Peak capacity in gradient reversedphase liquid chromatography of biopolymers. Theoretical and practical implications for the separation of oligonucleotides.
ABSTRACT Reversedphase ultraperformance liquid chromatography was used for biopolymer separations in isocratic and gradient mode. The gradient elution mode was employed to estimate the optimal mobile phase flow rate to obtain the best column efficiency and the peak capacity for three classes of analytes: peptides, oligonucleotides and proteins. The results indicate that the flow rate of the Van Deemter optimum for 2.1 mm I.D. columns packed with a porous 1.7 microm C18 sorbent is below 0.2 mL/min for our analytes. However, the maximum peak capacity is achieved at flow rates between 0.15 and 1.0 mL/min, depending on the molecular weight of the analyte. The isocratic separation mode was utilized to measure the dependence of the retention factor on the mobile phase composition. Constants derived from isocratic experiments were utilized in a mathematical model based on gradient theory. Column peak capacity was predicted as a function of flow rate, gradient slope and column length. Predicted peak capacity trends were compared to experimental results.

Article: Solvent selectivity and strength in reversedphase liquid chromatography separation of peptides
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ABSTRACT: A set of tryptic peptides was analyzed in reversedphase liquid chromatography using gradient elution with acetonitrile, methanol, or isopropanol. We used these retention data as training sets to develop retention prediction models of peptides for the three organic eluents used. The coefficients of determination, R2, between predicted and observed data were approximately 0.95 for all systems. Retention coefficient values of twenty amino acids calculated from a model were utilized to investigate differences in separation selectivity between acetonitrile, methanol, or isopropanol eluents. The experimentally observed difference in separation selectivity appears to be a complex interplay of multiple amino acids, each contributing to a different degree to overall peptide retention. While retention contribution of hydrophilic amino acids was higher in methanol than acetonitrile, peptides containing aromatic amino acids (tyrosine, phenylalanine, tryptophan) exhibit relatively lower retention in methanol compared to acetonitrile. The differences between acetonitrile and isopropanol eluents were less pronounced. We also compared the relative elution strength of the three organic eluents for peptides. The relationship between the elution strength of two solvents is not linear, rather it was best fitted by a cubic polynomial function. Three solvents can be arranged in the order of increasing elution power as methanol < acetonitrile < isopropanol. The equations for relative solvent strength conversion were proposed.Journal of Chromatography A 04/2014; · 4.61 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A dual labeled oligonucleotide used as TaqMan® or 5' nuclease probe for in vitro diagnostic has been purified through orthogonal ionpairing reversed phase chromatography, using polymeric semipreparative and preparative PRP1 column. We studied the mechanism of separation of oligonucleotides using ionpairing reversed phase chromatography. We found that elution profiles of dye labeled oligonucleotides can be controlled by use of specific ionpairing reagents. Here, we report a method for purification of an oligonucleotide containing an internally positioned rhodamine dye using two orthogonal chromatographic steps, in which the primary step resolves mostly by differences in hydrophobicity by using a weak ionpairing reagent, and a secondary step uses a strong ionpairing reagent for separation of length variants. Purification is demonstrated for both 1 and 15μmol scale syntheses, and amenable to further scale up for commercial lot production.Journal of Chromatography A 01/2014; · 4.61 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Recent findings have elucidated numerous novel biological functions for oligonucleotides. Current standard methods for the study of oligonucleotides (i.e., hybridization and PCR) are not fully equipped to deal with the experimental needs arising from these new discoveries. More importantly, as the intracellular capacity of oligonucleotides is being harnessed for biomedical applications, alternative bioanalytical techniques become indispensable in order to comply with everincreasing regulatory requirements. Owing to its ability to detect oligonucleotides independent of their sequence, LCMS is emerging as the analytical method of choice for oligonucleotides. In this article, the current applications of LCMS in the analysis of oligonucleotides, with an emphasis on RNA therapeutics and biomarkers, will be examined. In addition, the theoretical framework of oligonucleotide ESI is carefully inspected with the purpose of identifying the contributing factors to MS signal intensity.Bioanalysis 06/2014; 6(11):15251542. · 3.25 Impact Factor
Page 1
Journal of Chromatography A, 1169 (2007) 139–150
Peak capacity in gradient reversedphase liquid
chromatography of biopolymers
Theoretical and practical implications for the
separation of oligonucleotides
Martin Gilar∗, Uwe D. Neue
Waters Corporation, 34 Maple Street, Milford, MA 01757, USA
Received 15 June 2007; received in revised form 5 September 2007; accepted 6 September 2007
Available online 11 September 2007
Abstract
Reversedphase ultraperformance liquid chromatography was used for biopolymer separations in isocratic and gradient mode. The gradient
elution mode was employed to estimate the optimal mobile phase flow rate to obtain the best column efficiency and the peak capacity for three
classes of analytes: peptides, oligonucleotides and proteins. The results indicate that the flow rate of the Van Deemter optimum for 2.1mm I.D.
columns packed with a porous 1.7?m C18sorbent is below 0.2mL/min for our analytes. However, the maximum peak capacity is achieved at flow
rates between 0.15 and 1.0mL/min, depending on the molecular weight of the analyte. The isocratic separation mode was utilized to measure the
dependence of the retention factor on the mobile phase composition. Constants derived from isocratic experiments were utilized in a mathematical
model based on gradient theory. Column peak capacity was predicted as a function of flow rate, gradient slope and column length. Predicted peak
capacity trends were compared to experimental results.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Peak capacity; Biopolymers; Ultraperformance liquid chromatography; Van Deemter; Gradient theory
1. Introduction
The development and commercialization of novel biophar
maceuticals based on peptides, proteins, and oligonucleotides
renewed an interest in liquid chromatography (LC) as a tool for
biopolymers analysis. While LC theory and practice are well
developed for socalled “small molecules” (a term customarily
used for analytes with the molecular weight below ∼500Da),
the separation principles of “large molecules” are understood to
a lesser degree [1,2]. The reasons are several, among others: (i)
Thechromatographicbehaviorofbiopolymersiscomplex,com
prising effects such as the changes in molecular conformation
[3], incomplete recovery from the column [4], ghosting, peak
tailing, etc. This is especially noticeable for protein separations
in reversedphase mode. (ii) Dedicated sorbents for the separa
tionofbiopolymersweredevelopedlaterthantheonesfor“small
∗Corresponding author. Tel.: +1 508 482 2000; fax: +1 508 482 3625.
Email address: Martin Gilar@waters.com (M. Gilar).
molecules”. (iii) Biopolymer samples became readily available
onlyafter1990.Whenthepeptideandoligonucleotidesynthesis
becameroutine,theanalystsgainedaccesstostructurallyrelated
samples of their choice for systematic analytical studies.
Chromatographic theory developed for small molecules cer
tainly applies to biopolymers as well; however, practitioners
are well aware of characteristic differences in their retention
behavior. For example, the isocratic retention of biopolymers
(or in general all polymers and large molecular weight analytes)
is extremely sensitive to the changes in mobile phase elution
strength [2,5]. Since the reversedphase (RP)LC isocratic sepa
ration of biopolymers is difficult and impractical, only few such
reports can be found in the literature [6–9], and even fewer have
attemptedtomeasureVanDeemtercurvestoestablishanoptimal
mobile phase linear velocity [10].
One can circumvent the practical difficulties of column
efficiency estimation by using Van Deemter (or others) chro
matographic models, providing that the molecular diffusion
coefficient Dm of the analytes is known, and no irregular
adsorption–desorption behavior takes place. Unfortunately, the
00219673/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.chroma.2007.09.005
Page 2
140
M. Gilar, U.D. Neue / J. Chromatogr. A 1169 (2007) 139–150
Dmvalues of biopolymers are rarely known [11]. The diffusion
coefficients can be approximated using various models [9,12].
Calculations are complicated by the fact that the actual sep
arations are often carried out at elevated temperature [13,14],
and that solute diffusion in the stationary phase depends on the
sorbent pore size [9,10]. Therefore, the reliable prediction of
optimal LC conditions (column efficiency) for the separation of
peptides, oligonucleotides and proteins is not a trivial task.
As pointed out above, the separation of biopolymers is typ
ically performed in a gradient mode. Separation performance
can be measured as resolution between individual peaks or as
peak capacity [9,15,16], which represents the maximum theo
retical number of peaks that can be resolved within the gradient
time. The peak capacity of RPLC for peptides has been recently
evaluated both theoretically and experimentally [17].
Although it is possible to apply the peak capacity theory for
the prediction of optimal separation conditions, the challenges
of this approach are similar as outlined above. Any predic
tion requires the knowledge of Dm, retention parameters S or B
(definedbySnyder[9]orNeue[15,16]astheslopeoflogkorlnk
versusmobilephasecompositionΦ),andk0(extrapolatedreten
tion coefficient of the solute in a fully aqueous mobile phase).
Unfortunately, none of these parameters are typically known.
These constants are characteristic for each solute and must be
measured experimentally in isocratic or gradient LC mode.
In this work, we utilized an ultraperformance liquid chro
matography (UPLC) system and RP columns packed with
1.7?m C18sorbent to separate peptides, proteins, and oligonu
cleotides. We measured retention factors, peak widths, and peak
volumes of biopolymers under isocratic and gradient elution
conditions with several goals in mind. First, we estimated the
optimalmobilephaselinearvelocityforvariouslargemolecules
using the peak capacity theory. Second, we intended to illus
trate the retention factor dependence on mobile phase elution
strengths, represented by the retention parameter B. Third, we
investigated the relationship between the retention parameters
B and solute molecular weight. Fourth, a variant of the peak
capacity model was developed and applied to the separation of
oligonucleotides, which represent a class of biopolymers with
specific retention behavior.
2. Experimental
2.1. Materials and reagents
Triethylamine (TEA), 99.5%, acetic acid, and hexafluoroiso
propanol (HFIP), 99+, were purchased from Sigma (St. Louis,
MO, USA). Trifluoroacetic acid (TFA) was purchased from
Pierce (Rockford, IL, USA). A 2–2M solution of TEA and
acetic acid (triethylammonium acetate, TEAA) in water was
obtained from Fluka (Seelze, Germany). HPLC grade methanol
and acetonitrile were purchased from Fisher Scientific (Fair
Lawn, NJ, USA). A MilliQ system (Millipore, Bedford, MA,
USA) was used to prepare deionized water (18M?cm) for
HPLC mobile phases. Bradykinin, leucineenkephaline, renin
substrate, bovine insulin, bovine ubiquitin, bovine ribonucle
ase A, bovine serum albumin, bovine ?lactoglobulin A, and
phosphodiesterase I were purchased from Sigma. Oligonu
cleotides were purchased from Integrated DNA technologies
(IDT, Coralville, IA, USA). Oligonucleotides were purified by
HPLC and digested by phosphodiesterase I [18] to generate
oligonucleotideladders.DigestionwasmonitoredbyHPLCand
terminatedatthedesiredmomentbyboilingthereactionmixture
for 5min.
2.2. HPLC instrumentation, columns, and conditions
HPLC experiments were carried out using an ACQUITY
UPLC system with an ACQUITY UPLC photodiode array
detector (Waters, Milford, MA, USA). The columns used
in this study were 30mm×2.1mm, 50mm×2.1mm and
100mm×2.1mm ACQUITY UPLC OST C18columns packed
with1.7?msorbent.TheUPLCsystemwasoperatedwith50?L
or 425?L mixers as indicated in the discussion and in the figure
captions.
The mobile phases used for oligonucleotide separation
were A 0.1M TEAA in water, pH ∼7.5; B mobile phase
A:acetonitrile,80:20(v/v).TheTEAAionpairingmobilephase
(200mL) was prepared by pipetting 10mL of 2M TEAA stock
and adding 190g of water; the pH was not adjusted, the final
pH was approximately 7.5. The mobile phase B was prepared
by mixing 200mL of 0.1M TEAA with 39.3g (50mL) of ace
tonitrile. The alternative ionpairing system for oligonucleotide
separationconsistedof(A)15mMTEA,400mMHFIPinwater;
(B) mobile phase A:methanol, 50:50 (v/v). Mobile phase A
was prepared by mixing 191.3g of water, 13.44g of HFIP and
0.416mL of TEA. The mobile phase B was prepared as A with
the addition of 158.2g of methanol.
The separations of peptides and proteins were performed
with the mobile phase A 0.1% TFA in water; (B) 0.1% TFA in
acetonitrile (A: 200g of water, add 0.2mL of TFA; B: 157.6g
of acetonitrile, add 0.2mL of TFA). All separations were per
formed at 60◦C; gradient and other separation conditions are
specified in the figure captions.
For flow rates between 0.075 and 0.15mL/min we used
50mm×50?mPEEKsiltubing(UpchurchScientific,OakHar
bor, WA, USA), connected after the photodiode array detector
to maintain the combined pressure on the UPLC pump above
7MPa.
3. Results and discussion
3.1. Peak capacity model
Expressions useful for the peak capacity prediction in RPLC
forrandomsmallmoleculesandbiopolymerslikepeptideswere
developed by Neue at al. on the bases of the linearsolvent
strength gradient theory (LSS theory) [15,16,19]. These models
can be used for assessing the optimal mobile phase flow rate
for a separation under a given set of constraints. We will first
discuss the model for peptides, and then examine the case for
oligonucleotides.
ThesimplemodelforthepeakcapacityPforpeptidesaswell
asforthefastchromatographyofsmallmoleculesresultedinthe
Page 3
M. Gilar, U.D. Neue / J. Chromatogr. A 1169 (2007) 139–150
141
following relationship:
√N
4
P = 1 +
B?c
B?c(t0/tg) + 1
(1)
The peak capacity P depends on the column efficiency N
(validforisocraticseparation),theparameterB,whichisdefined
as the slope of the linear dependency of lnk versus the vol
ume fraction of the organic solvent in the mobile phase ϕ. The
parameter?crepresentsthevolumefractionofthegradientspan
deliveredoverthegradienttimetg;t0isretentiontimeofanunre
tained marker compound. For example, ?c of 0.1 represents the
gradient span of 10% organic modifier (typically acetonitrile or
methanol).
Itshouldbenotedthatthismodelisderivedontheunderlying
assumption that the analyte properties are reasonably uniform
over the elution range. In other words, any distribution of ana
lytes and their molecular weight (which affects the plate count
and the parameter B) is random over the chromatogram. This is
notanunreasonableassumptionforsmallmoleculesorpeptides.
The model can be expanded, if the plate count N is expressed
asafunctionoftheoperatingparameters,whichincludecolumn
lengthLandparticlesizedp,andthetypicaldiffusioncoefficient
Dmfor the analytes of interest [19]:
N =
L
Adp+ (βDmt0/L) + C(d2
A, β, and C are the terms of Van Deemter equation; the term β
is typically equal to 1, and can therefore be omitted in further
expressions.
We have recently utilized the model for the theoretical eval
uation of peak capacity in 2DLC peptide separation [17]. It
was found that with appropriately chosen parameters B and Dm,
the predictions and experimental data agreed with acceptable
accuracy.
The underlying assumption that the chromatographic prop
erties of the separated entities do not change over the course of
thegradientisnottruefortheseparationofoligomers,including
oligonucleotides. For these compounds, both the diffusion coef
ficient, which determines the plate count, and the parameter B
varyoverthecourseofthegradient.Itcanbeshown[2,7]thatthe
slope of the function lnk versus the volume fraction of organic
modifier in the mobile phase B becomes steeper with increasing
molecular weight, and that longer oligomers are more retained
in RPLC. It is also known that the diffusion slows down with
increasing molecular weight, which affects the plate count of
the analytes over the chromatogram.
From a practical point of view, Eq. (1) is suitable for evalu
ating the peak capacity for peptide mapping applications, since
peptides generally elute randomly between 0 and 50% gradient
oforganicmodifier.Anypeptidemapgeneratedbythedigestion
p/Dm)(L/t0)
(2)
of a protein yields peptides with similar range of lengths and
retention behavior. The peak capacity can be readily simulated
for different columns, gradient times, and flow rates using uni
formvalueof?c=0.5.Ontheotherhand,oligonucleotidestend
to elute within a narrow span of gradient, in most cases within
2–4% of organic modifier. Additionally, the separation selectiv
ity(andtheresolution)islowerforlargeroligomers.Thismakes
itdifficulttopredictan“average”peakcapacityfromEq.(1)for
oligonucleotides in general.
One therefore must use a different approach for the
assessment of the performance of a gradient separation of
oligonucleotides. We will use the resolution for a peak pair
for this calculation and then show that the overall sample peak
capacityisnothingbutthesum(ortheintegral)oftheresolutions
in the chromatogram as shown in Eq. (3):
?
TheresolutionRsforeveryneighboringpairofoligonucleotides
is defined as
P∗∗=
j
Rs,j
(3)
Rs=
tr,2− tr,1
(w2+ w1)/2
Denotationstrandwstandfortheretentiontimeandthepeak
width, indexes 1 and 2 indicate first or second eluting oligonu
cleotide. Under LSS conditions, the retention time of a peak is
a function of its retention factor at the beginning of the chro
matogram k0and the generalized gradient slope G (defined by
Eq. (10)) [19]:
?1
Thepeakwidth(alsointimeunits)isderivedfromthecolumn
efficiency N and the retention factor of the peak at the column
outlet ke:
(4)
tr,i= t0
Gi
ln(Gik0,i+ 1) + 1
?
(5)
wi= 4
t0
√Ni(ke,i+ 1)(6)
Theretentionfactoratthepointofelutioncanalsobederived
from the LSS theory:
ke,i=
k0,i
k0,iGi+ 1
Therefore the peak width becomes
?(Gi+ 1)k0,i+ 1
Wecannowassembletheequationfortheresolutioninevery
segment of our gradient:
(7)
wi= 4
t0
√Ni
Gik0,i+ 1
?
(8)
Rs=1
2
(1/G2) ln(G2k0,2+ 1) − (1/G1) ln(G1k0,1+ 1)
?(((G2+ 1)k0,2+ 1)/(G2k0,2+ 1)) +?1/√N1
?1/√N2
?(((G1+ 1)k0,1+ 1)/(G1k0,1+ 1))
The gradient slope G contains the gradient parameters and
the compoundspecific slope B of the log/linear relationship
(9)
Page 4
142
M. Gilar, U.D. Neue / J. Chromatogr. A 1169 (2007) 139–150
between the retention factor and the solvent composition:
G = B?ct0
tg
= Bg
(10)
g is the gradient slope that can be influenced by the investigator
g=?c×t0/tg. The resolution now is
1
2g
Rs=
(1/B2) ln(gB2k0,2+ 1) − (1/B1) ln(gB1k0,1+ 1)
?((((gB2+ 1)k0,2+ 1))/(gB2k0,2+ 1)) +?1/√N1
As we will see in Section 3 of this paper, both the reten
tion factor at the beginning of the gradient k0and the slope B
are the functions of the analyte. Furthermore, there is a linear
relationship between this retention factor and the slope B.
Eq. (11) can be further simplified for our purposes. If we
assume that the plate counts of the closely eluting neighbor
ing peaks as well as their gradient slopes are very similar, the
equation changes into
√N
4g
(gB + 1)k0+ 1
?1
?1/√N2
?(((gB1+ 1)k0,1+ 1)/(gB1k0,1+ 1))
(11)
Rs=
gBk0+ 1
×
B2
ln(gB2k0,2+ 1) −
1
B1
ln(gB1k0,1+ 1)
?
(12)
The N, B and k0here are the average values for closely elut
ing peaks of selected analytes. Next we assume that B1and B2
change much less with retention than k0and that the term in k0
is much larger than 1:
√N
4
k0,1
Rs=
gB
gB + 1ln
?k0,2
?
(13a)
Both the plate count N and the slope B depend on the MW
(size)ofanalytesthatweareconsidering.Sinceweareinterested
in the peak spacing for peak pairs, we can express Eq. (13a) as
a function of the specific retention range α0of the analytes in
which we investigate:
√Nav
4
Rs=
gBav
gBav+ 1ln(α0)(13b)
The dependence of B, k0, Dmand N on the molecular weight
MW of the analyte can be assessed from Eqs. (14a)–(14d).
Parameters a, b, e, and f are numerical constants obtained from
regression (see later in this paper); d represents the parameters
of the Wilke–Chang equation (333.16K, viscosity=2.6cP, sol
vent molecular volume=18mL, association factor=0.00468)
d=0.3604×10−3. For small molecules, the exponent of Eq.
(14c)is−0.6.Similarvalueshavebeenreportedintheliterature
for polymers [20]. The exact value depends on the environment
of the oligomer. A formula for the diffusion coefficient of poly
mers based on the solventdependent Mark Houwink constant
can be found in textbook [21], page 88. A commonly found
value is −0.6 for a good solvent, although Lukacs et al. [22]
reported a value of −0.71 for larger DNA (up to 6000bp) in
a salt solution. Considering the general recommendation for a
polymer in a good solvent as well as the fact that reversedphase
chromatography is carried out in the presence of some organic
modifier and a low salt concentration, we selected the literature
value of −0.6 for the dependence of the diffusion coefficient
on the molecular weight of the oligosaccharides. It needs to be
stressedthatoneshouldnotconfusethiscoefficientwiththeone
obtained for compact molecules such as proteins, where a value
of −1/3 is found [23,24]:
B = a ln(MW) − b
ln k0= e ln(MW) − f
Dm= d MW−0.6
N =L
(14a)
(14b)
(14c)
H=
L
A + C(d2
p/Dm)u=
L
A + C(d2
p/d)MW0.6u
(14d)
This gives the following expression for the resolution:
?
Rs=1
4
L
A + C(d2
p/d)MW0.6u
1
g(a ln(MW) − b) + 1ln(α)
(15)
The peak capacity P** for any part or the entire chro
matogram, can now be calculated from Eq. (3). For multiple
analytes we simply sum up the resolution of multiple oligonu
cleotides for every segment j of the chromatogram.
There are several advantages expressing the peak capacity
thisway.ContrarytoEq.(1),Eq.(3)doesnotrequiretheknowl
edge of the gradient span ?c. If a wider than necessary gradient
span is used in Eq. (1), the peak capacity is overestimated. Eq.
(3) also correctly predicts the decline of the peak capacity for
larger oligonucleotides, while Eq. (1) yields an opposite trend
(Eq. (1) relies on peak widths, larger oligonucleotides elute as
narrower peaks; see further discussion). Finally, the goal of a
typical oligonucleotide separation is to resolve the parent com
pound from several truncated oligomers called n−1, n−2, etc.
[25,26].Insuchacasetheanalystsareinterestedintheresolution
(peak capacity) of adjacent peaks, which can be readily calcu
lated from their molecular weight, provided that their retention
parameters B and k0are known.
3.2. Estimating optimal mobile phase flow rate for
biopolymer separation
For columns packed with conventional chromatographic sor
bents (3–5?m) the separation of biopolymers such as peptides,
proteins and oligonucleotides is generally performed with a
larger than optimal flow rates. While the <2?m chromato
graphicsorbentsprovideahigherseparationefficiencyandpeak
capacity,itremainstobeinvestigatedwhatistheoptimalmobile
phase velocity for biopolymers separation, and how it depends
on the molecular weight of the analytes.
Because the isocratic measurement of the theoretical plate
heightforthebiopolymersusingVanDeemtercurvesisdifficult
(theminimumoccursatverylowflowrate;someproteinsdonot
Page 5
M. Gilar, U.D. Neue / J. Chromatogr. A 1169 (2007) 139–150
143
elute as well defined peaks under isocratic conditions), we have
investigated the application of the peak capacity theory to the
same goals, employing a gradient elution mode.
If a constant gradient volume is maintained throughout the
experiment (by varying the experimental flow rate and the time
ofgradientproportionally),theplotof1/(Rs)2resultsinapattern
that is related to the theoretical plate height H of the analytes:
?
d
1
R2s
= const
A + C
?d2
p
?
MW0.6u
?
= constH
(16)
The resolution is inversely proportional to the peak volume Vr:
1
R2s
= 4
p2
v
(Vr,2− Vr,1)2
(17)
pvis a peak volume. And therefore
H = constp2
Thefollowingexperimentwasexecutedwiththegoaltoeval
uate the validity of the relationship proposed in Eq. (18). The
plot of squared peak volumes should permit an assessment of
the pattern of the theoretical plate height H as a function of the
flow rate.
The experiment depicted in Fig. 1A and B was carried out
by adjusting the flow rate proportionally to tg, so the gradient
volumeinkeptconstant.Fig.1Aillustratestheplotsofthesquare
of the peak volume p2
vversus the mobile phase flow rate for
15, 20, and 40mer oligodeoxythymidine peaks; the MWs of the
analytes were 4501, 6022, and 12105.9Da; respectively. The
shape of the curves indicated that the optimal flow rate is below
the flow rates used in this experiment.
Fig.1Ashowsthatthemeasuredpeakvolumesdecreaseinthe
oligonucleotide series from 15 to 20 to 40mer. This is the oppo
site behavior one intuitively expects. However, this behavior
does not imply a greater column efficiency for larger oligonu
cleotides; instead it is related to the fact that the retention factor
at the column outlet decreases with the increasing molecular
weight of the analyte. The retention factor changes faster from
thecolumninlettotheoutletfortheanalyteswithalargermolec
ular weight (larger B). This is captured in Eq. (9) in conjunction
v
(18)
with Eq. (13a). The reduced retention factor compensates for
the increase in peak width caused by the lower plate count for
large molecules. As a consequence, the peak volume becomes
smaller for larger oligonucleotides.
Similar p2
vversus flow rate curves were measured for pep
tides and small proteins as well (Fig. 1B). The analytes were:
Leucineenkephaline,555.6Da;bradykinin,1060Da;reninsub
strate, 1758Da; bovine insulin, 5733.5Da, bovine ribonuclease
A, 13,685Da; and bovine ?lactoglobuline A, 18,352Da. Only
selected plots are shown in Fig. 1B. As expected, the curves
for smaller peptides such as leucineenkephaline or bradykinin
reach the minimum at a larger mobile phase linear velocity
than proteins and oligonucleotides. The plots in Fig. 1 resem
ble Van Deemter curves. The optimal flow rate values for
leucineenkephaline and bradykinin were in agreement with
conventional Van Deemter plots measured at isocratic elution
conditions(thepositionofmaximumefficiencycloselymatched
the minimum on the curve p2
vversus flow rate; data not shown).
The results suggest that the proposed gradient method can
be used to evaluate the optimal chromatographic conditions for
the analysis of biopolymers. Nevertheless, the analysis of Fig. 1
reveals several features of the method that deserve additional
discussion.
3.3. Experimental evaluation of peak capacity: gradient
time
In Section 3.2, we assessed the flow rates that achieve the
maximum plate count for the various biopolymers for columns
packedwitha1.7?mC18sorbent.Despiteusingasmallparticle
sizesorbentandelevatedtemperatures,theseflowratesliebelow
the operational values of analytical LC instruments. Does that
mean that even stateoftheart columns are unsuitable for the
separation of biopolymers?
The answer to this question is certainly not. Columns packed
withalargersorbentparticlesizehavebeensuccessfullyapplied
fortheanalysisofbiopolymers,despitethefactthattheyaretyp
icallyoperatedatflowratesgreatlyexceedingtheflowraterange
where the minimum plate height occurs. In addition, the peak
capacity theory presented in Eqs. (1), (13a) and (13b) implies
Fig. 1. Pseudo Van Deemter curves measured in gradient RPLC mode represented as a plot of the squared peak volume vs. mobile phase flow rate. RPLC (A)
oligonucleotides, (B) peptides and proteins. Conditions: 50mm×2.1mm, 1.7?m ACQUTIY C18column, 60◦C, 425?L mixer. Mobile phases for oligonucleotides
were: A, 15mM TEA, 400mM HFIP; B, 50:50 mobile phase A:methanol. Oligonucleotide gradient: 30–54% B, proportionally varying flow rate and gradient time;
gradient slope ?c×(t0/tg) was kept constant. Example of gradient: FR=0.2mL/min, tg=40min. Mobile phases for protein/peptide separation: A, 0.1% TFA in
water; B, 0.1% TFA in 50:50 water:acetonitrile. Protein/peptide gradient: 20–100% B, proportionally varying flow rate and gradient time; gradient slope was kept
constant. Example of gradient: FR=0.2mL/min, tg=30min.
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Fig. 2. Estimation of optimal peak capacity for (A) oligonucleotides, and (B) peptides/proteins using gradient RPLC. Column, LC conditions, and mobile phases
were the same as in Fig. 1. Oligonucleotide gradient: 30–54% (B) in 26.67min. Protein/peptide gradient: 20–100% (B) in 10min. The gradient time was kept
constant, the flow rate (hence gradient slope) varied.
that the maximum peak capacity for a given analysis time is
achieved at flow rates much faster than those required for the
plate count maximum. These equations suggest that not only
the column efficiency N, but also the gradient slope g has an
importantimpactontheoverallpeakcapacity.Theoptimalcom
bination of both for a given analysis time determines the best
flow rate.
The peak capacity was experimentally evaluated for selected
biopolymers as shown in Fig. 2. The gradient time was fixed,
while the flow rate was varied. Please note that this is a dif
ferent experimental design than in Fig. 1, where the gradient
slope was maintained constant by adjusting the gradient time
and the flow rate proportionally. The approach used in Fig. 2
expands the gradient volume and flattens the gradient slope. At
the same time, the plate count deteriorates with increasing flow
rate.
The peak capacity in Fig. 2A was calculated directly
from chromatograms for 15–20mer, 20–25mer, and 25–30mer
oligonucleotide pairs (Fig. 2A). The retention times t1and t2
represent the first and second eluting peaks; similarly the peak
widths w1and w2(measured at 4σ, 13.4% of the peak height):
P = 1 +
t2− t1
(w2+ w1)/2
(19)
The peak capacity in Fig. 2B was calculated from Eq. (20);
the gradient time tgwas 10min. The use of different methods
for the calculation of the peak capacity for peptides/proteins
was forced by the fact that their selectivity (peak spacing in the
chromatogram) varied with the effective gradient slope:
P = 1 +tg
w
(20)
Fig. 2A and B illustrates that the overall peak capacity of
the column has indeed shifted towards faster than optimal flow
rates observed in Fig. 1A and B. Even though the column effi
ciency decreases at a higher mobile phase velocity, the peak
capacity loss is offset by the positive contribution of the shal
lower gradient (Eqs. (13a) and (13b)), which – on average –
expands the distance between the peaks. The shallower gradi
ent is caused by the increased flow rate at the fixed gradient
run time. As one would expect, the maximum peak capacity
for peptides was obtained at a faster flow rates than for pro
teins (Fig. 2B). Interestingly, the absolute peak capacity values
werenotindirectcorrelationwiththeanalytemolecularweight.
Peak compression [27] as well as other contributions to peak
width play a distinct role in protein/peptides chromatographic
behavior. For example insulin is formed by two chains cross
linked via disulphide bonds, which forms a highly compact
molecule. The penetration into the pores of a packing becomes
hindered for larger molecules, which in turn impedes perfor
mance.
Oligonucleotides appear to have substantially different pat
terns compared to peptides. The optimal peak capacity for
oligonucleotides is observed at about the same flow rate. This is
due to the difference in the influence of the molecular weight of
the analyte on the two parts of Eq. (15). As the flow rate (or bet
ter the linear velocity u) increases, the value of the square root
decreases, while the gradient steepness parameter g becomes
smaller, which increases the value of the gradient contribution
totheresolution.Consequently,thepositionofthepeakcapacity
maximum in Fig. 2A remains rather insensitive to the molecular
weight of the oligonucleotide.
The comparison of Figs. 1 and 2 reveals information that
should not be overlooked. The optimal peak capacity does not
coincide with the smallest peak volume. Therefore, operating at
flow rates providing the best peak capacity will result in a mod
erate(inthiscasetwotothreetimes)lossofdetectionsensitivity.
This is acceptable for many applications, where the resolution
is the most desirable goal of analysis.
3.4. Measurement of B parameters
The proposed peak capacity models in Eqs. (1), (13a) and
(13b)relyontheknowledgeorreliableestimatesoftheretention
factors such as B. Therefore, we investigated these parameters
experimentally.
The constant B for oligonucleotides was adapted from Ref.
[7] (Fig. 2 in [7]). Apparently, the B values increase with the
size of the molecule. This correlates to observation made earlier
by Snyder [1,2,9]. We used the log–log fit [9] that seems to be
universal for oligonucleotides, peptides and proteins (Fig. 3 and
Table 1).
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M. Gilar, U.D. Neue / J. Chromatogr. A 1169 (2007) 139–150
145
Fig. 3. Factor B was measured at isocratic conditions for oligonucleotides and
peptides/proteins, and plotted as function log B vs. logarithm of analyte molec
ular weight. B values are listed in Table 1. The column and the conditions for
proteins/peptides and oligonucleotides (TEAHFIP, MeOH experiment) were
the same as in Fig. 1. Data for TEAA, MeCN system for oligonucleotides were
adopted from Gilar et al. [7]. Circles: experimental data for oligonucleotides;
triangles: experimental data for proteins/peptides.
Eqs. (21) and (22) describe logB as a function of logMW or
the log length of oligonucleotides (n; number of nucleotides in
sequence). The linear fit for logB versus log(MW) and log (n)
gave a correlation coefficient of R2=0.983 and 0.979, respec
tively, for the TEAA ionpairing system:
log B = 0.42 log(MW) + 0.60
log B = 0.43 log(n) + 1.63
In Ref. [7] we used Eq. (21) for the prediction of the B factor
for peptides and proteins for data taken from the literature [8].
Although this equation predicts acceptable B values for tryptic
peptides in the MW range 1000–2000Da, we believe this equa
(21)
(22)
tion is incorrect. In light of recent experiments we propose Eq.
(23). The fit of logB versus logMW for 7 peptides/proteins was
linear with a correlation coefficient of R2=0.978.
log B = 0.46 log(MW) + 0.18
Eqs.(21)–(23)arevalidforthegivenchromatographiccondi
tions used for the separation. Understandably, the intercept and
theslopeoftheequationsmaychangewithtemperature,thetype
of stationary phase, organic modifier (acetonitrile, methanol,
isopropanol, ...), and the nature of the ionpairing system. We
investigated the impact of the last two parameters on oligonu
cleotide separations.
Fig. 3 compares data for two different ionpairing systems
and organic modifiers. TEAA was used in combination with
acetonitrile, while the TEAHFIP ionpairing system employed
methanolastheorganicmodifier[28–32].Eqs.(24)and(25)sig
nificantlydifferfromEqs.(21)–(23)(seealsoFig.3andTable1).
Correlation for both equations was R2=0.995:
(23)
log B = 1.27 log(MW) − 2.86
log B = 1.28 log(n) + 0.28
The predicted B values for the TEAHFIP/methanol system
(usingthesamecolumnandtemperature)arelowerthantheones
derived from Eqs. (21)–(23), at least for the shorter oligonu
cleotides. However, because the change of the slope B with the
volume fraction of the organic modifier is steeper, the two lines
cross at the position corresponding to a 36mer oligonucleotide.
The slope of the logB−log (MW) relationship is much steeper
for TEAHFIP ionpairing system. The reasons for that are not
clearatthispoint,buttheobservationcorrelateswiththefactthat
TEAHFIPseemstobeamoreefficientsystemfortheseparation
of oligonucleotides than TEAA [7,18].
(24)
(25)
Table 1
Experimentally measured B and lnk0parameters for oligonucleotides (deoxythymidines), peptides and proteins
SoluteMW (Da)
Ba
lnk0a
Conditions
2T
4T
8T
10T
15T
30T
546.4
1154.8
2371.6
2980
4501
9063.9
52.6
83.6
108.7
117.0
138.0
176.0
3.7
7.3
10.7
12.1
15.5
20.8
0.1M TEAA, acetonitrile, 60◦C
0.1M TEAA, acetonitrile, 60◦C
0.1M TEAA, acetonitrile, 60◦C
0.1M TEAA, acetonitrile, 60◦C
0.1M TEAA, acetonitrile, 60◦C
0.1M TEAA, acetonitrile, 60◦C
25T
26T
27T
28T
29T
30T
7542.9
7848.1
8151.3
8455.5
8759.7
9063.9
116.3
122.5
129.2
135.9
141.7
146.1
26.78
28.31
29.96
31.62
33.06
34.16
15mM TEA, 400mM HFIP, methanol, 60◦C
15mM TEA, 400mM HFIP, methanol, 60◦C
15mM TEA, 400mM HFIP, methanol, 60◦C
15mM TEA, 400mM HFIP, methanol, 60◦C
15mM TEA, 400mM HFIP, methanol, 60◦C
15mM TEA, 400mM HFIP, methanol, 60◦C
Leucineenkephaline
Bradykinin
Renin substrate
Insulin
Ubiquitin
Ribonuclease A
?Lactoglobulin A
555.6
1060
1758
5733.5
8565
13,685
18,352
28.65
42.75
41.57
76.37
109.5
127
141.2
7.087
9.196
9.551
24.81
33.39
32.73
59.33
0.1% TFA, acetonitrile, 60◦C
0.1% TFA, acetonitrile, 60◦C
0.1% TFA, acetonitrile, 60◦C
0.1% TFA, acetonitrile, 60◦C
0.1% TFA, acetonitrile, 60◦C
0.1% TFA, acetonitrile, 60◦C
0.1% TFA, acetonitrile, 60◦C
aFrom function lnk=lnk0−B×Φ [15,16]. Parameters S and logk0defined by Snyder [1,9] can be calculated as S=B/2.303 and logk0=lnk0/2.303.
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Table 2
Comparison of predicted and experimental peak capacity and retention times
15–20mer 20–25mer25–30mer 30–40mer40–50mer 50–60merSum 15–60merb
Experimental data
t1(min)a
t2(min)a
t2−t1(min)
Pexpc
12.89
16.49
3.60
19.8
16.49
19.07
2.58
13.1
19.07
21.11
2.04
10.1
21.11
24.18
3.07
15.2
24.18
26.35
2.17
11.0
26.35
28.05
1.70
8.5d
12.89
28.05
15.16
77.8
Predicted data
t1(min)e
t2(min)e
t2−t1(min)
Pcalc
11.20
13.9
2.70
16.2
13.90
15.79
1.89
11.6
15.79
17.20
1.41
8.8
17.20
19.20
2.00
12.7
19.20
20.58
1.38
8.9
20.58
21.60
1.02
6.8
11.20
21.60
10.40
64.9
P and trwere calculated for six selected segments, and for the entire 15–60mer range.
aRetention time tgvalues were obtained from Fig. 5A.
bThe sum 15–60mer peak capacity is calculated by summing the contributions from the selected segments.
cCalculated from Eq. (19), see also captions in Fig. 5.
dOnly 50mer peak width was used for the calculation.
ePredicted from the model, Eq. (11).
3.5. Peak capacity prediction for oligonucleotides and
comparison with experimental results
The peak capacity model developed here is a useful tool for
choosing the optimal experimental parameters for biopolymer
separation. We have investigated the impact of column length
L, gradient time tg, and sorbent particle size dpin silico and
compared the finding to experimental data. In this case study,
we utilized oligonucleotides as a sample. Unlike proteins and
peptides, oligonucleotides have a predictable chromatographic
behavior, unaffected by secondary structure.
The peak capacity in the following examples was predicted
from Eq. (11). Because the separation selectivity (hence the
peakcapacity)isgreaterforshorteroligonucleotides,wedivided
15–60mer oligonucleotides into six subgroups and summed the
results into an overall peak capacity. The comparison of exper
imental and predicted P values are shown in Table 2. The data
are discussed in greater depth in Section 3.7. The simplified Eq.
(12) provided comparable results, while the very simple Eqs.
(13a) and (13b) predicted slightly higher peak capacity values.
However, the trends observed with the simple Eqs. (13a) and
(13b) were the same as for the more complex equations.
Fig. 4A illustrates the impact of the particle size of the
chromatographic packing on the average peak capacity of
15–60mer oligonucleotides. The peak capacity was calculated
for 50mm×2.1mm columns packed with 1.7?m, 3?m, and
Fig. 4. Averaged peak capacity for 15–60mer oligonucleotides calculated for 2.1mm column I.D., 1.7?m sorbent, ?c=0.024, initial gradient strength 9% MeCN,
tg=16min, and Van Deemter C term=0.05, unless indicated otherwise. (A) P as a function of sorbent particle size; (B) P as a function of gradient run time at fixed
flow rate 0.2mL/min; (C) P as a function of flow rate at a fixed gradient run time of 16min; (D) P as a function of flow rate, the gradient time was scaled to column
length (16, 32, and 48min, for 50, 100, and 150mm columns, respectively).
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147
Fig. 5. 15–60mer oligodeoxythymidine separation using different gradient
slopes. Conditions: 50mm×2.1mm, 1.7?m ACQUTIY OST C18 column,
60◦C,425?Lmixer,flowrate0.2mL/min.Mobilephases—A,100mMTEAA;
B, 80:20 mobile phase A:acetonitrile. The gradient was 40–70% B (8–14%
MeCN). Gradient slopes are indicated in the figure. The programmed LC gra
dient was 40, 20, 13.3, and 10min for (A), (B), (C) and (D) chromatograms,
respectively. The experimental peak capacity Pexpwas estimated from the chro
matograms for 25–30mer using Eq. (19); peak widths measured at 50% peak
height were multiplied by 1.7 to obtain peak width at 4σ. Peak capacity Pcalc
25–30mer was calculated from Eq. (11), for 2.1mm×50mm, 1.7?m column,
gradientslope0.6,0.45,0.3,and0.15%MeCN/min;VanDeemterCterm=0.05.
5?m sorbents, respectively. The gradient time was 16min,
and the overall gradient span ?c was 0.024 (slope 0.15%
MeCN/min, similar to conditions in Fig. 5A). Not surprisingly,
the best peak capacity was obtained for the column packed
with the smallest particle size sorbent. The experimental data
illustrating this trend were published elsewhere [7].
Fig. 4B compares the peak capacity for three different col
umn lengths. In this prediction, the gradient span ?c was kept
constant, while the gradient time was varied. The flow rate was
0.2mL/min.Fig.4Billustratesascenariointuitivelyunderstood
bypractitioners:extendingthegradienttime(usingshallowgra
dients) is expected to improve the prospects for a successful
separation. The gradient span of 2.4% acetonitrile per analysis
may seem narrow; however, the separation of oligonucleotides
indeed occurs within such a limited range of mobile phase elu
tion strength (at least for the TEAA ionpairing system with
acetonitrile as the eluent).
Fig. 4C (as well as Fig. 4A and D for 1.7?m, 50mm long
column) shows the peak capacity as a function of flow rate for a
fixed 16min long gradient (?c=0.024). The predicted P curve
for a 50mm long column resembles the shape of experimental
curves shown in Fig. 2A, although the predicted peak capacity
maximum is shifted to a slightly larger flow rate. The absolute
P values are not directly comparable, since the data in Fig. 2A
were acquired with a TEAHFIP ion paring system, rather than
with TEAA, which was used for the prediction in Fig. 4.
Intriguingly,thegainsinresolutionforlongercolumnsshown
in both Fig. 4B and C are not as pronounced as one may expect.
The gains in P are certainly not proportional to column length.
Furthermore, at short gradient times and slow flow rates the
peak capacity predicted for longer columns is in fact less than
for shorter columns. This seemingly counterintuitive prediction
correlateswellwiththepracticalexperienceofmanychromatog
raphers. It has been reported that for gradient RPLC separation
of proteins the resolution is practically independent of the col
umn length [1,2]. This behavior is explained by the impact of
the gradient slope g defined as ?c×(t0/tg). Longer columns
have both greater efficiency N and volume (t0). At constant gra
dient run time tgthe gradient slope is proportionally shallower
for shorter columns. In other words, the peak capacity of longer
columns is reduced by proportionally sharper gradient, which
tendstoreduceoreliminatethepositiveimpactofhighercolumn
efficiency.
The full benefits of longer columns in a gradient separation
are realized when changing the gradient duration in proportion
with the column volume (length). This scenario is depicted in
Fig. 4D. All conditions are the same as in Fig. 4C, except for
extending the gradient time to 32min and 48min for 100 and
150mm columns, respectively. In this scenario, the gradient
slope ?c×(t0/tg) is the same for all three columns. In such a
case, the peak capacity calculated from Eq. (15) depends solely
on the square root of the column efficiency N, which is propor
tional to the column length L. The expected gain for the scale up
froma50mmcolumntoa100mmcolumnis(100/50)ˆ0.5=1.41.
Similarly, the peak capacity gain for the scale up from a 50 to
150mmcolumnis1.73.The41%or73%increaseinpeakcapac
ityisachievedattheexpenseof2×or3×longeranalysistimes.
The impact of the gradient slope predicted in Fig. 4B was
evaluated experimentally using a 15–60mer ladder of oligonu
cleotides. The results are shown in Fig. 5. Oligonucleotides
wereseparatedona50mm×2.1mm,1.7?mAcquityOSTC18
column; the gradient time (slope) was varied. Calculated peak
capacities Pcalcfor 25–30mer peaks can be compared to Pexp
obtained from chromatograms. The details are given in the cap
tion to Fig. 5. The experimental Pexpvalues clearly followed the
trends predicted from the model (see Figs. 5–7). The correla
tion coefficient between predicted and experimental results was
0.998.
Fig. 5 suggests that shortening the analysis time by using
sharp gradients is detrimental for resolution. Fig. 6 illustrates
an alternative approach. Oligonucleotide separations were per
formed at different flow rates, reducing the gradient time
proportionally to the flow rate. The gradient slope g was there
fore constant throughout this experiment.
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Fig. 6. 15–60mer oligodeoxythymidine separation at various flow rates. Gradi
ent slope ?c×(t0/tg) was kept constant by adjusting the gradient and the flow
rate proportionally. Conditions: 50mm×2.1mm, 1.7?m ACQUITY OST C18
column, 60◦C, 425?L mixer. Mobile phases—A, 100mM TEAA; B, 80:20
mobile phase A:acetonitrile. The gradient was 45–64.5% B (9–12.9% MeCN).
Flow rates are indicated in figure. The programmed LC gradient was 52, 26,
13, and 6.5min for (A), (B), (C) and (D) chromatograms, respectively. The Pexp
values for 25–30mer were obtained as described in Fig. 5. Peak capacity Pcalc
25–30mer was calculated as in Fig. 5, gradient slope 0.6, 0.3, 0.15, and 0.075%
MeCN/min; Van Deemter C term=0.05.
Fig. 7. Strategy for reducing analysis time without compromising peak capac
ity.15–60meroligonucleotideladderwasseparatedwithconstantgradientslope
(0.15% MeCN/min), initial gradient mobile phase strength was changed as
indicated in figure. Conditions: 50mm×2.1mm, 1.7?m ACQUITY OST C18
column, 60◦C, 425?L mixer. Mobile phases—A, 100mM TEAA; B, 80:20
mobile phase A:acetonitrile. The flow rate was 0.2mL/min. The Pcalcand Pexp
values for 25–30mer were obtained as described in Fig. 5.
When increasing the flow rate, the column efficiency
decreases as shown earlier in Fig. 1A. However, Fig. 6 indi
cates that the loss in peak capacity is less detrimental compared
to using sharp gradients (compare Figs. 5 and 6). Therefore,
it is more practical to maintain relatively shallow gradient and
reduce the analysis time by increasing the flow rate and gradient
time proportionally (maintaining constant gradient slope).
When applying Eq. (1), one can easily arrive to mislead
ing results by choosing a larger tgand ?c than justified by the
retention behavior of the chosen analytes. For example, while
peptides typically elute in a composition range between 0 and
50% acetonitrile (?c=0.5), the effective elution window for
oligonucleotidesisonlyseveralpercentoforganicmodifier.This
is illustrated in Fig. 7. The gradient slope ?c×(t0/tg) was kept
constant for all experiments, while the initial mobile phase elu
tion strength varied. Because oligonucleotides eluted within the
samemobilephaseelutionstrengthspan,theremainingspacein
thechromatogramisnotusefulfortheseparation.Predictingthe
peakcapacityfromunrealisticallylargetgand?c,theseparation
capabilities of the column will be overestimated. Therefore, we
prefer to calculate the P for experimental data from the newly
developed models (Eqs. (11), (12), (13a), (13b) and (15)). P can
berealisticallypredictedfromEq.(1)whenusingrationaltgand
?c values, if possible estimated from experiment.
Thepeakcapacitymodelpredictsthescenarioexperimentally
confirmed in Fig. 7. The figure illustrates a suitable approach
for reducing the analysis time without undesirable sacrifice in
peak capacity. The initial gradient strength may be optimized,
while keeping the gradient slope constant, and by doing so, the
resolution of oligonucleotides is virtually unaffected. A small
loss in the peak capacity P is observed only in Fig. 7D. Due
to the gradient delay of the LC system, the early eluting peaks
eluted under isocratic conditions (a 425?L mixer was used).
3.6. Fast analysis of oligonucleotides
Equipped with the knowledge of the optimal mobile phase
flow rate and column length/gradient time scaleup relation
ships, one can develop fast methods for the biopolymer
separation. Fig. 8A and B illustrate the method development for
a 15–35mer ladder. Flow rate, gradient slope, and initial mobile
phase elution strength were selected appropriately, guided by
datainFigs.2A,5and7.Fig.8Bshowsthefirstresult,usingthe
mobile phase flow rate of 0.2mL/min, a gradient slope 0.25%
MeOH/min and initial mobile phase strength of 19% MeOH.
The separation achieved for the 15–35mer ladder was more
than adequate, therefore it was possible to further shorten the
analysis time. This was achieved by doubling the flow rate and
reducing the gradient time to half of the initial value (there
fore, the gradient slope was unchanged). The initial gradient
elution strength was also adjusted to further reduce the analysis
time. The separation at 0.4mL/min was accomplished in less
than 4min (Fig. 8A). As expected, the peak capacity somewhat
decreased, but this is acceptable as long as the resolution meets
the requirements defined by the analyst.
Fig. 8C shows the separation of a 30–60mer oligonucleotide
ladder at the flow rate of 0.2mL/min. In this case, the peaks
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149
Fig. 8. Fast oligonucleotide separations in UPLC. (A) and (B) 15–35mer
oligodeoxythymidine ladder. (C) 30–60mer oligodeoxythymidine ladder. Con
ditions: 50mm×2.1mm, 1.7?m ACQUTIY C18column, 60◦C, 50?L mixer.
Mobile phases—A, 15mM TEA, 400mM HFIP; B, 50:50 mobile phase
A:methanol. Initial gradient strength, gradient slope and flow rate are indicated
next to chromatograms.
are not completely resolved. Therefore, it is not advisable to
further increase the flow rate and decrease the gradient time.
The achieved separation is a compromise between speed and
resolution.
One may consider using longer columns to improve the sep
aration. It is important to understand that this is possible at the
expense of the separation time. Fig. 4C shows the best strat
egy for scaling up column length. As discussed above, the peak
capacities achieved with 50–100 and 150mm columns are in
ratios of 1:1.41:1.73, when the gradient time is scaled to the
column volume (Fig. 4C). One may wonder whether it is possi
ble to avoid extending the analysis time for longer columns by
adjusting the flow rate as suggested in Fig. 6 (keeping the gradi
ent slope constant). The scenario can be as follows: 50, 100, and
150mm columns can be operated at 0.2, 0.4, and 0.6mL/min,
respectively, while maintaining a constant gradient time. One
apparent problem represents the high operational pressure of
long columns at high flow rates. More importantly, this strategy
fails to provide a higher peak capacity. Calculated P ratios for
50–100 and 150mm long columns are 1:1.07:1.10.
For fast separations, we prefer to use a 50?L mixer over
the 425?L one. The smaller mixer adds less gradient delay and
reduces the overall analysis time. Precautions have to be made
for the separation of biopolymers to avoid imperfect mobile
phase mixing, especially for shallow gradients. The premixed
mobilephasesusedhereresolvedanyissueswithartifactscaused
by insufficient mobile phase mixing.
3.7. Benefits and limitations of the peak capacity model
As discussed above, the peak capacity is a useful tool for
predictionofseparationqualityatvariouschromatographiccon
ditions. Some limitations of the model defined by Eq. (1) were
noted[17],suchasthenecessitytodefineanappropriategradient
span and B constant. The model in Eq. (1) has been successfully
used to estimate the peak capacity for RPLC separation of pep
tides, because the ?c is typically 0.5, and the elution pattern of
analytes in the chromatogram is random [17].
Notwithstanding its utility, this simple model is not appli
cable for oligonucleotides or oligomers with a specific elution
behavior. Most importantly, their retention increases, and the
separation selectivity decreases with the oligomer chain length.
Also,theytendtoeluteinanextremelynarrow?crange.Hence,
a different mathematical model must be used.
The model presented in Eq. (3) addresses this problem by
calculating the peak capacity as a sum of resolution values for
neighboring peaks (segments) across the chromatogram. The
definition of resolution (Eqs. (11), (12), (13a), (13b), (14a),
(14b), (14c), (14d), (15)) encompasses the selectivity term
ln(k0,2/k0,1),aswellasthesteepnessofBoftheretentionpattern.
Consequently, the peak capacity prediction accurately captures
the experimentally observed trends of diminishing separation
prospects for longer oligonucleotides, as illustrated in Table 2.
Themodelingcanbeperformedwithoutpriorknowledgeof?c.
Since the model contains predetermined k0and B values, it can
bealsousedtopredictoligonucleotideretentiontimes(Table2).
Althoughthenewproposedmodelissuitablefortheoligonu
cleotides peak capacity prediction, some limitations should be
mentioned: (i) The k0and B values have to be obtained experi
mentally for the desirable chromatographic system. The model
reliability depends on the accuracy of the k0and B estimates.
The values need to be adjusted when different ionpairing sys
tem, organic modifier, or the stationary phases are considered.
(ii) The oligonucleotide diffusion coefficients Dmwere calcu
lated from a theoretical model. Inaccurate Dmestimates will
introduce some bias into P prediction. (iii) The peak capac
ity model was developed for homooligonucleotides. Separation
of heterooligonucleotides partially depends on their sequence
[7,18]; the spacing between peaks is more irregular and reso
lution varies. However, when using experimentally measured
k0values for heterooligonucleotides of interest, Eq. (11) should
predictthecorrectPvalues.(iv)Peakcapacitycannotbereliable
calculated for oligonucleotides with strong secondary structure.
In such case the k0and B (hence the separation selectivity) will
changeunpredictably.(v)Themodeldoesnotincludetheimpact
of the gradient delay of the LC instrument. It is assumed that
the gradient starts immediately after the sample is injected onto
the column. Table 2 lists the predicted P for six segments of
the chromatogram, 15–20, 20–25, 25–30, 30–40, 40–50, and
Page 12
150
M. Gilar, U.D. Neue / J. Chromatogr. A 1169 (2007) 139–150
50–60mer; and the total 15–60mer peak capacity is defined as
the sum of all segments. The predicted P values were compared
to the experimental peak capacity obtained from Fig. 5A; sep
aration conditions were the same as used for the theoretical
prediction. Apparently, the model underestimates P; this was
also observed in Figs. 5–7 for the 25–30mer span.
Experimental and predicted retention times are listed in
Table 2. A systematic shift towards shorter times can be seen
for the experimental data. This could be partially explained by
the gradient delay of the LC system (in this case 0.5mL), which
is not considered in the prediction.
In spite of the limitations, the developed model is a suit
able tool for method development and in silico experiments,
allowing the users to semiquantitatively evaluate the impact of
chromatographic conditions on the oligonucleotide separation
performance.
4. Conclusions
The peak capacity theory was applied to solve several prac
tical problems in RP separation of biopolymers. First, the peak
capacity model was used to evaluate an optimal mobile phase
linear velocity for the separation of peptides, proteins and
oligonucleotides. The results obtained in gradient elution mode
were in agreement with the values derived from Van Deemter
equation. The proposed gradient method is simple and appli
cable to a range of analytes from moderate to large molecular
weight.
Theretentiondataofbiopolymersweremeasuredatisocratic
conditionsandusedtodefinetheslopeofthelnkfunctionversus
thefractionoforganicmodifierΦinthemobilephase(factorB).
The relationship of B to the molecular weight of the analyte was
defined for oligonucleotides, peptides and proteins. A rational
predictionofBallowsformoreaccuratepeakcapacitymodeling
in RPLC.
The peak capacity theory was validated by experimentally
measured trends using UPLC columns packed with a 1.7?m
sorbent. The flow rate for the maximum peak capacity for
50mm×2.1mm column was found to be 0.15mL/min for
oligonucleotides and 0.4–0.8mL for proteins and peptides (col
umn temperature 60◦C). The impact of gradient slope, initial
gradient strength and flow rate on the separation was evaluated.
The data indicate that the proposed peak capacity model realis
tically describes the separation behavior of oligonucleotides in
RPLC.
Acknowledgement
The authors thank Joomi Ahn for her helpful suggestions to
the manuscript.
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