Quantitative predictions to conditions of zwitterionic stacking by transient moving chemical reaction boundary created with weak electrolyte buffers in capillary electrophoresis.

Abstract

This paper develops a novel procedure of quantitative predictions for the on-column stacking conditions of a zwitterionic analyte by a moving chemical reaction boundary (MCRB) in capillary electrophoresis (CE). The procedure concerns the choice of the weak acidic running and alkaline sample buffers and the velocity design of MCRB created with the two buffers. Based on the theory of MCRB, the theoretical computations are performed. From the computations, the following two predictions are refined for the stacking conditions of zwitterion. (1) The zwitterion velocity in the acidic buffer should be greater than that of MCRB moving toward the cathode, or the zwitterion cannot be well stacked by the MCRB. (2) The gap between pH values of the acidic and alkaline sample buffers ought to comprise the isoelectric point (pI) of zwitterion to be stacked; namely, there exists the relation of pH (acidic buffer) < pI < pH (sample). The predictions are quantitatively proved by the experiments of zwitterionic stacking with two kinds of MCRBs. In addition, the experiments also show the tightly stacked peak of zwitterion existing in the process of MCRB, but not after the MCRB. The theoretical and experimental results hold obvious significances to other zwitterion (such as peptide and protein) on-column stacking in CE.

Full text

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Analytical Chemistry, Vol. 77, No. 4, February 15, 2005

Anal. Chem.2005, 77,955-963

Articles
Quantitative Predictions to Conditions of
Zwitterionic Stacking by Transient Moving
Chemical Reaction Boundary Created with Weak
Electrolyte Buffers in Capillary Electrophoresis

Cheng-Xi Cao,*,†,‡ Wei Zhang,† Wei-Hua Qin,† Shan Li,† Wei Zhu,† and Wei Liu‡

Laboratory of Analytical Biochemistry & Bioseparation, School of Life Science and Biotechnology,
Shanghai Jiao Tong University, Shanghai 200240, China, and Department of Chemistry,
University of Science and Technology of China, Hefei 230026, China

This paper develops a novel procedure of quantitativepredictions for the on-column stacking conditions of
a zwitterionic analyte by a moving chemical reaction boundary (MCRB) in capillary electrophoresis (CE).
The procedure concerns the choice of the weak acidic running and alkaline sample buffers and the velocity
design of MCRB created with the two buffers. Based on the theory of MCRB, the theoretical computations
are performed.From the computations, the following two predictions are refined for the stacking onditions
of zwitterion. (1) The zwitterion velocity in the acidic buffer should be greater than that of MCRB moving
toward the cathode, or the zwitterion cannot be well stacked by the MCRB. (2) The gap between pH
values of the acidic and alkaline sample buffers ought to comprise the isoelectric point (pI) of zwitterion to
be stacked; namely. there exists the relation of pH (acidic buffer) < pI < pH (sample). The predictions are
quantitatively proved by the experiments of zwitterionic stacking with two kinds of MCRBs. In addition,
the experiments also show the tightly stacked peak of zwitterion existing in the process of MCRB, but not
after the MCRB. The theoretical and experimental results hold obvious significances to other zwitterion
(such as peptide and protein) on-column stacking in CE.

On-column stacking, viz., preconcentration, of analytes in a sample matrix has become a simple, convenient, and
economical but very powerful tool used to greatly improve the detection sensitivity of capillary electrophoresis (CE). In
1988-1992, Bocˇek et al.1,2 developed the preconcentration of transient isotachophoresis (tITP) in CE and Jandik and
Jones3 achieved over 100-fold sensitivity increase by tITP. Almost at the same time, Chien and Burgi4-8 created the field
amplification sample injection (FASI) and really concentrated analytes up to 1000-fold in CE. In 1998, Quirino and
Terabe9 successfully enhanced the sensitivity of micellar electrokinetic chromatography over 5000-fold. Recently,
Yang et al.10 enhanced the sensitivity of CE 7000-fold with FASI coupled with nonuniform electrical field, and Zhang
et al.11decreased the detection limit of CE greater than 10 000-fold with a pure FASI technique. Significantly, Quirino
and Terabe12 improved the sensitivity of CE up to a millionfold with FASI joined with sweeping method.Importantly,
numerous methods of preconcentration for analytes were successfully developed during the past decade. The tITP1,2,12
and FASI 4-8,10,11 that were developed during the early stage of 1990s were mentioned above. The following will further
supply a few of notable cases. From 1998 to 2002, Quirino et al.9,13-15 and Palmer et al.16-18 pictured a novel sweeping
procedure for the stacking of neutral and charged analytes by the interaction between micellar molecular and analytes.
During the period 2000-2003, Britz-McKibbin, Chen et al.19-21 invented the pH junction stacking for the
reconcentration of analytes in a sample matrix. In 1996-2003, Lunte’s group22-25 advanced the pHmediated stacking
method for analyses of drugs in a biological sample matrix. In 2002, Shihabi26,27 added many kinds of watermiscible
organic solvents (such as acetonitrile, acetone, and alcohols) into salt sample matrixes. The water-miscible organic
solvents can induce a FASI mechanism by decreasing the ionization of salt in the sample matrix, can provide the high
electric field strength necessary for band sharpening, and consequently can lead to ionizable analyte concentration in
sample matrixes even with some salt.
In 2002, we28,29 developed the stacking procedure of moving chemical reaction boundary (MCRB) for the
enhancement of separation efficiency of CE and realized higher than 200-fold improvement of detection sensitivity of
analyte in the sample matrix with high salt. Recently, our group achieved up to 3 millionfold enhancement of detection
sensitivity and simultaneous separation of zwitterions induced by a single MCRB in CE.30 All of these experimental
studies on sample stacking28-30 were based on the concept of MCRB31,32 and its relative method33-35 developed from
1997 to 2002. However, the relative theoretical studies on the stacking of zwitterionic analytes by the MCRB method
have not been carried out up to now. In addition, there are still, to authors’ knowledge, no investigations of quantitative
theoretical design on conditions of sample stacking in CE.

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Figure 1. Mechanism of poor or good zwitterion stacking by MCRB moving toward the cathode. (A) The initial state of
stacking after injection of weak alkaline sample; (B) the formation of the MCRB after use of electric field, the fast movement
of the MCRB toward the cathode, and the poor stacking of zwitterion by the MCRB due to VRâ > Vz R; (C) the formation of
the MCRB after use of electric field, the slow movement of the MCRB toward the cathode, and the good stacking of
zwitterion by the MCRB due to VRâ e VzR.

Therefore, the main purposes in the paper are to first apply the theory of MCRB31,32 for accurate predictions to the
experimental conditions of MCRB stacking and quantitative illumination on the mechanism of MCRB stacking of
zwitterion. These studies are an important step to the quantitative design of zwitterion stacking by the MCRB.
Furthermore, we observe the tightly stacked peak of zwitterion existing during the process of MCRB but not after the
MCRB. Here, we describe the theoretical and experimental procedure and report the relative results. The
MCRB-induced 3 millionfold enhancement of detection sensitivity of zwitterions in CE will be presented in ref 30.

THEORY AND CALCULATION
Phase. A phase is a homogeneous solution demarcated by a moving or stationary boundary. In Figure 1A, there are
phases R, â, and ç, which are in correspondence with the acidic running buffer holding H+, the alkaline sample matrix
containing OH-, and the running buffer, respectively. Phases R and ç are the same running buffer, but they have
different functions. The MCRB in Figure 1A is created between phases R and â but not between phases â and ç. Thus,
phase R is used for the formation of MCRB, whereas phase ç is used for the separation of analytes after the end of
MCRB stacking (for the details, see Figure 7 in ref 29).
Expression of MCRB. Using an expression similar to that used for a moving boundary system by MacInnes and
Longs-worth,36-40 the MCRB system in Figure 1A can be briefly expressed as

where, jj implies a boundary being stationary or moving toward the anode or cathode, + and - indicate the anode and
cathode, respectively, and R and â mean phases R and â, respectively. With the basic expressing mode, one can well
write the two MCRB systems used here, as will be shown in boundaries 1 and 2 below.
Velocity of MCRB. As shown in Figure 1, the MCRB is created between phases R and â, when the electric field is
applied. The boundary velocity can be computed with the following equations as have been shown in refs 31 and 32,

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where c is the equivalent concentration (equiv m-3). The bar over c means the constituent concentration; it does not
apply to an ion but to the equilibrium mixture of all subspecies of a constituent (see eqs 4 and 5). The subscripts H+ and
OH- indicate the hydrogen and hdyroxyl ions, respectively, and the superscripts R and â imply phases R and â,
respectively. The signed quantity is positive if the ion carries net positive charge(s) and negative if net negative
charge(s), as has been treated by numerous scientists.31-40 i is the electric current intensity (A m-2) in capillary. m is the
mobility (m2 V-1 s-1). The bar over m indicates the constituent mobility (see eq 3 and 4). Other symbols are the same as
those for c. VRâ is the velocity (m s-1) of MCRB, and _ is the specific conductivity of electrolyte in a phase (S
m-1).Equation 1 holds validity for a MCRB created with system of strong electrolytes,31,32 e.g., HCl (+, R) jj NaOH (-,
â), while eq 2 is valid to the system of pure weak electrolytes,31-35 such as CH3COOH (+, R) jj NH3H2O (-, â). In eq 2,
the constituent mobility and concentration are respectively defined as

where mi is the mobility of subspecies i and ai is the fraction of subspecies i with mobility mi, viz.,

General Conditions of Stacking Zwitterion by MCRB. For convenience of computation, amino acid is used as the
zwitterion example for the theoretical investigation of stacking. In the electrolyte arrangement of Figure 1, the pH
values of phases R and â, which can produce the stacking effect to a zwitterion, are in accordance with the following
inequality

For near-maximum stacking of amino acid, inequality 6 shouldbe reexpressed as the much better conditional inequality
below

Over 99% of the zwitterion carries a negative charge if it is in phase â or a positive charge if it is in phase R under the
conditions of expression 7. In inequality 7, pK1 and pK2 are the negative logarithms of dissociation on carboxyl and
amino groups of amino acids, respectively. But for these amino acids of Lys, Arg, and His,41 inequality 7 should be
expressed as

because these three kinds of amino acids have an ionizable side group. In inequality 8, pKR is the negative logarithm of
dissociation on the side chain of an amino acid. In some cases (for example, the pK1 and pK2 of isoleucine are 2.36 and
9.69, respectively41), there is pK2 - pK1 > 7; hence, under this condition, inequality 7 and 8 are changed to

Inequality 9 means a huge gap between pHR and pHâ values.Therefore, if the design of pHR and pHâ in accordance with
inequalities 7-9 cannot be easily realized, one can use inequalities 10 and 11 to design the electrolytic system of MCRB
for stacking

which imply that at least 50% zwitterion carries a positive charge if it is in phase R or a negative charge if it is in phase
â. Inequality 11 is formulated for the these amino acids Lys, Arg, and His.41
Stacking Condition of Zwitterion by MCRB Created with Weak Electrolyte Buffer. For convenience, the
following assumptions are given briefly. (1) The absolute mobility of a monovalence negative amino acid is considered
to be approximately equal to that of the positive amino acid, as has been shown by Svensson.42,43 This treatment will be
used for the computation of amino acid mobility as shown in Table 1.

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Figure 2. Comparisons between Trp and MCRB velocities in the system of boundary 1. The boundary velocities are
computed with eqs 15 and 16 and Trp velocity with eqs 3 and 13. Conditions: i) 2265 A/m2 (set in accordance with the runs
in Figure 5); _ values of sodium formate solutions are given in Table 2, as well as the Supporting Information.

(2) The boundaries investigated here are designed to migrate toward the cathode. Figure 1A shows that initial state after
the injection of weak alkaline sample matrix. Figure 1B shows that if the velocity of the boundary toward the cathode is
over that of the zwitterion in phase R, there exist the following expressions,

the positive zwitterion in phase R near the MCRB cannot catch up with the boundary moving toward the cathode so can
be partially, even poorly, stacked. The larger the difference of VRâ – Vz R is, the poorer the stacking of the zwitterion by
the MCRB. These analyses will be indicated by the predictions of Figures 2 and 3 and proved by the experiments of
Figures 5, 7, and 8 as well as Figures S1 and S2 (Supporting Information). In eqs 12 and 13, Vz R is the velocity (m s-1)
of the zwitterion in phase R. mj z R is the constituent mobility (m2 V-1 s-1) of the zwitterion in phase R which can be
detected with a CZE as shown in Figure 4A.
To well stack the sample plug injected, evidently the velocity of MCRB must fit to the following expression

Under the condition of expression 14, good stacking of analyte can be achieved as shown in Figure 1C. The meanings
of expression 14 will be shown in Figures 2 and 3 and proved by the experiments of Trp stacking by the numerous
MCRBs in Figures 5-8 and S1-S5 (Supporting Information).

Figure 3. Comparisons of Trp and MCRB velocities in the system of boundary 2. MCRB velocities are computed with eqs
15 and 16 and Trp velocity with eqs 3 and 13. Conditions: i) 4530 A/m2; _ values of phase â are given in Table 3, as well as
the Supporting Information.

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Analytical Chemistry, Vol. 77, No. 4, February 15, 2005

As proved in the papers,33-35 eq 2 should be given as eq 15 under the conditions of MCRB moving toward the cathode
and of weak acidic buffer in phase R due to the background salts (sodium formate in the formic buffer of boundary 1
and sodium acetate in the acetic buffer of boundary 2 shown below).

Comparison of eqs 2 and 15 shows that the constituent concentration of H+ in phase R, cjH+ R , in the denominator of eq
2 becomes the concentration of H+ cH+ R in eq 15.
Computations of MCRB and Zwitterion Velocities. The MCRB systems used in this paper are boundaries 1 and 2,
viz.,
boundary 1:
pH 2.85 formate buffer (+, R) jj[f] sodium formate +5.0 íg/mL Trp (-, â)
boundary 2:
pH 3.50 acetic buffer + 20 mM NaCl (+,R) jj[f] NaAc +1.0 íg/mL Trp (-, â)

In boundaries 1 and 2, the symbol of [f] indicates the boundary of jj moving toward the cathode. Boundary 1 is formed
with the formic buffer and its conjugate salt. Boundary 1 is used for the stacking of Trp in phase â of sodium formate.
Boundary 1 moves toward the cathode, and the running buffer is a mixture of formic acid and sodium formate; thus the
velocities of boundary 1 should be computed with eq 15 as well as eq 16 given below, rather than eq 2 as has been
proved in refs 33-35. The results of computations for boundary 1 are shown in Figure 2. The velocity of Trp in Ph 2.85
formate buffer is calculated with eqs 3 and 13; the computed velocities of Trp are also seen in Figure 2. Boundary 2 is
created with acetic buffer and sodium acetate. Additionally, there is 20 mM NaCl in the acetic buffer. Thus, the
boundary system is quite different from boundary 1. The boundary moves toward the cathode too, so its velocity should
be evaluated

Figure 4. The normal electrophoregrams of CZE of Trp and DMSO in (A) 10- and (B) 120-s 15 mbar pressure injection
sample plugs.Conditions: 40 mM pH 3.5 acetic running buffer, 1.0 íg/mL Trp and 0.03‰ DMSO dissolved in the running
buffer, 50 cm total length (42 cm effective length), and 75-ím-i.d. capillary, 15 kV and 7-9 íA, detection at 214 nm, and 22
°C cooling air. The Trp and DMSO plateaus are observed in panel B; the vertical dotted lines indicate the times of the
“front” and “back” ends of the two plateaus.