Theory of DNA electrophoresis in physical gels and entangled polymer solutions

Reversible phospholipid nanogels for deoxyribonucleic acid fragment size determinations up to 1500 base pairs and integrated sample stacking

Phospholipid additives are a cost-effective medium to separate deoxyribonucleic acid (DNA) fragments and possess a thermally-responsive viscosity. This provides a mechanism to easily create and replace a highly viscous nanogel in a narrow bore capillary with only a 10°C change in temperature. Preparations composed of dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC) self-assemble, forming structures such as nanodisks and wormlike micelles. Factors that influence the morphology of a particular DMPC-DHPC preparation include the concentration of lipid in solution, the temperature, and the ratio of DMPC and DHPC. It has previously been established that an aqueous solution containing 10% phospholipid with a ratio of [DMPC]/[DHPC]=2.5 separates DNA fragments with nearly single base resolution for DNA fragments up to 500 base pairs in length, but beyond this size the resolution decreases dramatically. A new DMPC-DHPC medium is developed to effectively separate and size DNA fragments up to 1500 base pairs by decreasing the total lipid concentration to 2.5%. A 2.5% phospholipid nanogel generates a resolution of 1% of the DNA fragment size up to 1500 base pairs. This increase in the upper size limit is accomplished using commercially available phospholipids at an even lower material cost than is achieved with the 10% preparation. The separation additive is used to evaluate size markers ranging between 200 and 1500 base pairs in order to distinguish invasive strains of Streptococcus pyogenes and Aspergillus species by harnessing differences in gene sequences of collagen-like proteins in these organisms. For the first time, a reversible stacking gel is integrated in a capillary sieving separation by utilizing the thermally-responsive viscosity of these self-assembled phospholipid preparations. A discontinuous matrix is created that is composed of a cartridge of highly viscous phospholipid assimilated into a separation matrix of low viscosity. DNA sample stacking is facilitated with longer injection times without sacrificing separation efficiency.

Fast parallel detection of feline panleukopenia virus DNA by multi-channel microchip electrophoresis with programmed step electric field strength

A multi-channel microchip electrophoresis using a programmed step electric field strength (PSEFS) method was investigated for fast parallel detection of feline panleukopenia virus (FPV) DNA. An expanded laser beam, a 10× objective lens, and a charge-coupled device camera were used to simultaneously detect the separations in three parallel channels using laser-induced fluorescence detection. The parallel separations of a 100-bp DNA ladder were demonstrated on the system using a sieving gel matrix of 0.5% poly(ethylene oxide) (M(r) = 8 000 000) in the individual channels. In addition, the PSEFS method was also applied for faster DNA separation without loss of resolving power. A DNA size marker, FPV DNA sample, and a negative control were simultaneously analyzed with single-run and one-step detection. The FPV DNA was clearly distinguished within 30 s, which was more than 100 times faster than with conventional slab gel electrophoresis. The proposed multi-channel microchip electrophoresis with PSEFS was demonstrated to be a simple and powerful diagnostic method to analyze multiple disease-related DNA fragments in parallel with high speed, throughput, and accuracy.

Stretching and migration of DNA by solvent elasticity in an oscillatory flow

A model with solution viscoelasticity is proposed to explain the ratchetlike stretching of DNA by a symmetric ac electric field in polymer solutions. In this model, DNA is stretched by the interaction between the fluid elasticity and the oscillatory flow induced by DNA. Predictions of the model are confirmed by DNA stretching experiments performed in various polymer solutions and the corresponding rheological measurements of the solutions. In particular, experiments have verified that a net migration of stretched DNA in polymer solutions can be induced by a zero-mean asymmetric ac electric field. This last finding cannot be explained by other existing models.

Electrophoretic separation of DNA in gels and nanostructures

The development of nanostructure devices has opened the door to new DNA separation techniques and fundamental investigations. With advanced nanotechnologies, artificial gels (e.g. nanopillar arrays, nanofilters) can be manufactured with controlled and ordered geometries. This contrast with gels, where the pores are disordered and the range of available pore sizes is limited by the level of cross-linking and the mechanical properties of the gel. In this review, we recall the theories developed for free-solution and gel electrophoresis (extended Ogston model, biased reptation and entropic trapping) and from this perspective, suggestions for future concepts for fast DNA separation using nanostructures will be given.

Effects of novel quasi-interpenetrating network/gold nanoparticles composite matrices on DNA sequencing performances by CE

Gold nanoparticles (GNPs) with particle sizes of about 20, 40, and 60 nm were prepared and added into a quasi-interpenetrating network (quasi-IPN) composed of linear polyacrylamide (LPA) with different viscosity-average molecular masses of 1.5, 3.3, and 6.5 MDa and poly-N,N-dimethylacrylamide (PDMA) to form polymer/metal composite matrices, respectively. These novel matrices could improve ssDNA sequencing performances due to interactions between GNPs and polymer chains and the formation of physical cross-linking points as demonstrated by intrinsic viscosities and glass transition temperatures. The effects of the parameters in relation to quasi-IPN/GNPs matrices, such as GNP contents, GNP particle sizes, LPA molecular masses, and solution concentrations, on ssDNA sequencing performances were studied. In the presence of GNPs, the separation had the advantages of high resolution, speediness, excellent reproducibility, long shelf life and easy automation. Therefore, less viscous matrix solutions (with moderate size GNPs) due to lower solution concentration and lower-molecular-mass LPA could be used to replace more viscous solutions (without GNPs) due to higher solution concentration or higher-molecular-mass LPA to separate DNA, while the sieving performances were approximate even higher, which helped to achieve full automation especial for capillary array electrophoresis (CAE) and microchip electrophoresis (MCE).

Novel quasi-interpenetrating network/gold nanoparticles composite matrices for DNA sequencing by CE

In order to further improve ssDNA sequencing performances using quasi-interpenetrating network (quasi-IPN) as a matrix composed of linear polyacrylamide (LPA) with lower viscosity-average molecular mass (3.3 MDa) and poly(N,N-dimethylacrylamide) (PDMA), gold nanoparticles (GNPs) were prepared and added into this quasi-IPN to form polymer/metal composite sieving matrices. The studies of intrinsic viscosity and differential scanning calorimetry (DSC) on quasi-IPN and quasi-IPN/GNPs indicate that there were interactions between GNPs and polymer chains. The sequencing performances on ssDNA using quasi-IPN and quasi-IPN/GNPs (with different GNPs concentrations) as sieving matrices were studied and compared by CE at different temperatures. The results show that resolutions of quasi-IPN/GNPs were higher than those of quasi-IPN without GNPs and approximated those of quasi-IPN composed of LPA with higher MW (6.5 MDa) and PDMA without GNPs in the bare fused-silica capillaries. Furthermore, the sequencing time of quasi-IPN/GNPs was shorter than that of quasi-IPN under the same sequencing conditions. The influences of GNPs and sequencing temperature on the sequencing performances of ssDNA were also discussed. The separation reproducibility of quasi-IPN/GNPs solution was excellent and its shelf life was more than 8 months.

Electrophoretic mobility of linear and star-branched DNA in semidilute polymer solutions

Electrophoresis of large linear T2 (162 kbp) and 3-arm star-branched (N(Arm) = 48.5 kbp) DNA in linear polyacrylamide (LPA) solutions above the overlap concentration c* has been investigated using a fluorescence visualization technique that allows both the conformation and mobility mu of the DNA to be determined. LPA solutions of moderate polydispersity index (PI approximately 1.7-2.1) and variable polymer molecular weight Mw (0.59-2.05 MDa) are used as the sieving media. In unentangled semidilute solutions (c* < c < c(e)), we find that the conformational dynamics of linear and star-branched DNA in electric fields are strikingly different; the former migrating in predominantly U- or I-shaped conformations, depending on electric field strength E, and the latter migrating in a squid-like profile with the star-arms outstretched in the direction opposite to E and dragging the branch point through the sieving medium. Despite these visual differences, mu for linear and star-branched DNA of comparable size are found to be nearly identical in semidilute, unentangled LPA solutions. For LPA concentrations above the entanglement threshold (c > c(e)), the conformation of migrating linear and star-shaped DNA manifest only subtle changes from their unentangled solution features, but mu for the stars decreases strongly with increasing LPA concentration and molecular weight, while mu for linear DNA becomes nearly independent of c and Mw. These findings are discussed in the context of current theories for electrophoresis of large polyelectrolytes.

Size sorting of biological micro-particles by Newton-ring nano-gap device

The size determination and the size sorting of micrometer-sized particles were carried out by using a piezo-controlled nano-gap. The nano-gap was built by combining a plano-convex lens and a flat glass plate. The fabricated gap had a gradient, while the center of the lens was narrow and the outer side was wide. When the sample solution was injected into the gap, a meniscus force carried the sample particles toward the center of the lens with solvent evaporation; then the individual particle was trapped at the specific position where the particle diameter was equal to the gap distance. The size determination ability of this new method was certified by using the standard polystyrene particles and the size measurements of DNA molecules and yeast cells were demonstrated.

The hydrodynamics of DNA electrophoretic stretch and relaxation in a polymer solution

Theories of DNA electrophoretic separations generally treat the DNA as a free draining polymer moving in an electric field at a rate that depends on the effective charge density of the molecule. Separations can occur in sieving media ranging from ultradilute polymer solutions to tightly cross-linked gels. It has recently been shown that DNA is not free-draining when both electric and nonelectric forces simultaneously act on the molecule, as occurs when DNA collides with a polymer during electrophoretic separations. Here we show that a semidilute polymer solution screens the hydrodynamic interaction that results from the application of these forces. Fluorescently labeled DNA tethered at one end in a semidilute solution of hydroxyl-ethyl cellulose stretch more in an electric field than they stretch in free solution, and approach free-draining behavior. The steady stretching behavior is predicted without adjustable parameters by a theory developed by Stigter using a hydrodynamic screening length found from effective medium theory. Data on the relaxation of stretched molecules after the electric field is removed agree with the Rouse model prediction, which neglects hydrodynamic interactions. The slowest relaxation time constant, tau(R), scales with chain length as tau(R) approximately L(1.9+/-0.17) when analyzed by the data collapse method, and as tau(R) approximately L(2.17+/-0.17) when analyzed by multiexponential fit.

Nonequilibrium unfolding of polyelectrolyte condensates in electric fields

Using simulations and scaling methods, the effect of an electric field on a collapsed polyelectrolyte globule is investigated, where conduction by counterions and the polyelectrolyte itself is taken into account. At a critical field E(*), a nonequilibrium transition occurs at which the polyelectrolyte unfolds and aligns parallel to the external field. E(*) is determined using scaling results for the polarizability of a polyelectrolyte globule and exhibits a dependence on the chain length N, E(*) approximately N(-1/2), which might be useful for electrophoretic separation of charged biopolymers.

Three-dimensional observation of electrophoretic migration of dsDNA in semidilute hydroxyethylcellulose solution

Three-dimensional (3-D) video fluorescence microscopy is demonstrated for the investigation of biopolymer electrophoretic migration using double-stranded (ds)DNA in semidilute hydroxyethylcellulose (HEC) as a test system. It is shown that 3-D imaging enables visualization of segmental motion with greater detail than is available in conventional video microscopy. A high frame rate (50-110 frames per second (fps)) intensified progressive scan camera is used to acquire fifteen axial sections focused at different depths through the DNA molecule. A 3-D DNA image is generated from these sections using blind deconvolution image reconstruction and motion is represented as a succession of volume images. A 3-D extension of the Doi/Oana ellipsoidal model is used to fit the DNA envelope, allowing simple quantitative descriptions of the changing shape of the DNA as it interacts with the sieving polymer solution. With 3-D views of migrating DNA molecules we observe U-shaped conformations oriented at an angle to the microscope plane. We are also able to resolve ambiguities and artifacts resulting from loss of information from DNA segments that are not in focus.

DNA capillary electrophoresis in entangled dynamic polymers of surfactant molecules

Aqueous solutions of monomeric nonionic surfactants, n-alkyl polyoxyethylene ethers (C16E6, C16E8, C14E6), can be used as sieving matrixes for the separation of DNA fragments by capillary electrophoresis. Unlike ordinary polymer solutions, these surfactant solutions behave as dynamic polymers. By combining the "reversible gel" theory of DNA electrophoresis and the static and dynamic properties of wormlike surfactant micelles, a model is developed for describing the migration behavior of DNA molecules in these solutions. According to the model, the separation limit can be extended at low surfactant concentrations. Surfactant solutions as a separation medium provide many advantages over ordinary polymers, such as ease of preparation, solution homogeneity, stable structure, low viscosity, and self-coating property for reducing electroosmotic flow. More importantly, the properties of wormlike micelles (micelle size, entanglement concentration) can be adjusted by simply changing the monomer concentration, denaturant, and temperature to allow the separation of different size ranges of DNA fragments. Fast separation is achieved for DNA fragments ranging from 10 bp to 5 kb by using bare fused-silica columns. DNA sequencing fragments of BigDye G-labeled M13 up to 600 bases were separated within 60 min.

Optimization of high-performance DNA sequencing on short microfabricated electrophoretic devices

We have examined the parametric performance of short microfabricated electrophoresis devices that operate with a replaceable linear poly(acrylamide) (LPA) solution for the application of DNA sequencing. A systematic study is presented of the dependence of selectivity, separation efficiency, and resolution of sequencing fragments on buffer composition, LPA concentration, LPA composition, microdevice temperature, electric field, and device length. A specific optimization is made for DNA sequencing on 11.5-cm devices. Using a separation matrix composed of 3.0% (w/w) 10 MDa plus 1.0% (w/w) 50 kDa LPA, elevated microdevice temperature (50 degrees C), and 200 V/cm, high-speed DNA sequencing of 580 bases on standard M13mp18 was obtained in only 18 min with a base-calling accuracy of 98.5%. Read lengths of 640 bases at 98.5% accuracy were achieved in approximately 30 min by reducing the electric field strength to 125 V/cm. We believe that this constitutes matrix-limited performance for microdevices of this length using LPA sieving matrix and this buffer chemistry. In addition, it was confirmed, that shorter devices are rather impractical for production sequencing applications when LPA is used as sieving matrix.

DNA sequencing up to 1300 bases in two hours by capillary electrophoresis with mixed replaceable linear polyacrylamide solutions

This paper presents results on ultralong read DNA sequencing with relatively short separation times using capillary electrophoresis with replaceable polymer matrixes. In previous work, the effectiveness of mixed replaceable solutions of linear polyacrylamide (LPA) was demonstrated, and 1000 bases were routinely obtained in less than 1 h. Substantially longer read lengths have now been achieved by a combination of improved formulation of LPA mixtures, optimization of temperature and electric field, adjustment of the sequencing reaction, and refinement of the base-caller. The average molar masses of LPA used as DNA separation matrixes were measured by gel permeation chromatography and multiangle laser light scattering. Newly formulated matrixes comprising 0.5% (w/w) 270 kDa and 2% (w/w) 10 or 17 MDa LPA raised the optimum column temperature from 60 to 70 degrees C, increasing the selectivity for large DNA fragments, while maintaining high selectivity for small fragments as well. This improved resolution was further enhanced by reducing the electric field strength from 200 to 125 V/cm. In addition, because sequencing accuracy beyond 1000 bases was diminished by the low signal from G-terminated fragments when the standard reaction protocol for a commercial dye primer kit was used, the amount of these fragments was doubled. Augmenting the base-calling expert system with rules specific for low peak resolution also had a significant effect, contributing slightly less than half of the total increase in read length. With full optimization, this read length reached up to 1300 bases (average 1250) with 98.5% accuracy in 2 h for a single-stranded M13 template.

Routine DNA sequencing of 1000 bases in less than one hour by capillary electrophoresis with replaceable linear polyacrylamide solutions

Long, accurate reads are an important factor for high-throughput de novo DNA sequencing. In previous work from this laboratory, a separation matrix of high-weight-average molecular mass (HMM) linear polyacrylamide (LPA) at a concentration of 2% (w/w) was used to separate 1000 bases of DNA sequence in 80 min with an accuracy close to 97% (Carrilho, E.; et al. Anal. Chem. 1996, 68, 3305-3313). In the present work, significantly improved speed and sequencing accuracy have been achieved by further optimization of factors affecting electrophoretic separation and data processing. A replaceable matrix containing a mixture of 2.0% (w/w) HMM (9 MDa) and 0.5% (w/w) low-weight-average molecular mass (50 kDa) LPA was employed to enhance the separation of DNA sequencing fragments in CE. Experimental conditions, such as electric field strength and column temperature, as well as internal diameter of the capillary column, have been optimized for this mixed separation matrix. Under these conditions, in combination with energy-transfer (BigDye) dye-labeled primers for high signal-to-noise ratio and a newly developed expert system for base calling, the electrophoretic separation of 1000 DNA sequencing fragments of both standard (M13mp18) and cloned single-stranded templates from human chromosome 17 could be routinely achieved in less than 55 min, with a base-calling accuracy between 98 and 99%. Identical read length, accuracy, and migration time were achieved in more than 300 consecutive runs in a single column.

Replaceable polymers in DNA sequencing by capillary electrophoresis

Much progress has been made in the development of replaceable sieving polymers and capillary coatings for high-performance DNA sequencing by capillary electrophoresis. Several studies of parameters that affect resolution, read length and reproducibility have begun to reveal the physical mechanisms acting on single-stranded DNA during electrophoresis through semidilute polymer solutions. Recently developed electro-osmosis-inhibiting matrix polymers have simplified the process of coating capillaries, facilitating the automation of high-throughput parallel systems for large-scale sequencing.

The use of elevated column temperature to extend DNA sequencing read lengths in capillary electrophoresis with replaceable polymer matrices

Capillary electrophoresis with a replaceable linear polyacrylamide matrix operated at elevated column temperatures of 55 degrees and 60 degrees C was used to extend the separation of DNA sequencing fragments to lengths greater than 800 bases. A solid-state heater was employed to provide stable, uniform temperature control over a significant portion of the capillary. The polymer matrix, 3% w/v linear polyacrylamide in a denaturing buffer, was replaced in the capillary after each run. Using dye-labeled primers and Sequenase chemistry on an M13mp18 single-stranded template, four-color separations for the sequencing products were obtained, with read lengths in excess of 800 bases. This paper also briefly discusses the effects of buffer denaturants and capillary temperature on separation speed, resolution, and gel compression.

Activation energy of the separation of DNA sequencing fragments in denaturing noncross-linked polyacrylamide by capillary electrophoresis

We present the mobility of DNA sequencing fragments as a function of temperature in 5%T, 0%C noncross-linked polyacrylamide and at an electric field of 150 V/cm. The mobility of the fragments follows the Arrhenius equation. The activation energy for migration of a fragment through the polymer decreases monotonically with fragment length. The data were also analyzed in terms of the biased reptation model; the onset of biased reptation with stretching occurs for longer fragments as the temperature increase. These results are quite different from those observed for separation of DNA in cross-linked gels and represent a fundamental difference in the physics of the cross-linked and noncross-linked polyacrylamide.

Reptation theories of electrophoresis

In this review, we present the main aspects of the reptation theory, which has provided an essential insight into the processes at work during DNA electrophoretic separation in gels. We avoid mathematical developments, and rely as much as possible on an intuitive description. We first present the original biased reptation model, which assumes that the DNA threads its way as a "worm" of fixed length among the fibers of the gel. We then introduce a more recent version, the model of Biased Reptation with Fluctuations (BRF), which allows for longitudinal flexibility along the DNA. We then propose a quantitative comparison with experiments performed in constant field, and discuss the application of reptation theories to pulsed field techniques either with crossed fields or with field inversion. We also discuss at some length the different experiments that led to a criticism of reptation ideas, such as orientation measurements and videomicroscopy. Finally, we use these experiments together with various computer simulations developed recently for gel electrophoresis, to propose a more realistic qualitative description of DNA motion in gels, and we discuss what elements in this motion are relevant to reptation and what processes are not included in present analytical models.

Electrophoretic mobility of composite objects in free solution: application to DNA separation

We propose here a simple procedure to estimate the electrophoretic mobility of composite objects obtained by linking two charged subunits, stressing that this electrophoretic mobility is in general different from the ratio of the total charge to the total friction coefficient. We focus especially on the situation where at least one of the subunits is a polyelectrolyte. Our remarks in particular correct the existing theoretical analysis of separation capabilities of devices in which a buoy (sphere, protein, polymer) is attached to a DNA chain. We also predict that, in some cases, the direction of electrophoretic motion can be reversed by increasing the electric field amplitude.

The limiting mobility of DNA sequencing fragments for both cross-linked and noncross-linked polymers in capillary electrophoresis: DNA sequencing at 1200 V cm-1

The mobility of DNA sequencing fragments was measured in Long-Ranger gels at an electric field ranging from 200 to 1200 V cm-1 and in noncross-linked polyacrylamide at electric fields ranging from 100 to 300 V cm-1. In both cases, N*, the fragment length that denotes the onset of biased reptation with orientation, is inversely proportional to electric field. The inverse dependence of N* is inconsistent with the original biased reptation model but is consistent with modern models of DNA migration. While separation speed increases dramatically with electric field, the number of bases determined in a separation decreases in proportion to field strength. We present a DNA sequencing run at an electric field of 1200 V cm-1. Roughly 200 bases of sequence are determined in 3.5 min.

Capillary electrophoresis with polymeric separation media: considerations for theory

The theory of capillary electrophoresis with polymeric separation media is reviewed. Some of the major theories of gel electrophoresis are examined in terms of the experimental observations that they support. The considerations and difficulties in applying these theories to capillary electrophoresis with polymeric separation media are investigated, particularly the use of high electric field strengths and low concentration polymer solutions. Recent advances in this area, including some empirically-derived relationships and models currently found in the literature, and future directions for theory development are discussed.

The use of coated and uncoated capillaries for the electrophoretic separation of DNA in dilute polymer solutions

We show that both uncoated and polyacrylamide-coated capillaries provide separation of large DNA restriction fragments (2.0-23.1 kbp) by capillary electrophoresis in dilute cellulosic polymer solutions. Uncoated capillaries, however, provide significantly better resolution of DNA fragments, particularly when ultra-dilute polymer solutions are used. This is because electroosmotic flow in uncoated capillaries increases the residence time of DNA in the capillary, without significantly contributing to band-broadening. At a given field strength and polymer concentration in the buffer, the electrophoretic mobilities of DNA restriction fragments in coated capillaries are virtually identical to those previously measured in uncoated capillaries. It is concluded that the fused silica surface of the capillary does not play a significant role in the mechanism of DNA separation by capillary electrophoresis in uncrosslinked polymer solutions. Thus, the separation of large DNA which has been observed to occur in ultra-dilute polymer solutions arises primarily from entanglement interactions between the cellulosic polymers and DNA restriction fragments which occur within the bulk of the polymer solution.