The optimal size of protocells from simple entropic considerations

Potential constraints on protocell size are developed from simple entropic considerations. To do that, two new different indexes as measures of their structural and dynamic order were developed and applied to an elemental model of the heterotrophic protocell. According to our results, cell size should be a key factor determining the potential of these primitive systems to evolve and consequently to support life. Our analyses also suggest that the size of the optimal vesicles could be constrained to have radii in the interval (R_S ≤ R ≤ R_D), where the two extreme limits R_S and R_D represent the states of maximum structural order (largest accumulation of substrate inside the vesicle) and the maximum flux of entropy production, respectively. According to the above criteria, the size of the optimum vesicles falls, approximately, in the same spatial range estimated for biological living cells assuming plausible values for the second-order rate constant involved in the catabolic process. Furthermore, the existence of very small vesicles could be seriously affected by the limited efficiency, far from the theoretical limits, with which these catabolic processes may proceed in a prebiotic system.