Intrinsic Persistence Length Research Articles

Torsional Mechanics of Circular DNA.

Circular DNA found in the cell is actively regulated to an underwound state, with their superhelical density close to σ ∼ - 0.06. While this underwound state is essential to life, how it impacts the torsional mechanical properties of DNA is not fully understood. In this work, we performed simulations to understand the torsional mechanics of circular DNA and validated our results with single-molecule measurements and analytical theory. We found that the torque generated at σ ∼ - 0.06 is near but slightly below that required to melt DNA, significantly decreasing the energy barrier for proteins that interact with melted DNA. Furthermore, supercoiled circular DNA experiences force (tension) and torque that are equally distributed through the DNA contour. We have also extended a previous analytical framework to show how the plectonemic twist persistence length depends on the intrinsic bending persistence length and twist persistence length. Our work establishes a framework for understanding DNA supercoiling and torsional dynamics of circular DNA.

Dimension and Flexibility of Polystyrenesulfonate Chains in Methanol-Water.

The influence of the relative permittivity of the solvent medium on the single-chain dimension and flexibility of sodium polystyrenesulfonate chains has been investigated in mixed solvent media of methanol and water using viscosity experiments. Particular attention has been paid to explore the effect of the added low-molar-mass electrolyte. The root-mean-square (rms) radii of gyration of the chains in the unperturbed state have been calculated by applying the Flory model, while the intrinsic persistence lengths by the Benoit-Doty equation on the basis of the Kratky-Porod worm-like chain model. Estimation of the expansion factors for the rms radius of gyration, and the electrostatic persistence length helps evaluate the rms radii of gyration and the total persistence length of polystyrenesulfonate chains in the presence of varying amount of the supporting electrolyte. The polyion chains are highly extended at low ionic strengths but exhibit coil-like behavior with small persistence lengths when an excess of the supporting electrolyte is added in all the methanol-water mixtures investigated. Specifically, in the investigated solvent media, the polystyrenesulfonate chains have been found to shrink by ∼63-65% in the θ-state from their expanded conformation in the presence of 0.0001 mol L-1 NaCl. The chain dimensions pass through a maximum as the medium becomes richer in methanol, which could be explained by the formation and breakup of internal rings involving the polyion chain and water and/or methanol molecules. The intrinsic persistence length of sodium polystyrenesulfonate in a methanol-water mixture containing 0.1 mole fraction of methanol is ca. 1.3 times that in a medium with 0.3 mole fraction of methanol, indicating that flexibility of the polyion depends appreciably on the relative permittivity of the medium.

The origin of different bending stiffness between double-stranded RNA and DNA revealed by magnetic tweezers and simulations.

The subtle differences in the chemical structures of double-stranded (ds) RNA and DNA lead to significant variations in their biological roles and medical implications, largely due to their distinct biophysical properties, such as bending stiffness. Although it is well known that A-form dsRNA is stiffer than B-form dsDNA under physiological salt conditions, the underlying cause of this difference remains unclear. In this study, we employ high-precision magnetic-tweezer experiments along with molecular dynamics simulations and reveal that the relative bending stiffness between dsRNA and dsDNA is primarily determined by the structure- and salt-concentration-dependent ion distribution around their helical structures. At near-physiological salt conditions, dsRNA shows a sparser ion distribution surrounding its phosphate groups compared to dsDNA, causing its greater stiffness. However, at very high monovalent salt concentrations, phosphate groups in both dsRNA and dsDNA become fully neutralized by excess ions, resulting in a similar intrinsic bending persistence length of approximately 39 nm. This similarity in intrinsic bending stiffness of dsRNA and dsDNA is coupled to the analogous fluctuations in their total groove widths and further coupled to the similar fluctuation of base-pair inclination, despite their distinct A-form and B-form helical structures.

Polysaccharide-based polyampholyte complex formation: Investigating the role of intra-chain interactions

The difference in inter-chain and intra-chain electrostatic attraction was investigated in polyelectrolyte and polyampholyte electrostatic complex formation. Three polymers with similar backbone molecular structures including chitosan (Ch) polycation, carboxymethyl cellulose (CMCe) polyanion, and carboxymethyl chitosan (CMCh) polyampholyte were used for this purpose. The turbidimetric, water content, and rheological measurements for polyampholyte self-complex showed more dependence on the ionic strength rather than the polyelectrolyte one. The degree of dissociation (α), dissociation constant (pKa), and intrinsic persistence length were calculated by applying the Katchalsky-Lifson model to potentiometric data. We studied the gyration radii as a function of Debye length and observed the polyampholyte chain contractions due to the intra-chain electrostatic attractions, which minimize the entropic gain of the inter-chain complex formation. This is in accordance with the decrease in pKa by αc for CMCh which is the opposite of that for the Ch and CMCe samples. We also found that the polyampholyte has less intrinsic and electrostatic persistence length compared with both polyanion and polycation with similar chain structures indicating the impact of the inter-chain electrostatic interaction on the complex properties. This study deepens our insight about the behavior of CMCh and the nature of difference between CMCh and Ch/CMCe electrostatic complexes.

Insights into Extended Structures and Their Driving Force: Influence of Salt on Polyelectrolyte/Surfactant Mixtures at the Air/Water Interface.

This paper addresses the effect of polyelectrolyte stiffness on the surface structure of polyelectrolyte (P)/surfactant (S) mixtures. Therefore, two different anionic Ps with different intrinsic persistence length lP are studied while varying the salt concentration (0-10-2 M). Either monosulfonated polyphenylene sulfone (sPSO2-220, lP ∼20 nm) or sodium poly(styrenesulfonate) (PSS, lP ∼1 nm) is mixed with the cationic surfactant tetradecyltrimethylammonium bromide (C14TAB) well below its critical micelle concentration and studied with tensiometry and neutron reflectivity experiments. We kept the S concentration (10-4 M) constant, while we varied the P concentration (10-5-10-3 M of the monomer, denoted as monoM). P and S adsorb at the air/water interface for all studied mixtures. Around the bulk stoichiometric mixing point (BSMP), PSS/C14TAB mixtures lose their surface activity, whereas sPSO2-220/C14TAB mixtures form extended structures perpendicular to the surface (meaning a layer of S with attached P and additional layers of P and S underneath instead of only a monolayer of S with P). Considering the different P monomer structures as well as the impact of salt, we identified the driving force for the formation of these extended structures: compensation of all interfacial charges (P/S ratio ∼1) to maximize the gain of entropy. By increasing the flexibility of P, we can tune the interfacial structures from extended structures to monolayers. These findings may help improve applications based on the adsorption of P/S mixtures in the fields of cosmetic or oil recovery.

Polycation charge and conformation of aqueous poly(acrylamide-co-diallyldimethylammonium chloride): Effect of salinity and temperature

A comprehensive study on the polycation charge and conformation poly(acrylamide-co-dimethyldiallylammonium chloride) with a moar mass of 250 kDa (comprising of 45 mass% of dimethyldiallylammonium chloride) has been performed in aqueous media without and with an electrolyte as a function of temperature. Use has been made of a model of polyelectrolyte conductivity developed by Colby et al. [10] to analyze the electrical conductance-concentration data. The results indicated that the charge on each polycation reduced from a value of ∼ 450 in the maximally perturbed chain to ∼ 100 in an unperturbed chain at 298.15 K when the copolymer concentration was ∼ 0.06 monomol·L−1 (the highest concentration investigated). The intrinsic persistence length of the polycation (7.2 A0) estimated from viscosity measurements using the worm-like coil model of polymer was found to be smaller than the average length of each repeating unit, indicating inherent flexibility of this copolymer. It is observed that in salt-free solutions polycations adopt a slightly less flexible and extended conformation (upto around 4 repeating units) because of intra-chain electrostatic repulsions at 298.15 K when the copolymer concentration was ∼ 0.002 monomol·L−1 (the lowest concentration investigated). The variation of the coefficient of friction of the monomer with polymer concentration is found to be governed by the effect of chain charges over and above that of the chain stiffness; in the unperturbed state, however, the effect of chain charges is playing the pivotal role. This study sheds lights on the dependence of polycation charge and conformation with the concentration of copolymer, temperature, and salinity of the medium.

Conformation and persistence length of chitosan in aqueous solutions of different ionic strengths via asymmetric flow field-flow fractionation

Conformation of chitosan in acidic aqueous solutions is strongly influenced by ionic strength, but the conventional employed size exclusion chromatography is limited to high ionic strength. Here we show that conformation of chitosan in acetate buffer down to millimolar ionic strength can be studied via asymmetric flow field-flow fractionation (AF4), where the separation is governed by the diffusion properties of the chitosan molecules and assisted by the electrostatic repulsion of the polyelectrolyte from the channel membrane. The size of chitosan decreases with ionic strength due to increasing screening of the polyelectrolyte effect. The persistence length of chitosan in the solutions, obtained by fitting the conformation plot by the wormlike chain model, decreases linearly with the Debye screening length from 44.5 nm at a salt concentration of 1.25 mM dominated by the electrostatic contribution to 8.6 nm in 800 mM acetate buffer close to its intrinsic persistence length of 7.7 nm.

Mannobiose‐Grafting Shifts PEI Charge and Biphasic Dependence on pH

AbstractHow the 4% grafting of mannobiose alters the properties of the polyelectrolyte, linear polyethylenimine (PEI), which has protonable amines and is used widely for complexing DNA, is investigated. The pH‐dependence of the PEI charge, zeta potential, and hydrodynamic radius changes when the polymer charge increases beyond 50–60%. According to MD simulations, this transition in pH‐ or charge‐ dependence is a short‐range structural response to amine protonation (i.e., change in intrinsic persistence length) rather than a longer‐range charge‐repulsion response. Upon mannobiosylation, the 50% charge state of PEI shifts from ≈pH 6 toward ≈pH 4. The protonability of PEI is lowered and restricted to limited charge states. These mannobiosylation‐induced shifts are reversed by salt and uncharged chaotropes, indicating that hydrogen‐bonding interactions fostered by the grafted sugars are lowering the protonation pKa of PEI. These findings have broad implications for the analytical modeling of polyelectrolytes, the design of PEI‐based gene‐delivery systems, and for understanding how oligosaccharides modify cell and protein surfaces.

Sequence-Dependent Persistence Length of Long DNA.

Using a high-throughput genome-mapping approach, we obtained circa 50million measurements of the extension of internal human DNA segments in a 41 nm×41 nm nanochannel. The underlying DNA sequences, obtained by mapping to the reference human genome, are 2.5-393kilobase pairs long and contain percent GC contents between 32.5% and 60%. Using Odijk's theory for a channel-confined wormlike chain, these data reveal that the DNA persistence length increases by almost 20% as the percent GC content increases. The increased persistence length is rationalized by a model, containing no adjustable parameters, that treats the DNA as a statistical terpolymer with a sequence-dependent intrinsic persistence length and a sequence-independent electrostatic persistence length.

Role of the ratio of biopolyelectrolyte persistence length to nanoparticle size in the structural tuning of electrostatic complexes.

Aggregation of nanoparticles of given size R induced by addition of a polymer strongly depends on its degree of rigidity. This is shown here on a large variety of silica nanoparticle self-assemblies obtained by electrostatic complexation with carefully selected oppositely charged biopolyelectrolytes of different rigidity. The effective rigidity is quantified by the total persistence length L_{T} representing the sum of the intrinsic (L_{p}) and electrostatic (L_{e}) polyelectrolyte persistence length, which depends on the screening, i.e., on ionic strength due to counterions and external salt concentrations. We experimentally show that the ratio L_{T}/R is the main tuning parameter that controls the fractal dimension D_{f} of the nanoparticles' self-assemblies, which is determined using small-angle neutron scattering: (i) For L_{T}/R<0.3 (obtained with flexible poly-l-lysine in the presence of an excess of salt), chain flexibility promotes easy wrapping around nanoparticles in excess, hence ramified structures with D_{f}∼2. (ii) For 0.3<L_{T}/R≤1 (semiflexible chitosan or hyaluronan complexes), chain stiffness promotes the formation of one-dimensional nanorods (in excess of nanoparticles), in good agreement with computer simulations. (iii) For L_{T}/R>1,L_{e} is strongly increased due to the absence of salt and repulsions between nanoparticles cannot be compensated for by the polyelectrolyte wrapping, which allows a spacing between nanoparticles and the formation of one-dimensional pearl necklace complexes. (iv) Finally, electrostatic screening, i.e., ionic strength, turned out to be a reliable way of controlling D_{f} and the phase diagram behavior. It finely tunes the short-range interparticle potential, resulting in larger fractal dimensions at higher ionic strength.

Coacervation in Biopolymers

In this review, a detailed discussion on salient features of intermolecular interactions leading to phase separation and coacervation is discussed. Biomolecular solutions exist as gels, coacervates and melts with each of these phases having its signature physico-chemical properties which is discussed in this review. The discussions are supported by robust experimental data obtained from an array of methods like turbidimetry, electrophoresis, viscosity, light scattering etc. The inevitability of the phenomenon of self-organization in biopolymers results in generation of a variety of soft matter phases which do not, however, make it predictable. For instance the associate aggregation is a process which remains obscure, as every protein aggregates in a different manner under different conditions. One known feature to the aggregation of proteins is the strong dependence upon pH, salt concentration, and temperature. Beyond the influence of these factors and their effects on aggregation, the process is not well understood. In summary, a comprehensive account of biomolecular phase states and their inherent attributes are presented in this review. Potential applications of coacervates are many starting from protein purification, drug encapsulation to treatment of organic plumes. This calls for better understanding of the coacervate structure and the transport of biomolecules inside this phase. Several questions pertaining to the structure of coacervates can arise. The foremost of these is, is it a gel-like or a solution-like phase? Though presence of hydrogen bonding and hydrophobic sites on the polyions influence biomolecular binding, they hardly play any role in deciding the persistence length of the polyion unlike the surface charge. Interestingly, we observed that the differential binding (SPB versus EB) was found to be a function of intrinsic persistence length only which we conclude as a significant observation.

Elastic properties and secondary structure formation of single-stranded DNA at monovalent and divalent salt conditions.

Single-stranded DNA (ssDNA) plays a major role in several biological processes. It is therefore of fundamental interest to understand how the elastic response and the formation of secondary structures are modulated by the interplay between base pairing and electrostatic interactions. Here we measure force-extension curves (FECs) of ssDNA molecules in optical tweezers set up over two orders of magnitude of monovalent and divalent salt conditions, and obtain its elastic parameters by fitting the FECs to semiflexible models of polymers. For both monovalent and divalent salts, we find that the electrostatic contribution to the persistence length is proportional to the Debye screening length, varying as the inverse of the square root of cation concentration. The intrinsic persistence length is equal to 0.7 nm for both types of salts, and the effectivity of divalent cations in screening electrostatic interactions appears to be 100-fold as compared with monovalent salt, in line with what has been recently reported for single-stranded RNA. Finally, we propose an analysis of the FECs using a model that accounts for the effective thickness of the filament at low salt condition and a simple phenomenological description that quantifies the formation of non-specific secondary structure at low forces.

Periodate oxidation and macromolecular compaction of hyaluronan

Partial periodate oxidation of hyaluronan (HA) leads to ring opening of the 4-linked D-glucuronate (GlcA) residues, providing a particularly flexible element within otherwise semi-flexible chains. This leads to compaction of the chains as demonstrated by a pronounced decrease in the intrinsic persistence length, which was determined on the basis of the molecular weight dependence of radius of gyration (R G) and the intrinsic viscosity. These parameters were readily obtained using size-exclusion chromatography (SEC) with an online multi-angle laser light scattering (MALLS) detector, a viscosity detector, and a concentration-sensitive detector. The electrostatic contribution to the total persistence length increased with increasing degree of oxidation. Compared to alginates and chitosans, HA becomes less degraded during the oxidation, which is attributed to a protective effect of periodate-resistant N-acetyl-D-glucosamine (GlcNAc) residues adjacent to periodate-sensitive GlcA residues in HA.

Double-exponential decay of orientational correlations in semiflexible polyelectrolytes

In this paper we revisited the problem of persistence length of polyelectrolytes. We performed a series of Molecular Dynamics simulations using the Debye-Hückel approximation for electrostatics to test several equations which go beyond the classical description of Odijk, Skolnick and Fixman (OSF). The data confirm earlier observations that in the limit of large contour separations the decay of orientational correlations can be described by a single-exponential function and the decay length can be described by the OSF relation. However, at short countour separations the behaviour is more complex. Recent equations which introduce more complicated expressions and an additional length scale could describe the results very well on both the short and the long length scale. The equation of Manghi and Netz when used without adjustable parameters could capture the qualitative trend but deviated in a quantitative comparison. Better quantitative agreement within the estimated error could be obtained using three equations with one adjustable parameter: 1) the equation of Manghi and Netz; 2) the equation proposed by us in this paper; 3) the equation proposed by Cannavacciuolo and Pedersen. Two characteristic length scales can be identified in the data: the intrinsic or bare persistence length and the electrostatic persistence length. All three equations use a single parameter to describe a smooth crossover from the short-range behaviour dominated by the intrinsic stiffness of the chain to the long-range OSF-like behaviour.

Intermediate Filaments in Small Configuration Spaces

Intermediate filaments play a key role in cell mechanics. Apart from their great importance from a biomedical point of view, they also act as a very suitable micrometer-sized model system for semiflexible polymers. We perform a statistical analysis of the thermal fluctuations of individual filaments confined in microchannels. The small channel width and the resulting deflections at the walls give rise to a reduction of the configuration space by about 2 orders of magnitude. This circumstance enables us to precisely measure the intrinsic persistence length of vimentin intermediate filaments and to show that they behave as ideal wormlike chains; we observe that small fluctuations in perpendicular planes decouple. Furthermore, the inclusion of results for confined actin filaments demonstrates that the Odijk confinement regime is valid over at least 1 order of magnitude in persistence length.

Rodlike Complexes of a Polyelectrolyte (Hyaluronan) and a Protein (Lysozyme) Observed by SANS

We study by small-angle neutron scattering (SANS) the structure of hyaluronan -lysozyme complexes. Hyaluronan (HA) is a polysaccharide of 9 nm intrinsic persistence length that bears one negative charge per disaccharide monomer (M(mol) = 401.3 g/mol); two molecular weights, M(w) = 6000 and 500,000 Da were used. The pH was adjusted at 4.7 and 7.4 so that lysozyme has a global charge of +10 and +8, respectively. The lysozyme concentration was varied from 3 to 40 g/L at constant HA concentration (10 g/L). At low protein concentration, samples are monophasic, and SANS experiments reveal only fluctuations of concentration, although, at high protein concentration, clusters are observed by SANS in the dense phase of the diphasic samples. In between, close to the onset of the phase separation, a distinct original scattering is observed. It is characteristic of a rod-like shape, which could characterize "single" complexes involving one or a few polymer chains. For the large molecular weight (500,000), the rodlike rigid domains extend to much larger length scale than the persistence length of the HA chain alone in solution and the range of the SANS investigation. They can be described as a necklace of proteins attached along a backbone of diameter of one or a few HA chains. For the short chains (M(w) ≈ 6000), the rod length of the complexes is close to the chain contour length (∼ 15 nm).

Persistence length of DNA molecules confined in nanochannels

The influence of confinement on the persistence length of dsDNA molecules under a high ionic strength environment was explored by coarse-grained Monte Carlo simulations in channels of different profiles. It was found that under confinement three definitions of the persistence length of DNA molecules were not equivalent and represented different properties. In case of the global quantities, the projection and the WLC persistence lengths, the apparent values up to several hundred nanometres are observed for DNA confined in narrow channels. The orientational correlation function cos theta(s) of confined DNA shows a complex pattern, distinctive for semiflexible polymers. At weak and moderate confinements the function cos theta(s) suggests an unexpected increase in the apparent DNA flexibility. The orientational persistence length computed from the initial slope of the function cos theta(s) mirrors only short-scale correlations and gives the value close to the intrinsic persistence length of DNA. The simulation data of direct relevance to experimental studies of DNA in microfluidic devices are compared with analytical theories for stiff chains.

Physicochemical characterization of carrageenans—A critical reinvestigation

AbstractKappa‐, iota‐, and lambda‐carrageenan (food grade) were analyzed by static light scattering (MALS in batch mode) in 0.1M NaNO3 at 25 and 60°C, earlier heated up to 90°C or not. At 25°C, there was a strong tendency for a concentration‐dependent aggregation in the order lambda &lt; kappa &lt; iota. At 60°C, all samples were molecularly dispersed. The strongly temperature‐dependent refractive index increments (equilibrium dialysis) differ. Data interpretation in terms of the wormlike chain model using the Skolnik‐Odijk‐Fixman approach led to an intrinsic persistence length around 3 to 4 nm and expansion factors as high as 1.5 and above in a thermodynamically good solvent for all three types. Triple‐detector HPSEC (DRI, MALS, viscometry) on the three commercial samples plus a degraded (by acidic hydrolysis) kappa‐carrageenan in the same solvent/eluant at 60°C yielded a uniform and slightly curved [η]‐M relationship for 5 × 103 ≤ M/(g mol) ≤ 3 × 106 and a nearly identical molar mass dependence of the radius of gyration. HPSEC at 25°C on kappa‐carrageenan confirmed formation of soluble aggregates. Special emphasis was put on analytical and methodological aspects. The reliability of the experimental data was demonstrated by analogous measurements on dextran calibration standards. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

Persistence Lengths and Structure Factors of Wormlike Polymers under Confinement

The behavior of semiflexible chains modeling wormlike polymers such as DNA and actin in confined spaces was explored by coarse-grained Monte Carlo simulations. The persistence length P, mean end-to-end distance R2, mean radius of gyration Rg2, and the size ratio R2/Rg2 were computed for chains in slits, cylinders, and spheres. It was found that the intrinsic persistence length of a free chain undergoes on confinement substantial alteration into the apparent persistence length. The qualitative differences were found in trends of the apparent persistence lengths between slits and cylinders on one side and spheres on the other side. The quantities P, R2, Rg2, and R2/Rg2 display similar dependences upon squeezing the chains in nanopores. The above quantities change nonmonotonically with confinement in slits and cylinders, whereas they drop smoothly with decreasing radius of a sphere. For elongation of a chain in a cylinder, two regimes corresponding to strong and moderate confinements were found and compared to experiments and predictions of the blob and Odijk theories. In a spherical cavity, the toroidal chain structure with a hole in the center was detected under strong confinements. The scattering form factor S(q) computed for semiflexible confined chains revealed three regimes of behavior in a slit and a cylinder that matched up well with the scaling theory. The complex form of the function S(q) computed for a sphere was interpreted as a sign of the toroidal structure. A reasonable agreement was found between the simulations and measurements of DNA and actin filaments, confined in nano- and microfluidic channels and spherical droplets, pertaining to the changes of the persistence lengths, chain elongation, and toroidal structure formation.

Effect of confinement on properties of stiff biological macromolecules

The behaviour of semiflexible chains, modelling biopolymers such as DNA and actin in confined spaces, was investigated by means of Monte Carlo simulations. Simulations, based on the coarse-grained worm-like chain (WLC) model, assumed confinement length-scales comparable to those used in micro- and nanofluidic devices. The end-to-end chain elongation R was determined as a function of the channel dimensions and chain bending rigidity. Three regions of chain elongation R, identified in simulations in a cylinder and a slit, were described by current theoretical concepts. In harmony with the measurements of confined DNA, an abrupt transition between the blob region at moderate confinement and the deflection region at strong cylindrical confinement was found. The conditions for hairpin formation were elucidated as a trade-off between confinement and chain stiffness. The intrinsic persistence length of unconfined polymers was calculated by four methods that provided practically identical results. However, in confined geometries only the rigorous and WLC methods predicted the dependence of apparent persistence length P on confinement in a qualitatively correct way. It was found that the simple exponential function, suitable for the description of orientation correlations in free chains is, in confined systems, limited only to short distances along the chain contour and, thus, the apparent persistence length determined by this method just reproduces the intrinsic value of P. The orientation correlations from simulations were compared with analytical predictions in the deflection regime under strong confinement and with the measurements of actin filaments.