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Concept 04 / 05Biomolecules

Enzymes, Vitamins and Hormones

Enzymes as specific biological catalysts (lock-and-key model, examples and Michaelis-Menten behaviour), fat-soluble and water-soluble vitamins with their deficiency diseases, and hormones (peptide, amino acid derivatives and steroids) with their functions.

Figure 1
Enzymes are biological catalysts, almost all globular proteins, that speed up reactions in living cells. They are named after the substrate or reaction, usually ending in -ase. Examples: invertase (sucrose → glucose + fructose); maltase (maltose → glucose); diastase (starch → maltose); zymase (glucose → ethanol + CO2\mathrm{CO_{2}}); urease (urea → NH3+CO2\mathrm{NH_{3} + CO_{2}}); pepsin (proteins → peptides); oxidoreductases catalyse redox reactions. Features. Highly specific (each enzyme acts on one substrate or a narrow class); very efficient (turnover numbers up to millions per second); act under mild conditions (optimum temperature about 298-310 K and optimum pH, e.g. about 2 for pepsin and 7 to 8 for many others); lower the activation energy (sucrose hydrolysis: from about 107 to 36 kJ mol⁻¹ with invertase); activity is increased by activators and co-enzymes and reduced by inhibitors and poisons. Mechanism. In the lock-and-key model, the substrate fits the active site of the enzyme like a key in a lock, forming an enzyme-substrate complex that then gives the products: E+S⇌ES→E+P\mathrm{E + S \rightleftharpoons ES \rightarrow E + P}. This leads to Michaelis-Menten kinetics, v=Vmax[S]Km+[S]v = \frac{V_{max}[S]}{K_{m} + [S]} (see figure). Drugs often work by inhibiting a particular enzyme. Vitamins are organic compounds needed in small amounts for normal growth and health, which the body (mostly) cannot synthesise. Fat-soluble: A, D, E and K. They are stored in the liver and adipose tissue. Water-soluble: the B group and C. They are excreted in urine and so must be supplied regularly in the diet (except B12B_{12}, which is stored in the liver). Deficiency diseases: A (retinol): xerophthalmia (hardening of the cornea) and night blindness. B1B_{1} (thiamine): beriberi. B2B_{2} (riboflavin): cheilosis (cracking at the corners of the mouth), digestive disorders. B6B_{6} (pyridoxine): convulsions. B12B_{12} (cyanocobalamin, contains cobalt): pernicious anaemia. C (ascorbic acid): scurvy (bleeding gums). D: rickets in children and osteomalacia in adults. E (tocopherols): increased fragility of red blood cells and muscular weakness. K: increased blood-clotting time. Hormones are molecules produced by endocrine glands and carried by the blood to target cells; they act as intercellular messengers. Polypeptides and proteins: insulin and glucagon (pancreas) control blood glucose; insulin lowers it, glucagon raises it. Amino acid derivatives: epinephrine and norepinephrine (fight-or-flight response); thyroxine (an iodinated derivative of tyrosine) controls metabolic rate; low levels cause hypothyroidism and goitre, excess causes hyperthyroidism. Steroids: glucocorticoids (carbohydrate metabolism, anti-inflammatory, stress), mineralocorticoids (renal excretion of water and salts; deficiency leads to Addison's disease), and sex hormones (testosterone, estradiol, progesterone), which control sexual characteristics and the reproductive cycle. Key Takeaways: - Enzymes are specific, efficient protein catalysts that lower activation energy; they work best at an optimum temperature and pH. - Rate is Vmax/2V_{max}/2 when [S]=Km[S] = K_{m}. - Fat-soluble: A, D, E, K (stored); water-soluble: B and C (must be taken regularly). - Pair each vitamin with its disease: C scurvy, D rickets, B1B_{1} beriberi, B12B_{12} pernicious anaemia, K clotting. - Pitfall: vitamin B12B_{12} is water-soluble but, unlike the others, is stored in the liver. Brain-Teaser 1: An enzyme follows Michaelis-Menten kinetics. At what substrate concentration, in terms of KmK_{m}, is the rate 90%90\% of VmaxV_{max}? Solution: 0.9=[S]Km+[S]0.9 = \frac{[S]}{K_{m} + [S]} gives 0.9Km=0.1[S]0.9K_{m} = 0.1[S], so [S]=9Km[S] = 9K_{m}. Saturation is approached slowly: going from 50%50\% to 90%90\% needs nine times the substrate. Brain-Teaser 2: Why must vitamin C be supplied regularly, while vitamin A need not be? Solution: Vitamin C is water-soluble, so any excess is excreted in urine and cannot be stored. Vitamin A is fat-soluble and is stored in the liver and adipose tissue, so reserves last for some time (and very large doses can accumulate to toxic levels). Brain-Teaser 3: Enzymes lower the activation energy of sucrose hydrolysis from 107107 to 36 kJ mol−136\,\mathrm{kJ\,mol^{-1}}. By roughly what factor does the rate increase at 310 K, assuming the same pre-exponential factor? Solution: k2k1=eΔEa/RT=e71000/(8.314×310)=e27.5≈9×1011\frac{k_{2}}{k_{1}} = e^{\Delta E_{a}/RT} = e^{71000/(8.314 \times 310)} = e^{27.5} \approx 9 \times 10^{11}. Enzymes speed up this reaction by about a trillion times.