Chiral symmetry breaking and information accumulation in pre-biological protocell evolution

We study a linear evolutionary model based on the two-dimensional distribution of protocells by total enantiomeric excess and the amount of stored information, which they can pass from generation to generation, and without any mutual inhibition. We show that the evolution of such systems occurs in four distinct stages. The first stage is an exponential growth of the concentration of protocells near the point [Formula: see text] and it should take negligible time on a geological scale. The second stage is a diffusion-like process in both dimensions. This process can also be accompanied by a drift in the direction of increased information passed from generation to generation, provided that the appropriate linear coefficient in the information storage subspace is large enough. The third stage is a rapid symmetry breaking and formation of the species near [Formula: see text] value of enantiomeric excess (assuming a small positive global enantiomeric asymmetry factor). The fourth stage is a relaxation toward a global stationary point, which is a narrow peak located near [Formula: see text] value of enantiomeric excess and some optimal value of the amount of stored information.