Number of waste catalytic direction in a 3-step reaction network as a function of time in protocells with (a) individually replicating genes and random assortment; (b) potential for chromosome formation and random assortment; and (c) in protocells with chromosomes. Each line (black, red and green) shows the number of waste catalytic directions of the enzymes. For combinatorial and geometrical reasons the maximum number of waste catalytic direction in 3 dimensions is 9. (d) Change of frequency of cells with chromosome through time. The dynamic of the population is followed for 106 time steps, and the first 5·105 or 5·104 is shown with data recorded at every 103 time steps. The sizes of the three substrates are given by cyclic permutation of the sizes 1.0, 2.5 and 4.0 (1.0×2.5×4.0, 2.5×4.0×1.0 and 4.0×1.0×2.5). Initially all enzymes has size of 7.0×7.0×7.0, which is large enough to fit onto every substrate.