Parameters used in the Monte Carlo simulation.

aThe probability of the amphiphile leaving the membrane is assumed to be PALM/[1+FOP×n/(b/2)3/2], where n is the quantity of inner impermeable ions, including nucleotides and RNA (measured by the number of nucleotide residues), and b is the quantity of amphiphiles within the membrane. Wherein, b/2 (there are two layers in the membrane) is a “scale” representation of the surface area of the membrane. Consequently, (b/2)3/2 is a scale representation of the cellular space. Thus, n/(b/2)3/2 is a representation of the concentration of the ions. FOP×n/(b/2)3/2 represents the consideration for the “osmotic pressure effect”; a higher concentration of the inner impermeable ions would cause the protocell to be more swollen, and thus amphiphiles within the membrane are less likely to leave [57].bThe probability of RNA moving is assumed to be PMV/m1/3, where m is the mass of the RNA, relative to a nucleotide. The probability of the membrane forming is assumed to be , where a is the number of amphiphiles in the grid room. The probability of a nucleotide precursor permeating into a protocell is assumed to be [1−(1−PNPP)×(LAM/b)3/2]/[1+FSI×n/(b/2)3/2]; the probability of amphiphile precursors permeating into a protocell is assumed to be 1−(1−PAPP)×(LAM/b)3/2; and the probability of the protocell dividing is assumed to be PCD×(1–2×LAM/b), where n and b have the same meanings as in note a. These assumptions are completely the same as the ones in Ref. [12], and are therefore not explained in full detail.cThis set of parameter values is for the cases in Fig. 3b and c (the protocell stage). Parameter values for the case in Fig. 3a (the naked stage) are the same except that N = 20, PMV = 5×10−4, TAPB = 0, FBO = 1.dThis set of parameter values is the common parameter list for the parameter analysis in Fig. 5b and c (also in Fig. 6b and c; the protocell stage). The common parameter list for Fig. 5a (also for Fig. 6a; the naked stage) is the same except that N = 20, PMV = 1×10−3, TAPB = 0, FBO = 1. The set is somewhat different (underlined) from that for the cases in Fig. 3 in order to show the influence of the parameters more clearly.