Random Coil Polymers Research Articles

Isolation and physical characterization of an exocellular polysaccharide

The physical properties of a polysaccharide produced by the lactic acid bacterium Lactococcus lactis subsp. cremoris strain NIZO B40 were investigated. Separation of the polysaccharide from most low molar mass compounds in the culture broth was performed by filtration processes. Residual proteins and peptides were removed by washing with a mixture of formic acid, ethanol, and water. Gel permeation chromatography (GPC) was used to size fractionate the polysaccharide. Fractions were analyzed by multiangle static light scattering in aqueous 0.10M NaNO3 solutions from which a number- (Mn) and weight-averaged (Mw) molar mass of (1.47 ± 0.06) · 103 and (1.62 ± 0.07) · 103 kg/mol, respectively, were calculated so that Mw/Mn ≈ 1.13. The number-averaged radius of gyration was found to be 86 ± 2 nm. From dynamic light scattering an apparent z-averaged diffusion coefficient was obtained. Upon correcting for the contributions from intramolecular modes by extrapolating to zero wave vector a hydrodynamic radius of 86 ± 4 nm was calculated. Theoretical models for random coil polymers show that this z-averaged hydrodynamic radius is consistent with the z-averaged radius of gyration, 97 ± 3 nm, as found with GPC. © 1999 John Wiley & Sons, Inc. Biopoly 49: 1–9, 1999

Isolation and physical characterization of an exocellular polysaccharide

The physical properties of a polysaccharide produced by the lactic acid bacterium Lactococcus lactis subsp. cremoris strain NIZO B40 were investigated. Separation of the polysaccharide from most low molar mass compounds in the culture broth was performed by filtration processes. Residual proteins and peptides were removed by washing with a mixture of formic acid, ethanol, and water. Gel permeation chromatography (GPC) was used to size fractionate the polysaccharide. Fractions were analyzed by multiangle static light scattering in aqueous 0.10 M NaNO3 solutions from which a number- (Mn) and weight-averaged (Mw) molar mass of (1.47 +/- 0.06).10(3) and (1.62 +/- 0.07).10(3) kg/mol, respectively, were calculated so that Mw/Mn approximately 1.13. The number-averaged radius of gyration was found to be 86 +/- 2 nm. From dynamic light scattering an apparent z-averaged diffusion coefficient was obtained. Upon correcting for the contributions from intramolecular modes by extrapolating to zero wave vector a hydrodynamic radius of 86 +/- 4 nm was calculated. Theoretical models for random coil polymers show that this z-averaged hydrodynamic radius is consistent with the z-averaged radius of gyration, 97 +/- 3 nm, as found with GPC.

Segmental motion of entangled random coil polymers studied by pulsed gradient spin echo nuclear magnetic resonance

Pulsed gradient spin echo nuclear magnetic resonance (NMR) is used to investigate polymer mean-squared segmental displacements in semidilute solutions of high molar mass polystyrene in deuterio-toluene. Nine molar masses from 1 to 20 million daltons are studied at a fixed concentration of 5% w/v, and a range of concentrations from 5% to 20% at fixed molar mass of 3 million daltons. The distance and time scales accessed are 20 to 1000 nm and 10 to 3000 ms, respectively. Evidence for intrachain spin diffusion is found and its effect corrected for. The time dependence of mean-squared segmental displacements is fitted to the predictions of the Doi–Edwards model and tube disengagement times and tube diameters obtained.

Surface Charge Dependence of Polyelectrolyte-Induced Domain Size and Composition in Lipid Bilayer Membranes

2H NMR spectroscopy was used to investigate the response of specifically choline-deuterated 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) to changes in surface electrostatic charge in lipid bilayer membranes consisting of mixtures of POPC with the anionic lipid 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol (POPG), plus the cationic polyelectrolyte poly(vinylbenzyltrimethylammonium chloride) (PVTA). The 2H NMR spectra consisted of two overlapping Pake powder patterns, indicating the coexistence of two lipid domains with only slow exchange of lipids between the two. There was no evidence of any nonbilayer lipid arrangements. Analysis of the quadrupolar splittings of the two 2H NMR spectral components for POPC-α-d2 versus POPC-β-d2 demonstrated that the two domains differ with respect to their overall surface charge environments and that the PVTA-bound domain was enriched with respect to anionic lipids while the PVTA-free domain was depleted. When the initial bilayer POPG content was varied, the number of POPG molecules associated with each bound PVTA molecule remained constant at a 1:1 POPG anion: PVTA cation equivalents ratio. However, the number of POPC molecules associated with each bound PVTA molecule increased with decreasing initial POPG content. Thus, the surface area occupied per PVTA domain expanded or contracted as the available oppositely charged POPG decreased or increased. This indicates that the PVTA/POPG complex is behaving at the surface like a two-dimensional random-coil polymer undergoing swelling by a solvent, POPC. Within the PVTA-bound domain, the 2H NMR quadrupolar splittings suggest that the PVTA/POPG complex penetrates more deeply into the lipid bilayer than does POPG alone, as might be expected for a neutralized salt pair.

Pluronic copolymer liquid crystals: unique, replaceable media for capillary gel electrophoresis

Liquid crystalline solutions of Pluronic copolymers are versatile alternatives to solutions of entangled, random coil polymers as replaceable media for capillary gel electrophoresis (CGE). Pluronic copolymers are tri-block polymers of poly(ethylene oxide) [(EO) x ] and poly(propylene oxide) [(PO) y ] with the general formula (EO) x (PO) y (EO) x . Large micelles form in aqueous solutions in which central, hydrophobic cores of (PO) y segments are surrounded by “brushes” of hydrated (EO) x tails. Solutions of Pluronic F127 (BASF Performance Chemicals) in a concentration range of about 18–30% are liquids at refrigerator temperatures (≤5°C) and are easily introduced into capillaries. A self-supporting, gel-like liquid crystalline phase is formed as the temperature is raised to ≥20°C. This liquid crystalline phase consists of spherical micelles with diameters of 17–18 nm which pack with local cubic symmetry. CGE in Pluronic F127 liquid crystals separates species within several chemical classes as varied as nucleoside monophosphates and organic dyes, oligonucleotides of 4–60 nucleotides, DNA fragments of 50–3000 base pairs (bp), and supercoiled plasmid DNAs of 2000–10 000 bp. Mechanisms of molecular sieving in polymer liquid crystals must differ in fundamental ways from separations in random polymer gels because molecules move around uncrosslinked obstacles that are larger than the smallest dimensions of typical analytes. Molecular sieving in Pluronic liquid crystals is envisioned to occur as molecules squeeze between hydrated (EO) x strands of micelle brushes, or through brushtips and interstitial spaces between micelles. Small molecules such as nucleotides appear to separate by a different mechanism involving partitioning between hydrophilic and hydrophobic environments. This process is termed “hydrophobic interaction electrophoresis”. The unique structures of Pluronic copolymers and their liquid crystalline phases provide new challenges and opportunities in separations science.

Optimizing capillary gel electrophoretic separations of oligonucleotides in liquid crystalline Pluronic F127

Micellar, liquid crystalline solutions of poly(ethylene oxide) (EO)–poly(propylene oxide) (PO)–poly(ethylene oxide) copolymers are alternatives to solutions of random coil polymers as replaceable media for capillary `gel' electrophoresis. Excellent capillary gel electrophoresis separations of oligonucleotides were obtained in the liquid crystalline phase of 18–30% solutions of Pluronic F127 (approximate molecular formula [EO] 106[PO] 70[EO] 106). These solutions are isotropic and flow freely into capillaries at reduced temperatures (0–5°C), but rapidly transform into a gel-like, cubic liquid crystalline phase of spherical micelles at room temperature and above. Separations on Pluronic gels can be tuned because polymer chain packing in the liquid crystalline phase is sensitive to polymer concentration and temperature. Optimum resolution of short oligonucleotides of sizes typically used for DNA sequencing primers or oligonucleotide therapies (≤40 nucleotides) was obtained by capillary gel electrophoresis in 25% Pluronic F127 at 30°C with an applied voltage of 500 V/cm. Decreasing the Pluronic concentration to 20% and increasing the temperature to 50°C substantially reduced analysis time with a modest decrease in resolution. Individual nucleotides in dT 12–18 and dT 19–24 standards were separated in 8 min with baseline resolution. The complex dependencies of resolution and peak shape on oligonucleotide size, Pluronic concentration, temperature, and applied voltage are described.

Chain stiffness of liquid crystalline polyesters. 1. Characteristic ratio and persistence length

Calculations of the characteristic ratios (C∞) and persistence lengths (Lp) of novel liquid crystalline polyesters (LCPEs) containing the dihydroxy-α-methylstilbene (DHαMS) fragment were performed. The RIS Metropolis Monte Carlo (RMMC) method was used. RMMC enables the direct estimation of several key conformational properties of polymer chains from atomistic simulations. Calculations were also performed for a single-chain analogue of VECTRA ™ A900 (a commercial LCPE). The results, including the similar calculated exponential decrease of C∞ and Lp with increasing absolute temperature, were very similar. The DHαMS isophthalate repeat unit, which is present at 10% by mole in the DHαMS-based LCPE, introduces ‘kinks’ and reduces the calculated C∞ and Lp to the same level as for VECTRA ™ A900. If it is replaced by DHαMS terephthalate, C∞ and Lp increase to almost 20% greater than those of VECTRA™ A900 which does not contain any moieties with a propensity to introduce kinks. Finally, DHαMS polycarbonate was calculated to be much stiffer than an ordinary random coil polymer, but much more flexible than any of the LCPEs which were modelled.

Rheooptical Studies of Polydiacetylene Solutions

This work describes a rheooptical experiment with the ability to distinguish between orientation and deformation of polymers while quantifying the degree of deformation in shear using a polymeric chromophore. The chromophore used is poly(4-butoxycarbonylmethylurethane)diacetylene, referred to as 4BCMU, which is known to display varying optical properties that are attributed to conformational changes in the polymer backbone. The orientation may be measured by changes in the extinction coefficient both perpendicular and parallel to the shear field. The results obtained for dilute solutions of 4BCMU under shear are explained by an ellipsoidal random coil polymer in the quiescent state orientating in the shear field. In apparent contradiction to earlier theoretical models, no deformation of the polymer is observed within the range of shear fields used in this work. Extant theories have attributed the rheological behavior of polymer solutions to deformation of the spherical random polymer coils under shear.

Rotational and Translational Diffusion of a Rodlike Virus in Random Coil Polymer Solutions

Depolarized dynamic light scattering was used to measure the translational and rotational diffusion of tobacco mosaic virus, TMV, in aqueous solutions of dextran (M ∼505 000). TMV is an electrically charged, nucleoprotein assembly with the shape of a stiff, rigid rod. Dextran is an uncharged, flexible carbohydrate polymer. The TMV was held at a fixed, dilute concentration (0.5 mg/mL), while the concentration of dextran spanned both dilute and semidilute regimes (0−14.5% by weight). There was no evidence of phase separation or strong aggregation of the TMV particles in the presence of the dextran. The TMV particles dominated the depolarized scattering at all dextran concentrations. The angular variation of the decay rates of the autocorrelation functions always followed the form expected for symmetric top molecules in the absence of translational−rotational coupling. Nevertheless, translational and rotational motions are almost surely coupled in most dextran-containing solutions. The apparent translational...

Elasticity and unfolding of single molecules of the giant muscle protein titin.

The giant muscle protein titin, also called connectin, is responsible for the elasticity of relaxed striated muscle, as well as acting as the molecular scaffold for thick-filament formation. The titin molecule consists largely of tandem domains of the immunoglobulin and fibronectin-III types, together with specialized binding regions and a putative elastic region, the PEVK domain. We have done mechanical experiments on single molecules of titin to determine their visco-elastic properties, using an optical-tweezers technique. On a fast (0.1s) timescale titin is elastic and force-extension data can be fitted with standard random-coil polymer models, showing that there are two main sources of elasticity: one deriving from the entropy of straightening the molecule; the other consistent with extension of the polypeptide chain in the PEVK region. On a slower timescale and above a certain force threshold, the molecule displays stress-relaxation, which occurs in rapid steps of a few piconewtons, corresponding to yielding of internal structures by about 20 nm. This stress-relaxation probably derives from unfolding of immunoglobulin and fibronectin domains.

Derivation and testing of pair potentials for protein folding. When is the quasichemical approximation correct?

Many existing derivations of knowledge-based statistical pair potentials invoke the quasichemical approximation to estimate the expected side-chain contact frequency if there were no amino acid pair-specific interactions. At first glance, the quasichemical approximation that treats the residues in a protein as being disconnected and expresses the side-chain contact probability as being proportional to the product of the mole fractions of the pair of residues would appear to be rather severe. To investigate the validity of this approximation, we introduce two new reference states in which no specific pair interactions between amino acids are allowed, but in which the connectivity of the protein chain is retained. The first estimates the expected number of side-chain contracts by treating the protein as a Gaussian random coil polymer. The second, more realistic reference state includes the effects of chain connectivity, secondary structure, and chain compactness by estimating the expected side-chain contrast probability by placing the sequence of interest in each member of a library of structures of comparable compactness to the native conformation. The side-chain contact maps are not allowed to readjust to the sequence of interest, i.e., the side chains cannot repack. This situation would hold rigorously if all amino acids were the same size. Both reference states effectively permit the factorization of the side-chain contact probability into sequence-dependent and structure-dependent terms. Then, because the sequence distribution of amino acids in proteins is random, the quasichemical approximation to each of these reference states is shown to be excellent. Thus, the range of validity of the quasichemical approximation is determined by the magnitude of the side-chain repacking term, which is, at present, unknown. Finally, the performance of these two sets of pair interaction potentials as well as side-chain contact fraction-based interaction scales is assessed by inverse folding tests both without and with allowing for gaps.

Rheological properties of a seed galactomannan from Cassia siamea Lamk

The rheological properties of a natural polysaccharide isolated from seed endosperms of Cassia siamea Lamk. have been studied for a wide range of concentrations from 2 × 10 −4 to 5 × 10 −2 g/ml. Results showed that the seed gum is a typical galactomannan having a mannose:galactose ratio of 2.55; mol. wt 8.4 × 10 5, and an intrinsic viscosity of 1166 ml/g. Viscosity observations regarding dependence of flow curves versus shear rate, viscoelastic and critical shear rate behaviour clearly reveal the characteristics of a random coil polymer. The value of the critical concentration Cc * = 2.2/[η] is similar to the values obtained for some other galactomannans and polysaccharides although it is comparatively higher than the value obtained for more rigid polysaccharides. The slope of the log—log plot of specific viscosity versus C at zero shear rate is 4.34 in the concentrated region. This large dependence of the viscosity on the coil overlap parameter is lower than that found for guar with higher mannose proportion. The rheological behaviour of the galactomannan at concentrations higher than 15 g/l is that of a weak gel-like (pseudo network).

Conformation and properties of amylose in dilute solution

The conformation of amylose in aqueous solvents with or without salt and in dimethyl sulfoxide is discussed by summarizing typical experimental data for conformation-dependent properties such as the intrinsic viscosity and the radius of gyration. The major conclusion drawn is that regardless of the kind of solvent, the global conformation of the polysaccharide is a random coil having a characteristic ratio of ~5 at infinite molecular weight. Elaborate analysis of intrinsic viscosity data in terms of the helical wormlike chain model shows that, though the polysaccharide chain in dimethyl sulfoxide is as flexible as ordinary random coil polymers, it has some helical nature locally, as predicted by conformational calculations.

Use of factorial experimental design in static and dynamic light scattering characterization of water‐soluble polymers

AbstractWhen characterizing solutions of random coil polymers by static light scattering (SLS) or dynamic light scattering (DLS), linear regression is used to fit experimental data to theoretical relationships. These relationships are expressed as polynomial equations, which contain two independent variables—sample concentration and scattering angle—and a response or dependent variable that is related to radiation intensities (SLS) or intensity fluctuations (DLS). The coefficients of the terms in the polynomial are used to estimate parameters such as molecular weight and polymer coil radius of gyration. One major problem during data analysis involves deciding which polynomial model is appropriate for use with the data that inherently contains a high level of random noise that is produced by the presence of dust in the solutions. Dust is an especially troublesome problem when dealing with large polymers in aqueous solutions. Polynomial models having more terms than justified are unacceptable because the coefficients of these models are excessively corrupted by the noise. Thus, conclusions from unjustified models can be erroneous. This article discusses use of a factorial experimental design technique that obtains an acceptable model for fitting light scattering data containing high levels of random noise. © 1995 John Wiley & Sons, Inc.

Synthesis and properties of diarylsiloxane and (aryl/methyl)siloxane polymers: 2. Solution and rheological properties

Polydiarylsiloxanes and polydialkylsiloxanes, with alkyl groups larger than methyl, have liquid-crystalline states, presumably as the result of a chain-rigidifying effect from steric interactions of the bulky aryl or alkyl groups along the chain. In the first paper of this series, we reported on the thermal behaviour of a number of diarylsiloxane polymers with phenyl and/or p-tolyl substituents, all of which showed liquid-crystalline behaviour at high temperatures. The solution properties of several of the ‘mixed’ poly(phenyl p- tolyl)siloxane polymers have now been investigated in order to characterize their chain stiffness properties and to relate these to the tendency to form a liquid-crystalline state in bulk. The ‘mixed’ poly(phenyl p- tolyl)siloxanes were chosen for investigation since they have a major advantage in experimental convenience over the ‘unmixed parent’ polymers, polydiphenylsiloxane and polydi( p-tolyl)siloxane. The former are soluble at room temperature in common solvents, whereas the latter polymers are only soluble at temperatures above 150°C. The various diarylsiloxane polymers were prepared by anionic polymerization of the cyclic trimers, and the preservation of the triad sequences (absence of ‘scrambling’) was confirmed by 29Si n.m.r. Values of the Mark-Houwink-Sakurada exponent, a, for three different types of poly(phenyl p- tolyl)siloxanes are essentially equal, at ∼0.83. This value of the exponent is below the value expected for a rigid chain ( a>1.0) but is above the maximum value expected for a flexible random-coil polymer in a good solvent ( a⩽0.8). The shear viscosity of solutions of the mixed poly(phenyl p- tolyl)siloxane polymers increases monotonically with increasing polymer concentration up to 60 wt%, and does not show an abrupt drop in viscosity above a critical concentration, as is often observed with rigid-rod polymers. This observation, together with the value of the Mark-Houwink-Sakurada exponent, a<1, indicates that these polymers do not behave in solution as rigid-rod polymers, but most likely as worm-like chains with a relatively large persistence length.

Static and dynamic light scattering of a random coil polymer in rodlike polymer solution

We have studied ternary solutions of rodlike and random coil polymers in a common solvent. In these solutions, the rods scatter weakly, and almost all scattering comes from the coil component. From light scattering measurements, we gained information about the thermodynamic and hydrodynamic properties of the coil in rodlike polymer solutions.

Hydrodynamic chromatography of polymers in packed columns

Hydrodynamic chromatography (HDC) of linear random coil polymers in columns packed with 1.5-μm non-porous particles was investigated. For polymers with high molecular masses (10 4-10 7), the resolution appears to be almost independent of the eluent velocity. This allows for high-speed polymer separations with high efficiency. A model for the migration rate of polymers, based on the assumption that interstitial channels in a packed column can be represented by a bundle of capillary tubes, is compared with experimental elution data. The influence of polymer size and type, solvent goodness and mobile phase velocity on elution in HDC was investigated. Elution behaviour in packed columns appears to obey basically the simple migration theories developed for open tubes. The relative peak positions in the HDC trace depend slightly on the eluent velocity.

Chain and sphere diffusion in polyisobutylene-trichloromethane: a reanalysis

Previously reported (Brown and Zhou) experimental studies of diffusion in polyisobutylene (PIB)-CHCl 3 are reconsidered, comparing diffusion coefficients D p and D ch of silica spheres and random-coil polymers in PIB-CHCl 3 solutions. In solutions of low molecular mass matrix polymers, D p /D ch is virtually independent of matrix concentration c. In solutions of high molecular weight polymers, with increasing c D ch falls far more rapidly than D p . These results are consistent with the hydrodynamic scaling model but are inconsistent with models that grant to polymer chains an additional diffusive mode inaccessible to rigid spheres

Transport and separation of organic macromolecules in ultrafiltration processes

The membrane transport and separation characteristics of natural humic macromolecules and a model polyelectrolyte, poly(styrene sulfonate), in ultrafiltration systems employing hydrophilic, neutral, cellulosic-type membranes were studied. The application of a permeation model based on membrane flux equations was systematically validated for charged, random-coil polymers. It was possible to characterize transport behavior of various solute/membrane combinations by a single membrane permeation factor, which was found to depend strongly on solution ionic strength, but to be relatively independent of the ultrafiltration operating mode

Study of solution properties of galactomannan from the seeds of Mimosa scabrella

The rheological properties of the galactomannan from the seeds of a member of the Leguminosae have been studied. The sample used had a mannose/galactose ratio close to 1 and an intrinsic viscosity of 900 ml/g. The viscosity results are characteristic of a random coil polymer with a critical concentration c ∗ = 2·6/[η] which is similar to the values found for polystyrene and polystyrenesulphonate, but higher than the value obtained for more rigid polysaccharides. The slope of the logarithmic plot of the specific viscosity measured at zero shear rate against c[ η] in the semi-dilute regime was 4·2, a value in agreement with the theoretical predictions for linear polymers interacting by purely topological entanglements. The viscoelastic behaviour was lower than that found for solutions of other galactomannans and this and the less severe dependence of the viscosity on the coil overlap parameter is probably due to lower interactions because of the high galactose content.