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Abstract

While the chemistry considered in this model is an infinite one, numerical exploration requires us to work with a finite set of molecules that participate in the chemistry. This introduces an additional parameter N , the size of the largest molecule produced in the chemistry, in the model (for details see Appendix S1). Here we present evidence showing that certain important properties of the model become essentially N -independent at large enough N . A. Uncatalyzed chemistryThe steady state concentrations for an uncatalyzed chemistry can be approximated by an exponential function, x n = ce −γn = cΛ n , where c and Λ = e −γ are constants (see Eq. (3) in the main text). We calculate Λ from the slope of the straight line fit on the plot of the log of the steady state concentrations, x n , versus length, n. We found that for sufficiently large N , Λ becomes independent of N ; see Fig. S2.1.When Λ < 1, the concentrations of the large molecules are small. It is evident that if the concentrations of the large molecules produced in the chemistry are so small that their contribution to the dynamics of the (relatively) smaller molecules is negligible, then, including molecules larger than those already considered in such a chemistry would cause no difference to the results. B. Catalyzed chemistryFor chemistries with catalyzed reactions, including ACSs, we find that for sufficiently large N , the numerical results are independent of N . In Fig. S2.2 we show how the steady state concentrations in the chemistry that includes ACS65 (defined by Eq. (5) in main text) depend upon N .The results for the chemistry with f = 2 were also found to be N -independent (for sufficiently large values of N ). We find that for f = 2 the N -independence is reached at much smaller values of N than for f = 1.