscular nature of a cell.…”

Section: Population Balance Modelsmentioning

confidence: 99%

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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: Mathematical Modelsmentioning

confidence: 99%

Section: Population Balance Modelsmentioning

confidence: 99%

Modelling of Mammalian Cells and Cell Culture Processes

Sidoli¹,

Mantalaris

Asprey³

2004

Cytotechnology

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“…Thus, from a modeling perspective, the aforementioned sources of heterogeneity, with the exception of the random reaction occurrence, were explicitly taken into account in the deterministic cell population balance (CPB) framework developed by Tsuchiya et al (1966), and Fredrickson et al (1967). These models describe the temporal evolution of the distribution of the population over a state variable.…”

Section: Introductionmentioning

confidence: 99%

Cell population balance and hybrid modeling of population dynamics for a single gene with feedback

Stamatakis¹

2013

Computers & Chemical Engineering

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Latest research on biological systems is steadily shifting from isolated single cells to entire cell populations. The latter are inherently heterogeneous, and their modeling requires approaches that explicitly account for this property. A comprehensive such approach is the cell population balance (CPB), which, however, is computationally expensive and becomes intractable for multivariable models.In this work, we demonstrate the use of model-reduction to efficiently simulate cell population heterogeneity in a genetic network of a single gene with feedback. Starting from a 4-species model we use singular perturbation analysis to derive a single equation for the intracellular protein concentration. We subsequently incorporate this equation to a hybrid model consisting of a CPB for the cell volume, and a continuum equation for the protein concentration. We finally compare the results obtained with the hybrid model with those of the full CPB, demonstrating the accuracy and computational efficiency of the hybrid methodology.

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“…After some early work on sizestructured models mainly for cell populations (VonFoerster 1959;Tsuchiya et al 1966;Bell and Anderson 1967;Fredrickson et al 1967;Sinko and Streifer 1967;Bell 1968;Anderson et al 1969;Streifer 1969, 1971; VanSickle 1977;Murphy 1983) in the wake of McKendrick (1926), the work on 35 general PSPMs got in full swing during the last three decades after their general formulation by Odo Diekmann and collaborators in the mid 80's (summarised in Metz and Diekmann 1986). This has resulted not only in applications of PSPMs to a variety of systems but also in the development of a rigorous mathematical basis for the formulation of these models (Diekmann 40 et al 1998), methods for computation of their steady states (Diekmann et al 2003) and for analysis of their stability (Diekmann et al 2010), and special numerical techniques for their time integration (De Roos 1988) and bifurcation analysis (Kirkilionis et al 2001).…”

mentioning

confidence: 99%

Ontogenetic symmetry and asymmetry in energetics

2012

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Body size (≡ biomass) is the dominant determinant of population dynamical processes such as giving birth or dying in almost all species, with often drastically different behaviour occurring in different parts of the growth trajectory, while the latter is largely determined by food availability at the different life stages. This leads to the question under what conditions unstructured population models, formulated in terms of total population biomass, still do a fair job. To contribute to answering this question we first analyze the conditions under which a size-structured model collapses to a dynamically equivalent unstructured one in terms of total biomass. The only biologically meaningful case where this occurs is when body size does not affect any of the population dynamic processes, this is the case if and only if the mass-specific ingestion rate, the mass-specific biomass production and the mortality rate of the individuals are independent of size, a condition to which we refer as "ontogenetic symmetry". Intriguingly, under ontogenetic symmetry the equilibrium biomass-body size distribution is proportional to 1/size, a form that has been conjectured for marine size spectra and subsequently has been used as prior assumption in theoretical papers dealing with the latter. As a next step we consider an archetypical class of models in which reproduction takes over from growth upon reaching an adult body size, in order to determine how quickly discrepancies from ontogenetic symmetry lead to rele- vant novel population dynamical phenomena. The phenomena considered are biomass overcompensation, when additional imposed mortality leads, rather unexpectedly, to an increase in the equilibrium biomass of either the juveniles or the adults (a phenomenon with potentially big consequences for predators of the species), and the occurrence of two types of size-structure driven oscillations, juvenile-driven cycles with separated extended cohorts, and adult-driven cycles in which periodically a front of relatively steeply decreasing frequencies moves up the size distribution. A small discepancy from symmetry can already lead to biomass overcompensation; size-structure driven cycles only occur for somewhat larger discrepancies.

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Dynamics of Microbial Cell Populations

Cited by 190 publications

References 46 publications

Modelling of Mammalian Cells and Cell Culture Processes

Modelling of Mammalian Cells and Cell Culture Processes

Cell population balance and hybrid modeling of population dynamics for a single gene with feedback

Ontogenetic symmetry and asymmetry in energetics

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