# Simulation of column chromatography

## Authorship

• Fabiola Pagliero. Professor of Cell and Molecular Biology at La Pampa National University (Santa Rosa, Argentina)
• Angel Herráez. Professor of Biochemistry and Molecular Biology, Dept. of Systems Biology, University of Alcalá (Alcalá de Henares, Spain)

This project was developed during F.P.'s stay at UAH, financed by the Ministry of Education of the Argentine Republic, “Program for teaching mobility in Madrid”, January-February 2015.

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## Licence

This work, “Simulation of column chromatography”, created by Fabiola Pagliero and Angel Herráez, is offered under a Creative Commons Attribution-NonCommercial-ShareAlike Licence.

## Citation

If you use this application and wish to cite it, please use this format:

• Fabiola Pagliero and Angel Herráez. Simulation of column chromatography [on line]. Available at http://biomodel.uah.es/lab/cromat/  Accessed on day/month/year.

# How the simulation of column chromatography for proteins was made

## Source of data

Values of molecular mass, isoelectric point, etc. for proteins were collected from several accredited sources. Data for proteins.

## Size exclusion

Mobility is characterised by K (or K_(av)). The higher K, the larger elution volume, slower progress through the column (smaller molecules).

 K = (V_e - V_0) / ( V_h ) V_e = elution volume of each protein V_0 = exclusion volume or void volume V_h = volume of pores in the matrix
To calculate the velocity of progress through the column (v):
• flow, F = V_e / t_e = V_0 / t_0 = ( V_0 + V_h ) / t_max  ;
• V_e = V_0 ⇒  maximum velocity = L / t_0 = L * F / V_0  ; [L = length of the column]
• V_e = V_0 + V_h ⇒  minimum velocity = L / t_max = L * F / ( V_0 + V_h )  ;
• we assume:
V_e = V_0 + V_h * ( v_max - v) / ( v_max - v_min )
then:
v = v_max - ( V_e - V_0 ) / V_h * (v_max - v_min ) = v_max - K * (v_max - v_min )

Certain values are supposed for V_0 and V_h and for the flow F; the value of L is based on the drawing (px)
We calculate v_max and v_min for each protein; from them, with the reference K, we calculate the velocity of progress of each band along the column.

The value of K is calculated from the empirical straight line obtained with standards, K = a + b * ln(M_r) for each chromatographic matrix.

## Ion exchange

Mobility depends on the difference between pI and pH, in a nonlinear way.

 ΔQ=pI-pH resin with ⊖ charge cation exchange resin with ⊕ charge anion exchange ΔQ > 0 protein⊕ is retained, very low v falls through, high v ΔQ < 0 protein⊖ falls through, high v is retained, very low v

Dependency between ΔQ and the velocity of progress v was modelled empirically using the following logistic equation:
v = v_min + v_max / ( 1 + 10^(-p * ΔQ * s) )   (where s is the sign of the charge in the resin)
and a value of 0.3 was chosen for the slope parameter p after visual inspection of the separation achieved in the simulator.

For the basal value we chose v_min = 0.2 * flow (both are empirical);
and for the velocity of the chromatographic front, v_max = ( L * \text{flow} ) / ( V_0 + V_h )

## Affinity

The same method as for ion exchange is used, except that instead of ΔQ a value of 20 is assigned to proteins that are not retained at all, −20 for those with high affinity, and intermediate values for weaker affinities. The slope parameter p was empirically set at 0.1 and s is not used in this case.

## Interface

The simulation is built with HTML5 and JavaScript. The chromatogram is plotted using the Flot and jQuery libraries.