Salt-Induced Counterion-Mobility Anomaly in Polyelectrolyte Electrophoresis (original) (raw)
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Screening of hydrodynamic interactions for polyelectrolytes in salt solution
We provide numerical evidence that hydrodynamic interactions are screened for charged polymers in salt solution on time scales below the Zimm time. At very short times, a crossover to hydrodynamic behavior is observed. Our conclusions are drawn from extensive coarse-grained computer simulations of polyelectrolytes in explicit solvent and explicit salt, and discussed in terms of analytical arguments based on the Debye-Hückel approximation. PACS numbers: 82.35.Rs, 47.57.jd, 87.15.A-Macromolecules of biological relevance such as DNA are often highly charged polyelectrolytes. Under physiological conditions, these molecules are dissolved in salt solutions with Debye lengths of less than 1 nm. From the point of view of statics, the electrostatic interactions are thus screened: Large DNA strands in physiological buffers have similar static properties than regular self-avoiding chains with short range interactions. The dynamical properties are more complex. For neutral chains, solvent-mediated hydrodynamic interactions influence the mobility and the internal modes of the molecules. The signature of these hydrodynamic interactions is dynamical "Zimm scaling" 1 . For example, the mobility µ and the diffusion constant D of a self-avoiding Zimm chain scale as µ ∼ D ∼ N −ν with the chain length N , where ν = 0.588 is the well-known Flory exponent. In contrast, the same quantities scale as N −1 in a "Rouse" chain, where hydrodynamic interactions are absent or screened.
Importance of Hydrodynamic Shielding for the Dynamic Behavior of Short Polyelectrolyte Chains
Physical Review Letters, 2008
The dynamic behavior of polyelectrolyte chains in the oligomer range is investigated with coarsegrained molecular dynamics simulation and compared to data obtained by two different experimental methods, namely capillary electrophoresis and electrophoresis NMR. We find excellent agreement of experiments and simulations when hydrodynamic interactions are accounted for in the simulations. We show that the electrophoretic mobility exhibits a maximum in the oligomer range and for the first time illustrate that this maximum is due to the hydrodynamical shielding between the chain monomers. Our findings demonstrate convincingly that it is possible to model dynamic behavior of polyelectrolytes using coarse grained models for both, the polyelectrolyte chains and the solvent induced hydrodynamic interactions.
Electrophoresis of DNA Adsorbed to a Cationic Supported Bilayer
Langmuir, 2001
We report fluorescence microscopy studies of the electrophoresis of individual DNA molecules electrostatically adsorbed to a cationic supported lipid bilayer. Obstacles to uniform electrophoretic flow cause the 2-D chains to adopt hooked conformations similar to those previously observed in 3-D electrophoresis experiments. Analysis of the stretch-contraction dynamics allows for an estimate of the obstacle density in the bilayer. Increasing the electric field causes the DNA molecules to become more highly stretched and increases the electrophoretic mobility substantially. A comparison of the Rouse relaxation time of the polymers and the average time between chain-obstacle collisions reveals that a single-obstacle model is insufficient to describe the observed dynamics but the obstacles are not dense enough to use a reptative model. Analysis of the unhooking dynamics reveals an 80% increase in hydrodynamic drag as compared to free chains. Finally, we observe anomalous diffusion of the DNA chains, with a large increase in the diffusion coefficient after the repeated application of high electric fields. Implications of the flow obstacles in the engineering of separation applications are discussed.
Electrophoretic mobility of linear and star-branched DNA in semidilute polymer solutions
Electrophoresis, 2006
Electrophoresis of large linear T2 (162 kbp) and 3-arm star-branched (NArm = 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 μ of the DNA to be determined. LPA solutions of moderate polydispersity index (PI ∼ 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<ce), 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, μ 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>ce), the conformation of migrating linear and star-shaped DNA manifest only subtle changes from their unentangled solution features, but μ for the stars decreases strongly with increasing LPA concentration and molecular weight, while μ 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.
The Journal of Chemical Physics, 1998
The dynamics of a 20 base pair oligonucleotide is studied by dynamic light scattering-photon correlation spectroscopy and depolarized Fabry-Perot interferometry. The 20 base pair oligonucleotide is a well-defined, albeit short, rigid rod molecule that serves as a model for polyelectrolyte solution dynamics. The effects of added salt on the solution rotational and translational dynamics are examined in detail as functions of the 20-mer concentration. Coupled mode theory together with counterion condensation theory gives good predictions for the effects of salt on the translational diffusion of the 20-mer at the relatively low oligonucleotide concentrations studied. Comparison of the experimental results with these theories shows that the effective charge density of the polyion in solution is approximately equal to the reciprocal of the product of the Bjerrum length and the counterion charge, eff Х1/N B. Calculation shows that the numerical solution of the coupled mode theory matrix gives a better fit of our measured polyion diffusion coefficients than the approximate equation derived by Lin, Lee, and Schurr. Simple approximations for the effective rod length, L eff ϭLϩ Ϫ1 , and effective rod diameter, d eff ϭdϩ Ϫ1 , are used to model the thermodynamic-hydrodynamic interactions for charged rodlike molecules and to make predictions for the diffusion second virial coefficient as a function of added salt concentration. This alternative to the coupled mode theory also gives good agreement with experiment. The rotational diffusion constants of the oligonucleotide measured by depolarized Fabry-Perot interferometry show a slowing down of the rotation at low added salt concentrations as the oligonucleotide concentration is increased.
Electrophoresis without charge: Mobility of nanometer-size solutes in water
arXiv: Soft Condensed Matter, 2015
We investigate the mobility of nanometer-size solutes in water induced by a uniform external electric field. General arguments are presented to show that a closed surface cutting a volume from a polar liquid will carry an effective non-zero surface charge density when preferential orientation of dipoles exists in the interface. This effective charge will experience a non-vanishing drag in an external electric field even in the absence of free charge carriers. Numerical simulations of model solutes are used to estimate the magnitude of the surface charge density. We find it to be comparable to the values typically reported from the mobility measurements. Hydrated ions can potentially carry a significant excess of the effective charge due to over-polarization of the interface. As a result, the electrokinetic charge can significantly deviate from the physical charge of free charge carriers. We propose to test the model by manipulating the polarizability of hydrated semiconductor nanopa...
Conformation dependence of DNA electrophoretic mobility in a converging channel
ELECTROPHORESIS, 2010
The electrophoresis of l-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 shishkebabs 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 shishkebab 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.
A Commentary on the Screened-Oseen, Counterion-Condensation Formalism of Polyion Electrophoresis
Biophysical Journal, 2000
The use of linear theory, in particular, counterion condensation (CC) theory, in describing electrophoresis of polyelectrolyte chains, is criticized on several grounds. First, there are problems with CC theory in describing the equilibrium distribution of ions around polyelectrolytes. Second, CC theory is used to treat ion relaxation in a linear theory with respect to the polyion charge despite the fact that ion relaxation arises as a consequence of nonlinear charge effects. This nonlinearity has been well established by several investigators over the last 70 years for spherical, cylindrical, and arbitrarily shaped model polyions. Third, current use of CC theory ignores the electrophoretic hindrance as well as the ion relaxation for condensed counterions and only includes such interactions for uncondensed counterions. Because most of the condensed counterions lie outside the shear surface of the polyion (in the example of DNA), the assumption of ion condensation is artificial and unphysical. Fourth, the singular solution, based on a screened Oseen tensor, currently used in the above mentioned theories is simply wrong and fails to account for the incompressibility of the solvent. The actual singular solution, which has long been available, is discussed. In conclusion, it is pointed out that numerical alternatives based on classic electrophoresis theory (
Journal of Colloid and Interface Science, 2005
A boundary element (BE) procedure is developed to numerically calculate the electrophoretic mobility of highly charged, rigid model macroions in the thin double layer regime based on the continuum primitive model. The procedure is based on that of O'Brien (R.W. O'Brien, J. Colloid Interface Sci. 92 (1983) 204). The advantage of the present procedure over existing BE methodologies that are applicable to rigid model macroions in general (S. Allison, Macromolecules 29 (1996) 7391) is that computationally time consuming integrations over a large number of volume elements that surround the model particle are completely avoided. The procedure is tested by comparing the mobilities derived from it with independent theory of the mobility of spheres of radius a in a salt solution with Debye-Hückel screening parameter, κ. The procedure is shown to yield accurate mobilities provided κa exceeds approximately 50. The methodology is most relevant to model macroions of mean linear dimension, L, with 1000 > κL > 100 and reduced absolute zeta potential (q|ζ |/k B T) greater than 1.0. The procedure is then applied to the compact form of high molecular weight, duplex DNA that is formed in the presence of the trivalent counterion, spermidine, under low salt conditions. For T4 DNA (166,000 base pairs), the compact form is modeled as a sphere (diameter = 600 nm) and as a toroid (largest linear dimension = 600 nm). In order to reconcile experimental and model mobilities, approximately 95% of the DNA phosphates must be neutralized by bound counterions. This interpretation, based on electrokinetics, is consistent with independent studies.
Polyelectrolytes in Salt Solutions: Molecular Dynamics Simulations
We present results of the molecular dynamics simulations of salt solutions of polyelectrolyte chains with number of monomers N = 300. Polyelectrolyte solutions are modeled as an ensemble of beadÀspring chains of charged Lennard-Jones particles with explicit counterions and salt ions. Our simulations show that in dilute and semidilute polyelectrolyte solutions the electrostatic induced chain persistence length scales with the solution ionic strength as I À1/2 . This dependence of the chain persistence length is due to counterion condensation on the polymer backbone. In dilute polyelectrolyte solutions the chain size decreases with increasing the salt concentration as R µ I À1/5 . This is in agreement with the scaling of the chain persistence length on the solution ionic strength, l p µ I À1/2 . In semidilute solution regime at low salt concentrations the chain size decreases with increasing polymer concentration, R µ c p À1/4 , while at high salt concentrations we observed a weaker dependence of the chain size on the solution ionic strength, R µ I À1/8 . Our simulations also confirmed that the peak position in the polymer scattering function scales with the polymer concentration in dilute polyelectrolyte solutions as c p 1/3 . In semidilute polyelectrolyte solutions at low salt concentrations the location of the peak in the scattering function shifts toward the large values of q* µ c p 1/2 while at high salt concentrations the peak location depends on the solution ionic strength as I À1/4 . Analysis of the simulation data throughout the studied salt and polymer concentration ranges shows that there exist general scaling relations between multiple quantities X(I) in salt solutions and corresponding quantities X(I 0 ) in salt-free solutions, X(I) = X(I 0 )(I/I 0 ) β . The exponent β = À1/2 for chain persistence length l p , β = 1/4 for solution correlation length ξ, and β = À1/5 and β = À1/8 for chain size R in dilute and semidilute solution regimes, respectively.