Enzymes

An enzyme speeds up a reaction by lowering its activation energy ($\Delta G^{‡}$). It does not change $\Delta G$ of the reaction or its equilibrium constant, so it speeds the forward and reverse reactions by the same factor. Substrate binds in the active site, a cleft formed by a few residues that may be far apart in the primary sequence. Specificity comes from shape, charge, hydrogen bonding and hydrophobic contacts in the site. The lock-and-key model treats the site as a rigid shape complementary to the substrate. The induced-fit model, which describes most enzymes better, says that substrate binding changes the shape of the site so that the catalytic groups are brought into position.

Since 2018 the EC list also has a seventh class, translocases (EC 7), which catalyse the movement of ions or molecules across a membrane. The six classes above are the classical set.

Many enzymes need a non-protein partner. A cofactor is a metal ion (Zn${}^{2+}$, Mg${}^{2+}$, Fe${}^{2+}$/Fe${}^{3+}$) or an organic coenzyme. A coenzyme bound loosely acts as a co-substrate (for example NAD${}^{+}$). One bound tightly or covalently is a prosthetic group (for example heme, biotin, FAD in many enzymes). The protein part alone is the apoenzyme; the complete active enzyme is the holoenzyme. Many coenzymes come from vitamins: NAD${}^{+}$ and NADP${}^{+}$ from niacin (redox), FAD and FMN from riboflavin (redox), coenzyme A from pantothenate (acyl transfer), thiamine pyrophosphate from thiamine (decarboxylation), and pyridoxal phosphate from pyridoxine (transamination). Biotin (carboxylation) is itself a vitamin.

Enzymes use a small set of strategies, often several at once. The central idea behind all of them is that the enzyme binds the transition state more tightly than it binds the substrate, which lowers the activation energy.

Chymotrypsin uses several of these strategies together. Its catalytic triad is Ser195, His57 and Asp102. Asp102 holds His57 in place, His57 acts as a general base that takes the proton from Ser195, and the activated Ser195 attacks the carbonyl carbon of the peptide bond (covalent catalysis), forming an acyl-enzyme. The negatively charged tetrahedral intermediate is stabilised by hydrogen bonds in the oxyanion hole (transition-state stabilisation). Water then hydrolyses the acyl-enzyme and the second product is released.

For a single-substrate reaction $E+S\rightleftharpoons ES\to E+P$, the model assumes: (1) the rate is measured as the initial velocity, when product is negligible and the reverse step $E+P\to ES$ can be ignored; (2) $[S]\gg [E{]}_T$, so free $[S]$ is effectively the total and stays constant during the measurement; (3) the steady-state assumption, $d[ES]/dt=0$, which holds after a very short transient. When $[S]\ll K_m$ the rate is first order in $[S]$. When $[S]\gg K_m$ the enzyme is saturated and the rate becomes zero order, approaching $V_{max}$.

Enzyme activity units. One international unit (U) is the amount of enzyme that converts 1 $\mu$mol of substrate per minute under stated conditions. The SI unit is the katal (kat), 1 mol of substrate per second, so 1 U $=\frac{1}{60}\mu$mol s${}^{-1}\approx 16.67$ nkat. Specific activity is units per mg of total protein. It rises during purification as other proteins are removed, and fold purification $=$ specific activity after a step $÷$ specific activity of the crude extract.

Activity also depends on pH and temperature. A pH-activity curve is usually bell-shaped, because the groups that bind substrate and catalyse the reaction must be in the right ionisation state. Activity rises with temperature until the protein starts to denature, which gives an apparent temperature optimum that depends on how long the assay runs.

Rearranging the rate equation gives straight lines from which $K_m$ and $V_{max}$ are read. The double-reciprocal (Lineweaver-Burk) plot is the one most often used to identify the type of inhibition. It distorts errors, though: the low-$[S]$ points lie far out at large $1/[S]$, where small errors in $v$ become large errors in $1/v$ and dominate the fitted line, while the high-$[S]$ points crowd together near the y-axis.

A reversible inhibitor binds non-covalently, and activity returns when it is removed (for example by dialysis or dilution). Competitive inhibitors bind the free enzyme, usually at the active site and usually resembling the substrate, so substrate and inhibitor exclude each other. Uncompetitive inhibitors bind only the ES complex. Mixed inhibitors bind a site other than the active site and can bind both $E$ and $ES$, with different affinities. Pure non-competitive inhibition is the special case of mixed inhibition in which the affinities for $E$ and $ES$ are equal. Define $\alpha =1+[I]/K_i$ (binding to $E$, $K_i=[E][I]/[EI]$) and ${\alpha }^{\prime }=1+[I]/K_i^{\prime }$ (binding to $ES$, $K_i^{\prime }=[ES][I]/[ESI]$).

Irreversible inhibitors bind covalently or so tightly that they effectively remove active enzyme. Examples are diisopropyl fluorophosphate (DIFP) on the active-site serine of serine proteases and acetylcholinesterase, and iodoacetamide on cysteine. They lower the amount of active enzyme, so $V_{max}$ falls, while the enzyme that stays active keeps its normal $K_m$. This looks like non-competitive inhibition, but dialysis does not restore activity. A suicide (mechanism-based) inhibitor is converted by the enzyme's own catalytic cycle into a reactive species that then inactivates it.

Cells control flux through a pathway at a few key enzymes, using several mechanisms.

In a K-type allosteric enzyme the effector changes $K_{0.5}$ with $V_{max}$ unchanged (the curve shifts left or right). In a V-type enzyme the effector changes $V_{max}$ with $K_{0.5}$ unchanged. For a K-type enzyme in the concerted model, an allosteric activator shifts the curve to the left and makes it less sigmoidal, closer to a hyperbola. An allosteric inhibitor shifts it to the right and makes it more sigmoidal.