Molar mass and solution concentration

Everything reduces to relationships between three things:

• Mass (m), in milligrams — how much peptide.
• Molar mass (M), in g/mol or Da — a property of the sequence, calculable exactly from it.
• Volume (V), in millilitres — how much solvent.

Mass concentration is simply m / V, giving mg/mL. Molar concentration requires converting mass to moles first.

For a peptide of molar mass M (Da), mass m (mg) dissolved in volume V (mL):

Concentration (mM) = (m / M) × (1000 / V)

Working through it: m/M with m in mg and M in Da gives micromoles. Dividing by V in mL gives micromoles per mL, which is millimolar. The factor of 1000 in the form above is what converts the units consistently.

A worked example. A peptide of molar mass 1,419.5 Da, 2 mg dissolved in 2 mL:

• 2 / 1419.5 = 0.001409 mmol = 1.409 µmol
• 1.409 µmol / 2 mL = 0.705 µmol/mL = 0.705 mM
• Mass concentration is 2 mg / 2 mL = 1 mg/mL

Both figures describe the same solution. Which one you want depends on whether the downstream protocol specifies molarity or mass concentration.

The example above used 2 mg because the vial said 2 mg. That is where the error enters.

A lyophilised vial contains peptide plus bound water plus counterion plus residual salts. The nominal fill weight is the mass of everything. Net peptide content — the fraction that is actually peptide — is commonly in the region of 70–90% for TFA-salt material, and it is not visible on an HPLC purity figure because water and counterion do not absorb at 214 nm.

If a vial labelled 2 mg is 80% net peptide, the actual peptide mass is 1.6 mg and every concentration derived from 2 mg is 25% too high. That is a large systematic error to carry silently through an experiment.

The correction is straightforward when the number is available:

Corrected concentration (mM) = (m × NPC / M) × (1000 / V)

where NPC is net peptide content as a fraction. The difficulty is that most research-market Certificates of Analysis do not report it — a point covered in how to read a COA.

A frequent mistake is to correct using the HPLC purity figure instead. These are different quantities and correcting with the wrong one does not help.

• Purity is the proportion of detected material that is the target peptide. It excludes water and counterion entirely because they are never detected.
• Net peptide content is the proportion of total mass that is peptide. It includes them.

A sample can be 99% pure and 78% net peptide simultaneously, and applying the 99% figure as a mass correction leaves almost the whole error in place. Identity vs purity works through why these measurements are independent.

Two further sources of discrepancy between calculated and actual concentration:

• Incomplete dissolution. A poorly soluble sequence that has not fully dissolved gives a solution weaker than calculated, with the remainder sitting undetected on the vial wall. Visual inspection against light before use catches the obvious cases.
• Adsorption to surfaces. Peptides bind to glass and plastic. At working concentrations in the micromolar range and below, loss to container and tip surfaces becomes proportionally significant. Low-binding consumables and carrier protein where the assay permits are the usual mitigations.

1. Obtain the molar mass from the sequence, or from the COA where stated.
2. Obtain net peptide content from the COA. If it is absent, note that your concentration carries an unquantified positive bias, typically 10–30%.
3. Allow the sealed vial to reach room temperature before opening — see storage and stability.
4. Add solvent down the vial wall rather than directly onto the cake, and dissolve without vigorous shaking.
5. Inspect against light for undissolved material before use.
6. Aliquot into single-use volumes before freezing.

The reconstitution guide covers steps three to six in more detail.