Mathematical model for DNA separation by capillary electrophoresis in entangled polymer solutions

A mathematical model of DNA separation by capillary electrophoresis in entangled polymer solution is presented. The mechanism is modeled as a DNA molecule moving through transient pores formed in polymer solutions and colliding with blobs of polymer molecules encountered during migration. By taking account of the average retardation time (t(c)) of DNA-blob collision and calculating the total collision number (N(c)), a quantitative mathematical equation was reported, leading to predictions for the DNA mobility as a function of the experimental conditions like the size of DNA, the polymer concentration and the electric field strength. For DNA fragments in frequent size range, the initial experimental data agree well with the model. The DNA shape function (f(E)) was suggested and then discussed by the experimental data. The relationship between f(E) and electric field strength E was empirically estimated. Then, the average retardation time t(c) was obtained as about (2 approximately 3)x10(-6)s in linear polyacrylamide (LPA) and hydroxyethylcellulose (HEC) solution.     

Advances in DNA electrophoresis in polymer solutions.

DNA electrophoresis in gels and solutions of agarose and polyacrylamide was objectively evaluated with regard to separation efficiency at optimal polymer concentrations. In application to DNA fragments, polyacrylamide gels were superior for separating fragments of less than 7800 bp, and agarose gels are the best choice for larger fragments. Agarose solutions are nearly as good as polyacrylamide gels for small DNA (< 300 bp). Agarose solutions have a higher efficiency than polyacrylamide solutions for DNA of less than 1200 bp. Separation efficiency sharply decreases with increasing length of DNA. Retardation in polyacrylamide solutions was found to depend on polymer length in a biphasic fashion. The choice of resolving polymer concentrations depends on the progressive stretching of DNA in proportion to polymer concentration. The rate of that stretching appears higher in polyacrylmide solution than in gels or in liquid or gelled agarose. Application of polymer solutions to capillary electrophoresis raises further problems concerning agarose plugs, DNA interactions with the polymers, operation at low field strength and long durations as well as detection sensitivity.     

Capillary electrophoresis of DNA in entangled polymer solutions.

Electrophoretic separations of DNA restriction fragments were performed in solutions of hydroxyethylcellulose (HEC) using capillary electrophoresis. Rheological studies confirmed that the entanglement threshold (phi*) for the solution is ca. 0.003 g/ml, in good agreement with theoretical predictions. A mesh size an order of magnitude smaller than that found in agarose gels was calculated using polymer-entanglement theory and was confirmed by electrophoretic measurements. Electrophoretic migration was shown to follow the Ogston regime under most conditions. An approach for obtaining smaller mesh sizes is presented.     

Comparison of RNA, single-stranded DNA and double-stranded DNA behavior during capillary electrophoresis in semidilute polymer solutions

We present a study of the separation of RNA, single-stranded DNA (ssDNA) and double-stranded DNA (dsDNA) in semidilute linear hydroxyethylcellulose (HEC) solution. Our results strive to provide a better understanding of the mechanisms of nucleic acid migration during electrophoresis in polymer solutions under native and denaturing conditions. From a study of the dependence of mobility on chain length and applied electric field, we found that RNA and ssDNA show better separation and higher resolution over a larger range of sizes compared to dsDNA. In addition, RNA reptation without orientation extends to longer chain lengths in comparison to ssDNA, possibly as a result of different type of short-lived secondary structure formations. Such a comparative study between nucleic acid capillary electrophoresis helps to optimize RNA separation and provides better understanding of RNA migration mechanisms in semidilute polymer solutions under denaturing conditions.     

Hydrophilic domain structure in polymer exchange membranes: Simulations of NMR spin diffusion experiments to address ability for model discrimination

We detail the development of a flexible simulation program (NMR_DIFFSIM) that solves the nuclear magnetic resonance (NMR) spin diffusion equation for arbitrary polymer architectures. The program was used to explore the proton (¹H) NMR spin diffusion behavior predicted for a range of geometrical models describing polymer exchange membranes. These results were also directly compared with the NMR spin diffusion behavior predicted for more complex domain structures obtained from molecular dynamics (MD) simulations. The numerical implementation and capabilities of NMR_DIFFSIM were demonstrated by evaluating the experimental NMR spin diffusion behavior for the hydrophilic domain structure in sulfonated Diels‐Alder Poly(Phenylene) (SDAPP) polymer membranes. The impact of morphology variations as a function of sulfonation and hydration level on the resulting NMR spin diffusion behavior were determined. These simulations allowed us to critically address the ability of NMR spin diffusion to discriminate between different structural models, and to highlight the extremely high fidelity experimental data required to accomplish this. A direct comparison of experimental double‐quantum‐filtered ¹H NMR spin diffusion in SDAPP membranes to the spin diffusion behavior predicted for MD‐proposed morphologies revealed excellent agreement, providing experimental support for the MD structures at low to moderate hydration levels. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 62–78     

New silanization coating for DNA fragment analysis by capillary electrophoresis

We propose a new coating technique for fused silica capillaries using silanization with trimethylchlorosilane and diethylamine as a mediating agent in DNA separation using capillary electrophoresis. The proposed coating technique is simple and stable at a high pH. Capillaries coated by the new preparation method give excellent reproducibility for DNA fragment analysis with a good relative standard deviation of less than 0.7% for 150 runs and good stability at pH 8.2. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1405–1420, 2002     

Anisotropic plasticity and chain orientation in polymer glasses

The anisotropic mechanical response of oriented polymer glasses is studied through simulations with a coarse-grained model. Systems are first oriented by uniaxial compression or tension along an axis. Then the mechanical response to subsequent deformation along the same axis or along a perpendicular axis is measured. As in experiments, the flow stress and strain hardening modulus are both larger when deformation increases the degree of molecular orientation produced by prestrain, and smaller when deformation reduces the degree of orientation. All stress curves for parallel prestrains collapse when plotted against either the total integrated strain or the degree of molecular orientation. Stress curves for perpendicular prestrains can also be collapsed. The stress depends on the degree of strain or molecular orientation along the final deformation axis and is independent of the degree of orientation in the perpendicular plane. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1473–1482, 2010     

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 10⁶ 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 a high polymer concentrations (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.     

Size exclusive capillary electrophoresis separation of DNA oligonucleotides in small size linear polyacrylamide polymer solution

The mobility of analytes in capillary electrophoresis using polymer gels and solutions is usually described as having an inverse relationship with the molecular size (mobility decreases as molecular size increases). The most commonly used models for predicting such mobility are the Ogston model and the Reptation model. However, in this study a new separation phenomenon was observed in which the mobility of DNA oligonucleotides increased with molecular size in a capillary electrophoresis phase (CEP) coated capillary column. The polymer system used was a 11% linear polyacrylamide (Mr = 1500) solution. The log-transformed number of base pairs (log N) of three double stranded oligonucleotides had an inverse linear relationship (r2 > 0.9981) with their migration time in the capillary column. Such a relationship is similar to that observed with size exclusive chromatography.     

Mannitol influence on the separation of DNA fragments by capillary electrophoresis in entangled polymer solutions

A new kind of sieving matrix is presented in this paper to allow satisfactory separation of DNA fragments in a relatively low viscous solution. When a certain amount of mannitol was added to cellulose solution not concentrated enough to separate PGEM-3Zf(+)/HaeIII standards well, a polymer solution with low viscosity but with very good separation effects was obtained. The separation result of this sieving buffer was comparable with those using highly concentrated cellulose solutions. The sieving ability of solutions with different cellulose concentrations and different amounts of mannitol has been investigated. It was proved that 0.5% was the minimum hydroxypropylmethylcellulose (HPMC) concentration that could be used to separate DNA fragments satisfactorily. HPMC solutions with a concentration of less than 0.5% could not separate the standard DNA fragments even in the presence of mannitol. It was found that 6% was the optimized mannitol concentration because either more or less mannitol will lead a decrease of resolution. The principle of the positive influence of mannitol has also been discussed.     

Analysis of double-stranded DNA by microchip capillary electrophoresis using polymer solutions containing gold nanoparticles

The impact of gold nanoparticles (GNPs) on the microchip electrophoretic separation of double-stranded (ds) DNA using poly(ethylene oxide) (PEO) is described. Coating of the 75-microm separation channel on a poly(methyl methacrylate) (PMMA) plate in sequence with poly(vinyl pyrrolidone), PEO, and 13-nm GNPs is effective to improve reproducibility and resolution. In this study, we have also found that adding 13-nm GNPs to 1.5% PEO is extremely important to achieve high resolution and reproducibility for DNA separation. In terms of the stability of the GNPs, 100 mM glycine-citrate buffer at pH 9.2 is a good buffer system for preparing 1.5% PEO. The separation of DNA markers V and VI ranging in size from 8 to 2176 base pairs has been demonstrated using the three-layer-coated PMMA microdevice filled with 1.5% PEO containing the GNPs. Using these conditions, the analysis of the polymerase chain reaction products of UGT1A7 was complete in 7 min, with the relative standard deviation values of the peak heights and migration times less than 2.3% and 2.0%, respectively. In conjunction with stepwise changes of the concentrations of ethidium bromide (0.5 and 5 microg/ml), this method allows improved resolution and sensitivity for DNA markers V and VI.     

Capillary gel electrophoresis of oligonucleotides using polymer solutions

Summary Capillary gel electrophoresis (CGE) has been recognized as an effective method for the analysis of oligonucleotides. CGE using polymer solutions is especially useful and effective compared with that using crosslinked gels, because of easy change of media. Replacement of media leads to the reproducible separation of analytes. We have investigated CGE analysis of oligonucleotides of less than 20 bases employing various kinds of polymers. Polyacrylamide, dextrin, dextran, pullakin, and poly(ethylene glycol) were used as sieving matrixes at concentrations of 0–30 %. Polydeoxythymidylic acids [p(dT)_11–20] were used as a test sample. These small oligonucleotides were successfully resolved on the basis of their base number by CGE using some of these polymer solutions. In particular, dextran was found to be effective and baseline separation was observed when a 30 % dextran solution was employed. Some validations such as linearity and reproducibility were also established and this method was found to be an adequate quality control method for small oligonucleotides. Finally, CGE using a 30 % dextran solution was successfully applied to impurity profiling of some synthetic oligonucleotides.     

Prediction of DNA separation by capillary electrophoresis with polymer additives

The paper is focused on the powerful prediction ability of the quantitative DNA sieving model in DNA separations by capillary electrophoresis, which was proposed by us previously. First, the DNA resolution can be predicted by the theory. The model predicts that the most difficult and easiest separation will be 184bp/192bp and 234bp/267bp respectively, which is consist with experimental results. Furthermore, the average relative differences of predicted and experimental resolution values (R(S)) for ssDNA 184b/192b or dsDNA 184bp/192bp were all smaller than 2.8% if the diffuse parameter D considered was 8×10(-5) cm(2)/s. Secondly, the optimum polymer concentrations for DNA separation were also calculated by the model, and the results show that polymer concentration should be as high as possible in DNA separation. Thirdly, the sieving ability of polymer will be predicted by the model. Polymer with smaller k, a polymer parameter calculated by the model, is prior to use as DNA sieving media.     

Bead-spring models of entangled polymer melts: Comparison of hard-core and soft-core potentials

Two bead-spring models of flexible chains for generic coarse graining of entangled polymer melts, the excluded volume Kremer–Grest (KG) model and the modified segmental repulsive potential (mSRP) combined with a weakly repulsive potential, are compared. For chains containing an equivalent number of entanglements, we compare the chain characteristics of the KG and mSRP polymer models by determining the ratios of the entanglement lengths , the required total number of particles to capture comparable entanglement phenomena , and the time scaling ratios τ^mSRP/τ^KG. Our findings show that systems using the mSRP polymer model require half the number of particles and relax four times faster compared to the KG polymer model. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Capillary electrophoresis of RNA in dilute and semidilute polymer solutions

We report separations of RNA molecules (281-6583 nucleotides) by capillary electrophoresis in dilute and semidilute solutions of aqueous hydroxyethylcellulose (HEC) ether in varying buffers. RNA mobility and peak band widths are examined under both nondenaturing and also denaturing conditions. From studies of sieving polymer concentration and chain length, it is found that good separations can be obtained in semidilute solutions as well as in dilute solutions. The dependence of RNA mobility on its chain length is consistent with separation by a similar to transient entanglement mechanism in dilute solutions. In semidilute entangled solutions the separation proceeds by segmental motion.     

Self‐assembly of nanorod/nanoparticle mixtures in polymer brushes

The aggregation behavior and phase separation of nanorod (NR)/nanoparticle (NP) nanoinclusions immersed in semiflexible polymer brushes (PBs) are investigated by using molecular dynamics simulations. A variety of phases are formed by varying the size ratio q = σ_r/σ_p, where σ_r and σ_p are the diameters of NR and NPs, respectively, and the attractive interactions ε_M between NR/NP nanoinclusions and PBs. Ordered structures of NRs surrounded by large NPs are observed for the small size ratio q, and a dispersed mixture phase appears for the moderate size ratio q at weak attractive interaction. Meanwhile, the crystallization of NRs occurs at strong attractive interaction for the large size ratio q and a main face‐centered cubic (fcc) structure combined with a small amount of hexagonal‐closed packed (hcp) structure is observed. This investigation can provide some insights into the self‐assembly of complex nanoinclusions and promise a new approach for controlling the self‐assemble behavior of NPs. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 299–309     

Interfacial properties of compressible polymer solutions

A chemomechanical model for the interfacial concentration and density in compressible polymer solutions is formulated using variational principles. The nonlinear model with boundary conditions obtained from phase equilibrium calculations gives the coupled concentration and density profiles. The couplings between chemical and mechanical balances are identified and efficient ways to calculate the interfacial structure is identified. A specific model appropriate to high‐pressure processing of the polyolefins is developed using the modified Sanchez Lacombe equation of state. Bakker's formula for the interfacial tension is adapted to compressible polymer solutions. The structure and tension of a flat interface is characterized using the developed model and material properties of three molecular weight hydrogenated polybutadiene; the main variables of interest were the pressure, polymer molecular weight, and temperature. The relation between the pressure profile across the interface and the interfacial tension is characterized. Scaling power laws for interfacial tension and interfacial thickness as a function of pressure are obtained and contrasted with the corresponding laws observed and predicted for incompressible polymer solutions. It is found that the modified Sanchez Lacombe‐based power law prediction predictions for compressible solutions in terms of pressure quenches are similar to those from those obtained by the Flory‐Huggins incompressible model for temperature quenches. The present results provide the basis for the future study of the kinetics of pressure‐induced phase separation in compressible polymer solutions. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 640–654, 2009     

Kinetics of thermally induced phase separation in ternary polymer solutions. II. Comparison of theory and experiment

Light‐scattering measurements and spinodal decomposition modeling have been used to quantify the kinetics of pore growth in thermally quenched polymer‐solvent–nonsolvent [poly(methyl methacrylate) (PMMA)/1‐methyl‐2‐pyrrolidinone (NMP)/glycerin] solutions. Solutions of fixed composition were quenched to a series of temperatures and light‐scattering measurements and model calculations were performed to determine the temperature dependence of the pore growth rate. Both the experimental results and the model calculations show that the growth rate exhibits a maximum at an intermediate quench temperature that is related to an interplay between the thermodynamic and transport effects that govern pore growth. A similar growth‐rate maximum is also observed when a series of solutions of varying nonsolvent composition are all quenched to the same temperature. The relevance of these experiments to the dynamics of pore growth and the eventual locking‐in of the two‐phase structure that forms during nonsolvent‐induced phase inversion is discussed. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1461–1467, 1999