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The wikipedia page on the Belousov-Zhabotinsky reaction states the following:

The discovery of the phenomenon is credited to Boris Belousov. In 1951, while trying to find the non-organic analog to the Krebs cycle, he noted that in a mix of potassium bromate, cerium(IV) sulfate, malonic acid, and citric acid in dilute sulfuric acid, the ratio of concentration of the cerium(IV) and cerium(III) ions oscillated, causing the colour of the solution to oscillate between a yellow solution and a colorless solution.

Perhaps Boris Belousov didn't really know what he was looking for, but perhaps he did. My thoughts go to network analysis and graph theory to identify equivalence classes induced by graph isomorphism or other 'structure-preserving' maps between two representations of a collection of chemical reactions. Perhaps the structure would include information about which steps were oxidative/reductive or SN1/SN2/E1/etc.

What would have been true of such a non-organic system if Boris Belousov had succeeded?

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    $\begingroup$ And my thoughts are he neither knew or cared about "equivalence classes induced by graph isomorphism", but just wanted to make something remotely similar using the stuff he had in the lab ;> BTW too broad questions are closed not moved to meta, where mostly internal site stuff is discussed. $\endgroup$
    – Mithoron
    Jul 22 at 18:06
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    $\begingroup$ It simply means replacing enzymes with inorganic catalysts. In this case, the goal is to oxidize citrate to CO2, which is sort of what happens in the Krebs cycle. Finding inorganic catalysts for metabolic reactions was a way to approach understanding how the enzymatic catalysis might work $\endgroup$
    – Andrew
    Jul 22 at 18:14
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Let me first acknowledge that Belusov published very little, and what he did publish is hard to get a hold of in English, so this answer is not based on any specific writing of his, but rather is speculation based on what other scientists were doing at the time.

In those days, it was quite difficult to study enzyme-catalyzed reactions, because the structures of the active sites and even the identity of most of the relevant residues were generally unknown. Obviously, techniques such as recombinant overproduction systems and targeted mutagenesis were not available.

In this environment, cofactor-dependent enzymes (including metalloenzymes) were of particular interest because it was presumed that in those enzymes, the catalytic function might be primarily provided by the cofacter, and the role of the protein might be as simple as just providing a scaffold for the cofactor and a binding pocket to bring the substrate to it. If that were true, then it might be possible to mimic the enzyme and effect catalysis with a much simpler system consisting of the cofactor bound to a small scaffold or even free in solution. As an example, pyridoxal was found to catalyze a wide variety of reactions by itself in solution, albeit with slower rates and much less specificity than enzyme-bound pyridoxal phosphate.

The benefit of these simplified systems is that it is much easier to probe the reaction mechanisms, though with the caveat that the mechanism might not be the same as when the reaction happens on an enzyme.

In the case of Belusov, it had been observed that a number of the enzymes in the Krebs cycle are metalloenzymes, including the first two reactions from citrate, ie those catalyzed by aconitase (with an iron-sulfur cluster) and isocitrate dehydrogenase (with a Mn(II) ion). It is likely that Belusov was mixing citrate with different metals in the hopes of reproducing one or both of these reactions in a non-enzymatic system with the goal of furthering the understanding of the reaction mechanisms and the role of the metals.

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