Abstract
In silico, cell based approaches for modeling biological morphogenesis are used to test and validate our understanding of the biological and mechanical processes that are at work during the growth and the organization of multi-cell tissues. As compared to in vivo experiments, computer based frameworks dedicated to tissue modeling allow us to easily test different hypotheses, and to quantify the impact of various biophysically relevant parameters. Here, we propose a formalism based on a detailed, yet simple, description of cells that accounts for intra-, inter- and extra-cellular mechanisms. More precisely, cell growth and division are described through the space and time evolution of the membrane vertices. These vertices follow a Newtonian dynamics, meaning that their evolution is controlled by different types of forces: a membrane force (spring and bending), an adherence force (inter-cellular spring), external and internal pressure forces. Different evolution laws can be applied to the internal pressure, depending on the intra-cellular mechanism of interest. In addition to the cells dynamics, our formalism further relies on a lattice Boltzmann method, using the Palabos library, to simulate the diffusion of chemical signals. The latter aims at driving the growth and migration of a tissue by simply changing the state of the cells. All of this leads to an accurate description of the growth and division of cells, with realistic cell shapes and where membranes can have different properties. While this work is mainly of methodological nature, we also propose to validate our framework through simple, yet biologically relevant benchmark tests at both single-cell and full tissue scales. This includes free and chemically controlled cell tissue growth in an unbounded domain. The ability of our framework to simulate cell migration, cell compression and morphogenesis under external constraints is also investigated in a qualitative manner.
Highlights
Morphogenesis is the biological mechanism that drives the development of cells, tissues, and organs, by directly impacting their shape and function
Obtaining quantitative results in a reproducible manner remains a tedious task, the growing interest in computational methods [Fletcher et al, 2014; Van Liedekerke et al, 2015; Tanaka, 2016; Sharpe, 2017; Merzouki, 2018; Buttenschön and Edelstein-Keshet, 2020]. These methods obviously rely on empirical observations and ad-hoc parameters in order to compensate for our reduced understanding of active and mechanical properties of living cells
The main advantage of immersedboundary formulations is that they self-adjust to the number of vertices, no constant modification is required during cell proliferation and apoptosis
Summary
Morphogenesis is the biological mechanism that drives the development of cells, tissues, and organs, by directly impacting their shape and function. The main advantage of immersedboundary formulations is that they self-adjust to the number of vertices, no constant modification is required during cell proliferation and apoptosis This particular approach was notably used to simulate, tissue bending [Rejniak et al, 2004], pattern formation and necrosis [Dillon et al, 2008], and morphogenic signaling [Tanaka et al, 2015]. We dynamically adjust the number of vertices used for the evolution of the cell membrane (as in [Jamali et al, 2010]), but, to [Tamulonis et al, 2011], the cell nucleus, cytoskeleton and cytoplasm do not explicitly appear in our formulation This is possible assuming the same cell division mechanism as in immersed boundary cell-based approaches [Tanaka et al, 2015].
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