Semiflexible Polymer Networks Research Articles

Active Diffusion of Self-Propelled Particles in Semiflexible Polymer Networks

Active Diffusion of Self-Propelled Particles in Semiflexible Polymer Networks

The structure and mechanics of the cell cortex depend on the location and adhesion state

Cells exist in different phenotypes and can transition between them. A phenotype may be characterized by many different aspects. Here, we focus on the example of whether the cell is adhered or suspended and choose particular parameters related to the structure and mechanics of the actin cortex. The cortex is essential to cell mechanics, morphology, and function, such as for adhesion, migration, and division of animal cells. To predict and control cellular functions and prevent malfunctioning, it is necessary to understand the actin cortex. The structure of the cortex governs cell mechanics; however, the relationship between the architecture and mechanics of the cortex is not yet well enough understood to be able to predict one from the other. Therefore, we quantitatively measured structural and mechanical cortex parameters, including cortical thickness, cortex mesh size, actin bundling, and cortex stiffness. These measurements required developing a combination of measurement techniques in scanning electron, expansion, confocal, and atomic force microscopy. We found that the structure and mechanics of the cortex of cells in interphase are different depending on whether the cell is suspended or adhered. We deduced general correlations between structural and mechanical properties and show how these findings can be explained within the framework of semiflexible polymer network theory. We tested the model predictions by perturbing the properties of the actin within the cortex using compounds. Our work provides an important step toward predictions of cell mechanics from cortical structures and suggests how cortex remodeling between different phenotypes impacts the mechanical properties of cells.

Nonlinear Poisson effect in affine semiflexible polymer networks.

Stretching an elastic material along one axis typically induces contraction along the transverse axes, a phenomenon known as the Poisson effect. From these strains, one can compute the specific volume, which generally either increases or, in the incompressible limit, remains constant as the material is stretched. However, in networks of semiflexible or stiff polymers, which are typically highly compressible yet stiffen significantly when stretched, one instead sees a significant reduction in specific volume under finite strains. This volume reduction is accompanied by increasing alignment of filaments along the strain axis and a nonlinear elastic response, with stiffening of the apparent Young's modulus. For semiflexible networks, in which entropic bending elasticity governs the linear elastic regime, the nonlinear Poisson effect is caused by the nonlinear force-extension relationship of the constituent filaments, which produces a highly asymmetric response of the constituent polymers to stretching and compression. The details of this relationship depend on the geometric and elastic properties of the underlying filaments, which can vary greatly in experimental systems. Here, we provide a comprehensive characterization of the nonlinear Poisson effect in an affine network model and explore the influence of filament properties on essential features of both microscopic and macroscopic response, including strain-driven alignment and volume reduction.

A Science Friction Story: Molecular Interactions in Semiflexible Polymer Networks

AbstractEstablished model theories, developed to capture the mechanical behavior of soft, complex materials composed of semiflexible polymers, assume that entropic interactions between filaments are primarily responsible for determining the mechanical response. In recent studies, the generally accepted tube model has been challenged in terms of this basic assumption about filament–filament interactions, but also because of its predictions regarding the frequency dependence of the elastic modulus in the intermediate frequency regime. A central question is how molecular interactions and friction between network constituents influence the rheological response of isotropic entangled networks of semiflexible polymers. It has been previously shown that friction forces between aligned pairs of actin filaments are not negligible. Here, the influence of friction forces and attractive interactions on network rheology is systematically investigated by means of targeted surface modification. It is shown that these forces have a qualitative and quantitative influence on the viscoelastic properties of semiflexible polymer networks and contribute to their response to nonlinear deformations. By comparing two polymer model systems with respect to their surface compositions, a possible explanation is given about the origin of acting forces on a molecular level.

Highly flexible PEG-LifeAct constructs act as tunable biomimetic actin crosslinkers.

In vitro studies of actin filament networks crosslinked with dynamic actin binding proteins provide critical insights into cytoskeletal mechanics as well as inspiration for new adaptive materials design. However, discontinuous variance in the physiochemical properties of actin binding proteins impedes holistic relationships between crosslinker molecular parameters, network structure, and mechanics. Bio-synthetic constructs composed of synthetic polymer backbones and actin binding motifs would enable crosslinkers with engineered physiochemical properties to directly target the desired structure-property relationships. As a proof of concept, bio-synthetic crosslinkers composed of highly flexible polyethylene glycol (PEG) polymers functionalized with the actin binding peptide LifeAct, are explored as actin crosslinkers. Using bulk rheology and fluorescence microscopy, these constructs are shown to modulate actin filament network structure and mechanics in a contour length dependent manner, while maintaining the stress-stiffening behavior inherent to actin filament networks. These results encourage the design of more diverse and complex peptide-polymer crosslinkers to interrogate and control semi-flexible polymer networks.

Mechanical criticality of fiber networks at a finite temperature.

At zero temperature, spring networks with connectivity below Maxwell's isostatic threshold undergo a mechanical phase transition from a floppy state at small strains to a rigid state for applied shear strain above a critical strain threshold. Disordered networks in the floppy mechanical regime can be stabilized by entropic effects at finite temperature. We develop a scaling theory for this mechanical phase transition at finite temperature, yielding relationships between various scaling exponents. Using Monte Carlo simulations, we verify these scaling relations and identify anomalous entropic elasticity with sublinear T dependence in the linear elastic regime. While our results are consistent with prior studies of phase behavior near the isostatic point, the present work also makes predictions relevant to the broad class of disordered thermal semiflexible polymer networks for which the connectivity generally lies far below the isostatic threshold.

Nonequilibrium diffusion of active particles bound to a semiflexible polymer network: Simulations and fractional Langevin equation.

In a viscoelastic environment, the diffusion of a particle becomes non-Markovian due to the memory effect. An open question concerns quantitatively explaining how self-propulsion particles with directional memory diffuse in such a medium. Based on simulations and analytic theory, we address this issue with active viscoelastic systems where an active particle is connected with multiple semiflexible filaments. Our Langevin dynamics simulations show that the active cross-linker displays superdiffusive and subdiffusive athermal motion with a time-dependent anomalous exponent α. In such viscoelastic feedback, the active particle always exhibits superdiffusion with α = 3/2 at times shorter than the self-propulsion time (τA). At times greater than τA, the subdiffusive motion emerges with α bounded between 1/2 and 3/4. Remarkably, active subdiffusion is reinforced as the active propulsion (Pe) is more vigorous. In the high Pe limit, athermal fluctuation in the stiff filament eventually leads to α = 1/2, which can be misinterpreted with the thermal Rouse motion in a flexible chain. We demonstrate that the motion of active particles cross-linking a network of semiflexible filaments can be governed by a fractional Langevin equation combined with fractional Gaussian noise and an Ornstein-Uhlenbeck noise. We analytically derive the velocity autocorrelation function and mean-squared displacement of the model, explaining their scaling relations as well as the prefactors. We find that there exist the threshold Pe (Pe∗) and crossover times (τ∗ and τ†) above which active viscoelastic dynamics emerge on timescales of τ∗≲ t ≲ τ†. Our study may provide theoretical insight into various nonequilibrium active dynamics in intracellular viscoelastic environments.

Nonaffine Deformation of Semiflexible Polymer and Fiber Networks

Networks of semiflexible or stiff polymers such as most biopolymers are known to deform inhomogeneously when sheared. The effects of such nonaffine deformation have been shown to be much stronger than for flexible polymers. To date, our understanding of nonaffinity in such systems is limited to simulations or specific 2D models of athermal fibers. Here, we present an effective medium theory for nonaffine deformation of semiflexible polymer and fiber networks, which is general to both 2D and 3D and in both thermal and athermal limits. The predictions of this model are in good agreement with both prior computational and experimental results for linear elasticity. Moreover, the framework we introduce can be extended to address nonlinear elasticity and network dynamics.

Linear polymer chain diffusion in semi-flexible polymer network: A dissipative particle dynamics study

Linear polymer chains transport in the crowded biological environment is profoundly important to biomedical engineering and nanotechnology. Cytoskeleton, which can be modeled as a semi-flexible polymer network, acts as a barrier when linear polymers diffuse inside the cell. The diffusion of linear polymers with length N in this polymer network is investigated by the dissipative particle dynamics (DPD) in the present study. Rouse theory is applied to analyze the conformational dynamics of the linear polymers based on the numerical results. It is found that the geometric constraint length Na is a crucial parameter to describe the role of the network of the polymer diffusion. Analyses on Rouse modes show that, in a short wavelength regime, the relaxation time obtained in numerical simulation follows the prediction of the Rouse theory. With the increasing wavelength, the linear polymer exhibits a transition from reptation behavior to the spatially homogeneous behavior at critical length scale Na, which is illustrated by different scaling laws dependent on wavelength. Based on the analyses on the Rouse modes and mean square displacements of the linear polymer, we present a non-dimensional conformational dynamics function dependent on time, with which a scaling law is proposed to predict the long time diffusivity of the linear polymer in a semi-flexible polymer network with different mesh sizes. It is shown that the prediction is well consistent with our DPD simulation results.

Systematic altering of semiflexible DNA-based polymer networks via tunable crosslinking.

In order to understand and predict the mechanical behaviours of complex, soft biomaterials such as cells or stimuli-responsive hydrogels, it is important to connect how the nanoscale properties of their constituent components impact those of the bulk material. Crosslinked networks of semiflexible polymers are particularly ubiquitous, being underlying mechanical components of biological systems such as cells or ECM, as well as many synthetic or biomimetic materials. Cell-derived components such as filamentous biopolymers or protein crosslinkers are readily available and well-studied model systems. However, as evolutionarily derived materials, they are constrained to a fixed set of structural parameters such as the rigidity and size of the filaments, or the valency and strength of binding of crosslinkers forming inter-filament connections. By implementing a synthetic model system based on the self-assembly of DNA oligonucleotides into nanometer-scale tubes and simple crosslinking constructs, we used the thermodynamic programmability of DNA hybridization to explore the impact of binding affinity on bulk mechanical response. Stepwise tuning the crosslinking affinity over a range from transient to thermodynamically stable shows an according change in viscoelastic behaviour from loosely entangled to elastic, consistent with models accounting for generalized inter-filament interactions. While characteristic signatures of concentration-dependent changes in network morphology found in some other natural and synthetic filament-crosslinker systems were not apparent, the presence of a distinct elasticity increase within a narrow range of conditions points towards potential subtle alterations of crosslink-filament architecture. Here, we demonstrate a new synthetic approach for gaining a deeper understanding of both biological as well as engineered hydrogel systems.

Structural Features and Nonlinear Rheology of Self-Assembled Networks of Cross-Linked Semiflexible Polymers.

Disordered networks of semiflexible filaments are common support structures in biology. Familiar examples include fibrous matrices in blood clots, bacterial biofilms, and essential components of cells and tissues of plants, animals, and fungi. Despite the ubiquity of these networks in biomaterials, we have only a limited understanding of the relationship between their structural features and their highly strain-sensitive mechanical properties. In this work, we perform simulations of three-dimensional networks produced by the irreversible formation of cross-links between linker-decorated semiflexible filaments. We characterize the structure of networks formed by a simple diffusion-dependent assembly process and measure their associated steady-state rheological features at finite temperature over a range of applied prestrains that encompass the strain-stiffening transition. We quantify the dependence of network connectivity on cross-linker availability and detail the associated connectivity dependence of both linear elasticity and nonlinear strain-stiffening behavior, drawing comparisons with prior experimental measurements of the cross-linker concentration-dependent elasticity of actin gels.

Constraint Release for Reptating Filaments in Semiflexible Networks Depends on Background Fluctuations.

Entangled semiflexible polymer networks are usually described by the tube model, although this concept has not been able to explain all experimental observations. One of its major shortcomings is neglecting the thermal fluctuations of the polymers surrounding the examined test filament, such that disentanglement effects are not captured. In this study, we present experimental evidence that correlated constraint release which has been predicted theoretically occurs in entangled, but not in crosslinked semiflexible polymer networks. By tracking single semiflexible DNA nanotubes embedded both in entangled and crosslinked F-actin networks, we observed different reptation dynamics in both systems, emphasizing the need for a revision of the classical tube theory for entangled polymer solutions.

Mechanics of 3D Cell-Hydrogel Interactions: Experiments, Models, and Mechanisms.

Hydrogels are highly water-swollen molecular networks that are ideal platforms to create tissue mimetics owing to their vast and tunable properties. As such, hydrogels are promising cell-delivery vehicles for applications in tissue engineering and have also emerged as an important base for ex vivo models to study healthy and pathophysiological events in a carefully controlled three-dimensional environment. Cells are readily encapsulated in hydrogels resulting in a plethora of biochemical and mechanical communication mechanisms, which recapitulates the natural cell and extracellular matrix interaction in tissues. These interactions are complex, with multiple events that are invariably coupled and spanning multiple length and time scales. To study and identify the underlying mechanisms involved, an integrated experimental and computational approach is ideally needed. This review discusses the state of our knowledge on cell-hydrogel interactions, with a focus on mechanics and transport, and in this context, highlights recent advancements in experiments, mathematical and computational modeling. The review begins with a background on the thermodynamics and physics fundamentals that govern hydrogel mechanics and transport. The review focuses on two main classes of hydrogels, described as semiflexible polymer networks that represent physically cross-linked fibrous hydrogels and flexible polymer networks representing the chemically cross-linked synthetic and natural hydrogels. In this review, we highlight five main cell-hydrogel interactions that involve key cellular functions related to communication, mechanosensing, migration, growth, and tissue deposition and elaboration. For each of these cellular functions, recent experiments and the most up to date modeling strategies are discussed and then followed by a summary of how to tune hydrogel properties to achieve a desired functional cellular outcome. We conclude with a summary linking these advancements and make the case for the need to integrate experiments and modeling to advance our fundamental understanding of cell-matrix interactions that will ultimately help identify new therapeutic approaches and enable successful tissue engineering.

The role of vimentin–nuclear interactions in persistent cell motility through confined spaces

The ability of cells to move through small spaces depends on the mechanical properties of the cellular cytoskeleton and on nuclear deformability. In mammalian cells, the cytoskeleton is composed of three interacting, semi-flexible polymer networks: actin, microtubules, and intermediate filaments (IF). Recent experiments of mouse embryonic fibroblasts with and without vimentin have shown that the IF vimentin plays a role in confined cell motility. Here, we develop a minimal model of a cell moving through a microchannel that incorporates explicit effects of actin and vimentin and implicit effects of microtubules. Specifically, the model consists of a cell with an actomyosin cortex and a deformable cell nucleus and mechanical linkages between the two. By decreasing the amount of vimentin, we find that the cell speed increases for vimentin-null cells compared to cells with vimentin. The loss of vimentin increases nuclear deformation and alters nuclear positioning in the cell. Assuming nuclear positioning is a read-out for cell polarity, we propose a new polarity mechanism which couples cell directional motion with cytoskeletal strength and nuclear positioning and captures the abnormally persistent motion of vimentin-null cells, as observed in experiments. The enhanced persistence indicates that the vimentin-null cells are more controlled by the confinement and so less autonomous, relying more heavily on external cues than their wild-type counterparts. Our modeling results present a quantitative interpretation for recent experiments and have implications for understanding the role of vimentin in the epithelial–mesenchymal transition.

Segmental Lennard-Jones interactions for semi-flexible polymer networks

ABSTRACT Simulating soft matter systems such as the cytoskeleton can enable deep understanding of experimentally observed phenomena. One challenge of modelling such systems is realistic description of the steric repulsion between nearby polymers. Previous models of the polymeric excluded volume interaction have the deficit of being non-analytic, being computationally expensive, or allowing polymers to erroneously cross each other. A recent solution to these issues, implemented in the MEDYAN simulation platform, uses analytical expressions obtained from integrating an interaction kernel along the lengths of two polymer segments to describe their repulsion. Here, we extend this model by re-deriving it for lower-dimensional geometrical configurations, deriving similar expressions using a steeper interaction kernel, comparing it to other commonly used potentials, and showing how to parameterise these models. We also generalise this new integrated style of potential by introducing a segmental Lennard-Jones potential, which enables modelling both attractive and repulsive interactions in semi-flexible polymer networks. These results can be further generalised to facilitate the development of effective interaction potentials for other finite elements in simulations of softmatter systems.

Shear rheology and scaling of semiflexible polymers: Effect of polymer‐solvent interactions in the semidilute regime

AbstractSemiflexible polymers and their assemblies are important in biology as cross‐linked networks of semiflexible polymers form a major structural component of tissue and living cells. This research used shear rheology to demonstrate the tuning from worm‐like to rod‐like conformation in semiflexible polymers by polymer‐solvent interactions. The conformation was assessed by the persistence length lp, and its influence, in the semidilute regime, was assessed by the scaling of zero‐shear viscosity ηo with concentration c and molecular weight . The polymers were poly n‐butyl and poly n‐octyl isocyanate (PBIC and POIC, respectively). PBIC exhibited the largest lp in chlorinated solvents, and the solutions obeyed the scaling law . However, when PBIC was dissolved in benzene the lp was greatly reduced and the scaling law now was , consistent with a worm‐like conformation. On the other hand, POIC dissolved in chlorinated and benzenic solvents exhibited a worm‐like conformation and the scaling was . These results were contrasted with those of hydroxypropyl cellulose (HPC) aqueous solutions, which exhibit worm‐like conformation, the solutions obeyed the scaling ηo ∝ c2.5. Finally, the shear viscosity of the polyisocyanates and HPC obeyed the Saito scaling, valid for anisotropic particles in solution.

Structure and Mechanics of Bundled Semiflexible Polymer Networks

Fibrous networks of semiflexible polymers are prevalent in biological materials such as connective tissues, the cytoskeleton, and biofilm extracellular matrices. While the mechanical behavior of pe...

Spectroscopic photonic force optical coherence elastography.

We demonstrate spectroscopic photonic force optical coherence elastography (PF-OCE). Oscillations of microparticles embedded in viscoelastic hydrogels were induced by harmonically modulated optical radiation pressure and measured by phase-sensitive spectral-domain optical coherence tomography. PF-OCE can detect microparticle displacements with pico- to nano-meter sensitivity and millimeter-scale volumetric coverage. With spectroscopic PF-OCE, we quantified viscoelasticity over a broad frequency range from 1Hz to 7kHz, revealing rich microstructural dynamics of polymer networks across multiple microrheological regimes. Reconstructed frequency-dependent loss moduli of polyacrylamide hydrogels were observed to follow a general power scaling law G''∼ω0.75, consistent with that of semiflexible polymer networks. Spectroscopic PF-OCE provides an all-optical approach to microrheological studies with high sensitivity and high spatiotemporal resolution, and could be especially beneficial for time-lapse and volumetric mechanical characterization of viscoelastic materials.

Emergence of tissue-like mechanics from fibrous networks confined by close-packed cells.

The viscoelasticity of the crosslinked semiflexible polymer networks-such as the internal cytoskeleton and the extracellular matrix-thatprovide shape and mechanical resistance against deformationis assumed to dominate tissue mechanics.However, the mechanical responses of soft tissues and semiflexible polymer gels differ in many respects. Tissues stiffen in compression but not in extension1-5, whereas semiflexible polymer networks soften in compression and stiffen in extension6,7. In shear deformation, semiflexible polymer gels stiffen with increasing strain, but tissues do not1-8. Here we use multiple experimental systems and a theoretical model to show that a combination of nonlinear polymer network elasticity and particle (cell) inclusions is essential to mimic tissue mechanics that cannot be reproduced by either biopolymer networks or colloidal particle systems alone. Tissue rheology emerges from an interplay between strain-stiffening polymer networks and volume-conserving cells within them. Polymer networks that soften in compression but stiffen in extension can be converted to materials that stiffen in compression but not in extension by including within the network either cells or inert particles to restrict the relaxation modes of the fibrous networks that surround them. Particle inclusions also suppress stiffening in shear deformation; when the particle volume fraction is low, they have little effect on the elasticity of the polymer networks. However, as the particles become more closely packed, the material switches from compression softening to compression stiffening. The emergence of an elastic response in these composite materials has implications for how tissue stiffness is altered in disease and can lead to cellular dysfunction9-11. Additionally, the findings could be used in the design of biomaterials with physiologically relevant mechanical properties.

Relaxation dynamics of semiflexible treelike small-world polymer networks.

We study the relaxation dynamics of the polymer networks that are constructed based on a degree distribution specific to small-world networks. The employed building algorithm generates polymers with a large variety of architectures, thus allowing for a detailed study of the structural transition from a pure linear chain to dendritic polymer networks. This is done by varying a single parameter p, which measures the randomness in the degree of the network's nodes. The dynamics is investigated in the framework of the generalized Gaussian structures model by monitoring the influence of the parameter p and of the stiffness parameter q on the behavior of the relaxation quantities: averaged monomer displacement, storage modulus, and loss modulus. The structure properties of the constructed polymers are described by the mean-square radius of gyration. In the absence of stiffness, in the intermediate frequencies domain of the dynamical quantities we encounter different behaviours, such as a dendritic behavior followed by a linear one for very small values of p or a single well-marked dendritic behavior for higher values of p. The stiffness parameter q influences drastically the relaxation dynamics of these polymer networks and in general no evident scaling regions were encountered. However, for some values of the parameter set (p,q), such as (0.8,0.4), an extremely short constant slope region, less than one order of magnitude, was found.