Where Initial rates are directly proportional to Substrate concentrations with Application in Molar-mass Determination, Zero-order Specificity constant is Inappropriate

Background"High-ranking scientists" employ the initial rate (vi), expression without consideration for the conditions under which the vi expression can be used. The consequence is the suggestion that the vi is equal to the product of maximum velocity, Vmax, and substrate concentration [S0] divided by the Michaelis-Menten constant, KM. ObjectivesThe main objectives are: 1) to show that vi is not equal to Vmax[S0]/KM; 2) to show that the equilibrium dissociation constant, Kd, is strictly proportional to the concentration ([E0]) 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. MethodsThe study was experimental and theoretical, supported by the Bernfeld method of enzyme assay. ResultKd is directly proportional to [E0], and vi is not equal to Vmax[S0]/KM.. A KM-like value that is greater than the putative Kd value, 2.482 g/L, is equal to 2.569 g/L. The KM-like values in other situations are 2.396 and 2.407 g/L; the corresponding equilibrium dissociation constant (Kd) 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. ConclusionThe equations that invalidate the assumption that vi is equal to Vmax[S0]/KM whenever [S0] is much less than KM were derived; the proposition that Kd is strictly proportional to [E0] 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 KM-like value that is greater than the putative Kd value is possible. GRAPHICAL ABSTRACT O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=95 SRC="FIGDIR/small/535898v1_ufig1.gif" ALT="Figure 1"> View larger version (16K): org.highwire.dtl.DTLVardef@5eff08org.highwire.dtl.DTLVardef@b97aecorg.highwire.dtl.DTLVardef@13557d2org.highwire.dtl.DTLVardef@118bb62_HPS_FORMAT_FIGEXP M_FIG 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 [S0]/[E0] 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 [S0]/[E0] ratio (>1 to >>1). The enzyme-substrate complex (ES) is in a quasi-steady state with respect to S as depicted by {partial} [ES]/ {partial}t{approx}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 {partial}[S0]/{partial}t{approx}0. The double-headed arrow merely shows, artistically, the limit of the data points. C_FIG