Comprehensive theory, key formulas, diagrams, and memory aids for Enzymes.
Enzymes are highly specialized protein catalysts (except for ribozymes, which are RNA-based) that accelerate biochemical reactions by lowering the activation energy barrier ($E_a$). They do not change the equilibrium constant ($K_{eq}$) or the overall free energy change ($\Delta G$) of the reaction.
Holoenzyme: The active, complete enzyme-cofactor complex: $$\text{Apoenzyme} + \text{Cofactor} = \text{Holoenzyme}$$
Active Site: A 3D cleft or pocket in the enzyme structure composed of amino acid residues that bind the substrate (binding site) and catalyze the chemical reaction (catalytic site).
graph LR
A[Enzyme + Substrate] -->|Induced Fit| B[Enzyme-Substrate Complex]
B -->|Catalysis| C[Enzyme-Product Complex]
C --> D[Enzyme + Product]
Enzyme kinetics describes the rate of enzyme-catalyzed reactions. The standard model assumes the formation of an enzyme-substrate ($ES$) complex:
$$\text{E} + \text{S} \underset{k_{-1}}{\overset{k_1}{\rightleftharpoons}} \text{ES} \xrightarrow{k_2} \text{E} + \text{P}$$
Assuming a steady-state where the concentration of $[ES]$ is constant, the initial velocity ($v_0$) is given by:
$$v_0 = \frac{V_{max} [S]}{K_m + [S]}$$
Where: - $V_{max}$ = maximum velocity of the reaction when the enzyme is fully saturated with substrate ($V_{max} = k_2 [E]_{\text{total}}$). - $[S]$ = substrate concentration. - $K_m$ = Michaelis constant, representing the substrate concentration at which the reaction velocity is half of $V_{max}$: $$K_m = \frac{k_{-1} + k_2}{k_1}$$
A lower $K_m$ value indicates a higher affinity of the enzyme for its substrate.
Taking the reciprocal of both sides of the Michaelis-Menten equation yields a linear equation ($y = mx + c$):
$$\frac{1}{v_0} = \frac{K_m}{V_{max}} \cdot \frac{1}{[S]} + \frac{1}{V_{max}}$$
Plotting $1/v_0$ against $1/[S]$ yields a straight line: - The y-intercept is $\frac{1}{V_{max}}$ - The x-intercept is $-\frac{1}{K_m}$ - The slope is $\frac{K_m}{V_{max}}$
This plot is highly useful for determining $V_{max}$ and $K_m$ and analyzing types of enzyme inhibition.
Inhibitors are molecules that reduce enzyme activity. They are classified as competitive, noncompetitive, or irreversible.
The inhibitor structurally resembles the substrate and competes directly for binding at the active site. - Kinetics: $V_{max}$ remains unchanged (can be overcome by adding excess substrate). $K_m$ increases (apparent affinity decreases). - Lineweaver-Burk: The line rotates about the y-intercept ($\frac{1}{V_{max}}$ is same, but the x-intercept moves closer to zero).
The inhibitor binds to an allosteric site (a site other than the active site), regardless of whether the substrate is bound. This alters the enzyme's conformation, preventing catalysis. - Kinetics: $V_{max}$ decreases. $K_m$ remains unchanged. - Lineweaver-Burk: The line rotates about the x-intercept ($-\frac{1}{K_m}$ is same, but the y-intercept increases).
The inhibitor binds covalently to active site residues, permanently destroying enzyme activity. Examples include aspirin, penicillin, and sarin nerve gas.
graph TD
A[Enzyme Inhibition] --> B{Does inhibitor bind to active site?}
B -- Yes --> C[Competitive: Km increases, Vmax unchanged]
B -- No --> D[Noncompetitive: Km unchanged, Vmax decreases]
Enzymes are classified into six major classes based on the type of reaction they catalyze:
Cofactors can be inorganic metal ions or organic molecules. - Metal ions: Act as electrophilic catalysts or stabilize charges (e.g., $Mg^{2+}$, $Fe^{2+}$, $Zn^{2+}$). - Coenzymes: Small organic molecules derived from vitamins. - Cosubstrates: Reversibly bind to the enzyme and undergo chemical modification (e.g., $NAD^+$, Coenzyme A). - Prosthetic Groups: Covalently or tightly bound to the enzyme and remain associated during the reaction (e.g., Heme, Biotin).