The dynamics of band (peak) shape development in capillary zone electrophoresis in light of the linear theory of electromigration

Dvořák, Martin; Dubský, Pavel; Dovhunová, Magda; Gaš, Bohuslav

doi:10.1002/elps.201800444

Cited by 10 publications

(18 citation statements)

References 43 publications

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“…(28) in ref. []). This allows us to avoid the abstract language of propagating waves in CZE and to speak of the propagation of an analyte peak, when focused on analytes.…”

Section: Resultsmentioning

confidence: 99%

“…In the cited review paper , we discussed that the resulting PDEs rather surprisingly resemble those describing chromatographic separations with Langmuir isotherm. Under the simplification that (i) Only analyte peaks co‐migrate for a certain period of time and they do not interact with system peaks from the very beginning of the separation process; (ii) pH is constant throughout the zones of analytes, equal to that of the BGE, that is, analytes do not change their dissociation states within their own peak(s); (iii) diffusion (along with the diffusion current density) is neglected altogether; the following set of PDEs describes the propagation of analyte peaks in electrophoresis:

\frac{\partial c_{i} (x, t)}{\partial t} + \frac{\partial}{\partial x} (\frac{{\tilde{v}}_{i} c_{i} ((), x, t)}{1 + \sum_{j = 1}^{N_{A}} \frac{κ_{j}}{κ_{BGE}} c_{j} (x, t)}) = 0,

where i stands for analyte constituents only and the constituents are indexed so that the first up to the

N_{A}

th constituents are analyte constituents,

{\overset{v}{true}}_{i} = μ_{eff, i} \frac{j}{κ_{BGE}}

is the (effective) velocity of the i th analyte in the given BGE and

κ_{j}

is a quantity defined in ref.…”

Section: Resultsmentioning

confidence: 99%

“…Several theoretical models attempted to predict the peak shape distribution of an analyte in CZE based on the physical‐chemical properties, pKa values and electrophoretic mobilities, of the analyte and BGE constituents. We have summarized various approaches in our recent review paper . All of the models discussed in ref.…”

Section: Introductionmentioning

confidence: 99%

“…All of the models discussed in ref. [] adopt an approximation of an immediate separation of all waves in CZE, that is, they assume independent migration of analyte (and system) peaks from the very beginning of the separation process.…”

Section: Introductionmentioning

confidence: 99%

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The dynamics of band (peak) shape development in capillary zone electrophoresis in the case of two co‐migrating analytes: The displacement and the tag‐along effects

et al. 2019

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The dynamics of band (peak) shape development in capillary zone electrophoresis in the case of two co-migrating analytes: The displacement and the tag-along effects Peak shapes in electrophoresis are often distorted from the ideal Gaussian shape due to disturbing phenomena, of which the most important is electromigration dispersion. For fully dissociated analytes, there is a tight analogy between nonlinear models describing a separation process in chromatography and electrophoresis. When the velocity of the separated analyte depends on the concentration of the co-analyte, the consequence is a mutual influence of the analytes couples, which distorts both analyte zones. In this paper, we introduce a nonlinear model of electromigration for the analysis of two co-migrating fully dissociated analytes. In the initial stages of separation, they influence each other, which causes much more complicated peak shapes. The analysis has revealed that the two most important phenomena-the displacement and the tag-along effects-are common both for nonlinear chromatography and electrophoresis, though their description is partly based on rather different phenomena. The comparison between the nonlinear model of electromigration we describe and the numerical computer solution of the original continuity equations has proven an almost perfect agreement. The predicted features in peak shapes in initial stages of separation have been fully confirmed by the experiments.

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“…(28) in ref. []). This allows us to avoid the abstract language of propagating waves in CZE and to speak of the propagation of an analyte peak, when focused on analytes.…”

Section: Resultsmentioning

confidence: 99%

\frac{\partial c_{i} (x, t)}{\partial t} + \frac{\partial}{\partial x} (\frac{{\tilde{v}}_{i} c_{i} ((), x, t)}{1 + \sum_{j = 1}^{N_{A}} \frac{κ_{j}}{κ_{BGE}} c_{j} (x, t)}) = 0,

where i stands for analyte constituents only and the constituents are indexed so that the first up to the

N_{A}

th constituents are analyte constituents,

{\overset{v}{true}}_{i} = μ_{eff, i} \frac{j}{κ_{BGE}}

is the (effective) velocity of the i th analyte in the given BGE and

κ_{j}

is a quantity defined in ref.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The dynamics of band (peak) shape development in capillary zone electrophoresis in the case of two co‐migrating analytes: The displacement and the tag‐along effects

et al. 2019

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“…We refer the reader to Supporting Information for a complete theory, including several essential technical details that may not be clear in the original papers. Our second paper published in this special issue provides a concise summary of (N)LTEM (yet in simple CZE systems only). In short, the mathematical analysis reveals that BGE forms an environment in which N independent wave functions,

{\tilde{w}}_{i}

, tend to propagate with velocities

(\frac{j}{κ_{B G E}} λ_{i}) .

λ_{i}

are eigenvalues of a matrix

{boldM}_{0} = bold-italic M false({\vec{boldC}}_{BGE} false)

evaluated at the composition of BGE.…”

Section: Theorymentioning

confidence: 99%

Generalized model of the linear theory of electromigration and its application to electrokinetic chromatography: Theory and software PeakMaster 6—Next Generation

et al. 2019

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The linear theory of electromigration, including the first‐order nonlinear approximation, is generalized to systems with any equilibria fast enough to be considered instantaneous in comparison with the timescale of peak movement. For example, this theory is practically applied in the electrokinetic chromatography (EKC) mode of the CZE. The model enables the calculation of positions and shapes of analyte and system peaks without restricting the number of selectors, the complexation stoichiometry, or simultaneous acid–base equilibria. The latest version of our PeakMaster software, PeakMaster 6—Next Generation, implements the theory in a user‐friendly way. It is a free and open‐source software that performs all calculations and shows the properties of the background electrolyte and the expected electropherogram within a few seconds. In this paper, we mathematically derive the model, discuss its applicability to EKC systems, and introduce the PeakMaster 6 software.

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Microscale electrokinetic‐based analysis of intact cells and viruses

Vaghef-Koodehi

Lapizco‐Encinas

2021

Electrophoresis

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Miniaturized electrokinetic methods have proven to be robust platforms for the analysis and assessment of intact microorganisms, offering short response times and higher integration than their bench‐scale counterparts. The present review article discusses three types of electrokinetic‐based methodologies: electromigration or motion‐based techniques, electrode‐based electrokinetics, and insulator‐based electrokinetics. The fundamentals of each type of methodology are discussed and relevant examples from recent reports are examined, to provide the reader with an overview of the state‐of‐the‐art on the latest advancements on the analysis of intact cells and viruses with microscale electrokinetic techniques. The concluding remarks discuss the potential applications and future directions.

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The dynamics of band (peak) shape development in capillary zone electrophoresis in light of the linear theory of electromigration

Cited by 10 publications

References 43 publications

The dynamics of band (peak) shape development in capillary zone electrophoresis in the case of two co‐migrating analytes: The displacement and the tag‐along effects

The dynamics of band (peak) shape development in capillary zone electrophoresis in the case of two co‐migrating analytes: The displacement and the tag‐along effects

Generalized model of the linear theory of electromigration and its application to electrokinetic chromatography: Theory and software PeakMaster 6—Next Generation

Microscale electrokinetic‐based analysis of intact cells and viruses

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