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Explanation of exponential growth in self-reproduction is an important steptoward elucidation of the origins of life because optimization of the growthpotential across rounds of selection is necessary for Darwinian evolution. Toproduce another copy with approximately the same composition, the exponentialgrowth rates for all components have to be equal. How such balanced growth isachieved, however, is not a trivial question, because this kind of growthrequires orchestrated replication of the components in stochastic and nonlinearcatalytic reactions. By considering a mutually catalyzing reaction in two- andthree-dimensional lattices, as represented by a cellular automaton model, weshow that self-reproduction with exponential growth is possible only when thereplication and degradation of one molecular species is much slower than thoseof the others, i.e., when there is a minority molecule. Here, the synergeticeffect of molecular discreteness and crowding is necessary to produce theexponential growth. Otherwise, the growth curves show superexponential growthbecause of nonlinearity of the catalytic reactions or subexponential growth dueto replication inhibition by overcrowding of molecules. Our study emphasizesthat the minority molecular species in a catalytic reaction network isnecessary to acquire evolvability at the primitive stage of life.

Exponential growth for self-reproduction in a catalytic reaction network: relevance of a minority molecular species and crowdedness