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bioRxiv · 10.64898/2026.05.29.728646

Title: Catalytic rate constant for the utilization of biopolymers

Udema, I. I.
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Abstract

The catalytic rate constant (kcat) for product formation is considered a turnover number. Therefore, it is often mistakenly believed that kcat equals the turnover number and the number of substrate molecules changed per unit of time. Therefore, the aim of this study is to show that the rate constant for product synthesis and release is not always the same as the rate constant [Formula] for substrate utilization. To determine the precise substrate concentration at which these two rate constants are identical, it is appropriate to derive equations that allow the computation of [Formula]. In the end, the study will provide the most likely concentration of enzymes that can guarantee minimal or no recycling. An analysis of the literature on invertase (EC 3.2.1.26) and the Bernfeld method of generating Michaelian kinetic parameters for human salivary alpha-amylase (HSAA, EC 3.2.1.1) revealed that all kinetic parameters except [Formula] increased with substrate concentration. Meanwhile, the values for invertase decreased from 0.0697 to 0.0361/min, and the values for HSAA decreased from 5,802.4687 to 3,213.0124/min. The magnitude of [Formula] for each substrate concentration ([ST]) is not always equal, except when [ST] is determined post-assay by computation or extrapolation. The lower [ST] at which [Formula] and kcat for [HSAA] are equal is 3.667540128 g/L (5.682584642 M), which is similar to the molarity of HSAA (5.6101967709 M). The kcat for HSAA was 11,930.9885/min. Future assays should aim to generate large amounts of data for a robust statistical analysis. Graphical abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=164 SRC="FIGDIR/small/728646v1_ufig1.gif" ALT="Figure 1"> View larger version (36K): org.highwire.dtl.DTLVardef@c49b65org.highwire.dtl.DTLVardef@1b60655org.highwire.dtl.DTLVardef@159ba67org.highwire.dtl.DTLVardef@1dce0af_HPS_FORMAT_FIGEXP M_FIG C_FIG

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Udema, I. I.. 2026-05-29. Title: Catalytic rate constant for the utilization of biopolymers. https://doi.org/10.64898/2026.05.29.728646

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