A comparison of probabilistic and stochastic formulations in modelling growth uncertainty and variability

Banks, Harvey Thomas; Davis, Jimena L.; Ernstberger, Stacey L.; Hu, Shuhua; Artimovich, E.; Dhar, Arun K.; Browdy, Craig L.

doi:10.1080/17513750802304877

Cited by 28 publications

(43 citation statements)

References 16 publications

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“…To better understand rates at the generation number cohort or division number cohort level, one should attempt to develop individual (cohort) dynamics to investigate the CFSE data in a Type I framework of Aggregate Data/Individual (Cohort) Dynamics inverse problems such as those discussed in [1,Chapter 14] and [5]. Similar approaches have been successfully pursued in marine and insect population models [3,6,10,12,22] as well as in physiologically based pharmacokinetic (PBPK) models in toxicology [5,17]. Fortunately, a simple reformulation of (1) allows such an approach and permits both the accurate quantification of total cells per division number and the accurate estimation of proliferation and death rates in terms of division number in such a framework.…”

Section: Introductionmentioning

confidence: 99%

A Division-Dependent Compartmental Model for Computing Cell Numbers in CFSE-based Lymphocyte Proliferation Assays

Banks¹,

Thompson²,

Peligero³

et al. 2012

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Some key features of a mathematical description of an immune response are an estimate of the number of responding cells and the manner in which those cells divide, differentiate, and die. The intracellular dye CFSE is a powerful experimental tool for the analysis of a population of dividing cells, and numerous mathematical treatments have been aimed at using CFSE data to describe an immune response [30,31,32,37,38,41,47,48]. Recently, partial differential equation structured population models, with measured CFSE fluorescence intensity as the structure variable, have been shown to accurately fit histogram data obtained from CFSE flow cytometry experiments [18,19,51,53]. In this report, the population of cells is mathematically organized into compartments, with all cells in a single compartment having undergone the same number of divisions. A system of structured partial differential equations is derived which can be fit directly to CFSE histogram data. From such a model, cell counts (in terms of the number of divisions undergone) can be directly computed and thus key biological parameters such as population doubling time and precursor viability can be determined. Mathematical aspects of this compartmental model are discussed, and the model is fit to a data set. As in [18,19], we find temporal and division dependence in the rates of proliferation and death to be essential features of a structured population model for CFSE data. Variability in cellular autofluorescence is found to play a significant role in the data, as well. Finally, the compartmental model is compared to previous work, and statistical aspects of the experimental data are discussed.Key words: Cell proliferation, cell division number, CFSE, label structured population dynamics, partial differential equations, inverse problems. 1 Report Documentation Page

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Section: Introductionmentioning

confidence: 99%

A Division-Dependent Compartmental Model for Computing Cell Numbers in CFSE-based Lymphocyte Proliferation Assays

Banks¹,

Thompson²,

Peligero³

et al. 2012

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“…This model, referred to as growth rate distributed size-structured (GRDSS) population model, was first formulated in [1,6] in 1986, and has been successfully used to model mosquitofish population in the rice fields, where the data exhibits both bimodality and dispersion in size as time increases (e.g., see [1]). In addition, this model was also used to model the early growth of shrimp populations, which exhibits a great deal of variability in size as time evolves even though the shrimp begin with approximately similar size [3,4]. Based on the above discussions, we see that the GRDSS model can be associated with some stochastic process, which is obtained due to the variability in the individual's growth rate and also the variability in the initial size of individuals in the population.…”

Section: Evolution Of Conditional Probability Density Function Of X(tmentioning

confidence: 99%

“…Fokker-Planck equations have also been used in the literature (e.g., [3,8]) to describe the population density in a sizestructured population where the growth process is a diffusion process satisfying the Itô stochastic differential equation. There are several approaches that can be used to derive the Fokker-Planck equation.…”

Section: Equation (22) Is Often Referred To As Fokkerplanck Equationmentioning

confidence: 99%

Propagation of Uncertainty in Dynamical Systems

Banks¹,

Hu²

2011

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“…The fitted curves can be used to approximate the numbers of cells having divided a given number of times. variable environment vs. individual stochastic mechanisms has been treated specifically in [4,11,12,25] as well as more generically in [9,10,16,17]. While probability and stochasticity is fundamental to all of these models, the mathematical constructs used to incorporate asynchrony/variability into the modeling is strikingly different conceptually and computationally.…”

Section: Mathematical Modelsmentioning

confidence: 99%

Mathematical Models of Dividing Cell Populations: Application to CFSE Data

Banks

Thompson

2012

Math. Model. Nat. Phenom.

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Abstract. Flow cytometric analysis using intracellular dyes such as CFSE is a powerful experimental tool which can be used in conjunction with mathematical modeling to quantify the dynamic behavior of a population of lymphocytes. In this survey we begin by providing an overview of the mathematically relevant aspects of the data collection procedure. We then present an overview of the large body of mathematical models, along with their assumptions and uses, which have been proposed to describe the dynamics of proliferating cell populations. While much of this body of work has been aimed at modeling the generation structure (cells per generation) of the proliferating population, several recent models have considered the more fundamental task of modeling CFSE histogram data directly. Such models are analyzed and recent results are discussed. Finally, directions for future research are suggested.

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A comparison of probabilistic and stochastic formulations in modelling growth uncertainty and variability

Cited by 28 publications

References 16 publications

A Division-Dependent Compartmental Model for Computing Cell Numbers in CFSE-based Lymphocyte Proliferation Assays

A Division-Dependent Compartmental Model for Computing Cell Numbers in CFSE-based Lymphocyte Proliferation Assays

Propagation of Uncertainty in Dynamical Systems

Mathematical Models of Dividing Cell Populations: Application to CFSE Data

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