Peptide units and concentration: milligrams, moles and international units

Mass: milligrams and micrograms

Peptides are weighed in milligrams and micrograms. The prefixes are those of the International System of Units (SI): milli for one thousandth, micro for one millionth and nano for one billionth.¹

The abbreviation mcg, seen on some labels, is a non-SI way of writing µg. The mass printed on a vial is the first number in every calculation that follows, and the section on net peptide content explains why it is not the last.

Amount: the mole and molecular weight

Mass says how much material there is. The mole says how many molecules. It is the SI unit of amount of substance, and one mole contains exactly 6.022 140 76 × 10²³ elementary entities, here molecules.¹

The link between the two is the molecular weight, the mass of one mole in grams (g/mol):

amount (mol) = mass (g) ÷ molecular weight (g/mol)

The distinction matters because equal masses are rarely equal numbers of molecules. Take 1 mg each of two peptides, one of 1,000 g/mol and one of 4,000 g/mol. The first is 1 micromole and the second 0.25 micromole: the same mass, and a fourfold difference in the number of molecules. This is one reason published methods often state concentrations in molar units.

A molecular weight can be read from a public compound record, and a certificate of analysis may state a calculated mass for the molecule. The figure used should be the weight of the peptide itself, not of its salt, whenever the mass has been corrected to peptide content as described below.

Concentration

Concentration is an amount in a volume, and it is written three ways.

• Mass concentration: milligrams per millilitre (mg/mL) or micrograms per millilitre (µg/mL).
• Molar concentration, or molarity: moles per litre, written M, with the same prefixes (mM, µM, nM).
• Per cent weight in volume: grams per 100 mL, so 1% is 10 mg/mL. The label of one preserved water, for example, gives its 0.9% benzyl alcohol as 9 mg/mL.⁵ That product is the subject of bacteriostatic water explained.

Mass and molar concentration convert through the molecular weight. Because 1 mg/mL is the same as 1 g/L:

molar concentration (mol/L) = mass concentration (mg/mL) ÷ molecular weight (g/mol)

For an invented peptide of 2,000 g/mol the scale runs as follows.

International units

Some biological substances are not measured by mass at all. The SI brochure itself says why: there is a class of units for biological activity that cannot yet be defined in SI terms, because the mechanism of the biological effect is not understood well enough to be expressed in physical and chemical quantities.¹ The World Health Organization has taken responsibility for defining international units (IU) for such substances.¹

Review An international unit is tied to a physical reference material. International standards are prepared as materials to which the WHO Expert Committee on Biological Standardization assigns an arbitrary number of units for a biological activity, and working reference materials calibrated against them give laboratories a common unit of measurement.² The value is set by a collaborative study that includes all relevant assays and reflects a consensus of the valid methods, where an SI unit rests on a single reference method.²

The committee was established in 1947.⁶ The British institute that produces most of these standards gives the reason for the system: the activity of biological medicines cannot be quantified in SI units such as mass, so it is measured with biological or immunological assays, which are inherently variable.⁷

An international unit is therefore defined by a reference material and the assays calibrated against it, not by a mass. Three things follow.

• Review One IU of one substance need bear no relation to one IU of another, because each unit is an arbitrary value attached to its own reference material.²
• Review The unit lives in a physical preparation that must eventually be replaced, and keeping the unit constant across a replacement is a recognized difficulty.²
• Converting IU to mass needs a factor that belongs to one substance and one standard.

Review Two hormone cases show how conversion goes wrong. For growth hormone assays, reporting in mass units or in international units, with variable conversion factors, led to confusion, and international collaborations recommended a single recombinant calibrator and reporting in mass units only.⁸ For insulin, conventional units are based on biological efficacy while SI concentrations are given in picomoles per litre; a commentary found at least two well-accepted conversion factors where there should be one, and reported that the incorrect one under-reports insulin concentrations by about 15%.³

Chemistry study Some reference materials for well-defined molecules carry SI quantities instead. The first WHO reference reagents for six molecules related to human chorionic gonadotropin were assigned values in moles per litre.⁹ The first International Standard for human C-peptide was calibrated in mass units, starting from amino acid analysis, at 8.64 µg per ampoule with an expanded uncertainty of 8.21 to 9.07 µg.¹⁰

For bench arithmetic the consequence is simple. A vial labelled in IU states an activity, not a mass. A mass or molar concentration can be calculated from it only if the specific activity of that batch, in IU per milligram against a named standard, is documented. This page supplies no conversion factors.

Gross mass and net peptide content

Review The powder in a vial is not all peptide. A review of counter-ions notes that peptide drugs often occur as salts, paired with counter-ions.¹¹ The powder can also hold some water. Net peptide content is the share of the powder’s mass that is peptide; where the rest comes from is the subject of peptide salts and net peptide content.

Chemistry study Content has to be measured. A multi-laboratory study organized by the United States Pharmacopeia compared three methods on the peptide oxytocin: an HPLC assay against a standard, quantitative nuclear magnetic resonance and amino acid analysis.¹² Amino acid analysis, which measures stable amino acids released when the peptide is completely hydrolyzed, is common practice for finding the mass concentration of a peptide solution.¹³ It counts amino acids from peptide impurities too: for one angiotensin I material, leaving the impurities uncorrected would have caused an error of 1%.¹³

Purity and content are therefore two separate corrections. To a first approximation:

mass of target peptide = mass of powder × net peptide content × purity

With 10 mg of powder, a net peptide content of 80% and a purity of 98%, the target peptide is 10 × 0.80 × 0.98 = 7.84 mg. What a purity figure does and does not measure is explained in what a purity figure means.

Chemistry study The stated content of a commercial material is itself a claim. When laboratory standards of parathyroid hormone from different manufacturers were compared with the WHO international standard, some held twice the content stated on the label, a finding confirmed by amino acid analysis.⁴

Making and diluting a stock: worked examples

The examples use one invented case: a vial labelled 10 mg, a net peptide content of 80%, a molecular weight of 2,000 g/mol, and purity taken as 100% to keep the numbers round. Volumes are those of pipettes and tubes.

The single dilution uses the relation C₁ × V₁ = C₂ × V₂: concentration times volume is unchanged by dilution, because dilution adds solvent and removes nothing. A serial dilution reaches a large factor in small steps, which avoids measuring a volume too small to pipette accurately.

The same factor applies to everything in the stock. A stock in pure dimethyl sulfoxide diluted 1 in 200 leaves 0.5% of that solvent by volume, and preserved water with 0.9% benzyl alcohol diluted 1 in 10 leaves 0.09%. Why that matters to an assay is covered in reconstitution concepts.

The laboratory calculators cover concentration, molarity, dilution and unit conversion, and show the arithmetic for each result.

Nominal and actual concentration

A calculated concentration is nominal. It assumes that all of the stated mass dissolved and stayed dissolved.

Chemistry study That assumption can fail badly. At typical experimental concentrations, 90% or more of three cationic peptides could be lost from solution by adsorption to glass and plastic containers.¹⁴

Chemistry study A concentration can be measured instead of assumed. Absorbance of ultraviolet light is proportional to concentration: absorbance = absorption coefficient × concentration × path length. At 280 nm the coefficient depends on tryptophan, tyrosine and cystine, and it can be predicted as 5,500 for each tryptophan, 1,490 for each tyrosine and 125 for each cystine, in units of M⁻¹ cm⁻¹.¹⁵ The prediction is reliable for proteins that contain tryptophan and less so for those that do not, and the authors’ advice is to measure the coefficient where possible.¹⁵ For sequences with neither tryptophan nor tyrosine, a later method predicts the absorptivity at 205 nm from the sequence.¹⁶

As an example, a peptide with one tryptophan and one tyrosine has a predicted coefficient of 6,990 M⁻¹ cm⁻¹. An absorbance of 0.35 in a 1 cm cell then corresponds to 0.35 ÷ 6,990 = 5.0 × 10⁻⁵ mol/L, or 50 µM. The guide to analytical methods for peptides describes amino acid analysis and the other techniques.

Human evidence

This page reports no finding about the effect of any substance in people, in animals or in cells. Its sources are metrology documents and analytical chemistry papers. The papers on growth hormone and insulin assays come from clinical laboratory medicine, and they are cited for what they say about units of measurement, not about any effect of those hormones.