Anatomie et physiologie : recherches en cours
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Use of the Catastrophe Model to Preliminarily Explore the Principles of Multicellular Organisms

Zheming Cao, Weidong Ding, Jun Qiang, Meiyao Wang, Haojun Zhu,

Thermodynamic studies consider living entities as dissipative structures. Organisms maintain and develop an orderly structure by exchanging matter, energy, and entropy with the surrounding environment; thus, maintaining life and growth. For a single cell, the temperature, volume, content concentration, and content complexity are four control variables. For warm-blooded animals, both temperature and content concentration are assumed to be constant and only volume and content complexity, i.e., various proteins, nucleic acids, and small molecular substances in the cell and their interactions, are considered as acting variables. Thus, the potential function of a single cell should conform to the cusp catastrophe model. As the studies on the specific mathematical models of the relationship between the volume and content complexity are not available, we could not propose specific methods for the specific variants of the potential function of this cusp catastrophe model. We could only present our approximate results based on the basic characteristics of the cusp catastrophe model. We speculated that when a single cell is in a stable state, it cannot undergo differentiation, dedifferentiation, and division. These behaviors occur only when the cell enters an unstable state. Based on this speculation, we divided somatic cells of warm-blooded animals into two types, namely stable cells and non-steady cells. If we consider a warm-blooded animal as a whole dissipative structure, its control variables should have steady-state cells, non-steady-state cells, and negative entropy input. If we assume that the negative entropy input is constant, the proportion of non-steady cells and the total number of cells can be used as the control variables of the potential function. For warm-blooded animals, their potential function also conforms to the cusp catastrophe model. Because the studies on the relationship between the proportion of non-steady-state cells and the total cell number are rare, we could not propose specific methods for the variation of the potential function of this cusp catastrophe model. We could only present our approximate results according to the basic characteristics of the cusp catastrophe model. We speculated that as individuals, animals should be in a stable state during development. Once they enter an unstable state, they will fall ill or die. For humans, the proportion of non-steady cells decreases during the growth process from a fertilized egg to old age. From the fertilized egg to adulthood, the total cell number increases; however, in old age, the total cell number begins to decrease gradually. The entire developmental curve will gradually enter an unstable state. We speculated that once the developmental curve of a human enters an unstable state, it is death for the elderly.