On a kinetic origin of heredity: minority control in a replicating system with mutually catalytic molecules

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 catalysing 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 the 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 carrier of heredity, 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 minority controlled state may give rise to a selection pressure for mechanisms that ensure the transmission of the minority molecule. Once those mechanisms are in place, the minority molecule becomes the ideal storage device for information to be transmitted across generations, thus giving rise to "genetic information". The relevance of this minority controlled state to evolvability is also discussed.