How did primitive living cells originate? The formation of early cells, which were probably solute-filled vesicles capable of performing a rudimentary metabolism (and possibly self-reproduction), is still one of the big unsolved questions in origin of life. We have recently used lipid vesicles (liposomes) as primitive cell models, aiming at the study of the physical mechanisms for macromolecules encapsulation. We have reported that proteins and ribosomes can be encapsulated very efficiently, against statistical expectations, inside a small number of liposomes. Moreover the transcription-translation mixture, which realistically mimics a sort of minimal metabolic network, can be functionally reconstituted in liposomes owing to a self-concentration mechanism. Here we firstly summarize the recent advancements in this research line, highlighting how these results open a new vista on the phenomena that could have been important for the formation of functional primitive cells. Then, we present new evidences on the non-random entrapment of macromolecules (proteins, dextrans) in phospholipid vesicle, and in particular we show how enzymatic reactions can be accelerated because of the enhancement of their concentration inside liposomes.