Mathematical modeling and computer simulation of isoelectric focusing with electrochemically defined ampholytes

Palusinski, O.A.; Allgyer, Thomas T.; Mosher, Richard A.; Bier, M.; Saville, D. A.

doi:10.1016/0301-4622(81)80001-4

Cited by 45 publications

(30 citation statements)

References 12 publications

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“…The numerical results are obtained for a 2-D straight (planar) channel as shown in Fig. 2, and all results are extracted at the channel 2 6.5 6.1 pK 3 7.12 6.8 pK 4 7.25 7.15 pK 5 7.5 7.22 pK 6 8.5 8.19 pK 7 9.8 8.58 pK 8 10.31 9.5 pK 9 11.18 9.55…”

Section: Resultsmentioning

confidence: 99%

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Effects of ampholyte concentration on protein behavior in on‐chip isoelectric focusing

2008

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The effects of mobility corrections on carrier ampholytes are studied at various ampholyte concentrations to understand protein behavior during IEF. IEF simulations are conducted in the presence of 25 biprotic carrier ampholytes within a pH range of 6-9 after applying the Onsager-Debye-Hückel correction to the carrier ampholytes. Two model proteins with ten charge states but without ionic strength corrections are allowed to focus under an electric field of 300 V/cm in a 1 cm long channel. The IEF simulation results show that higher ionic strengths (50 - 100 mM) cause significant changes in the transient movement as well as the final focused profiles of both ampholytes and proteins. The time required for a single, well-defined peak to form increases with ionic strength when Onsager corrections are applied to the carrier ampholytes. For a particular ampholyte concentration, the space-averaged conductivity does not change during the final focusing stage, but the magnitude of space averaged conductivity is different for different ampholyte concentration. The simulation results also reveal that at steady-state ionic strength profiles remain flat throughout the channel except at the locations of proteins where a significant change in ampholyte concentration is obtained.

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Section: Resultsmentioning

confidence: 99%

“…In 1981, Palusinski et al [3] introduced a computer model of IEF which could be used in a multicomponent system. Their mathematical model described how to predict the concentration of ampholytes, pH gradient, and conductance at the steady state.…”

Section: Introductionmentioning

confidence: 99%

Effects of ampholyte concentration on protein behavior in on‐chip isoelectric focusing

2008

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“…However, all of the early mathematical models of electrophoresis were established as separate models. In 1981, a universal model of electrophoresis was introduced by Palusinski et al [9] for steady-state processes. Later, Bier et al [10] extended this model to transient problems.…”

Section: Introductionmentioning

confidence: 99%

Modeling and simulation of IEF in 2‐D microgeometries

2007

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A 2-D finite-volume model is developed to simulate nonlinear IEF in complex microgeometries. This mathematical model is formulated based on the mass conservation and ionic dissociation relations of amphoteric macromolecules, charge conservation, and the electroneutrality condition. Based on the 2-D model, three different separation cases are studied: an IPG in a planar channel, an ampholyte-based pH gradient in a planar channel, and an ampholyte-based pH gradient in a contraction-expansion channel. In the IPG case, cacodylic acid (pK(1) = 6.21) and Tris (pK(1) = 8.3) are used as the acid and base, respectively, to validate the 2-D IEF model. In the ampholyte-based pH gradient cases, IEF is performed in the pH range, 6.21-8.3 using 10 ampholytes in the planar channel and 20 ampholytes in the contraction-expansion channel. The numerical results reveal different focusing efficiencies and resolution in the narrow and wide sections of the contraction-expansion channel. To explain this, the expressions for separation resolution and peak concentrations of separands in the contraction-expansion channel are presented in terms of the channel shape factor. In a 2-D planar channel, a focused band remains straight all the time. However, in a contraction-expansion channel, initially straight bands take on a crescent profile as they pass through the trapezoidal sections joining the contraction and expansion sections.

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“…These restrictions were removed in the model developed for IEF by Palusinski et al (1981b) wherein assumptions regarding the shapes of the pH or the conductivity profiles are avoided. (See also Palusinski et al, 1981a;Bier et al, 1981;and Bier et al (1983). The current model is based on this work, expanded so as to cover a wide variety of electrophoretic modes.…”

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confidence: 98%

Theory of electrophoretic separations. Part I: Formulation of a mathematical model

1986

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A general model is developed for the electrophoresis of soluble materials. The model describes the evolution of concentration fields for a set of compounds which undergo transport by flow, diffusion, and migration in an electric field and simultaneously participate in rapid dissociation-association reactions. Modes of electrophoresis requiring special treatment can now be studied in a unified context. As an example of its utility, the model is used analytically to study a process known as isotachophoresis. In Part I1 two electrophoretic separation processes are simulated numerically, demonstrating the model's versatility. D. A. SAVILLE Department of Chemical EngineeringPrinceton University Princeton, NJ 08544 A. PALUSINSKI Biophysics Technology Laboratory and Department of Electrical and Computer Engineering University of ArizonaTucson, AZ 85721 SCOPEWhen a solution containing amphoteric compounds is exposed to an electric field, the migration of ions and uncharged species occurs in the presence of rapid dissociation-recombination reactions. If a zone containingseveral species is inserted in a column containinga homogeneous buffer, the various species will migrate at different rates according to their relative electrophoretic mobilities. Conversely, if the ends of the column are made impermeable to the amphoteric species, a stationary pH gradient will eventually be formed and sample constituents will migrate to their equilibrium isoelectric points under the influence ofthe electric field. These phenomena form the basis of several separation methodologies that have been difficult to model mathematically. The purpose of this paper is to present a generally applicable model of electrophoretic processes and apply it to a specific situation. The application is designed to illustrate the interplay between reaction, electromigration, and diffusion in simple configurations where complications due to lateral boundaries, bulk flow, and nonuniform temperature are supressed. The situation studied in detail is isotachophoresis in a one-dimensional column; more diverse applications that require numerical treatment of the equations are described in Part 11. CONCLUSIONS AND SIGNIFICANCEAlthough electrophoretic processes can be described by familiar conservation relations, the structure of the mathematical model differs from that used to describe systems with strong electrolytes due to the presence of rapid dissociation-recombination reactions that tie the concentrations of ionic species to those of the undissociated solutes. It is shown that since the reactions are fast relative to transport by diffusion and electromigration, it is possible to treat the reactions as being in local equilibrium. Similarly, the ratio of an electrical length (the Debye scale) to the physical scale of the process is small, and this leads to the electroneutrality approximation. The model that is developed consists of a set of conservation equations for the total concentration of each amphoteric compound and the current. Appended to this set of partial...

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Mathematical modeling and computer simulation of isoelectric focusing with electrochemically defined ampholytes

Cited by 45 publications

References 12 publications

Effects of ampholyte concentration on protein behavior in on‐chip isoelectric focusing

Effects of ampholyte concentration on protein behavior in on‐chip isoelectric focusing

Modeling and simulation of IEF in 2‐D microgeometries

Theory of electrophoretic separations. Part I: Formulation of a mathematical model

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