Vesicles paradox

If you have followed closely what has been said before, you might now be wondering why dopamine should be too polar to cross the membranes that represent the blood brain barrier, but should readily cross those of the presynaptic vesicles. The answer to this apparent paradox (aside from the fact that the blood brain barrier actually consists of four membranes in series) lies in the vastly different surface-to-volume ratios of the two compartments. Think of a pinhole in a thimble vs. one in a swimming pool. 

The conventional approach of equilibrium thermodynamics is applicable only in the case of the so-called thermodynamic limit N/V = const, at F 00, where iV is a number of particles in the volume V, This approach ignores all the factors mentioned above and being applied to small systems may therefore lead to erroneous results. For example, considering within the formalism of the thermodynamic approach the transmembrane transfer of neutral P particles from closed vesicles loaded with the reaction mixture of P and Q particles (P -h Q PQ), we have obtained one paradoxical result for small enough vesicles the transfer of even one P particle along its concentration gradient can be thermodynamically unfavorable under certain conditions... 

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