Fractones and basement membranes for the mathematical modeling of tissue growth and regeneration.

Abstract

Biological growth can be defined as a set of processes that cause tissues or organs to develop and maintain. When simulating this growth in DynCell, a C++ virtual reality simulator, questions arise about how the shape is controlled and maintained in a stable state whilst cells renew. In order to understand tissue growth, we elaborated a mathematical model based on viability theory and morphological analysis. In our model, each cell is defined as a control system. Moreover, each cell includes the same genetic information, which can lead to differentiated cell types. Cells interact with each other during the growth process and take decisions on their fate (cell division, differentiation, migration or apoptosis) according to the genetic information, the position of the other cells and the micro‐environmental cues provided by the extra cellular matrix. From a mathematical point of view, cellular division implies a multi‐valued dynamic. To formalize this dynamic, we have used mutational equations instead of differential equations usually utilized for classic dynamical systems. Cells successively divide according to a controlled topology, and ultimately generate the shape of the organism. This shape reaches a morphological equilibrium, up to a time horizon. To attain a defined topology, it is essential to control cell polarization and cell division. In biological organisms, this control is performed by fractones, extra‐cellular matrix structures anchored near the surface of the cells. Fractones contains heparan sulfate proteoglycans (HSPG) that bind, concentrate and dispatch growth factors to the target cells to ultimatly control cell proliferation and differentiation. Fractones constantly change their HSPG motives to bind different growth factors that either promote or inhibit stem cell proliferation and differentiation. The role of fractones as captors or activators of growth factors ultimately permits biological construction in a much finer mode than with simple reaction‐diffusion models. Using our fractone model, it is possible to generate and renew shapes throughout the tissue except at the interface of tissue layers. Indeed, we have found that our model is not sufficient for cells bordering tissue layers. Therefore, we hypothesize that basement membranes, i.e. specialized coats of extracellular matrix, chemically similar to fractones, become the leading components that control cell proliferation and the layout interface between organized tissues. In conclusion, our model strongly suggests that basement membranes and fractones are essential for the proper control of development and maintenance of biological organisms.This abstract is from the Experimental Biology 2018 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.