About Biochemistry
Biochemistry questions in a recruitment paper cover the breadth of the subject - water and pH, the four classes of biomolecule, enzymes and their kinetics, bioenergetics, the pathways of metabolism, vitamins and coenzymes, and the laboratory techniques - and most of them turn on a relation that has to be applied to the numbers given. This topic covers that whole breadth on one page, with the arithmetic that goes with it.
What you need to understand
- pH is the negative logarithm to base ten of the hydrogen ion concentration, so a tenfold change in concentration moves the pH by one unit. pH plus pOH comes to fourteen at room temperature.
- A buffer resists change in pH because it holds a weak acid and its conjugate base in equilibrium. Its pH follows the Henderson-Hasselbalch relation: pH = pKa + log of base over acid.
- A buffer works best within about one pH unit of its pKa, and best of all at the pKa itself, where the acid and the base are equal and the logarithm is nought.
- Absorbance follows the Beer-Lambert relation, A = epsilon c l. Absorbance is a logarithm, so it adds up in proportion to the light-absorbing material the beam passes through.
- An absorbance is only linear over about 0.1 to 1.0, which is why an unknown is diluted to bring it into that range rather than read at the top of the scale.
- Enzymes lower the activation energy of a reaction without changing its equilibrium. They are not used up, and the reaction they catalyse is the one that would happen anyway, only very much faster.
- The rate of an enzyme follows v = Vmax S / (Km + S). At a substrate concentration equal to the Km the rate is exactly half the maximum, and when the substrate is far above the Km the rate approaches the maximum.
- Km is the substrate concentration at half the maximum rate and it measures how tightly the enzyme binds its substrate: a small Km means tight binding and a high affinity.
- A competitive inhibitor raises the apparent Km without changing Vmax, because it can be outcompeted by more substrate. A non-competitive inhibitor lowers Vmax without changing Km.
- Free energy change is dG = dH - T dS. A negative value means the reaction releases energy and can go on its own; a positive one means it needs to be driven by another reaction.
- The units must be aligned before the entropy term is subtracted, because enthalpies are quoted in kilojoules and entropies in joules. That factor of a thousand is the commonest arithmetic slip in the topic.
- Glycolysis converts one glucose into two pyruvate, with a net gain of two ATP and two NADH. The two ATP that are invested at the start are why the net figure is two and not four.
- The citric acid cycle turns acetyl CoA into carbon dioxide and reduced coenzymes, and it is the point at which carbohydrate, fat and protein metabolism all converge.
- Oxidative phosphorylation turns the reduced coenzymes back by passing electrons down the chain and pumping protons, and the proton gradient drives ATP synthase with a yield of about two and a half ATP per NADH.
- Specific activity is the enzyme activity per milligram of protein. It rises through a purification while the total activity falls, which is how a purification is judged to be working.
- Chromatography separates by how far a substance travels up the plate, and that distance as a fraction of the solvent front is the Rf value - a number between nought and one by definition.
How to work through these questions
- Decide first which relation the question is about: a pH, an absorbance, an enzyme rate, a buffer, an Rf or an energy change. Each has exactly one, and naming it settles the rest.
- For anything with a logarithm in it, ask whether the quantity given is the concentration or the logarithm of it. Confusing the two is the commonest error in pH and absorbance questions.
- For an enzyme rate, write the denominator out in full as Km plus S. Dropping the Km makes the rate look larger than the maximum, which is impossible.
- For a buffer, work out the ratio of base to acid first, take its logarithm, and only then add the pKa. Doing it in the other order invites the log of the wrong quantity.
- For a free energy change, convert the entropy into the same units as the enthalpy before subtracting. One factor of a thousand decides the answer.
- Check every answer against what is physically possible: a pH outside nought to fourteen, an Rf above one, or a rate above Vmax all mean the relation has been applied the wrong way round.
Mistakes that cost marks
- Forgetting to convert micromoles into moles before using the Beer-Lambert relation, which makes the absorbance a million times too large.
- Leaving the path length out of A = epsilon c l, which matters whenever the cuvette is not the standard 1 cm.
- Dividing the two distances the wrong way round in an Rf value, which gives a figure above one - impossible, as nothing travels further than the solvent front.
- Dropping the Km from the denominator of the Michaelis-Menten relation, which gives a rate above the maximum velocity.
- Inverting the ratio in the Henderson-Hasselbalch relation, which moves the pH the wrong side of the pKa.
- Subtracting a temperature times an entropy in joules from an enthalpy in kilojoules without converting, which throws the answer out by a thousand.
- Reading a pH of 3 as a concentration of 3 mol per litre rather than 10 to the minus 3. The pH is a logarithm, not an amount.
- Treating specific activity and total activity as the same number. One rises through a purification and the other falls, and a question can ask about either.
Worked example
A solution of a substance with a molar absorptivity of 15 000 litre per mole per centimetre is 20 micromol per litre and is read in a 1 cm cuvette. What is its absorbance? An enzyme with a maximum velocity of 100 micromol per minute and a Km of 25 millimol per litre has substrate at 25 millimol per litre: what rate does it work at?
- For the absorbance, the concentration is in micromoles per litre, so it is 20 x 10 to the minus 6 mol per litre. Working in moles is the step that is most often missed.
- The absorbance is epsilon c l: 15 000 x 20 x 10 to the minus 6 x 1 = 0.30.
- Check that the answer is within the linear range. An absorbance of 0.30 sits comfortably between 0.1 and 1.0, so the reading is a good one; a figure of 3 would mean the solution had to be diluted.
- For the enzyme, the substrate concentration equals the Km, and whenever the two are equal the rate is exactly half the maximum.
- The rate is therefore 100 / 2 = 50 micromol per minute. Working it through the relation gives the same: 100 x 25 / (25 + 25) = 2500 / 50 = 50. This is worth remembering as a fact, because questions are often set at that point deliberately.
Answer: Absorbance 0.30; rate 50 micromol per minute
Practice questions with answers
A few Biochemistry questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
A solution has a hydrogen ion concentration of 1 x 10^-4 mol per litre. What is its pH?
Answer: Option D — with explanation
pH is the negative logarithm to base ten of the hydrogen ion concentration. Because the concentration is a power of ten, the pH is simply the exponent - with its sign flipped.
A concentration of 1 x 10^-4 mol per litre is 10 to the power minus 4, so the logarithm is minus 4 and the pH is 4.
The scale runs from nought for a strong acid to fourteen for a strong alkali, and pH plus pOH comes to fourteen at room temperature. That is why the other answers include the pOH - it is the complement of the answer, not the answer.
Common mistakes
- 18 is not the answer: 18
- 5 is not the answer: 5
- 10 is not the answer: 10
Question 2
A substance has a molar absorptivity of 150000 litre per mole per centimetre. A solution of it is 10 micromol per litre and is read in a 1 cm cuvette. What is the absorbance?
Answer: Option B — with explanation
The Beer-Lambert relation says that absorbance is the molar absorptivity times the concentration times the path length: A = \(\epsilon\) c l. It works because the absorbance is a logarithm, so the fraction of light absorbed adds up in proportion to how much absorbing material the beam meets.
The concentration is given in micromoles per litre, so it is 10 x 10^-6 mol per litre, and the absorbance is 150000 x 10 x 10^-6 x 1 = 1.50.
Two things go wrong here. One is forgetting to turn micromoles into moles, which makes the answer a million times too large. The other is forgetting the path length, which matters whenever the cuvette is not the standard 1 cm.
Common mistakes
- 1.60 is not the answer: 1.60
- 3 is not the answer: 3
- 0.75 is not the answer: 0.75
Question 3
An enzyme has a maximum velocity of 40 micromol per minute and a Michaelis constant of 20 millimol per litre. At a substrate concentration of 40 millimol per litre, what is the rate, in micromol per minute?
Answer: Option C — with explanation
The Michaelis-Menten relation gives the rate as the maximum velocity times the substrate concentration, divided by the Michaelis constant plus the substrate concentration: v = Vmax S / (Km + S).
That is 40 x 40 / (20 + 40) = 1600 / 60 = 26.67 micromol per minute.
The relation has two limits worth knowing. When the substrate is well above the Km the rate approaches the maximum, because the denominator is then almost the substrate itself. When the substrate equals the Km the rate is exactly half the maximum, whatever the numbers - and that is what the Michaelis constant means.
Common mistakes
- 20 is not the answer: 20
- 40 is not the answer: 40
- 80 is not the answer: 80
Question 4
In a buffer the concentration of the conjugate base is 5 times that of the acid. The pKa of the acid is 12.4. What is the pH?
-
A
11.70
-
B
13.10
-
C
0.90
-
D
13.80
Answer: Option B — with explanation
The Henderson-Hasselbalch relation gives the pH of a buffer as the pKa of the acid plus the logarithm to base ten of the ratio of the conjugate base to the acid: pH = pKa + log([A-]/[HA]).
The base is 5 times the acid, so the logarithm is 0.6990 and the pH is 12.4 + 0.6990 = 13.10.
Two things fall out of the relation worth remembering. When the two are equal the logarithm is nought and the pH equals the pKa, which is the point of best buffering. A tenfold excess of base over acid raises the pH by exactly one, and a tenfold excess of acid over base lowers it by one.
Common mistakes
- 0.90 is not the answer: 0.90
- 11.70 is not the answer: 11.70
- 13.80 is not the answer: 13.80
Question 5
A spot travels 8 cm from the start line in a chromatogram while the solvent front travels 10 cm. What Rf value does the substance have?
Answer: Option A — with explanation
An Rf value is the distance the substance moved divided by the distance the solvent moved in the same time, both measured from the start line. It says how far up the plate the substance travels, as a fraction of the journey available to it.
The spot moved 8 cm while the front moved 10 cm, so the Rf is 8 / 10 = 0.80.
An Rf value always lies between nought and one, because nothing can travel further than the solvent that carries it. An answer larger than one means the two distances have been divided the wrong way round.
Common mistakes
- 8 is not the answer: 8
- 1.25 is not the answer: 1.25
- 10 is not the answer: 10
Frequently asked questions
Why does a buffer work best at its pKa?
Because that is where the acid and the conjugate base are present in equal amounts, so there is plenty of each to mop up added acid or alkali. Away from the pKa one of the pair runs out quickly and the pH changes as soon as it does.
What does the Km actually tell me?
It is the substrate concentration at which the enzyme works at half its maximum rate, and it is an inverse measure of how tightly the substrate binds. A low Km means the enzyme reaches half speed at a low concentration, which is tight binding and high affinity.
Why is the net ATP from glycolysis two and not four?
Because two ATP are spent at the start of the pathway to prepare the glucose for splitting, and four are produced later. Four less two is two. It is the investment at the front that is forgotten when the answer comes out as four.
Why cannot an absorbance be read above about 1?
Because the relation is only linear while the absorbing molecules are independent of each other, and at high concentrations they interact and the detector runs out of light to measure. The cure is to dilute the sample and multiply the reading back up.
What is the difference between total activity and specific activity?
Total activity is how much enzyme you have altogether and specific activity is how pure it is - units per milligram of protein. During a purification the total falls because enzyme is lost at every step, while the specific activity rises, and it is the rise that shows the steps are working.
How do I know whether a reaction will go on its own?
Work out the free energy change. A negative value means it releases energy and can proceed; a positive value means it needs energy put in, which in a cell comes from coupling it to the hydrolysis of ATP.
