Simultaneous action of electric fields and nonelectric forces on a polyelectrolyte: Motion and deformation

Electrostatic focusing of unlabelled DNA into nanoscale pores using a salt gradient

Solid-state nanopores are sensors capable of analysing individual unlabelled DNA molecules in solution. Although the critical information obtained from nanopores (for example, DNA sequence) comes from the signal collected during DNA translocation, the throughput of the method is determined by the rate at which molecules arrive and thread into the pores. Here, we study the process of DNA capture into nanofabricated SiN pores of molecular dimensions. For fixed analyte concentrations we find an increase in capture rate as the DNA length increases from 800 to 8,000 base pairs, a length-independent capture rate for longer molecules, and increasing capture rates when ionic gradients are established across the pore. Furthermore, we show that application of a 20-fold salt gradient allows the detection of picomolar DNA concentrations at high throughput. The salt gradients enhance the electric field, focusing more molecules into the pore, thereby advancing the possibility of analysing unamplified DNA samples using nanopores.

Electric and Electrophoretic Inversion of the DNA Charge in Multivalent Electrolytes

Counterion-induced inversion of the DNA charge was characterized through extensive molecular dynamics simulations. We observed reversal of the DNA motion in an external electric field upon increasing the concentration of trivalent or quadrivalent counterions. In the case of a divalent electrolyte, inversion of the DNA's electric charge was observed at high concentrations of the electrolyte but not reversal of the DNA' electrophoretic motion. We demonstrate that inversion of the DNA's electrophoretic mobility results from a complex interplay of electrostatics and hydrodynamics.

Unfolding polyelectrolytes in trivalent salt solutions using dc electric fields: A study by Langevin dynamics simulations

We study the behavior of single linear polyelectrolytes condensed by trivalent salt under the action of electric fields through computer simulations. The chain is unfolded when the strength of the electric field is stronger than a critical value. This critical electric field follows a scaling law against chain length, and the exponent of the scaling law is -0.77(1), smaller than the theoretical prediction, -3nu2 [R. R. Netz, Phys. Rev. Lett. 90, 128104 (2003)], and the one obtained by simulations in tetravalent salt solutions, -0.453(3) [P.-Y. Hsiao and K.-M. Wu, J. Phys. Chem. B 112, 13177 (2008)]. It demonstrates that the scaling exponent depends sensitively on the salt valence. Hence, it is easier to unfold chains condensed by multivalent salt of a smaller valence. Moreover, the absolute value of chain electrophoretic mobility increases drastically when the chain is unfolded in an electric field. The fact that the mobility depends on electric field and on chain length provides a plausible way to impart chain-length dependence in free-solution electrophoresis via chain unfolding transition induced by electric fields. Finally, we show that, in addition to an elongated structure, a condensed chain can be unfolded into a U-shaped structure. The formation of this structure in our study is purely a result of the electric polarization, not of the elastohydrodynamics dominated in sedimentation of polymers.

Static and dynamic responses of polyelectrolyte brushes under external electric field

The static and dynamic behaviors of partially charged and end-grafted polyelectrolyte brushes in response to electric fields were investigated by means of molecular dynamics simulation. The results show that the polymer brushes can be partially or fully stretched by applying an external electric field. Moreover, the brushes can switch reversibly from collapsed to stretched states, fully responding to the AC electric stimuli, and the gating response frequency can reach a few hundred MHz. The effects of the grafting density, the charge fraction of the brushes and the strength of the electric field on the average height of the polymer brushes were studied through the simulations.

Motion of microgels in electric fields

We review existing experimental results on the motion of microgels in the presence of electric fields and find that there can be striking differences depending on whether the polymer network comprising the microgel is neutral or charged: While for neutral microgels, the electrophoretic mobility, micro, typically decreases as the particle swells, in the case of ionic microgels, micro typically increases with particle swelling. We explain this difference in behavior by recurring to electro-osmotic fluid flows inside the particles, which are relevant in the presence of electric fields when the polymer network is ionized; these flows render the particles permeable to the solvent qualitatively changing the way to think about their electrophoretic behavior. We show that this interpretation is consistent with calculations of the drag force experienced by a permeable object as it moves inside a liquid and with recent theoretical models for the electrophoresis of soft particles. The analysis emphasizes that the electrophoresis of neutral microgels can be qualitatively treated as that of charged hard spheres, irrespective on whether the particles are swollen or de-swollen. By contrast, ionic microgels behave like free-draining polyelectrolytes in the presence of electric fields.

Freely relaxing polymers remember how they were straightened

The relaxation of initially straight semiflexible polymers has been discussed mainly with respect to the longest relaxation time. The biologically relevant nonequilibrium dynamics on shorter times is comparatively poorly understood, partly because "initially straight" can be realized in manifold ways. Combining Brownian dynamics simulations and systematic theory, we demonstrate how different experimental preparations give rise to specific short-time and universal long-time dynamics. We also discuss boundary effects and the onset of the stretch-coil transition.

Electro-osmotic screening of the DNA charge in a nanopore

Extensive all-atom molecular dynamics simulations were performed to characterize the microscopic origin of the force experienced by DNA in a bulk electrolyte and a solid-state nanopore when subject to an external electrostatic field E. The effective screening of the DNA charge was found to originate from the hydrodynamic drag of the electro-osmotic flow that is driven by the motion of counterions along the surface of DNA. We show that the effective driving force F in a nanopore obeys the same law as in a bulk electrolyte: F=ximuE , where xi and mu are the friction coefficient and electrophoretic mobility of DNA, respectively. Using this relationship, we suggest a method for determining the effective driving force on DNA in a nanopore that does not require a direct force measurement.

Overcharging, charge inversion, and reentrant condensation: using highly charged polyelectrolytes in tetravalent salt solutions as an example of study

We study salt-induced charge overcompensation and charge inversion of flexible polyelectrolytes via computer simulations and demonstrate the importance of ion excluded volume. Reentrant condensation takes place when the ion size is comparable to monomer size, and happens in a middle region of salt concentration. In a high-salt region, ions can overcharge a chain near its surface and charge distribution around a chain displays an oscillatory behavior. Unambiguous evidence obtained by electrophoresis shows that charge inversion does not necessarily appear with overcharging and occurs when the ion size is not big. These findings suggest a disconnection of resolubilization of polyelectrolyte condensates at high salt concentration with charge inversion.

Artificial molecular sieves and filters: a new paradigm for biomolecule separation

Patterned regular sieves and filters with comparable molecular dimensions hold great promise as an alternative to conventional polymeric gels and fibrous membranes to improve biomolecule separation. Recent developments of microfabricated nanofluidic sieves and filters have demonstrated superior performance for both analytical and preparative separation of various physiologically relevant macromolecules, including proteins. The insights gained from designing these artificial molecular sieves and filters, along with the promising results gathered from their first applications, serve to illustrate the impact that they can have on improving future separation of complex biological samples. Further development of artificial sieves and filters with more elaborate geometrical constraints and tailored surface functionality is believed to provide more promising ideals and results for biomolecule separation, which has great implications for proteomic research and biomarker discovery.

Electrophoretic separation of large DNAs using steric confinement

We report an alternative method for electrophoretic separation of large DNAs using steric confinement between solid walls, without gel or obstacles. The change of electrophoretic mobility vs confinement thickness is investigated using fluorescence video microscopy. We observe separation at small confinement thicknesses followed by a transition to the bulk behavior (no separation) at a thickness of about 4 mum (a few radii of gyration for the studied DNA chains). We present tentative explanations of our original observations.

Electrokinetic-flow-induced viscous drag on a tethered DNA inside a nanopore

Recent work has shown that the resistive force arising from viscous effects within the pore region could explain observed translocation times in certain experiments involving voltage-driven translocations of DNA through nanopores [Ghosal, Phys. Rev. E 71, 051904 (2006); Phys. Rev. Lett. 98, 238104 (2007)]. The electrokinetic flow inside the pore and the accompanying viscous effects also play a crucial role in the interpretation of experiments where the DNA is immobilized inside a nanopore [Keyser, Nat. Phys. 2, 473 (2006)]. In this paper the viscous force is explicitly calculated for a nanopore of cylindrical geometry. It is found that the reductions of the tether force due to viscous drag and due to charge reduction by Manning condensation are of similar size. The result is of importance in the interpretation of experimental data on tethered DNA.

Lattice-Boltzmann simulation of the sedimentation of charged disks

We report a series of lattice-Boltzmann simulations of the sedimentation velocity of charged disks. In these simulations, we explicitly account for the hydrodynamic and electrostatic forces on disks and on their electrical double layer. By comparing our results with those for spheres with equal surface and charge, we can clarify the effect of the particle shape on the sedimentation process. We find that disks and spheres exhibit a different dependence of the sedimentation velocity on the Debye screening length. An analysis of the behavior of highly charged disks (beyond the scope of the linearized Poisson-Boltzmann equation) shows that, in that regime, the charge dependence of the sedimentation velocity of disks and spheres is similar. This suggests that, at high charge, the effective hydrodynamic shape of the disks becomes more spherical.

Electric and hydrodynamic stretching of DNA-polymer conjugates in free-solution electrophoresis

The conjugation of an uncharged polymer to DNA fragments makes it possible to separate DNA by free-solution electrophoresis. This end-labeled free-solution electrophoresis method has been shown to successfully separate ssDNA with single monomer resolution up to about 110 bases. It is the aim of this paper to investigate in more detail the coupled hydrodynamic and electrophoretic deformation of the ssDNA-label conjugate at fields below 400 V/cm. Our model is an extension of the theoretical approach originally developed by Stigter and Bustamante [Biophys. J. 75, 1197 (1998)] to investigate the problems of a tethered chain stretching in a hydrodynamic flow and of the electrophoretic stretch of a tethered polyelectrolyte. These two separate models are now used together since the charged DNA is "tethered" to the uncharged polymer (and vice versa), and the resulting self-consistent model is used to predict the deformation and the electrophoretic velocity for the hybrid molecule. Our theoretical and experimental results are in good qualitative agreement.

DNA stretch during electrophoresis due to a step change in mobility

We investigate DNA stretching during electrophoresis when the mobility abruptly changes. This is a simplified geometry that produces a nonhomogeneous strain rate over the scale of a single molecule. An effective Weissenberg number (Wi) and Deborah number were identified, and the degree of stretching was examined as a function of these two parameters. The system does not undergo a coil-stretch transition. The finite extensibility of the chains only affects the response if the chain is stretched to a significant fraction of the contour length. The wormlike chain shows a characteristic approach to full extension of Wi(-1/2).

Tethered polyelectrolytes under the action of an electrical field: a molecular-dynamics study

For a polyelectrolyte undergoing electrophoretic motion, it is predicted (D. Long, J.L. Viovy, A. Ajdari, Phys. Rev. Lett. 76, 3858 (1996); D. Long, A. Ajdari, Electrophoresis 17, 1161 (1996)) that the mechanical force necessary to stall the molecule is substantially smaller than the sum of electrical forces applied on all monomers. In fact, it should be proportional to its hydrodynamic friction coefficient and therefore to the size of its conformation. In our work we examine this prediction using coarse-grained molecular-dynamics simulations in which we explicitly include the polymer, the solvent, the counterions and salt. The electrophoretic mobility of polyelectrolytes is evaluated, the mechanical force necessary to keep the molecules tethered is measured and the resulting anisotropic polymer conformations are observed and quantified. Our results corroborate Long et al.'s prediction.

Pulsed-field separation of particles in a microfluidic device

We demonstrate the proof-of-principle of a new separation concept for micrometer-sized particles in a structured microfluidic device. Under the action of externally applied, periodic voltage-pulses two different species of like-charged polystyrene beads are observed to simultaneously migrate into opposite directions. Based on a theoretical model of the particle motion in the microdevice that shows good agreement with the experimental measurements, the underlying separation mechanism is identified and explained. Potential biophysical applications, such as cell sorting, are briefly addressed.

Transverse migration of a confined polymer driven by an external force

We demonstrate that a polymer confined to a narrow channel migrates towards the center when driven by an external force parallel to the channel walls. This migration results from asymmetric hydrodynamic interactions between polymer segments and the confining walls. A weak pressure-driven flow, applied in the same direction as the external force, enhances the migration. However, when the pressure gradient and the external force act in opposite directions the polymer can migrate towards the boundaries. Nevertheless, for sufficiently strong forces the polymer always migrates towards the center. A dumbbell kinetic theory explains these results qualitatively. A comparison of our results with experimental measurements on DNA suggests that hydrodynamic interactions in polyelectrolytes are only partially screened. We propose new experiments and analysis to investigate the extent of the screening in polyelectrolyte solutions.

Effective charge and free energy of DNA inside an ion channel

Translocation of a single stranded DNA (ssDNA) through an alpha -hemolysin channel in a lipid membrane driven by applied transmembrane voltage V was extensively studied recently. While the bare charge of the ssDNA piece inside the channel is approximately 12 (in units of electron charge) measurements of different effective charges resulted in values between one and two. We explain these challenging observations by a large self-energy of a charge in the narrow water filled gap between ssDNA and channel walls, related to large difference between dielectric constants of water and lipid, and calculate effective charges of ssDNA. We start from the most fundamental stall charge q(s), which determines the force F(s)=q(s)V/L stalling DNA against the voltage V ( L is the length of the channel). We show that the stall charge q(s) is proportional to the ion current blocked by DNA, which is small due to the self-energy barrier. Large voltage V reduces the capture barrier which DNA molecule should overcome in order to enter the channel by /q(c)/V, where q(c) is the effective capture charge. We expressed it through the stall charge q(s). We also relate the stall charge q(s) to two other effective charges measured for ssDNA with a hairpin in the back end: the charge q(u) responsible for reduction of the barrier for unzipping of the hairpin and the charge q(e) responsible for DNA escape in the direction of hairpin against the voltage. At small V we explain reduction of the capture barrier with the salt concentration.

A Brownian dynamics-finite element method for simulating DNA electrophoresis in nonhomogeneous electric fields

The objective of this work is to develop a numerical method to simulate DNA electrophoresis in complicated geometries. The proposed numerical scheme is composed of three parts: (1) a bead-spring Brownian dynamics (BD) simulation, (2) an iterative solver-enhanced finite element method (FEM) for the electric field, and (3) the connection algorithm between FEM and BD. A target-induced searching algorithm is developed to quickly address the electric field in the complex geometry which is discretized into unstructured finite element meshes. We also develop a method to use the hard-sphere interaction algorithm proposed by Heyes and Melrose [J. Non-Newtonian Fluid Mech. 46, 1 (1993)] in FEM. To verify the accuracy of our numerical schemes, our method is applied to the problem of lambda-DNA deformation around an isolated cylindrical obstacle for which the analytical solution of the electric field is available and experimental data exist. We compare our schemes with an analytical approach and there is a good agreement between the two. We expect that the present numerical method will be useful for the design of future microfluidic devices to stretch and/or separate DNA.

DNA electrophoresis in microfluidic post arrays under moderate electric fields

The dynamics of long DNA moving through microfluidic arrays of micron-sized posts under a moderate electric field are modeled by a Scher-Lax continuous-time random walk. The microscale model consists of a repetitive sequence of three steps: (i) collision with the post and extension into two arms, (ii) electric-field-driven unhooking from the post, and (iii) uniform translation until the next collision. The model features two random variables: the initial offset between the two arms of the polymer during a given collision and the distance traveled between collisions. For experimentally realistic values of the electric field strength and DNA molecular weight, scaling laws indicate that the chain will generally be in a stem-flower conformation when unhooking from the post. Compared to a taut-chain model at the same field strength, the stem-flower conformation reduces the time engaged with the post and increases the collision frequency. Analytical expressions for the mean velocity and dispersivity are derived as a function of the post density, post spacing, free-solution mobility, Kuhn length, and sequence length. The incomplete extension of the chain does not strongly affect the mean velocity, but tends to increase the dispersivity relative to a taut chain. As a result, the separation resolution decreases as the field decreases for a moderate field, in agreement with experiments. The quantitative agreement between the model and experimental data is satisfactory, especially considering that the model contains no adjustable parameters.

DNA electrophoresis in designed channels

We present a simple description on the electrophoretic dynamics of polyelectrolytes going through designed channels with narrow constrictions of slit geometry. By analyzing rheological behaviours of the stuck chain, which is coupled to the effect of solvent flow, three critical electric fields (permeation field E((per)) approximately N(-1), deformation field E((def)) approximately N(-3/5) and injection field E((inj)) approximately N(0), with N polymerization index) are clarified. Between E((per)) and E((inj)), the chain migration is dictated by the driven activation process. In particular, at E > E((def)), the stuck chain at the slit entrance is strongly deformed, which enhances the rate of the permeation. From these observations, electrophoretic mobility at a given electric field is deduced, which shows non-monotonic dependence on N. For long enough chains, mobility increases with N, in good agreement with experiments. An abrupt change in the electrophoretic flow at a threshold electric field is formally regarded as a nonequilibrium phase transition.

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.

Motion of single long DNA molecules through arrays of magnetic columns

We present a videomicroscopy study of T4 DNA (169 kbp) in microfluidic arrays of posts formed by the self-assembly of magnetic beads. We observe DNA moving through an area of 10 000 microm(2), typically containing 100-600 posts. We determine the distribution of the contact times with the posts and the distribution of passage times across the field of view for hundreds of DNA per experiment. The contact time is well approximated by a Poisson process, scaling like the inverse of the field strength, independent of the density of the array. The distribution of passage times allows us to estimate the mean velocity and dispersivity of the DNA during its motion over distances long compared to our field of view. We compare these values with those computed from a lattice Monte Carlo model and geometration theory. We find reasonable quantitative agreement between the lattice Monte Carlo model and experiment, with the error increasing with increasing post density. The deviation between theory and experiment is attributed to the high mobility of DNA after disengaging from the posts, which leads to a difference between the contact time and the total time lost by colliding. Classical geometration theory furnishes surprisingly good agreement for the dispersivity, while geometration theory with a mean free path significantly overestimates the dispersivity.

Mechanisms of DNA separation in entropic trap arrays: a Brownian dynamics simulation

Using Brownian dynamics simulations, we study the migration of long charged chains in an electrophoretic microchannel device consisting of an array of microscopic entropic traps with alternating deep regions and narrow constrictions. Such a device has been designed and fabricated recently by Han and Craighead [Science 288 (2000) 1026] for the separation of DNA molecules. Our simulation reproduces the experimental observation that the mobility increases with the length of the DNA. A detailed data analysis allows to identify the reasons for this behavior. Two distinct mechanisms contribute to slowing down shorter chains. One has been described earlier by Han and Craighead [Science 288 (2000) 1026]: the chains are delayed at the entrance of the constriction and escape with a rate that increases with chain length. The other, actually dominating mechanism is here reported for the first time: some chains diffuse out of their main path into the corners of the box, where they remain trapped for a long time. The probability that this happens increases with the diffusion constant, i.e., the inverse chain length.

Two-state migration of DNA in a structured microchannel

DNA migration in topologically structured microchannels with periodic cavities is investigated experimentally and with Brownian dynamics simulations of a simple bead-spring model. The results are in very good agreement with one another. In particular, the experimentally observed migration order of lambda - and T2-DNA molecules is reproduced by the simulations. The simulation data indicate that the mobility may depend on the chain length in a nonmonotonic way at high electric fields. This is found to be the signature of a nonequilibrium bistability between two different migration states, a slow one and a fast one. The latter can also be observed experimentally under appropriate conditions.

Electrokinetic stretching of tethered DNA

During electrophoretic separations of DNA in a sieving medium, DNA molecules stretch from a compact coil into elongated conformations when encountering an obstacle and relax back to a coil upon release from the obstacle. These stretching dynamics are thought to play an important role in the separation mechanism. In this article we describe a silicon microfabricated device to measure the stretching of tethered DNA in electric fields. Upon application of an electric field, electro-osmosis generates bulk fluid flow in the device, and a protocol for eliminating this flow by attaching a polymer brush to all silicon oxide surfaces is shown to be effective. Data on the steady stretching of DNA in constant electric fields is presented. The data corroborate the approximate theory of hydrodynamic equivalence, indicating that DNA is not free-draining in the presence of both electric and nonelectric forces. Finally, these data provide the first quantitative test of a Stigter and Bustamante's detailed theory of electrophoretic stretching of DNA without adjustable parameters. The agreement between theory and experiment is good.

Nonequilibrium thermodynamics of membrane-confined electrophoresis

Membrane-confined electrophoresis (MCE) is an electrophoretic transport method in which macromolecules in solution are confined within a cuvette through which a current flows. Small ions that can permeate the membranes permit current flow. The method is the electrophoretic analog to analytical ultracentrifugation. Systems in the MCE instrument are described by nonequilibrium thermodynamics. This description forms the basis of a program, implemented using finite element methods, that can model transport processes in such systems over an extended time, from arbitrary starting conditions to steady state. Issues relevant to the analysis of systems in which macromolecular species are involved in mass-action associations are discussed. Particular attention is given to steady-state electrophoresis, from which measurements of reduced molecular charge are sought. The relationship of such measurements to valence is discussed.

Effects of asymmetric salt and a cylindrical macroion on charge inversion: electrophoresis by molecular dynamics simulations

The charge inversion phenomenon is studied by molecular dynamics simulations, focusing on size and valence asymmetric salts, and a threshold of surface charge density for charge inversion. The charge inversion criteria by the electrophoretic mobility and the radial distribution functions of ions coincide except around the charge inversion threshold. The reversed electrophoretic mobility increases with the ratio of coion to counterion radii, a(-)/a(+), while it decreases with the ratio of coion to counterion valences, Z(-)/Z(+). The monovalent salt enhances charge inversion of a strongly charged macroion at small salt ionic strength, while it reduces reversed mobility otherwise. A cylindrical macroion is more persistent to monovalent salt than a spherical macroion of the same radius and surface charge density.

DNA electrophoresis in dilute polymer solutions: a nonbinary mechanism

The dynamical behavior of the neutral polymer (dextran, M(w)=2 x 10(6)) is investigated during DNA electrophoresis in a dilute solution. Using a fluorescence recovery after photobleaching setup, we measured the velocity of fluorescein-labeled dextran induced by the migration of the DNA. We found that each DNA molecule drags a large number of dextrans with it. We show that DNA-dextran interactions are not only binary but long range and indirect. We conclude that the DNA-dextran complex creates a hydrodynamic field that entrains polymers far from the DNA during electrophoresis.

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.

Thermodynamics of ionic microgels

We present a theory of dilute aqueous suspensions of microgel particles. It is found that as the number of charged monomers in the polymer network composing mesoscopic gel increases, the particles undergo a swelling transition. Depending on the hydrophobicity of the polymer, this transition can be either continuous or discontinuous. Furthermore, similar to charge stabilized colloidal particles, we find that the electrophoretic mobility of the microgel is controlled by an effective charge. Unlike the colloids, however, for which the effective charge grows asymptotically with the logarithm of the bare charge, the effective charge of an ionic microgel scales as Z(eff) approximately Z0.5. The findings are in good agreement with the experimental measurements.

Diffusion coefficient of DNA molecules during free solution electrophoresis

The free-draining properties of DNA normally make it impossible to separate nucleic acids by free-flow electrophoresis. However, little is known, either theoretically or experimentally, about the diffusion coefficient of DNA molecules during free-flow electrophoresis. In fact, many authors simply assume that the Nernst-Einstein relation between the mobility and the diffusion coefficient still holds under such conditions. In this paper, we present an experimental study of the diffusion coefficient of both ssDNA and dsDNA molecules during free-flow electrophoresis. Our results unequivocally show that a simplistic use of Nernst-Einstein's relation fails, and that the electric field actually has no effect on the thermal diffusion process. Finally, we compare the dependence of the diffusion coefficient upon DNA molecular size to results obtained previously by other groups and to Zimm's theory.

On the characteristics of migration of oligomeric DNA in polyacrylamide gels and in free solution

We review a model for the free-solution electrophoretic mobility of oligomeric double-stranded (ds) DNA. We have found that the free-solution mobility of ds DNA increases as the molecular weight of the fragment increases, up to a few hundred base pairs. This insight is combined with recent advances in the nature of counterion condensation theory of very short DNA fragments to describe quantitatively the electrophoretic mobility of oligomeric single-stranded DNA in polyacrylamide gels. The model predicts, in agreement with recent experiments, that significant anomalous migration exists with short DNA sequences, the onset of which is dependent on the size of polyacrylamide gel pores. For terminal phosphate-labeled DNA fragments, the free-solution mobility is no longer proportional to the ratio of the total effective charge and the friction coefficient. These changes in properties affect the characteristics of migration of end-labeled DNA fragments in polyacrylamide gels.

Theory of DNA electrophoresis: a look at some current challenges

Although electrophoresis is one of the basic methods of the modern molecular biology laboratory, new ideas are being suggested at an accelerated rate, in large part because of the pressing demands of the biomedical community. Although we now have, at least for some methods, a fairly good theoretical understanding of the physical mechanisms that lead to the observed peak spacings, widths and shapes, this knowledge is often too qualitative to be used to guide further technical developments and improvements. In this article, we review some selected elements of the current state of our theoretical ignorance, focusing mostly on DNA electrophoresis, and we offer several suggestions for further theoretical investigations.