Question 8: from a set of chemical reactions to reproducing cells.

As a prerequisite for a reproducing cell, we first discuss how non-equilibrium states are sustained endogenously in a catalytic reaction network. Negative correlation between abundances of resource chemicals and of catalysts for their consumption is shown to lead to hindrance of relaxation to equilibrium. Mutual reinforcement among such sustainment of non-equilibrium state, spatial structure formation, and reproduction of a compartment is discussed as a mechanism to further suppress the relaxation to equilibrium. As a next step to protocell, consistency between cell reproduction and replication of constituent molecules is theoretically studied, which leads to a power-law on abundance of molecules as well as log-normal distribution over cells, which are shown to be universal, and also confirmed experimentally in the present cells.