SARS-CoV-2 Main Protease: a Kinetic Approach
Authors: Rebetez Thierry 
Published: May 2022

ABSTRACTIn this article, I present a new model of the interaction of the main protease (Mpro) from SARS-CoV-2 virus with its substrate. The reaction scheme used to describe this mechanism is an extension of the well-known Michaelis-Menten model proposed in 1913 by Leonor Michaelis and Maud Menten [1]. The model I present here takes into account that one Mproenzyme monomer interacts with another Mpromonomer in the presence of the substrate, leading to the formation of an enzyme dimer bound to one substrate molecule. Indeed, this dimer is formed by the sequentially binding of one Mproenzyme monomer to one molecule of substrate, followed by another Mproenzyme monomer binding to this Mpro-substrate complex. This reaction mechanism is also known in the literature as substrate-induced dimerization [3]. Starting from this new reaction scheme established for this catalytic mechanism, I derived a mathematical expression describing the catalytic rate of the active Mproenzyme dimer as a function of the substrate concentration [S]. The plot corresponding to this substrate-induced dimerization reaction shows a functionf([S]) that is not monotonic,i.e. not strictly increasing or decreasing, but with a second derivative initially negative and then becoming positive after having passed theVmaxpoint. This is typically a type of curve showing a phenomenon like the one of substrate inhibition (for instance, inhibition by excess-substrate [7]). The graphical representation of this process shows an interesting behaviour: from zeroμM/s, the reaction rate increases progressively, similar to the kind of curve described by the Michaelis-Menten model. However, after having reached its maximum catalytic rate,Vmax, the reaction rate decreases progressively as we continue to increase the substrate concentration. I propose an explanation to this interesting behavior. At the moment whereVcatis maximum, we can assume that, in theory, every single substrate molecule in solution is bound to two enzyme monomers (i.e. to one active dimer). The catalytic rate is thus theoretically maximized. At the time where the reaction rate begins to decrease, we observe a new phenomenon that appears: the enzyme monomers begin to be “diluted” in the solution containing the excess substrate. The dimers begin to dissociate and to bind increasingly to the substrate as inactive monomers instead of active dimers. Hence, it is more and more unlikely for the enzyme monomers to sequentially bind twice to the same substrate molecule (here, [E]≪[S]). Thus, at this stage, the substrate-induced dimerization occurs less often. At the limit, when the substrate is in high excess, there is virtually no more dimerization which occurs. This is one example of excess-substrate inhibition. Furthermore, after having established this fact, I wanted to see if this catalytic behavior was also observedin vitro. Therefore, I conducted an experiment where I measured the catalytic rate of the Mprodimer for different substrate concentrations. The properties of my substrate construct were such, that I could determine the catalytic rate of the enzyme dimer by directly measuring the spectrophotometric absorbance of the cleaved substrate atλ= 405 nm. The results show explicitly — within a margin of error — that the overall shape of the experimental curve looks like the one of the theoretical curve. I thus conclude that the biochemical behavior of the Mproin vitrofollows a new path when it is in contact with its substrate: an excess substrate concentration decreases the activity of the enzyme by the phenomenon of a type of excess-substrate inhibition. This finding could open a new door in the discovery of drugs directed against the Mproenzyme of the SARS-CoV-2 virus, acting on the inhibition by excess-substrate of the Mproenzyme, this protein being a key component in the metabolism of the virus. Furthermore, I have established that the maximum of the fitted curve,Vmax, depends only on [E]Tand not on [S].exhibits the same dependence pattern. Therefore, if I keep [E]Tclose to zero, the catalytic rate of the enzyme will also be greatly reduced, which can be understood intuitively. Finally, if we dilute the enzyme sufficiently in the host cell by injecting a suitably high concentration of the octapeptide substrate AVLQSGFR (an inhibitor of the original substrate), this artificial substrate will bind to the “intermediate” dimer from the polypeptide and prevent the precursor Mprofrom auto-cleaving and dimerizing due to the “distorted key” effect of the octapeptide on the “intermediate” dimer. The precursor peptide Mprowill auto-cleave to a lesser extent than in the absence of the artificial octapeptide and thus the concentration of the total enzyme [E]Twill be lowered in the cell. It would therefore be possible to control the virulence of the virus by adjusting the concentration of the artificial inhibitory octapeptide. However, this is only speculation and has yet to be verified in practice.