Peptide Calculations

Molecular Weight Determination

The molecular weight (MW) of a peptide is calculated from its primary sequence. During solid-phase peptide synthesis (SPPS), each amino acid coupling releases one water molecule (H₂O, MW 18.015 Da) as the peptide bond forms between the α-carboxyl of the incoming residue and the α-amino of the growing chain:

\text{MW} = \sum_{i=1}^{n} \text{MW}_{\text{residue},i} - (n-1) \times 18.015

where $n$ is the number of amino acid residues and each residue MW is the molecular weight of the amino acid minus water (i.e., the residue mass as incorporated into the chain).

Quick estimation: Average amino acid residue weight is ~110 Da. For a 20-mer peptide, MW ≈ 20 × 110 = 2,200 Da. This ignores the N-terminal H (+1.008 Da) and C-terminal OH (+17.007 Da), which contribute a net +18.015 Da (one water molecule) to the free peptide.

Common modifications to account for:

N-terminal acetyl: +42.011 Da (blocks N-terminus)
C-terminal amide: -0.984 Da (replaces OH with NH₂)
Disulfide bond (Cys-Cys): -2.016 Da (loss of 2H)
Phosphorylation (Ser/Thr): +79.966 Da
TFA counterion: +114.01 Da per TFA (if lyophilized from TFA)

Molar Concentration

Molarity (M) relates mass to concentration through molecular weight:

C (\text{M}) = \frac{m (\text{g})}{\text{MW} (\text{g/mol}) \times V (\text{L})}

Rearranged for practical use:

C (\text{mg/mL}) = \frac{m (\text{mg})}{V (\text{mL})}

For molar concentrations:

C (\text{mM}) = \frac{m (\text{mg}) \times 1000}{\text{MW} (\text{Da}) \times V (\text{mL})}

Example: 5 mg of a 2,000 Da peptide dissolved in 2.5 mL:

C = \frac{5 \times 1000}{2000 \times 2.5} = 1.0 \text{ mM}

Unit Conversions

Unit	Equivalent
1 M	1 mol/L
1 mM	1 mmol/L = 1 μmol/mL
1 μM	1 μmol/L = 1 nmol/mL
1 mg/mL	1 g/L

For a 1,000 Da peptide: 1 mM = 1 mg/mL. This equivalence scales linearly—for a 2,000 Da peptide, 1 mM = 2 mg/mL.

Dose Calculation

The fundamental dosing equation:

\text{Dose (mg)} = C (\text{mg/mL}) \times V (\text{mL})

Rearranged for volume:

V (\text{mL}) = \frac{\text{Dose (mg)}}{C (\text{mg/mL})}

Example: A 2 mg/mL solution, target dose 0.5 mg:

V = \frac{0.5}{2} = 0.25 \text{ mL} = 250 \text{ μL}

From Molar Dose

If the dose is specified in moles or μmol:

\text{Dose (mg)} = \text{Dose (μmol)} \times \frac{\text{MW (Da)}}{1000}

Example: 50 μmol dose of a 2,000 Da peptide:

\text{Dose} = 50 \times \frac{2000}{1000} = 100 \text{ mg}

Reconstitution Volume

To reconstitute a lyophilized peptide to a target concentration:

V_{\text{add}} (\text{mL}) = \frac{m_{\text{peptide}} (\text{mg})}{C_{\text{target}} (\text{mg/mL})}

Worked examples:

Example 1 — Direct reconstitution: 5 mg vial, target 2 mg/mL:

V = \frac{5}{2} = 2.5 \text{ mL}

Example 2 — Targeting a specific dose and volume: 10 mg vial, target dose 200 μg in 0.25 mL injection volume:

First, find required concentration:

C = \frac{0.2 \text{ mg}}{0.25 \text{ mL}} = 0.8 \text{ mg/mL}

Then reconstitution volume:

V = \frac{10}{0.8} = 12.5 \text{ mL}

Example 3 — Multi-dose vial: 5 mg vial, target 200 μg/dose in 100 μL injection, for 25 doses:

Required concentration:

C = \frac{0.2 \text{ mg}}{0.1 \text{ mL}} = 2 \text{ mg/mL}

Total volume for 25 doses: 25 × 0.1 = 2.5 mL. Reconstitution volume for the full vial:

V = \frac{5}{2} = 2.5 \text{ mL}

Insulin Syringe Conversions

Standard insulin syringes provide the most practical measurement for microgram-scale peptide doses.

Key relationship: 1 insulin unit = 0.01 mL = 10 μL, regardless of total syringe capacity.

Syringe Capacity	Graduation	Maximum Units
0.3 mL	1 unit (0.01 mL)	30 units
0.5 mL	1 unit (0.01 mL)	50 units
1.0 mL	1 unit (0.01 mL)	100 units

Volume-to-Units Table

Desired Volume	Units on Syringe
50 μL	5 units
100 μL	10 units
150 μL	15 units
200 μL	20 units
250 μL	25 units
300 μL	30 units
500 μL	50 units

Dose from Concentration and Units

\text{Dose (μg)} = C (\text{mg/mL}) \times \text{Units} \times 0.01 \times 1000

Example: 2 mg/mL solution, drawing 15 units:

\text{Dose} = 2 \times 15 \times 0.01 \times 1000 = 300 \text{ μg}

Precision and Error Propagation

Measurement Uncertainty

Every measurement introduces uncertainty. The cumulative error in a multi-step procedure propagates multiplicatively:

\sigma_C / C = \sqrt{(\sigma_m / m)^2 + (\sigma_V / V)^2}

where $\sigma_C$ is the concentration uncertainty, $\sigma_m$ is the mass uncertainty, and $\sigma_V$ is the volume uncertainty.

Practical limits:

Analytical balance: ±0.1 mg (typical)
1 mL insulin syringe: ±2% (±2 μL at 100 μL)
5 mL syringe: ±2% (±10 μL at 500 μL)
P1000 pipette: ±1% (±10 μL at 1000 μL)

For precision laboratory equipment and peptide research supplies, see here.

Dead Volume

Needles retain 5–10 μL of solution due to surface tension and capillary action. For volumes >200 μL, this is negligible (<5%). For volumes <50 μL, account for dead volume by drawing an additional 5–10 μL.

Significant Figures

Report concentrations to 2–3 significant figures. A 2.5 mg/mL solution measured with a 0.1 mg balance and a 5 mL syringe has a practical precision of ±3–5%. Claiming “2.500 mg/mL” implies 0.02% precision, which exceeds the measurement capability.

Common Errors

Error	Magnitude	Prevention
Unit confusion (reading mL as units)	100×	Verify syringe markings; 1 unit = 0.01 mL
Incorrect reconstitution volume	Variable	Calculate twice, verify once
Meniscus misreading (glass syringes)	5–10%	Read at bottom of meniscus
Dead volume neglect	5–10 μL	Account for needle retention
Temperature-dependent volume	~0.1%/°C	Measure at 20–25°C

Quick Reference

Goal	Formula	Example
Dose	$D = C \times V$	2 mg/mL × 0.3 mL = 0.6 mg
Volume	$V = D / C$	0.4 mg / 2 mg/mL = 0.2 mL
Reconstitution volume	$V = m / C$	5 mg / 2.5 mg/mL = 2 mL
Concentration	$C = m / V$	10 mg / 5 mL = 2 mg/mL
Molar concentration	$C = m / (\text{MW} \times V)$	5 mg / (2000 × 2.5) = 1 mM

For research use only. Verify all calculations before preparing solutions.