Abstract
A fundamental evolutionary step in the onset of living cells is thought to be the spontaneous formation of lipid vesicles (liposomes) in the pre-biotic mixture. Even though it is well known that hydrophobic forces drive spontaneous liposome formation in aqueous solutions, how the components of the earliest biochemical pathways were trapped and concentrated in the forming vesicles is an issue that still needs to be clarified. In recent years, some authors carried out a set of experiments where a unexpectedly high amount of solutes were found in a small number of liposomes, spontaneously formed in aqueous solution. A great number of empty liposomes were found in the same experiments and the global observed behavior was that of a distribution of solute particles into liposomes in agreement with a inverse power-law function rather than with the expected Poisson distribution. The chemical and physical mechanisms leading to the observed "anomalous solute crowding" are still unclear, but the non-Poisson power-law behavior is associated with some cooperative behavior with strong non-linear interactions in the biochemical processes occurring in the solution. For tackling this issue we propose a model grounding on the Cox's theory of renewal point processes, which many authors consider to play a central role in the description of complex cooperative systems. Starting from two very basic hypotheses and the renewal assumption, we derive a model reproducing the behavior outlined above. In particular, we show that the assumption of a "cooperative" interaction between the solute molecules and the forming liposomes is sufficient for the emergence of the observed power-law behavior. Even though our approach does not provide experimental evidences of the chemical and physical bases of the solute crowding, it suggests promising directions for experimental research and it also provide a first theoretical prediction that could possibly be tested in future experimental investigations.
Highlights
In research concerning the origins of life, many efforts focus on understanding of the very first steps which led to the emergence of organic compounds and metabolic pathways in pre-biotic chemical solutions
A renewal process is rigorously defined as a sequence of events randomly occurring in time, without any dependence from the previous events or from external forces, and it is described as a sequence of event occurrence times {tn}, enjoying the property that the Waiting Times (WTs) between two subsequent events τn = tn − tn−1 are mutually statistically independent random variables
The characterization of this phenomenon would be of paramount relevance for shedding some light on the very first steps which led to the formation of the earliest proto-cellular structures, which are supposed to be the ancestors of living cells
Summary
Background and Motivations In research concerning the origins of life, many efforts focus on understanding of the very first steps which led to the emergence of organic compounds and metabolic pathways in pre-biotic chemical solutions. A less investigated issue regards a crucial evolutionary stage, i.e., the spontaneous compartmentalization of both early biochemical reactions and related metabolites into cell-like structures. This is a crucial aspect, as high concentration levels of metabolites are needed to get a reasonable probability for the occurrence of biochemical reactions. A strong argument supporting this hypothesis comes from the well known behavior exhibited by (amphipathic) lipids when they are put in water solutions. In this setting, lipids aggregate to form liposomes, a spontaneous process driven by hydrophobic forces [1]. Even though the mechanism of vesicle formation is well assessed, a critical issue that needs to be clarified concerns the mechanisms by which components of metabolic pathways can reach concentration levels that can be much higher inside the vesicles than outside
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