Exchangeable Liquid Crystalline Elastomers and Their Applications.

This Review presents and discusses the current state of the art in "exchangeable liquid crystalline elastomers", that is, LCE materials utilizing dynamically cross-linked networks capable of reprocessing, reprogramming, and recycling. The focus here is on the chemistry and the specific reaction mechanisms that enable the dynamic bond exchange, of which there is a variety. We compare and contrast these different chemical mechanisms and the key properties of their resulting elastomers. In the conclusion, we discuss the most promising applications that are enabled by dynamic cross-linking and present a summary table: a library of currently available materials and their main characteristics.

Thiol-acrylate side-chain liquid crystal elastomers.

The Michael addition 'click' chemistry was used to graft acrylate-terminated mesogenic groups onto the polysiloxane backbone polymer chain with thiol functional groups, with a constant 15% fraction of diacrylate reacting monomers as crosslinkers. Three different types of mesogens were used, and also their 50 : 50 mixtures, and in all cases we have obtained the smectic-A phase of the resulting liquid crystalline elastomer. Using X-ray diffraction, calorimetry and dynamic mechanical analysis, we investigated the relationship between the molecular structure of mesogenic side groups and the structure and properties of the elastomers. The shape-memory of smectic elastomers was verified. The unusual features were the semi-crystalline nature of elastomers with non-polar mesogens and the clear role of side-by-side rod dimerization of polar mesogens leading to a higher smectic layer spacing. We investigated the evolution of the smectic alignment on uniaxial stretching along the layer normal and identified two distinct ways in which the elastomer responds: the coarsened Helfrich-Hurault zig-zag layer texture and the large-scale stripe domains of uniform layer rotation in the systems with lower order parameter and the associated layer constraints.

Why exercise builds muscles: titin mechanosensing controls skeletal muscle growth under load.

Muscles sense internally generated and externally applied forces, responding to these in a coordinated hierarchical manner at different timescales. The center of the basic unit of the muscle, the sarcomeric M-band, is perfectly placed to sense the different types of load to which the muscle is subjected. In particular, the kinase domain of titin (TK) located at the M-band is a known candidate for mechanical signaling. Here, we develop a quantitative mathematical model that describes the kinetics of TK-based mechanosensitive signaling and predicts trophic changes in response to exercise and rehabilitation regimes. First, we build the kinetic model for TK conformational changes under force: opening, phosphorylation, signaling, and autoinhibition. We find that TK opens as a metastable mechanosensitive switch, which naturally produces a much greater signal after high-load resistance exercise than an equally energetically costly endurance effort. Next, for the model to be stable and give coherent predictions, in particular for the lag after the onset of an exercise regime, we have to account for the associated kinetics of phosphate (carried by ATP) and for the nonlinear dependence of protein synthesis rates on muscle fiber size. We suggest that the latter effect may occur via the steric inhibition of ribosome diffusion through the sieve-like myofilament lattice. The full model yields a steady-state solution (homeostasis) for muscle cross-sectional area and tension and, a quantitatively plausible hypertrophic response to training, as well as atrophy after an extended reduction in tension.

Guided assembly of cancer ellipsoid on suspended hydrogel microfibers estimates multi-cellular traction force.

Three-dimensional (3D) multi-cellular aggregates hold important applications in tissue engineering and in vitro biological modeling. Probing the intrinsic forces generated during the aggregation process, could open up new possibilities in advancing the discovery of tissue mechanics-based biomarkers. We use individually suspended, and tethered gelatin hydrogel microfibers to guide multicellular aggregation of brain cancer cells (glioblastoma cell line, U87), forming characteristic cancer 'ellipsoids'. Over a culture period of up to 13 days, U87 aggregates evolve from a flexible cell string with cell coverage following the relaxed and curly fiber contour; to a distinct ellipsoid-on-string morphology, where the fiber segment connecting the ellipsoid poles become taut. Fluorescence imaging revealed the fiber segment embedded within the ellipsoidal aggregate to exhibit a morphological transition analogous to filament buckling under a compressive force. By treating the multicellular aggregate as an effective elastic medium where the microfiber is embedded, we applied a filament post-buckling theory to model the fiber morphology, deducing the apparent elasticity of the cancer ellipsoid medium, as well as the collective traction force inherent in the aggregation process.

Continuous spinning aligned liquid crystal elastomer fibers with a 3D printer setup.

Fibrous liquid crystalline elastomers (LCE) are an attractive variant of LCE-based actuators due to their small thickness, leading to faster response times to stimuli, as well as the increased mechanical strength. Fabrication of LCE fibers has been attempted by various research groups using electro-spinning or micro-fluidic techniques, without much success. Here we propose an alternative way to achieve single-step continuous spinning LCE fibers in a more scalable and robust way, based on a liquid-ink 3D printer. We demonstrate this technique in our home-made device by dynamically extruding/stretching liquid crystalline oligomer mixed with photo-reactive cross-linker, to fix the aligned network under UV light after extrusion. The report also describes a protocol for material synthesis and identifies optimal conditions for the stable fiber spinning process. Microns-thick LCE fibers with two different compositions have been successfully spun, and demonstrated enhanced mechanical properties with the inherited thermal-actuation capability. This technique also demonstrates the potential to fine-tune the mechanical properties of fibers to enable further development in fiber-based LCE applications.

Development of Nascent Focal Adhesions in Spreading Cells.

The eukaryotic cell develops organelles to sense and respond to the mechanical properties of its surroundings. These mechanosensing organelles aggregate into symmetry-breaking patterns to mediate cell motion and differentiation on substrate. The spreading of a cell plated onto a substrate is one of the simplest paradigms in which angular symmetry-breaking assemblies of mechanical sensors are seen to develop. We review evidence for the importance of the edge of the cell-extracellular matrix adhesion area in the aggregation of mechanosensors and develop a theoretical model for the clustering of mechanosensors into nascent focal adhesions on this contact ring. To study the spatial patterns arising on this topological feature, we use a one-dimensional lattice model with a nearest-neighbor interaction between individual integrin-mediated mechanosensors. We find the effective Ginzburg-Landau free energy for this model and determine the spectrum of spatial modes as the cell spreads and increases its contact area with the substrate. To test our model, we compare its predictions with measured distributions of paxillin in spreading fibroblasts.

Rates of transesterification in epoxy-thiol vitrimers.

Vitrimers, an important subset of dynamically crosslinked polymer networks, have many technological applications for their excellent properties, and the ability to be re-processed through plastic flow above the so-called vitrification temperature. We report a simple and efficient method of generating such adaptive crosslinked networks relying on transesterification for their bond exchange by utilising the 'click' chemistry of epoxy and thiols, which also has the advantage of a low glass transition temperature. We vary the chemical structure of thiol spacers to probe the effects of concentration and the local environment of ester groups on the macroscopic elastic-plastic transition. The thermal activation energy of transesterification bond exchange is determined for each chemical structure, and for a varying concentration of catalyst, establishing the conditions for the optimal, and for the suppressed bond exchange. However, we also discover that the temperature of elastic-plastic transition is strongly affected by the stiffness (dynamic rubber modulus) of the network, with softer networks having a much lower vitrification temperature even when their bond-exchange activation energy is higher. This combination of chemical and physical control factors should help optimise the processability of vitrimer plastics.

Universal Kinetics of the Onset of Cell Spreading on Substrates of Different Stiffness.

When plated onto substrates, cell morphology and even stem-cell differentiation are influenced by the stiffness of their environment. Stiffer substrates give strongly spread (eventually polarized) cells with strong focal adhesions and stress fibers; very soft substrates give a less developed cytoskeleton and much lower cell spreading. The kinetics of this process of cell spreading is studied extensively, and important universal relationships are established on how the cell area grows with time. Here, we study the population dynamics of spreading cells, investigating the characteristic processes involved in the cell response to the substrate. We show that unlike the individual cell morphology, this population dynamics does not depend on the substrate stiffness. Instead, a strong activation temperature dependence is observed. Different cell lines on different substrates all have long-time statistics controlled by the thermal activation over a single energy barrier ΔG ≈ 18 kcal/mol, whereas the early-time kinetics follows a power law ∼t5. This implies that the rate of spreading depends on an internal process of adhesion complex assembly and activation; the operational complex must have five component proteins, and the last process in the sequence (which we believe is the activation of focal adhesion kinase) is controlled by the binding energy ΔG.

Unfolding of polymers tethered to viscoelastic substrates.

The problem of globular polymer unfolding under applied force is a widely-studied fundamental topic in biological and chemical physics, with important applications in cell biology. Much of the existing theoretical and experimental literature focuses on the case where force is applied while fixing the opposite end of the polymer chain in space. However, in a realistic biological microenvironment, forces will be applied against viscoelastic references, and the deformation of the folded polymer chain will be combined with the deformation of viscoelastic substrate. In this paper, we consider several simple viscoelastic models for the substrate, and show that its relaxation properties determine the unfolding kinetics. In particular, for low pulling forces, substrates with longer relaxation times cause lower unfolding rates for the pulled polymer chain, whereas for high forces, those substrates with longer relaxation times instead produce higher unfolding rates.

A chain mechanism for flagellum growth.

Bacteria swim by means of long flagella extending from the cell surface. These are assembled from thousands of protein subunits translocated across the cell membrane by an export machinery at the base of each flagellum. Unfolded subunits then transit through a narrow channel at the core of the growing flagellum to the tip, where they crystallize into the nascent structure. As the flagellum lengthens outside the cell, the rate of flagellum growth does not change. The mystery is how subunit transit is maintained at a constant rate without a discernible energy source in the channel of the external flagellum. We present evidence for a simple physical mechanism for flagellum growth that harnesses the entropic force of the unfolded subunits themselves. We show that a subunit docked at the export machinery can be captured by a free subunit through head-to-tail linkage of juxtaposed amino (N)- and carboxy (C)-terminal helices. We propose that sequential rounds of linkage would generate a multisubunit chain that pulls successive subunits into and through the channel to the flagellum tip, and by isolating filaments growing on bacterial cells we reveal the predicted chain of head-to-tail linked subunits in the transit channel of flagella. Thermodynamic analysis confirms that links in the subunit chain can withstand the pulling force generated by rounds of subunit crystallization at the flagellum tip, and polymer theory predicts that as the N terminus of each unfolded subunit crystallizes, the entropic force at the subunit C terminus would increase, rapidly overcoming the threshold required to pull the next subunit from the export machinery. This pulling force would adjust automatically over the increasing length of the growing flagellum, maintaining a constant rate of subunit delivery to the tip.

Structural effects of cap, crack, and intrinsic curvature on the microtubule catastrophe kinetics.

Microtubules (MTs) experience an effect called "catastrophe," which is the transition from the MT growth to a sudden dramatic shrinkage in length. The straight guanosine triphosphate (GTP)-tubulin cap at the filament tip and the intrinsic curvature of guanosine diphosphate (GDP)-tubulins are known to be the key thermodynamic factors that determine MT catastrophe, while the hydrolysis of this GTP-cap acts as the kinetic control of the process. Although several theoretical models have been developed, assuming the catastrophe occurs when the GTP-cap shrinks to a minimal stabilizing size, the structural effect of the GTP-cap and GDP-curvature is not explicitly included; thus, their influence on catastrophe kinetics remains less understood. To investigate this structural effect, we apply a single-protofilament model with one GTP-cap while assuming a random hydrolysis mechanism and take the occurrence of a crack in the lateral bonds between neighboring protofilaments as the onset of the catastrophe. Therein, we find the effective potential of the tip along the peel-off direction and formulate the catastrophe kinetics as a mean first-passage time problem, subject to thermal fluctuations. We consider cases with and without a compressive force on the MT tip, both of which give a quadratic effective potential, making MT catastrophe an Ornstein-Uhlenbeck process in our formalism. In the free-standing case, the mean catastrophe time has a sensitive tubulin-concentration dependence, similar to a double-exponential function, and agrees well with the experiment. For a compressed MT, we find a modified exponential function of force that shortens the catastrophe time.

Reprocessable Thermoset Soft Actuators.

Widely used traditional thermosets are good candidates for construction of 3D soft actuators because of their excellent stability; however, it is generally acknowledged that they cannot be reprocessed. The time-temperature equivalence principle enables reprocessing of traditional liquid crystalline epoxy thermosets (LCETs) into 3D soft actuators. Even though the transesterification reaction of LCETs is extremely slow, it is fast enough to induce a topology rearrangement and subsequent reprocessing when prolonging the transesterification time according to aforementioned principle. Therefore, LCETs can be aligned by a simple procedure. The alignment is quite stable at high temperature and remains after more than 1000 heating-cooling actuation cycles. The resulting 3D soft actuators are remouldable, reprogrammable, reconfigurable, weldable, self-healable, recyclable, and stable, which is impossible for any traditional thermosets and is therefore a compelling advance in terms of the applications open to 3D soft actuators.

Influence of Type I Fimbriae and Fluid Shear Stress on Bacterial Behavior and Multicellular Architecture of Early Escherichia coli Biofilms at Single-Cell Resolution.

Biofilm formation on abiotic surfaces in the food and medical industry can cause severe contamination and infection, yet how biological and physical factors determine the cellular architecture of early biofilms and the bacterial behavior of the constituent cells remains largely unknown. In this study, we examined the specific role of type I fimbriae in nascent stages of biofilm formation and the response of microcolonies to environmental flow shear at the single-cell resolution. The results show that type I fimbriae are not required for reversible adhesion from plankton, but they are critical for the irreversible adhesion of Escherichia coli strain MG1655 cells that form biofilms on polyethylene terephthalate (PET) surfaces. Besides establishing firm cell surface contact, the irreversible adhesion seems necessary to initiate the proliferation of E. coli on the surface. After the application of shear stress, bacterial retention is dominated by the three-dimensional architecture of colonies, independent of the population size, and the multilayered structure could protect the embedded cells from being insulted by fluid shear, while the cell membrane permeability mainly depends on the biofilm population size and the duration of the shear stress.IMPORTANCE Bacterial biofilms could lead to severe contamination problems in medical devices and food processing equipment. However, biofilms are usually studied at a rough macroscopic level; thus, little is known about how individual bacterium behavior within biofilms and the multicellular architecture are influenced by bacterial appendages (e.g., pili/fimbriae) and environmental factors during early biofilm formation. We applied confocal laser scanning microscopy (CLSM) to visualize Escherichia coli microcolonies at a single-cell resolution. Our findings suggest that type I fimbriae are vital to the initiation of bacterial proliferation on surfaces. We also found that the fluid shear stress affects the biofilm architecture and cell membrane permeability of the constituent bacteria in a different way: the onset of the biofilm is linked with the three-dimensional morphology, while membranes are regulated by the overall population of microcolonies.

Microtubule buckling in an elastic matrix with quenched disorder.

The intracellular elastic matrix has been recognized as an important factor to stabilize microtubules and increase their critical buckling force P c in vivo. This phenomenon was qualitatively explained by the Winkler model, which investigated the buckling of a filament embedded in a homogeneous elastic medium. However, the assumption of homogeneity of the matrix in Winkler's, and other advanced models, is unrealistic inside cells, where the local environment is highly variable along the filament. Considering this to be a quenched-disorder system, we use a Poisson distribution for confinements and apply the replica technique combined with the Gaussian variational method to study the buckling of a long filament. The results show two types of filament bucklings: one corresponding to the first-order, and the other to a continuous second-order phase transition. The critical point, i.e., the switch from first- to second-order buckling transition, is induced by the increase in disorder strength. We also discover that this random disorder of the elastic environment destabilizes the filament by decreasing P c from the Winkler result and the matrix with stronger mean elasticity has a stronger role of disorder (inhomogeneity). For microtubules in vivo, buckling follows the discontinuous first-order transition, with P c reduced to the fraction between 0.9 and 0.75 of the Winkler prediction for the homogeneous elastic matrix. We also show that disorder can affect the force-displacement relationship at non-zero temperature, while at zero temperature this effect vanishes.

Force generation by the growth of amyloid aggregates.

The generation of mechanical forces are central to a wide range of vital biological processes, including the function of the cytoskeleton. Although the forces emerging from the polymerization of native proteins have been studied in detail, the potential for force generation by aberrant protein polymerization has not yet been explored. Here, we show that the growth of amyloid fibrils, archetypical aberrant protein polymers, is capable of unleashing mechanical forces on the piconewton scale for individual filaments. We apply microfluidic techniques to measure the forces released by amyloid growth for two systems: insulin and lysozyme. The level of force measured for amyloid growth in both systems is comparable to that observed for actin and tubulin, systems that have evolved to generate force during their native functions and, unlike amyloid growth, rely on the input of external energy in the form of nucleotide hydrolysis for maximum force generation. Furthermore, we find that the power density released from growing amyloid fibrils is comparable to that of high-performance synthetic polymer actuators. These findings highlight the potential of amyloid structures as active materials and shed light on the criteria for regulation and reversibility that guide molecular evolution of functional polymers.

Focal Adhesion Kinase: The Reversible Molecular Mechanosensor.

Sensors are the first element of the pathways that control the response of cells to their environment. Protein complexes that produce or enable a chemical signal in response to a mechanical stimulus are called "mechanosensors". In this work, we develop a theoretical model describing the physical mechanism of a reversible single-molecule stiffness sensor. Although this has the potential for general application, here we apply the model to focal adhesion kinase, which initiates the chemical signal in its active phosphorylated conformation, but can spontaneously return to its closed folded conformation. We find how the rates of conformation changes depend on the substrate stiffness and the pulling force applied from the cell cytoskeleton. We find the sensor is homeostatic, spontaneously self-adjusting to reach a state where its range of maximum sensitivity matches the substrate stiffness. The results compare well with the phenotype observations of cells on different substrates.

Mechanisms and rates of nucleation of amyloid fibrils.

The classical nucleation theory finds the rate of nucleation proportional to the monomer concentration raised to the power, which is the "critical nucleus size," nc. The implicit assumption, that amyloids nucleate in the same way, has been recently challenged by an alternative two-step mechanism, when the soluble monomers first form a metastable aggregate (micelle) and then undergo conversion into the conformation rich in ß-strands that are able to form a stable growing nucleus for the protofilament. Here we put together the elements of extensive knowledge about aggregation and nucleation kinetics, using a specific case of Aß1-42 amyloidogenic peptide for illustration, to find theoretical expressions for the effective rate of amyloid nucleation. We find that at low monomer concentrations in solution and also at low interaction energy between two peptide conformations in the micelle, the nucleation occurs via the classical route. At higher monomer concentrations, and a range of other interaction parameters between peptides, the two-step "aggregation-conversion" mechanism of nucleation takes over. In this regime, the effective rate of the process can be interpreted as a power of monomer concentration in a certain range of parameters; however, the exponent is determined by a complicated interplay of interaction parameters and is not related to the minimum size of the growing nucleus (which we find to be ∼7-8 for Aß1-42).

Nonlinear elasticity of semiflexible filament networks.

We develop a continuum theory for equilibrium elasticity of a network of crosslinked semiflexible filaments, spanning the full range between flexible entropy-driven chains to stiff athermal rods. We choose the 3-chain constitutive model of network elasticity over several plausible candidates, and derive analytical expressions for the elastic energy at arbitrary strain, with the corresponding stress-strain relationship. The theory fits well to a wide range of experimental data on simple shear in different filament networks, quantitatively matching the differential shear modulus variation with stress, with only two adjustable parameters (which represent the filament stiffness and the pre-tension in the network, respectively). The general theory accurately describes the crossover between the positive and negative Poynting effect (normal stress on imposed shear) on increasing the stiffness of filaments forming the network. We discuss the network stability (the point of marginal rigidity) and the phenomenon of tensegrity, showing that filament pre-tension on crosslinking into the network determines the magnitude of linear modulus G0.

Polymer glass transition occurs at the marginal rigidity point with connectivity z* = 4.

We re-examine the physical origin of the polymer glass transition from the point of view of marginal rigidity, which is achieved at a certain average number of mechanically active intermolecular contacts per monomer. In the case of polymer chains in a melt/poor solvent, each monomer has two neighbors bound by covalent bonds and also a number of central-force contacts modelled by the Lennard-Jones (LJ) potential. We find that when the average number of contacts per monomer (covalent and non-covalent) exceeds the critical value z* ≈ 4, the system becomes solid and the dynamics arrested - a state that we declare the glass. Coarse-grained Brownian dynamics simulations show that at sufficient strength of LJ attraction (which effectively represents the depth of quenching, or the quality of solvent) the polymer globule indeed crosses the threshold of z*, and becomes a glass with a finite zero-frequency shear modulus, G∝ (z-z*). We verify this by showing the distinction between the 'liquid' polymer droplet at z < z*, which changes shape and adopts the spherical conformation in equilibrium, and the glassy 'solid' droplet at z > z*, which retains its shape frozen at the moment of z* crossover. These results provide a robust microscopic criterion to tell the liquid apart from the glass for the linear polymers.

Non-exponential kinetics of unfolding under a constant force.

We examine the population dynamics of naturally folded globular polymers, with a super-hydrophobic "core" inserted at a prescribed point in the polymer chain, unfolding under an application of external force, as in AFM force-clamp spectroscopy. This acts as a crude model for a large class of folded biomolecules with hydrophobic or hydrogen-bonded cores. We find that the introduction of super-hydrophobic units leads to a stochastic variation in the unfolding rate, even when the positions of the added monomers are fixed. This leads to the average non-exponential population dynamics, which is consistent with a variety of experimental data and does not require any intrinsic quenched disorder that was traditionally thought to be at the origin of non-exponential relaxation laws.