Molarity, Concentration and the Arithmetic of a Peptide Stock

Two numbers describe a peptide stock: how much compound is in it, and how much liquid that compound is in. Everything else — molarity, the volume that carries a target mass, the dilution series that reaches a working concentration — is arithmetic on those two. The arithmetic is straightforward. What makes concentration a recurring source of quiet error at the bench is that the first number, the mass of peptide, is normally assumed rather than measured, and the assumption is wrong in the same direction every time.

This page works through the conversions, then through why the answer they produce is a nominal concentration rather than an actual one. What follows is the reasoning behind those conversions.

The two conversions everything rests on

Mass concentration is mass divided by volume:

C (mg/mL) = mass of peptide (mg) ÷ volume (mL)

Molarity converts that into an amount of substance per unit volume, which requires the compound's molecular weight:

M (mol/L) = C (g/L) ÷ MW (g/mol)

The unit bookkeeping between the two lines is the step people skip. A concentration in mg/mL and the same concentration in g/L are numerically identical: 5 mg/mL is 5,000 mg per liter, which is 5 g/L. The factor of 1,000 in the mass units and the factor of 1,000 in the volume units cancel. So a stock quoted in mg/mL can go straight into the molarity expression without conversion, and a stock quoted in µg/mL cannot.

Worked through: a vial holding 10 mg of peptide, reconstituted with 2 mL of diluent, gives 10 ÷ 2 = 5 mg/mL, which is 5 g/L. If that peptide has a molecular weight of 2,000 g/mol, the molarity is 5 ÷ 2,000 = 0.0025 mol/L, or 2.5 mM.

Why the molar unit is the one worth quoting

Mass is not a count. Two solutions at 1 mg/mL of two different peptides contain different numbers of molecules, in inverse proportion to their molecular weights, so a mass concentration is not comparable across compounds and a molar one is. Because peptides are large relative to small molecules, stocks in the low mg/mL range land in the low millimolar range, and working concentrations are conventionally quoted in micromolar or nanomolar.

Net peptide content changes the answer

The mass in the numerator is where the calculation usually goes wrong. A lyophilized peptide solid is not pure peptide by weight. Synthetic peptide samples may carry counter-ions such as acetate or trifluoroacetate as a consequence of how they were prepared, and because acetic acid and trifluoroacetic acid are frequently used reagents in peptide synthesis, the free acids may also be present as impurities ^[1]. Bound water contributes as well. The fraction of the solid that is actually peptide is its net peptide content, and it is not a rounding correction.

Two value-assignment studies give a sense of the range. In assigning purity to a candidate certified reference material for angiotensin II, the trifluoroacetic acid counter-ion was measured by a validated ¹⁹F-qNMR method and, in that material, amounted to nearly 25% by mass; combining orthogonal methods, the final assigned purity was 691 ± 9 mg/g (k = 2) ^[2]. For a synthetic glucagon sample quantified by a mass balance approach — Karl Fischer titration for water, ion chromatography for trifluoroacetic acid, and ICP-MS for inorganic ions — the assigned purity was 896.36 ± 0.68 mg/g ^[3] — a mass balance purity, which is a mass fraction of the whole solid and therefore the same kind of quantity as a net peptide content, not the chromatographic purity discussed below. Those two numbers are far apart, and that is the useful lesson: content is a property of a specific lot of a specific material, not a constant you can look up for peptides in general.

Run the first of those through the arithmetic. Take a vial holding 10 mg of solid at 691 mg/g net peptide content. The peptide present is 10 × 0.691 = 6.91 mg. In 2 mL that is 6.91 ÷ 2 = 3.455 mg/mL, or 3.455 g/L. At a molecular weight of 2,000 g/mol the molarity is 3.455 ÷ 2,000 = 0.0017275 mol/L, or 1.73 mM — against the 2.5 mM the label mass implied. The error is not small, it is not random, and it is always in the same direction: the nominal figure overstates the peptide.

It carries forward. Suppose you want 1 mL at 10 µM. Working from the nominal 2.5 mM stock you would take 1,000 × 10 ÷ 2,500 = 4.0 µL. Working from the actual 1.7275 mM stock you would need 1,000 × 10 ÷ 1,727.5 = 5.79 µL. A researcher who pipetted 4.0 µL believing the label would end up at 1.7275 × 4 ÷ 1,000 = 0.00691 mM, that is 6.91 µM rather than 10 µM. The ratio is exactly the content fraction, 0.691, which is the general result: every concentration downstream of an uncorrected label mass is off by the same multiplicative factor.

Purity and content are different measurements

Purity and peptide content get conflated constantly, and they answer different questions. Purity describes the composition of the peptide fraction — how much of the peptide present is the intended sequence. Content describes what share of the vial's mass that fraction is. A sample can be highly pure and still be appreciably less than 100% peptide by weight.

The methods differ accordingly. In the mass balance approach, purity is what is left after the mass fractions of all identified impurities are subtracted from the whole, which is why water, counter-ion and inorganic ion determinations appear alongside the chromatography ^{[2, 3]}. Amino acid analysis by isotope dilution LC-MS/MS is conventionally used as a reference method, and requires hydrolysis; quantitative NMR instead quantitates the intact peptide, which eliminates potential bias due to hydrolysis. Both are susceptible to interference from related peptide impurities, which have to be measured and accounted for ^[2]. In one study of a complex cyclic peptide reference standard, a ¹H-qNMR method showed no significant difference in quantification compared with the mass balance method ^[4].

Which method a certificate used therefore matters as much as the number it reports. A multi-laboratory collaborative study organized by USP compared an HPLC assay, qNMR and amino acid analysis for quantitating the nonapeptide oxytocin; the HPLC assay run against the same peptide bulk material as the standard showed the lowest inter-laboratory variability, and the authors noted that qNMR, being a direct measurement of the peptide against an internal standard and simpler to operate, deserves further exploration as a primary method for value assignment ^[5]. Note the qualifier on the HPLC result: it depended on the standard being the same bulk material, which is not the situation a downstream user is in.

Which molecular weight goes in the denominator

The molecular weight and the mass have to refer to the same species. If a certificate reports peptide content as the mass fraction of the peptide itself, the mass you carry into the calculation is peptide mass, and the molecular weight to divide by is the free base — not the salt. If instead you treat the whole solid as if it were the compound, you have implicitly used a salt-form mass with a free-base molecular weight, and the two errors do not cancel.

A second, smaller mismatch: a molecular weight computed from the molecular formula as a sum of standard atomic weights is an average mass, while mass spectrometry may report a monoisotopic mass, which is a different and slightly smaller number for the same molecule. For concentration arithmetic the average mass is the correct one, because the sample is an ordinary isotopic mixture. This is convention rather than a measured finding, and it is worth stating explicitly on a record because the two numbers are close enough to look like a transcription error.

Measuring the concentration instead of computing it

Where the number has to be defensible, concentration can be measured rather than inferred from a label. The routes differ in what they require.

Ultraviolet absorbance. Absorbance at 280 nm depends on a protein's content of tryptophan, tyrosine and cystine. From a sample of 116 measured absorption coefficients for 80 proteins, a predictive equation assigning 5,500 M⁻¹ cm⁻¹ per tryptophan was found to work well for proteins containing tryptophan and to be less reliable for those that do not; the authors' recommendation was that the best approach is to measure the coefficient rather than predict it ^[6]. That constraint bites for peptides, many of which carry no aromatic residue at all. For those, a method has been proposed and validated for predicting molar absorptivity at 205 nm directly from the sequence, requiring no calibration, which its authors expected should be suitable for a wide range of proteins and peptides ^[7].

Amino acid analysis. Hydrolyze the peptide, quantify the released amino acids against isotope-labeled internal standards, and back-calculate. At NIST, amino acid analysis is used to assign concentration values to protein and peptide standard reference materials, and the isotope dilution LC-MS/MS implementation is the technique routinely used there to certify analyte concentrations ^[8]. The sample requirement is modest: in one hydrophilic-interaction implementation with isotope dilution mass spectrometry, as little as 25 pmol of peptide or protein hydrolysate was reported to be sufficient for determining absolute content ^[9].

Neither route is a bench-side convenience. For most work the practical position is to take content from the certificate of analysis for the specific lot, and to record that you did.

Serial dilution is where small errors become large ones

Serial dilution methods are particularly prone to error propagation, because each dilution depends on the concentration of the one before it ^[10]. That observation came from characterizing DMSO-based compound dilution plates in a screening context, but the structure of the problem is general: errors multiply along the chain rather than averaging out.

The arithmetic makes the scale of it concrete. Suppose each transfer in a five-step 1-in-10 series leaves the result 2% high. The final tube is not 2% high but 1.02⁵ = 1.104, about 10.4% high — and because each step is a deliberate tenfold change, a few percent of drift per step looks like nothing beside it — the offset stays invisible unless a tube is measured against something other than the series that produced it. A single direct dilution to the same endpoint carries one step's error instead of five. Where the dynamic range allows it, fewer and larger steps are the cheaper form of accuracy.

The same reasoning argues against very small transfer volumes. In the example above, 5.79 µL has to be delivered by an instrument whose relative uncertainty grows as the requested volume approaches the bottom of its range, and a retained droplet is a larger fraction of a small delivery than of a large one. How much that costs depends on which pipette is used, so the specification for the volume actually being dispensed — not for the pipette's nominal size — is the number to check. Diluting the stock once into an intermediate, then taking a larger volume from that, moves the transfer into a range the instrument handles better.

What the container takes out of solution

A solution also loses peptide to the surfaces it touches. The work below was done at trace levels rather than on concentrated stocks, so it speaks to dilute working solutions — where an adsorbed layer is a meaningful fraction of what is present — more than to a vial at milligrams per millilitre. Using a reference mixture of thousands of tryptic peptides and differential LC-MS/MS quantification, a significant number of hydrophobic peptides were found to adsorb to conventional polypropylene vials, while only a few adsorbed to polypropylene vials designated low-protein-binding; the highest number adsorbed to glass vials, which the authors attributed to electrostatic interactions ^[11]. A separate study of nonspecific adsorption in peptide analysis reported good overall recoveries — above 80% within 24 hours — using centrifuge tubes and sample vials made of a modified polypropylene material, and found that although the HPLC index — a chromatographic measure of hydrophobicity — and peptide length correlated significantly with the degree of adsorption (p < 0.05), those parameters explained the adsorption behavior of only about 30% of the peptides tested ^[12].

That last figure is the honest part. Adsorption is real, it is sequence-dependent, and it is not well predicted from properties you can read off a sequence. Low-binding plastic is the standard mitigation, though the vial comparison behind that recommendation was run in cooperation with the manufacturer of the vials tested, one of whose employees is an author ^[11]. Whether low-binding plastic is sufficient for a particular peptide at a particular concentration is an empirical question, and for dilute working solutions it is worth treating as an open one.

Nominal, actual, and what to write down

A nominal concentration is what the arithmetic gives from the label. An actual concentration is what the solution contains. The gap between them is the sum of net peptide content, the accuracy of the fill against the labeled mass, dilution error, adsorptive loss, and any degradation since reconstitution. Most of those push in the same direction: actual is lower than nominal, more often than not.

None of that makes nominal concentrations useless. Within a single experiment prepared from a single stock, a systematic offset shared by every condition cancels out of a comparison between conditions. It does not cancel when a result is compared against a literature value, when an absolute concentration is reported, or when two lots are used across a study — which is where the correction has to be applied, and where the record has to be good enough to apply it retrospectively.

The practical minimum is to record, on the vial and in the notebook, the compound, the lot, the labeled mass, the diluent and volume added, the resulting concentration, whether that concentration is nominal or content-corrected, and the date. A concentration written without stating which of the two it is cannot be reinterpreted later, and reinterpreting it later is exactly what a surprising result will require.

What is not established

Much of what surrounds this arithmetic is convention with thin primary literature behind it. There is a well-developed measurement science for assigning content and purity to reference materials, and the studies cited above come from it — but that work is about metrologically traceable standards, not about routine vials, and it does not tell you what any given research-grade lot contains. Content varies by lot; the only way to know is a lot-specific certificate.

Some specific gaps worth naming. Adsorptive loss is documented but not predictable from sequence ^{[11, 12]}, so the magnitude for a given peptide at a given concentration is unknown until measured. The comparison between quantification methods has been made for individual peptides, and the ranking of methods observed for oxytocin ^[5] should not be assumed to transfer to a different peptide. Whether a stock's concentration has drifted since preparation is not answerable by arithmetic at all; it is a stability question, and the arithmetic on this page is silent about it.

The conversions themselves are exact. Everything uncertain sits in the inputs, which is the reason to be explicit about where each one came from.