Abstract
Mathematical modeling aims at understanding the effects of biological perturbations, suggesting ways to intervene and to reestablish proper cell functioning in diseases such as cancer or in autoimmune disorders. This is a difficult task for obvious reasons: the level of details needed to describe the intra-cellular processes involved, the numerous interactions between cells and cell types, and the complex dynamical properties of such populations where cells die, divide and interact constantly, to cite a few. Another important difficulty comes from the spatial distribution of these cells, their diffusion and motility. All of these aspects cannot be easily resolved in a unique mathematical model or with a unique formalism. To cope with some of these issues, we introduce here a novel framework, UPMaBoSS (for Update Population MaBoSS), dedicated to modeling dynamic populations of interacting cells. We rely on the preexisting tool MaBoSS, which enables probabilistic simulations of cellular networks. A novel software layer is added to account for cell interactions and population dynamics, but without considering the spatial dimension. This modeling approach can be seen as an intermediate step towards more complex spatial descriptions. We illustrate our methodology by means of a case study dealing with TNF-induced cell death. Interestingly, the simulation of cell population dynamics with UPMaBoSS reveals a mechanism of resistance triggered by TNF treatment. Relatively easy to encode, UPMaBoSS simulations require only moderate computational power and execution time. To ease the reproduction of simulations, we provide several Jupyter notebooks that can be accessed within the CoLoMoTo Docker image, which contains all software and models used for this study.
Highlights
One of the key challenges in cell biology or in biochemistry is to understand how perturbations of genes, proteins or metabolites affect cellular behavior
We illustrate the use of UPMaBoSS with two examples, the first one focusing on cell-cell interactions, and the second one extending a published model of cell fate decision in response to the activation of death receptors (Calzone et al, 2010)
Using a simple toy model, we first showed that the results of the simulations are different if we consider a homogeneous, noninteracting cell population compared to a dynamic population of interacting cells
Summary
One of the key challenges in cell biology or in biochemistry is to understand how perturbations of genes, proteins or metabolites affect cellular behavior. The difficulty grows when considering inter-cellular signals and their effect at the organ level or the role of the micro-environment on the cell fate. The mathematical model should include detailed pathway descriptions for every cell, and key events occurring at the population level, e.g., extra-cellular diffusion, cell motility, intercellular communications, death or division of cells. Cell populations are considered as a large set of single entities (cells), diffusing and moving throughout the environment, giving rise to reproducible spatial organizations. Formal frameworks borrowed from physics are often used, such as partial differential equations. These approaches allow detailed and accurate temporal and spatial descriptions of collective cellular behaviors (Cowan et al, 2012)
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