Buckling-induced zebra stripe patterns in nematic F-actin

Organization and Formation of the Crossed-Foliated Biomineral Microstructure of Limpet Shells

To construct their shells, molluscs are able to produce a large array of calcified materials including granular, prismatic, lamellar, fibrous, foliated, and plywood-like microstructures. The latter includes an aragonitic (the crossed-lamellar) and a calcitic (the crossed-foliated) variety, whose modes of formation are particularly enigmatic. We studied the crossed-foliated calcitic layers secreted solely by members of the limpet family Patellidae using scanning and transmission electron microscopy and electron backscatter diffraction. From the exterior to the interior, the material becomes progressively organized into commarginal first-order lamellae, with second and third order lamellae dipping in opposite directions in alternating lamellae. At the same time, the crystallographic texture becomes stronger because each set of the first order lamellae develops a particular orientation for the c-axis, while both sets maintain common orientations for one {104} face (parallel to the growth surface) and one a-axis (perpendicular to the planes of the first order lamellae). Each first order lamella shows a progressive migration of its crystallographic axes with growth in order to adapt to the orientation of the set of first order lamellae to which it belongs. To explain the progressive organization of the material, we hypothesize that a secretional zebra pattern, mirrored by the first order lamellae on the shell growth surface, is developed on the shell-secreting mantle surface. Cells belonging to alternating stripes behave differently to determine the growth orientation of the laths composing the first order lamellae. In this way, we provide an explanation as to how plywood-like materials can be fabricated, which is based mainly on the activity of mantle cells.

Crowding alters F-actin secondary structure and hydration

Actin, an important component of eukaryotic cell cytoskeleton, regulates cell shape and transport. The morphology and biochemical properties of actin filaments are determined by their structure and protein-protein contacts. Crowded environments can organize filaments into bundles, but less is known about how they affect F-actin structure. This study used 2D IR spectroscopy and spectral calculations to examine how crowding and bundling impact the secondary structure and local environments in filaments and weakly or strongly bundled networks. The results reveal that bundling induces changes in actin's secondary structure, leading to a decrease in β-sheet and an increase in loop conformations. Strongly bundled networks exhibit a decrease in backbone solvent exposure, with less perturbed α-helices and nearly "locked" β-sheets. Similarly, the loops become less hydrated but maintain a dynamic environment. These findings highlight the role of loop structure in actin network morphology and stability under morphology control by PEG.

Large and stable: actin aster networks formed via entropic forces

Biopolymer networks play a major role as part of the cytoskeleton. They provide stable structures and act as a medium for signal transport. These features encourage the application of such networks as organic computation devices. While research on this topic is not advanced yet, previous results are very promising. The protein actin in particular appears advantageous. It can be arranged to various stable structures and transmit several signals. In this study aster shaped networks were self-assembled via entropic forces by the crowding agent methyl cellulose. These networks are characterised by a regular and uniquely thick bundle structure, but have so far only been accounted in droplets of 100 μm diameter. We report now regular asters in an area of a few mm² that could be observed even after months. Such stability outside of an organism is striking and underlines the great potential actin aster networks display.

Shape and structural relaxation of colloidal tactoids

Facile geometric-structural response of liquid crystalline colloids to external fields enables many technological advances. However, the relaxation mechanisms for liquid crystalline colloids under mobile boundaries remain still unexplored. Here, by combining experiments, numerical simulations and theory, we describe the shape and structural relaxation of colloidal liquid crystalline micro-droplets, called tactoids, where amyloid fibrils and cellulose nanocrystals are used as model systems. We show that tactoids shape relaxation bears a universal single exponential decay signature and derive an analytic expression to predict this out of equilibrium process, which is governed by liquid crystalline anisotropic and isotropic contributions. The tactoids structural relaxation shows fundamentally different paths, with first- and second-order exponential decays, depending on the existence of splay/bend/twist orientation structures in the ground state. Our findings offer a comprehensive understanding on dynamic confinement effects in liquid crystalline colloidal systems and may set unexplored directions in the development of novel responsive materials.

Tactoids, consisting of micro-confined liquid crystalline colloids with self-selected shape, bear both fundamental and technological significance. The authors show that the shape relaxation of tactoids follows an exponential decay and develop a model to predict this out-of-the-equilibrium process.

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.

Cells in Slow Motion: Apparent Undercooling Increases Glassy Behavior at Physiological Temperatures

Solvent conditions are unexpectedly sufficient to drastically and reversibly slow down cells. In vitro on the molecular level, protein-solvent interactions drastically change in the presence of heavy water (D2 O) and its stronger hydrogen bonds. Adding D2 O to the cell medium of living cells increases the molecular intracellular viscosity. While cell morphology and phenotype remain unchanged, cellular dynamics transform into slow motion in a changeable manner. This is exemplified in the slowdown of cell proliferation and migration, which is caused by a reversible gelation of the cytoplasm. In analogy to the time-temperature superposition principle, where temperature is replaced by D2 O, an increase in viscosity slows down the effective time. Actin networks, crucial structures in the cytoplasm, switch from a power-law-like viscoelastic to a more rubber-like elastic behavior. The resulting intracellular resistance and dissipation impair cell movement. Since cells are highly adaptive non-equilibrium systems, they usually respond irreversibly from a thermodynamic perspective. D2 O induced changes, however, are fully reversible and their effects are independent of signaling as well as expression. The stronger hydrogen bonds lead to glass-like, drawn-out intramolecular dynamics, which may facilitate longer storage times of biological matter, for instance, during transport of organ transplants.

Measuring structural parameters of crosslinked and entangled semiflexible polymer networks with single-filament tracing

Single-filament tracing has been a valuable tool to directly determine geometrical and mechanical properties of entangled polymer networks. However, systematically verifying how the stiffness of the tracer filament or its molecular interactions with the surrounding network impacts the measurement of these parameters has not been possible with the established experimental systems. Here we use mechanically programmable DNA nanotubes embedded in crosslinked and entangled F-actin networks, as well as in synthetic DNA networks, in order to measure fundamental, structural network properties like tube width and mesh size with respect to the stiffness of the tracers. While we confirm some predictions derived from models based purely on steric interactions, our results indicate that these models should be expanded to account for additional interfilament interactions, thereby describing the behavior of real polymer networks.

Keratins determine network stress responsiveness in reconstituted actin-keratin filament systems

The cytoskeleton is a major determinant of cell mechanics, and alterations in the central mechanical aspects of cells are observed during many pathological situations. Therefore, it is essential to investigate the interplay between the main filament systems of the cytoskeleton in the form of composite networks. Here, we investigate the role of keratin intermediate filaments (IFs) in network strength by studying in vitro reconstituted actin and keratin 8/18 composite filament networks via bulk shear rheology. We co-polymerized these structural proteins in varying ratios and recorded how their relative content affects the overall mechanical response of the various composites. For relatively small deformations, we found that all composites exhibited an intermediate linear viscoelastic behaviour compared to that of the pure networks. In stark contrast, when larger deformations were imposed the composites displayed increasing strain stiffening behaviour with increasing keratin content. The extent of strain stiffening is much more pronounced than in corresponding experiments performed with vimentin IF as a composite network partner for actin. Our results provide new insights into the mechanical interplay between actin and keratin filaments in which keratin provides reinforcement to actin. This interplay may contribute to the overall integrity of cells. Hence, the high keratin 8/18 content of mechanically stressed simple epithelial cell layers, as found in the lung and the intestine, provides an explanation for their exceptional stability.

Evidence for a liquid-crystal precursor involved in the formation of the crossed-lamellar microstructure of the mollusc shell

Many biological structures use liquid crystals as self-organizing templates for their formation. We review and analyse evidence that the crossed-lamellar biomineral microstructure of mollusc shells may be formed from such a liquid-crystal precursor. STATEMENT OF SIGNIFICANCE: Many biological structures use liquid crystals as self-organizing templates for their formation. We review and analyse evidence that the crossed-lamellar biomineral microstructure of mollusc shells may be formed from such a liquid-crystal precursor.

Tunable corrugated patterns in an active nematic sheet

Active matter locally converts chemical energy into mechanical work and, for this reason, it provides new mechanisms of pattern formation. In particular, active nematic fluids made of protein motors and filaments are far-from-equilibrium systems that may exhibit spontaneous motion, leading to actively driven spatiotemporally chaotic states in 2 and 3 dimensions and coherent flows in 3 dimensions (3D). Although these dynamic flows reveal a characteristic length scale resulting from the interplay between active forcing and passive restoring forces, the observation of static and large-scale spatial patterns in active nematic fluids has remained elusive. In this work, we demonstrate that a 3D solution of kinesin motors and microtubule filaments spontaneously forms a 2D free-standing nematic active sheet that actively buckles out of plane into a centimeter-sized periodic corrugated sheet that is stable for several days at low activity. Importantly, the nematic orientational field does not display topological defects in the corrugated state and the wavelength and stability of the corrugations are controlled by the motor concentration, in agreement with a hydrodynamic theory. At higher activities these patterns are transient and chaotic flows are observed at longer times. Our results underline the importance of both passive and active forces in shaping active matter and demonstrate that a spontaneously flowing active fluid can be sculpted into a static material through an active mechanism.

The role of stickiness in the rheology of semiflexible polymers

Semiflexible polymers form central structures in biological material. Modelling approaches usually neglect influences of polymer-specific molecular features aiming to describe semiflexible polymers universally. Here, we investigate the influence of molecular details on networks assembled from filamentous actin, intermediate filaments, and synthetic DNA nanotubes. In contrast to prevalent theoretical assumptions, we find that bulk properties are affected by various inter-filament interactions. We present evidence that these interactions can be merged into a single parameter in the frame of the glassy wormlike chain model. The interpretation of this parameter as a polymer specific stickiness is consistent with observations from macro-rheological measurements and reptation behaviour. Our findings demonstrate that stickiness should generally not be ignored in semiflexible polymer models.

First passage of molecular motors on networks of cytoskeletal filaments

Molecular motors facilitate intracellular transport through a combination of passive motion in the cytoplasm and active transport along cytoskeletal filaments. Although the motion of motors on individual filaments is often well characterized, it remains a challenge to understand their transport on networks of filaments. Here we use computer simulations of a stochastic jump process to determine first-passage times (FPTs) of a molecular motor traversing an interval containing randomly distributed filaments of fixed length. We characterize the mean first-passage time (MFPT) as a function of the number and length of filaments. Intervals containing moderate numbers of long filaments lead to the largest MFPTs with the largest relative standard deviation; in this regime, some filament configurations lead to anomalously large FPTs due to spatial regions where motors become trapped for long times. For specific filament configurations, we systematically reverse the directionality of single filaments and determine the MFPT of the perturbed configuration. Surprisingly, altering a single filament can dramatically impact the MFPT, and filaments leading to the largest changes are commonly found in different regions than the traps. We conclude by analyzing the mean square displacement of motors in unconfined systems with a large density of filaments and show that they behave diffusively at times substantially less than the MFPT to traverse the interval. However, the effective diffusion coefficient underestimates the MFPT across the bounded interval, emphasizing the importance of local configurations of filaments on first-passage properties.

Long-Range Anisotropic Structural Films and Fibers Formed from Lyotropic Liquid Crystal Gels Containing Hetero-Double-Helices with C16 Terminal Groups

Long-range anisotropic structural materials exhibit notable optical and mechanical properties, and an efficient method for synthesizing such materials involving self-assembly of well-defined monodispersed organic molecules is described here. Hetero-double-helices are formed in toluene using a pseudoenantiomeric mixture of an ethynylhelicene ( M)-tetramer with C₁₆ terminal groups and a ( P)-pentamer. When the concentration of the mixture was increased, the hetero-double-helices self-assembled to form lyotropic liquid crystal gels. On evaporating the solvent by drop casting, a long-range anisotropic structural film with a single domain and a size of up to centimeter order was spontaneously formed. Kinetics analysis of the film formation indicated the generation of perpendicularly aligned liquid crystal domains at the interface of the liquid and solid phases. When the lyotropic liquid crystal gel was extruded into methanol, a long-range anisotropic structural fiber with a single domain was formed. Different shapes of long-range anisotropic structural materials were obtained by different mechanical treatments of lyotropic liquid crystal gels.

Glassy dynamics in composite biopolymer networks

The cytoskeleton is a highly interconnected meshwork of strongly coupled subsystems providing mechanical stability as well as dynamic functions to cells. To elucidate the underlying biophysical principles, it is central to investigate not only one distinct functional subsystem but rather their interplay as composite biopolymeric structures. Two of the key cytoskeletal elements are actin and vimentin filaments. Here, we show that composite networks reconstituted from actin and vimentin can be described by a superposition of two non-interacting scaffolds. Arising effects are demonstrated in a scale-spanning frame connecting single filament dynamics to macro-rheological network properties. The acquired results of the linear and non-linear bulk mechanics can be captured within an inelastic glassy wormlike chain model. In contrast to previous studies, we find no emergent effects in these composite networks. Thus, our study paves the way to predict the mechanics of the cytoskeleton based on the properties of its single structural components.

Synthetic Transient Crosslinks Program the Mechanics of Soft, Biopolymer-Based Materials

Actin networks are adaptive materials enabling dynamic and static functions of living cells. A central element for tuning their underlying structural and mechanical properties is the ability to reversibly connect, i.e., transiently crosslink, filaments within the networks. Natural crosslinkers, however, vary across many parameters. Therefore, systematically studying the impact of their fundamental properties like size and binding strength is unfeasible since their structural parameters cannot be independently tuned. Herein, this problem is circumvented by employing a modular strategy to construct purely synthetic actin crosslinkers from DNA and peptides. These crosslinkers mimic both intuitive and noncanonical mechanical properties of their natural counterparts. By isolating binding affinity as the primary control parameter, effects on structural and dynamic behaviors of actin networks are characterized. A concentration-dependent triphasic behavior arises from both strong and weak crosslinkers due to emergent structural polymorphism. Beyond a certain threshold, strong binding leads to a nonmonotonic elastic pulse, which is a consequence of self-destruction of the mechanical structure of the underlying network. The modular design also facilitates an orthogonal regulatory mechanism based on enzymatic cleaving. This approach can be used to guide the rational design of further biomimetic components for programmable modulation of the properties of biomaterials and cells.

Direct observation of orientation distributions of actin filaments in a solution undergoing shear banding

Shear banding is frequently observed in complex fluids. However, the configuration of macromolecules in solutions undergoing shear banding has not yet been directly observed. In this study, by using the fact that F-actin solutions exhibit shear banding and actin filaments are visualized by fluorescent labels, we directly observed the intrinsic states of an actin solution undergoing shear banding. By combining the 3D imaging of labeled actin filaments and particle image velocimetry (PIV), we obtained orientation distributions of actin filaments in both high and low shear rate regions, whose quantitative differences are indicated. In addition, by using the orientation distributions and applying stress expression for rod-like polymers, we estimated stress tensors in both high and low shear rate regions. This evaluation indicates that different orientation distributions of filamentous macromolecules can exhibit a common shear stress.

Tuning Synthetic Semiflexible Networks by Bending Stiffness

The mechanics of complex soft matter often cannot be understood in the classical physical frame of flexible polymers or rigid rods. The underlying constituents are semiflexible polymers, whose finite bending stiffness (κ) leads to nontrivial mechanical responses. A natural model for such polymers is the protein actin. Experimental studies of actin networks, however, are limited since the persistence length (l_{p}∝κ) cannot be tuned. Here, we experimentally characterize this parameter for the first time in entangled networks formed by synthetically produced, structurally tunable DNA nanotubes. This material enabled the validation of characteristics inherent to semiflexible polymers and networks thereof, i.e., persistence length, inextensibility, reptation, and mesh size scaling. While the scaling of the elastic plateau modulus with concentration G_{0}∝c^{7/5} is consistent with previous measurements and established theories, the emerging persistence length scaling G_{0}∝l_{p} opposes predominant theoretical predictions.

Transition from a Linear to a Harmonic Potential in Collective Dynamics of a Multifilament Actin Bundle

Attractive depletion forces between rodlike particles in highly crowded environments have been shown through recent modeling and experimental approaches to induce different structural and dynamic signatures depending on relative orientation between rods. For example, it has been demonstrated that the axial attraction between two parallel rods yields a linear energy potential corresponding to a constant contractile force of 0.1 pN. Here, we extend pairwise, depletion-induced interactions to a multifilament level with actin bundles, and find contractile forces up to 3 pN. Forces generated due to bundle relaxation were not constant, but displayed a harmonic potential and decayed exponentially with a mean decay time of 3.4 s. Through an analytical model, we explain these different fundamental dynamics as an emergent, collective phenomenon stemming from the additive, pairwise interactions of filaments within a bundle.

Alignment of nematic and bundled semiflexible polymers in cell-sized confinement

The finite size of cells poses severe spatial constraints on the network of semiflexible filaments called the cytoskeleton, a main determinant of cell shape. At the same time, the high packing density of cytoskeletal filaments poses mutual packing constraints. Here we investigate the competition between excluded volume interactions in the bulk and surface packing constraints on the orientational ordering of confined actin filaments as a function of filament density and the presence of crosslinks. We grow fluorescently labeled actin filaments in shallow (thickness dz 3 μm), rectangular microchambers with a systematically varied length (dy between 5 and 100 μm) and in-plane aspect ratio (dx/dy between 1 and 10). We determine the nematic director field by image analysis of fluorescence confocal images. We find that high-density (nematic) solutions respond sensitively to changes in the size and aspect ratio of the chambers. In small chambers (dy ≤ 20 μm), filaments align parallel to the long walls as soon as the aspect ratio is ≥1.5, indicating that surface-induced ordering dominates. In larger chambers, the filaments instead align along the chamber diagonal, indicating that bulk packing constraints dominate. The nematic order parameter is maximal in small and highly anisometric chambers. In contrast to the nematic solutions, low-density (isotropic) solutions are rather insensitive to confinement. Bundled actin solutions behave similarly to nematic solutions, but are less well-ordered. Our observations imply that the orientational order of actin filaments in flat confining geometries is primarily determined by a balance between bulk and surface packing constraints with a minimal effect of the enthalpic cost of filament bending. Our assay provides an interesting platform for the future reconstitution of more complex, active cytoskeletal systems with actively treadmilling filaments or molecular motors.

Fluorescent beads disintegrate actin networks

We studied the influence of fluorescent polystyrene beads on both entangled and cross-linked actin networks. Thermal bead fluctuations were observed via video particle tracking and analyzed with one-point microrheology. Illumination of fluorescent beads with their appropriate excitation wavelength leads to a drastic softening of actin gels. Other wavelengths and bright field microscopy do not increase thermal bead fluctuations. This effect cannot be significantly reduced by adding common oxygen scavengers. We conclude that the usage of fluorescent beads impairs results when studying the microrheology of actin networks.

Emergent complexity of the cytoskeleton: from single filaments to tissue

Despite their overwhelming complexity, living cells display a high degree of internal mechanical and functional organization which can largely be attributed to the intracellular biopolymer scaffold, the cytoskeleton. Being a very complex system far from thermodynamic equilibrium, the cytoskeleton's ability to organize is at the same time challenging and fascinating. The extensive amounts of frequently interacting cellular building blocks and their inherent multifunctionality permits highly adaptive behavior and obstructs a purely reductionist approach. Nevertheless (and despite the field's relative novelty), the physics approach has already proved to be extremely successful in revealing very fundamental concepts of cytoskeleton organization and behavior. This review aims at introducing the physics of the cytoskeleton ranging from single biopolymer filaments to multicellular organisms. Throughout this wide range of phenomena, the focus is set on the intertwined nature of the different physical scales (levels of complexity) that give rise to numerous emergent properties by means of self-organization or self-assembly.

THE CYTOSKELETON: AN ACTIVE POLYMER-BASED SCAFFOLD

The motility of cells is a multifaceted and complicated cytoskeletal process. Significant inroads can be made into gaining a more detailed understanding, however, by focusing on the smaller, more simple subunits of the motile system in an effort to isolate the essential protein components necessary to perform a certain task. Identification of such functional modules has proven to be an effective means of working towards a comprehensive understanding of complex, interacting systems. By following a bottom-up approach in studying minimal actin-related sub-systems for keratocyte motility, we revealed several fundamentally important effects ranging from an estimation of the force generated by the polymerization of a single actin filament, to assembly dynamics and the production of force and tension of composite actin networks, to the contraction of actin networks or smaller bundled structures by the motor myosin II. While even motile keratocyte fragments represent a far more complex situation than the simple reconstituted systems presented here, clear parallels can be seen between in vivo cell motility and the idealized in vitro functional modules presented here, giving more weight to their continued focus.

Measuring forces between two single actin filaments during bundle formation

Bundles of filamentous actin are dominant cytoskeletal structures, which play a crucial role in various cellular processes. As yet quantifying the fundamental interaction between two individual actin filaments forming the smallest possible bundle has not been realized. Applying holographic optical tweezers integrated with a microfluidic platform, we were able to measure the forces between two actin filaments during bundle formation. Quantitative analysis yields forces up to 0.2 pN depending on the concentration of bundling agents.