Modeling Morphogenesisin silicoandin vitro: Towards Quantitative, Predictive, Cell-based Modeling

Abstract

Abstract. Cell-based, mathematical models help make sense of morphogenesis-i.e. cells organizing into shape and pattern-by capturing cell behavior in simple, purely descriptive models. Cell-based models then predict the tissue-level patterns the cells produce collectively. The first step in a cell-based modeling approach is to isolate sub-processes, e.g. the patterning capabilities of one or a few cell types in cell cultures. Cell-based models can then identify the mechanisms responsible for patterning in vitro. This review discusses two cell culture models of morphogenesis that have been studied using this combined experimental-mathematical approach: chondrogenesis (cartilage patterning) and vasculogenesis (de novo blood vessel growth). In both these systems, radically different models can equally plausibly explain the in vitro patterns. Quantitative descriptions of cell behavior would help choose between alternative models. We will briefly review the experimental methodology (microfluidics technology and traction force microscopy) used to measure responses of individual cells to their micro-environment, including chemical gradients, physical forces and neighboring cells. We conclude by discussing how to include quantitative cell descriptions into a cell-based model: the Cellular Potts model.

A semi-stochastic cell-based formalism to model the dynamics of migration of cells in colonies

“…Vascularization has been modeled using the cellular potts model extensively by Merks and Koolwijk (2009), among others. The cellular potts model is a lattice-based model in which each pixel can represent a cell and hence falls within the class of discrete cellular automata models.…”

A Hybrid Model Describing Different Morphologies of Tumor Invasion Fronts

“…However, all these approaches overlook the behavior and the mutual interactions of single cells, which, as seen, are fundamental in determining the invasiveness of cancers and the subsequent metastatization. Discrete techniques, which include cellular automata and agent-based models [2,4,34,37,44,56,71], are instead able to preserve the identity of each simulated indi- vidual, to more naturally capture their biophysical properties, such as shape change, adhesion and intrinsic motility, and to handle local dynamics. On the contrary, purely discrete models translate complex microscopic processes into simple phenomenological rules, are difficult to study analytically and the associated computational cost rapidly increases with the number of cells modeled, which makes it difficult to simulate lesions longer than one millimeter.…”

A phenomenological model for chemico-mechanically induced cell shape changes during migration and cell–cell contacts

“…Furthermore, these models are lattice-based, which means that cells are allowed to take a discrete set of positions, classically distributed in a Cartesian way, within a certain domain of computation. Using these models, one succeeds in modeling the complicated process of angiogenesis (Merks and Koolwijk 2009). …”