The physical sense of simulation models of liquid chromatography: propagation through a grid or solution of the mass balance equation

Abstract

Two distinctly different approaches have been used to simulate the movement of bands through a chromatographic column. One example of the first approach Is the Craig distribution model, which replaces the continuous column with a specific number of discrete equilibration processes. Thus It Introduces the concept of (theoretical) plates Into chromatography, but Is not able to explain satisfactorily their significance. The second approach is based on the mass balance equation which can be Integrated numerically over time and space to give the elution profile. This calculation can be performed by using finite difference methods to extrapolate from the concentration value at a given time and position In the column to the next value. In this paper we discuss the physical meaning of the numerical Integration process followed by the finite difference methods. We show that both approaches are equivalent and that the band broadening produced by the different methods, due to "numerical diffusion", can be explained similarly. Since this effect Is sufficiently well-known now, we can introduce a variable amount of additional diffusion and thereby control the overall dispersion.

Intermolecular interactions between the SH3 domain and the proline‐rich TH region of Bruton's tyrosine kinase

“…Here we ¢nd that this is not the case for Btk SH3. Instead, GPC elution pro¢les, intermolecular NMR cross-relaxation and 15 N NMR relaxation measurements are consistent with a monomer^dimer equilibrium with a dissociation constant on the order of 60 WM. In addition, comparison of chemical shifts and resonance linewidths as a function of concentration with those observed in TH-peptide titrations indicate that peptide binding competes with dimerization.…”

“…For the N-terminally extended SH3 (PRR-SH3), the DNA fragment encoding residues 178^275 of human Btk was ampli¢ed by PCR and the fragment was cloned into the pGEX-4T-3 vector (Amersham Pharmacia Biotech, Sweden) for expression in Escherichia coli BL21 (DE3). The expression and puri¢ca-tion of unlabeled, 15 N-labeled, and 13 C, 15 N-labeled Btk PRR-SH3 and SH3 for the present study was essentially carried out as reported previously [14]. In addition, puri¢ed protein samples were heat-stabilized in Eppendorf tubes at 65³C for 30 min immediately followed by cooling to 4³C and centrifugation at 21 000Ug for 10 min.…”

“…The retention behavior was characterized by an average partition coe¤-cient c av = (V e 3V M )/V S , where V e is the elution volume corresponding to the maximum of the elution pro¢le, V M is the void volume of the mobile phase and V S is the volume available to a totally included solute. The suitability of the selected column for separation in a mo- The non-linear retention behavior of PRR-SH3 at various concentrations was modeled using the Craig method of propagating the injected volume through a grid of theoretical plates [15]. The retention at each plate along the grid was calculated from the e¡ective concentration-dependent partition coe¤cient for a monomer^dimer equilibrium given by c eff = c 2 +K(c 1 3c 2 ), where c 1 and c 2 represent partition coe¤cients for monomeric and dimeric PRR-SH3, respectively.…”

“…Two-dimensional 1 H-15 N HSQC and three-dimensional NOESY-HSQC experiments were carried out and processed using conventional methods [16]. Intermolecular cross-relaxation was detected in two-dimensional F 1 -13 C-edited,F 2 -13 C, 15 N-¢ltered NOESY experiments (following the principles described in [17]) recorded at 45³C on a sample containing a mixture of unlabeled and doubly labeled PRR-SH3 at a total concentration of 2.5 mM. The 13 C transmitter o¡-set and refocusing delays for the purge scheme were set to optimize purging of either aliphatic or aromatic 13 C-bound proton resonances.…”

“…Longitudinal and transverse relaxation rates, R 1 and R 2 , of backbone 15 N nuclei in well structured regions of the SH3 domain were measured as reported previously [14]. The overall rotation correlation time, d c , was estimated from d c = 1/g 0 (2GR 2 /R 1 f) 1a2 where g 0 is the 15 N Larmor frequency and the GR 2 /R 1 f average was measured for residues in stable secondary structure elements within the SH3 domain [16].…”