Enzyme kinetics is challenging for students to understand and apply. Why? Perhaps it's because we teach it in isolation and rarely revisit it in a class or throughout the biology and chemistry curricula. It also requires students to integrate mathematical, structural, and mechanistic understandings, a tall order requiring cognitive processing in multiple fields. Students generally understand the conservation of mass, length, and volume by about age 11, but derivative quantities take longer. Examples include density (m/V, age 15) and both concentration (mol/L) and velocity (m/s) in high school. Michaelis-Menten kinetics uses a more nuanced derivative quantity, the initial velocity (mol/L/s) at time = 0). We then focus almost exclusively on plots of v0 vs [S] +/- effectors where time is not an obvious parameter. No wonder students struggle with enzyme kinetics. To make the mathematics more understandable, we have developed a series of interactive progress curves (concentration vs time) models in Fundamentals of Biochemistry (FOB). This online free, multivolume biochemistry textbook is part of the LibreText collections. Users can move sliders to change constants and initial concentrations and observe immediate changes in the concentration of reactants and products with time. These progress curves are generally intuitive (for example, reactant concentrations decrease to zero for an irreversible reaction or to equilibrium/steady-state levels). They also require more intentional and repetitive processing to derive initial rate data for use in Michaelis-Menten kinetics, which logically follows after the presentation of progress curves. Progress curves also can clarify topics such as the steady state and product inhibition. We present in FOB a series of interactive and graded progress curves that allow students a more intuitive and repetitive approach to analyze simple reactions (noncatalyzed first-order to single substrate enzyme-catalyzed), coupled reactions (steady state, enzyme inhibitions, signaling motifs), and finally entire metabolic and signaling pathways. FOB explains how to write (or use) binding, differential, and mass action equations for the reaction schemes. Computational models for the graphs are performed behind the scenes using models imported from Vcell and Biomodels. MiniSidewinder: NIH/NIGMS (Grant R01-GM123032-04) LibreText: Department of Education Open Textbook Pilot Project (FIPSE), the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot.
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Jakubowski et al. (2024) studied this question.
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