The molecular end effect and its critical impact on the behavior of charged-uncharged polymer conjugates during free-solution electrophoresis

Recently two novel techniques using free-solution electrophoresis to separate charged-uncharged polymer conjugates have proven successful: end-labeled free-solution electrophoresis (ELFSE) for DNA sequencing, and free-solution conjugate electrophoresis (FSCE) for molar mass profiling of uncharged polymers. The approach taken to analyze the experimental data was an extension of the theory of Long and co-workers (Long, D., Dobrynin, A. V., Rubinstein, M., Ajdari, A., J. Chem. Phys. 1998, 108, 1234-1244) for the electrophoresis of molecules with varying charge distributions. This theory also predicts that the ends of the polymers play a large role in determining the polymer's overall mobility; however, this aspect of the theory was neglected in previous work. Until now this "end effect" has, to the knowledge of the authors, not been recognized in experimental data. Through a careful investigation of the predicted end effect and a reanalysis of the experimental data, we demonstrate that indeed this effect critically impacts on the behavior of charged-uncharged polymer conjugates during electrophoresis. This work indicates that not only does the end effect need to be taken into account to avoid significant errors in data analysis, but also it provides novel system optimization approaches.     

Protein polymer drag-tags for DNA separations by end-labeled free-solution electrophoresis

We demonstrate the feasibility of end-labeled free-solution electrophoresis (ELFSE) separation of DNA using genetically engineered protein polymers as drag-tags. Protein polymers are promising candidates for ELFSE drag-tags because their sequences and lengths are controllable not only to generate monodisperse polymers with high frictional drag, but also to meet other drag-tag requirements for high-resolution separations by microchannel electrophoresis. A series of repetitive polypeptides was designed, expressed in Escherichia coli, and purified. By performing an end-on conjugation of the protein polymers to a fluorescently labeled DNA oligomer (22 bases) and analyzing the electrophoretic mobilities of the conjugate molecules by free-solution capillary electrophoresis (CE), effects of the size and charge of the protein polymer drag-tags were investigated. In addition, the electrophoretic behavior of bioconjugates comprising relatively long DNA fragments (108 and 208 bases) and attached to uncharged drag-tags was observed, by conjugating fluorescently labeled polymerase chain reaction (PCR) products to charge-neutral protein polymers, and analyzing via CE. We calculated the amount of friction generated by the various drag-tags, and estimated the potential read-lengths that could be obtained if these drag-tags were used for DNA sequencing in our current system. The results of these studies indicate that larger and uncharged drag-tags will have the best DNA-resolving capability for ELFSE separations, and that theoretically, up to 233 DNA bases could be sequenced using one of the protein polymer drag-tags we produced, which is electrostatically neutral with a chain length of 337 amino acids. We also show that denatured (unfolded) polypeptide chains impose much greater frictional drag per unit molecular weight than folded proteins, such as streptavidin, which has been used as a drag-tag before.     

Molecular deformation and free-solution electrophoresis of DNA-uncharged polymer conjugates at high field strengths: theoretical predictions Part 2: Stretching

DNA sequencing by electrophoresis can be dramatically sped up by overcoming the need for the sieving medium. Normally it is possible to separate DNA based on size in free solution; however, not end-labeled free-solution electrophoresis (ELFSE) uses a neutral drag-tag molecule to make it possible. In experiments to date, the drag-tag and DNA together form a random coil conformation; while with future generation drag-tags and high fields, deformation of this conformation may occur. In the first paper in this series we investigated the conditions under which the DNA and label become hydrodynamically distinct (or segregated), based on a theoretical approach developed for the electrophoresis of polyampholytes. In this paper we study further deformation wherein either the DNA and/or a polymeric label stretch. We show that deformation may dramatically improve the capabilities of ELFSE, especially when both the DNA and a polymeric drag-tag fully stretch; however, reaching these regimes will require extremely high field intensities, something that only microchip technologies may be able to achieve.     

Length-dependent DNA separations using multiple end-attached peptide nucleic acid amphiphiles in micellar electrokinetic chromatography

End-labeled free-solution electrophoresis (ELFSE) is an alternative approach to gel-based methods for size-based electrophoretic separation of DNA. In ELFSE, an electrically neutral "drag-tag" is appended to DNA to add significant hydrodynamic drag, thereby breaking its constant charge-to-friction ratio. Current drag-tag architecture relies on covalent attachment of polymers to each DNA molecule. We have recently proposed the use of micellar drag-tags in conjunction with sequence-specific hybridization of peptide nucleic acid amphiphiles (PNAAs). This work investigates the effect of multiple PNAA attachment on DNA resolution using MEKC. Simultaneous PNAA hybridization allows for the separation of long DNA targets, up to 1012 bases, using micellar drag-tags. Each PNAA handle independently interacts with the micellar phase, reducing the overall mobility of this complex relative to individual PNAA binding. The sequence- and size-based dependence of this separation technique is maintained with multiple PNAA binding over a range of DNA sizes. Results are accurately described by ELFSE theory, yielding alpha=54 for single-micelle tagging and alpha=142 for dual-micelle tagging. This method is the first example of a non-covalent drag-tag used to separate DNA of 1000 bases based on both size and sequence.     

End-labeled free-solution electrophoresis of DNA

DNA is a free-draining polymer. This subtle but "unfortunate" property of highly charged polyelectrolytes makes it impossible to separate nucleic acids by free-flow electrophoresis. This is why one must typically use a sieving matrix, such as a gel or an entangled polymer solution, in order to obtain some electrophoretic size separation. An alternative approach consists of breaking the charge to friction balance of free-draining DNA molecules. This can be achieved by labeling the DNA with a large, uncharged molecule (essentially a hydrodynamic parachute, which we also call a drag-tag) prior to electrophoresis; the resulting methodology is called end-labeled free-solution electrophoresis (ELFSE). In this article, we review the development of ELFSE over the last decade. In particular, we examine the theoretical concepts used to predict the ultimate performance of ELFSE for single-stranded (ssDNA) sequencing, the experimental results showing that ELFSE can indeed overcome the free-draining issue raised above, and the technological advances that are needed to speed the development of competitive ELFSE-based sequencing and separation technologies. Finally, we also review the reverse process, called free-solution conjugate electrophoresis (FSCE), wherein uncharged polymers of different sizes can be analyzed using a short DNA molecule as an electrophoretic engine.     

Free-solution electrophoresis of DNA modified with drag-tags at both ends

In end-labeled free-solution electrophoresis (ELFSE), DNA molecules are labeled with a frictional modifier or "drag-tag", allowing their size-based electrophoretic separation in free solution. Among the interesting observations from early work with dsDNA using streptavidin as a drag-tag was that the drag induced by including a streptavidin label at both ends was significantly more than double that from a single streptavidin (Heller, C. et al.., J. Chromatogr. A 1998, 806, 113-121). This finding was assumed to be in error, and subsequent work focused on experiments in which only a single drag-tag is appended to one end of the DNA molecule. Recent theoretical work (McCormick, L. C., Slater, G. W., Electrophoresis 2005, 26, 1659-1667) has examined the contribution of end-effects to the free-solution electrophoretic mobility of charged-uncharged polymer conjugates, reopening the question of enhanced drag from placing a drag-tag at both ends. In this study, this effect is investigated experimentally, using custom-synthesized ssDNA oligonucleotides allowing the attachment of drag-tags to one or both ends, as well as dsDNA PCR products generated with primers appropriate for the attachment of drag-tags at one or both ends. A range of sizes of drag-tags are used, including synthetic polypeptoid drag-tags as well as genetically engineered protein polymer drag-tags. The enhanced drag arising from labeling both ends has been confirmed, with 6-9% additional drag for the ssDNA and 10-23% additional drag for the dsDNA arising from labeling both ends than would be expected from simply doubling the size of the drag-tag at one end. The experimental results for ssDNA labeled at both ends are compared to the predictions of the recent theory of end-effects, with reasonably good quantitative agreement. These experimental findings demonstrate the feasibility of enhancing ELFSE separations by labeling both ends of the DNA molecule, leading to greater resolving power and a wider range of applications for this technique.     

Molecular deformation and free-solution electrophoresis of DNA-uncharged polymer conjugates at high field strengths: theoretical predictions. Part 1: hydrodynamic segregation

Recent advancements in DNA sequencing by end-labeled free-solution electrophoresis (ELFSE) show the promise of this novel technique which overcomes the need for a gel by using a label (or drag-tag) to render the free solution mobility of the DNA size-dependent. It is the attachment of an uncharged drag-tag molecule of a set size to various lengths of DNA in the sample that selectively slows down smaller DNA chains which have less force to pull the drag-tag than larger DNA. So far, only globally random coil conformations have been associated with ELFSE, i.e., the DNA and the label together form a single, undeformed hydrodynamic unit. This paper investigates the conditions under which the DNA and label will segregate into two hydrodynamically distinct units, based on a theoretical approach developed for the electrophoresis of polyampholytes. Optimal experimental conditions tailored to the available label sizes and voltages are predicted along with insight into ideal label architecture.     

Determining the electrophoretic mobility and translational diffusion coefficients of DNA molecules in free solution

The free solution mobility of DNA molecules of different molecular weights, the sequence dependence of the mobility, and the diffusion coefficients of small single- and double-stranded DNA (ss- and dsDNA) molecules can be measured accurately by capillary zone electrophoresis, using coated capillaries to minimize the electroosmotic flow (EOF) of the solvent. Very small differences in mobility between various analytes can be quantified if a mobility marker is used to correct for small differences in EOF between successive experiments. Using mobility markers, the molecular weight at which the free solution mobility of dsDNA becomes independent of molecular weight is found to be approximately 170 bp in 40 mM Tris-acetate-EDTA buffer. A DNA fragment containing 170 bp has a contour length of approximately 58 nm, close to the persistence length of DNA under these buffer conditions. Hence, the approach of the free solution mobility of DNA to a plateau value may be associated with the transition from a rod-like to a coil-like conformation in solution. Markers have also been used to determine that the free solution mobilities of ss- and dsDNA oligomers are sequence-dependent. Double-stranded 20-bp oligomers containing runs of three or more adenine residues in a row (A-tracts) migrate somewhat more slowly than 20-mers without A-tracts, suggesting that somewhat larger numbers of counterions are condensed in the ion atmospheres of A-tract DNAs, decreasing their net effective charge. Single-stranded 20-mers with symmetric sequences migrate approximately 1% faster than their double-stranded counterparts, and faster than single-stranded 20-mers containing A(5)- or T(5)-tracts. Interestingly, the average mobility of two complementary single-stranded 20-mers is equal to the mobility of the double-stranded oligomer formed upon annealing. Finally, the stopped migration method has been used to measure the diffusion coefficients of single- and double-stranded oligomers. The diffusion coefficients of ssDNA oligomers containing 20 nucleotides are approximately 50% larger than those of double-stranded DNA oligomers of the same size, reflecting the greater flexibility of ssDNA molecules. The methods used to carry out these experiments are also described in detail.     

Branched polymeric labels used as drag-tags in free-solution electrophoresis of ssDNA

In the framework of the classical blob theory of end-labeled free-solution electrophoresis of ssDNA, and based on recent experimental data with linear and branched polymeric labels (or drag-tags), the present study puts forward design principles for the optimal type of branching that would give, for a given total number of monomers, the highest effective frictional drag for ssDNA sequencing purposes. The hydrodynamic radii of the linear and branched labels are calculated using standard models like the freely jointed chain model and the Kratky-Porod worm-like chain model. Based on comparisons of the theory with the experimental data, we propose that the design of new branched labels should use either side chains whose length is comparable to the distance between the branching points or two long branches located near the ends of the molecule's backbone.     

Contaminant-induced current decline in capillary array electrophoresis

High-throughput capillary array electrophoresis (CAE) instruments for DNA sequencing suffer to varying degrees from read length degradation associated with electrophoretic current decline and inhibition or delay in the arrival of fragments at the detector. This effect is known to be associated with residual amounts of large, slow-moving fragments of template or genomic DNA carried through from sample preparation and sequencing reactions. Here, we investigate the creation and expansion of an ionic depletion region induced by overloading the capillary with low-mobility DNA fragments, and the effect of growth of this region on electrophoresis run failure. Slow-moving fragments are analytically and experimentally shown to reduce the ionic concentration of the downstream electrolyte. With injection of large fragments beyond a threshold quantity, the anode-side boundary of the nascent depletion region begins to propagate toward the anode at a rate faster than the contaminant DNA migration. Under such conditions, the depletion region expands, the capillary current declines dramatically, and the electrophoresis run yields a short read length or fails completely.     

Electrophoretic ratcheting of spherical particles in well/channel microfluidic devices: Making particles move against the net field

We examine the electrophoresis of spherical particles in microfluidic devices made of alternating wells and narrow channels, including a system previously used to separate DNA molecules. Our computer simulations predict that such systems can be used to separate spherical particles of different sizes that share the same free-solution mobility. Interestingly, the electrophoretic velocity shows an inversion as the field intensity is increased: while small particles have higher velocities at low field, the situation is reversed at high fields with the larger particles then moving faster. The resulting nonlinearity suggests that asymmetric pulsed electric fields could be used to build separation ratchets: particles then have a net size-dependent velocity in the presence of a zero-mean external field. Exploiting the inversion mentioned above, we show how to design pulsed field sequences that make particles move against the mean field (an example of negative mobility). Finally, we demonstrate that it is possible to use pulsed fields to make particles of different sizes move in opposite directions, even though their charge have the same sign.     

Control of the EOF in CE using polyelectrolytes of different charge densities

The control of the EOF direction and magnitude remains one of the more challenging issues for the optimization of separations in CE. In this work, we investigated the possibility to use variously charged polyanions for a fine-tuning of the EOF using polyelectrolyte multilayers. For that purpose, polyanions of poly(acrylamide-co-2-acrylamido-2-methyl-1-propanesulfonate) (PAMAMPS) with different chemical charge rates varying between 3 and 100% were used. These copolymers are statistic hydrophilic copolymers of acrylamide (AM) and 2-acrylamido-2-methyl-1-propanesulfonate (AMPS). The study of the influence of the chemical charge rate (AMPS molar proportion in the copolymer) on the electroosmotic mobility (mu(eo)) of a capillary modified by a polyelectrolyte bilayer (polycation/PAMAMPS) revealed that the fine-tuning of the EOF was possible, at least for cathodic or slightly anodic EOF (micro(eo) from -5 x 10(-5) to +35 x 10(-5) cm(2)V(-1)s(-1)). Electroosmotic mobility values were compared with the free-draining electrophoretic mobilities of the PAMAMPS constituting the last layer of the capillary coating. The stability of the EOF is discussed in detail on the basis of successive determinations of electroosmotic mobility and migration times. The application to the separation of a model peptide mixture demonstrated the interest (and the simplicity) of this approach for optimizing resolution and analysis time. Experimental resolutions were compared to the theoretical ones that we would obtain on a fused-silica capillary having the same EOF as the coated capillary.     

自由溶液和筛分介质条件下芯片DNA瞬间等速电泳预浓缩的比较

利用芯片电泳方法考察瞬间等速电泳-筛分电泳偶联分析的结果,比较了自由溶液和筛分介质中DNA瞬间等速电泳的预浓缩效果.结果显示,相比较于筛分介质条件,自由溶液瞬间等速电泳有利于改善预浓缩和后续筛分电泳分离效果.对此结果的解释是:自由溶液条件下DNA迁移速度的提高可以延长瞬间等速电泳持续时间,有利于提高预浓缩效率.此外,样品压缩区带在自由溶液-筛分介质界面的二次富集也是预浓缩效果得到改善的原因之一.     

Conformation dependence of DNA electrophoretic mobility in a converging channel

The electrophoresis of λ‐DNA is observed in a microscale converging channel where the center‐of‐masses trajectories of DNA molecules are tracked to measure instantaneous electrophoretic (EP) mobilities of DNA molecules of various stretch lengths and conformations. Contrary to the usual assumption that DNA mobility is a constant, independent of field and DNA length in free solution, we find DNA EP mobility varies along the axis in the contracting geometry. We correlate this mobility variation with the local stretch and conformational changes of the DNA, which are induced by the electric field gradient produced by the contraction. A “shish‐kebab” model of a rigid polymer segment is developed, which consists of aligned spheres acting as charge and drag centers. The EP mobility of the shish‐kebab is obtained by determining the electrohydrodynamic interactions of aligned spheres driven by the electric field. Multiple shish‐kebabs are then connected end‐to‐end to form a freely jointed chain model for a flexible DNA chain. DNA EP mobility is finally obtained as an ensemble average over the shish‐kebab orientations that are biased to match the overall stretch of the DNA chain. Using physically reasonable parameters, the model agrees well with experimental results for the dependence of EP mobility on stretch and conformation. We find that the magnitude of the EP mobility increases with DNA stretch, and that this increase is more pronounced for folded conformations.     

Capillary electrophoresis using core‐based hyperbranched polyethyleneimine (CHPEI) static‐coated capillaries

With unique 3‐D architecture, the application of core‐based hyperbranched polyethyleneimine (CHPEI), as a capillary coating in capillary electrophoresis, is demonstrated by manipulation of the electroosmotic mobility (EOF). CHPEI coatings (CHPEI5, M_w ≈? 5000 and CHPEI25, M_w ≈? 25 000) were physically adsorbed onto the inner surface of bare fused‐silica capillary (BFS) via electrostatic interaction of the oppositely charged molecules by rinsing the capillaries with different CHPEI aqueous solutions. The EOF values of the coated capillaries were measured over the pH range of 4.0–9.0. At higher pH (pH >6) the coated capillary surface possesses excess negative charges, which causes the reversal of the EOF. The magnitudes of the EOF obtained from the coated capillaries were three‐fold lower than that of BFS capillary. Desirable reproducibility of the EOF with % RSD (n = 5) ? 2 was obtained. Effect of ionic strength, stability of the coating (% RSD = 0.3) and the dependence of the EOF on pH (% RSD = 0.5) were also investigated. The CHPEI‐coated capillaries were successfully utilized to separate phenolic compounds, B vitamins, as well as basic drugs and related compounds with reasonable analysis time (<20 min) and acceptable migration‐time repeatability (<0.7% RSD for intra‐capillary and <2% RSD for inter‐capillary).     

High-speed DNA sequencing by tube-based capillary electrophoresis

We assessed the feasibility of high-speed DNA sequencing by tube-based capillary electrophoresis (TCE) with electrokinetic sample injections. We developed a water-circulated TCE system to control the capillary temperature precisely. Using this system and a ready-made sieving matrix at 50 degrees C, single-stranded DNA size marker fragments were separated at various pairs of the electric field strength, E, of 128-480 V/cm and the capillary effective length, L, of 100-360 mm. Assuming the read length (RL) is the fragment size at which the peak width equals the peak interval per base in obtained electropherograms, we estimated the values of RL (E, L), the RL at the pair (E, L). The points in ELz-space, (E, L, RL(E, L)), form a curved surface expressed by z = RL(E, L). Analyzing the contour lines of this curved surface, we determined the pairs of E and L providing target RLs of 300-500 bases within a minimum time. At a pair optimized for a 500-base RL (330 V/cm, 200 mm), one-color sequencing fragments were successfully separated up to 529 bases within 9.6 min. These results demonstrate that high-speed DNA sequencing comparable with that obtained by microfabricated chip-based capillary electrophoresis (MCE) can be achieved with TCE, which is more suitable in automation than MCE.     

Separating DNA sequencing fragments without a sieving matrix.

The possibility of separating appropriately labeled DNA fragments using free-flow capillary electrophoresis was predicted a few years ago based on simple theoretical arguments. Free-flow separation of double-stranded DNA (dsDNA) fragments in the 100-1000 base range was later demonstrated using a streptavidin label. In this article, we now report that end-labeled free-flow electrophoresis (ELFSE) can also be used to sequence single-stranded DNA (ssDNA). The first 100 bases of a DNA sequencing reaction were read without any sieving matrix when fractionated streptavidin was added to the 5'-end of the ssDNA fragments. These separations required only 18 min and did not require coated capillaries. An analysis of the results indicates that sample injection, analyte-wall interactions and thermal diffusion are the limiting factors at this time. Extrapolating from our data, we predict that several hundred bases could be sequenced in less than 30 min with the proper conditions. ELFSE thus offers an attractive potential alternative to polymer solutions for DNA sequencing in capillaries and microchips.     

Correlation free-solution capillary electrophoresis migration times of small peptides with physicochemical properties

Summary A series of small peptides containing varying degree of charge and size was used to study the effects of physicochemical properties on migration in free-solution capillary electrophoresis (FSCE). A semiempirical relationship between migration time under acidic conditions and the square root of molecular weight divided by the quantity of the number of the positively ionizable groups has been established. The ionization of the carboxyl terminal group in the polypeptides is negligible under acidic conditions. The relationship developed from this work has been used for the prediction of migration parameters in free solution capillary electrophoresis.     

Quantitative experimental determination of primer-dimer formation risk by free-solution conjugate electrophoresis

DNA barcodes are short, unique ssDNA primers that "mark" individual biomolecules. To gain better understanding of biophysical parameters constraining primer-dimer formation between primers that incorporate barcode sequences, we have developed a capillary electrophoresis method that utilizes drag-tag-DNA conjugates to quantify dimerization risk between primer-barcode pairs. Results obtained with this unique free-solution conjugate electrophoresis approach are useful as quantitatively precise input data to parameterize computation models of dimerization risk. A set of fluorescently labeled, model primer-barcode conjugates were designed with complementary regions of differing lengths to quantify heterodimerization as a function of temperature. Primer-dimer cases comprised two 30-mer primers, one of which was covalently conjugated to a lab-made, chemically synthesized poly-N-methoxyethylglycine drag-tag, which reduced electrophoretic mobility of ssDNA to distinguish it from ds primer-dimers. The drag-tags also provided a shift in mobility for the dsDNA species, which allowed us to quantitate primer-dimer formation. In the experimental studies, pairs of oligonucleotide primer barcodes with fully or partially complementary sequences were annealed, and then separated by free-solution conjugate CE at different temperatures, to assess effects on primer-dimer formation. When less than 30 out of 30 base-pairs were bonded, dimerization was inversely correlated to temperature. Dimerization occurred when more than 15 consecutive base-pairs formed, yet non-consecutive base-pairs did not create stable dimers even when 20 out of 30 possible base-pairs bonded. The use of free-solution electrophoresis in combination with a peptoid drag-tag and different fluorophores enabled precise separation of short DNA fragments to establish a new mobility shift assay for detection of primer-dimer formation.     

DNA sequencing with hydrophilic and hydrophobic polymers at elevated column temperatures

Read length in DNA sequencing by capillary electrophoresis at elevated temperatures is shown to be greatly affected by the extent of hydrophobicity of the polymer separation matrix. At column temperatures of up to 80 degrees C, hydrophilic linear polyacrylamide (LPA) provides superior read length and separation speed compared to poly(N,N-dimethylacrylamide) (PDMA) and a 70:30 copolymer of N,N-dimethylacrylamide and N,N-diethylacrylamide (PDEA30). DNA-polymer and polymer intramolecular interactions are presumed to be a major cause of band broadening and the subsequent loss of separation efficiency with the more hydrophobic polymers at higher column temperatures. With LPA, these interactions were reduced, and a read length of 1000 bases at an optimum temperature of 70 degrees -75 degrees C was achieved in less than 59 min. By comparison, PDMA produced a read length of roughly 800 bases at 50 degrees C, which was close to the read length attained in LPA at the same temperature; however, the migration time was approximately 20% longer, mainly because of the higher polymer concentration required. At 60 degrees C, the maximum read length was 850 bases for PDMA, while at higher temperatures, read lengths for this polymer were substantially lower. With the copolymer DEA30, read length was 650 bases at the optimum temperature of 50 degrees C. Molecular masses of these polymers were determined by tandem gel permeation chromatography-multiangle laser light scattering method (GPC-MALLS). The results indicate that for long read, rapid DNA sequencing and analysis, hydrophilic polymers such as LPA provide the best overall performance.