Enzyme Kinetics

Enzymes are biological catalysts that lower the activation energy of a reaction. The Michaelis-Menten model describes how reaction velocity (V) varies with substrate concentration ([S]). The two key parameters are Vmax (maximum reaction velocity at saturating substrate) and Km (substrate concentration at which velocity is half Vmax). A low Km indicates high affinity for the substrate. Real-world kinetics are often analyzed using the Lineweaver-Burk plot (a double-reciprocal plot). Enzyme activity can be influenced by temperature, pH, and inhibitors. Inhibition is categorized as competitive (where the inhibitor competes for the active site, increasing Km but not changing Vmax) and non-competitive (where the inhibitor binds elsewhere, reducing Vmax but not changing Km). Allosteric enzymes, such as PFK-1 in glycolysis, do not follow Michaelis-Menten kinetics; they show a sigmoidal curve due to cooperativity, allowing for fine-tuned metabolic control in response to small changes in metabolite concentrations.

The Michaelis-Menten equation is V = (Vmax * [S]) / (Km + [S]). In the Lineweaver-Burk plot (1/V vs 1/[S]), the x-intercept is -1/Km and the y-intercept is 1/Vmax. Competitive inhibitors shift the x-intercept toward zero but leave the y-intercept alone. Non-competitive inhibitors move the y-intercept higher but leave the x-intercept alone. Irreversible inhibitors (like Aspirin binding to COX) covalently bond to the enzyme, permanently reducing Vmax. Enzyme activity is also regulated by covalent modification, most commonly phosphorylation/dephosphorylation. For example, insulin triggers the dephosphorylation of glycogen synthase to activate it. Many metabolic enzymes are also subject to 'feedback inhibition,' where the end-product of a pathway inhibits an earlier enzyme (typically the rate-limiting one) to prevent overaccumulation and conserve energy.

Most drugs act as enzyme inhibitors. Statins are competitive inhibitors; hence, their effect depends on the concentration of HMG-CoA. Non-competitive inhibition is exemplified by many poisons (e.g., organophosphates inhibiting acetylcholinesterase). Understanding kinetics is crucial for clinical pharmacology: drugs metabolized by zero-order kinetics (like high-dose Aspirin, Phenytoin, and Ethanol) have a high risk of toxicity because the body's clearance mechanisms become saturated. Methanol poisoning is treated with ethanol because ethanol is a competitive inhibitor for alcohol dehydrogenase, preventing the formation of toxic formaldehyde.

Investigations involving enzyme activity include: Plasma enzyme levels (e.g., Creatine Kinase in MI or Myositis, Amylase in Pancreatitis), and therapeutic drug monitoring (for drugs with narrow therapeutic windows like Phenytoin). Genetic testing can identify 'slow metabolizers' for enzymes like CYP2D6, which affects how patients respond to Codeine or Tamoxifen.

Management involving enzyme kinetics often relates to overdose situations. In Paracetamol overdose, N-acetylcysteine (NAC) is given to replenish glutathione stores required for the safe metabolism of the toxic metabolite NAPQI. In Methanol or Ethylene glycol poisoning, Fomepizole or Ethanol is given to inhibit alcohol dehydrogenase, diverting the enzymes' activity away from the toxin. Statin doses are adjusted based on their effectiveness and the patient's individual metabolic clearance.