Salt gradient planner

A salt gradient is programmed as %B, the share of buffer B the pump delivers, over a number of column volumes. What the protein sees is the salt concentration and how fast it rises per column volume. This planner converts one into the other, lays out the method from wash to strip, and adds up how much of each buffer you need.

The arithmetic

• Salt at a given %B: c = c_A + (c_B − c_A) × %B / 100. This assumes the pump mixes A and B by volume and the salt concentration follows linearly.
• Slope: (end %B − start %B) / n_CV in %B per CV, and the same times (c_B − c_A) / 100 in mM per CV.
• Volume and time: each segment is n_CV × CV in mL, and volume / flow in min.
• Buffer use: a linear segment from s to e %B averages (s + e) / 2, so it uses V × (s + e) / 200 of buffer B and the rest of buffer A.

Worked example (the defaults): a 5 mL column at 1 mL/min, A with 0 mM and B with 1000 mM NaCl, a 5 CV wash, then 0 → 50 %B over 20 CV and a 5 CV strip. The gradient rises by 2.5 %B, or 25 mM, per CV. It is 100 mL long and takes 100 min. The method uses 150 mL: 100 mL of A and 50 mL of B, before priming and equilibration.

Why the gradient is given in column volumes

Writing every step in CV makes a method independent of column size: 20 CV is 20 mL on a 1 mL column and 2 L on a 100 mL column. The Cytiva™ IEX handbook expresses buffer volumes in CV for this reason and, for scale-up, keeps the ratio of gradient volume to column volume. Yamamoto, Nomura and Sano derived how resolution in a linear gradient depends on operating conditions. In their result, the gradient enters as the slope multiplied by the column volume, which is the salt change per column volume up to a constant. Keep the slope in mM per CV, the bed height and the linear velocity, and that term does not change with the column diameter. See scale up at constant residence time and bed height.

Slope, resolution and dilution

Long, shallow gradients separate peaks further apart, at the cost of longer runs and broader peaks; short, steep gradients are faster and give sharper peaks that elute closer together. That is the handbook’s summary. Yamamoto, Nomura and Sano give the scaling: resolution is proportional to the inverse square root of slope × column volume, at fixed column length, velocity and particle size. By that relation, halving the slope per CV raises resolution by about √2 ≈ 1.4 and doubles the gradient volume and time (our arithmetic). They found the relation holds except for very short columns with shallow gradients and at low flow rates. A broader peak in more volume is also more dilute. If you shorten the gradient, the handbook suggests lowering the sample load to keep the same resolution.

Dwell volume: the gradient arrives late

The pump forms the gradient at the mixer. It reaches the column only after it has filled the tubing, mixer and valves in between: the system dwell volume. Keulen et al. define it on an ÄKTA™ system, measure it with a 1 M NaCl pulse and subtract it, with the dead volume, from retention volumes so that peaks line up with the gradient. The handbook advises the shortest possible flow path between mixer and column top for accurate gradients.

Enter the dwell volume to see when the gradient start reaches the column inlet. It reaches the column outlet later still, by the liquid volume in the column that salt can enter. That volume is the total porosity times the CV, so it is at most one CV, and the planner shows that upper bound; the exact value depends on the resin. Then it passes the tubing to the conductivity monitor. Dwell volume belongs to the system, not the column, so it does not scale: the planner shows it as a fraction of a CV, and the same 2 mL is 0.4 CV on a 5 mL column but 0.02 CV on a 100 mL one. See extra-column volume in the scale-up tutorial.

Conductivity

The planner gives salt in mM, not conductivity. The conductivity of a buffer depends on all of its ions and their concentrations, and we know of no simple, sourced conversion from mM NaCl that holds across buffers. Read it from the conductivity monitor in a blank run or in your buffers. The handbook uses the conductivity trace the same way: equilibrate until the outlet conductivity and pH are stable.

Sources and scope

• Cytiva™, Ion Exchange Chromatography: Principles and Methods (handbook; read 2026-11-07). Buffer volumes in CV to transfer methods between column sizes; scale-up at the same ratio of gradient volume to column volume; long, shallow versus short, steep gradients; lowering the load when gradients are shortened; the shortest flow path between mixer and column; equilibration until outlet pH and conductivity are stable.
• Yamamoto, Nomura and Sano (1987), Resolution of proteins in linear gradient elution ion-exchange and hydrophobic interaction chromatography, Journal of Chromatography 409, 101–110. Rs ∝ [(column length × diffusivity) / (gradient slope × column volume × velocity × particle diameter²)]^1/2, its validity range and its use for scale-up. Cited from the abstract.
• Itoh, Yoshimoto and Yamamoto (2018), Retention mechanism of proteins in hydroxyapatite chromatography, Current Protein & Peptide Science 20, 75–81 (online 2018, volume dated 2019). Writes the normalized gradient slope as GH = g(V_t − V₀), the salt slope per mL times a column volume. Open access, CC BY-NC; cited for facts only.
• Keulen et al. (2024), From protein structure to an optimized chromatographic capture step using multiscale modeling, Biotechnology Progress 41, e3505 (volume dated 2025). Dwell and dead volume on an ÄKTA system, measured with salt pulses and subtracted from linear-gradient retention volumes; salt enters the pores, so it measures total column porosity. Open access, CC BY-NC-ND; cited for facts only.

Volumes, times, slopes and buffer use are arithmetic; the √2 example and the dwell fractions are ours. The page text is original. Nothing you enter is saved or sent.