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The discovery of two fundamental laws concerning cellular dynamics with recursive growth is reported. Firstly, the chemical abundances measured over many cells were found to obey a log-normal distribution and secondly, the relationship between the average and standard deviation of the abundances was found to be linear. The ubiquity of these laws was explored both theoretically and experimentally. By means of a model with a catalytic reaction network, the laws were shown to exist near a critical state with efficient self-reproduction. Additionally, by measuring distributions of fluorescent proteins in bacteria cells, the ubiquity of log-normal distribution of protein abundances was confirmed. Relevance of these findings to cellular function and biological plasticity is briefly discussed.

Ubiquity of log-normal distributions in intra-cellular reaction dynamics