Filament Bending Research Articles

Small organic osmolytes accelerate actin filament assembly and stiffen filaments.

Actin filament assembly and mechanics are crucial for maintenance of cell structure, motility, and division. Actin filament assembly occurs in a crowded intracellular environment consisting of various types of molecules, including small organic molecules known as osmolytes. Ample evidence highlights the protective functions of osmolytes such as trimethylamine-N-oxide (TMAO), including their effects on protein stability and their ability to counteract cellular osmotic stress. Yet, how TMAO affects individual actin filament assembly dynamics and mechanics is not well understood. We hypothesize that, owing to its protective nature, TMAO will enhance filament dynamics and stiffen actin filaments due to increased stability. In this study, we investigate osmolyte-dependent actin filament assembly and bending mechanics by measuring filament elongation rates, steady-state filament lengths, and bending persistence lengths in the presence of TMAO using total internal reflection fluorescence microscopy and pyrene assays. Our results demonstrate that TMAO increases filament elongation rates as well as steady-state average filament lengths, and enhances filament bending stiffness. Together, these results will help us understand how small organic osmolytes modulate cytoskeletal protein assembly and mechanics in living cells.

Growth-induced collective bending and kinetic trapping of cytoskeletal filaments.

Growth and turnover of actin filaments play a crucial role in the construction and maintenance of actin networks within cells. Actin filament growth occurs within limited space and finite subunit resources in the actin cortex. To understand how filament growth shapes the emergent architecture of actin networks, we developed a minimal agent-based model coupling filament mechanics and growth in a limiting subunit pool. We find that rapid filament growth induces kinetic trapping of highly bent actin filaments. Such collective bending patterns are long-lived, organized around nematic defects, and arise from competition between filament polymerization and bending elasticity. The stability of nematic defects and the extent of kinetic trapping are amplified by an increase in the abundance of the actin pool and by crosslinking the network. These findings suggest that kinetic trapping is a robust consequence of growth in crowded environments, providing a route to program shape memory in actin networks.

Spin-lattice-dynamics analysis of magnetic properties of iron under compression

Compression of a magnetic material leads to a change in its magnetic properties. We examine this effect using spin-lattice dynamics for the special case of bcc-Fe, using both single- and poly-crystalline Fe and a bicontinuous nanofoam structure. We find that during the elastic phase of compression, the magnetization increases due to a higher population of the nearest-neighbor shell of atoms and the resulting higher exchange interaction of neighboring spins. In contrast, in the plastic phase of compression, the magnetization sinks, as defects are created, increasing the disorder and typically decreasing the average atom coordination number. The effects are more pronounced in single crystals than in polycrystals, since the presence of defects in the form of grain boundaries counteracts the increase in magnetization during the elastic phase of compression. Also, the effects are more pronounced at temperatures close to the Curie temperature than at room temperature. In nanofoams, the effect of compression is minor since compression proceeds more by void reduction and filament bending—with negligible effect on magnetization—than by strain within the ligaments. These findings will prove useful for tailoring magnetization under strain by introducing plasticity.

Polymerization force–regulated actin filament–Arp2/3 complex interaction dominates self-adaptive cell migrations

Cells migrate by adapting their leading-edge behaviors to heterogeneous extracellular microenvironments (ECMs) during cancer invasions and immune responses. Yet it remains poorly understood how such complicated dynamic behaviors emerge from millisecond-scale assembling activities of protein molecules, which are hard to probe experimentally. To address this gap, we establish a spatiotemporal "resistance-adaptive propulsion" theory based on the interactions between Arp2/3 complexes and polymerizing actin filaments and a multiscale dynamic modeling system spanning from molecular proteins to the cell. We quantitatively find that cells can accurately self-adapt propulsive forces to overcome heterogeneous ECMs via a resistance-triggered positive feedback mechanism, dominated by polymerization-induced actin filament bending and the bending-regulated actin-Arp2/3 binding. However, for high resistance regions, resistance triggers a negative feedback, hindering branched filament assembly, which adapts cellular morphologies to circumnavigate the obstacles. Strikingly, the synergy of the two opposite feedbacks not only empowers the cell with both powerful and flexible migratory capabilities to deal with complex ECMs but also enables efficient utilization of intracellular proteins by the cell. In addition, we identify that the nature of cell migration velocity depending on ECM history stems from the inherent temporal hysteresis of cytoskeleton remodeling. We also show that directional cell migration is dictated by the competition between the local stiffness of ECMs and the local polymerizing rate of actin network caused by chemotactic cues. Our results reveal that it is the polymerization force-regulated actin filament-Arp2/3 complex binding interaction that dominates self-adaptive cell migrations in complex ECMs, and we provide a predictive theory and a spatiotemporal multiscale modeling system at the protein level.

Constriction of Actin Rings by Passive Crosslinkers.

In many organisms, cell division is driven by the constriction of a cytokinetic ring, which consists of actin filaments and crosslinking proteins. While it has long been believed that the constriction is driven by motor proteins, it has recently been discovered that passive crosslinkers that do not turn over fuel are able to generate enough force to constrict actin filament rings. To study the ring constriction dynamics, we develop a model that includes the driving force of crosslinker condensation and the opposing forces of friction and filament bending. We analyze the constriction force as a function of ring topology and crosslinker concentration, and predict forces that are sufficient to constrict an unadorned plasma membrane. Our model also predicts that actin-filament sliding arises from an interplay between filament rotation and crosslinker hopping, producing frictional forces that are low compared with those of crosslinker-mediated microtubule sliding.

Bending actin filaments: twists of fate.

In many cellular contexts, intracellular actomyosin networks must generate directional forces to carry out cellular tasks such as migration and endocytosis, which play important roles during normal developmental processes. A number of different actin binding proteins have been identified that form linear or branched actin, and that regulate these filaments through activities such as bundling, crosslinking, and depolymerization to create a wide variety of functional actin assemblies. The helical nature of actin filaments allows them to better accommodate tensile stresses by untwisting, as well as to bend to great curvatures without breaking. Interestingly, this latter property, the bending of actin filaments, is emerging as an exciting new feature for determining dynamic actin configurations and functions. Indeed, recent studies using in vitro assays have found that proteins including IQGAP, Cofilin, Septins, Anillin, α-Actinin, Fascin, and Myosins-alone or in combination-can influence the bending or curvature of actin filaments. This bending increases the number and types of dynamic assemblies that can be generated, as well as the spectrum of their functions. Intriguingly, in some cases, actin bending creates directionality within a cell, resulting in a chiral cell shape. This actin-dependent cell chirality is highly conserved in vertebrates and invertebrates and is essential for cell migration and breaking L-R symmetry of tissues/organs. Here, we review how different types of actin binding protein can bend actin filaments, induce curved filament geometries, and how they impact on cellular functions.

Generation of intense magnetic wakes by relativistic laser pulses in plasma

The emergence of petawatt lasers focused to relativistic intensities enables all-optical laboratory generation of intense magnetic fields in plasmas, which are of great interest due to their ubiquity in astrophysical phenomena. In this work, we study generation of spatially extended and long-lived intense magnetic fields. We show that such magnetic fields, scaling up to the gigagauss range, can be generated by interaction of petawatt laser pulses with relativistically underdense plasma. With three-dimensional particle-in-cell simulations we investigate generation of magnetic fields with strengths up to 10^{10} G and perform a large multi-parametric study of magnetic field in dependence on dimensionless laser amplitude a_{0} and normalized plasma density n_{e}/n_{c}. The numerical results yield scaling laws that closely follow derived analytical result B propto sqrt{a_{0}n_{e}/n_{c}}, and further show a close match with previous experimental works. Furthermore, we show in three-dimensional geometry that the decay of the magnetic wake is governed by current filament bending instability, which develops similarly to von Kármán vortex street in its nonlinear stage.

Production of compression and flexural test samples in 3D printer with PLA polymeric biomaterial and bone compression with appropriate properties

In this study, it is planned to design and develop a structure close to the real bone strength properties by using PLA (polylactic acid) material. 3D printers have started to take place in our daily lives with today's developing technology and are preferred because of their ease of production and low cost. It has been determined that the PLA biomaterial can be used as a bone substitute in the body. The samples produced have different filling ratios and different internal structures. In the study, the effects of changes in the internal structure on the mechanical properties were investigated. Bone geometry is considered as an important factor among the parameters affecting biomechanical properties. In order to determine the mechanical properties of PLA filament material, bending and compression samples were prepared as 3 pieces for each test. The aim of this study is to determine whether it can be used as bone in the body by measuring the mechanical properties of biocompatible PLA polymer material. In the current work, the quality of the 3d printer and the material used in production directly affects the mechanical properties. In bones in the human body, trabecular bone has 80% porosity and cortical bone 10% infill. In this study, it was tried to obtain structures with properties close to real bone strength by using test specimens with different infill rates. It has been determined from the obtained data that PLA polymer material can be developed and meet the mechanical values in bone.

Numerical simulation and predictive modeling of an inextensible filament in two-dimensional viscous shear flow using the Immersed Boundary/Coarse-Graining Method and Artificial Neural Networks

This article presents a hybrid IBM/CGM scheme for the study of two-dimensional orbital regimes of flexible and inextensible filaments in low-Reynolds number shear flows. The study includes a parametric analysis of the mechanical response for a range of the filament length, bending rigidity and shear-strain rate. The results are compared to theoretical estimates and previous numerical and experimental analyses. These results are subsequently used to develop a prediction model using Artificial Neural Networks to effectively forecast the orbital regime of a filament immersed in shear flow.

Flagella-like beating of actin bundles driven by self-organized myosin waves.

Wave-like beating of eukaryotic cilia and flagella-threadlike protrusions found in many cells and microorganisms-is a classic example of spontaneous mechanical oscillations in biology. This type of self-organized active matter raises the question of the coordination mechanism between molecular motor activity and cytoskeletal filament bending. Here we show that in the presence of myosin motors, polymerizing actin filaments self-assemble into polar bundles that exhibit wave-like beating. Importantly, filament beating is associated with myosin density waves initiated at twice the frequency of the actin-bending waves. A theoretical description based on curvature control of motor binding to the filaments and of motor activity explains our observations in a regime of high internal friction. Overall, our results indicate that the binding of myosin to actin depends on the actin bundle shape, providing a feedback mechanism between the myosin activity and filament deformations for the self-organization of large motor filament assemblies.

Drag reduction by flapping a flexible filament behind a stationary cylinder

The hydrodynamic mechanism of drag reduction by flapping a flexible filament behind a stationary cylinder was explored using the penalty immersed boundary method. The effects of the filament length, bending rigidity, pitching amplitude, and frequency on drag reduction were systematically examined. We analyzed the underlying mechanism of drag reduction in detail by examining flapping modes, wake patterns, pressure distributions, and flapping dynamics of the flapping filament. The flapping motion of the flexible filament is determined by the combined effect of forcing parameters and the surrounding flow. Three distinct flapping modes are observed when the aforementioned parameters are varied: an oscillation mode, an undulation mode, and a vortex-dominated mode. The oscillation and undulation modes are more beneficial to drag reduction than the vortex-dominated mode. In the oscillation mode, drag reduction is mainly realized by the high thrust generated by the filament overwhelming the increased form drag of the cylinder caused by the trailing edge vortex. A flexible filament flapping in the oscillation mode generates thrust more efficiently. In the undulation mode, a long filament reduces the form drag of the cylinder and generates relatively low thrust, showing a similar drag reduction as a short oscillating filament. In the vortex-dominated mode, the thrust of the filament is very low because of the weakened trailing edge vortex, yielding a weakened drag reduction effect.

On Stretching, Bending, Shearing, and Twisting of Actin Filaments I: Variational Models.

Mechanochemical simulations of actomyosin networks are traditionally based on one-dimensional models of actin filaments having zero width. Here, and in the follow up paper (arXiv, DOI 10.48550/arXiv.2203.01284), approaches are presented for more efficient modeling that incorporates stretching, shearing, and twisting of actin filaments. Our modeling of a semiflexible filament with a small but finite width is based on the Cosserat theory of elastic rods, which allows for six degrees of freedom at every point on the filament's backbone. In the variational models presented in this paper, a small and discrete set of parameters is used to describe a smooth filament shape having all degrees of freedom allowed in the Cosserat theory. Two main approaches are introduced: one where polynomial spline functions describe the filament's configuration, and one in which geodesic curves in the space of the configurational degrees of freedom are used. We find that in the latter representation the strain energy function can be calculated without resorting to a small-angle expansion, so it can describe arbitrarily large filament deformations without systematic error. These approaches are validated by a dynamical model of a Cosserat filament, which can be further extended by using multiresolution methods to allow more detailed monomer-based resolution in certain parts of the actin filament, as introduced in the follow up paper. The presented framework is illustrated by showing how torsional compliance in a finite-width filament can induce broken chiral symmetry in the structure of a cross-linked bundle.

F-actin bending facilitates net actomyosin contraction By inhibiting expansion with plus-end-located myosin motors

Contraction of actomyosin networks underpins important cellular processes including motility and division. The mechanical origin of actomyosin contraction is not fully-understood. We investigate whether contraction arises on the scale of individual filaments, without needing to invoke network-scale interactions. We derive discrete force-balance and continuum partial differential equations for two symmetric, semi-flexible actin filaments with an attached myosin motor. Assuming the system exists within a homogeneous background material, our method enables computation of the stress tensor, providing a measure of contractility. After deriving the model, we use a combination of asymptotic analysis and numerical solutions to show how F-actin bending facilitates contraction on the scale of two filaments. Rigid filaments exhibit polarity-reversal symmetry as the motor travels from the minus to plus-ends, such that contractile and expansive components cancel. Filament bending induces a geometric asymmetry that brings the filaments closer to parallel as a myosin motor approaches their plus-ends, decreasing the effective spring force opposing motor motion. The reduced spring force enables the motor to move faster close to filament plus-ends, which reduces expansive stress and gives rise to net contraction. Bending-induced geometric asymmetry provides both new understanding of actomyosin contraction mechanics, and a hypothesis that can be tested in experiments.

Enhancing the magnetic response on polycrystalline nanoframes through mechanical deformation

The mechanical and magnetic properties of polycrystalline nanoframes were investigated using atomistic molecular dynamics and micromagnetic simulations. The magneto-mechanical response of Fe hollow-like nanocubes was addressed by uniaxial compression carried out by nanoindentation. Our results show that the deformation of a nanoframe is dominated at lower strains by the compression of the nanostructure due to filament bending. This leads to the nanoframe twisting perpendicular to the indentation direction for larger indentation depths. Bending and twisting reduce stress concentration and, at the same time, increase coercivity. This unexpected increase of the coercivity occurs because the mechanical deformation changes the cubic shape of the nanoframe, which in turn drives the system to more stable magnetic states. A coercivity increase of almost 100 mT is found for strains close to 0.03, which are within the elastic regime of the Fe nanoframe. Coercivity then decreases at larger strains. However, in all cases, the coercivity is higher than for the undeformed nanoframe. These results can help in the design of new magnetic devices where mechanical deformation can be used as a primary tool to tailor the magnetic response on nanoscale solids.

Drag reduction by a rotationally oscillating cylinder with a flexible filament

The hydrodynamic mechanism of drag reduction by a rotationally oscillating cylinder with a flexible filament was explored using the penalty immersed boundary method. A simulation of a stationary cylinder without a filament was also performed for comparison. The effects of the filament length, bending rigidity, oscillatory frequency, and oscillatory amplitude on drag reduction were systematically examined. The underlying mechanism of drag reduction was characterized in terms of the shape deformation of the filament, wake pattern, pressure distribution, and flapping dynamics. Two dominant flapping modes were observed: an oscillation mode with less than half a wave on the filament and an undulation mode with more than one wave on the filament. In the oscillation mode, drag reduction is mainly achieved by the thrust generated by the filament, accompanied by an increase in lift fluctuations. The pressure difference caused by the flapping motion between the upper and lower sides of the filament is the main cause of the thrust. In the undulation mode, drag reduction is realized by both the thrust generated by the filament and the decreased form drag of the cylinder. A filament flapping in the oscillation mode can generate greater thrust than a filament flapping in the undulation mode. A long undulatory filament with relatively low oscillatory amplitude effectively stabilizes the wake, resulting in a decrease in the lift fluctuations.

Nanoindentation of nanoporous tungsten: A molecular dynamics approach

Nanoporous metals, also known as metallic nanofoams, offer a wide range of functionalities and improved mechanical properties enabled by nanoscale effects. In particular, tungsten nanofoams are a novel class of materials with potential applications as radiation-resistant coating, and they share some similarities with the fuzz structure arising in fusion devices. We approach their study by nanoindentation tests using molecular dynamics simulations, for a single crystal nanofoam. To help understanding the foam mechanical behavior we also carry out simulations of W nanowire compression, finding elastic moduli of 375–450 GPa, and plastic yielding at ≈15 GPa. For the nanofoam, we obtain an elastic modulus of 64 GPa, in reasonable agreement with experiments, but our hardness value of ∼15 GPa is higher, likely due to nanocrystalline effects in the experiment. Atomistic simulations reveal that plastic deformation is caused by a combination of 12〈111〉 dislocations and twinning in the neighborhood of the indenter surface. It was found that twins also promote complete amorphization of some thin filaments in contact with the indenter tip. Dislocation activity also produces vacancies in the plastic region. Besides, the displacement induced by the indenter also drives changes of the network topology mainly due to densification, filament bending and twisting. Dislocation density is lower in the foam than in bulk indentation, due to the dislocation annihilation on the filament surfaces, but also because of changes in network topology help accommodate strain. Based on the simulation results, a nanoporous bcc foam behaves differently than a fcc foam, but still displays excellent mechanical properties for a low density material, and also offer additional technological advantages.

Simulations of dynamically cross-linked actin networks: Morphology, rheology, and hydrodynamic interactions.

Cross-linked actin networks are the primary component of the cell cytoskeleton and have been the subject of numerous experimental and modeling studies. While these studies have demonstrated that the networks are viscoelastic materials, evolving from elastic solids on short timescales to viscous fluids on long ones, questions remain about the duration of each asymptotic regime, the role of the surrounding fluid, and the behavior of the networks on intermediate timescales. Here we perform detailed simulations of passively cross-linked non-Brownian actin networks to quantify the principal timescales involved in the elastoviscous behavior, study the role of nonlocal hydrodynamic interactions, and parameterize continuum models from discrete stochastic simulations. To do this, we extend our recent computational framework for semiflexible filament suspensions, which is based on nonlocal slender body theory, to actin networks with dynamic cross linkers and finite filament lifetime. We introduce a model where the cross linkers are elastic springs with sticky ends stochastically binding to and unbinding from the elastic filaments, which randomly turn over at a characteristic rate. We show that, depending on the parameters, the network evolves to a steady state morphology that is either an isotropic actin mesh or a mesh with embedded actin bundles. For different degrees of bundling, we numerically apply small-amplitude oscillatory shear deformation to extract three timescales from networks of hundreds of filaments and cross linkers. We analyze the dependence of these timescales, which range from the order of hundredths of a second to the actin turnover time of several seconds, on the dynamic nature of the links, solvent viscosity, and filament bending stiffness. We show that the network is mostly elastic on the short time scale, with the elasticity coming mainly from the cross links, and viscous on the long time scale, with the effective viscosity originating primarily from stretching and breaking of the cross links. We show that the influence of nonlocal hydrodynamic interactions depends on the network morphology: for homogeneous meshworks, nonlocal hydrodynamics gives only a small correction to the viscous behavior, but for bundled networks it both hinders the formation of bundles and significantly lowers the resistance to shear once bundles are formed. We use our results to construct three-timescale generalized Maxwell models of the networks.

Field-induced deformation of ferromagnetic soft nanocomposites

Uniaxial ferromagnetic Ni nanorods were prepared by the anodic aluminum oxide (AAO) template method. Reversible magnetization changes, measured perpendicular to the texture axis, were analyzed in terms of the Stoner–Wohlfarth model (SW). Using empirical model parameters, a quantitative and consistent description of the orientation- and field-dependent magnetic torque per particle was achieved. The model was extended (eSW) to take into account the local rotation of the magnetic nanorods in a soft-elastic matrix. The nanorods were characterized regarding their size, using transmission electron microscopy (TEM), their magnetic moment and colloidal volume fraction, determined from static field-dependent optical transmission (SFOT) measurements, and their rotational shape factor, obtained from oscillating field-dependent optical transmission (OFOT). The eSW-model was used in the simulation of simple bending and torsion of thin composite filaments. These simulations were compared with experimental results with the focus on the effect of finite magnetic anisotropy and local elastic rotation on the field-induced deformation of soft nanocomposites. The high sensitivity of thin filaments enabled the investigation of torque-induced deformation at nanorod volume density as low as 10−4 at which particle-particle interactions were negligible. In addition, reprogramming of the magnetic texture by magnetization reversal and the resulting modification in the deformation pattern was investigated.

Discrete mechanical model of lamellipodial actin network implements molecular clutch mechanism and generates arcs and microspikes.

Mechanical forces, actin filament turnover, and adhesion to the extracellular environment regulate lamellipodial protrusions. Computational and mathematical models at the continuum level have been used to investigate the molecular clutch mechanism, calculating the stress profile through the lamellipodium and around focal adhesions. However, the forces and deformations of individual actin filaments have not been considered while interactions between actin networks and actin bundles is not easily accounted with such methods. We develop a filament-level model of a lamellipodial actin network undergoing retrograde flow using 3D Brownian dynamics. Retrograde flow is promoted in simulations by pushing forces from the leading edge (due to actin polymerization), pulling forces (due to molecular motors), and opposed by viscous drag in cytoplasm and focal adhesions. Simulated networks have densities similar to measurements in prior electron micrographs. Connectivity between individual actin segments is maintained by permanent and dynamic crosslinkers. Remodeling of the network occurs via the addition of single actin filaments near the leading edge and via filament bond severing. We investigated how several parameters affect the stress distribution, network deformation and retrograde flow speed. The model captures the decrease in retrograde flow upon increase of focal adhesion strength. The stress profile changes from compression to extension across the leading edge, with regions of filament bending around focal adhesions. The model reproduces the observed reduction in retrograde flow speed upon exposure to cytochalasin D, which halts actin polymerization. Changes in crosslinker concentration and dynamics, as well as in the orientation pattern of newly added filaments demonstrate the model's ability to generate bundles of filaments perpendicular (actin arcs) or parallel (microspikes) to the protruding direction.

Motor-Driven Restructuring of Cytoskeleton Composites Leads to Tunable Time-Varying Elasticity.

The composite cytoskeleton, comprising interacting networks of semiflexible actin and rigid microtubules, generates forces and restructures by using motor proteins such as myosins to enable key processes including cell motility and mitosis. Yet, how motor-driven activity alters the mechanics of cytoskeleton composites remains an open challenge. Here, we perform optical tweezers microrheology and confocal imaging of composites with varying actin-tubulin molar percentages (25-75, 50-50, and 75-25), driven by light-activated myosin II motors, to show that motor activity increases the elastic plateau modulus by over 2 orders of magnitude by active restructuring of both actin and microtubules that persists for hours after motor activation has ceased. Nonlinear microrheology measurements show that motor-driven restructuring increases the force response and stiffness and suppresses actin bending. The 50-50 composite exhibits the most dramatic mechanical response to motor activity due to the synergistic effects of added stiffness from the microtubules and sufficient motor substrate for pronounced activity.