Retention-time normalisation across gradients

Retention time is the cheapest orthogonal identity check available and it is routinely discarded because results come from laboratories running different gradients. The index normalises them, which recovers most of the information at the cost of an explicit approximation.

The model

In linear-solvent-strength theory the retention of a compound under gradient elution depends on the gradient steepness. For two gradients spanning the same organic range, retention scales approximately linearly with gradient duration, plus a duration-independent term for the column dead time and the initial hold.

t_norm(t_ref, G)  =  t_ref × (G / G_ref) × (1 − f)  +  t_ref × f

  t_ref  = nominal retention on the index reference method
  G      = the laboratory's gradient duration (min)
  G_ref  = 30 min (reference method RG-2)
  f      = 0.08, the duration-independent fraction

Worked: semaglutide, t_ref = 18.42 min on RG-2.

  Kestrel, G = 15:   18.42 × 0.5   × 0.92 + 18.42 × 0.08 =  9.95 min
  Medutest, G = 25:  18.42 × 0.833 × 0.92 + 18.42 × 0.08 = 15.59 min
  Janoshik, G = 30:  18.42 × 1.0   × 0.92 + 18.42 × 0.08 = 18.42 min
  Nordanalyt, G=35:  18.42 × 1.167 × 0.92 + 18.42 × 0.08 = 21.25 min

A peak reported at 9.9 min by a 15-minute method and one reported at
21.2 min by a 35-minute method are the same compound.

Where it breaks

• Very early elution. Below about 6 min on the reference scale, the dead volume and the initial hold dominate and the linear term is a poor description. The short bioregulator class is the worst affected and produces most of the index's false AX-R11 flags.
• Very late elution. The most hydrophobic compounds — pemvidutide, retatrutide — may not elute at all if a laboratory's gradient tops out below the required organic strength. The index records "no peak detected" as a method finding, not a material finding.
• Different column chemistry. Normalisation corrects for gradient duration and nothing else. A C8 column, a different pore size, or a different ion-pairing additive changes retention order, not just retention time.
• Different temperature. A 5 °C difference shifts peptide retention by several per cent and is rarely documented.