Direct Estimate of the Specificity Constant: A Possibility or a Fluke? Pre-steady-state Substrate Concentrations and Enabling Mathematical Equations

BackgroundA high-ranking scientist has recently proposed the need for direct estimation of the specificity constant rather than by calculation after a separate determination of maximum velocity and the Michaelis-Menten constant (KM). ObjectivesThe objectives of this study are to derive novel equations for the zero-arbitrary determination of pre-steady-state (PSS) concentration of the substrate suitable for PSS assays, direct estimation of specificity constant (SC) under a PSS scenario, saturating concentration [ST] of the substrate, and instantaneous initial rate (otherwise called the "burst phase-like" rate), including its corresponding [ST]0, and to quantitatively evaluate the derived equations so as to give credence to their robustness and applicability. MethodsThe study was experimental and theoretical. It is supported by the Bernfeld method of enzyme assay. ResultThe SC values from the two newest methods for the three different concentrations of the enzyme range between 2,197.546 and 11,101.74 L/g min in one of the methods and 2,185.649 and 13,860.014 L/g min in the other method. The sub-KM values of the SC for the three different concentrations of the enzyme range between 1304.368 and 7943 L/g min. The burst phase-like initial rate, v0, and corresponding [ST]0, respectively, range between 14.26 and 55.448 micro-mol./min and 0.171 and 3.752 g/L. ConclusionThe derivation of the equations for the direct calculations of SC in conditions that validate the reverse and standard quasi-steady-state approximations was a possibility; the SC values are higher at lower concentrations of the enzyme. The concept of SC is very different from catalytic efficiency. The total absence of any calculation is impossible. O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=145 SRC="FIGDIR/small/536186v1_ufig1.gif" ALT="Figure 1"> View larger version (29K): org.highwire.dtl.DTLVardef@18f14d0org.highwire.dtl.DTLVardef@9f7d1borg.highwire.dtl.DTLVardef@ce8c72org.highwire.dtl.DTLVardef@66d168_HPS_FORMAT_FIGEXP M_FIG Graphical abstract figure for the direct estimate of the specificity constant For the purpose of this study, the legends, SUB (S), ENZ (E), and PRD represents substrate, enzyme and product respectively. Lower number density (red) of the enzyme molecules in Figure 1 showing > number density of the product (light green) for the same concentration of the substrate (darker blue) than in Figure 2 implies that the catalytic efficiency in Figure 1 is > the illustration in Figure 2. C_FIG O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=96 SRC="FIGDIR/small/536186v1_fig1.gif" ALT="Figure 1"> View larger version (11K): org.highwire.dtl.DTLVardef@3e1897org.highwire.dtl.DTLVardef@c08481org.highwire.dtl.DTLVardef@13b5677org.highwire.dtl.DTLVardef@a9cb5e_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFigure 1:C_FLOATNO Plot illustrating the non-Michaelian characteristics of initial rates which is directly proportional to the sub-Michaelis-Menten constant concentration of the substrate where the concentrations of the enzyme are 0.0002 g/L ([Figure 1]) and 0.0005 g/L ([Figure 1]). The SC for 0.0005 g/L is = 7223.84 L/g. min; SC for 0.0002 g/L is = 7943 L/g min. C_FIG O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=139 SRC="FIGDIR/small/536186v1_fig2.gif" ALT="Figure 2"> View larger version (11K): org.highwire.dtl.DTLVardef@166c635org.highwire.dtl.DTLVardef@5eec5aorg.highwire.dtl.DTLVardef@1ef08e6org.highwire.dtl.DTLVardef@316124_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFigure 2:C_FLOATNO Plot illustrating the non-Michaelian characteristics of initial rates which is directly proportional to the sub-Michaelis-Menten constant concentration of the substrate where the concentration of the enzyme is 0.002 g/L. The SC value is 1304.368 L/g min. C_FIG