On the mass distribution model for microbial cell populations

Subramanian, G. B. V.; Ramkrishna, Doraiswami; Fredrickson, A. G.; Tsuchiya, H. M.

doi:10.1007/bf02476769

Cited by 32 publications

(23 citation statements)

References 5 publications

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“…Indeed, proteins and metabolites become to a certain extent diluted, as the volume grows and, both the uptake of nutrients and the disposal of waste depend on the cell surface, which grows as v 2/3 with volume v for a roughly spherical cell shape. A well known example for a model, in which the cell cycle is controlled by cell size, goes back to the work of Bell and Anderson [18], which can be cast in the more general framework of population balance equations (PBE) [19,20]. The models specified therein quite generally allow for the balance of growth, division and partitioning mechanisms (see also Ref.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Stationary Size Distributions of Growing Cells with Binary and Multiple Cell Division

et al. 2011

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Populations of unicellular organisms that grow under constant environmental conditions are considered theoretically. The size distribution of these cells is calculated analytically, both for the usual process of binary division, in which one mother cell produces always two daughter cells, and for the more complex process of multiple division, in which one mother cell can produce 2 n daughter cells with n = 1, 2, 3, . . . . The latter mode of division is inspired by the unicellular algae Chlamydomonas reinhardtii. The uniform response of the whole population to different environmental conditions is encoded in the individual rates of growth and division of the cells. The analytical treatment of the problem is based on size-dependent rules for cell growth and stochastic transition processes for cell division. The comparison between binary and multiple division shows that these different division processes lead to qualitatively different results for the size distribution and the population growth rates.

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Section: Theoretical Frameworkmentioning

confidence: 99%

Stationary Size Distributions of Growing Cells with Binary and Multiple Cell Division

et al. 2011

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“…(B21).

\begin{matrix} \frac{\partial n_{boldY} (y, r, t)}{\partial t} + \nabla_{boldy} \cdot \dot{boldY} (y ∣ {boldC}_{boldY}) n_{boldY} (y, r, t) + \nabla_{boldr} \cdot \dot{boldR} n_{boldY} (y, r, t) = \\ - σ_{boldy} (y ∣ {boldC}_{boldY}) n_{boldY} (y, r, t) + 2 \int σ_{boldY} ({boldy}^{'} ∣ {boldC}_{boldY}) p_{Y ∣ {boldY}^{'}} (y ∣ {boldy}^{'}, {boldC}_{boldY}) n_{boldY} ({boldy}^{'}, r, t) d {boldy}^{'} \end{matrix}

The solution to this problem as it has been addressed by numerous investigators in the literature over the last few decades (Subramanian et al ., 1970; Subramanian and Ramkrishna, 1971; Mantzaris, 2006) for varying degrees of complexity with respect to the choice of intracellular variables y . We have thus the means to compute μ ( r , t ∣ C Y ), C Y ( r , t ).…”

Section: B1 Number Densitymentioning

confidence: 99%

Modeling of gene regulatory processes by population-mediated signaling: New applications of population balances

Shu

Chatterjee

et al. 2012

Chemical Engineering Science

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Population balance modeling is considered for cell populations in gene regulatory processes in which one or more intracellular variables undergo stochastic dynamics as determined by Ito stochastic differential equations. This paper addresses formulation and computational issues with sample applications to the spread of drug resistance among bacterial cells. It is shown that predictions from population balances can display qualitative differences from those made with single cell models which are usually encountered in the literature. Such differences are deemed to be important.

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“…the temporal derivative of N, reflects the accumulation as a function of three specific lifecycle events: single cell growth, division and birth. A comprehensive explanation of this approach is provided by [7], where all terms are described in detail and units of the quantities are quoted. In this article, we briefly sketch the main concepts.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…, c 6 ≥ 0 are constants. This approach can be interpreted as an extension of [7]. The outline of the model is completed by the characterization of the partitioning function p [8],…”

Section: Mathematical Modelmentioning

confidence: 99%

Parameter Estimation in Population Balance Models

Groh¹

2010

AIP Conference Proceedings

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The aim of this manuscript is to elucidate some models focusing on the dynamics of cell populations in vitro and to bring them in line with methods established in the context of inverse problems. We concentrate on a population balance model that describes the cell number as a function of time and single cell mass, where the key variable fulfills a partial integro-differential equation (PIDE). According to this popular approach, three generally unknown physiological functions enter into the representation and the objective is to identify the corresponding parameters. In this article, the main concept of this equation type is outlined, some possibilities of data retrieval are explained and mathematical methods to solve the problem are expounded.

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On the mass distribution model for microbial cell populations

Cited by 32 publications

References 5 publications

Stationary Size Distributions of Growing Cells with Binary and Multiple Cell Division

Stationary Size Distributions of Growing Cells with Binary and Multiple Cell Division

Modeling of gene regulatory processes by population-mediated signaling: New applications of population balances

Parameter Estimation in Population Balance Models

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