On the stable size distribution of populations reproducing by fission into two unequal parts

Heijmans, H.J.A.M.

doi:10.1016/0025-5564(84)90059-2

Cited by 69 publications

(59 citation statements)

References 18 publications

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“…A thorough presentation of key aspects of the mathematical framework is given by Ramkrishna in [20,21]. The stability and uniqueness of solutions of some simple models were systematically discussed in the literature [22][23][24]. However, because of the intricate functional form of the PBEs, it is difficult to find analytical solutions to these equations.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

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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%

“…On the other hand, one has also to find the value of γ that satisfies (23). The numerical estimation of (23) with (26) as function of γ shows that the only physical value that verifies R(0) = 0 is given by γ = 1 h −1 .…”

Section: Explicit Solution For a Particular Choice Of Parametersmentioning

confidence: 99%

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

et al. 2011

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“…A survey of many applications is given in the book edited by Metz and Diekmann [20]. Our model includes models of a population of organisms reproducing by binary fission with equal [8,10,12,16,17] and unequal division [2,11,13,15]. Both types of binary fission models were considered in [29].…”

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confidence: 99%

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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“…Of course, for the model (1), there are many results on the well-posedness and the essential properties. For more detail one can refer to [5][6][7][8][9]. The fact that, at any time we can have observation of the size distribution of the cell population allows us to focus the estimation of the division rate on the time asymptotic behavior of the model (1).…”

Section: Introductionmentioning

confidence: 99%

Inverse problem for cell division rate in population dynamics

Matar-Tine

2015

ITM Web of Conferences

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Abstract. In population dynamics, more precisely in cell structured population, experimental measures of the temporal dynamics of some parameters are often difficult or even impossible because of the lack of appropriate technology. It is the case of the division rate parameter for a structured population of cells. So theoretical and numerical approaches are needed to recover such parameters by indirect observation of the solution of the modeling system. In this work we present how to estimate the division rate from a growth-fragmentation type equation as done in the work of Doumic and Tine (see [1]) and following the work done in [2] and [3]. The estimation strategy is based on the observation of the long-term solution of the model for a size structured population when the growth and division rates are fully general. The issue of the theoretical and numerical results are discussed here.

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On the stable size distribution of populations reproducing by fission into two unequal parts

Cited by 69 publications

References 18 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

Asynchronous Exponential Growth of a General Structured Population Model

Inverse problem for cell division rate in population dynamics

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