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Abstract
Isotachophoresis (ITP) is a versatile electrophoretic technique that can be used for sample preconcentration, separation, purification, and mixing, and to control and accelerate chemical reactions. Although the basic technique is nearly a century old and widely used, there is a persistent need for an easily approachable, succinct, and rigorous review of ITP theory and analysis. This is important because the interest and adoption of the technique has grown over the last two decades, especially with its implementation in microfluidics and integration with on-chip chemical and biochemical assays. We here provide a review of ITP theory starting from physicochemical first-principles, including conservation of species, conservation of current, approximation of charge neutrality, pH equilibrium of weak electrolytes, and so-called regulating functions that govern transport dynamics, with a strong emphasis on steady and unsteady transport. We combine these generally applicable (to all types of ITP) theoretical discussions with applications of ITP in the field of microfluidic systems, particularly on-chip biochemical analyses. Our discussion includes principles that govern the ITP focusing of weak and strong electrolytes; ITP dynamics in peak and plateau modes; a review of simulation tools, experimental tools, and detection methods; applications of ITP for on-chip separations and trace analyte manipulation; and design considerations and challenges for microfluidic ITP systems. We conclude with remarks on possible future research directions. The intent of this review is to help make ITP analysis and design principles more accessible to the scientific and engineering communities and to provide a rigorous basis for the increased adoption of ITP in microfluidics.
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Affiliation(s)
- Ashwin Ramachandran
- Department of Aeronautics and Astronautics, Stanford University, Stanford, California 94305, United States
| | - Juan G Santiago
- Department of Mechanical Engineering, Stanford University, Stanford, California 94305, United States
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2
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Akram W, Gupta A, Bahga SS. A simplified model of oscillating electrolytes. Electrophoresis 2022; 43:708-716. [DOI: 10.1002/elps.202100257] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2021] [Revised: 12/04/2021] [Accepted: 01/04/2022] [Indexed: 11/11/2022]
Affiliation(s)
- Wasim Akram
- Department of Mechanical Engineering Indian Institute of Technology Delhi Delhi India
| | - Amit Gupta
- Department of Mechanical Engineering Indian Institute of Technology Delhi Delhi India
| | - Supreet Singh Bahga
- Department of Mechanical Engineering Indian Institute of Technology Delhi Delhi India
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3
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Bahga SS, Gupta P. Electrophoresis simulations using Chebyshev pseudo-spectral method on a moving mesh. Electrophoresis 2021; 43:688-695. [PMID: 34910828 DOI: 10.1002/elps.202100279] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2021] [Revised: 12/04/2021] [Accepted: 12/06/2021] [Indexed: 11/12/2022]
Abstract
We present the implementation and demonstration of the Chebyshev pseudo-spectral method coupled with an adaptive mesh method for performing fast and highly accurate electrophoresis simulations. The Chebyshev pseudo-spectral method offers higher numerical accuracy than all other finite difference methods and is applicable for simulating all electrophoresis techniques in channels with open or closed boundaries. To improve the computational efficiency, we use a novel moving mesh scheme that clusters the grid points in the regions with poor numerical resolution. We demonstrate the application of the Chebyshev pseudo-spectral method on a moving mesh for simulating nonlinear electrophoretic processes through examples of isotachophoresis (ITP), isoelectric focusing (IEF), and electromigration-dispersion in capillary zone electrophoresis (CZE) at current densities as high as 1000 A/m 2 . We also show the efficacy of our moving mesh method over existing methods that cluster the grid points in the regions with large concentration gradients. We have integrated the adaptive Chebyshev pseudo-spectral method in the open-source SPYCE simulator and verified its implementation with other electrophoresis simulators.
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Affiliation(s)
- Supreet Singh Bahga
- Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi, India
| | - Prateek Gupta
- Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi, India
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4
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Thormann W, Mosher RA. Dynamic computer simulations of electrophoresis: 2010-2020. Electrophoresis 2021; 43:10-36. [PMID: 34287996 PMCID: PMC9292373 DOI: 10.1002/elps.202100191] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2021] [Revised: 07/12/2021] [Accepted: 07/15/2021] [Indexed: 02/05/2023]
Abstract
The transport of components in liquid media under the influence of an applied electric field can be described with the continuity equation. It represents a nonlinear conservation law that is based upon the balance laws of continuous transport processes and can be solved in time and space numerically. This procedure is referred to as dynamic computer simulation. Since its inception four decades ago, the state of dynamic computer simulation software and its use has progressed significantly. Dynamic models are the most versatile tools to explore the fundamentals of electrokinetic separations and provide insights into the behavior of buffer systems and sample components of all electrophoretic separation methods, including moving boundary electrophoresis, CZE, CGE, ITP, IEF, EKC, ACE, and CEC. This article is a continuation of previous reviews (Electrophoresis 2009, 30, S16–S26 and Electrophoresis 2010, 31, 726–754) and summarizes the progress and achievements made during the 2010 to 2020 time period in which some of the existing dynamic simulators were extended and new simulation packages were developed. This review presents the basics and extensions of the three most used one‐dimensional simulators, provides a survey of new one‐dimensional simulators, outlines an overview of multi‐dimensional models, and mentions models that were briefly reported in the literature. A comprehensive discussion of simulation applications and achievements of the 2010 to 2020 time period is also included.
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Affiliation(s)
- Wolfgang Thormann
- Institute for Infectious Diseases, University of Bern, Bern, Switzerland
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5
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Gaš B, Bravenec P. Simul 6: A fast dynamic simulator of electromigration. Electrophoresis 2021; 42:1291-1299. [PMID: 33811678 DOI: 10.1002/elps.202100048] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Revised: 03/22/2021] [Accepted: 03/26/2021] [Indexed: 11/09/2022]
Abstract
Simul 6 is a 1D dynamic simulator of electromigration based on the mathematical model of electromigration in free solutions. The model consists of continuity equations for the movement of electrolytes in a separation channel, acid-base equilibria of weak electrolytes, and the electroneutrality condition. It accounts for any number of multivalent electrolytes or ampholytes and provides a complete picture about dynamics of electromigration and diffusion in the separation channel. The equations are solved numerically using software means which allow for parallelization and multithreaded computation. Simul 6 has a user-friendly graphical interface. It is typically used for inspection of system peaks (zones) in electrophoresis, stacking and preconcentrating analytes, optimization of separation conditions, method development in either capillary zone electrophoresis, isotachophoresis, and isoelectric focusing. Simul 6 is the successor of Simul 5, and has been launched as a free software available for download at https://simul6.app/.
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Affiliation(s)
- Bohuslav Gaš
- Faculty of Science, Department of Physical and Macromolecular Chemistry, Charles University in Prague, Prague, Czech Republic
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6
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Gupta P, Bahga SS. High-resolution numerical simulations of electrophoresis using the Fourier pseudo-spectral method. Electrophoresis 2020; 42:890-898. [PMID: 33300129 DOI: 10.1002/elps.202000259] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2020] [Revised: 11/22/2020] [Accepted: 12/03/2020] [Indexed: 11/09/2022]
Abstract
We present the formulation, implementation, and performance evaluation of the Fourier pseudo-spectral method for performing fast and accurate simulations of electrophoresis. We demonstrate the applicability of this method for simulating a wide variety of electrophoretic processes such as capillary zone electrophoresis, transient-isotachophoresis, field amplified sample stacking, and oscillating electrolytes. Through these simulations, we show that the Fourier pseudo-spectral method yields accurate and stable solutions on coarser computational grids compared with other nondissipative spatial discretization schemes. Moreover, due to the use of coarser grids, the Fourier pseudo-spectral method requires lower computational time to achieve the same degree of accuracy. We have demonstrated the application of the Fourier pseudo-spectral method for simulating realistic electrophoresis problems with current densities as high as 5000 A/m2 with over tenfold speed-up compared to the commonly used second-order central difference scheme, to achieve a given degree of accuracy. The Fourier pseudo-spectral method is also suitable for simulating electrophoretic processes involving a large number of concentration gradients, which render the adaptive grid-refinement techniques ineffective. We have integrated the numerical scheme in a new electrophoresis simulator named SPYCE, which we offer to the community as open-source code.
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Affiliation(s)
- Prateek Gupta
- ETH Zürich, Department of Mechanical and Process Engineering, Zürich, 8092, Switzerland
| | - Supreet Singh Bahga
- Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi, India
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Thormann W, Mosher RA. Instabilities of the pH gradient in carrier ampholyte-based isoelectric focusing: Elucidation of the contributing electrokinetic processes by computer simulation. Electrophoresis 2020; 42:814-833. [PMID: 33184847 DOI: 10.1002/elps.202000269] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2020] [Revised: 10/22/2020] [Accepted: 11/05/2020] [Indexed: 11/05/2022]
Abstract
Electrokinetic processes that lead to pH gradient instabilities in carrier ampholyte-based IEF are reviewed. In addition to electroosmosis, there are four of electrophoretic nature, namely (i) the stabilizing phase with the plateau phenomenon, (ii) the gradual isotachophoretic loss of carrier ampholytes at the two column ends in presence of electrode solutions, (iii) the inequality of the mobilities of positively and negatively charged species of ampholytes, and (iv) the continuous penetration of carbonate from the catholyte into the focusing column. The impact of these factors to cathodic and anodic drifts was analyzed by simulation of carrier ampholyte-based focusing in closed and open columns. Focusing under realistic conditions within a 5 cm long capillary in which three amphoteric low molecular mass dyes were focused in a pH 3-10 gradient formed by 140 carrier ampholytes was investigated. In open columns, electroosmosis displaces the entire gradient toward the cathode or anode whereas the electrophoretic processes act bidirectionally with a transition around pH 4 (drifts for pI > 4 and pI < 4 typically toward the cathode and anode, respectively). The data illustrate that focused zones of carrier ampholytes have an electrophoretic flux and that dynamic simulation can be effectively used to assess the magnitude of each of the electrokinetic destabilizing factors and the resulting drift for a combination of these effects. Predicted drifts of focused marker dyes are compared to those observed experimentally in a setup with coated capillary and whole column optical imaging.
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Affiliation(s)
- Wolfgang Thormann
- Institute for Infectious Diseases, University of Bern, Bern, Switzerland
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Caslavska J, Mosher RA, Thormann W. Computer simulation of the isotachophoretic migration and separation of norpseudoephedrine stereoisomers with a free or immobilized neutral chiral selector. J Chromatogr A 2020; 1623:461176. [PMID: 32505280 DOI: 10.1016/j.chroma.2020.461176] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2020] [Revised: 04/24/2020] [Accepted: 04/27/2020] [Indexed: 11/27/2022]
Abstract
A detailed computer simulation study of the isotachophoretic migration and separation of norpseudoephedrine stereoisomers for cases with the neutral selector added to the leader, immobilized to the capillary wall or support, or partially present in the separation column is presented. The electrophoretic transport of the analytes from the sampling compartment into the separation medium with the selector, the formation of a transient mixed zone, the separation dynamics of the stereoisomers with a free or immobilized selector, the dependence of the leader pH, the ionic mobility of norpseudoephedrine, the complexation constant and selector immobilization on steady-state plateau zone properties, and zone changes occurring during the transition from the chiral environment into a selector free leader are thereby visualized in a hitherto unexplored way. For the case with the selector dissolved in the leading electrolyte, simulation data are compared to those observed in experimental setups with coated fused-silica capillaries that feature minimized electroosmosis and zone detection with conductivity and absorbance detectors.
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Affiliation(s)
- Jitka Caslavska
- Clinical Pharmacology Laboratory, Institute for Infectious Diseases, University of Bern, Bern, Switzerland
| | | | - Wolfgang Thormann
- Clinical Pharmacology Laboratory, Institute for Infectious Diseases, University of Bern, Bern, Switzerland.
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9
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Schaumburg F, Kler PA, Berli CLA. Comprehensive model of electromigrative transport in microfluidic paper based analytical devices. Electrophoresis 2020; 41:598-606. [DOI: 10.1002/elps.201900353] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Revised: 11/28/2019] [Accepted: 12/08/2019] [Indexed: 11/06/2022]
Affiliation(s)
- Federico Schaumburg
- INTEC (Universidad Nacional del Litoral–CONICET)Colectora RN 168 Km 472 S3000GLN Santa Fe Argentina
| | - Pablo A. Kler
- CIMEC (Universidad Nacional del Litoral–CONICET)Colectora RN 168 Km 472 S3000GLN Santa Fe Argentina
- Departamento de Ingeniería en Sistemas de InformaciónFRSF‐UTN.Lavaise 610 S3004EWB Santa Fe Argentina
| | - Claudio L. A. Berli
- INTEC (Universidad Nacional del Litoral–CONICET)Colectora RN 168 Km 472 S3000GLN Santa Fe Argentina
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Malá Z, Gebauer P. Recent progress in analytical capillary isotachophoresis. Electrophoresis 2018; 40:55-64. [DOI: 10.1002/elps.201800239] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2018] [Revised: 07/12/2018] [Accepted: 07/13/2018] [Indexed: 12/30/2022]
Affiliation(s)
- Zdena Malá
- Institute of Analytical Chemistry of the Czech Academy of Sciences; Brno Czech Republic
| | - Petr Gebauer
- Institute of Analytical Chemistry of the Czech Academy of Sciences; Brno Czech Republic
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