Mathematically Modeling Enzyme Kinetics

Explore how enzymes act as proteins that catalyze reactions, binding substrates at active sites in a lock-and-key model, lowering activation energy through substrate positioning, interaction, and transition-state stabilization.

Explore competitive, noncompetitive, and uncompetitive inhibition, how inhibitors form EI, ES, and ESI complexes, and how they impact product formation and kinetic parameters like V max and Km.

Explore substrate concentration and product formation in a non-inhibition enzyme reaction, with enzyme concentration, plotting x-axis as substrate and y-axis as product to show a slope that plateaus at saturation.

Examine how substrate concentration shapes product formation in enzyme-catalyzed reactions with competitive inhibitors. Compare inhibited vs non-inhibited graphs, noting slower initial rates and delayed saturation toward V max.

Explore graphs of product concentration in enzyme-catalyzed reactions with noncompetitive inhibitors, compare with non inhibitor and competitive inhibitor graphs, and illustrate the ISI complex effects on the plateau and rate.

Analyze graphs of product formation in enzyme-catalyzed reactions with uncompetitive inhibition, where the inhibitor binds to the enzyme–substrate complex, slowing the initial rate and lowering the maximum velocity.

Explore the law of mass action and chemical equilibrium, showing forward and reverse rates converge, and how enzymes and inhibitors affect rates, while temperature and pressure influence the balance.

Learn the law of mass action in quantitative terms, deriving rate equations from substrate and product concentrations. Apply to simple enzyme-catalyzed irreversible reactions with forward rate.

Explore the background of Michaelis-Menten kinetics, linking qualitative enzyme reactions, inhibition types, and graphs to quantitative models of product formation using substrate affinity and forward/reverse rates.

Define the axes for substrate changes (x) and product changes (y) and introduce notation for substrate, enzyme, inhibitor, and key complexes, plus v max and Km.

Derive the Michaelis-Menten kinetic law from the law of mass action using rapid equilibrium and the Briggs-Haldane steady-state assumptions, yielding v = Vmax [S] / ([S] + Km).

Derive the competitive inhibition kinetic law using mass action and rapid equilibrium, expressing the rate as v = Vmax[S]/([S] + Km(1 + [I]/Ki)).

Derive the uncompetitive inhibition kinetic law using mass action and dynamic equilibrium for the enzyme-substrate and the enzyme-substrate inhibitor complexes. Relate results to V max and Ki.