Biomolecules and Enzymes

1The four families

Grind up a tissue, precipitate it with acid, and the cell splits into two pools. The acid-soluble pool holds small molecules — sugars, amino acids, nucleotides, nothing much above 1000 Da. The acid-insoluble fraction holds the macromolecules: carbohydrates, proteins and nucleic acids, each a long chain of one repeating kind of monomer joined by one characteristic bond.

Lipids are the odd family out. A fat is one glycerol esterified to three fatty acids — a small, fixed assembly, not a chain of repeating units, and its mass sits around 800 Da rather than the tens of thousands a protein reaches. It still turns up in the acid-insoluble fraction, because lipids come out of the cell as fragments of membrane and those fragments sediment with the macromolecules. That accident of technique is the whole reason fats are taught alongside true polymers.

Figure. Four macromolecule families of the acid-insoluble pool, each named by monomer and bond. Composition, not a structural drawing of any polymer.

2Amino acids and the peptide bond

Every amino acid found in a protein carries an amino group, a carboxyl group, a hydrogen and a side chain R on the same carbon — the alpha carbon. Proline is the standing exception: its nitrogen is closed into a ring rather than left as a free amino group, which is why it is called an imino acid. Twenty different R groups is the whole alphabet. Two amino acids join when the carboxyl of one condenses with the amino group of the next: a water molecule leaves and a covalent peptide bond forms in its place.

The chain that results has direction. One end keeps a free amino group and one end a free carboxyl group, so a sequence read N-terminal to C-terminal is not the same protein as the same letters read backwards. That ordered sequence is the primary structure, and everything the protein later does follows from it.

Figure. Count the gaps, not the boxes. Four residues leave three gaps, so three peptide bonds formed and three water molecules left. The free amino group at the far left and the free carboxyl at the far right are what give the chain its N-to-C direction.

How a chain is built

1. Two ends meetThe carboxyl of one amino acid is brought up to the amino group of the next.
2. CondensationOne H and one OH leave together as water; the C and the N left behind are now joined by a peptide bond.
3. Repeat, and countEvery residue added past the first costs exactly one more water and buys exactly one more bond, which is why an unbranched chain of n residues has n − 1 of them.

3Four levels of protein structure

Primary structure is the sequence. Secondary structure is what short stretches of that sequence do locally — a right-handed alpha helix or a beta pleated sheet, held by hydrogen bonds running along the backbone. Tertiary structure is the whole chain folded into one compact three-dimensional shape, held by hydrogen bonds, ionic attractions, hydrophobic clustering and covalent disulfide bridges. Quaternary structure exists only where several folded chains assemble: haemoglobin is four subunits, two alpha and two beta.

The active site of an enzyme is a tertiary-structure object. It is a pocket assembled from residues that may sit far apart in the sequence and are brought together only by the fold — which is why anything that unfolds a protein abolishes its catalysis while leaving its sequence untouched.

Figure. Hierarchy of protein structure: each level builds on the one above. Secondary is local H-bonding; tertiary is the whole-chain fold; quaternary is multi-subunit.

4Enzymes lower the activation energy

A reaction that is thermodynamically downhill can still be immeasurably slow, because the molecules must climb through a strained, high-energy transition state on the way. The height of that hump above the reactants is the activation energy. An enzyme binds the transition state more tightly than it binds the substrate, which lowers the hump — and that is the entire trick. It adds no energy, and it changes neither end of the profile.

Not every enzyme is a complete catalyst on its own. The protein alone is the apoenzyme; with its non-protein cofactor bound it becomes the working holoenzyme. And proteins do not have a monopoly on catalysis: a few RNA molecules, the ribozymes, catalyse reactions with no protein present at all.

Figure. Both paths start at the same reactant level and finish at the same product level — the enzyme has moved neither. The dashed catalysed route peaks at half the barrier height of the solid uncatalysed one, and a lower barrier is crossed by a far larger fraction of molecules per second. The same drop applies to the reverse journey, which is why equilibrium arrives sooner but lands in the same place.

5Specificity and the ES complex

Catalysis begins with binding. The substrate must enter the active site, a cleft in the folded enzyme lined with the particular residues that will do the chemistry, and it must fit that cleft in shape, in charge and in the placement of the groups that will be attacked. Urease acts on urea and on nothing else for exactly this reason.

The older lock-and-key picture treats the site as a rigid preformed complement of the substrate. Induced fit keeps the specificity but drops the rigidity: the site is flexible and moulds itself around the substrate as it arrives, closing on it and straining the bonds that are about to break. Enzyme and substrate are not consumed by each other — the enzyme leaves each cycle exactly as it entered, which is why a few molecules of it can turn over a great deal of substrate.

One catalytic cycle

1. BindSubstrate diffuses into the active site and is held by weak interactions alone: E + S becomes ES.
2. Fit closesThe site adjusts its shape around the substrate, putting the reacting bonds under strain and lining up the catalytic residues.
3. ReactThe strained substrate crosses a lowered barrier and is converted while still held: ES becomes EP.
4. ReleaseThe product no longer matches the site and leaves; the enzyme, unchanged, takes the next substrate molecule.

6Saturation, and what K_m means

Hold the enzyme fixed and raise the substrate. At low concentrations almost every active site is free, so nearly every substrate molecule that arrives is processed and the rate climbs almost in proportion. As the sites fill, arriving molecules increasingly find them occupied, and the climb flattens. In the limit every site is working every moment: the rate reaches V_max, and no further substrate can improve it.

The whole curve is one equation, V = V_max[S]/(K_m + [S]) — a rectangular hyperbola that approaches V_max but never touches it. K_m is not a rate. It is the substrate concentration at which the enzyme runs at half its maximum, and the lower it is, the less substrate the enzyme needs in order to work near its best.

Figure. The curve is steepest where substrate is scarcest and flattens as the sites fill. The marked point is the definition of K_m: drop from half the V_max line onto the curve and read the concentration underneath. The right-hand end of this plot is at ten times K_m and has still only reached 91% of V_max — the dashed line is approached, never met.

Where K_m comes from

1. Start from the rate lawV = V_max[S]/(K_m + [S]), with K_m and V_max fixed for a given enzyme and substrate.
2. Set [S] equal to K_mThe right-hand side becomes V_max·K_m/(K_m + K_m), which is V_max·K_m/2K_m.
3. CancelV = V_max/2. The half-maximal point is not measured off a graph — it falls out of the equation, and it is the definition of K_m.

7Competitive and non-competitive inhibition

A competitive inhibitor resembles the substrate closely enough to occupy the active site, and does nothing once it is there. Malonate resembles succinate and blocks succinate dehydrogenase this way. Because inhibitor and substrate compete for the same site, whichever is in excess wins: enough substrate restores the rate, so V_max is untouched, and the enzyme merely needs more substrate to reach any given fraction of it — the apparent K_m rises.

A non-competitive inhibitor binds somewhere else on the enzyme and distorts the active site from a distance. The substrate cannot displace it, because they are not competing for the same place. Those enzyme molecules are simply out of service: the top speed falls, while the molecules still working bind substrate exactly as well as before, so V_max drops and K_m does not. Which constant moves is how the two are told apart.

Figure. The two marked points sit at exactly the same height — half of V_max — and differ only in how far right they lie: here the inhibitor has tripled the substrate needed to get there. Both curves climb towards the same horizontal V_max line, which is what "beatable by excess substrate" looks like on a graph. A non-competitive inhibitor would look entirely different: the horizontal line itself would drop, and the half-maximal point would not move sideways at all.

8Optimum temperature and optimum pH

Warming a reaction speeds it up: molecules collide more often and more of them arrive with enough energy to react. For a human enzyme this holds until about 37 °C. Past that, a second process takes over — the weak bonds holding the tertiary fold begin to give way, the active site loses its shape, and the number of working enzyme molecules collapses. Above about 45 °C the collapse dominates completely.

So the temperature curve is not a symmetric bell. It rises gently over tens of degrees and falls off a cliff over a few, and the two halves mean different things: cooling an enzyme merely slows it and is fully reversed by rewarming, whereas heating past the optimum denatures it and is generally not reversed by cooling. pH acts differently again. It changes the ionisation of the acidic and basic side chains that build and hold the active site, so each enzyme has an optimum matching the compartment it works in.

Figure. Look at the two sides of the peak, not the peak itself. The climb takes some thirty degrees; the fall is essentially over within ten. That asymmetry is the whole point — the rise is ordinary chemistry speeding up, the fall is the protein being destroyed — and it is why drawing this as a tidy symmetric bell teaches the wrong biology. The left half is reversible, the right half is not.