Lab and Clinical Calculation Practice Problems

The calculators behind the questions

Every question is generated from one of these 10 calculators, and links back to the one it came from: A-a Gradient and Alveolar Gas Equation Calculator, Albumin Corrected Calcium Calculator, Body Surface Area Calculator, Cell Doubling Time Calculator, Centrifuge RCF Calculator, Ligation Calculator, Mean Arterial Pressure Calculator, Nucleic Acid Quantification Calculator, QTc Calculator and Serum Osmolality and Osmolar Gap Calculator.

Write down the assumption, not just the numbers

Each lab calculation here turns a proxy into the thing you want, and each proxy holds only while its assumption does. Absorbance stands in for mass of nucleic acid, which needs the right extinction factor. Rotor speed stands in for the force on a pellet, which needs the rotor radius. Two counts stand in for a growth rate, which needs exponential growth between them. The formula returns a plausible figure whether or not the assumption held. The clinical questions rest on assumptions of their own: a QTc depends on which correction formula was applied, and an A-a gradient on the barometric pressure given to the alveolar gas equation.

So write the assumption beside the numbers, put both times in the same unit, and take the rotor radius from the rotor’s documentation rather than the length of the tube.

Where lab calculations go wrong

• A spin quoted in RPM. Speed is not force. 13,000 rpm in a rotor of 8.5 cm radius is about 16,000 × g, and the same speed in a larger rotor delivers more. A protocol in RPM is reproducible only on the centrifuge it was written on.
• The wrong extinction factor. An absorbance of 1.0 over a 1 cm path is 50 µg/mL for double-stranded DNA, 40 for RNA and 33 for single-stranded DNA. Applying 50 to an RNA sample overstates the concentration by 25 percent, and nothing flags it. Keep the reading between 0.1 and 1.0, where the instrument is linear.
• The dilution factor dropped. An A260 of 0.15 read on a 1 in 10 dilution is 0.15 × 50 × 10 = 75 ng/µL. Without the factor it is 7.5, and both are concentrations a real prep might have.
• Counts that straddle the wrong phase. A doubling time is defined for exponential growth. Two counts spanning a lag phase, or a culture that has hit confluence, return a figure that overstates the true doubling time.

Checking a result you cannot repeat

Use the exponents. Relative centrifugal force goes as the square of the speed, so a 10 percent error in RPM is a 21 percent error in force, while it is only linear in radius. Concentration from absorbance is linear in all three inputs, which makes an answer out by exactly ten a dilution factor.

Doubling times have an exact check whenever the counts are related by a power of two. Going from 100,000 to 800,000 is three doublings however long it took, so 48 hours of that growth is a 16 hour doubling time, no logarithms required. Then compare against what is normal: E. coli in rich medium manages about 20 minutes, yeast about 90 minutes and HeLa cells roughly 24 hours.

Units that look different and are not

One pair is identical and often treated as though it were not: 1 ng/µL is exactly 1 µg/mL. Relative centrifugal force is the other quiet one, a dimensionless multiple of 9.80665 m/s² rather than a force in newtons, which is why it is written × g.

Mass and molar amount are not interchangeable, and the conversion depends on length. A base pair of double-stranded DNA averages about 650 g/mol, so a 1 kb fragment is around 650,000 g/mol and 1 µg of it is roughly 1.5 pmol. Molecule count scales inversely with length, so 100 ng of a 200 bp fragment holds about 50 times as many molecules as 100 ng of a 10 kb fragment.