| Component | Elutes at (CV) | Elution salt (mM) | Peak width σ (CV) | In pool |
|---|
Each protein binds through a number of charged contacts. The stoichiometric displacement model gives k′ = (Ce/C)Z, where C is the salt concentration, Ce is the salt at which the protein is half released and Z is the number of charges used to bind. Because Z is an exponent, a small rise in salt collapses retention. As the gradient sweeps up the bed, each protein waits until the salt reaches its own Ce, then leaves. That converts a difference in binding strength into a difference in elution volume.
Resolution is peak separation divided by combined peak width. A shallow gradient spreads the salt change over more column volumes, so two proteins with slightly different Ce values elute further apart. The peaks do not widen in proportion, because a gradient also focuses each band: the rear of the band sits in higher salt, moves faster and catches up. The cost is buffer and time, which is why fast methods co-elute contaminants. Drag the gradient volume slider to 3 CV and watch the peaks merge.
Rs = (tR2 − tR1) / (2(σ1 + σ2)). Rs = 1.5 is baseline separation: about 99.7% of each peak clears the other, so a cut between them is essentially pure. Rs = 1.0 leaves roughly 2% overlap and forces a purity-versus-yield choice. Below about 0.6 the peaks merge into one envelope and no cut point recovers both.
Plate height follows the Knox reduced-plate-height equation h = Aν1/3 + B/ν + Cν, with h = H/dp and ν = u·dp/Dm. At process velocities the C term dominates, and it is intraparticle mass transfer resistance: a bigger bead is a longer diffusion path, and faster flow gives less time to equilibrate. Since N = L/H and peak width scales as 1/√N, both levers fatten the peak. This is why polishing steps use small beads and capture steps do not.
Bind-elute holds the product on the resin, washes contaminants away and releases the product with a gradient or step. Capacity limits the batch, but the product is concentrated and the purification factor is high. Flow-through picks conditions where the product does not bind at all: AEX polishing of a monoclonal antibody is the classic case, where the antibody passes through while DNA, HCP and endotoxin bind. Loading per litre of resin is far higher because capacity is set by the contaminants.
A qualification HETP test uses a small tracer such as acetone, whose free diffusion coefficient is about 1×10−5 cm²/s. A monoclonal antibody diffuses roughly fifteen times slower, near 5×10−7 cm²/s, which raises the reduced velocity and blows up the C term. The same column that gives several hundred plates on acetone gives only tens of plates for a protein at process flow. That is intraparticle mass transfer, not a packing fault, and it is why process peaks are far broader than analytical HPLC peaks.
The collection window is set by a threshold on the detector signal. The simulator finds the product's apex, walks outward until the total signal drops below that fraction of the apex on each side, then integrates every component across the window. Purity is product mass in the window over total mass in the window; yield is product mass in the window over product mass loaded. Raise the threshold and the window narrows: purity rises, yield falls. Choosing where on that curve to sit is the pooling strategy.