Investigating the Reproducibility of In Vitro Cell Biology Assays Using Mathematical Models

Wang, Jin

doi:10.5204/thesis.eprints.109790

Cited by 1 publication

(2 citation statements)

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“…Traditionally, mathematical models of development and repair account for such tissue-level processes by modelling the cell population density with ordinary dierential equations (ODEs) [47] and partial dierential equations (PDEs) [810]. These continuum descriptions can be parametrised to predict the cell population density growth prole in commonlyused cell biology assays, such as proliferation assays [57,11,12] and scratch assays [810,13,14]. In a proliferation assay (Figure 1), cells are seeded uniformly on a two-dimensional substrate.…”

Section: Introductionmentioning

confidence: 99%

“…While Equations (1)(2) can match the evolution of cell population densities in experiments [8], these models focus exclusively on the characteristics of the global cell population. However, recent technology [9,14,20,21] has made it possible to perform these assays in a high-throughput fashion, al- with epithelial 3T3 broblast cells (cell line 1) [17], while images in (c)(d) show a cell proliferation assay with mesenchymal MDA-MB-231 breast cancer cells (cell line 2) [18]. The location of cells are highlighted with a yellow marker.…”

Section: Introductionmentioning

confidence: 99%

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Accurate and efficient discretisations for stochastic models providing near agent-based spatial resolution at low computational cost

Fadai

Baker

Simpson

2019

Preprint

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Understanding how cells proliferate, migrate, and die in various environments is essential in determining how organisms develop and repair themselves. Continuum mathematical models, such as the logistic equation and the Fisher-Kolmogorov equation, can describe the global characteristics observed in commonly-used cell biology assays, such as proliferation and scratch assays.However, these continuum models do not account for single-cell-level mechanics observed in highthroughput experiments. Mathematical modelling frameworks that represent individual cells, often called agent-based models, can successfully describe key single-cell-level features of these assays, but are computationally infeasible when dealing with large populations. In this work, we propose an agent-based model with crowding eects that is computationally ecient and matches the logistic and Fisher-Kolmogorov equations in parameter regimes relevant to proliferation and scratch assays, respectively. This stochastic agent-based model allows multiple agents to be contained within compartments on an underlying lattice, thereby reducing the computational storage compared to existing agent-based models that allow one agent per site only. We propose a systematic method to determine a suitable compartment size. Implementing this compartment-based model with this compartment size provides a balance between computational storage, local resolution of agent behaviour, and agreement with classical continuum descriptions. sub ject: biomathematics, computational biology keywords: compartment based model, lattice based model, proliferation assay, scratch assay, crowding eects, volume exclusion 1

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Section: Introductionmentioning

confidence: 99%