Enzyme Kinetics and Regulation (1A) - MCAT Biological and Biochemical Foundations of Living Systems

$vV_{max}$. Enzyme saturation at high [S] limits the rate to V_max, independent of further increases in substrate concentration.

$vrac{V_{max}}{K_m}[S]$. This linear approximation derives from the Michaelis-Menten equation when [S] is much less than Km, simplifying to a first-order rate.

Only to the $ES$ complex (not to free enzyme). Uncompetitive inhibition requires substrate-bound enzyme, forming a dead-end complex that lowers apparent Km and V_max.

Active site (mutually exclusive with substrate). Competitive inhibitors mimic substrate structure, binding reversibly to the same site and preventing substrate access.

Competitive inhibition. Increasing [S] can outcompete competitive inhibitors for the active site, restoring V_max unlike other inhibition types.

$K_m$ decreases; $V_{max}$ decreases. Uncompetitive inhibitors bind only to ES complex, decreasing both Km and V_max by stabilizing the complex.

$V_{max}$ decreases; $K_m$ unchanged. Noncompetitive inhibitors bind elsewhere, reducing effective enzyme concentration and thus V_max, without altering Km.

$K_m$ increases; $V_{max}$ unchanged. Competitive inhibitors compete for the active site, increasing apparent Km but not affecting V_max at high [S].

$rac{K_m}{V_{max}}$. The slope reflects the ratio of Km to V_max, indicating how quickly velocity approaches maximum as [S] increases.

$-rac{1}{K_m}$. The x-intercept occurs where 1/v = 0, solving to -1/Km in the Lineweaver-Burk equation.

$rac{1}{V_{max}}$. The y-intercept in the Lineweaver-Burk plot corresponds to infinite [S], where velocity equals V_max.

$[S]K_m$. At high [S] relative to Km, the enzyme is saturated, making velocity independent of [S] and zero-order in substrate.

Catalytic cycles per enzyme per second at saturation. k_cat quantifies an enzyme's efficiency by measuring product formation rate per active site when fully saturated.

Substrate concentration where $v=V_{max}$. Km represents enzyme-substrate affinity, as it is the [S] at which half-maximal velocity is achieved in the Michaelis-Menten model.

$v=rac{V_{max}[S]}{K_m+[S]}$. The equation describes hyperbolic kinetics, where velocity approaches V_max as [S] increases, based on enzyme-substrate binding equilibrium.

$V_{max}=k_{cat}[E]_T$. V_max scales with total enzyme concentration, as k_cat is the turnover rate per enzyme molecule at saturation.

Maximum initial rate at saturating $[S]$. V_max is achieved when all enzyme active sites are saturated with substrate, reflecting the enzyme's maximum catalytic capacity.

$rac{k_{cat}}{K_m}$. Catalytic efficiency measures how well an enzyme converts substrate to product at low [S], combining turnover and affinity.

$[S]K_m$. At low [S] relative to Km, velocity is directly proportional to [S], following first-order kinetics in the Michaelis-Menten approximation.

Covalent modification that can increase or decrease activity. Phosphorylation adds a phosphate group via kinases, modulating enzyme conformation to either activate or inhibit catalysis.

End product inhibits an earlier enzyme, often the first committed step. Feedback inhibition regulates pathways by allosterically inhibiting upstream enzymes to prevent overproduction of end products.

Positive cooperativity. A Hill coefficient greater than 1 signifies enhanced binding affinity after initial substrate attachment in multimeric enzymes.

Sigmoidal $v$ versus $[S]$ (cooperativity). Allosteric enzymes exhibit cooperative binding, yielding a sigmoidal curve unlike the hyperbolic Michaelis-Menten kinetics.

Covalent or extremely tight binding permanently inactivates enzyme. Irreversible inhibitors form stable bonds with the enzyme, reducing active enzyme concentration permanently.