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According to literature, dimethyl paraoxon has a reaction rate constant for the aging (spontaneous dealkylation) of acetylcholinesterase of $\pu{0.186 h-1}$, a spontaneous reactivation rate constant of $\pu{1.01 h-1}$, and an inhibition reaction rate constant of $\pu{1.2 \times 10^6 M-1 min-1}$, compared to $\pu{0.022 h-1}$, $\pu{0.022 h-1}$, and $\pu{2.2 \times 10^6 M-1 min-1}$, respectively for paraoxon.[1] It has been shown that the process of aging, at least for the nerve agent tabun, proceeds through cleavage of the $\ce{O-C}$ bond [2], which would presumably mean that a carbocation is generated as an intermediate, and thus, ethyl breakage, rather than methyl, should be more favorable. However, as the referenced paper shows, this is not the case, and methyl paraoxon, rather than paraoxon (with ethyl groups), ages more rapidly, and is also more susceptible to spontaneous reactivation. Furthermore, paraoxon (with ethyl groups) also has a higher inhibition rate constant. Why is this so?

References:

[1] Franz Worek, Horst Thiermann, Ladislaus Szinicz, Peter Eyer, "Kinetic analysis of interactions between human acetylcholinesterase, structurally different organophosphorus compounds and oximes," Biochemical Pharmacology 2004, 68(11), 2237–2248 (doi: https://doi.org/10.1016/j.bcp.2004.07.038).

[2] Eugénie Carletti, He Li, Bin Li, Fredrik Ekström, Yvain Nicolet, Mélanie Loiodice, Emilie Gillon, Marie T. Froment, Oksana Lockridge, Lawrence M. Schopfer, Patrick Masson, Florian Nachon, "Aging of Cholinesterases Phosphylated by Tabun Proceeds through O-Dealkylation," Journal of the American Chemical Society 2008, 130(47), 16011–16020 (doi: https://doi.org/10.1021/ja804941z)

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Aging is an unfortunately complex mechanism that was more well studied for branched phosphorus esters like sarin (R=isopropyl) or soman (R=neohexyl) that when attached to a cholinesterase, looks like Ser-OP(O)(CH3)-O-R. Protonation of the ester oxygen allows delocalization of the cation to a branched carbon that can undergo elimination forming the aged product. It is unclear although unlikely that methyl paraoxon and paraoxon undergo traditional 'aging' as defined by cation rearrangement but could undergo a hydrolytic mechanism (attack of OH- at the phosphorus) that might explain why methyl ester undergo this subtype of 'aging' more rapidly than the ethyl ester. The relative rates, are in fact, similar to what one might find when comparing the hydrolysis of methyl and ethyl carboxyesters.

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