  As the first step in an investigation of the origin of genetic information,
we study how some species of molecules are preserved over cell generations and
play an important role in controlling the growth of a cell. We consider a model
consisting of protocells. Each protocell contains two mutually catalyzing
molecule species ($X$ and $Y$), each of which has catalytically active and
inactive types. One of the species $Y$ is assumed to have a slower synthesis
speed. Through divisions of the protocells, the system reaches and remains in a
state in which there are only a few active $Y$ and almost no inactive $Y$
molecules in most protocells, through selection of very rare fluctuations. In
this state, the active $Y$ molecules are shown to control the behavior of the
protocell. The minority molecule species act as the information carrier, due to
the relatively discrete nature of its population, in comparison with the
majority species which behaves statistically in accordance with the law of
large numbers. The relevance of this minority controlled state to evolvability
is discussed.
