Abstract. The PURESystem TM (for short: PS) is a defined set of about 80 different macromolecular species which can perform protein synthesis starting from a coding DNA. To understand the processes that take place inside a liposome with entrapped PS, several simulation approaches, of either a deterministic or stochastic nature, have been proposed in the literature. To correctly describe some peculiar phenomena that are observed only in very small liposomes (such as power-law distribution of solutes and supercrowding effect), a stochastic approach seems necessary, due to the very small average number of molecules contained in these liposomes. Here we recall the results reported in other works published by us and by other Authors, discussing the importance of a stochastic simulation approach and of a fine description of the system: both these aspects, in fact, were not properly acknowledged in such previous papers.