Free-solution Electrophoresis Research Articles

Transient Gel Electrophoresis of a Spherical Colloidal Particle

The general theory is developed for the time-dependent transient electrophoresis of a weakly charged spherical colloidal particle with an electrical double layer of arbitrary thickness in an uncharged or charged polymer gel medium. The Laplace transform of the transient electrophoretic mobility of the particle with respect to time is derived by considering the long-range hydrodynamic interaction between the particle and the polymer gel medium on the basis of the Brinkman-Debye-Bueche model. According to the obtained Laplace transform of the particle's transient electrophoretic mobility, the transient gel electrophoretic mobility approaches the steady gel electrophoretic mobility as time approaches infinity. The present theory of the transient gel electrophoresis also covers the transient free-solution electrophoresis as its limiting case. It is shown that the relaxation time for the transient gel electrophoretic mobility to reach its steady value is shorter than that of the transient free-solution electrophoretic mobility and becomes shorter as the Brinkman screening length decreases. Some limiting or approximate expressions are derived for the Laplace transform of the transient gel electrophoretic mobility.

Using capillary electrophoresis to characterize the hydrodynamic and electrostatic properties of DNA in solutions containing various monovalent cations.

This review describes the results obtained by using free-solution capillary electrophoresis to probe the electrostatic and hydrodynamic properties of DNA in solutions containing various monovalent cations. In brief, we found that the mobilities of double-stranded DNAs (dsDNAs) increase with increasing molecular weight before leveling off and becoming constant at molecular weights ≥400bp. The mobilities of single-stranded DNAs (ssDNAs) go through a maximum at ∼10-20 nucleotides before decreasing and becoming constant for oligomers larger than ∼30-50 bases. The mobilities of both ss- and dsDNAs increase linearly with the logarithm of increasing charge per unit length and decrease linearly with the logarithm of increasing ionic strength. Surprisingly, ss- and dsDNA mobilities level off and become nearly constant at ionic strengths ≥0.6 M. The thermal stabilities of dsDNAs decrease linearly with increasing solution viscosity. The diffusion coefficients of dsDNA are modulated by the diffusion coefficients of their counterions because of electrostatic DNA-cation coupling interactions. Finally, the anomalously slow mobilities observed for A-tract-containing DNAs can be attributed both to differences in shape and to the preferential localization of small cations in the A-tract minor groove. Since many of these results are mirrored in other polyion-counterion systems, free-solution electrophoresis can be viewed as a reporter of the electrostatics and hydrodynamics of highly charged polyions. New results describing the mobilities of dsDNA analogues of a microRNA-messenger RNA complex are also presented.

Electrokinetic identification of ribonucleotide monophosphates (rNMPs) using thermoplastic nanochannels

With advances in the design and fabrication of nanofluidic devices during the last decade, there have been a few reports on nucleic acid analysis using nanoscale electrophoresis. The attractive nature of nanofluidics is the unique phenomena associated with this length scale that are not observed using microchip electrophoresis. Many of these effects are surface-related and include electrostatics, surface roughness, van der Waals interactions, hydrogen bonding, and the electric double layer. The majority of reports related to nanoscale electrophoresis have utilized glass-based devices, which are not suitable for broad dissemination into the separation community because of the sophisticated, time consuming, and high-cost fabrication methods required to produce the relevant devices. In this study, we report the use of thermoplastic nanochannels (110 nm x 110 nm, depth x width) for the free solution electrokinetic analysis of ribonucleotide monophosphates (rNMPs). Thermoplastic devices with micro- and nanofluidic networks were fabricated using nanoimprint lithography (NIL) with the structures enclosed via thermal fusion bonding of a cover plate to the fluidic substrate. Unique to this report is that we fabricated devices in cyclic olefin copolymer (COC) that was thermally fusion bonded to a COC cover plate. Results using COC/COC devices were compared to poly(methyl methacrylate), PMMA, devices with a COC cover plate. Our results indicated that at pH = 7.9, the electrophoresis in free solution resulted in an average resolution of the rNMPs >4 (COC/COC device range = 1.94 – 8.88; PMMA/COC device range = 1.4 – 7.8) with some of the rNMPs showing field-dependent electrophoretic mobilities. Baseline separation of the rNMPs was not possible using PMMA- or COC-based microchip electrophoresis. We also found that COC/COC devices could be assembled and UV/O3 activated after device assembly with the dose of the UV/O3 affecting the magnitude of the electroosmotic flow, EOF. In addition, the bond strength between the substrate and cover plate of unmodified COC/COC devices was higher compared to PMMA/COC devices. The large differences in the electrophoretic mobilities of the rNMPs afforded by nanoscale electrophoresis will enable a new single-molecule sequencing platform we envision, which uses molecular-dependent electrophoretic mobilities to identify the constituent rNMPs generated from an intact RNA molecule using a processive exonuclease. With optimized nanoscale electrophoresis, the rNMPs could be identified via mobility matching at an accuracy >99% in both COC/COC and PMMA/COC devices.

A simplified model for gel electrophoresis of a hydrophobic rigid colloid.

Electrophoresis of a charged dielectric hydrophobic colloid embedded in a charged hydrogel medium is addressed. A slip velocity condition at the particle surface is considered. The characteristic of the gel electrophoresis is different compared with the free-solution electrophoresis due to the presence of immobile charges of the gel medium, which induces a strong background electroosmotic flow and modifies the Debye layer of the colloid. The gel electrophoresis of the dielectric hydrophobic charged colloid is made based on first-order perturbation analysis. A closed form solution involving simple exponential integrals for the mobility is derived, which reduces to several existing mobility expressions under limiting conditions such as for the gel electrophoresis of hydrophilic particles and a hydrophobic colloid in free-solution electrophoresis. We find that the mobility reversal is achieved by varying the Debye length or gel permeability. For the present first-order perturbation analysis, unlike free-solution electrophoresis, the particle dielectric permittivity is found to influence the mobility. One of the intriguing features of the present study is the derivation of the simplified mobility expression, which can be easily computed for a given set of parameter values.

Nonaqueous electrophoresis on microchips: A review.

The use of organic solvents as electrolytic medium in electrophoresis has become an important alternative for the analysis of compounds that exhibit low or no solubility in water. In recent years, nonaqueous electrophoresis has been extensively explored in conventional capillary systems for different applications. On the other hand, this separation strategy is still not as popular as free solution electrophoresis on chip-based platforms due to the effects of solvent in the background electrolyte on the sample injection, detection performance, and microfluidic platform compatibility. In this way, this review summarizes the main achievements on nonaqueous microchip electrophoresis (NAME). To the best of our knowledge, this is the first review dedicated to discuss exclusively nonaqueous electrophoresis on chip-based systems. For this purpose, some important theoretical aspects involved when separations are performed in organic medium, such as equilibrium, interactions and electrophoretic considerations, are included in the review. In addition, the main challenges, advantages and influences of nonaqueous media on the sample injection, detection as well as the choice of the substrate to fabricate chip-based electrophoresis devices are highlighted. Last, examples showing the feasibility of nonaqueous microchip electrophoresis for applications exploiting different methodologies, operational, and instrumental conditions are summarized and discussed. We hope this review can be useful to spread the huge potential of nonaqueous electrophoresis on microfluidic platforms.

Droplet sample introduction to microchip gel and zone electrophoresis for rapid analysis of protein-protein complexes and enzymatic reactions.

Electrophoresis has demonstrated utility as tool for screening of small molecule modulators of protein-protein interactions and enzyme targets. Screening of large chemical libraries requires high-throughput separations. Such fast separation can be accessed by microchip electrophoresis. Here, microchip gel electrophoresis separations of proteins are achieved in 2.6s with 1200V/cm and 3-mm separation lengths. However, such fast separations can still suffer from limited overall throughput from sample introduction constraints. Automated introduction of microfluidic droplets has been demonstrated to overcome this limitation. Most devices for coupling microfluidic droplets to microchip electrophoresis are only compatible with free-solution separations. Here, we present a device that is compatible with coupling droplets to gel and free-solution electrophoresis. In this device, automated sample introduction is based on a novel mechanism of carrier phase separation using the difference in density of the carrier phase and the running buffer. This device is demonstrated for microchip gel electrophoresis and free-solution electrophoresis separations of protein-protein interaction and enzyme samples, respectively. Throughputs of about 10s per sample are achieved and over 1000 separations are demonstrated without reconditioning of the device. Graphical abstract.

Nonlinear effects on electrophoresis of a charged dielectric nanoparticle in a charged hydrogel medium

The impact of the solid polarization of a charged dielectric particle in gel electrophoresis is studied without imposing a weak-field or a thin Debye length assumption. The electric polarization of a dielectric particle due to an external electric field creates a non-uniform surface charge density, which in turn creates a non-uniform Debye layer at the solid-gel interface. The solid polarization of the particle, the polarization of the double layer, and the electro-osmosis of mobile ions within the hydrogel medium create a nonlinear effect on the electrophoresis. We have incorporated those nonlinear effects by considering the electrokinetics governed by the Stokes-Brinkman-Nernst-Planck-Poisson equations. We have computed the governing nonlinear coupled set of equations numerically by adopting a finite volume based iterative algorithm. Our numerical method is tested for accuracy by comparing with several existing results on free-solution electrophoresis as well as results based on the Debye-Hückel approximation. Our computed result shows that the electrophoretic velocity decreases with the rise of the particle dielectric permittivity constant and attains a saturation limit at large values of permittivity. A significant impact of the solid polarization is found in gel electrophoresis compared to the free-solution electrophoresis.

Separation efficiency of free-solution conjugated electrophoresis with drag-tags incorporating a synthetic amino acid.

DNA sequencing or separation by conventional capillary electrophoresis with a polymer matrix has some inherent drawbacks, such as the expense of polymer matrix and limitations in sequencing read length. As DNA fragments have a linear charge-to-friction ratio in free solution, DNA fragments cannot be separated by size. However, size-based separation of DNA is possible in free-solution conjugate electrophoresis (FSCE) if a "drag-tag" is attached to DNA fragments because the tag breaks the linear charge-to-friction scaling. Although several previous studies have demonstrated the feasibility of DNA separation by free-solution conjugated electrophoresis, generation of a monodisperse drag-tag and identification of a strong, site-specific conjugation method between a DNA fragment and a drag-tag are challenges that still remain. In this study, we demonstrate an efficient FSCE method by conjugating a biologically synthesized elastin-like polypeptide (ELP) and green fluorescent protein (GFP) to DNA fragments. In addition, to produce strong and site-specific conjugation, a methionine residue in drag-tags is replaced with homopropargylglycine (Hpg), which can be conjugated specifically to a DNA fragment with an azide site.

Electrokinetics of nanoparticle gel-electrophoresis.

Gel-electrophoresis has been demonstrated in recent decades to successfully sort a great variety of nanoparticles according to their size, charge, surface chemistry, and corona architecture. However, quantitative theoretical interpetations have been limited by the number and complexity of factors that influence particle migration. Theoretical models have been fragmented and incomplete with respect to their counterparts for free-solution electrophoresis. This paper unifies electrokinetic models that address complex nanoparticle corona architectures, corona and gel charge regulation (e.g., by the local pH), multi-component electrolytes, and non-linear electrostatics and relaxation effects. By comprehensively addressing the electrokinetic aspects of the more general gel-electrophoresis problem, in which short-ranged steric interactions are significant, a stage is set to better focus on the physicochemical and steric factors. In this manner, it is envisioned that noparticle gel-electrophoresis may eventually be advanced from a nanoparticle-characterization tool to one that explicitly probes the short-ranged interactions of nanoparticles with soft networks, such as synthetic gels and biological tissues. In this paper, calculations are undertaken that identify a generalized Hückel limit for nanoparticles in low-conductivity gels, and a new Smoluchowski limit for polyelectrolyte-coated particles in high-conductivity gels that is independent of the gel permeability. Also of fundamental interest is a finite, albeit small, electrophoretic mobility for uncharged particles in charged gels. Electrophoretic mobilities and drag coefficients (with electroviscous effects) for nanoparticles bearing non-uniform coronas show that relaxation effects are typically weak for the small nanoparticles (radius ≈3-10 nm) to which gel-electrophoresis has customarily been applied, but are profound for the larger nanoparticles (radius ≳ 40 nm in low conductivity gels) to which passivated gel-electrophoresis experiments have recently been applied. To demonstrate its practical application, the model is applied to (pH charge regulating) carboxylated polystyrene nanospheres in low-density passivated agarose gels (weak steric effects). This furnishes a new theoretical interpretation of literature data for which a finite diffuse-layer-thickness, pH-charge regulation, high charge, and relaxation effects dominate over the steric influences.

Hydrogel charge regulation and electrolyte ion-concentration perturbations in nanoparticle gel electrophoresis

Gel electrophoresis of spherical nanoparticles (NPs) is studied using an electrokinetic model that couples the ion conservation equations to the Poisson and fluid momentum equations, thus including the so-called polarization and relaxation processes. This model is therefore the charged gel electrophoresis analogue of the well-known O’Brien and White solution of the standard electrokinetic model for free-solution electrophoresis. Results are provided for the small NPs (size around 10 nm) to which gel electrophoresis is relevant, because particles must be small enough to permeate the gel: these include the particle drag coefficient (or Brownian diffusivity), which is subject to hydrodynamic screening and electroviscous effects, and the electrophoretic mobility, which is subject to nonlinear electrostatic and charge polarization influences. Also addressed are the influences of charge-regulating gels and the accompanying particle-induced immobile charge-density perturbations. Ion-concentration perturbations attenuate the electrophoretic mobility and enhance the drag coefficient according to the particle charge and the mobility of the most abundant counterion. However, dynamic regulation of the hydrogel charge—termed the secondary immobile charge-density perturbation—has a negligible influence on the particle mobility, and may therefore be neglected for most practical purposes.

A 502-Base Free-Solution Electrophoretic DNA Sequencing Method Using End-Attached Wormlike Micelles.

We demonstrate that the use of wormlike nonionic micelles as drag-tags in end-labeled free-solution electrophoresis ("micelle-ELFSE") provides single-base resolution of Sanger sequencing products up to 502 bases in length, a nearly 2-fold improvement over reported ELFSE separations. "CiEj" running buffers containing 48 mM C12E5, 6 mM C10E5, and 3 M urea (32.5 °C) form wormlike micelles that provide a drag equivalent to an uncharged DNA fragment with a length (α) of 509 bases (effective Rh = 27 nm). Runtime in a 40 cm capillary (30 kV) was 35 min for elution of all products down to the 26-base primer. We also show that smaller Triton X-100 micelles give a read length of 103 bases in a 4 min run, so that a combined analysis of the Sanger products using the two buffers in separate capillaries could be completed in 14 min for the full range of lengths. A van Deemter analysis shows that resolution is limited by diffusion-based peak broadening and wall adsorption. Effects of drag-tag polydispersity are not observed, despite the inherent polydispersity of the wormlike micelles. We ascribe this to a stochastic size-sampling process that occurs as micelle size fluctuates rapidly during the runtime. A theoretical model of the process suggests that fluctuations occur with a time scale less than 10 ms, consistent with the monomer exchange process in nonionic micelles. The CiEj buffer has a low viscosity (2.7 cP) and appears to be semidilute in micelle concentration. The large drag-tag size of the CiEj buffers leads to steric segregation of the DNA and tag for short fragments and attendant mobility shifts.

Concurrent DNA preconcentration and separation in bipolar electrode-based microfluidic device

This paper presents a bipolar electrode (BPE) device in a microfluidic dual-channel design for concurrent preconcentration and separation of composite DNA containing samples. The novelty of the present effort relies on the combination of BPE-induced ion concentration polarization (ICP) and end-labeled free-solution electrophoresis (ELFSE). The ion concentration polarization effect arising from the faradaic reaction on the BPE is utilized to exert opposing electrophoretic and electroosmotic forces on the DNA samples. Meanwhile, end-labeled free-solution electrophoresis alters the mass-charge ratio to enable simultaneous DNA separation in free solution. The microfluidic device was fabricated using standard and soft lithography techniques to form gold-on-glass electrode capped with a PDMS microfluidic channel. Experimental testing with various DNA samples was carried out over a range of applied electric field. Concentration ratios up to 285× within 5 minutes for a 102-mer DNA, and concurrent preconcentration and free-solution separation of binary mixture of free and bound 102-mer DNA within 6 minutes was demonstrated. The effect of applied electric field was also interrogated with respect to pertinent performance metrics of preconcentration and separation.

Optimization of ELFSE DNA sequencing with EOF counterflow and microfluidics.

We present a nonlinear optimization study of different implementations of the DNA electrophoretic method "End-labeled Free-solution Electrophoresis" in commercial capillary electrophoresis systems and microfluidics to improve the time required for readout. Here, the effect of electro-osmotic counterflows and snap-shot detection are considered to allow for detection of peaks soon after they are electorphoretically resolved. Using drag tags available in micelle form, we identify a design capable of sequencing 600 bases in 2.8 min.

Nanoparticle gel electrophoresis: Soft spheres in polyelectrolyte hydrogels under the Debye–Hückel approximation

A mathematical model for electrophoresis of polyelectrolyte coated nanoparticles (soft spheres) in polyelectrolyte hydrogels is proposed, and evaluated by comparison to literature models for bare-sphere gel electrophoresis and free-solution electrophoresis. The utilities of approximations based on the bare-particle electrophoretic mobility, free-solution mobility, and electroosmotic flow in hydrogels are explored. Noteworthy are the influences of the particle–core dielectric constant and overlap of the polyelectrolyte shell. The present theory, which neglects ion-concentration and charge-density perturbations, indicates that the gel electrophoretic mobilities of metallic-core nanoparticles in polyelectrolyte gels can be qualitatively different than for their non-metallic counterparts. These insights will be beneficial for interpreting nanoparticle gel-electrophoresis data, optimizing electrophoretic separations, and engineering nanoparticles for technological applications.

Nafion Film Based Micro-nanofluidic Device for Concurrent DNA Preconcentration and Separation in Free Solution.

This paper presents a Nafion film based micro-nanofluidic device for concurrent DNA preconcentration and separation. The principle of the device is based on the combination of (a) ion concentration polarization phenomenon at the junction of the microchannel and the nanochannels in the Nafion film to form opposing electrophoretic and electroosmotic forces acting on the DNAs, and (b) end-labeled free solution electrophoresis to harness the charge-to-mass ratio for molecular differentiation. The experiments successfully demonstrated concurrent preconcentration and separation of DNA mixture in free solution within 240s, yielding concentration ratios up to 1,150X and separation resolution of 1.85. The effect of applied electric field on the concentration and separation performance was also investigated. The device can be used as a key sample preparation element in conjunction with micro- or nano-fluidic sensors for microTAS functionality.

Theory of end‐labeled free‐solution electrophoresis: Is the end effect important?

In the theory of free-solution electrophoresis of a polyelectrolyte (such as the DNA) conjugated with a "drag-tag," the conjugate is divided into segments of equal hydrodynamic friction and its electrophoretic mobility is calculated as a weighted average of the mobilities of individual segments. If all the weights are assumed equal, then for an electrically neutral drag-tag, the elution time t is predicted to depend linearly on the inverse DNA length 1/M. While it is well-known that the equal-weights assumption is approximate and in reality the weights increase toward the ends, this "end effect" has been assumed to be small, since in experiments the t(1/M) dependence seems to be nearly perfectly linear. We challenge this assumption pointing out that some experimental linear fits do not extrapolate to the free (i.e. untagged) DNA elution time in the limit 1/M→0, indicating nonlinearity outside the fitting range. We show that a theory for a flexible polymer taking the end effect into account produces a nonlinear curve that, however, can be fitted with a straight line over a limited range of 1/M typical of experiments, but with a "wrong" intercept, which explains the experimental results without additional assumptions. We also study the influence of the flexibilities of the charged and neutral parts.

Modeling and global optimization of DNA separation

We develop a non-convex non-linear programming problem that determines the minimum run time to resolve different lengths of DNA using a gel-free micelle end-labeled free solution electrophoresis separation method. Our optimization framework allows for an efficient determination of the utility of different DNA separation platforms and enables the identification of the optimal operating conditions for these DNA separation devices. The non-linear programming problem requires a model for signal spacing and signal width, which is known for many DNA separation methods. As a case study, we show how our approach is used to determine the optimal run conditions for micelle end-labeled free-solution electrophoresis and examine the trade-offs between a single capillary system and a parallel capillary system. Parallel capillaries are shown to only be beneficial for DNA lengths above 230 bases using a polydisperse micelle end-label otherwise single capillaries produce faster separations.

Microchip electrophoresis at elevated temperatures and high separation field strengths

We report free-solution microchip electrophoresis performed at elevated temperatures and high separation field strengths. We used microfluidic devices with 11 cm long separation channels to conduct separations at temperatures between 22 (ambient) and 45°C and field strengths from 100 to 1000 V/cm. To evaluate separation performance, N-glycans were used as a model system and labeled with 8-aminopyrene-1,3,6-trisulfonic acid to impart charge for electrophoresis and render them fluorescent. Typically, increased diffusivity at higher temperatures leads to increased axial dispersion and poor separation performance; however, we demonstrate that sufficiently high separation field strengths offset the impact of increased diffusivity in order to maintain separation efficiency. Efficiencies for these free-solution separations are the same at temperatures of 25, 35, and 45°C with separation field strengths ≥ 500 V/cm.

DNA-Conjugated Polymers for Reliable SNP Genotyping Based on Affinity Capillary Electrophoresis

Abstract To quantitatively detect single-base mutations in genetic samples, free-solution affinity capillary electrophoresis was developed using a diblock copolymer probe composed of allele-specific oligodeoxyribonucleotide (ODN) and poly(ethylene glycol) (PEG). When the probe is designed to be complementary to a wild-type single-stranded DNA sample (WT), WT migrates more slowly than its single-base mutant (MT). This is because WT forms a reversible complex with the probe via hybridization during the electrophoresis, resulting in a large amount of hydrodynamic friction. In contrast, a negligibly weak interaction takes place between MT and the probe due to a single-base mismatch. Accordingly, the MT peak appears earlier than the WT peak on the electropherogram. The difference of the migration time between WT and MT depends on the thermodynamic stability of the complex and also on the amount of hydrodynamic friction that the complex encounters. Therefore, the peak resolution is rationally controlled by the base-number of the ODN segment and by the molecular weight of the PEG segment. Importantly, the peak area ratio provides the occurrence ratio of the single-base mutant within the given population. This facile and accurate method to estimate SNP allele frequency should find applications in various research fields.

Simultaneous detection of 19 K-ras mutations by free-solution conjugate electrophoresis of ligase detection reaction products on glass microchips.

We demonstrate here the power and flexibility of free-solution conjugate electrophoresis (FSCE) as a method of separating DNA fragments by electrophoresis with no sieving polymer network. Previous work introduced the coupling of FSCE with ligase detection reaction (LDR) to detect point mutations, even at low abundance compared to the wild-type DNA. Here, four large drag-tags are used to achieve free-solution electrophoretic separation of 19 LDR products ranging in size from 42 to 66 nt that correspond to mutations in the K-ras oncogene. LDR-FSCE enabled electrophoretic resolution of these 19 LDR-FSCE products by CE in 13.5 min (E = 310 V/cm) and by microchip electrophoresis in 140 s (E = 350 V/cm). The power of FSCE is demonstrated in the unique characteristic of free-solution separations where the separation resolution is constant no matter the electric field strength. By microchip electrophoresis, the electric field was increased to the maximum of the power supply (E = 700 V/cm), and the 19 LDR-FSCE products were separated in less than 70 s with almost identical resolution to the separation at E = 350 V/cm. These results will aid the goal of screening K-ras mutations on integrated "sample-in/answer-out" devices with amplification, LDR, and detection all on one platform.