High peak capacity separations of peptides in reversed-phase gradient elution liquid chromatography on columns packed with porous shell particles

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Journal of Chromatography A, 1176 (2007) 206–216

High peak capacity separations of peptides in reversed-phase gradient elution liquid chromatography on columns packed with porous shell particles Nicola Marchetti a,b , Georges Guiochon a,b,∗ a

Department of Chemistry, The University of Tennessee, Knoxville, TN 37996-1600, USA Division of Chemical Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, USA

b

Received 13 September 2007; received in revised form 31 October 2007; accepted 5 November 2007 Available online 12 November 2007

Abstract The performance of 5 and 15 cm long columns packed with shell particles (Halo, AMT) is compared in gradient elution separations of the tryptic digests of myoglobin and bovine serum albumin. The influences of the temperature and the mobile phase flow rate on the column efficiency for two peptides are discussed. The influences of this flow rate, of the temperature, and of the gradient slopes on the peak capacities are also considered. Peak capacities in excess of 400 were achieved in 6 h with the longer column. Peak capacities of 200 could be achieved in 30 min with the shorter column. © 2007 Elsevier B.V. All rights reserved. Keywords: Column performance; BSA trypsin digest; Gradient elution; Myoglobin trypsin digest; Peak capacity; Shell particles

1. Introduction Recent publications [1–3] investigated the general chromatographic properties of a new packing material [4], Halo (Advanced Materials Technology, Wilmington, DE, USA), made with fine shell particles. These particles have a solid silica core coated with a shell of porous silica. Since the core radius and the shell thickness are close (0.85 and 0.5 ␮m, respectively), the volume fraction of the particle core is small and the surface area of the C18 bonded silica is comparable in this new type of column to that observed in the columns packed with classical porous silica particles [3]. Accordingly, the retention factors of analytes and their saturation capacities are in the same range on this new material as they are for conventional RPLC columns and the composition of the mobile phases needed for their elution is very similar. While retention patterns and separation factors are similar on Halo columns and on columns packed with conventional silica B particles derivatized with the same reagents, columns packed with this new material have an unusually high

∗

Corresponding author. Tel.: +1 865 974 0733; fax: +1 865 974 2667. E-mail address: [email protected] (G. Guiochon).

0021-9673/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2007.11.012

efficiency that is characterized by extremely low values of the A term of their van Deemter plate height equation [2,3]. They also have a rather high external porosity and a low value of the B term of their plate height equation [3]. Halo columns provide fast separations of mixtures of small molecular weight compounds [2,4], although they cannot be operated at reduced velocities in excess of ca. 10, due to the small average size of their particles (2.7 ␮m) and the low permeability of the columns packed with these particles [3]. Because the average size of the mesopores in the porous silica shell is only ca. 9 nm, Halo columns are not suitable for the separation of proteins [3,5]. However, in spite of their small particle diameter, the Halo columns could be operated at relatively high reduced velocities for peptides that are in the 0.5–2 kDa molecular weight range. Accordingly, they can provide extremely fast elution of these peptides and rapid separations of peptide mixtures, particularly of peptide digests [3,6]. Peak capacities exceeding 150 were achieved in less than 5 min at 60 ◦ C and peak capacities larger than 250 in 30 min with a 5 cm long column [6]. The goal of this paper is to investigate in detail the behavior of Halo columns under gradient elution conditions, their potential use in the separation of peptide mixtures, and the estimates of the complexity of complex mixtures that the analysis of the

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chromatograms recorded may provide. Numerous publications have already discussed the analysis of complex mixtures of peptides, particularly those obtained by the tryptic digestion of pure proteins or of protein mixtures [7–10]. However, the purpose of this paper is not a comparison of the performance of Halo columns and those investigated in these earlier publications.

Gradient elution is based on the dramatic influence of the composition of the mobile phase on the retention volumes of most compounds. Since most complex mixtures contain components that have a wide range of retention factors, best separations are achieved by increasing progressively the concentration of the strong eluent in the mobile phase [11,12]. 2.1. Retention under gradient elution conditions In reversed phase HPLC, the retention factor of a compound is related to the concentration of the organic modifier in the mobile phase. In most cases, a quadratic equation gives satisfactory results and the retention factor is related to the concentration of organic modifier through: log k (φ) = log k0 − Sφ + bφ2

(1)

In this equation, k (φ) is the isocratic retention factor of the compound considered in a mobile phase having a modifier concentration φ and k0 the isocratic retention factor of that compound in the pure weak solvent. S and b are numerical coefficients, which are characteristics of the compound studied and of the phase system used. In many cases, however, a linear relationship (b = 0) is sufficient (linear solvent strength model or LSS). The coefficient S increases rapidly with increasing molecular weight of the compound considered [12,13]. Under gradient elution conditions, it is possible to define an apparent gradient retention factor, kG , as kG =

tR − t0 t0

(2)

where tR and t0 are the retention time of the compound considered and the hold-up time of the column, respectively. It was shown that, within the range of applicability of the LSS model, this gradient retention factor is related to the experimental conditions through the following equation [11,12]  kG =

1 log(1 + Gk0 ) G

(3)

whereG is the intrinsic gradient slope, G=S

φt0 φV0 =S tG F v tG

its elution, ke . This retention factor increases with increasing gradient slope [14]. Under optimum conditions, it is of the order of 3. For long analyses with large changes in the concentration of the strong solvent, and except for the early eluted peaks, it is given by [13]: ke =

2. Theory

(4)

where φ is the difference between the initial and the final concentrations of the strong solvent during the gradient run, tG is the duration of this gradient run, Fv is the mobile phase flow rate, and V0 is the column hold-up volume. Another important characteristics of a gradient run is the retention factor of the compound considered at the moment of

207

tG 1 = S t0 φ G

(5)

2.2. Elution band width and column peak capacity Horv´ath and Lipsky assumed that the widths of the peaks obtained during a gradient run are constant and showed that the peak capacity is then given by [15] √   N tR,G,n −1 (6) nc = 1 + 4 tR,G,1 where tR,G,n and tR,G,1 are the retention times of the last and the first components of an n-component mixture. Actually, Eq. (6) is only approximate since the width of a peak depends on the molecular diffusivity of the corresponding compound and this diffusivity decreases with increasing molecular weight while retention tends to increase with increasing molecular weight, at least in RPLC. However, and particularly if the column is operated at a flow velocity that is close to the optimum value for maximum efficiency, the approximation is satisfactory [11–13,15,16]. Eq. (6) suggests that the peak capacity in gradient elution increases linearly with increasing analysis time. This result is valid, however, only if the slope of the gradient initially selected is large. It is not possible to increase indefinitely the peak capacity of a column for a complex mixture merely by slowing down the gradient to infinitely small values. During a linear gradient, the band width remains nearly constant and equal to [13]    H V0 (1 + ke )t0 tG √ σt,G = + = (7) L Fv Sδφ N For a given column, Eqs. (5) and (7) show that increasing the gradient duration at constant gradient amplitude increases ke , hence σt,G (because S is a physico-chemical characteristic of the compound studied and t0 depends only on the mobile phase flow rate). Thus, the resolution of the sample components and nc tends toward limits when tG is increased indefinitely (see later, Fig. 6). As a consequence, Schoenmakers et al. [17] showed that the peak capacity under gradient elution conditions can be approximated by √ tG tG N (8) = nc = 4σt,G 4t0 (1 + ke )  In the particular case √ in which tG ≈ 10t0 , and ke ≈ 3, the peak capacity is about N/1.6 [17]. In this work as in many studies on the analysis of complex mixtures of peptides, however, tG  10tm , as will be seen later. Neue has shown that the peak capacity in a retention window characterized by a (wide) range of strong solvent concentration,

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φ, is given by [13] √ (G + 1) eS φ − 1 N nc = 1 + ln 4(G + 1) G

(9)

For the separation of large molecules, for which S is relatively large, and for gradients that stretch over a large range of solvent concentration, the product S φ is huge compared to unity, (G + 1)/G is nearly unity and this equation simplifies to [13]: √ N S φ nc = 1 + (10) 4 G+1 Eq. (10) gives the peak capacity offered by the column when it is operated with a concentration gradient of amplitude φ. However, in order to benefit from this possibility, the analyst must be able to spread the elution of the different components of the analyzed mixture over the entire separation space that corresponds to this gradient. If the last sample component to be eluted exits the column before the end of the gradient, the corresponding fraction of the separation space is wasted and the peak capacity available for the separation is reduced. For each mixture, there is a maximum peak capacity that is given by the equation: √ N ln k0,l nc = 1 + (11) 4 G+1 where k0,l is the retention factor of the last eluted component of the mixture at the beginning of the gradient run. Finally, the second Eq. (7) shows that the flow rate affects the band width in gradient elution for two reasons. First, it does so because the HETP depends on the flow rate through the plate height equation, as it does under isocratic conditions. Second, the flow rate also affects the band width through the term V0 /Fv that decreases with increasing flow rate. This would explain the trends that are seen in Fig. 5 and are discussed later. 2.3. Measurements of peak capacities As it was introduced by other authors [18] and accepted in previous works, the term conditional peak capacity, noted n∗c , will be used to identify values as obtained by specific experimental conditions. It is calculated by the following equation n∗c =

tR,n − tR,1 W

[6] we used the conditional peak capacity as a measure of the column performance. In a recent study, Wang et al. [20] used a synthetic peptide mixture to obtain a reliable, precise estimate of the average peak width. We found that it is difficult to make consistently precise, reliable, and comparable measurements of n∗c from different highly complex chromatograms (see later). Partial or complete peak overlapping, occasional overloading of some compounds can easily influence the peak capacity estimate. This is especially true when, due to significant changes in the gradient conditions, the elution orders of numerous compounds are scrambled and the chromatographic bands cannot be identified and followed from one chromatogram to another (as illustrated elsewhere [21]). In this work, we used the tryptic digests of myoglobin and BSA prepared under standard conditions (see Section 3) and analyzed them under the same gradient conditions (see later). Because the former mixture is markedly less complex than the latter but its different components are eluted practically within the same retention range as those of the BSA digest (see later in Section , the results obtained with the long Halo column, and Fig. 8 a and b), the analysis of the chromatogram of myoglobin digest provides a more reliable measurement of the average peak width under a given set of experimental conditions, hence a more accurate estimate of the peak capacity. These values were used to calculate n∗c for the corresponding BSA digest separations. 3. Experimental 3.1. Chemicals Bovine serum albumin (BSA), myoglobin (from bovine heart), trypsin (TPCK treated), dithiothreitol (DTT), iodoacetamide (IAA), and tris(hydroxymethyl)aminomethane (TRIS base) were purchased from Sigma (St. Louis, MO, USA). Acetonitrile (ACN) and H2 O, both HPLC grade, urea and trifluoroacetic acid (TFA) were from Fisher Scientific (Pittsburgh, PA, USA). Kallidin and bradykinin were from American Peptides Co. Inc. (Sunnyvale, CA, USA). Concentrated HCl was from Mallinckrodt (Phillipsburg, NJ, USA). The mobile phases used were solutions of 0.1% (v/v) TFA in pure H2 O and 0.1% (v/v) TFA in 50/50 ACN/H2 O. These solutions were mixed through the solvent delivery system, according to the gradient program desired.

(12)

where tR,n indicates the retention time of the last eluted chromatographic band, while tR,1 is the first eluted one and W is the average width of the components eluted during this time window. In Eq. (12) the numerator is also referred to as the experimental retention window. Changes in separation conditions used for gradient elution can strongly modify both the width of the separation space and the relative retention of the mixture components (particularly that of the first and last eluted components, that define the useful width of the separation space) [19]. Moreover, the average band width depends also on the gradient duration and the mobile phase velocity (see later). These are the main reasons why in the present and previous works

3.2. HPLC instrumentation The chromatographic experiments were conducted using an Agilent 1100 HPLC (Agilent Technologies, Palo Alto, CA) equipped with a degasser, an autosampler, a binary pump, a column compartment and a photodiode-array UV–vis detector (cell volume, 13 ␮L; optical path length, 10 mm). This instrument has a data station that controls its operating parameters, runs the desired programs, and records the detector signal. The detector signal was recorded with a sampling rate of 10 Hz. The wavelength used for recording the chromatograms of peptide mixtures was 210 nm. The instrument dwell volume was 0.74 mL and the extra-column volume was 0.035 mL. The pump

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Fig. 1. Van Deemter plots for Kallidin (a and c) and Bradykinin (b and d) at T = 20 ◦ C () and T = 60 ◦ C (䊉) for 5 cm (a and b) and 15 cm (c and d) long Halo columns.

flow path included an in-line high pressure solvent filter (0.5 ␮m frit porosity), providing also for the solvent channels mixing, which was connected through two 35 mm × 0.12 mm ID capillaries. The same kind of tubing was used to connect the column inlet and outlet to the column compartment and to the detector (total lenght of 250 mm), respectively. Connections between autosampler, pump and column compartment were made via 600 mm × 0.17 mm ID and 180 mm × 0.17 mm ID capillaries. The measurements were carried out with the column kept at constant temperatures of either 20 ± 1 ◦ C or 60 ± 2 ◦ C. 3.3. Columns This work was undertaken using columns packed with a new type of C18 -bonded silica particles, the Halo shell particles [2–4]. The columns used were two Halo columns (Advanced Materials Technology, Wilmington, DE), 50 mm × 4.6 mm and 150 × 4.6 mm, both packed with shell particles having an average diameter of 2.7 ␮m (standard deviation 0.125 ␮m [3]) and a shell thickness of 0.5 ␮m. The porous shells of these particles have an average mesopore size of 9 nm prior to the bonding of the C18 alkyl chains. Column hold-up volumes were measured by pycnometry and were found to be 0.455 and 1.279 mL for the 5 cm and the 15 cm long column, respectively. 3.4. Protein tryptic digest procedures The procedures used in this study to prepare the samples were modified from an in-solution digestion protocol obtained

from the Proteomics Center at Stony Brook (New York State University, NY). Fully detailed procedure was already described elsewhere [6]. 3.5. Experimental conditions Mobile phase for the acquisition of the Van Deemter HETP data were obtained by mixing through the solvent delivery system 0.1% (v/v) solutions of TFA in pure H2 O and ACN. The mobile phase composition was 80/20 H2 O/ACN. The mobile phases for all the gradient elution experiments were solutions of 0.1% (v/v) TFA in pure H2 O and 0.1% (v/v) TFA in 50/50 ACN/H2 O. These solutions were mixed through the solvent delivery system, according to the gradient program desired. Four series of chromatographic runs were carried out under gradient elution conditions with the 15 cm long Halo column. They were done at different flow rates, with increasing gradient durations. The initial and final concentrations of ACN were 5 and 36%, respectively (i.e., φ = 0.31). The gradient time was kept the same for each series. The constant flow rates in each of these series were 0.3, 0.5, 0.7 and 0.9 mL/min. The gradient times were 30, 90, 120, 150, 180, 240 and 360 min at each flow rate. These series of measurements were done at temperatures of 20 and 60 ◦ C. The same set of measurements and separations was made with a 5 cm long column packed with the same Halo particles, operated at the same flow rates and the same initial and final concentrations of ACN, as reported above for the 15 cm long column. The gradient times were adjusted according to the ratio of the two column hold-up volumes, in order to keep constant

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Table 1 Best Van Deemter parameters accounting for HETP data of Kallidin and Bradykinin on the two Halo columns at high and low temperatures Kallidin L = 5 cm

A (cm) B (cm2 /s) C (s)

L = 15 cm

20 ◦ C

60 ◦ C

20 ◦ C

60 ◦ C

3.92 × 10−5 3.91 × 10−6 3.82 × 10−2

2.08 × 10−4 4.92 × 10−6 5.07 × 10−3

9.21 × 10−4 8.62 × 10−7 1.63 × 10−2

2.48 × 10−4 3.32 × 10−6 6.61 × 10−3

Bradykinin L = 5 cm

A (cm) B (cm2 /s) C (s)

L = 15 cm

20 ◦ C

60 ◦ C

20 ◦ C

60 ◦ C

8.79 × 10−5 1.45 × 10−6 4.13 × 10−2

1.82 × 10−4 5.62 × 10−6 5.11 × 10−3

8.80 × 10−4 7.76 × 10−7 7.74 × 10−2

2.64 × 10−4 3.56 × 10−6 6.48 × 10−3

the gradient slope. The corresponding gradient times were: 10.7, 21.3, 32, 42.7, 53.4, 64, 85.4 and 128.1 min. 4. Results and discussion 4.1. Column efficiency, peak symmetry, and peak capacity The efficiencies of the two columns used in this work were measured at the temperatures of 20 ◦ C and 60 ◦ C by means of Van Deemter plots. A small amount (0.1 ␮g) of two peptides, Kallidin (Lys-Arg-Pro-Pro-Gly-Phe-Ser-Pro-Phe-Arg, MW = 1205 Da) and Bradykinin (Arg-Pro-Pro-Gly-Phe-SerPro-Phe-Arg, MW = 1059 Da) was injected to acquire the efficiency data. These peptides were eluted with a mobile phase composition of 80/20 (v/v) water/acetonitrile containing 0.1% (v/v) of TFA. The retention factors were measured at a flow rate of 1 mL/min. They were 3.70 and 5.09 for Kallidin and Bradykinin, respectively, at 20 ◦ C, and 1.41 and 2.14 at 60 ◦ C, on the short Halo column (5 cm). On the long column (15 cm) the retention factors were 3.02 and 4.27 for Kallidin and Bradykinin, respectively, at 20 ◦ C and 1.12 and 1.74 at 60 ◦ C. The difference between the values of the retention factors of these two basic peptides on the two columns might be due to the 5 cm column coming from the very first lot of production of Halo while the long column comes from a later lot. Fig. 1 a–d shows the reduced HETPs (h = H/dp ) versus the superficial mobile phase velocity (us = Fv /(πre2 )), with H = A + B/us + Cus , dp the particle size and re the inner column radius. In Table 1 the best fitting parameters are reported. For each measurement of the column HETP, the inlet pressure was also measured. Fig. 2 shows plots of the pressure drop versus the flow rate for the two columns, at the two temperatures. The permeability of the two columns are close, although that of the 5 cm long column that has a slightly lower external porosity than the 15 cm long column [2,3] is also lower. The two columns display a very close efficiency (h = 2) at the highest temperature (䊉 symbols) with the optimum mobile phase velocity between 0.2 and 0.35 mm/s. Data are

Fig. 2. Comparison between the pressure drops (corrected for the extra-column contribution) measured on the two Halo columns ((䊉) and () for 15 cm; () and ( ) for 5 cm) at T = 20 ◦ C (() and ( )) and T = 60 ◦ C ((䊉) and ()).

more scattered, particularly for the shorter column, at the lower temperature ( symbols) and the measurements are consequently less precise. The overall trend shows a higher value of the reduced HETP, between 3 and 4.3 for Kallidin and 5 for Bradykinin, and an optimum velocity always below 0.1 mm/s. This low efficiency at the lower temperature is due to a significant tailing of the peaks of these basic peptides at 20 ◦ C, tailing that disappears at 60 ◦ C. Insets in Fig. 1 a–d enhances the HETP plots in the region of maximum efficiency. The band widths are small, due to the high column efficiency and this explains in part the limited accuracy of the data. Note also that it is not unusual that the efficiency of short and long columns packed with the same material are somewhat different. The packing density is different and this may explain different values of the A term of the plate height equation [22]. The column efficiency was also measured as a function of the amount of Kallidin injected at fixed flow rate. This was done at the higher and lower flow rate limits at which the gradient separations were undertaken (see following sections), 0.3 and

Fig. 3. Plot of the apparent column efficiency against the injected mass of Kallidin at 20 ◦ C on the 15 cm long Halo column: () Fv = 0.3 mL/min and ( ) Fv = 0.9 mL/min.

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of Kallidin values. However, it seems that both the width and height of the sigmoid transition have comparable values. The effect can be probably addressed to the large extent of the dilution process occurring at higher flow rate, which causes the curve shifting to the right. Finally, using Eqs. (5) and (7), we calculated that the retention factor at elution of the peaks is ke = 16.7 for a 750 min gradient run at a flow rate Fv = 0.3 mL/min (hence, t0 = 4.26 min), at which flow rate the efficiency of the 15 cm long column is 30140 theoretical plates. This gives a peak capacity of 431. This value is to be compared to the experimental value derived from the width of the separation space and the average width of the isolated peaks of the myoglobin digest, 434. This shows that the equation of Schoenmakers et al. [17] is an excellent approximation. 4.2. Results obtained with the long Halo column Fig. 4 a and b shows the variation of the width of the separation window of reparation time range with the flow rate, Fv , at increasing gradient times, tG , and at 20 and 60 ◦ C, respectively. The separation window is the difference between the retention

Fig. 4. Dependence of the retention window on the flow rate for increasing gradient times at (a) T = 20 ◦ C and (b) T = 60 ◦ C. tG = 30 min (䊉), 60 min (), 90 min (), 120 min (), 150 min (), 180 min (), 240 min ( ) and 360 min (); L = 15 cm.

0.9 mL/min, respectively. The mobile phase composition used for this set of experiments was the same as used before for acquiring the HETP plots. The theoretical plate number was calculated for each data point by means of the half width at half height method. Then, each value was normalized to the theoretcal plate number corresponding to the lower amount injected (N0 ). Fig. 3 shows the results obtained at the temperature of 20 ◦ C. Thexaxis is a logarithmic scale. The open circle symbols refer to the lower flow rate (0.3 mL/min), while the others ( ) to the higher one (0.9 mL/min). An asymmetric sigmoid function was fitted to the experimental points. The log–normal function   a − ln(x/b) √ f (x) = erf (13) 2 c 2 was used for this purpose. In this equation, a, b, and c are empirical, numerical parameters while x is the amount of kallidin injected (in μg). Fitting curves are plotted as dashed lines in Fig. 3. The agreement between data points and the fitting curves is very good. The column efficiency related to the linear range (below 0.1 ␮g of mass injected) is in the order of 12460 and 5530 theoretical plates at 0.3 and 0.9 mL/min, respectively. The plot shows an efficiency drop at 0.3 mL/min occurring at lower mass

Fig. 5. Dependence of conditional peak capacity of the 15 cm Halo column on the mobile phase flow rate for increasing gradient times at T = 20 ◦ C (top) and T = 60 ◦ C (bottom). tG = 30 min (䊉), 60 min (), 90 min (), 120 min (), 150 min (), 180 min (), 240 min ( ) and 360 min ().

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times of the last (tR,n ) and the first (tR,1 ) eluted peptides. In practice, the first eluted peptides are small and they are hardly retained at all, so the separation window is almost equal to the retention time of the last eluted peptide, which is practically independent of the flow rate. The data points in Fig. 4 a and b, which were fitted to a linear, first order equation, show that the width of the retention window in time units decreases only slightly with increasing flow rate, at a rate that decreases in proportion to tG (see Fig. 4b), as indicated by the slopes of the fitting lines. The retention time of the last eluted peptide increases linearly with increasing gradient time at constant flow rate. The comparison of Fig. 4 a and b shows that the width of the retention window at constant gradient time is nearly independent of the temperature. Finally, it should be noted that the total elution of the sample components does not take place under gradient elution conditions when φ is too small. This was the case for a gradient run of 30 min. Fig. 5 a and b illustrates the dependence of the peak capacity on the mobile phase flow rate at 20 and 60 ◦ C, respectively. For low gradient time, there is a weak maximum of the peak capacity for a flow rate of about 0.5–0.6 mL/min. For long gradient time, the peak capacity decreases slowly with increasing flow rate. Fig. 6 a–d shows the relationships between the conditional peak capacity and the gradient time at the four mobile phase flow rates and at the two temperatures. The dashed lines are the best fit of the experimental data to Eqs. (11) and (10), which provide the best empirical estimates of the two parameters S and N. Since the flow rate does not affect the value of S, we averaged these values

Table 2 Best Van Deemter and S coefficients obtained by fitting the experimental data under gradient elution conditions (Figs. 9 and 12) to Eq. (10) L=5

S A (cm) B (cm2 /s) C (s)

L = 15

20 ◦ C

60 ◦ C

20 ◦ C

60 ◦ C

49 3.03 × 10−4 1.92 × 10−2 2.93 × 10−4

43 3.47 × 10−4 6.23 × 10−3 1.84 × 10−4

57 1.82 × 10−4 1.55 × 10−2 2.18 × 10−3

34 1.33 × 10−4 4.02 × 10−3 7.82 × 10−4

for each set. The gain in column efficiency associated with the increase in the column temperature from 20 to 60 ◦ C is modest. This does not seem to agree with previous results of Neue and Mazzeo [23]. However, these authors had considered the column peak capacity while we measured here the peak capacity that is available for the sample. When the column temperature changes, the width of the part of the separation space that is used by the sample varies. In the present case, it decreases and this loss compensates the gain actually achieved in column peak capacity, which explains our results. Our results are consistent with the theoretical results of Wang et al. [18] predicting that an increase of the column temperature results in a significant increase of the peak capacity only for very fast gradients but has little effect on the peak capacities that are obtained with slow gradients [18]. One of the aims of this work was to investigate the influence of the various operational variables on the peak capacity and to map the conditional experimental peak capacity to determine

Fig. 6. Effect of the temperature and the flow rate on the conditional peak capacity. T = 60 ◦ C (䊉), T = 20 ◦ C (), (a) 0.3 mL/min, (b) 0.5 mL/min, (c) 0.7 mL/min and (d) 0.9 mL/min. Other parameters: φ = 0.31 and L = 15 cm.

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Table 3 Reproducibility of Retention Times Flow rate (mL/min)

Component

RSD a (%)

RSD b (%)

0.3

First eluted Last eluted

0.21 0.07

1.73 0.97

0.9

First eluted Last eluted

0.14 0.01

2.5 0.97

a Calculated for three chromatograms of BSA tryptic digest recorded the same day. b Calculated for four chromatograms of BSA tryptic digest recorded on different days.

Fig. 7. Peak width distribution for separations of a Myoglobin tryptic digest sample at T = 60 ◦ C and gradient time of 30, 60, 90, 180, 240, 360 and 750 min. Flow rate: 0.5 mL/min.

the conditions under which this capacity is maximum. This was why S and N were considered as floating variables during the nonlinear 2-D fitting procedure of the conditional peak capacity n∗c as a function of Fv and tG . The best values of these parameters are summarized in Table 2 for each set of conditions (different column length and temperature). We found that a critical step in the calculation of the conditional peak capacity from chromatograms is the determination of a reliable estimate of the average peak width at large gradient times (Note that all the values of the peak capacity reported in this work are conditional peak capacities that were estimated using the procedure described in Section 2.3). Fig. 7 shows the overlaid histograms of the peak width distributions measured at different gradient time. The open circle symbols are located at the center of each histogram column and the bin size was chosen in order to have a comparable number of intervals in each histogram. This figure shows that the peak width may vary significantly during a separation, particularly for the shallow gradients. For example, for a gradient time of 750 min, there are ten peaks in the myoglobin digest with a width between 0.5 and 0.6 min, eight peaks with a width between 0.4 and 0.5 min, six peaks with a width between 0.6 and 0.7 min, and so on. The distribution of the peak widths broadens markedly with increasing gradient time (see Fig. 7). This result illustrates the approximate character of the assumption of a constant peak width during a gradient run that was made by Horv´ath and Lipsky [15]. It explains why the estimate of the peak capacity is really difficult, is often approximate, and why the straightforward use of Eqs. (6), (9), (10), or (12) may not provide a result that is as accurate as often believed. These changes in the peptide band widths may be due to tailing or fronting of the peaks and may be explained by isotherm overload or by effects related to the electric charges of the molecules or their different degree of basicity. Since the peak capacities level off at high gradient times (see Figs. 6, 9 and

12), we did not further consider gradient times in excess of 360 min. Although the calculated average peak width provides a somewhat inaccurate estimate of the peak capacity, it gives a precise one. The repeatability of the gradient separations was checked. The relative standard deviations of the peak retention times and of the retention windows are of the order of 1% (see Table 3). In general, we found that we could obtain a reliable estimate of the average peak width by injecting a similar but less complex peptide mixture (e.g., myoglobin digest), as described in Section 2.3, that is eluted in a retention window of width similar to that of the BSA digest. Fig. 8 a and b compares chromatograms of myoglobin and BSA digests. The good resolution between most myoglobin fragments and the similar concentration and retention time ranges in these chromatograms allows a correct estimate of the average peak width over the entire retention window used. Fig. 9 a and b shows the peak capacity maps at 20 and 60 ◦ C, respectively, as functions of both the flow rate and the gradient

Fig. 8. Gradient separations of BSA digest (a) and myoglobin digest (b). Separation conditions are: Fv = 0.3 mL/min, tG = 90 min, T = 60 ◦ C, φ = 0.31. Dashed lines show the gradient profile (%ACN scale on right y-axis).

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time. These figures were obtained by combining the dependence of the peak capacity on the flow rate (see Fig. 5) and the dependence of this peak capacity on the gradient time (see Fig. 6). Values of the peak capacity at different flow rates and gradient times can be obtained by extrapolation from the surfaces in Fig. 9 a and b. To validate these results, it was verified that no gain in peak capacity can be obtained by increasing the gradient time. The surface shows that a peak capacity of 422 can be achieved with Fv = 0.3 mL/min and tG = 750 min at 60 ◦ C. Experimentally a value of 434 was obtained, a relative error of only 2.8%. However, the retention time of the last eluted peak is only 0.65 times the gradient duration, tG , meaning that with this large value of the gradient time, only 65% of the separation space is used. In other words, the theoretical peak capacity of the column increases considerably but a large part of this increase is not useful for the separation of the tryptic digests studied. Figs. 1 and 5 suggest that the flow rate should be kept relatively low to maximize the peak capacity. The optimum value is practically achieved for a gradient time of 360 min. A comparison of Fig. 9 a and b shows that increasing the temperature from 20 to 60 ◦ C does not increase much the peak capacity of the column at low flow rates (ca. 0.3–0.4 mL/min, i.e., in the highest range of the peak capacities). However, this does increase significantly the peak capacity at high flow rates, at flow rates of 0.8–1 mL/min. Increasing the gradient time beyond 360 min brings only small gains in peak capacity (see Fig. 9 a and b). The reason seems to be in the linear increase of both the retention window and the peak width with increasing gradient time, consistent with Eqs. (5) and (7). Another reason that prevents obtaining high peak capacity values with very shallow gradi-

Fig. 10. Examples of gradient optimization for BSA digest separation (from Table 4. Gradient elution conditions are: (a) Fv = 0.3 mL/min, tG = 180 min, φ = 0.31, n∗c = 367; (b) Fv = 0.361 mL/min, tG = 360 min, φ = 0.247, n∗c = 438. Dashed lines show the gradient profile (%ACN scale on right y-axis).

ents can be found in the decrease of the separation space with increasing gradient time. Although the retention time window increases, it does so less rapidly than the gradient time (see Fig. 4). For a gradient time of 360 min, the elution of the sample of BSA digest takes between 79 and 89% of the gradient time at 20 ◦ C and still less than that at 60 ◦ C (results not shown). Fig. 10. We studied the influence of the final mobile phase composition at the end of the gradient on the peak capacity of the column, at the optimum flow rate. By interpolating the fitting surface (Fig. 9 a and b), the best flow rates maximizing the peak capacities can be calculated for each desired gradient time. We did it for tG = 150, 180, 240, and 360 min. Then, we were able to keep the ratio tR,n /tG close to 1 by adjusting φ as the gradient time increases. This procedure allows the separation space to be larger and produces higher peak capacities. It was also applied to separations made at 60 ◦ C. The best experimental conditions and the obtained peak capacities are summarized in Table 4. Two chromatograms are given as examples in Fig. 8 a and b. The effects of the optimizations of the mobile phase composition and the flow rate on the width of the retention window is illustrated at two gradient times, 180 (Fig. 8a) and 360 min (Fig. 8b). 4.3. Results obtained with the short Halo column

Fig. 9. Peak capacity surface for the 15cm long Halo column at (a) 20 ◦ C and (b) 60 ◦ C.

The same experiments were repeated with a 5 cm long Halo column and the peak capacity surface was obtained. The gradient time was varied to keep the same gradient slope ((φVm )/(Fv tG )) for the two columns (15 and 5 cm). The value

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215

Table 4 Optimization of gradient elution for very shallow gradient slope Reference conditions tG (min)

¯ 1/2 (min) W

150 180 240 360

0.189 0.216 0.270 0.370

Optimized conditions tR,n /tG

n∗c

Fv (mL/min)

φ

¯ 1/2 (min) W

tR,n /tG

n∗c

0.933 0.911 0.881 0.838

355 367 382 400

0.385 0.379 0.370 0.361

0.275 0.269 0.259 0.247

0.183 0.216 0.283 0.408

0.993 0.992 1.002 1.011

397 402 416 438

The obtained peak capacities are compared with those ones used to fit the 2-D surface. Reference conditions refer to the following separation variables: Fv = 0.3 mL/min, φ = 0.31. Common experimental conditions are: L = 15 cm, T = 60 ◦ C.

of φ selected was the same as indicated above for the longer column. The results obtained regarding the width of the separation window and the peak widths were similar and are not shown. They demonstrate that keeping constant the gradient slope permits the proper transfer of the experimental conditions for optimum gradient separation from the 15 to the 5 cm long column, although we did not take into account a possible slight change in the value of the S parameter. Fig. 11 a and b illustrates this aspect further by showing the variation of the width of the retention windows and the peak width in unit of elution volume (mL) for the four different mobile phase flow rates used.

Fig. 11. Results of the gradient method transfer between the 15 cm ( ) and the 5 cm () long column: (a) retention windows and (b) peak widths are plotted in elution volume units versus the gradient time for different flow rates. Graphs are given for experimental data at T = 20 ◦ C.

These plots show that the data are practically overlaid for the two columns, confirming the overlap between the two trends. In theory, the two sets of data points (15 cm, symbols, and 5 cm, () symbols) should be found on the same straight line for a given flow rate. The agreement between the sets of data for the two columns is better for the retention windows than for the peak widths. Similar results were obtained at 60 ◦ C (data not shown). The linear relationships seen in Fig. 11 a and b are consistent with the recent literature discussing the effect of the gradient time on the peak capacity [10]. They show that both the width of the retention window and the peak width have almost the same values at a given gradient time (e.g., 30 min and 90 min), for columns of different lengths. This means that, for a given gradient slope, the two columns will provide nearly the same degree of separation of the mixture components. This is in agreement with the values of the peak capacity obtained for the two column at the four different flow rates. For example, at 20 ◦ C and for a 90 min gradient time, the 5 and the 15 cm long columns gave

Fig. 12. Peak capacity surface at (a) 20 ◦ C and (b) 60 ◦ C for the 5 cm Halo column.

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peak capacities of 278 and 277 at 0.3 mL/min, 280 and 292 at 0.5 mL/min, 268 and 306 at 0.7 mL/min, and 237 and 269 at 0.9 mL/min. For a 30 min gradient time the peak capacities are, respectively, 210 and 190, 199 and 207, 189 and 204, 157 and 158 for the two columns. Fig. 12 a and b shows the peak capacity surface as function of tG and Fv for the short column at 20 ◦ C and 60 ◦ C, respectively. The two surfaces were plotted with the same x- and y-axis ranges as the plots in Fig. 9 a and b. These ranges are wider than those experimentally exploited better to show the surface trends. The best fitting parameters are listed in Table 2. The main difference between the surfaces obtained for the two column is that the flow rates at which the peak capacities are maximum is higher for the 5 cm long column, particularly at 60 ◦ C. One possible reason for that could be in the average peak widths. For medium and long gradient times, the lowest W1/2 values were obtained at flow rates of about 0.9 mL/min (20 ◦ C) and 1.3 mL/min (60 ◦ C). Another reason of this can be related to the column efficiency (see Fig. 1 a and b). Under isocratic conditions the short column still display a higher optimum mobile phase velocity than the long one.

2 kDa. The results reported in this work show that it is possible to obtain fast separations of peptide mixtures exhibiting a high separation power, as illustrated by peak capacities between 100 and up to nearly 500.

5. Conclusions

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The Halo particles provide columns that have an extremely high maximum efficiency. However, as all columns packed with modern fine particles, these columns cannot be operated at very high actual velocities of the mobile phase, due to their low permeability. With aqueous solutions of acetonitrile rich in ACN, the largest velocity achieved with conventional instruments (maximum inlet pressure, 400 atm) is approximately 4 mm/s, because it is necessary to use very narrow connecting tubes to limit the extra-column volume and reduce the band broadening contribution of this volume. This is due to the small volume that is occupied by the band width on these highly efficient, short columns. At this velocity of 4 mm/s, the contribution of the instrument, including that of the connecting tubes, to the pressure drop is approximately 100 atm. Modern, advanced instruments might allow operating 150 mm × 4.6 mm Halo columns at a flow rate close to 10 mL/min. However, it is important to realize that, at constant mobile phase velocity, the reduced velocity of the mobile phase decreases rapidly with increasing molecular weight of the sample components, due to the correlative decrease in the molecular diffusivity of these compounds [24]. So, while it is not possible to reach reduced velocities exceeding 10 with anthracene or other low molecular weight analytes, a reduced velocity of 20 can easily be reached with kallidin (decapeptide with MW = 1212 g/mol) and 30 with insulin at the same actual flow velocity. So, Halo can be used successfully to separate peptide mixtures because the size exclusion effect is negligible below

Acknowledgments This work was supported in part by Grant DE-FG05-88-ER13869 of the US Department of Energy, by the cooperative agreement between the University of Tennessee and Oak Ridge National Laboratory and by Grant RBPR05NWWC 008 (CHEM-PROFARMA-NET) of the Italian University and Scientific Research Ministry. The authors acknowledge P. Jandera (University of Pardubice, Czech Republic) for informative discussions, J.J. Kirkland (Advanced Materials Technology, Wilmington, DE), and U.D. Neue (Waters Corp., Milford, MA) for fruitful discussions and the generous gift of Halo columns. NM thanks F. Dondi (University of Ferrara, Italy) for his sustaining role, his continued support and important efforts made. References