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