On a Model of Pattern Regeneration Based on Cell Memory

Abstract

We present here a new model of the cellular dynamics that enable regeneration of complex biological morphologies. Biological cell structures are considered as an ensemble of mathematical points on the plane. Each cell produces a signal which propagates in space and is received by other cells. The total signal received by each cell forms a signal distribution defined on the cell structure. This distribution characterizes the geometry of the cell structure. If a part of this structure is removed, the remaining cells have two signals. They keep the value of the signal which they had before the amputation (memory), and they receive a new signal produced after the amputation. Regeneration of the cell structure is stimulated by the difference between the old and the new signals. It is stopped when the two signals coincide. The algorithm of regeneration contains certain rules which are essential for its functioning, being the first quantitative model of cellular memory that implements regeneration of complex patterns to a specific target morphology. Correct regeneration depends on the form and the size of the cell structure, as well as on some parameters of regeneration.

Transcriptomic, proteomic, and metabolomic landscape of positional memory in the caudal fin of zebrafish

“…Thus, only structures lost because of injury are regrown. Although considerable research has focused on understanding how regeneration is initiated in different organisms (6)(7)(8)(9)(10)(11), and computational models have predicted how positional information can regulate regenerative outgrowth (12,13), much less is known about the cellular mechanisms underlying positional memory (2)(3)(4)(5)14).…”

Deformable Cell Model of Tissue Growth

“…It should also be noted that this tissue continues to grow even when the initial form is regenerated. Therefore, there are additional mechanisms which control the size of the tissue [57][58][59].…”

A Conceptual Model of Morphogenesis and Regeneration

“…It contains two submodels – one global and one local. The main assumptions of the first submodel are similar to those in the previous work (Bessonov et al, 2015): cells exchange signals, keep the information about the values of these signals and react when these values are changed. In comparison with the previous work, we do not amputate a part of the cell structure but instead alter the positions of cells.…”

“…A model of tissue regeneration based on cell memory is suggested in our previous work (Bessonov et al, 2015), where we consider a tissue as an ensemble of points on the plane, each point corresponding to a single cell. Each cell produces a signal that spreads in space and decays as a function of distance from the cell.…”

“…In (Bessonov et al, 2015), all cells produce and receive the same signal. Hence, each cell is supposed to keep only one real number: the value of the total initial signal.…”