Buckling of Microtubules on a 2D Elastic Medium

Growth directions and stiffness across cell layers determine whether tissues stay smooth or buckle

From smooth shapes to buckles, nature exhibits organs of various shapes and forms. How cells grow to produce smooth shaped leaves and sepals remain unclear. Here, we show that growth along the longitudinal axis during early developmental stages and comparable stiffness across both epidermal layers of Arabidopsis sepals are essential for smoothness, as seen in the wild type. We identified a mutant (as2-7D) with ectopic expression of ASYMMETRIC LEAVES 2 (AS2) on the outer epidermis. Our analysis reveals that ectopic AS2 expression causes the outer epidermis of as2-7D sepals to buckle during early stages of sepal development. We show that buckling of the outer epidermis occurs due to conflicting cell growth directions and unequal tissue stiffness across the epidermal layers. Overexpression of cyclin-dependent kinase (CDK) inhibitor Kip-related protein 1 (KRP1) in as2-7D restores sepal smoothness by aligning the growth directions of the outer epidermal cells along the longitudinal axis, while also increasing the overall stiffness of the outer epidermis. Furthermore, buckling is associated with the convergence of auxin efflux transporter protein PIN-FORMED 1 (PIN1) to generate outgrowth in the sepals at later stages, suggesting that buckling can initiate outgrowths. Our findings suggest that in addition to molecular cues influencing tissue mechanics, tissue mechanics can also modulate molecular signals, giving rise to well-defined shapes.

Microtubule Deformation Modulates Intracellular Transport by Kinesin Differently Than Dynein

Mechanical stress on cells is transmitted through many biological processes, for example, cell shape control, tissue patterning, and axonal homeostasis. Microtubules, a cytoskeletal component, presumably play a significant role in the mechanoregulation of cellular processes. We investigate motor protein-driven transport of quantum dots along mechanically deformed microtubules. We found that microtubule deformation significantly slowed kinesin-driven transport, whereas we previously reported dynein-driven transport was rather robust. Such dualistic modulation of transportation dynamics of the motor proteins by microtubule deformation can be attributed to the altered affinity of the motor proteins for buckled microtubules. Our results may form the basis for understanding microtubules' role in regulating cellular processes in a mechanically adverse environment through its detection ability and response to mechanical stress.

Multi-kinesin clusters impart mechanical stress that reveals mechanisms of microtubule breakage in cells

Microtubules are cytoskeletal filaments that provide structural support for numerous cellular processes. Despite their high rigidity, microtubules can be dramatically bent in cells and it is unknown how much force a microtubule can withstand before breaking. We find that liquid-liquid phase separation of the kinesin-3 motor KIF1C results in multi-kinesin clusters that entangle neighboring microtubules and impose a high level of mechanical stress that results in microtubule breakage and disassembly. Combining computational simulations and experiments, we show that microtubule fragmentation is enhanced by having a highly processive kinesin motor domain, a stiff clustering mechanism, and sufficient drag force on the microtubules. We estimate a rupture force for microtubules in cells of 70-120 pN, which is lower than previous estimates based on in vitro studies with taxol-stabilized microtubules. These results indicate that the presence of multiple kinesins on a cargo has the potential to cause microtubule breakage. We propose that mechanisms exist to protect microtubule integrity by releasing either the motor-cargo or motor-microtubule interaction, thereby preventing the accumulation of mechanical stress upon the engagement of multi-motor clusters with microtubules.

Global alignment and local curvature of microtubules in mouse fibroblasts are robust against perturbations of vimentin and actin

The eukaryotic cytoskeleton is an intricate network of three types of mechanically distinct biopolymers - actin filaments, microtubules and intermediate filaments (IFs). These filamentous networks determine essential cellular functions and properties. Among them, microtubules are important for intracellular transport and establishing cell polarity during migration. Despite their intrinsic stiffness, they exhibit characteristic bending and buckling in cells due to nonthermal forces acting on them. Interactions between cytoskeletal filaments have been found but are complex and diverse with respect to their effect on the mechanical behavior of the filaments and the architecture of networks. We systematically study how actin and vimentin IFs influence the network structure and local bending of microtubules by analyzing fluorescence microscopy images of mouse fibroblasts on protein micropatterns. Our automated analysis averages over large amounts of data to mitigate the effect of the considerable natural variance in biological cell data. We find that the radial orientation of microtubules in circular cells is robust and is established independently of vimentin and actin networks. Observing the local curvature of microtubules, we find highly similar average bending of microtubules in the entire cell regardless of the cytoskeletal surrounding. Small systematic differences cannot be attributed directly to vimentin and actin densities. Our results suggest that, on average, microtubules in unpolarized mouse fibroblasts are unexpectedly independent of the rest of the cytoskeleton in their global network structure and their local curvature.

Nonequilibrium Self-Assembly of Microtubules Through Stepwise Sequential Interactions of DNA

The assembly of biological systems forms nonequilibrium patterns with different functionalities through molecular-level communication via stepwise sequential interaction and activation. The mimicking of this molecular signaling offers extensive opportunities to design self-assemblies of bioinspired synthetic nonequilibrium systems to develop molecular robots with active, adaptive, and autonomous behavior. Herein, the design and construction of biomolecular motor system, microtubule (MT)-kinesin based molecular swarm system, are reported through stepwise sequential interactions of DNA. DNA signals are exchanged between three different DNA-tethered MTs, whereby the DNA signal from the first MT can activate the DNA strand on the second MT by communicating through physical contact, which facilitates assembly formation between the second and third DNA-tethered MTs. The DNA strands on the MTs can recognize the specific sequences of other DNA strands in the system and communicate with the complementary DNA on other MTs. This work will pave the way for developing autonomous molecular machines with advanced functionalities for complex nanotechnological applications.

Mechanical fatigue in microtubules

Mechanical failure of biological nanostructures due to sustained force application has been studied in great detail. In contrast, fatigue failure arising from repeated application of subcritical stresses has received little attention despite its prominent role in engineering and potentially biology. Here, paclitaxel-stabilized microtubules are up to 256 times bent into sinusoidal shapes of varying wavelength and the frequency of breaking events are observed. These experiments allow the calculation of fatigue life parameters for microtubules. Repeated buckling due to 12.5% compression-equal to the compression level experienced by microtubules in contracting cardiomyocytes - results in failure after in average 5 million cycles, whereas at 20.0% compression failure occurs after in average one thousand cycles. The fatigue strength (Basquin) exponent B is estimated as - 0.054±0.009.

Tensile Stress on Microtubules Facilitates Dynein-Driven Cargo Transport

Mechanical stress significantly affects the physiological functions of cells, including tissue homeostasis, cytoskeletal alterations, and intracellular transport. As a major cytoskeletal component, microtubules respond to mechanical stimulation by altering their alignment and polymerization dynamics. Previously, we reported that microtubules may modulate cargo transport by one of the microtubule-associated motor proteins, dynein, under compressive mechanical stress. Despite the critical role of tensile stress in many biological functions, how tensile stress on microtubules regulates cargo transport is yet to be unveiled. The present study demonstrates that the low-level tensile stress-induced microtubule deformation facilitates dynein-driven transport. We validate our experimental findings using all-atom molecular dynamics simulation. Our study may provide important implications for developing new therapies for diseases that involve impaired intracellular transport.

Can repetitive mechanical motion cause structural damage to axons?

Biological structures have evolved to very efficiently generate, transmit, and withstand mechanical forces. These biological examples have inspired mechanical engineers for centuries and led to the development of critical insights and concepts. However, progress in mechanical engineering also raises new questions about biological structures. The past decades have seen the increasing study of failure of engineered structures due to repetitive loading, and its origin in processes such as materials fatigue. Repetitive loading is also experienced by some neurons, for example in the peripheral nervous system. This perspective, after briefly introducing the engineering concept of mechanical fatigue, aims to discuss the potential effects based on our knowledge of cellular responses to mechanical stresses. A particular focus of our discussion are the effects of mechanical stress on axons and their cytoskeletal structures. Furthermore, we highlight the difficulty of imaging these structures and the promise of new microscopy techniques. The identification of repair mechanisms and paradigms underlying long-term stability is an exciting and emerging topic in biology as well as a potential source of inspiration for engineers.

A mechanical transition from tension to buckling underlies the jigsaw puzzle shape morphogenesis of histoblasts in the Drosophila epidermis

The polygonal shape of cells in proliferating epithelia is a result of the tensile forces of the cytoskeletal cortex and packing geometry set by the cell cycle. In the larval Drosophila epidermis, two cell populations, histoblasts and larval epithelial cells, compete for space as they grow on a limited body surface. They do so in the absence of cell divisions. We report a striking morphological transition of histoblasts during larval development, where they change from a tensed network configuration with straight cell outlines at the level of adherens junctions to a highly folded morphology. The apical surface of histoblasts shrinks while their growing adherens junctions fold, forming deep lobules. Volume increase of growing histoblasts is accommodated basally, compensating for the shrinking apical area. The folded geometry of apical junctions resembles elastic buckling, and we show that the imbalance between the shrinkage of the apical domain of histoblasts and the continuous growth of junctions triggers buckling. Our model is supported by laser dissections and optical tweezer experiments together with computer simulations. Our analysis pinpoints the ability of histoblasts to store mechanical energy to a much greater extent than most other epithelial cell types investigated so far, while retaining the ability to dissipate stress on the hours time scale. Finally, we propose a possible mechanism for size regulation of histoblast apical size through the lateral pressure of the epidermis, driven by the growth of cells on a limited surface. Buckling effectively compacts histoblasts at their apical plane and may serve to avoid physical harm to these adult epidermis precursors during larval life. Our work indicates that in growing nondividing cells, compressive forces, instead of tension, may drive cell morphology.

Role of tubulin C-terminal tail on mechanical properties of microtubule

Tubulin C-terminal tail (CTT) is a disordered segment extended from each tubulin monomer of αβ tubulin heterodimers, the building blocks of microtubules. The tubulin CTT contributes to the cellular function of microtubules such as intracellular transportation by regulating their interaction with other proteins and cell shape regulation by controlling microtubule polymerization dynamics. Although the mechanical integrity of microtubules is crucial for their functions, the role of tubulin CTT on microtubule mechanical properties has remained elusive. In this work, we investigate the role of tubulin CTTs in regulating the mechanical properties of microtubules by estimating the persistence lengths and investigating the buckling behavior of microtubules with and without CTT. We find that microtubules with intact CTTs exhibit twice the rigidity of microtubules lacking tubulin CTTs. Our study will widen the scope of altering microtubule mechanical properties for its application in nano bio-devices and lead to novel therapeutic approaches for neurodegenerative diseases with altered microtubule properties.

Measuring mechanical properties with high-speed atomic force microscopy

High-speed atomic force microscopy (HS-AFM) is now a widely used technique to study the dynamics of single biomolecules and complex structures. In the past, it has mainly been used to capture surface topography as structural analysis, leading to important discoveries not attainable by other methods. Similar to conventional AFM, the scope of HS-AFM was recently expanded to encompass quantities beyond topography, such as the measurement of mechanical properties. This review delves into various methodologies for assessing mechanical properties, ranging from semi-quantitative approaches to precise force measurements and their corresponding sample responses. We will focus on the application to single proteins such as bridging integrator-1, ion channels such as Piezo1, complex structures such as microtubules and supramolecular fibers. In all these examples, the unique combination of quantifiable force application and high spatiotemporal resolution allows to unravel mechanisms that cannot be investigated by conventional means.

Coordination, cooperation, competition, crowding and congestion of molecular motors: Theoretical models and computer simulations

Cytoskeletal motor proteins are biological nanomachines that convert chemical energy into mechanical work to carry out various functions such as cell division, cell motility, cargo transport, muscle contraction, beating of cilia and flagella, and ciliogenesis. Most of these processes are driven by the collective operation of several motors in the crowded viscous intracellular environment. Imaging and manipulation of the motors with powerful experimental probes have been complemented by mathematical analysis and computer simulations of the corresponding theoretical models. In this article, we illustrate some of the key theoretical approaches used to understand how coordination, cooperation and competition of multiple motors in the crowded intra-cellular environment drive the processes that are essential for biological function of a cell. In spite of the focus on theory, experimentalists will also find this article as an useful summary of the progress made so far in understanding multiple motor systems.

Effects of three microtubule-associated proteins (MAP2, MAP4, and Tau) on microtubules' physical properties and neurite morphology

The physical properties of cytoskeletal microtubules have a multifaceted effect on the expression of their cellular functions. A superfamily of microtubule-associated proteins, MAP2, MAP4, and tau, promote the polymerization of microtubules, stabilize the formed microtubules, and affect the physical properties of microtubules. Here, we show differences in the effects of these three MAPs on the physical properties of microtubules. When microtubule-binding domain fragments of MAP2, tau, and three MAP4 isoforms were added to microtubules in vitro and observed by fluorescence microscopy, tau-bound microtubules showed a straighter morphology than the microtubules bound by MAP2 and the three MAP4 isoforms. Flexural rigidity was evaluated by the shape of the teardrop pattern formed when microtubules were placed in a hydrodynamic flow, revealing that tau-bound microtubules were the least flexible. When full-length MAPs fused with EGFP were expressed in human neuroblastoma (SH-SY5Y) cells, the microtubules in apical regions of protrusions expressing tau were straighter than in cells expressing MAP2 and MAP4. On the other hand, the protrusions of tau-expressing cells had the fewest branches. These results suggest that the properties of microtubules, which are regulated by MAPs, contribute to the morphogenesis of neurites.

Molecular and cellular level characterization of cytoskeletal mechanics using a quartz crystal microbalance

A quartz crystal microbalance (QCM) is an instrument that has the ability to measure nanogram-level changes in mass on a quartz sensor and is traditionally used to probe surface interactions and assembly kinetics of synthetic systems. The addition of dissipation monitoring (QCM-D) facilitates the study of viscoelastic systems, such as those relevant to molecular and cellular mechanics. Due to real-time recording of frequency and dissipation changes and single protein-level precision, the QCM-D is effective in interrogating the viscoelastic properties of cell surfaces and in vitro cellular components. However, few studies focus on the application of this instrument to cytoskeletal systems, whose dynamic parts create interesting emergent mechanics as ensembles that drive essential tasks, such as division and motility. Here, we review the ability of the QCM-D to characterize key kinetic and mechanical features of the cytoskeleton through in vitro reconstitution and cellular assays and outline how QCM-D studies can yield insightful mechanical data alone and in tandem with other biophysical characterization techniques.

Biomechanical, biophysical and biochemical modulators of cytoskeletal remodelling and emergent stem cell lineage commitment

Across complex, multi-time and -length scale biological systems, redundancy confers robustness and resilience, enabling adaptation and increasing survival under dynamic environmental conditions; this review addresses ubiquitous effects of cytoskeletal remodelling, triggered by biomechanical, biophysical and biochemical cues, on stem cell mechanoadaptation and emergent lineage commitment. The cytoskeleton provides an adaptive structural scaffold to the cell, regulating the emergence of stem cell structure-function relationships during tissue neogenesis, both in prenatal development as well as postnatal healing. Identification and mapping of the mechanical cues conducive to cytoskeletal remodelling and cell adaptation may help to establish environmental contexts that can be used prospectively as translational design specifications to target tissue neogenesis for regenerative medicine. In this review, we summarize findings on cytoskeletal remodelling in the context of tissue neogenesis during early development and postnatal healing, and its relevance in guiding lineage commitment for targeted tissue regeneration. We highlight how cytoskeleton-targeting chemical agents modulate stem cell differentiation and govern responses to mechanical cues in stem cells' emerging form and function. We further review methods for spatiotemporal visualization and measurement of cytoskeletal remodelling, as well as its effects on the mechanical properties of cells, as a function of adaptation. Research in these areas may facilitate translation of stem cells' own healing potential and improve the design of materials, therapies, and devices for regenerative medicine.

A minimal model of elastic instabilities in biological filament bundles

We present a model of a system of elastic fibres which exhibits complex, coupled, nonlinear deformations via a connecting elastic spring network. This model can capture physically observed deformations such as global buckling, pinching and internal collapse. We explore the transitions between these deformation modes numerically, using an energy minimization approach, highlighting how supported environments, or stiff outer sheath structures, favour internal structural collapse over global deformation. We then derive a novel analytic buckling criterion for the internal collapse of the system, a mode of structural collapse pertinent in many biological filament bundles such as the optic nerve bundle and microtubule bundles involved in cell abscission.

Microtubule Preparation for Investigation with High-Speed Atomic Force Microscopy

High-speed atomic force microscopy (AFM) is a versatile method that can visualize proteins and protein systems on the nanometer scale and at a temporal resolution of 100 ms. The application to microtubules can not only reveal structural information with single-tubulin resolution but can also extract mechanical information and allows to study single motor proteins walking on microtubules, among others. This chapter provides a step-by-step guide from microtubule polymerization to successful observation with high-speed AFM.

Dynamic Pattern Formation of Active Matters Triggered by Mechanical Stimuli

In vitro gliding assay of the filamentous protein microtubule (MT) on a kinesin motor protein coated surface has appeared as a classic platform for studying active matters. At high densities, the gliding MTs spontaneously align and self-organize into fascinating large-scale patterns. Application of mechanical stimuli e.g., stretching stimuli to the MTs gliding on a kinesin-coated surface can modulate their self-organization and patterns according to the boundary conditions. Depending on the mode of stretching, MT at high densities change their moving direction and exhibit various kinds of patterns such as stream, zigzag and vortex pattern. In this chapter, we discuss detail procedures on how to apply mechanical stimuli to the moving MTs on a kinesin coated substrate.

Cargo Transport by Microtubule-Associated Motor Protein Along Mechanically Deformed Microtubules

Mechanical forces play pivotal roles in regulating various cellular functions. Biomolecular motor protein-driven intracellular transportation is one example which is affected by mechanical forces, although the mechanism at molecular level is unknown. In this chapter, we describe deformation of microtubules under compressive stress and we show that such deformation of microtubules affects the kinetics of dynein-driven cargo transportation along the microtubules. The extent of alteration in the kinetics of dynein-driven transportation is found strongly dependent on the extent of deformation of microtubules under compressive stress.

Mechanical Deformation of Microtubules on a Two-Dimensional Elastic Medium

Microtubule, the most rigid filamentous protein in cytoskeleton, plays significant roles in cellular mechano-transduction and mechano-regulation of cellular functions. In cells, the mechanical stress serves as a prevalent stimulus to frequently cause deformation of the microtubules participating in various cellular events. While the experimental and simulation-based approaches have confirmed the role of mechanical stress to tune mechanical properties of microtubule. Yet, the effect of mechanical force on the structural stability and the mechanism of microtubule deformation have remained obscure. Here, we describe the mechanical stress-induced deformation of microtubules using a custom-made mechanical device. We designed the device in a way which allows the microtubules to undergo deformation as response to the applied stress while attached on a two-dimensional elastic substrate through interaction with microtubule-associated motor protein, kinesin. We provide here the method to cause controlled bucking or fragmentation of microtubules by applying compressive or tensile stress on the microtubules, respectively. Such study is crucial to understand the mechanism of deformation in microtubules in cellular environment and their consequences in physiological activities.

Cytoskeletal Tensegrity in Microgravity

In order for Man to venture further into Space he will have to adapt to its conditions, including microgravity. Life as we know it has evolved on Earth with a substantial gravitational field. If they spend considerable time away from Earth, astronauts experience physiological, mental, and anatomical changes. It is not clear if these are pathological or adaptations. However, it is true that they experience difficulties on their return to stronger gravity. The cytoskeleton is a key site for the detection of gravitational force within the body, due to its tensegrity architecture. In order to understand what happens to living beings in space, we will need to unravel the role cytoskeletal tensegrity architecture plays in the building and function of cells, organs, the body, and mind.

Controlling the length of self-assembled microtubes through mechanical stress-induced scission

We demonstrate that mechanical stress-induced scission is an effective strategy to control the length of self-assembled microtubes. By applying mechanical stress with variable magnitude and mode, the length of microtubes can be tightly regulated. We have succeeded in reducing the average length of microtubes ∼twenty-fold through stretching and compression. The mechanical stress-induced scission of self-assembled, long microtubes into smaller fragments has no adverse effect on the functionality of the microtubes. This work will foster the applications of length-controlled, self-assembled microtubes in various fields.

Buckling and Torsional Instabilities of a Nanoscale Biological Rope Bound to an Elastic Substrate

Rope-like structures are ubiquitous in Nature. They are supermolecular assemblies of macromolecules responsible for the structural and mechanical integrity of plant and animal tissues. Collagen fibrils with diameters between 50 and 500 nm and their helical supermolecular structure are good examples of such nanoscale biological ropes. Like man-made laid ropes, fibrils are typically loaded in tension, and due to their large aspect ratio, they are, in principle, prone to buckling and torsional instabilities. One way to study buckling of a rigid rod is to attach it to a stretched elastic substrate that is then returned to its original length. In the case of single collagen fibrils, the observed behavior depends on the degree of hydration. By going from buckling in ambient conditions to immersed in a buffer, fibrils go from the well-known sine wave response to a localized behavior reminiscent of the bird-caging of laid ropes. In addition, in ambient conditions, the sine wave response coexists with the formation of loops along the length of the fibrils, as observed for the torsional instability of a twisted filament when tension is decreased. This work provides direct evidence that single collagen fibrils are highly susceptible to axial compression because of their helical supermolecular structure. As a result, mammals that use collagen fibrils as their main load-bearing element in many tissues have evolved mitigating strategies that protect single fibrils from axial compression damage.

Coupling Polar Adhesion with Traction, Spring, and Torque Forces Allows High-Speed Helical Migration of the Protozoan Parasite Toxoplasma

Among the eukaryotic cells that navigate through fully developed metazoan tissues, protozoans from the Apicomplexa phylum have evolved motile developmental stages that move much faster than the fastest crawling cells owing to a peculiar substrate-dependent type of motility, known as gliding. Best-studied models are the Plasmodium sporozoite and the Toxoplasma tachyzoite polarized cells for which motility is vital to achieve their developmental programs in the metazoan hosts. The gliding machinery is shared between the two parasites and is largely characterized. Localized beneath the cell surface, it includes actin filaments, unconventional myosin motors housed within a multimember glideosome unit, and apically secreted transmembrane adhesins. In contrast, less is known about the force mechanisms powering cell movement. Pioneered biophysical studies on the sporozoite and phenotypic analysis of tachyzoite actin-related mutants have added complexity to the general view that force production for parasite forward movement directly results from the myosin-driven rearward motion of the actin-coupled adhesion sites. Here, we have interrogated how forces and substrate adhesion-de-adhesion cycles operate and coordinate to allow the typical left-handed helical gliding mode of the tachyzoite. By combining quantitative traction force and reflection interference microscopy with micropatterning and expansion microscopy, we unveil at the millisecond and nanometer scales the integration of a critical apical anchoring adhesion with specific traction and spring-like forces. We propose that the acto-myoA motor directs the traction force which allows transient energy storage by the microtubule cytoskeleton and therefore sets the thrust force required for T. gondii tachyzoite vital helical gliding capacity.

Breaking of buckled microtubules is mediated by kinesins

Microtubule is the most rigid component of eukaryotic cytoskeleton that plays pivotal roles in many important cellular events. Microtubules are known to undergo bending or buckling in cells which often results in breaking of this cytoskeletal protein filament. Various cellular events such as cell migration, chromosome segregation, etc. are dependent on the buckling induced breaking of microtubules. However, the reason behind the breaking of buckled microtubules in cell has remained obscure yet. In this work, we have demonstrated breaking of microtubules on a 2D elastic medium by applying compressive stress. The applied compressive stress caused buckling of the microtubules which ultimately resulted in their breaking. We show that breaking of the buckled microtubules cannot be accounted for by considering the changes in curvature of the microtubules due to mechanical deformation. Our results confirm that, it is the interaction of kinesin, a microtubule-associated motor protein, with microtubules which plays the key role in breaking of the buckled microtubules on the 2D elastic medium. The breaking of buckled microtubules is ascribed to decrease in rigidity of microtubules upon interaction with kinesins. This work for the first time confirms the involvement of a microtubule-associated motor protein in breaking of microtubules under compressive stress, which will help further clarify the mechanism of breaking of buckled microtubules in cells and its significance in the cellular events.

Controlling the kinetics of interaction between microtubules and kinesins over a wide temperature range using the deep-sea osmolyte trimethylamine N-oxide

Trimethylamine N-oxide is found to be effective in regulating the interaction between microtubules and kinesins over a wide temperature range. The lifetime of the motility of microtubules on kinesins at high temperatures is prolonged using trimethylamine N-oxide. The activation energy of microtubule motility is increased by trimethylamine N-oxide. Prolonged operation at high temperatures decreased the activation energy of MT motility despite the increase in concentration of trimethylamine N-oxide.

Adaptation of Patterns of Motile Filaments under Dynamic Boundary Conditions

Boundary conditions are important for pattern formation in active matter. However, it is still not well-understood how alterations in the boundary conditions (dynamic boundary conditions) impact pattern formation. To elucidate the effect of dynamic boundary conditions on the pattern formation by active matter, we investigate an in vitro gliding assay of microtubules on a deformable soft substrate. The dynamic boundary conditions were realized by applying mechanical stress through stretching and compression of the substrate during the gliding assay. A single cycle of stretch-and-compression (relaxation) of the substrate induces perpendicular alignment of microtubules relative to the stretch axis, whereas repeated cycles resulted in zigzag patterns of microtubules. Our model shows that the orientation angles of microtubules correspond to the direction to attain smooth movement without buckling, which is further amplified by the collective migration of the microtubules. Our results provide an insight into understanding the rich dynamics in self-organization arising in active matter subjected to time-dependent boundary conditions.

Are microtubules tension sensors?

Mechanical signals play many roles in cell and developmental biology. Several mechanotransduction pathways have been uncovered, but the mechanisms identified so far only address the perception of stress intensity. Mechanical stresses are tensorial in nature, and thus provide dual mechanical information: stress magnitude and direction. Here we propose a parsimonious mechanism for the perception of the principal stress direction. In vitro experiments show that microtubules are stabilized under tension. Based on these results, we explore the possibility that such microtubule stabilization operates in vivo, most notably in plant cells where turgor-driven tensile stresses exceed greatly those observed in animal cells.

Cellular mechanical stress is a key determinant of cell shape and function, but how the cell senses stress direction is unclear. In this Perspective the authors propose that microtubules autonomously sense stress directions in plant cells, where tensile stresses are higher than in animal cells.

Kinesin motor density and dynamics in gliding microtubule motility

Kinesin motors and their associated filaments, microtubules, are essential to many biological processes. The motor and filament system can be reconstituted in vitro with the surface-adhered motors transporting the filaments along the surface. In this format, the system has been used to study active self-assembly and to power microdevices or perform analyte detection. However, fundamental properties of the system, such as the spacing of the kinesin motors bound to the microtubule and the dynamics of binding, remain poorly understood. We show that Fluorescence Interference Contrast (FLIC) microscopy can illuminate the exact height of the microtubule, which for a sufficiently low surface density of kinesin, reveals the locations of the bound motors. We examine the spacing of the kinesin motors on the microtubules at various kinesin surface densities and compare the results with theory. FLIC reveals that the system is highly dynamic, with kinesin binding and unbinding along the length of the microtubule as it is transported along the surface.

Control of swarming of molecular robots

Recently we demonstrated swarming of a self-propelled biomolecular motor system microtubule (MT)-kinesin where interactions among thousands of motile MTs were regulated in a highly programmable fashion by using DNA as a processor. However, precise control of this potential system is yet to be achieved to optimize the swarm behavior. In this work, we systematically controlled swarming of MTs on kinesin adhered surface by different physicochemical parameters of MT-kinesin and DNA. Tuning the length of DNA sequences swarming was precisely controlled with thermodynamic and kinetic feasibility. In addition, swarming was regulated using different concentration of DNA crosslinkers. Reversibility of swarming was further controlled by changing the concentration of strand displacement DNA signal allowing dissociation of swarm. The control over the swarm was accompanied by variable stiffness of MTs successfully, providing translational and circular motion. Moreover, the morphology of swarm was also found to be changed not only depending on the stiffness but also body length of MTs. Such detail study of precise control of swarming would provide new insights in developing a promising molecular swarm robotic system with desired functions.

Role of extrinsic mechanical force in the development of the RA-I tactile mechanoreceptor

Rapidly adapting type I (RA-I) mechanoreceptors play an important role in sensing the low-frequency vibration aspects of touch. The structure of the RA-I mechanoreceptor is extremely complex regardless of its small size, limiting our understanding of its mechanotransduction. As a result of the emergence of bioengineering, we previously proposed an in vitro bioengineering approach for RA-I receptors to overcome this limitation. Currently, the in vitro bioengineering approach for the RA-I receptor is not realizable given the lack of knowledge of its morphogenesis. This paper demonstrates our first attempt to interpret the cellular morphogenesis of the RA-I receptor. We found indications of extrinsic mechanical force nearby the RA-I receptor in the developing fingertip. Using a mechanical compression device, the axon of dorsal root ganglion (DRG) neurons buckled in vitro into a profile that resembled the morphology of the RA-I receptor. This work encourages further implementation of this bioengineering approach in tactile receptor-related research.

DNA-assisted swarm control in a biomolecular motor system

In nature, swarming behavior has evolved repeatedly among motile organisms because it confers a variety of beneficial emergent properties. These include improved information gathering, protection from predators, and resource utilization. Some organisms, e.g., locusts, switch between solitary and swarm behavior in response to external stimuli. Aspects of swarming behavior have been demonstrated for motile supramolecular systems composed of biomolecular motors and cytoskeletal filaments, where cross-linkers induce large scale organization. The capabilities of such supramolecular systems may be further extended if the swarming behavior can be programmed and controlled. Here, we demonstrate that the swarming of DNA-functionalized microtubules (MTs) propelled by surface-adhered kinesin motors can be programmed and reversibly regulated by DNA signals. Emergent swarm behavior, such as translational and circular motion, can be selected by tuning the MT stiffness. Photoresponsive DNA containing azobenzene groups enables switching between solitary and swarm behavior in response to stimulation with visible or ultraviolet light.

High-Resolution Imaging of a Single Gliding Protofilament of Tubulins by HS-AFM

In vitro gliding assay of microtubules (MTs) on kinesins has provided us with valuable biophysical and chemo-mechanical insights of this biomolecular motor system. Visualization of MTs in an in vitro gliding assay has been mainly dependent on optical microscopes, limited resolution of which often render them insufficient sources of desired information. In this work, using high speed atomic force microscopy (HS-AFM), which allows imaging with higher resolution, we monitored MTs and protofilaments (PFs) of tubulins while gliding on kinesins. Moreover, under the HS-AFM, we also observed splitting of gliding MTs into single PFs at their leading ends. The split single PFs interacted with kinesins and exhibited translational motion, but with a slower velocity than the MTs. Our investigation at the molecular level, using the HS-AFM, would provide new insights to the mechanics of MTs in dynamic systems and their interaction with motor proteins.

Characterization of microtubule buckling in living cells

Microtubules are filamentous biopolymers involved in essential biological processes. They form key structures in eukaryotic cells, and thus it is very important to determine the mechanisms involved in the formation and maintenance of the microtubule network. Microtubule bucklings are transient and localized events commonly observed in living cells and characterized by a fast bending and its posterior relaxation. Active forces provided by molecular motors have been indicated as responsible for most of these rapid deformations. However, the factors that control the shape amplitude and the time scales of the rising and release stages remain unexplored. In this work, we study microtubule buckling in living cells using Xenopus laevis melanophores as a model system. We tracked single fluorescent microtubules from high temporal resolution (0.3-2 s) confocal movies. We recovered the center coordinates of the filaments with 10-nm precision and analyzed the amplitude of the deformation as a function of time. Using numerical simulations, we explored different force mechanisms resulting in microtubule bending. The simulated events reproduce many features observed for microtubules, suggesting that a mechanistic model captures the essential processes underlying microtubule buckling. Also, we studied the interplay between actively transported vesicles and the microtubule network using a two-color technique. Our results suggest that microtubules may affect transport indirectly besides serving as tracks of motor-driven organelles. For example, they could obstruct organelles at microtubule intersections or push them during filament mechanical relaxation.

Buckling of microtubules on elastic media via breakable bonds

Buckling of microtubules observed in cells has been reconstructed on a two-dimensional elastic medium consisting of kinesins grafted over compressible substrates, enabling precise control of experimental conditions and quantitative analysis. However, interpretations of the observations have ambiguities due to inevitable experimental difficulties. In this study, with computer simulations, we investigated importance of the mode of interaction of microtubule with elastic medium in the buckling behavior of microtubule. By taking into consideration of forced-induced detachments of kinesins from microtubules, our simulations reproduced the previous experimental results, and showed deviations from predictions of the elastic foundation model. On the other hand, with hypothetical linkers permanently bound to microtubules, our simulation reproduced the predictions of the elastic foundation model. By analyzing the results of the simulations, we investigated as to why the difference arose. These findings indicate the importance of the mode of interaction of microtubule with the medium in the buckling behavior of microtubule. Our findings would bring new insights on buckling of microtubules in living cells.

Edge wrinkling in elastically supported pre-stressed incompressible isotropic plates

The equations governing the appearance of flexural static perturbations at the edge of a semi-infinite thin elastic isotropic plate, subjected to a state of homogeneous bi-axial pre-stress, are derived and solved. The plate is incompressible and supported by a Winkler elastic foundation with, possibly, wavenumber dependence. Small perturbations superposed onto the homogeneous state of pre-stress, within the three-dimensional elasticity theory, are considered. A series expansion of the plate kinematics in the plate thickness provides a consistent expression for the second variation of the potential energy, whose minimization gives the plate governing equations. Consistency considerations supplement a constraint on the scaling of the pre-stress so that the classical Kirchhoff-Love linear theory of pre-stretched elastic plates is retrieved. Moreover, a scaling constraint for the foundation stiffness is also introduced. Edge wrinkling is investigated and compared with body wrinkling. We find that the former always precedes the latter in a state of uni-axial pre-stretch, regardless of the foundation stiffness. By contrast, a general bi-axial pre-stretch state may favour body wrinkling for moderate foundation stiffness. Wavenumber dependence significantly alters the predicted behaviour. The results may be especially relevant to modelling soft biological materials, such as skin or tissues, or stretchable organic thin-films, embedded in a compliant elastic matrix.

Sensing surface mechanical deformation using active probes driven by motor proteins

Studying mechanical deformation at the surface of soft materials has been challenging due to the difficulty in separating surface deformation from the bulk elasticity of the materials. Here, we introduce a new approach for studying the surface mechanical deformation of a soft material by utilizing a large number of self-propelled microprobes driven by motor proteins on the surface of the material. Information about the surface mechanical deformation of the soft material is obtained through changes in mobility of the microprobes wandering across the surface of the soft material. The active microprobes respond to mechanical deformation of the surface and readily change their velocity and direction depending on the extent and mode of surface deformation. This highly parallel and reliable method of sensing mechanical deformation at the surface of soft materials is expected to find applications that explore surface mechanics of soft materials and consequently would greatly benefit the surface science.