Peak compression factor of proteins

Abstract

An experimental protocol is proposed in order to measure with accuracy and precision the band compression factor $G_{12}^2$ of a protein in gradient RPLC. Extra-column contributions to bandwidth and the dependency of both the retention factor and the reduced height equivalent to a theoretical plate (HETP) on the mobile phase composition were taken into account. The band compression factor of a small protein (insulin, MW $=5.8$ kDa) was measured on a $2.1\text{mm}\times 50$ mm column packed with 1.7 $\mu$m C₄-bonded bridged ethylsiloxane BEH-silica particles, for 1 $\mu$L samples of dilute insulin solution ($<0.05$ g/L). A linear gradient profile of acetonitrile (25–28% acetonitrile in water containing 0.1% trifluoroacetic acid) was applied during three different gradient times (5, 12.5, and 20 min). The mobile phase flow rate was set at 0.20 mL/min in order to avoid heat friction effects (maximum column inlet pressure 180 bar).

The band compression factor of insulin is defined as the ratio of the experimental space band variance measured under gradient conditions to the reference space band variance, which would be observed if no thermodynamic compression would take place during gradient elution. It was 0.56, 0.71, and 0.76 with gradient times of 5, 12.5, and 20 min, respectively. These factors are 20–30% smaller than the theoretical band compression factors (0.79, 0.89, and 0.93) calculated from an equation derived from the well-known Poppe equation, later extended to any retention models and columns whose HETP depends on the mobile phase composition. This difference is explained in part by the omission in the model of the effect of the pressure gradient on the local retention factor of insulin during gradient elution. A much better agreement is obtained for insulin when this effect is taken into account. For lower molecular weight compounds, the pressure gradient has little effect but the finite retention of acetonitrile causes a distortion of the gradient shape during the migration of its breakthrough front along the column. This phenomenon should be taken into account in the theoretical models.

Introduction

Gradient elution is a successful chromatographic mode because it considerably shortens analysis times and allows single run separations of most complex mixtures containing molecules having a wide range of molecular weights, from less than 100 (small molecules) to a million Daltons (macro biomolecules). So, it provides large increases in the peak capacity usually observed under isocratic conditions [1]. The theory of gradient elution chromatography has since long been reviewed in several monographs [2], [3]. Its practical aspects for practitioners of liquid chromatography have recently been illustrated [4].

In addition to a reduction in analysis time and to the associated reduction in the width of eluted peaks, gradient elution also provides narrower band widths due to thermodynamic compression of bands. Because the rear part of the sample band constantly moves faster than its front in gradient elution analyses, both peak boundaries tend to merge. Were actual columns to be ideal (infinite efficiency), the rear and front boundaries of a peak would eventually collapse, forming a $\delta$-Dirac peak at the column outlet [5]. Because real columns have a finite efficiency, the band keeps broadening during gradient elution, due to axial dispersion. Thermodynamic peak compression and axial dispersion act in opposite directions [6].

The notion of peak compression has so far attracted only limited attention in the chromatographic community [7], [8]. Literature data comfort the idea that peak compression is negligible and that it does not affect calculations of peak capacity. This lack of interest is deeply related to the difficulties encountered in measuring band compression factors, which is rarely handled properly. Significant extra-column contributions, complex retention behavior differing often from the LSS model, and the dependence of the column HETP on the mobile phase composition are important, practical issues that have not received much attention in the literature. We need to define a rigorous protocol that would allow the assessment of band compression factors with accuracy and precision.

The band compression factor is the ratio of the actual band variance observed in gradient elution to the value expected under the same eluent conditions if there were no thermodynamic compression, i.e., if the rear of the band were to migrate at the same velocity as its front [9]. This theoretical band variance cannot be measured unless the column HETP remains independent of the mobile phase composition. Poppe et al. [6] modeled the evolution of the variance of the chromatographic zone during its migration along the column by assuming that (1) the linear solvent strength model (LSSM) applies; (2) the gradient shape does not change while it migrates along the column; (3) the strong solvent breakthrough moves at the velocity of an unretained compound; (4) the relative retention factor of concentrations relative to that at the band center varies linearly through the peak width; and (5) the reduced HETP, $h$, does not depend on the mobile phase composition. The resulting Poppe equation is found in most current textbooks on gradient elution in LC. Some variations of this equation were derived in order to account for more complex situations, such as when the retention of the organic modifier is finite (hence the speed of the gradient breakthrough front is lower than that of an unretained compound [9]); the LSS model does not apply; the HETP depends on the mobile phase composition; and the relative retention factor of concentrations relative to that at the band center varies in a parabolic manner across the peak width [10].

However, a clear experimental protocol allowing the measurement of the peak compression factor in liquid chromatography is still missing. The accurate and precise measurement of this parameter is not straightforward [11], especially for high molecular weight compounds the retention factors of which are most sensitive to small changes in the mobile phase composition and in the local pressure, pressure which decreases along the column. To our knowledge, the band compression factor of proteins has never been measured correctly. A well-defined experimental protocol that should allow the accurate measurements of band compression factors, which would be reproducible in different laboratories is needed. Extra-column volume contributions and the dependence of $k^{\prime }$ and $h$ versus $\varphi$ must be carefully measured in order to determine the reference band variance under the absence of thermodynamic compression.

In this work, we propose an experimental protocol that allows the accurate and precise measurement of the band compression factor of any compound, either low- or high-molecular weight ones. We illustrate this method by applying it to a large biomolecule, the protein insulin, and to a small molecule, naphtho[2,3-a]pyrene. The mobile phase was a mixture of acetonitrile and water containing 0.1% TFA (v/v). The RPLC column was packed with 1.7 $\mu$m particles of C₄-bonded bridged ethylsiloxane BEH-silica (Waters, Mildford, USA), designed to elute large molecule analytes (300 Å pore size). The experimental band compression factors were measured carefully and are compared to recently derived theoretical expressions.