Performance optimization in electric field gradient focusing

Electric field gradient focusing (EFGF) is a technique used to simultaneously separate and concentrate biomacromolecules, such as proteins, based on the opposing forces of an electric field gradient and a hydrodynamic flow. Recently, we reported EFGF devices fabricated completely from copolymers functionalized with poly(ethylene glycol), which display excellent resistance to protein adsorption. However, the previous devices did not provide the predicted linear electric field gradient and stable current. To improve performance, Tris–HCl buffer that was previously doped in the hydrogel was replaced with a phosphate buffer containing a salt (i.e., potassium chloride, KCl) with high mobility ions. The new devices exhibited stable current, good reproducibility, and a linear electric field distribution in agreement with the shaped gradient region design due to improved ion transport in the hydrogel. The field gradient was calculated based on theory to be approximately 5.76 V/cm² for R-phycoerythrin when the applied voltage was 500 V. The effect of EFGF separation channel dimensions was also investigated; a narrower focused band was achieved in a smaller diameter channel. The relationship between the bandwidth and channel diameter is consistent with theory. Three model proteins were resolved in an EFGF channel of this design. The improved device demonstrated 14,000-fold concentration of a protein sample (from 2 ng/mL to 27 μg/mL).     

Protein separation using preparative-scale dynamic field gradient focusing

Dynamic field gradient focusing uses an electric field gradient to separate and concentrate proteins in native buffers. A prototype preparative-scale dynamic field gradient focusing apparatus reproducibly separated hemoglobin and bovine serum albumin with a mean resolution of 2.64+/-0.503. Run-to-run variations in the hemoglobin's focal point and peak width appeared to be related to fluctuations in the shape of the electric field, rather than the 5% accuracy of the pump that provided the counter-flow in the separation annulus. The variation in the electric field gradient was probably due to the formation and expansion of an ion-depleted region at the top of the separation annulus.     

Electrophoretic field gradient focusing: an investigation of the experimental parameters

Electrophoretic field gradient focusing has been used to separate the two oxidation states of myoglobin (Mb), and to separate Mb from bromophenol blue (BPB). Polyacrylamide and Sephadex were shown to be suitable packing materials whilst silica led to band broadening with Mb. BPB and Mb could be simultaneously focused apart using either a fixed 21-electrode setup or a dynamic 6-electrode setup. Using a dynamic three-electrode setup either analyte could be focused but not both simultaneously. It was shown that a higher ionic strength buffer in the separation channel compared to the coolant channel enhanced focusing between electrodes due to a conductivity gradient. Different running buffers were investigated and it was found that using a pH 8.6 buffer containing N,N,N-tris(hydroxymethyl)aminomethane (Tris) and phosphate ions the oxidation states of Mb could be separated but the separation of Mb from BPB was not as good as would be hoped for. Using a pH 8.6 buffer containing Tris, N-2-hydroxyethylpiperazine-N'-3-propanesulphonate and chloride ions as running buffer, BPB and Mb could be well separated but the two oxidation states of Mb merged.     

Influence of varying electroosmotic flow on the effective diffusion in electric field gradient separations

Recently the use electric field gradient focusing (EFGF) to enhance focusing of proteins has been proposed and explored to provide significant improvement in separation resolution. The objective of EFGF is to focus proteins of specific electrophoretic mobilities at distinct stationary locations in a column or channel. This can be accomplished in a capillary by allowing the electric potential to vary in the streamwise direction. Because the electric field is varying, so also is the electrokinetic force exerted on the proteins and the electroosmotic velocity of the buffer solution. Due to the varying electric field, the Taylor diffusion characteristics will also vary along the column, causing a degradation of peak widths of some proteins, dependent on their equilibrium positions and local velocity distributions. The focus of this paper is an analysis that allows characterization of the local Taylor diffusion and resulting protein band peak width as a function of the local magnitude of the EOF relative to the average fluid velocity for both cylindrical and rectangular channels. In general the analysis shows that as the ratio of the local electroosmotic velocity to the average velocity deviates from unity, the effective diffusion increases significantly. The effectiveness of EFGF devices over a range of protein diffusivities, capillary diameters, flow velocities, and electric field gradient is discussed.     

Assessing the scalability of dynamic field gradient focusing by linear modeling

Dynamic field gradient focusing (DFGF) separates and concentrates proteins in native buffers, where proteins are most soluble, using a computer-controlled electric field gradient which lets the operator adjust the pace and resolution of the separation in real-time. The work in this paper assessed whether DFGF could be scaled up from microgram analytical-scale protein loads to milligram preparative-scale loads. Linear modeling of the electric potential, protein transport, and heat transfer simulated the performance of a preparative-scale DFGF instrument. The electric potential model showed where the electrodes should be placed to optimize the shape and strength of the electric field gradient. Results from the protein transport model suggested that in 10 min the device should separate 10 mg each of two proteins whose electrophoretic mobilities differ by 5 x. Proteins with electrophoretic mobilities differing by only 5% should separate in 3 h. The heat transfer model showed that the preparative DFGF design could dissipate 1 kW of Joule heat while keeping the separation chamber at 25 degrees C. Model results pointed to DFGF successfully scaling up by 1000 x using the proposed instrument design.     

Isoperichoric focusing field-flow fractionation and thin layer isoperichoric focusing based on coupling of gradient generated by primary field with secondary field action: general principles and performances

The primary field forces can generate spatially oriented gradient of the effective property of a continuum or pseudo-continuum fluid (carrier liquid). When this gradient is coupled with the action of a secondary field of identical or different nature the isoperichoric focused zones of the dispersed species can appear. Consequently, they can be separated according to differences responding to the property gradient of the carrier liquid. This concept can be applied under static (non-flow) conditions in thin layer focusing as well as under dynamic conditions with the elution due to the carrier liquid flow in focusing field-flow fractionation. The gradient established by the action of the primary field and the concentration distribution of the isoperichoric focused zone formed by the coupled effect of the gradient and of the primary or secondary field are described theoretically. The rigorous relationship describing the shape of the focused zone is compared with the approximate solutions. The performances of the proposed principle were evaluated by model calculations. Potential experimental configurations considering the implementation of the static and dynamic conditions are discussed. The generalized isoperichoric focusing theory can be applied to describe the particular processes operating in analytical and preparative focusing separations of the particles of various, but especially of biological origin.     

Taylor-Aris dispersion in temperature gradient focusing

Microfluidic temperature gradient focusing (TGF) uses an axial temperature gradient to induce a gradient in electrophoretic flux within a microchannel. When balanced with an opposing fluid flow, charged analytes simultaneously focus and separate according to their electrophoretic mobilities. We present a theoretical and experimental study of dispersion in TGF. We model the system using generalized dispersion analysis that yields a 1-D convection-diffusion equation that contains dispersion terms particular to TGF. We consider analytical solutions for the model under uniform temperature gradient conditions. Using a custom TGF experimental setup, we compare focusing measurements with the theoretical predictions. We find that the theory well represents the focusing behavior for flows within the Taylor-Aris dispersion regime.     

Investigating peak dispersion in free-flow counterflow gradient focusing

Free-flow electrophoresis (FFE) enables the continuous separation and collection of charged solutes, and as a result, it has drawn interest as both a preparative and an analytical tool for biological applications. Recently, a free-flow counterflow gradient focusing (FF-CGF) mechanism has been proposed with the goal of improving the resolution and versatility of FFE. To realize this potential, the factors that influence solute dispersion deserve further attention, including the gradient strength and the parabolic profile of the counterflow. Therefore, the goal of this work is to develop a theoretical model to study the interplay between these factors and molecular diffusion. Overall, an asymmetric solute distribution emerges for a wide range of parameters, and this behavior can be characterized with an exponentially modified Gaussian function. Results show that FF-CGF can achieve high-resolution separations, with the potential for high-throughput protein purification. Moreover, this work provides a practical guide for optimizing experimental conditions, as well as a strong framework for understanding and developing FF-CGF further.     

Hydrogen bond interactions in sulfamerazine: DFT study of the O-17, N-14, and H-2 electric field gradient tensors

Hydrogen bond (HB) interactions are studied in the real crystalline structure of sulfamerazine by density functional theory (DFT) calculations of the electric field gradient (EFG) tensors at the sites of O-17, N-14, and H-2 nuclei. One-molecule (single) and four-molecule (cluster) models of sulfamerazine are created by available crystal coordinates and the EFG tensors are calculated in both models to indicate the influence of HB interactions on the tensors. Directly relate to the experiments, the calculated EFG tensors are converted to the experimentally measurable nuclear quadrupole resonance (NQR) parameters, quadrupole coupling constant (qcc) and asymmetry parameter (η_Q). The evaluated NQR parameters reveal that due to contribution of the target molecule to N–HN and N–HO types of HB interactions, the EFG tensors at the sites of various nuclei are influenced from single model to the target molecule in cluster. Additionally, O2, N4, and H2 nuclei of the target molecule are significantly influenced by HB interactions, consequently, they have the major contributions to HB interactions in cluster model of sulfamerazine. The calculations are performed employing B3LYP method and 6-311++G** basis set using GAUSSIAN 98 suite of program.     

Calculation of the deuterium electric field gradients in HD and LiD using a variation-perturbation method with a Gaussian basis set

Summary We present calculations of the deuterium electric field gradients in the HD and LiD molecules obtained with a variation-perturbation method using Gaussian atomic orbitals. The differences between our theoretical values and the corresponding experimental or best calculated values are 2%. We conclude that high accuracy can be obtained with the variation-perturbation method using either Gaussian or Slater orbitals.     

Determination of the electric field gradient asymmetry from Berry’s phase in NQR of powder samples

An effect of Berry’s phase on the NQR spectrum of the rotating powder sample is described and applied for the determination of the electric field gradient asymmetry. The proposed method involves the analysis of the frequency singularities in the NQR powder patterns of the rotating samples. The Berry’s phases for the eigenstates, associated with an adiabatically changing quadrupole hamiltonian, are calculated for nuclei with a spin I = 3/2 and I = 1 as a function of the asymmetry parameter.     

Quantitative temperature gradient focusing performed using background electrolytes at various pH values

Temperature gradient focusing (TGF) has previously been shown to be a practical technique for simultaneous concentration and separation of a variety of samples. In this paper, we demonstrate that TGF can be conducted at a wide range of pH values. Techniques for first-order prediction of the suitability of a given BGE for focusing are discussed. Buffer suitability for TGF is assessed experimentally by simultaneously concentrating and separating a pair of fluorescent analytes. One analyte is held at constant concentration for use as an internal standard while the concentration of the other dye is varied. Peak area is shown to vary linearly with the input dye concentration. A high degree of resolution (R(s) >3) of fluorescein and carboxyfluorescein, as well as for two LysoSensor-based dyes, is also observed. Foucusing and separation by TGF was successfully conducted quantitatively in BGE solutions of pH from 3.0 to 10.5.     

Microchannel protein separation by electric field gradient focusing

A microchannel device is presented which separates and focuses charged proteins based on electric field gradient focusing. Separation is achieved by setting a constant electroosmotic flow velocity against step changes in electrophoretic velocity. Where these two velocities are balanced for a given analyte, the analyte focuses at that point because it is driven to it from all points within the channel. We demonstrate the separation and focusing of a binary mixture of bovine serum albumin and phycoerythrin. The device is constructed of intersecting microchannels in poly(dimethylsiloxane)(PDMS) inlaid with hollow dialysis fibers. The device uses no exotic chemicals such as antibodies or synthetic ampholytes, but operates instead by purely physical means involving the independent manipulation of electrophoretic and electroosmotic velocities. One important difference between this apparatus and most other devices designed for field-gradient focusing is the injection of current at discrete intersections in the channel rather than continuously along the length of a membrane-bound separation channel.     

Influence of transport properties in electric field gradient focusing

Miniaturized devices for electric field gradient focusing (EFGF) were developed that consist of a cylindrical separation channel surrounded by an acrylic-based polymer hydrogel. The ionic transport properties of the hydrogel enable the manipulation of the electric field inside the separation channel. A changing cross-section design was used in which the hydrogel is shaped such that an electric field gradient is established in the separation channel. One of the challenges with this type of EFGF device has been that experimental resolution between protein analytes is lower than theoretically predicted. In order to investigate this phenomenon, a mathematical transport model was developed using FEMLAB. Model results and experimental observations showed that the reduced performance was caused by concentration gradients formed in the EFGF channel, and that these concentration gradients were the result of an imbalance in cation transport between the open separation channel and the hydrogel. Removing acidic impurities from the monomers that form the hydrogel reduced this tendency and improved the resolution. These transport-induced concentration gradients can be used to establish electric field gradients that may be useful for sample pre-concentration. Both the results of simulation and experiments demonstrate how transport-induced concentration gradients lead to the establishment of electric field gradients.     

Bipolar electrode focusing: tuning the electric field gradient

Bipolar electrode (BPE) focusing is a developing technique for enrichment and separation of charged analytes in a microfluidic channel. The technique employs a bipolar electrode that initiates faradaic processes that subsequently lead to formation of an ion depletion zone. The electric field gradient resulting from this depletion zone focuses ions on the basis of their individual electrophoretic mobilities. The nature of the gradient is of primary importance to the performance of the technique. Here, we report dynamic measurements of the electric field gradient showing that it is stable over time and that its axial position in the microchannel is directly correlated to the location of an enriched tracer band. The position of the gradient can be tuned with pressure-driven flow. We also show that a steeper electric field gradient decreases the breadth of the enriched tracer band and therefore enhances the enrichment process. The slope of the gradient can be tuned by altering the buffer concentration: higher concentrations result in a steeper gradient. Coating the channel with the neutral block co-polymer Pluronic also results in enhanced enrichment.     

Two-dimensional gel isoelectric focusing

Two-dimensional gel isoelectric focusing (2-D gel IEF) is presented as the combination of the same separation method used consecutively in two directions of the same gel. In this new method, after completion of IEF process in the first dimension the gel was cut into the separate strips, each containing selected analytes together with the appropriate part of the original broad pH gradient, and the strips were rotated by 90 degrees (with regard to the first IEF) and left to diffuse overnight. After diffusion the strips were subjected to the second IEF. During the second IEF, the corresponding narrow part of pH gradient in each strip was restored again, however, now along the strip. The progress of the separation process can be monitored visually by using colored low-molecular-weight isoelectric point (pI) markers loaded into the gel simultaneously with proteins. The unique properties of IEF, focusing and resolution power were enhanced by using the same technique twice. Two forms of beta-lactoglobulin (pI values 5.14 and 5.31, respectively) non-separated in the first IEF were successfully separated in the second dimension at relatively low voltage (330 V) with the resolution power comparable to the high-resolution gels requiring the high voltage during the run and long separation time. Glucose oxidase loaded as diluted solution into ten positions across the gel was finally focused into a single band during 2-D gel IEF. Since the first and second IEF are carried out on the same gel, no losses and contamination of analyte occur. The suggested method can be used for separation/fractionation of complex biological mixtures, similarly as other multidimensional separation techniques applied in proteomics, and can be followed by further processing, e.g., mass spectrometry analysis. The focusing properties of IEF could be useful especially in separation of mixtures, where components are at low concentration levels.     

Convergence of electric field and electric field gradient versus atomic basis sets in all-siliceous and Mg substituted phillipsites

Electrostatic potential (EP), electric field (EF), and electric field gradient (EFG) values are calculated in periodic models of magnesium substituted phillipsite (MgPHI) zeolite forms using periodic DFT (PDFT) hybrid B3LYP level with fourteen different basis sets. Relative root mean square differences between the EP, EF, or EFG values estimated between different basis sets are evaluated in several spatial domains available for adsorbate molecules in the zeolite. In these areas, the EF increase in MgPHI is evaluated relative to all-siliceous PHI types. The EP is interpreted in terms of framework ionicity for MgPHI and all-siliceous PHI models. Angular Si-O-Si dependence of the EFG asymmetry at (17)O atoms in all-siliceous zeolites is discussed.     

Experimental study of isopycnic focusing generated by coupled electric and gravitational field forces: Use in thin layer focusing and focusing field-flow fractionation

Various operational parameters affecting the formation of the density gradient generated by the electric field action on a binary pseudo-continuous carrier liquid composed of charged colloidal silica particles suspended in water and the isopycnic focusing of sample particles were investigated under conditions of static thin layer focusing and dynamic focusing field-flow fractionation. The properties and the behavior of the density gradient forming carrier liquid were studied. The experimental results are compared with theoretical predictions and discussed with respect to potential applications of the proposed concept not only for separation purposes but also for studies of interparticle interactions.     

The transitional isoelectric focusing process

The transitional isoelectric focusing (IEF) process (the course of pH gradient formation by carrier ampholytes (CAs) and the correlation of the focusing time with CA concentration) were investigated using a whole-column detection capillary isoelectric focusing (CIEF) system. The transitional double-peak phenomenon in IEF was explained as a result of migration of protons from the anodic end and hydroxyl ions from the cathodic end into the separation channel and the higher electric field at both acidic and basic sides of the separation channel. It was observed that focusing times increase logarithmically with CA concentration under a constant applied voltage. The correlation of focusing time with CA concentration was explained by the dependence of the charge-transfer rate on the amount of charged CAs within the separation channel during focusing.     

Investigation of the pH gradient formation and cathodic drift in microchip isoelectric focusing with imaged UV detection

This paper reports the protein analysis by using microchip IEF carried on an automated chip system. We herein focused on two important topics of microchip IEF, the pH gradient and cathodic drift. The computer simulation clarified that the EOF could delay the establishment of pH gradient and move the carrier ampholytes (CAs) to cathode, which probably caused a cathodic drift to happen. After focusing, the peak positions of components in a calibration kit with broad pI were plotted against their pI values to know the actual pH gradient in a microchannel varying time. It was found that the formed pH gradient was stable, not decayed after readily steady state, and migrated to cathode at a rate of 10.0 μm/s that determined by the experimental conditions such as chip material, internal surface coating and field strength. The theoretical pH gradient was parallel with the actual pH gradient, which was demonstrated in two types of microchip with different channel lengths. No compression of pH gradient was observed when 2% w/v hydroxypropyl methyl cellulose was added in sample and electrolytes. The effect of CAs concentration on current and cathodic drift was also explored. With the current automatic chip system, the calculated peak capacity was 23–48, and the minimal pI difference was 0.20–0.42 for the used single channel microchip with the effective length of 40.5 mm. The LOD for the analysis of CA‐I and CA‐II was around 0.32 μg/mL by using normal imaged UV detection, the detected amount is ca. 0.07 ng.