Enzyme

biology

Definition

Enzyme

An enzyme is a protein-based catalyst that accelerates a specific chemical reaction in a living system without being consumed. It lowers the activation energy $E_a$ of the reaction while leaving the equilibrium unchanged.

Formally, for a reaction converting substrate $S$ to product $P$,

$$S\stackrel{E}{\to }P,$$

the enzyme $E$ binds $S$ at an active site, stabilises the transition state, and is regenerated:

$$E+S\underset{k_{-1}}{\stackrel{k_1}{\rightleftharpoons }}ES\stackrel{k_2}{\to }E+P.$$

Catalytic Mechanism

The enzyme does not change whether $S\to P$ is favourable; it changes how fast the system gets there. By binding the transition state more tightly than the substrate, it lowers $E_a$ and so increases the reaction rate by the Arrhenius factor $e^{-E_a/RT}$. A small drop in $E_a$ produces a large speed-up, which is why enzymes achieve rate enhancements of $10^6$–$10^{12}$.

Three properties follow from the cycle above:

• Specificity: the active site’s geometry selects which $S$ binds, so each enzyme typically catalyses one reaction.
• Regeneration: $E$ appears on both sides of the equation, so it is not stoichiometrically consumed.
• Catalytic efficiency: the ratio $k_2/K_M$ measures how effectively $E$ converts $S$ at low concentration.

Kinetics

Under the steady-state assumption $d[ES]/dt\approx 0$, the rate follows the Michaelis–Menten law:

$$v=\frac{v_{\max }[S]}{K_M+[S]},$$

where $v_{\max }=k_2[E{]}_{\text{tot}}$ is the maximum rate and $K_M=(k_{-1}+k_2)/k_1$ is the substrate concentration at half-maximum velocity. At low $[S]$, $v\propto [S]$ (first order); at high $[S]$, $v\to v_{\max }$ (zero order, saturated). Enzymes thus couple metabolism to substrate availability, making reaction rates responsive rather than fixed.