Persistent draining crossover in DNA and other semi-flexible polymers: Evidence from hydrodynamic models and extensive measurements on DNA solutions

Coexistence of Crumpling and Flat Sheet Conformations in Two-Dimensional Polymer Networks: An Understanding of Aggrecan Self-Assembly

We investigate the conformational properties of self-avoiding two-dimensional (2D) ideal polymer networks with tunable mesh sizes as a model of self-assembled structures formed by aggrecan. Polymer networks having few branching points and large enough mesh tend to crumple, resulting in a fractal dimension of d_{f}≈2.7. The flat sheet behavior (d_{f}=2) emerges in 2D polymer networks having more branching points at large length scales; however, it coexists with crumpling conformations at intermediate length scales, a feature found in scattering profiles of aggrecan solutions. Our findings bridge the long-standing gap between theories and simulations of polymer sheets.

Solution properties of spherical gold nanoparticles with grafted DNA chains from simulation and theory

There has been a rapidly growing interest in the use of functionalized Au nanoparticles (NPs) as platforms in multiple applications in medicine and manufacturing. The sensing and targeting characteristics of these NPs, and the realization of precisely organized structures in manufacturing applications using such NPs, depend on the control of their surface functionalization. NP functionalization typically takes the form of polymer grafted layers, and a detailed knowledge of the chemical and structural properties of these layers is required to molecularly engineer the particle characteristics for specific applications. However, the prediction and experimental determination of these properties to enable the rational engineering of these particles is a persistent problem in the development of this class of materials. To address this situation, molecular dynamic simulations were performed based on a previously established coarse-grained single-stranded DNA (ssDNA) model to determine basic solution properties of model ssDNA-grafted NP-layers under a wide range of conditions. In particular, we emphasize the calculation of the hydrodynamic radius for ssDNA-grafted Au NPs as a function of structural parameters such as ssDNA length, NP core size, and surface coverage. We also numerically estimate the radius of gyration and the intrinsic viscosity of these NPs, which in combination with hydrodynamic radius estimates, provide valuable information about the fluctuating structure of the grafted polymer layers. We may then understand the origin of the commonly reported variation in effective NP "size" by different measurement methods, and then exploit this information in connection to material design and characterization in connection with the ever-growing number of applications utilizing polymer-grafted NPs.

Influence of network defects on the conformational structure of nanogel particles: From "closed compact" to "open fractal" nanogel particles

We propose an approach to generate a wide range of randomly branched polymeric structures to gain general insights into how polymer topology encodes a configurational structure in solution. Nanogel particles can take forms ranging from relatively symmetric sponge-like compact structures to relatively anisotropic open fractal structures observed in some nanogel clusters and in some self-associating polymers in solutions, such as aggrecan solutions under physiologically relevant conditions. We hypothesize that this broad "spectrum" of branched polymer structures derives from the degree of regularity of bonding in the network defining these structures. Accordingly, we systematically introduce bonding defects in an initially perfect network having a lattice structure in three and two topological dimensions corresponding to "sponge" and "sheet" structures, respectively. The introduction of bonding defects causes these "closed" and relatively compact nanogel particles to transform near a well-defined bond percolation threshold into "open" fractal objects with the inherent anisotropy of randomly branched polymers. Moreover, with increasing network decimation, the network structure of these polymers acquires other configurational properties similar to those of randomly branched polymers. In particular, the mass scaling of the radius of gyration and its eigenvalues, as well as hydrodynamic radius, intrinsic viscosity, and form factor for scattering, all undergo abrupt changes that accompany these topological transitions. Our findings support the idea that randomly branched polymers can be considered to be equivalent to perforated sheets from a "universality class" standpoint. We utilize our model to gain insight into scattering measurements made on aggrecan solutions.

Structure-dilute solution property relationships of comb-like macromolecules in a good solvent

The structural characterization of branched polymers still poses experimental challenges despite their technological potential. This lack of clarity is egregious in linear low-density polyethylene (LLDPE), a common industrial plastic. Here, we design a coarse-grain, implicit solvent molecular dynamics model for LLDPE in 1,2,4-trichlorobenzene, a canonical good solvent, that replicates all-atom simulations and experiments. We employ this model to test the relationship between the contraction factors, the ratios of branched to linear dilute solution properties. In particular, we relate the contraction factor of the radius of gyration to that of the intrinsic viscosity and the hydrodynamic radius. The contraction exponents are constant as we vary branch length and spacing in contrast to theoretical expectations. We use this observation to develop a general theory for the dilute solution properties of linear polymers with linear side-chain branches, comb-like macromolecules, in a good solvent and validate the theory by generating master curves for LLDPE.

Diffusion of Short Semiflexible DNA Polymer Chains in Strong and Moderate Confinement

In many technological applications, DNA is confined within nanoenvironments that are smaller than the size of the unconfined polymer in solution. However, the dependence of the diffusion coefficient on molecular weight and characteristic confinement dimension remains poorly understood in this regime. Here, convex lens-induced confinement (CLiC) was leveraged to examine how the diffusion of short DNA fragments varied as a function of slit height by using single-molecule fluorescence tracking microscopy. The diffusion coefficient followed approximate power law behavior versus confinement height, with exponents of 0.27 ± 0.01, 0.32 ± 0.02, and 0.42 ± 0.06 for 692, 1343, and 2686 base pair chains, respectively. The weak dependence on slit height suggests that shorter semiflexible chains may adopt increasingly rodlike conformations and therefore experience weaker excluded-volume interactions as the confinement dimension is reduced. The diffusion coefficient versus molecular weight also exhibited apparent power law behavior, with exponents that varied slightly (from -0.89 to -0.85) with slit height, consistent with hydrodynamic interactions intermediate between Rouse and Zimm model predictions.

Structure and conformational properties of ideal nanogel particles in athermal solutions

We investigate the conformational properties of "ideal" nanogel particles having a lattice network topology by molecular dynamics simulations to quantify the influence of polymer topology on the solution properties of this type of branched molecular architecture. In particular, we calculate the mass scaling of the radius of gyration (Rg), the hydrodynamic radius, as well as the intrinsic viscosity with the variation of the degree of branching, the length of the chains between the branched points, and the average mesh size within these nanogel particles under good solvent conditions. We find competing trends between the molecular characteristics, where an increase in mesh size or degree of branching results in the emergence of particle-like characteristics, while an increase in the chain length enhances linear polymer-like characteristics. This crossover between these limiting behaviors is also apparent in our calculation of the form factor, P(q), for these structures. Specifically, a primary scattering peak emerges, characterizing the overall nanogel particle size. Moreover, a distinct power-law regime emerges in P(q) at length scales larger than the chain size but smaller than Rg of the nanogel particle, and the Rg mass scaling exponent progressively approaches zero as the mesh size increases, the same scaling as for an infinite network of Gaussian chains. The "fuzzy sphere" model does not capture this feature, and we propose an extension to this popular model. These structural features become more pronounced for values of molecular parameters that enhance the localization of the branching segments within the nanogel particle.

The biofilm matrix scaffold of Pseudomonas aeruginosa contains G-quadruplex extracellular DNA structures

Extracellular DNA, or eDNA, is recognised as a critical biofilm component; however, it is not understood how it forms networked matrix structures. Here, we isolate eDNA from static-culture Pseudomonas aeruginosa biofilms using ionic liquids to preserve its biophysical signatures of fluid viscoelasticity and the temperature dependency of DNA transitions. We describe a loss of eDNA network structure as resulting from a change in nucleic acid conformation, and propose that its ability to form viscoelastic structures is key to its role in building biofilm matrices. Solid-state analysis of isolated eDNA, as a proxy for eDNA structure in biofilms, reveals non-canonical Hoogsteen base pairs, triads or tetrads involving thymine or uracil, and guanine, suggesting that the eDNA forms G-quadruplex structures. These are less abundant in chromosomal DNA and disappear when eDNA undergoes conformation transition. We verify the occurrence of G-quadruplex structures in the extracellular matrix of intact static and flow-cell biofilms of P. aeruginosa, as displayed by the matrix to G-quadruplex-specific antibody binding, and validate the loss of G-quadruplex structures in vivo to occur coincident with the disappearance of eDNA fibres. Given their stability, understanding how extracellular G-quadruplex structures form will elucidate how P. aeruginosa eDNA builds viscoelastic networks, which are a foundational biofilm property.

Violation of Stokes-Einstein and Stokes-Einstein-Debye relations in polymers at the gas-supercooled liquid coexistence

Molecular dynamics simulations are performed on a system of model linear polymers to look at the violations of Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations near the mode coupling theory transition temperatureT_cat three (one higher and two lower) densities. At low temperatures, both lower density systems show stable gas-supercooled-liquid coexistence whereas the higher density system is homogeneous. We show that monomer density relaxation exhibits SE violation for all three densities, whereas molecular density relaxation shows a weak violation of the SE relation nearT_cin both lower density systems. This study identifies disparity in monomer mobility and observation of jumplike motion in the typical monomer trajectories resulting in the SE violations. In addition to the SE violation, a weak SED violation is observed in the gas-supercooled-liquid coexisting domains of the lower densities. Both lower density systems also show a decoupling of translational and rotational dynamics in this polymer system.

Solvation and diffusion of poly(vinyl alcohol) chains in a hydrated inorganic ionic liquid

While the behavior of polyelectrolyte chains in aqueous salt solutions has been extensively studied, little is known about polar polymer chains in solvents with extremely high concentrations of inorganic ions, such as those found in ionic liquids (ILs). Here, we report on expansion, solvation and diffusion of poly(vinyl alcohol), PVA, chains in dilute solutions of a hydrated inorganic IL phase change material (PCM), lithium nitrate trihydrate (LNH). This solvent has an extremely high concentration of inorganic ions (≈18 M) with a low concentration of water molecules largely forming solvation shells of Li⁺ and NO₃^- ions, as shown using ATR-FTIR spectroscopy. Diffusion and hydrodynamic size of PVA chains of different molecular weights in this unusual solvent were studied using fluorescence correlation spectroscopy (FCS). A higher scaling exponent obtained from the molecular weight dependences of the diffusion coefficients of PVA chains as well as a lower overlap concentration (c*) of PVA in LNH solutions as measured by FCS suggest an expansion of the polymer coils in this solvent. We argue that enhanced solubility of PVA in LNH solutions is likely a result of increased rigidification of polymer chains due to the binding of solvated Li⁺ ions, which is demonstrated using ⁷Li NMR spectroscopy. We believe that an understanding of solvation and ion-binding capability can offer crucial insight into designing polymer-based shape stabilization matrices for inorganic PCMs.

Molecular rigidity and enthalpy-entropy compensation in DNA melting

Enthalpy-entropy compensation (EEC) is observed in diverse molecular binding processes of importance to living systems and manufacturing applications, but this widely occurring phenomenon is not sufficiently understood from a molecular physics standpoint. To gain insight into this fundamental problem, we focus on the melting of double-stranded DNA (dsDNA) since measurements exhibiting EEC are extensive for nucleic acid complexes and existing coarse-grained models of DNA allow us to explore the influence of changes in molecular parameters on the energetic parameters by using molecular dynamics simulations. Previous experimental and computational studies have indicated a correlation between EEC and changes in molecular rigidity in certain binding-unbinding processes, and, correspondingly, we estimate measures of DNA molecular rigidity under a wide range of conditions, along with resultant changes in the enthalpy and entropy of binding. In particular, we consider variations in dsDNA rigidity that arise from changes of intrinsic molecular rigidity such as varying the associative interaction strength between the DNA bases, the length of the DNA chains, and the bending stiffness of the individual DNA chains. We also consider extrinsic changes of molecular rigidity arising from the addition of polymer additives and geometrical confinement of DNA between parallel plates. All our computations confirm EEC and indicate that this phenomenon is indeed highly correlated with changes in molecular rigidity. However, two distinct patterns relating to how DNA rigidity influences the entropy of association emerge from our analysis. Increasing the intrinsic DNA rigidity increases the entropy of binding, but increases in molecular rigidity from external constraints decreases the entropy of binding. EEC arises in numerous synthetic and biological binding processes and we suggest that changes in molecular rigidity might provide a common origin of this ubiquitous phenomenon in the mutual binding and unbinding of complex molecules.

Knot Energy, Complexity, and Mobility of Knotted Polymers

The Coulomb energy E C is defined by the energy required to charge a conductive object and scales inversely to the self-capacity C, a basic measure of object size and shape. It is known that C is minimized for a sphere for all objects having the same volume, and that C increases as the symmetry of an object is reduced at fixed volume. Mathematically similar energy functionals have been related to the average knot crossing number 〈m〉, a natural measure of knot complexity and, correspondingly, we find E C to be directly related to 〈m〉 of knotted DNA. To establish this relation, we employ molecular dynamics simulations to generate knotted polymeric configurations having different length and stiffness, and minimum knot crossing number values m for a wide class of knot types relevant to the real DNA. We then compute E C for all these knotted polymers using the program ZENO and find that the average Coulomb energy 〈E C〉 is directly proportional to 〈m〉. Finally, we calculate estimates of the ratio of the hydrodynamic radius, radius of gyration, and the intrinsic viscosity of semi-flexible knotted polymers in comparison to the linear polymeric chains since these ratios should be useful in characterizing knotted polymers experimentally.

Influence of polymer architectures on diffusion in unentangled polymer melts

Recent simulations have indicated that the thermodynamic properties and the glassy dynamics of polymer melts are strongly influenced by the average molecular shape, as quantified by the radius of gyration tensor of the polymer molecules, and that the average molecular shape can be tuned by varying the molecular topology (e.g., ring, star, linear chain, etc.). In the present work, we investigate if the molecular shape is similarly a predominant factor in understanding the polymer center of mass diffusion D in the melt, as already established for polymer solutions. We find that all our D data for unentangled polymer melts having a range of topologies can be reasonably described as a power law of the polymer hydrodynamic radius, Rh. In particular, this scaling is similar to the scaling of D for a tracer sphere having a radius on the order of the chain radius of gyration, Rg. We conclude that the chain topology influences the molecular dynamics in as much as the polymer topology influences the average molecular shape. Experimental evidence seems to suggest that this situation is also true for entangled polymer melts.

Universal interrelation between measures of particle and polymer size

The characterization of many objects involves the determination of a basic set of particle size measures derived mainly from scattering and transport property measurements. For polymers, these basic properties include the radius of gyration Rg, hydrodynamic radius Rh, intrinsic viscosity [η], and sedimentation coefficient S, and for conductive particles, the electric polarizability tensor αE and self-capacity C. It is often found that hydrodynamic measurements of size deviate from each other and from geometric estimates of particle size when the particle or polymer shape is complex, a phenomenon that greatly complicates both nanoparticle and polymer characterizations. The present work explores a general quantitative relation between αE, C, and Rg for nanoparticles and polymers of general shape and the corresponding properties η, Rh, and Rg using a hydrodynamic-electrostatic property interrelation.

Interfacial diffusion of a single cyclic polymer chain

Lateral diffusion of cyclic polystyrene at the interface between fused silica and dichloromethane is investigated at the single-molecular level. Narrowly distributed cyclic polystyrene (c-PS) of high purity with molecular weights spanning nearly an order of magnitude is prepared via atom transfer radical polymerization (ATRP) and Cu-catalyzed azide/alkyne cycloaddition (CuAAC) click reaction. The diffusion coefficients (D) of c-PS and its linear analogue (l-PS) on the surface are measured by fluorescence correlation spectroscopy (FCS). The diffusion coefficient of c-PS is discovered to have an inverse dependence on molecular weight, D ∼ M^-1, in contrast to the case of linear polystyrene, which reproduces a stronger molecular weight dependence, D ∼ M^-3/2. The slower interfacial motion of cyclic chains is attributed to their stronger binding to the surface and more importantly, the unique surface diffusion mechanism due to the absence of free chain ends.

Impact of Monovalent Counter-ions on the Conformation of Flexible Polyelectrolytes Having Different Molecular Architectures

We explore the impact of monovalent counter-ions on the molecular conformation of highly charged flexible polyelectrolytes for a range of molecular topologies (linear chains, stars, and unknotted and trefoil rings) by molecular dynamics simulations that include an explicit solvent having short range interaction with the polyelectrolyte. In particular, we investigate how the counter-ions near the polyelectrolytes with variable mass influence the average molecular shape. We also characterize the interfatially "bound" counter-ions by calculating the time-averaged number of interfacial counter-ions, as well as the degree to which the polyelectrolytes wrap around the counter-ions by calculating the number of contacts between the counter-ions and the polyelectrolyte.