I'm currently reviewing the literature about lognormal distributions describing/approximating the variability of a given chemical compound across different cells/ samples etc etc. The main argument pro lognormality is the multiplicative central limit theorem, that many authors mention without providing a clear example of a reaction pathway where a targeted concentration can be approximated by the multiplication of many factors. In https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5036630/ and http://web.mit.edu/jakebeal/www/Publications/ENB17-Lognormal-Biology.pdf they make the case of autocatalytic/ catalytic processes. What would be the simplest example of a chemical reaction system where the concentration of a target chemical (not the rate) would appear Lognormal?
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2$\begingroup$ I looked at the first paper quickly. It seems that they are measuring concentrations of chemicals within living cells. Living cells don't have a static equilibrium. Living cells are dynamic. $\endgroup$– MaxWMar 21, 2019 at 1:42
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$\begingroup$ "concentration of target chemical appears lognormal". What exactly do you mean? Concentration when? Where? $\endgroup$– Buck Thorn ♦Mar 21, 2019 at 15:06
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