Ikechukwu Iloh Udema
ABSTRACT Background “High-ranking scientists” employ the initial rate ( v i ), expression without consideration for the conditions under which the v i expression can be used. The consequence is the suggestion that the v i is equal to the product of maximum velocity, V max , and substrate concentration [ S 0 ] divided by the Michaelis-Menten constant, K M . Objectives The main objectives are: 1) to show that v i is not equal to V max [ S 0 ]/ K M ; 2) to show that the equilibrium dissociation constant, K d , is strictly proportional to the concentration ([ E 0 ]) of the enzyme; and 3) to show that the two standard quasi-steady-state assumptions (sQSSA) and reverse QSSA (rQSSA) have a limited domain of validity. Methods The study was experimental and theoretical, supported by the Bernfeld method of enzyme assay. Result K d is directly proportional to [ E 0 ], and v i is not equal to V max [ S 0 ]/ K M. . A K M -like value that is greater than the putative K d value, 2.482 g/L, is equal to 2.569 g/L. The K M -like values in other situations are 2.396 and 2.407 g/L; the corresponding equilibrium dissociation constant ( K d ) values are, respectively, 2.288 and 2.299 g/L; the molar mass of insoluble potato starch ranges between 62.296 and 65.616 exp. (+6) g/mol. Conclusion The equations that invalidate the assumption that v i is equal to V max [ S 0 ]/ K M whenever [ S 0 ] is much less than K M were derived; the proposition that K d is strictly proportional to [ E 0 ] was confirmed; the molar mass of starch could be calculated from the derived equation; and it was shown graphically and mathematically that both the sQSSA and rQSSA domains have a limit of validity; the equation with which to calculate the second order rate constant based on the conditions that validate the rQSSA is not applicable to the sQSSA. A K M -like value that is greater than the putative K d value is possible. GRAPHICAL ABSTRACT The graphical abstract illustrates three zones: the zone in which the sQSSA is valid, the zone in which the rQSSA is valid, and the zone in which neither assumption is exclusively valid. The curved arrow (oxblood) pointing to the red line depicts a tendency towards conditions that validate the rQSSA if the assay is conducted with an appropriate [S 0 ]/[E 0 ] ratio (< 1 to ≪1) while the red curved arrow pointing to the blue line depicts a tendency towards conditions that validate the sQSSA if the assay is conducted with an appropriate [S 0 ]/[E 0 ] ratio (>1 to ≫1). The enzyme-substrate complex (ES) is in a quasi-steady state with respect to S as depicted by ∂ [ES]/ ∂t≈0, the sQSSA case, while in the rQSSA, it is the S that is in a quasi-steady state with respect to ES as depicted by ∂[S 0 ]/∂t≈0. The double-headed arrow merely shows, artistically, the limit of the data points.