Polymer Contour Research Articles

Sequence disorder-induced first order phase transition in confined polyelectrolytes.

We consider a statistical mechanical model of a generic flexible polyelectrolyte, comprised of identically charged monomers with long-range electrostatic interactions and short-range interactions quantified by a disorder field along the polymer contour sequence, which is randomly quenched. The free energy and the monomer density profile of the system for no electrolyte screening are calculated in the case of a system composed of two infinite planar bounding surfaces with an intervening oppositely charged polyelectrolyte chain. We show that the effect of the contour sequence disorder, mediated by short-range interactions, leads to an enhanced localization of the polyelectrolyte chain and a first order phase transition at a critical value of the inter-surface spacing. This phase transition results in an abrupt change of the pressure from negative to positive values, effectively eliminating polyelectrolyte mediated bridging attraction.

Variation of Spring Stiffness, Monomeric Friction, and Brownian Intensity in the Simulation System of Unentangled Melt under Steady Flow

Understanding the nonlinear dynamics of an unentangled polymer melt from the bead-spring chain model requires knowledge of the variation of spring stiffness, monomeric friction, and Brownian intensity. In this work, these nonequilibrium (NE) parameters are quantified in the model simulation systems of unentangled melt under steady-flow conditions. We focus on a particular version of the model with undefined NE parameters. Some expressions to relate the NE parameters with the rheological and structural properties are pointed out. The spring stiffening parameter rκ is proven to be easily accessible in the planar flows. The distribution of the stiffening effect along the polymer contour is identified. The alignment-induced reduction of monomeric friction is confirmed in the simulation systems, but the anisotropic feature of friction is also emphasized. The constraint on the cooperative variation of spring stiffness and friction is proven to be an important property of extensional flow. The variation of Brownian intensity is found to be decoupled with the variation of friction, which means the violation of the fluctuation–dissipation (FD) theorem. The NE parameters of the simulation systems are further compared with those from the experimental systems.

Dilute polymer solutions under shear flow: Comprehensive qualitative analysis using a bead-spring chain model with a FENE-Fraenkel spring

Although the nonequilibrium behavior of polymer solutions is generally well understood, particularly in extensional flow, there remain several unanswered questions for dilute solutions in simple shear flow, and full quantitative agreement with experiments has not been achieved. For example, experimental viscosity data exhibit qualitative differences in shear-thinning exponents, the shear rate for the onset of shear-thinning, and high-shear Newtonian plateaus depending on polymer semiflexibility, contour length, and solvent quality. While polymer models are able to incorporate all of these effects through various spring force laws, bending potentials, excluded volume (EV) potentials, and hydrodynamic interaction (HI), the inclusion of each piece of physics has not been systematically matched to experimentally observed behavior. Furthermore, attempts to develop multiscale models (in the sense of representing an arbitrarily small or large polymer chain) which can make quantitative predictions are hindered by the lack of ability to fully match the results of bead-rod models, often used to represent a polymer chain at the Kuhn-step level, with bead-spring models, which take into account the entropic elasticity. In light of these difficulties, this work aims to develop a general model based on the so-called FENE-Fraenkel spring, originally formulated by Larson and co-workers [J. Chem. Phys. 124 (2006)], which can span the range from rigid rod to traditional entropic spring, as well as include a bending potential, EV, and HI. As we show, this model can reproduce, and smoothly move between, a wide range of previously observed polymer solution rheology in shear flow.

Path integral description of semiflexible active Brownian polymers.

Semiflexible polymers comprised of active Brownian particles (ABPOs) exhibit intriguing activity-driven conformational and dynamical features. Analytically, the generic properties of ABPOs can be obtained in a mean-field description applying the Gaussian semiflexible polymer model. In this article, we derive a path integral representation of the stationary-state distribution function of such ABPOs, based on the stationary-state distribution function of the normal mode amplitudes following from the Langevin equation of motion. The path integral includes characteristic semiflexible polymer contributions from entropy and bending energy, with activity dependent coefficients, and, in addition, activity-induced torsional and higher order correlations along the polymer contour. Focusing on a semiflexible polymer approximation, we determine various properties such as the tangent-vector correlation function, effective persistence length, and the mean-square end-to-end distance. The latter reflects the characteristic features of ABPOs, and good quantitative agreement is obtained with the full solution for larger activities, specifically for flexible polymers. Moreover, the approximation indicates the relevance of torsional and higher order contour correlations for the ABPO conformations. In general, the ABPO path integral illustrates how colored noise (active fluctuations) affects semiflexible polymer conformations in comparison to white noise thermal fluctuations.

Emergent slow dynamics of collapsed polymers flowing through porous media.

Using hydrodynamic simulations, we study the single polymers flowing through model porous media (close-packed colloidal crystal). In good solvent or high flow rates, the polymer transport is similar to gel electrophoresis, with size-dependent sieving for L_{c}/L≲1 and size-independent biased reptation for L_{c}/L≳1 (L_{c} is the polymer contour length and L is the diameter of colloids forming the porous media). Importantly, in bad solvent and low flow rates, the polymers show an extra window of size-dependent velocity for 1≲L_{c}/L≲2, where the polymer transport is controlled by a globule-stretch transition at pore throats, and the transport velocity is much slower than reptation.

Single-Event Spectroscopy and Unravelling Kinetics of Covalent Domains Based on Cyclobutane Mechanophores.

Mechanochemical reactions that lead to an increase in polymer contour length have the potential to serve as covalent synthetic mimics of the mechanical unfolding of noncovalent "stored length" domains in structural proteins. Here we report the force-dependent kinetics of stored length release in a family of covalent domain polymers based on cis-1,2-substituted cyclobutane mechanophores. The stored length is determined by the size (n) of a fused ring in an [n.2.0] bicyclic architecture, and it can be made sufficiently large (>3 nm per event) that individual unravelling events are resolved in both constant-velocity and constant-force single-molecule force spectroscopy (SMFS) experiments. Replacing a methylene in the pulling attachment with a phenyl group drops the force necessary to achieve rate constants of 1 s-1 from ca. 1970 pN (dialkyl handles) to 630 pN (diaryl handles), and the substituent effect is attributed to a combination of electronic stabilization and mechanical leverage effects. In contrast, the kinetics are negligibly perturbed by changes in the amount of stored length. The independent control of unravelling force and extension holds promise as a probe of molecular behavior in polymer networks and for optimizing the behaviors of materials made from covalent domain polymers.

The hierarchical emergence of worm-like chain behaviour from globular domain polymer chains.

Biological organisms make use of hierarchically organised structures to modulate mechanical behaviour across multiple lengthscales, allowing microscopic objects to generate macroscopic effects. Within these structural hierarchies, the resultant physical behaviour of the entire system is determined not only by the intrinsic mechanical properties of constituent subunits, but also by their organisation in three-dimensional space. When these subunits are polyproteins, colloidal chains or other globular domain polymers, the Kratky-Porod model is often assumed for the individual subunits. Hence, it is implicitly asserted that the polymeric object has an intrinsic parameter, the persistence length, that defines its flexibility. However, the persistence lengths extracted from experiment vary, and are often relatively small. Through a series of simulations on polymer chains formed of globular subunits, we show that the persistence length itself is a hierarchical structural property, related not only to the intrinsic mechanical properties of the underlying monomeric subunits, but emerging due to the organisation of inhomogenous geometry along the polymer contour.

Biopolymer dynamics driven by helical flagella

Microbial flagellates typically inhabit complex suspensions of polymeric material which can impact the swimming speed of motile microbes, filter-feeding of sessile cells, and the generation of biofilms. There is currently a need to better understand how the fundamental dynamics of polymers near active cells or flagella impacts these various phenomena, in particular the hydrodynamic and steric influence of a rotating helical filament on suspended polymers. Our Stokesian dynamics simulations show that as a stationary rotating helix pumps fluid along its long axis, polymers migrate radially inwards while being elongated. We observe that the actuation of the helix tends to increase the probability of finding polymeric material within its pervaded volume. This accumulation of polymers within the vicinity of the helix is stronger for longer polymers. We further analyse the stochastic work performed by the helix on the polymers and show that this quantity is positive on average and increases with polymer contour length.

Tensile elasticity of semiflexible polymers with hinge defects.

It has become clear in recent years that the simple uniform wormlike chain model needs to be modified in order to account for more complex behavior which has been observed experimentally in some important biopolymers. For example, the large flexibility of short ds-DNA has been attributed to kink or hinge defects. In this paper, we calculate analytically, within the weak bending approximation, the force-extension relation of a wormlike chain with a permanent hinge defect along its contour. The defect is characterized by its bending energy (which can be zero, in the completely flexible case) and its position along the polymer contour. Besides the bending rigidity of the chain, these are the only parameters which describe our model. We show that a hinge defect causes a significant increase in the differential tensile compliance of a prestressed chain. In the small force limit, a hinge defect significantly increases the entropic elasticity. Our results apply to any pair of semiflexible segments connected by a hinge. As such, they may also be relevant to cytoskeletal filaments (F-actin, microtubules), where one may treat the cross-link connecting two filaments as a hinge defect.

DNA Binding Fluorescent Proteins for the Direct Visualization of Large DNA Molecules

Fluorescent proteins that also bind DNA molecules are promising reagents for a broad range of biological applications because they can be optically localized and tracked within cells, or provide versatile labels for in vitro experiments. We report a novel design for a fluorescent, DNA-binding protein (FP-DBP) that completely “paints” entire DNA molecules, whereby sequence-independent DNA binding is accomplished by linking a fluorescent protein to two small peptides (KWKWKKA) using lysine for binding to the DNA phosphates, and tryptophan for partial intercalating between DNA bases (1). Importantly, this ubiquitous binding motif enables fluorescent proteins (Kd =14.7 µM, 7-8 bp/FP-DBP of base occupancies per dye) to confluently stain DNA molecules and such binding is reversible via pH shifts of buffer solution. These proteins offer robust advantages for lack of fluorophore mediated photocleavage, which makes them ideal staining reagents for imaging of DNA molecules over extended time periods even without anti-bleaching agent because the DNA binding moiety of the FP is separated from the fluorophore moiety. Further, the staining with FP-DBPs does not perturb polymer contour lengths, showing that the λ DNA monomer is about 48 502 bp × 0.34 nm/bp = 16.5 μm long, while most of the intercalating dyes, such as EtBr and YOYO-1, are known to distort the DNA structure and increase its full contour length. Moreover, the most significant advantage of FP-DBPs for DNA staining is its application to live cells, or entire living organisms. In a unique fashion, the FP-DBP fluorescence localized in three or four discrete regions within the bacterial cells: one, or two spots in the middle, and some at both ends of cells, as well as DAPI stained bacterial cells.1. Lee, S. et al., 2015, Nucleic Acids Research http://dx.doi.org/10.1093/nar/gkv834

DNA binding fluorescent proteins for the direct visualization of large DNA molecules.

Fluorescent proteins that also bind DNA molecules are useful reagents for a broad range of biological applications because they can be optically localized and tracked within cells, or provide versatile labels for in vitro experiments. We report a novel design for a fluorescent, DNA-binding protein (FP-DBP) that completely ‘paints’ entire DNA molecules, whereby sequence-independent DNA binding is accomplished by linking a fluorescent protein to two small peptides (KWKWKKA) using lysine for binding to the DNA phosphates, and tryptophan for intercalating between DNA bases. Importantly, this ubiquitous binding motif enables fluorescent proteins (Kd = 14.7 μM) to confluently stain DNA molecules and such binding is reversible via pH shifts. These proteins offer useful robust advantages for single DNA molecule studies: lack of fluorophore mediated photocleavage and staining that does not perturb polymer contour lengths. Accordingly, we demonstrate confluent staining of naked DNA molecules presented within microfluidic devices, or localized within live bacterial cells.

Peptide Desorption Kinetics from Single Molecule Force Spectroscopy Studies

We use a combined experimental/theoretical approach to determine the intrinsic monomeric desorption rate k0 of polytyrosine and polylysine homopeptides from flat surfaces. To this end, single polypeptide molecules are covalently attached to an AFM cantilever tip and desorbed from hydrophobic self-assembled monolayers in two complementary experimental protocols. In the constant-pulling-velocity protocol, the cantilever is moved at finite velocity away from the surface and the distance at which the constant plateau force regime ends and the polymer detaches is recorded. In the waiting-time protocol, the cantilever is held at a fixed distance above the surface and the time until the polymer detaches is recorded. The desorption plateau force is varied between 10 and 90 pN, by systematically changing the aqueous solvent quality via the addition of ethanol or salt. A simultaneous fit of the experimental data from both protocols with simple two-state kinetic polymer theory allows to unambiguously disentangle and determine the model parameters corresponding to polymer contour length L, Kuhn length a, adsorption free energy λ, and intrinsic monomeric desorption rate k0. Crucial to our analysis is that a statistically significant number of single-polymer desorption experiments are done with one and the same single polymer molecule for different solvent qualities. The surprisingly low value of about k0 ≈ 10(5) Hz points to significant cooperativity in the desorption process of single polymers.

The topological glass in ring polymers

We study the dynamics of concentrated, long, semi-flexible, unknotted and unlinked ring polymers embedded in a gel by Monte Carlo simulation of a coarse-grained model. This involves the ansatz that the rings compactify into a duplex structure where they can be modelled as linear polymers. The classical polymer glass transition involves a rapid loss of microscopic freedom within the polymer molecule as the temperature is reduced toward Tg. Here we are interested in temperatures well above Tg where the polymers retain high microscopic mobility. We analyse the slowing of stress relaxation originating from inter-ring penetrations (threadings). For long polymers an extended network of quasi-topological penetrations forms. The longest relaxation time appears to depend exponentially on the ring polymer contour length, reminiscent of the usual exponential slowing (e.g., with temperature) in classical glasses. Finally, we discuss how this represents a universality class for glassy dynamics.

Simulation and modelling of slip flow over surfaces grafted with polymer brushes and glycocalyx fibres

Fabrication of functionalized surfaces using polymer brushes is a relatively simple process and parallels the presence of glycocalyx filaments coating the luminal surface of our vasculature. In this paper, we perform atomistic-like simulations based on dissipative particle dynamics (DPD) to study both polymer brushes and glycocalyx filaments subject to shear flow, and we apply mean-field theory to extract useful scaling arguments on their response. For polymer brushes, a weak shear flow has no effect on the brush density profile or its height, while the slip length is independent of the shear rate and is of the order of the brush mesh size as a result of screening by hydrodynamic interactions. However, for strong shear flow, the polymer brush is penetrated deeper and is deformed, with a corresponding decrease of the brush height and an increase of the slip length. The transition from the weak to the strong shear regime can be described by a simple 'blob' argument, leading to the scaling γ̇0 ∝ σ3/2, where γ̇0 is the critical transition shear rate and σ is the grafting density. Furthermore, in the strong shear regime, we observe a cyclic dynamic motion of individual polymers, causing a reversal in the direction of surface flow. To study the glycocalyx layer, we first assume a homogeneous flow that ignores the discrete effects of blood cells, and we simulate microchannel flows at different flow rates. Surprisingly, we find that, at low Reynolds number, the slip length decreases with the mean flow velocity, unlike the behaviour of polymer brushes, for which the slip length remains constant under similar conditions. (The slip length and brush height are measured with respect to polymer mesh size and polymer contour length, respectively.) We also performed additional DPD simulations of blood flow in a tube with walls having a glycocalyx layer and with the deformable red blood cells modelled accurately at the spectrin level. In this case, a plasma cell-free layer is formed, with thickness more than three times the glycocalyx layer. We then find our scaling arguments based on the homogeneous flow assumption to be valid for this physiologically correct case as well. Taken together, our findings point to the opposing roles of conformational entropy and bending rigidity - dominant effects for the brush and glycocalyx, respectively - which, in turn, lead to different flow characteristics, despite the apparent similarity of the two systems.

Substrate-Independent Method for Growing and Modulating the Density of Polymer Brushes from Surfaces by ATRP

We describe a method for grafting PEG-based polymer chains of variable surface density using a substrate independent approach, allowing grafting from virtually any material substrate. The approach relies upon initial coupling of a macroinitiator to plasma polymer treated surfaces. The macroinitiator is a novel random terpolymer containing ATRP initiator residues, strongly negatively charged groups, and carboxylic acid moieties that facilitate covalent surface anchoring. Surface-initiated ATRP (SI-ATRP) using polyethylene glycol methyl ether methacrylate (PEGMA) at different concentrations led to grafted surfaces of controlled thickness in either the "brush" or "mushroom" morphology, which was controlled by the abundance of initiator residues in the macroinitiator. Grafted polymer layer structure was investigated via direct interaction force measurements using colloid probe atomic force microscopy (AFM). Equilibrium, hydrated graft layer thicknesses inferred from the highly repulsive AFM force data suggest that the polymer brush graft layer contained polymer chains which were fully stretched. Since the degree of stretching resulted in layer thicknesses approaching the polymer contour length, the polymer brushes studied must be very close to maximum graft density. Grafted layers where the polymer molecules were in the mushroom regime resulted in much thinner layers but the chains had greater chain entropic freedom as indicated by strongly attractive bridging interactions between tethered chains and the silica colloid probe. Use of this experimental methodology would be suitable for preparing grafted polymer layers of a preferred density free from substrate-specific linking chemistries.

PH-triggered shape response of cubical ultrathin hydrogel capsules

We report on two types of poly(methacrylic acid) (PMAA)-based hydrogel microcontainers (capsules) of cubical shape with distinctly different shape responses upon pH variations. The microcontainers were prepared as replicas of cubical inorganic templates through chemical cross-linking of hydrogen-bonded layer-by-layer (LbL) films. The two types of hollow hydrogels, a single-component (PMAA) and PMAA–poly(N-vinylpyrrolidone) (PMAA–PVPON), showed drastic differences in their shape response to pH variations. Cubical (PMAA)20 capsules turned into bulged sphere-like structures of the same size when transitioned from pH 3 to pH 8. In contrast, cubical (PMAA–PVPON)5 capsules retained their cubical shape at pH 3 while increasing in size at pH 8. The pH-triggered size change of cubical capsules was completely reversible. The difference in pH-triggered shape responses was rationalized through the difference in hydrogel rigidity expressed as the ratio of the polymer contour length between the neighboring cross-links to the persistence polymer length. The ratios of 22.7 and 2 for (PMAA) and (PMAA–PVPON) systems, respectively, suggested that the dual-component system is more rigid and therefore expands uniformly in all directions. We believe that the results provide new prospects for developing polymeric materials with predictable shape and size-changing properties for controlled drug delivery, cellular uptake, and pH-regulating transport behavior in microfluidic devices.

Anisotropic Hydrodynamic Mean-Field Theory for Semiflexible Polymers under Tension

We introduce an anisotropic mean-field approach for the dynamics of semiflexible polymers under intermediate tension, the force range where a chain is partially extended but not in the asymptotic regime of a nearly straight contour. The theory is designed to exactly reproduce the lowest order equilibrium averages of a stretched polymer, and it treats the full complexity of the problem: the resulting dynamics include the coupled effects of long-range hydrodynamic interactions, backbone stiffness, and large-scale polymer contour fluctuations. Validated by Brownian hydrodynamics simulations and comparison to optical tweezer measurements on stretched DNA, the theory is highly accurate in the intermediate tension regime over a broad dynamical range, without the need for additional dynamic fitting parameters.

Constrained random-force model for weakly bending semiflexible polymers

The random-force (Larkin) model of a directed elastic string subject to quenched random forces in the transverse directions has been a paradigm in the statistical physics of disordered systems. In this Brief Report, we investigate a modified version of the above model where the total transverse force along the polymer contour and the related total torque, in each realization of disorder, vanish. We discuss the merits of adding these constraints and show that they leave the qualitative behavior in the strong stretching regime unchanged, but they reduce the effects of the random force by significant numerical prefactors. We also show that a transverse random force effectively makes the filament softer to compression by inducing undulations. We calculate the related linear compression coefficient in both the usual and the constrained random-force model.

Microscopic origin of the terminal relaxation time in polymer nanocomposites: an experimental precedent

By means of rheology and neutron spin echo spectroscopy, both a macroscopic and a microscopic view on the relaxation dynamics of polymers in the presence of non-attractive nanoparticles could be realized. The results enabled us to show a direct correlation between the microscopically observed confinement length and the macroscopically measured dissipation maximum, which corresponds to the terminal relaxation time. Moreover, the impact of nanoparticle presence on the effectiveness of polymer contour length fluctuations and constraint release is discussed.

Molecular Stress Relief through a Force-Induced Irreversible Extension in Polymer Contour Length

Single-molecule force spectroscopy is used to observe the irreversible extension of a gem-dibromocyclopropane (gDBC)-functionalized polybutadiene under tension, a process akin to polymer necking at a single-molecule level. The extension of close to 28% in the contour length of the polymer backbone occurs at roughly 1.2 nN (tip velocity of 3 μm/s) and is attributed to the force-induced isomerization of the gDBCs into 2,3-dibromoalkenes. The rearrangement represents a possible new mechanism for localized stress relief in polymers and polymer networks under load, and the quantification of the force dependency provides a benchmark value for further studies of mechanically triggered chemistry in bulk polymers.