"Modelling the Development of Complex Tissues using Individual Viscoelastic Cells",

Katarzyna A. Rejniak

chapter IV.3 of the book "Single-cell-based Models in Biology and Medicine", edited by: A.R.A. Anderson, M.A.J. Chaplain & K.A. Rejniak, 2007, Birkhauser-Verlag in the Mathematics and Biosciences in Interaction (MBI) series, ISBN 978-3-7643-8101-1, publisher website

Abstract:

This chapter describes a biomechanical model of individual deformable viscoelastic cells that can be arranged into tissues of various topologies. The model is based on an immersed boundary method with distributed sources and couples a continuous description of a viscous incompressible cytoplasm with the dynamics of separate elastic cells. Several key cellular processes, such as cell growth, division, apoptosis and polarisation, are also defined within this framework. This approach enables one to focus on the biomechanical properties of individual cells and on communication between cells and their microenvironment, and to investigate how individual cells cooperate and contribute to the overall structure and function of a particular tissue. Three applications of this model are presented: the folding of a trophoblast bilayer, clonal tumoural growth and self-arrangement into a hollow acinus, the hollow multicellular sphere. Further extensions of this model are also discussed.

simulation movies:

Immersed Boundary Method-An illustrative example of a single growing cell Interplay between the off-diagonal forces and a central point source in the growing cell. Due to the stretching of the off-diagonal forces that are transmitted to the fluid grid, the resulting fluid flow is directed along the force field, and the cell growth is off-diagonal; When the off-diagonal forces are in the resting state and prevent the off-diagonal expansion, the fluid flow produced by the active fluid source can only move across the unforced boundaries of the cell and the cell grows along its diagonal.

Trophoblast development: Model of the trophoblast bilayer. Four different configurations of a trophoblast bilayer arising upon the proliferation of one CT cell---in each case the viscoelastic properties of cytotrophoblasts (CT) and of the syncytium (ST) are different.

Trophoblast invagination: Model of the trophoblast bilayer. This simulation shows a deep inward tissue bending, called an invagination, that if formed as a result of multiple proliferation of CT cells occupying the same small area of the tissue.

Tumour clones development: Clonal growth of tumour cells due to cell competition for nutrients. Left: colour-coded clones of cells arising from common predecessors. Right: three different cell subpopulations: an inner core of necrotic cells (blue), an outer rim of proliferating cells (red) and a zone of quiescent cells between them (grey). A round and regular tumour cluster at an early stage of tumour growth acquires a fingering morphology due to competition for nutrients between individual tumour cells.

Acinus development: Development of a hollow acinar structure. Starting with a single eukaryotic cell, a small cluster of randomly oriented cells is produced, upon cell-to-cell interactions all cells in the outer layer develop an apical-basal epithelial polarisation, that triggers the inner cells to start apoptotic death, that in turn leads to a hollow acinar structure. The intercellular elements are stained as follows: cell nuclei (blue), apoptotic cells (red), cell membranes (green), cell basal domains (red), cell-to-cell tight junctions (yellow).

Cell directional movement: Cell chemotactic/haptotactic motility due to the drag motility forces defined on the cell boundary and directed toward the increased concentration of chemo/hapto-attractant.