Semiphenomenological model for the dispersion of DNA during electrophoresis in a microfluidic array of posts

A lattice Monte Carlo model is proposed for quantifying the dispersion of DNA during microfluidic electrophoresis in a quasiperiodic array of posts similar to that encountered in the microfluidic self-assembly of magnetic bead columns. The transport model is semiphenomenological in the sense that all parameters, such as the post geometry, average collision time, and collision probability, are assumed to be accessible either directly from experiment or from a model of the microscale physics. Asymptotically exact formulas are obtained for the mean velocity and dispersivity using Taylor-Aris dispersion theory, which permits a straightforward analysis of the separation efficiency. The model is applicable to a variety of situations involving collision-retardation processes.

Sieving mechanisms in polymeric matrices

A critical review of the existing theoretical models and experimental evidences for sieving mechanisms during separation of macromolecules, paying particular attention to capillary electrophoresis applications is presented. Gel models (Ogston and reptation) have been successfully applied to highly entangled polymer solutions, where fast and efficient separations can occur. In order to account for the DNA/polymers collision-interaction mechanisms during separation in dilute solutions - characterized by a poorer resolution -, approximated analytical models have been developed. An insight in the mechanism regulating the intermediate case of moderately entangled polymer solutions, for low fields and concentrations of small multiples of the overlap concentration c*, is given by the constraint release approach. This model proposes an upper limit of size separation, increasing with matrix concentration and molecular mass. Finally, the coupling between the reptative motion of the analytes and the effect of matrix constraint release very likely plays a fundamental role in the separation mechanism and requires therefore further and deeper investigation, both theoretically and experimentally.

Comb-like copolymers as self-coating, low-viscosity and high-resolution matrices for DNA sequencing

Comb-like copolymers with a polyacrylamide backbone and poly(N,N-dimethylacrylamide) grafts were prepared, as a way to combine the superior sieving properties of polyacrylamide with the self-coating properties of polydimethylacrylamide. These matrices function well in the absence of a capillary coating, and achieve separation performances for single-stranded DNA that are comparable to those of state-of-the-art long-chain linear polyacrylamide. Structural parameters such as the grafting density and the polymer molecular mass were varied, and good performance appears to be achieved with a relatively large range of parameters. Surprisingly, excellent separation is achieved even with matrices that have a viscosity as low as 200 mPa/s. A discussion of the physics underlying this behavior is provided.

New block-copolymer thermoassociating matrices for DNA sequencing: effect of molecular structure on rheology and resolution

A new family of matrices for DNA sequencing by capillary electrophoresis is presented. These matrices combine easy injection with high sieving performances, due to thermal switching between a low and a high viscosity state through a modest increase in temperature (approximately 20 degrees C). They are constructed from a hydrophilic polymer backbone with grafted lower critical solution temperature (LCST) side chains. The comb-like LCST copolymers are characterized in terms of size of the polymer backbone, the size of LCST side chains and the grafting densities. The dependance of rheological behavior and electrophoretic performance of these copolymers is correlated with their microstructure. Without complete optimization, a resolution of order 0.5, corresponding to a very reasonable limit for read length with current base calling softwares, could be achieved for segments around 800 bases differing by 1 base in less than one hour in a commercial ABI 310 apparatus.

Direct imaging of single-molecules: from dynamics of a single DNA chain to the study of complex DNA-protein interactions

Recent years have seen significant advances in the characterization and manipulation of individual molecules. The combination of single-molecule fluorescence and micromanipulation enables one to study physical and biological systems at new length scales, to unravel qualitative mechanisms, and to measure kinetic parameters that cannot be addressed by traditional biochemistry. DNA is one of the most studied biomolecules. Imaging single DNA molecules eliminates important limitations of classical techniques and provides a new method for testing polymer dynamics and DNA-protein interactions. Here we review some applications of this new approach to physical and biological problems, focusing on videomicroscopy observations of individual DNA chains extended in a shear flow. We will first describe data obtained on the stretching, relaxation and dynamics of a single tethered polymer in a shear flow, to demonstrate that the deformation of sheared tethered chains is partially governed by the thermally driven fluctuations of the chain transverse to the flow direction. Next, we will show how single-molecule videomicroscopy can be used to study in real time DNA folding into chromatin, a complex association of DNA and proteins responsible for the packaging of DNA in the nucleus of an eukaryotic cell.

Fast kinetics of chromatin assembly revealed by single-molecule videomicroscopy and scanning force microscopy

Fluorescence videomicroscopy and scanning force microscopy were used to follow, in real time, chromatin assembly on individual DNA molecules immersed in cell-free systems competent for physiological chromatin assembly. Within a few seconds, molecules are already compacted into a form exhibiting strong similarities to native chromatin fibers. In these extracts, the compaction rate is more than 100 times faster than expected from standard biochemical assays. Our data provide definite information on the forces involved (a few piconewtons) and on the reaction path. DNA compaction as a function of time revealed unique features of the assembly reaction in these extracts. They imply a sequential process with at least three steps, involving DNA wrapping as the final event. An absolute and quantitative measure of the kinetic parameters of the early steps in chromatin assembly under physiological conditions could thus be obtained.

Dynamics of a tethered polymer in shear flow

The dynamics of a single polymer tethered to a solid surface in a shear flow was observed using fluorescently labeled DNA chains. Dramatic shear enhanced temporal fluctuations in the chain extension were observed. The rate of these fluctuations initially decreased for increasing shear rate gamma; and increased above a critical gamma;. Simulations revealed that these anomalous dynamics arise from a continual recirculating motion of the chain or cyclic dynamics. These dynamics arise from a coupling of the chain velocity in the flow direction to thermally driven fluctuations of the chain in the shear gradient direction.

Electrohydrodynamically induced aggregation during constant and pulsed field capillary electrophoresis of DNA

We present a study aimed at understanding the factors affecting the separation of large DNA molecules by capillary electrophoresis in polymer solutions. In a first series of experiments, a systematic study of the effect of operational parameters on the development of an electrohydrodynamic instability resulting in DNA aggregation and spurious peaks in the electropherograms is presented. The results are discussed in regard to a recent theory of electrohydrodynamic instabilities in macroion suspensions, recently proposed by Isambert et al. Overall, the results provide strong support to the theory. Some situations of interest for applications, and not explicitly considered in the theory, such as asymmetric field pulsing and the use of polymer additives in the buffer, were also considered. Furthermore, robust optimized protocols for high resolution separation of DNA in the range of 100 base pairs to 160 kilobase pairs, are proposed. As predicted by the model, it is shown that using a concentrated isoelectric buffer (histidine) strongly reduces aggregation as compared to the use of a conventional buffer at the same concentration, and allows separation of DNA from 100 bp to 160 kbp in less than 10 min. We also present a systematic study of the dependence of the mobility vs DNA size, pulse frequency, and field strength. The results are discussed with respect to the Biased Reptation with Fluctuations model and a good agreement is obtained. Copyright 1999 John Wiley & Sons, Inc.

The effect of blob size and network dynamics on the size-based separation of polystyrenesulfonates by capillary electrophoresis in the presence of entangled polymer solutions

This work focuses on the separation of standard polystyrenesulfonates (PSS), with molecular masses (Mr) between 16 and 990 x 10(3) in capillaries filled with semidilute (entangled) linear hydrophilic polymers. Contrary to cross-linked chemical gels, which produce permanent networks, solutions of linear polymers lead to dynamic networks. The analytical performances and migration mechanisms are discussed on the basis of experiments performed in solutions of linear polyethyleneoxides and derivatized celluloses of various molecular masses. The influence of the mesh size and of the lifetime of the obstacles of the separating network has been investigated in detail. The mesh size is assimilated to the blob size of the separating polymer and is a decreasing function of its concentration. The lifetime of the obstacles of the network, identified with the reptation time of the polymer chain, characterizes its dynamics. This characteristic time increases with both the molecular weight of the separating polymer and its concentration. Its impact was first examined at fixed blob size. Then, the influence of the blob size was studied while keeping the reptation time of the network constant. By doing so, the existence of interactions between the solute and the separating polymer or between the solute and capillary wall can be more safely assessed. It appears that the reptation time of the mesh has a large influence on the electrophoretic mobility of the PSSs under a threshold value, which is of the order of magnitude of the time taken by the PSS to migrate on the blob size. Also shown are separations using networks made up with mixtures of polyethyleneoxides of the same nature and same mass concentration, but of very different molecular masses. This latter approach allows one to adapt the viscosity of the solution and the dynamics of the network, keeping the blob size constant.

Acting on actin: the electric motility assay

We have developed a novel technique which allows one to direct the two dimensional motion of actin filaments on a myosin coated sheet using a weak electric field parallel to the plane of motion. The filament velocity can be increased or decreased, and even reversed, as a function of orientation and strength of the field. PMMA (poly(methylmethacrylate)) gratings, which act as rails for actin, allow one for the first time to explore three quadrants of the force velocity diagram. We discuss effective friction, duty ratio and stall force at different myosin densities. A discontinuity in the velocity force relationship suggests the existence of dynamical phase transition.

High resolution capillary electrophoretic separation of oligonucleotides in low-viscosity, hydrophobically end-capped polyethylene oxide with cubic order

A triblock self-associating polymer with the structure n-dodecane-poly(ethylene oxide)-n-dodecane and a very low polydispersity has been used as a matrix to separate a sample of single-stranded oligonucleotides containing Pd(A)25-30 and Pd(A)40-60. Above a concentration of 4%, this associative polymer forms a micellar network with cubic order and a well-defined micellar spacing, in which the dodecane micellar cores are bridged by polyoxyethylene segments. This medium combines a low viscosity with excellent resolution of oligonucleotides. This work confirms that associative polymers are potentially powerful media for separation in capillary electrophoresis, and argues in favor of the use of monodisperse products presenting a high-order in the physical gel state.

Micropreparative capillary electrophoresis of DNA by direct transfer onto a membrane

We have developed a new technique for the collection of DNA fragments separated by capillary electrophoresis, by direct transfer from the capillary outlet to a positively charged membrane. Transfer and post-run detection of two different nonradioactively labeled DNA standards, ranging in size from 150 bp to 2 kbp and 120 bp to 23 kbp are presented, and discussed. Capillary electrophoresis with direct blotting presents several advantages over the blotting from gels: the separation is faster and requires less manual steps, the resolution is higher, and each DNA fragment is collected into a very concentrated spot on the membrane due to the small surface of the capillary outlet and to a design of the collection device inducing a refocusing of field lines across the hybridization membrane. Therefore, very small amounts of DNA (in the pg range) can be detected. This fraction collection makes further analysis of the sample possible, e.g. by hybridization, thus suppressing one of the major present limitations of the capillary electrophoresis technique for DNA analysis.

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.

DNA: an extensible molecule

The force-displacement response of a single duplex DNA molecule was measured. The force saturates at a plateau around 70 piconewtons, which ends when the DNA has been stretched about 1.7 times its contour length. This behavior reveals a highly cooperative transition to a state here termed S-DNA. Addition of an intercalator suppresses this transition. Molecular modeling of the process also yields a force plateau and suggests a structure for the extended form. These results may shed light on biological processes involving DNA extension and open the route for mechanical studies on individual molecules in a previously unexplored range.

Systematic study of field and concentration effects in capillary electrophoresis of DNA in polymer solutions

A systematic study of the separation of double-stranded DNA in hydroxypropylcellulose (HPC) with a molecular mass of 10(6) was undertaken, using a variety of concentrations (from 0.1 to 1%) and different electric fields (from 6 to 540 V/cm). The data show that at high polymer concentrations ( > or = 0.4%) and low fields, the separation mechanism is similar to that occurring in gels. The results are in good agreement with theoretical models, and in particular with a recently proposed theory for gels with a pore size smaller than the persistence length of DNA. For more dilute solutions and high fields, however, the separation pattern cannot be explained by existing theories. The existence of an original mechanism was confirmed by the direct observation of the conformation of double-stranded DNA molecules in the polymer solution by fluorescence videomicroscopy. Practical conclusions for the capillary electrophoretic separation of duplex DNA are drawn.

DNA separation with field inversion capillary electrophoresis

We have built an automated pulsed field capillary electrophoresis system on the basis of a commercially available device. Using entangled polymer solutions as separating matrix, we demonstrate a considerable improvement of separation of double-stranded DNA in the range of 1-50 kbp under pulsed field conditions. The influence of the main parameters, i.e. pulse frequency and electric field, is studied and the results are compared to existing electrophoresis theories.

Segregation in DNA solutions induced by electric fields

DNA solutions subjected to an electric field exhibit an instability that leads to DNA segregation in aggregates tilted with regard to the field. With the use of epifluorescence videomicroscopy, the evolution of DNA patterns in capillaries as a function of DNA concentration, DNA size, field strength, and field frequency was studied. The field threshold for segregation was decreased when the frequency was lowered or when the DNA molecular weight or concentration was increased. Aggregation is attributed to an electrohydrodynamic instability triggered by the dipole-dipole interaction. This phenomenon explains the failure of earlier attempts to separate large DNA in capillaries.

[Sequencing of DNA by mechanical opening of the double helix: a theoretical evaluation]

We propose and evaluate a model experiment, in which the sequence of a DNA fragment is determined by mechanically opening the double helix in a controlled manner (e.g. pulling on the 3' end of one strand), and measuring the variation of the force exerted by the base pairs on a nanodynamometer (e.g. on a bead in an optical trap or a glass microneedle attached to the 5' end of the other strand). We show that the major limitation of the approach is the longitudinal elasticity of the already sequenced single strand sections, which soften the displacement-force function, and facilitate spontaneous thermal opening of the base pairs.

Gel electrophoresis of end-labeled DNA. II. Dynamics and detrapping in pulsed fields

A theory for field-inversion gel electrophoresis of a flexible polyelectrolyte bearing an uncharged bulky label at one end is described, and the evolution of the mobility with chain length, field strength, friction of the label, and the duration of the forward and reverse pulses is predicted. A new critical size, Ndetrap, is introduced, and its value calculated. It increases roughly linearly with the duration of the reverse pulses. Chains smaller than Ndetrap are detrapped by reverse pulses, and may have a high mobility, whereas chains larger than Ndetrap are not trapped, and have a very small mobility. This leads to an increase of the mobility (as compared with constant field) in a given range of sizes, and to a strong selectivity around Ndetrap. Depending on the parameters, numerous other effects, including a secondary mobility plateau and band inversion, may appear. The corresponding regimes are predicted and discussed. All predictions are qualitatively consistent with available experimental data. We use them to suggest efficient conditions for the development of pulsed-field trapping electrophoresis, a possible tool for improved DNA sequencing. In particular, we recommend using a ramping of pulse times, with a constant ratio of forward to reverse time in the range 3 to 5.

Control of electrohydrodynamic distortion of sample streams in continuous flow electrophoresis using oscillating fields

Continuous flow electrophoresis is a method to separate ions contained in a sample continuously injected into a laminar flow of electrolyte as a cylindrical stream. Usually, the sample is more conductive than the electrolyte, and the charges created at the sample-electrolyte interface lead to electrohydrodynamic distortions which reduce the separation power of this technique. We demonstrate theoretically that the rate of electrohydrodynamic distortion of a cylindrical sample stream can be reduced to zero, by superimposing to the AC field responsible for the separation of a DC field transverse to it and to the flow direction, with an appropriate frequency, and an effective strength equal to that of the DC field. Using a continuous flow electrophoresis chamber, in which such a field is produced using capacitive electrodes, the major predictions of the theory are confirmed. In particular, it is shown that a sample stream more conductive than the carrying electrolyte, which was seriously deformed in the absence of a transverse AC field, recovers its cylindrical shape in presence of the field. The implications of this discovery for the separating power of continuous-flow electrophoresis are discussed.

DNA electrophoresis in polymer solutions: Ogston sieving, reptation and constraint release

The electrophoresis of long polyelectrolytes is considered theoretically, with special attention to duplex DNA. We first discuss quantitative approaches to determine unambiguously the entanglement properties of polymer solutions. Following an idea proposed by Grossman and Soane, we then assume that the "mesh" size of the solution plays the role of a dynamic "pore size" in order to apply theories for gel electrophoresis. In the framework of the Ogston model, we predict that duplex DNA up to 1 kb or more should be separable in dilute (i.e. nonentangled) solutions of high molecular weight polymers. In an entangled solution, and for DNA larger than the pore size, we use a recently developed fluctuation-reptation model to predict the range of sizes in which separation should be possible as a function of electric field E and pore size zeta b. For zeta b larger than the Kuhn length of DNA, we predict a separation up to a size N*scaling as E-1 zeta b-1. For zeta b smaller than the Kuhn length, two different regimes are expected. For small electric fields (typically of the order of 10 V/cm), N*should be proportional to E-1 zeta b-3/2, whereas for high electric fields such as encountered in capillary electrophoresis, we expect that N*is proportional to E-2/5 zeta b-12/5. These predictions are qualitatively different from earlier ones. Finally, we demonstrate that the finite lifetime of the "pores" in an entangled solution (as opposed to a gel) may lead to a new migration mechanism by constraint release, which is not size-dependent.(ABSTRACT TRUNCATED AT 250 WORDS)

Gel electrophoresis of an end-labeled DNA. I. Dynamics and trapping in constant fields

A theory for the gel electrophoresis of a flexible polyelectrolyte, bearing an uncharged bulky label or an uncharged section at one end, is presented. We first consider a gel that is fully permeable to the label: we calculate the degree of stretching of the polyelectrolyte and its mobility as a function of chain size, electric field and label friction. Various regimes are identified, and their "existence domains" are calculated. For increasing friction, we predict a transition from a mobility decreasing with chain size to a mobility increasing with chain size. Secondly, we consider the possibility that the label may get trapped at some locations of the gel, a situation relevant to a method of "trapping electrophoresis" recently proposed by Ulanovsky et al. for DNA sequencing. A molecular model for detrapping by thermally activated "backward reptation" is constructed and solved using the Kramers rate-equation theory. Different closed analytical expressions and approximate scaling laws corresponding to different regimes of stretching and field strengths are predicted. The most striking result is a mobility which exponentially decreases past a critical size Np*, which decreases with increasing field. In the regime relevant to the experiments by Ulanowsky et al., we predict Np* approximately E-2/3. The predictions are in good qualitative agreement with presently available experiments, but further experimental investigations are suggested.

Irreversible trapping of DNA during crossed-field gel electrophoresis

Using an original protocol with a rotating gel electrophoresis apparatus, it is shown that duplex DNA undergoing crossed-field electrophoresis in agarose gets trapped in the gel when the field is increased above a threshold value which decreases with the chain length and depends on the angle between the fields in a non-monotonous manner. This trapping is irreversible, i.e. once trapped at a high field strength, chains are unable to resume their motion when the field is returned to a lower value at which they moved prior to trapping. A model of trapping by "tight knots" is proposed. It predicts a trapping threshold proportional to the inverse square of the electric field, in qualitative agreement with the data. The implications of our results for the separation of large DNA molecules are discussed.

Reptation-breathing theory of pulsed electrophoresis: dynamic regimes, antiresonance and symmetry breakdown effects

We apply the concepts of tube and reptation to the pulsed electrophoresis of DNA, considering both biased reptation and "breathing" modes (internal modes of the chain). Using suitable preaveraging approximations, analytical expressions are derived which relate displacement in crossed field electrophoresis to molecular weight, field strength, field period, pore size of the gel, and the angle between the field. These expressions provide scaling laws for the change of mobility when one (or more) of the parameters is varied as well as "universal" velocity versus molecular weight versus pulse time curves. These results are quantitatively compared with experiments. At some point which depends on field angle, field strength and chain length, however, we predict a failure of this model due to symmetry breakdown and loss of ergodicity. Qualitatively, this should lead to considerable band spreading and/or splitting of the highest DNA bands into two bands migrating sideways from the diagonal. The case of field inversion is also investigated. It is shown that only breathing modes can explain the strong differences in mobility experienced by chains of different length when opposite fields of equal amplitude are applied: the "trapping" of chains in conformations of low mobility is associated with an antiresonance-like coupling between the external field and the internal modes.

Generalized tube model of biased reptation for gel electrophoresis of DNA

A theoretical analysis of the reptational motion of DNA in a gel that includes the effects of molecular fluctuations has been used to explain the main features found in experiments involving periodic inversion of the electric field. The resonance-like decrease of the electrophoretic mobility as a function of pulse duration is related to transient "undershoots" in the orientation of the molecule, in agreement with recent experimental data. These features arise from a delicate interplay of internal and center of mass motion of the molecules under pulsed field conditions, and are important for the separation of DNA molecules in the size range 0.2 to 10 million base pairs.