Endosymbiosis as a compact ecosystem with material cycling: parasitism or mutualism?

To discover the evolutionary logic of intracellular endosymbiosis, we investigated a theoretical model (simultaneous ordinary differential equations) of a material-cycling system inside a host cell. In the model, we introduced a recently developed cell biology concept called "autophagy", which is a decomposing-recycle process of self-compiled materials found universally among eukaryote cells. Our model is based on traditional simultaneous ODE for natural ecosystems that involve producing, grazing, and decomposing processes in material cycling. In the basic intracellular metabolic system, several enzymes regulate metabolism by synthesizing and converting metabolites into biomolecules that are precursors for enzymes involved in the producing process. Symbionts are involved in grazing processes and autophagosomes that degrade materials are involved in decomposing recycles. We compared and analyzed the local stability of ODE systems in three cases: (1) the independent, free-living cell (the basal state of a cell), (2) the case where symbionts invade and exploit macrobiomaterials as parasites inside a host cell, and (3) the combination where symbionts assist the host's metabolism. We conclude that: (i) as consumers, symbionts are required to have a growth rate that is higher than the rate of autophagosome decomposition, (ii) the host cell with a biomass larger than the threshold size would realize the mutualistic relationship with its symbiont, and (iii) this partnership accelerates the biomaterial turnover flow on the basis of biomaterials.