Particle Simulations of Morphogenesis

Abstract

The simulation of the creation and evolution of biological forms requires the development of computational methods that are capable of resolving their hierarchical, spatial and temporal complexity. Computations based on interacting particles, provide a unique computational tool for discrete and continuous descriptions of morphogenesis of systems ranging from the molecular to the organismal level. The capabilities of particle methods hinge on the simplicity of their formulation which enables the formulation of a unifying computational framework encompassing deterministic and stochastic models. In this paper, we discuss recent advances in particle methods for the simulation of biological systems at the mesoscopic and the macroscale level. We present results from applications of particle methods including reaction diffusion on deforming surfaces, deterministic and stochastic descriptions of tumor growth and angiogenesis and discuss successes and challenges of this approach.

Variability and constancy in cellular growth of Arabidopsis sepals

“…A decreasing wall extensibility w may be obtained by strain stiffening (Kierzkowski et al, 2012), wall hardening (Huang et al, 2012), or by having a thicker cell wall (Schopfer, 2006). In future studies, it will be interesting to use the results of our study to validate numerical models (Dupuy et al, 2010;Koumoutsakos et al, 2011;Huang et al, 2012;Kierzkowski et al, 2012;Fozard et al, 2013) within a Bayesian uncertainty quantification and propagation framework (Angelikopoulos et al, 2012). Such a framework would be able to quantify which model is most probable given the data.…”

Deformable Cell Model of Tissue Growth

“…There are various realizations of the deformable cell model, including the immersed boundary method [44], the subcellular element method [45], and the level set method [46] (see [30] and references therein). The deformable cell model coupled with Navier-Stokes equations was used to study the development of epithelial acini [47,48] and ductal tumor [49].…”

SEM++: A particle model of cellular growth, signaling and migration

“…When cells are modeled at a continuum level, a single cell does not exist. The emergence of phenomena initiated by single cells, a result of mutation or phenotypic activation, can therefore not be studied in these models [31]. We wish to study such phenomena in computer simulations and we employ a cell-based model that can represent individual cells subject to mechanical stresses, migration, proliferation, cell-cell and cell-substrate adhesion and cell-cell mediated signaling.…”