Lately there has been a growing interest in evolutionary studies concerning how the regularities and patterns found in the living cell could have emerged spontaneously by way of self-assembly and self-organization. It is reasonable to postulate that the chemical compounds found in the primitive Earth would have mostly been very simple in nature, and would have been immersed in the natural dynamics of the physical world, some of which would have involved self-organization. It seems likely that some molecular processes self-organized spontaneously into a hierarchy of complex behaviours. Our conceptual search herein reaches back to the time when prebiotic phenomena began to take shape. This was before the origin of life, so in this paper we hope to shed new light on some of the theoretical issues that surround the ways in which cellular organization might have evolved without the aid of replicated information.