Microtubule curvatures under perpendicular electric forces reveal a low persistence length

Building on-chip cytoskeletal circuits via branched microtubule networks

Controllable platforms to engineer robust cytoskeletal scaffolds have the potential to create novel on-chip nanotechnologies. Inspired by axons, we combined the branching microtubule (MT) nucleation pathway with microfabrication to develop "cytoskeletal circuits." This active matter platform allows control over the adaptive self-organization of uniformly polarized MT arrays via geometric features of microstructures designed within a microfluidic confinement. We build and characterize basic elements, including turns and divisions, as well as complex regulatory elements, such as biased division and MT diodes, to construct various MT architectures on a chip. Our platform could be used in diverse applications, ranging from efficient on-chip molecular transport to mechanical nano-actuators. Further, cytoskeletal circuits can serve as a tool to study how the physical environment contributes to MT architecture in living cells.

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.

Confined-microtubule assembly shapes three-dimensional cell wall structures in xylem vessels

Properly patterned deposition of cell wall polymers is prerequisite for the morphogenesis of plant cells. A cortical microtubule array guides the two-dimensional pattern of cell wall deposition. Yet, the mechanism underlying the three-dimensional patterning of cell wall deposition is poorly understood. In metaxylem vessels, cell wall arches are formed over numerous pit membranes, forming highly organized three-dimensional cell wall structures. Here, we show that the microtubule-associated proteins, MAP70-5 and MAP70-1, regulate arch development. The map70-1 map70-5 plants formed oblique arches in an abnormal orientation in pits. Microtubules fit the aperture of developing arches in wild-type cells, whereas microtubules in map70-1 map70-5 cells extended over the boundaries of pit arches. MAP70 caused the bending and bundling of microtubules. These results suggest that MAP70 confines microtubules within the pit apertures by altering the physical properties of microtubules, thereby directing the growth of pit arches in the proper orientation. This study provides clues to understanding how plants develop three-dimensional structure of cell walls.

The cyto-linker and scaffolding protein "plectin" mis-localization leads to softening of cancer cells

Discovering tools to prevent cancer progression requires understanding the fundamental differences between normal and cancer cells. More than a decade ago, atomic force microscopy (AFM) revealed cancer cells' softer body compared to their healthy counterparts. Here, we investigated the mechanism underlying the softening of cancerous cells in comparison with their healthy counterparts based on AFM high resolution stiffness tomography and 3D confocal microscopy. We showed microtubules (MTs) network in invasive ductal carcinoma cell cytoskeleton is basally located and segmented for around 400 nm from the cell periphery. Additionally, the cytoskeleton scaffolding protein plectin exhibits a mis-localization from the cytoplasm to the surface of cells in the carcinoma which justifies the dissociation of the MT network from the cell's cortex. Furthermore, the assessment of MTs' persistence length using a worm-like-chain (WLC) model in high resolution AFM images showed lower persistence length of the single MTs in ductal carcinoma compared to that in the normal state. Overall, these tuned mechanics support the invasive cells to ascertain more flexibility under compressive forces in small deformations. These data provide new insights into the structural origins of cancer aids in progression.

Filament displacement image analytics tool for use in investigating dynamics of dense microtubule networks

The fate and motion of cells is influenced by a variety of physical characteristics of their microenvironments. Traditionally, mechanobiology focuses on external mechanical phenomena such as cell movement and environmental sensing. However, cells are inherently dynamic, where internal waves and internal oscillations are a hallmark of living cells observed under a microscope. We propose that these internal mechanical rhythms provide valuable information about cell health. Therefore, it is valuable to capture the rhythms inside cells and quantify how drugs or physical interventions affect a cell's internal dynamics. One of the key dynamical entities inside cells is the microtubule network. Typically, microtubule dynamics are measured by end-protein tracking. In contrast, this paper introduces an easy-to-implement approach to measure the lateral motion of the microtubule filaments embedded within dense networks with (at least) confocal resolution image sequences. Our tool couples the computer vision algorithm Optical Flow with an anisotropic, rotating Laplacian of Gaussian filtering to characterize the lateral motion of dense microtubule networks. We then showcase additional image analytics used to understand the effect of microtubule orientation and regional location on lateral motion. We argue that our tool and these additional metrics provide a fuller picture of the active forcing environment within cells.

Biophysical ordering transitions underlie genome 3D re-organization during cricket spermiogenesis

Spermiogenesis is a radical process of differentiation whereby sperm cells acquire a compact and specialized morphology to cope with the constraints of sexual reproduction while preserving their main cargo, an intact copy of the paternal genome. In animals, this often involves the replacement of most histones by sperm-specific nuclear basic proteins (SNBPs). Yet, how the SNBP-structured genome achieves compaction and accommodates shaping remain largely unknown. Here, we exploit confocal, electron and super-resolution microscopy, coupled with polymer modeling to identify the higher-order architecture of sperm chromatin in the needle-shaped nucleus of the emerging model cricket Gryllus bimaculatus. Accompanying spermatid differentiation, the SNBP-based genome is strikingly reorganized as ~25nm-thick fibers orderly coiled along the elongated nucleus axis. This chromatin spool is further found to achieve large-scale helical twisting in the final stages of spermiogenesis, favoring its ultracompaction. We reveal that these dramatic transitions may be recapitulated by a surprisingly simple biophysical principle based on a nucleated rigidification of chromatin linked to the histone-to-SNBP transition within a confined nuclear space. Our work highlights a unique, liquid crystal-like mode of higher-order genome organization in ultracompact cricket sperm, and establishes a multidisciplinary methodological framework to explore the diversity of non-canonical modes of DNA organization.

Electro-detachment of kinesin motor domain from microtubule in silico

Kinesin is a motor protein essential in cellular functions, such as intracellular transport and cell-division, as well as for enabling nanoscopic transport in bio-nanotechnology. Therefore, for effective control of function for nanotechnological applications, it is important to be able to modify the function of kinesin. To circumvent the limitations of chemical modifications, here we identify another potential approach for kinesin control: the use of electric forces. Using full-atom molecular dynamics simulations (247,358 atoms, total time ∼ 4.4 μs), we demonstrate, for the first time, that the kinesin-1 motor domain can be detached from a microtubule by an intense electric field within the nanosecond timescale. We show that this effect is field-direction dependent and field-strength dependent. A detailed analysis of the electric forces and the work carried out by electric field acting on the microtubule-kinesin system shows that it is the combined action of the electric field pulling on the β-tubulin C-terminus and the electric-field-induced torque on the kinesin dipole moment that causes kinesin detachment from the microtubule. It is shown, for the first time in a mechanistic manner, that an electric field can dramatically affect molecular interactions in a heterologous functional protein assembly. Our results contribute to understanding of electromagnetic field-biomatter interactions on a molecular level, with potential biomedical and bio-nanotechnological applications for harnessing control of protein nanomotors.

Surface-limited reactions for spatial control of kinesin-microtubule motility assays using indirect irradiation of an electron beam

Gliding of microtubules (MTs) on kinesins has been applied to lab-on-a-chip devices, which enable autonomous transportation and detection of biomolecules in the field of bioengineering. For rapid fabrication and evaluation of the kinesin-MT based devices, optical control techniques have been developed for control of kinesin activity and density; however, use of caged molecules lacks spatial controllability for long-term experiments, and direct irradiations of UV light onto kinesin-coated surfaces are inherently damaging to MTs due to their depth limit since the heights of the kinesin-MT systems are at the tens of a nanometer scale. Considering surface electric fields in electrolytic solutions are shielded at the nanometer scale due to Debye shielding, in this study, we show that fine spatial control of kinesin density and activity is enabled using surface-limited electrochemical reactions induced by indirect irradiations of an electron beam (EB). An EB is indirectly irradiated onto the kinesins through a 100-nm-thick silicon nitride membrane, and the electrons scattered in the membrane can cause localized electrochemical effects to the kinesins. We show that these localized electrochemical effects cause both ablation of kinesins and motility control of kinesin activity by changing the EB acceleration voltage. In particular, the latter is achieved without complete ablation of MTs, though the MTs are indirectly irradiated by the EB. As a demonstration of on-demand control of gliding MTs, we show the accumulation of the MTs on a target area by scanning the EB. The proposed accumulation technique will lead to rapid prototyping of microdevices based on MT-kinesin motility assay systems.

Actin Architecture Steers Microtubules in Active Cytoskeletal Composite

Motility assays use surface-immobilized molecular motors to propel cytoskeletal filaments. They have been widely used to characterize motor properties and their impact on cytoskeletal self-organization. Moreover, the motility assays are a promising class of bioinspired active tools for nanotechnological applications. While these assays involve controlling the filament direction and speed, either as a sensory readout or a functional feature, designing a subtle control embedded in the assay is an ongoing challenge. Here, we investigate the interaction between gliding microtubules and networks of actin filaments. We demonstrate that the microtubule's behavior depends on the actin architecture. Both unbranched and branched actin decelerate microtubule gliding; however, an unbranched actin network provides additional guidance and effectively steers the microtubules. This effect, which resembles the recognition of cortical actin by microtubules, is a conceptually new means of controlling the filament gliding with potential application in the design of active materials and cytoskeletal nanodevices.

Dual-wavelength stopped-flow analysis of the lateral and longitudinal assembly kinetics of vimentin

Vimentin is a highly charged intermediate filament protein that inherently forms extended dimeric coiled coils, which serve as the basic building blocks of intermediate filaments. Under low ionic strength conditions, vimentin filaments dissociate into uniform tetrameric complexes of two anti-parallel-oriented, half-staggered coiled-coil dimers. By addition of salt, vimentin tetramers spontaneously reassemble into filaments in a time-dependent process: 1) lateral assembly of tetramers into unit-length filaments, 2) longitudinal annealing of unit-length filaments, and 3) longitudinal assembly of filaments coupled with subsequent radial compaction. To independently determine the lateral and longitudinal assembly kinetics, we measure with a stopped-flow instrument the static light scattering signal at two different wavelengths (405 and 594 nm) with a temporal resolution of 3 ms and analyze the signals based on Rayleigh-Gans theory. This theory considers that the intensity of the scattered light depends not only on the molecular weight of the scattering object but also on its shape. This shape dependence is more pronounced at shorter wavelengths, allowing us to decompose the scattered light signal into its components arising from lateral and longitudinal filament assembly. We demonstrate that both the lateral and longitudinal filament assembly kinetics increase with salt concentration.

Durability of Aligned Microtubules Dependent on Persistence Length Determines Phase Transition and Pattern Formation in Collective Motion

Collective motion is a ubiquitous phenomenon in nature. The collective motion of cytoskeleton filaments results mainly from dynamic collisions and alignments; however, the detailed mechanism of pattern formation still needs to be clarified. In particular, the influence of persistence length, which is a measure of filament flexibility, on collective motion is still unclear and lacks experimental verifications although it is likely to directly affect the orientational flexibility of filaments. Here, we investigated the collective motion of microtubules with different persistence lengths using a microtubule-kinesin motility system. We showed that local interactions between microtubules significantly vary depending on their persistence length. We demonstrated that the bundling of microtubules is enhanced by more durable alignment, rather than by greater likelihood of alignment. An agent-based computational model confirmed that the rigidity-dependent durability of microtubule alignment dominates their collective behavior.

Motility resilience of molecular shuttles against defective motors

Myosin and kinesin are biomolecular motors found in living cells. By propelling their associated cytoskeletal filaments, these biomolecular motors facilitate force generation and material transport in the cells. When extracted, the biomolecular motors are promising candidates for in vitro applications such as biosensor devices, on account of their high operating efficiency and nanoscale size. However, during integration into these devices, some of the motors become defective due to unfavorable adhesion to the substrate surface. These defective motors inhibit the motility of the cytoskeletal filaments which make up the molecular shuttles used in the devices. Difficulties in controlling the fraction of active and defective motors in experiments discourage systematic studies concerning the resilience of the molecular shuttle motility against the impedance of defective motors. Here, we used mathematical modelling to systematically examine the resilience of the propulsion by these molecular shuttles against the impedance of the defective motors. The model showed that the fraction of active motors on the substrate is the essential factor determining the resilience of the molecular shuttle motility. Approximately 40% of active kinesin or 80% of active myosin motors are required to constitute continuous gliding of molecular shuttles in their respective substrates. The simplicity of the mathematical model in describing motility behavior offers utility in elucidating the mechanisms of the motility resilience of molecular shuttles.

Measurement of the Persistence Length of Cytoskeletal Filaments using Curvature Distributions

Cytoskeletal filaments such as microtubules and actin filaments play important roles in the mechanical integrity of cells and the ability of cells to respond to their environment. Measuring the mechanical properties of cytoskeletal structures is crucial for gaining insight into intracellular mechanical stresses and their role in regulating cellular processes. One of the ways to characterize these mechanical properties is by measuring their persistence length, the average length over which filaments stay straight. There are several approaches in the literature for measuring filament deformations, such as Fourier analysis of images obtained using fluorescence microscopy. Here, we show how curvature distributions can be used as an alternative tool to quantify bio-filament deformations, and investigate how the apparent stiffness of filaments depends on the resolution and noise of the imaging system. We present analytical calculations of the scaling curvature distributions as a function of filament discretization, and test our predictions by comparing Monte Carlo simulations to results from existing techniques. We also apply our approach to microtubules and actin filaments obtained from in vitro gliding assay experiments with high densities of non-functional motors, and calculate the persistence length of these filaments. The presented curvature analysis is significantly more accurate compared to existing approaches for small data sets, and can be readily applied to both in vitro or in vivo filament data through the use of the open-source codes we provide.

Modeling material transport regulation and traffic jam in neurons using PDE-constrained optimization

The intracellular transport process plays an important role in delivering essential materials throughout branched geometries of neurons for their survival and function. Many neurodegenerative diseases have been associated with the disruption of transport. Therefore, it is essential to study how neurons control the transport process to localize materials to necessary locations. Here, we develop a novel optimization model to simulate the traffic regulation mechanism of material transport in complex geometries of neurons. The transport is controlled to avoid traffic jam of materials by minimizing a pre-defined objective function. The optimization subjects to a set of partial differential equation (PDE) constraints that describe the material transport process based on a macroscopic molecular-motor-assisted transport model of intracellular particles. The proposed PDE-constrained optimization model is solved in complex tree structures by using isogeometric analysis (IGA). Different simulation parameters are used to introduce traffic jams and study how neurons handle the transport issue. Specifically, we successfully model and explain the traffic jam caused by reduced number of microtubules (MTs) and MT swirls. In summary, our model effectively simulates the material transport process in healthy neurons and also explains the formation of a traffic jam in abnormal neurons. Our results demonstrate that both geometry and MT structure play important roles in achieving an optimal transport process in neuron.

Linking path and filament persistence lengths of microtubules gliding over kinesin

Microtubules and kinesin motor proteins are involved in intracellular transports in living cells. Such intracellular material transport systems can be reconstructed for utilisation in synthetic environments, and they are called molecular shuttles driven by kinesin motors. The performance of the molecular shuttles depends on the nature of their trajectories, which can be characterized by the path persistence length of microtubules. It has been theoretically predicted that the path persistence length should be equal to the filament persistence length of the microtubules, where the filament persistence length is a measure of microtubule flexural stiffness. However, previous experiments have shown that there is a significant discrepancy between the path and filament persistence lengths. Here, we showed how this discrepancy arises by using computer simulation. By simulating molecular shuttle movements under external forces, the discrepancy between the path and filament persistence lengths was reproduced as observed in experiments. Our close investigations of molecular shuttle movements revealed that the part of the microtubules bent due to the external force was extended more than it was assumed in the theory. By considering the extended length, we could elucidate the discrepancy. The insights obtained here are expected to lead to better control of molecular shuttle movements.

Design of Mechanical and Electrical Properties for Multidirectional Control of Microtubules

Microtubule (MT)-motor systems show promise as nanoscale actuator platforms for performing molecular manipulations in nanobiotechnology and micro total analysis systems. These systems have been demonstrated to exert a variety of functions, including the concentration, transportation, and detection of molecular cargos. Although gliding direction control of MTs is necessary for these applications, most direction control methods are currently conducted using micro/nanofabricated guiding structures and/or flow, magnetic, and electric field forces. These control methods force all MTs to exhibit identical gliding behaviors and destinations. In this chapter, we describe an active multidirectional control method for MT without guiding tracks. The bottom-up molecular design allowed MTs to be guided in designated directions under an electric field in a microfluidic device. By designing the stiffness and surface charge density of MTs, three types of MT (Stiff-MT, Soft-MT, and Charged soft-MT) with different mechanical and electrical properties are prepared. The gliding directions within an electric field are predicted according to the measured stiffness and electrophoretic mobility. Finally, the Stiff-MTs are separated from Soft-MTs and Charged soft-MTs with a microfluidic sorter.

Growth rate-dependent flexural rigidity of microtubules influences pattern formation in collective motion

Background

Microtubules (MTs) are highly dynamic tubular cytoskeleton filaments that are essential for cellular morphology and intracellular transport. In vivo, the flexural rigidity of MTs can be dynamically regulated depending on their intracellular function. In the in vitro reconstructed MT-motor system, flexural rigidity affects MT gliding behaviors and trajectories. Despite the importance of flexural rigidity for both biological functions and in vitro applications, there is no clear interpretation of the regulation of MT flexural rigidity, and the results of many studies are contradictory. These discrepancies impede our understanding of the regulation of MT flexural rigidity, thereby challenging its precise manipulation.

Results

Here, plausible explanations for these discrepancies are provided and a new method to evaluate the MT rigidity is developed. Moreover, a new relationship of the dynamic and mechanic of MTs is revealed that MT flexural rigidity decreases through three phases with the growth rate increases, which offers a method of designing MT flexural rigidity by regulating its growth rate. To test the validity of this method, the gliding performances of MTs with different flexural rigidities polymerized at different growth rates are examined. The growth rate-dependent flexural rigidity of MTs is experimentally found to influence the pattern formation in collective motion using gliding motility assay, which is further validated using machine learning.

Conclusion

Our study establishes a robust quantitative method for measurement and design of MT flexural rigidity to study its influences on MT gliding assays, collective motion, and other biological activities in vitro. The new relationship about the growth rate and rigidity of MTs updates current concepts on the dynamics and mechanics of MTs and provides comparable data for investigating the regulation mechanism of MT rigidity in vivo in the future.

Graphic Abstract

Supplementary Information

The online version contains supplementary material available at 10.1186/s12951-021-00960-y.

Tumor Treating Fields (TTFields) Hinder Cancer Cell Motility through Regulation of Microtubule and Acting Dynamics

Simple Summary

Tumor Treating Fields (TTFields), encompassing alternating electric fields within the intermediate frequency range, is an anticancer treatment delivered to the tumor region through transducer arrays placed non-invasively on the skin. Although established as an anti-mitotic treatment modality, the anti-metastatic potential of TTFields and their effect on rapid cytoskeletal dynamics during cellular motility warrant further investigation. In this study, we report that TTFields application induces changes in microtubule organization leading to interference with the directionality and robustness of cancer cell migration. We show that these changes in microtubule organization result in activation of GEF-H1/RhoA/ROCK signaling pathway, and the consequent formation of focal adhesions and changes in actin cytoskeleton architecture. Together, these results propose a novel mechanism by which TTFields induce changes in microtubule and actin organization and dynamics, thereby disrupting processes important for polarity generation and motility in cancer cells.

Abstract

Tumor Treating Fields (TTFields) are noninvasive, alternating electric fields within the intermediate frequency range (100–300 kHz) that are utilized as an antimitotic cancer treatment. TTFields are loco-regionally delivered to the tumor region through 2 pairs of transducer arrays placed on the skin. This novel treatment modality has been FDA-approved for use in patients with glioblastoma and malignant pleural mesothelioma based on clinical trial data demonstrating efficacy and safety; and is currently under investigation in other types of solid tumors. TTFields were shown to induce an anti-mitotic effect by exerting bi-directional forces on highly polar intracellular elements, such as tubulin and septin molecules, eliciting abnormal microtubule polymerization during spindle formation as well as aberrant cleavage furrow formation. Previous studies have demonstrated that TTFields inhibit metastatic properties in cancer cells. However, the consequences of TTFields application on cytoskeleton dynamics remain undetermined. In this study, methods utilized in combination to study the effects of TTFields on cancer cell motility through regulation of microtubule and actin dynamics included confocal microscopy, computational tools, and biochemical analyses. Mechanisms by which TTFields treatment disrupted cellular polarity were (1) interference with microtubule assembly and directionality; (2) altered regulation of Guanine nucleotide exchange factor-H1 (GEF-H1), Ras homolog family member A (RhoA), and Rho-associated coiled-coil kinase (ROCK) activity; and (3) induced formation of radial protrusions of peripheral actin filaments and focal adhesions. Overall, these data identified discrete effects of TTFields that disrupt processes crucial for cancer cell motility.

Molecular recognition mechanisms directing the self-assembly of biological structures

Self-assembling may be defined as the spontaneous association of material units into structures that are often capable of cyclic reorganization and functional behavior. Various molecular recognition processes stabilize assemblies of polymers and biological structures. The present article analyzes cases in which chemical, shape and other recognition mechanisms are individually or cooperatively operative. Simpler self-assembling theories reported in the literature are highlighted. Detailed processes for which chemical recognition is the prevailing, enthalpy-driven, process include the non-ideal component of miscibility, supramolecular polymerization, host-guest complexes and template polymerization. Also discussed are systems such as liquid crystalline closed polymers, ternary mesogenic systems and rigid crystalline polymers for which shape recognition is the prevailing entropy-driven process. Other recognition mechanisms include ion condensation effects, hydrophobic bonding and growth-coupled-to-orientation. Combinations of various recognition mechanisms are particularly evident in biological structures. Self-assembling mechanisms involved in the genesis of some biological systems can be scientifically identified, but much more needs to be known to describe the "engineered" assembling modes that support complex functional organs.

Different motilities of microtubules driven by kinesin-1 and kinesin-14 motors patterned on nanopillars

Kinesin is a motor protein that plays important roles in a variety of cellular functions. In vivo, multiple kinesin molecules are bound to cargo and work as a team to produce larger forces or higher speeds than a single kinesin. However, the coordination of kinesins remains poorly understood because of the experimental difficulty in controlling the number and arrangement of kinesins, which are considered to affect their coordination. Here, we report that both the number and spacing significantly influence the velocity of microtubules driven by nonprocessive kinesin-14 (Ncd), whereas neither the number nor the spacing changes the velocity in the case of highly processive kinesin-1. This result was realized by the optimum nanopatterning method of kinesins that enables immobilization of a single kinesin on a nanopillar. Our proposed method enables us to study the individual effects of the number and spacing of motors on the collective dynamics of multiple motors.

Transport of microtubules according to the number and spacing of kinesin motors on gold nano-pillars

Motor proteins function in in vivo ensembles to achieve cargo transport, flagellum motion, and mitotic cell division. Although the cooperativity of multiple motors is indispensable for physiological function, reconstituting the arrangement of motors in vitro is challenging, so detailed analysis of the functions of motor ensembles has not yet been achieved. Here, we developed an assay platform to study the motility of microtubules driven by a defined number of kinesin motors spaced in a definite manner. Gold (Au) nano-pillar arrays were fabricated on a silicon/silicon dioxide (Si/SiO₂) substrate with spacings of 100 nm to 500 nm. The thiol-polyethylene glycol (PEG)-biotin self-assembled monolayer (SAM) and silane-PEG-CH₃ SAM were then selectively formed on the pillars and SiO₂ surface, respectively. This allowed for both immobilization of kinesin molecules on Au nano-pillars in a precise manner and repulsion of kinesins from the SiO₂ surface. Using arrayed kinesin motors, we report that motor number and spacing do not influence the motility of microtubules driven by kinesin-1 motors. This assay platform is applicable to all kinds of biotinylated motors, allows the study of the effects of motor number and spacing, and is expected to reveal novel behaviors of motor proteins.

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.

Local direction change of surface gliding microtubules

In vitro gliding assay, microtubule translocation by kinesin motor proteins on a surface, has been used as an engineering tool in analyte detection, molecular cargo transport, and other applications. Although controlling the moving direction is often necessary to realize these applications, current direction control methods focus largely on lithographic microfabrication of tracks or external fields on the microtubules. These methods are effective, but are relatively complicated. In addition, they cannot target particular microtubules without affecting others. In this study, we propose a facile approach that can make local direction changes for selected microtubules using a polystyrene particle as a circular motion center and a DNA double helix with streptavidin as a capture arm. The DNA arm captures a microtubule in the close proximity of the immobilized particle via biotin-streptavidin interaction and changes the moving direction ~10° on average. In contrast, no significant direction changes are observed other than random variations with streptavidin-less DNA arms (normal distribution centered at 0°), similar to regular motility assay. The particle-assisted local direction change scheme is compared with a flow field-based ensemble method. The combination of flow and kinesin interactions with each microtubule exerts a force to change the direction, ultimately aligning it to the flow field, regardless of its initial direction. A simple model based on the force balance predicts the time needed for such an alignment. Overall, the particle-based local scheme is distinct and different from ensemble methods such as crossflow that changes directions of all microtubules in the field, thus offering unique utility in engineering applications.

Effect of Nucleotide State on the Protofilament Conformation of Tubulin Octamers

At the molecular level, the dynamic instability (random growth and shrinkage) of the microtubule (MT) is driven by the nucleotide state (GTP vs GDP) in the β subunit of the tubulin dimers at the MT cap. Here, we use large-scale molecular dynamics (MD) simulations and normal-mode analysis (NMA) to characterize the effect of a single GTP cap layer on tubulin octamers composed of two neighboring protofilaments (PFs). We utilize recently reported high-resolution structures of dynamic MTs to simulate a GDP octamer both with and without a single GTP cap layer. We perform multiple replicas of long-time atomistic MD simulations (3 replicas, 0.3 μs for each replica, 0.9 μs for each octamer system, and 1.8 μs total) of both octamers. We observe that a single GTP cap layer induces structural differences in neighboring PFs, finding that one PF possesses a gradual curvature, compared to the second PF which possesses a kinked conformation. This results in either curling or splaying between these PFs. We suggest that this is due to asymmetric strengths of longitudinal contacts between the two PFs. Furthermore, using NMA, we calculate mechanical properties of these octamer systems and find that octamer system with a single GTP cap layer possesses a lower flexural rigidity.

Microtubules soften due to cross-sectional flattening

We use optical trapping to continuously bend an isolated microtubule while simultaneously measuring the applied force and the resulting filament strain, thus allowing us to determine its elastic properties over a wide range of applied strains. We find that, while in the low-strain regime, microtubules may be quantitatively described in terms of the classical Euler-Bernoulli elastic filament, above a critical strain they deviate from this simple elastic model, showing a softening response with increasingdeformations. A three-dimensional thin-shell model, in which the increased mechanical compliance is caused by flattening and eventual buckling of the filament cross-section, captures this softening effect in the high strain regime and yields quantitative values of the effective mechanical properties of microtubules. Our results demonstrate that properties of microtubules are highly dependent on the magnitude of the applied strain and offer a new interpretation for the large variety in microtubule mechanical data measured by different methods.

A computational framework for cortical microtubule dynamics in realistically shaped plant cells

Plant morphogenesis is strongly dependent on the directional growth and the subsequent oriented division of individual cells. It has been shown that the plant cortical microtubule array plays a key role in controlling both these processes. This ordered structure emerges as the collective result of stochastic interactions between large numbers of dynamic microtubules. To elucidate this complex self-organization process a number of analytical and computational approaches to study the dynamics of cortical microtubules have been proposed. To date, however, these models have been restricted to two dimensional planes or geometrically simple surfaces in three dimensions, which strongly limits their applicability as plant cells display a wide variety of shapes. This limitation is even more acute, as both local as well as global geometrical features of cells are expected to influence the overall organization of the array. Here we describe a framework for efficiently simulating microtubule dynamics on triangulated approximations of arbitrary three dimensional surfaces. This allows the study of microtubule array organization on realistic cell surfaces obtained by segmentation of microscopic images. We validate the framework against expected or known results for the spherical and cubical geometry. We then use it to systematically study the individual contributions of global geometry, cell-edge induced catastrophes and cell-face induced stability to array organization in a cuboidal geometry. Finally, we apply our framework to analyze the highly non-trivial geometry of leaf pavement cells of Arabidopsis thaliana, Nicotiana benthamiana and Hedera helix. We show that our simulations can predict multiple features of the microtubule array structure in these cells, revealing, among others, strong constraints on the orientation of division planes.

Control of molecular shuttles by designing electrical and mechanical properties of microtubules

Kinesin-driven microtubules have been focused on to serve as molecular transporters, called "molecular shuttles," to replace micro/nanoscale molecular manipulations necessitated in micro total analysis systems. Although transport, concentration, and detection of target molecules have been demonstrated, controllability of the transport directions is still a major challenge. Toward broad applications of molecular shuttles by defining multiple moving directions for selective molecular transport, we integrated a bottom-up molecular design of microtubules and a top-down design of a microfluidic device. The surface charge density and stiffness of microtubules were controlled, allowing us to create three different types of microtubules, each with different gliding directions corresponding to their electrical and mechanical properties. The measured curvature of the gliding microtubules enabled us to optimize the size and design of the device for molecular sorting in a top-down approach. The integrated bottom-up and top-down design achieved separation of stiff microtubules from negatively charged, soft microtubules under an electric field. Our method guides multiple microtubules by integrating molecular control and microfluidic device design; it is not only limited to molecular sorters but is also applicable to various molecular shuttles with the high controllability in their movement directions.

Systems chemistry

A series of exciting phenomena that can occur in supramolecular systems away from equilibrium are reviewed.

Spatiotemporal control of kinesin motor protein by photoswitches enabling selective single microtubule regulations

Artificial control of bio-nanomachines should have a major impact on the development of controllable transport systems for specific cargo transport on chips. Precise spatiotemporal control and local regulation of the bio-motor activity will, however, be necessary if we are to accomplish such a goal. In this study, we exploited the photoswitching properties of azobenzene-based high-energy molecules and inhibitors to control a single kinesin-driven microtubule that has potential to work as a nanocarrier for molecular cargos. In particular, we could influence the local concentration and dispersion of the microtubules at any desired position and time by irradiating a local area of the motility system at one wavelength, while irradiating the entire area at another wavelength, to enrich either cis or trans isomers of photoswitches in the selected region. Furthermore, various regulations (e.g., transporting, bending, breaking) of single microtubules were possible while almost arresting ambient microtubules-all without the need for any surface patterning.

Elastic Anisotropy Scenario for Cooperative Binding of Kinesin-Coated Beads on Microtubules

Muto et al. reported in 2005 an observation called cooperative binding, according to which the initial binding of a bead covered with active kinesins on a microtubule filament was capable of favoring the subsequent binding of similar beads on the same filament up to distances of the order of a few microns. This positive bias is stronger ahead of the initially bound bead than behind. We explain this effect by combining the recently proposed notion of shear screening length with the notion of localized tubulin conformational transition induced by motor binding. Elastic terms linked to the polarity of protofilaments, up to now ignored, provide adequate description to the long-range elastic shear generated by motor binding. The subsequent binding is favored when and where the shear displacement of protofilaments meets the requirement for specific strong binding. We propose experimental tests of our model, which open the way to a new type of spectroscopy for biomolecular processes.

A nonequilibrium power balance relation for analyzing dissipative filament dynamics

Biofilaments like F-actin or microtubules, as well as cilia, flagella, or filament bundles, are often deformed by distributed and time-dependent external forces. It is highly desirable to characterize these filaments' mechanics in an efficient way, either using a single experiment or a high throughput method. We here propose a dynamic power balance approach to study nonequilibrium filament dynamics and exemplify it both experimentally and theoretically by applying it to microtubule gliding assay dynamics. Its usefulness is highlighted by the experimental determination of the lateral friction coefficient for microtubules on kinesins. In contrast to what is usually assumed, friction is anisotropic, in a similar fashion as hydrodynamic friction. We also exemplify, by considering a microtubule buckling event, that if at least one parameter is known in advance, all other parameters can be determined by analyzing a single time-dependent experiment.

Buckling of Microtubules on a 2D Elastic Medium

We have demonstrated compression stress induced mechanical deformation of microtubules (MTs) on a two-dimensional elastic medium and investigated the role of compression strain, strain rate, and a MT-associated protein in the deformation of MTs. We show that MTs, supported on a two-dimensional substrate by a MT-associated protein kinesin, undergo buckling when they are subjected to compression stress. Compression strain strongly affects the extent of buckling, although compression rate has no substantial effect on the buckling of MTs. Most importantly, the density of kinesin is found to play the key role in determining the buckling mode of MTs. We have made a comparison between our experimental results and the ‘elastic foundation model’ that theoretically predicts the buckling behavior of MTs and its connection to MT-associated proteins. Taking into consideration the role of kinesin in altering the mechanical property of MTs, we are able to explain the buckling behavior of MTs by the elastic foundation model. This work will help understand the buckling mechanism of MTs and its connection to MT-associated proteins or surrounding medium, and consequently will aid in obtaining a meticulous scenario of the compression stress induced deformation of MTs in cells.

Control of microtubule trajectory within an electric field by altering surface charge density

One of challenges for using microtubules (MTs) driven by kinesin motors in microfluidic environments is to control their direction of movement. Although applying physical biases to rectify MTs is prevalent, it has not been established as a design methodology in conjunction with microfluidic devices. In the future, the methodology is expected to achieve functional motor-driven nanosystems. Here, we propose a method to guide kinesin-propelled MTs in multiple directions under an electric field by designing a charged surface of MT minus ends labeled with dsDNA via a streptavidin-biotin interaction. MTs labeled with 20-bp or 50-bp dsDNA molecules showed significantly different trajectories according to the DNA length, which were in good agreement with values predicted from electrophoretic mobilities measured for their minus ends. Since the effective charge of labeled DNA molecules was equal to that of freely dispersed DNA molecules in a buffer solution, MT trajectory could be estimated by selecting labeling molecules with known charges. Moreover, the estimated trajectory enables to define geometrical sizes of a microfluidic device. This rational molecular design and prediction methodology allows MTs to be guided in multiple directions, demonstrating the feasibility of using molecular sorters driven by motor proteins.

Tug-of-war of microtubule filaments at the boundary of a kinesin- and dynein-patterned surface

Intracellular cargo is transported by multiple motor proteins. Because of the force balance of motors with mixed polarities, cargo moves bidirectionally to achieve biological functions. Here, we propose a microtubule gliding assay for a tug-of-war study of kinesin and dynein. A boundary of the two motor groups is created by photolithographically patterning gold to selectively attach kinesin to the glass and dynein to the gold surface using a self-assembled monolayer. The relationship between the ratio of two antagonistic motor numbers and the velocity is derived from a force-velocity relationship for each motor to calculate the detachment force and motor backward velocity. Although the tug-of-war involves >100 motors, values are calculated for a single molecule and reflect the collective dynein and non-collective kinesin functions when they work as a team. This assay would be useful for detailed in vitro analysis of intracellular motility, e.g., mitosis, where a large number of motors with mixed polarities are involved.

Persistence length of fascin-cross-linked actin filament bundles in solution and the in vitro motility assay

BACKGROUND

Bundles of unipolar actin filaments (F-actin), cross-linked via the actin-binding protein fascin, are important in filopodia of motile cells and stereocilia of inner ear sensory cells. However, such bundles are also useful as shuttles in myosin-driven nanotechnological applications. Therefore, and for elucidating aspects of biological function, we investigate if the bundle tendency to follow straight paths (quantified by path persistence length) when propelled by myosin motors is directly determined by material properties quantified by persistence length of thermally fluctuating bundles.

METHODS

Fluorescent bundles, labeled with rhodamine-phalloidin, were studied at fascin:actin molar ratios: 0:1 (F-actin), 1:7, 1:4 and 1:2. Persistence lengths (Lp) were obtained by fitting the cosine correlation function (CCF) to a single exponential function: <cos(θ(0)-θ(s))>=exp(-s/(2Lp)) where θ(s) is tangent angle; s: path or contour lengths. < > denotes averaging over filaments.

RESULTS

Bundle-Lp (bundles<15μm long) increased from ~10 to 150μm with increased fascin:actin ratio. The increase was similar for path-Lp (path<15μm), with highly linear correlation. For longer bundle paths, the CCF-decay deviated from a single exponential, consistent with superimposition of the random path with a circular path as suggested by theoretical analysis.

CONCLUSIONS

Fascin-actin bundles have similar path-Lp and bundle-Lp, both increasing with fascin:actin ratio. Path-Lp is determined by the flexural rigidity of the bundle.

GENERAL SIGNIFICANCE

The findings give general insight into mechanics of cytoskeletal polymers that interact with molecular motors, aid rational development of nanotechnological applications and have implications for structure and in vivo functions of fascin-actin bundles.

Analysis of flexural rigidity of actin filaments propelled by surface adsorbed myosin motors

Actin filaments are central components of the cytoskeleton and the contractile machinery of muscle. The filaments are known to exist in a range of conformational states presumably with different flexural rigidity and thereby different persistence lengths. Our results analyze the approaches proposed previously to measure the persistence length from the statistics of the winding paths of actin filaments that are propelled by surface-adsorbed myosin motor fragments in the in vitro motility assay. Our results suggest that the persistence length of heavy meromyosin propelled actin filaments can be estimated with high accuracy and reproducibility using this approach provided that: (1) the in vitro motility assay experiments are designed to prevent bias in filament sliding directions, (2) at least 200 independent filament paths are studied, (3) the ratio between the sliding distance between measurements and the camera pixel-size is between 4 and 12, (4) the sliding distances between measurements is less than 50% of the expected persistence length, and (5) an appropriate cut-off value is chosen to exclude abrupt large angular changes in sliding direction that are complications, e.g., due to the presence of rigor heads. If the above precautions are taken the described method should be a useful routine part of in vitro motility assays thus expanding the amount of information to be gained from these.

Optimization of isopolar microtubule arrays

Isopolar arrays of aligned cytoskeletal filaments are components in a number of designs of hybrid nanodevices incorporating biomolecular motors. For example, a combination of filament arrays and motor arrays can form an actuator or a molecular engine resembling an artificial muscle. Here, isopolar arrays of microtubules are fabricated by flow alignment, and their quality is characterized by their degree of alignment. We find, in agreement with our analytical models, that the degree of alignment is ultimately limited by thermal forces, while the kinetics of the alignment process are influenced by the flow strength, the microtubule stiffness, the gliding velocity, and the tip length. Strong flows remove microtubules from the surface and reduce the filament density, suggesting that there is an optimal flow strength for the fabrication of ordered arrays.

Measuring microtubule persistence length using a microtubule gliding assay

The mechanical properties of microtubules have been an area of active research for the past two decades, in part because understanding the mechanics of individual microtubules contributes to modeling whole-cell rigidity and structure and hence to better understanding the processes underlying motility and transport. Moreover, the role of microtubule structure and microtubule-associated proteins (MAPs) in microtubule stiffness remains unclear. In this chapter, we present a kinesin-driven microtubule gliding assay analysis of persistence length that is amenable to simultaneous variation of microtubule parameters such as length, structure, or MAP coverage and determination of persistence length. By combining sparse fluorescent labeling of individual microtubules with single particle tracking of individual fluorophores, microtubule gliding trajectories are tracked with nanometer-level precision. The fluctuations in these trajectories, due to thermal fluctuations in the microtubules themselves, are analyzed to extract the microtubule persistence length. In the following, we describe this gliding assay and analysis and discuss two example microtubule variables, length and diameter, in anticipation that the method may be of wide use for in vitro study of microtubule mechanical properties.

Patterns of molecular motors that guide and sort filaments

Molecular motors can be immobilized to transport filaments and loads that are attached to these filaments inside a nano-device. However, if motors are distributed uniformly over a flat surface, the motility is undirected, and the filaments move equally in all directions. For many applications it is important to control the direction in which the filaments move, and two strategies have been explored to achieve this: applying external forces and confining the filaments inside channels. In this article, we discuss a third strategy in which the topography of the sample remains flat, but the motors are distributed non-uniformly over the surface. Systems of filaments and patterned molecular motors were simulated using a stochastic engine that included Brownian motion and filament bending elasticity. Using an evolutionary algorithm, patterns were optimized for their capacity to precisely control the paths of the filaments. We identified patterns of motors that could either direct the filaments in a particular direction, or separate short and long filaments. These functionalities already exceed what has been achieved with confinement. The patterns are composed of one or two types of motors positioned in lines or along arcs and should be easy to manufacture. Finally, these patterns can be easily combined into larger designs, allowing one to precisely control the motion of microscopic objects inside a device.

Flexural rigidity measurements of biopolymers using gliding assays

Microtubules are cytoskeletal polymers which play a role in cell division, cell mechanics, and intracellular transport. Each of these functions requires microtubules that are stiff and straight enough to span a significant fraction of the cell diameter. As a result, the microtubule persistence length, a measure of stiffness, has been actively studied for the past two decades(1). Nonetheless, open questions remain: short microtubules are 10-50 times less stiff than long microtubules(2-4), and even long microtubules have measured persistence lengths which vary by an order of magnitude(5-9). Here, we present a method to measure microtubule persistence length. The method is based on a kinesin-driven microtubule gliding assay(10). By combining sparse fluorescent labeling of individual microtubules with single particle tracking of individual fluorophores attached to the microtubule, the gliding trajectories of single microtubules are tracked with nanometer-level precision. The persistence length of the trajectories is the same as the persistence length of the microtubule under the conditions used(11). An automated tracking routine is used to create microtubule trajectories from fluorophores attached to individual microtubules, and the persistence length of this trajectory is calculated using routines written in IDL. This technique is rapidly implementable, and capable of measuring the persistence length of 100 microtubules in one day of experimentation. The method can be extended to measure persistence length under a variety of conditions, including persistence length as a function of length along microtubules. Moreover, the analysis routines used can be extended to myosin-based acting gliding assays, to measure the persistence length of actin filaments as well.

Comparative studies of microtubule mechanics with two competing models suggest functional roles of alternative tubulin lateral interactions

The dynamic assembly and disassembly of microtubules and the mechanical properties of these polymers are essential for many key cellular processes. Mathematical and computational modeling, especially coupled mechanochemical modeling, has contributed significantly to our understanding of microtubule dynamics. However, critical discrepancies exist between experimental observations and modeling results that need to be resolved before further progress toward a complete model can be made. Open sheet structures ranging in length from several hundred nanometers to one micron have often been observed at the growing ends of microtubules in in vitro studies. Existing modeling studies predict these sheet structures to be short and rare intermediates of microtubule disassembly rather than important components of the assembly process. Atomic force microscopy (AFM) studies also reveal interesting step-like gaps of the force-indentation curve that cannot yet be explained by existing theoretical models. We have carried out computational studies to compare the mechanical properties of two alternative models: a more conventional model where tubulin dimers are added directly into a microtubule lattice, and one that considers an additional type of tubulin lateral interaction proposed to exist in intermediate sheet structures during the microtubule assembly process. The first model involves a single type of lateral interactions between tubulin subunits, whereas the latter considers a second type that can convert to the canonical lateral contact during microtubule closure into a cylinder. Our analysis shows that only the second model can reproduce the AFM results over a broad parameter range. We propose additional studies using different sizes of AFM tips that would allow to unambiguously distinguish the relative validity of the two models.

Spectral analysis methods for the robust measurement of the flexural rigidity of biopolymers

The mechanical properties of biopolymers can be determined from a statistical analysis of the ensemble of shapes they exhibit when subjected to thermal forces. In practice, extracting information from fluorescence microscopy images can be challenging due to low signal/noise ratios and other artifacts. To address these issues, we develop a suite of tools for image processing and spectral data analysis that is based on a biopolymer contour representation expressed in a spectral basis of orthogonal polynomials. We determine biopolymer shape and stiffness using global fitting routines that optimize a utility function measuring the amount of fluorescence intensity overlapped by such contours. This approach allows for filtering of high-frequency noise and interpolation over sporadic gaps in fluorescence. We use benchmarking to demonstrate the validity of our methods, by analyzing an ensemble of simulated images generated using a simulated biopolymer with known stiffness and subjected to various types of image noise. We then use these methods to determine the persistence lengths of taxol-stabilized microtubules. We find that single microtubules are well described by the wormlike chain polymer model, and that ensembles of chemically identical microtubules show significant heterogeneity in bending stiffness, which cannot be attributed to sampling or fitting errors. We expect these approaches to be useful in the study of biopolymer mechanics and the effects of associated regulatory molecules.

Cooperative lattice dynamics and anomalous fluctuations of microtubules

Microtubules have been in the focus of biophysical research for several decades. However, the confusing and mutually contradictory results regarding their elasticity and fluctuations have cast doubt on their present understanding. In this paper, we present the empirical evidence for the existence of discrete guanosine diphosphate (GDP)-tubulin fluctuations between a curved and a straight configuration at room temperature as well as for conformational tubulin cooperativity. Guided by a number of experimental findings, we build the case for a novel microtubule model, with the principal result that microtubules can spontaneously form micron-sized cooperative helical states with unique elastic and dynamic features. The polymorphic dynamics of the microtubule lattice resulting from the tubulin bistability quantitatively explains several experimental puzzles, including anomalous scaling of dynamic fluctuations of grafted microtubules, their apparent length-stiffness relation, and their remarkable curved-helical appearance in general. We point out that the multistability and cooperative switching of tubulin dimers could participate in important cellular processes, and could in particular lead to efficient mechanochemical signaling along single microtubules.

A fluorescent GTP analog as a specific, high-precision label of microtubules

Fluorescent imaging of cytoskeletal structures permits studies of both organization within the cell and dynamic reorganization of the cytoskeleton itself. Traditional fluorescent labels of microtubules, part of the cytoskeleton, have been used to study microtubule localization, structure, and dynamics, both in vivo and in vitro. However, shortcomings of existing labels make imaging of microtubules with high precision light microscopy difficult. In this paper, we report a new fluorescent labeling technique for microtubules, which involves a GTP analog modified with a bright, organic fluorophore (TAMRA, Cy3, or Cy5). This fluorescent GTP binds to a specific site, the exchangeable site, on tubulin in solution with a dissociation constant of 1.0±0.4 µM. Furthermore, the label becomes permanently incorporated into the microtubule lattice once tubulin polymerizes. We show that this label is usable as a single molecule fluorescence probe with nanometer precision and expect it to be useful for modern subdiffraction optical microscopy of microtubules and the cytoskeleton.

3-D reconstruction of microtubules from multi-angle total internal reflection fluorescence microscopy using Bayesian framework

Total internal reflection fluorescence (TIRF) microscopy excites a thin evanescent field which theoretically decays exponentially. Each TIRF image is actually the projection of a 3-D volume and hence cannot alone produce an accurate localization of structures in the z-dimension, however, it provides greatly improved axial resolution for biological samples. Multiple angle-TIRF microscopy allows controlled variation of the incident angle of the illuminating laser beam, thus generating a set of images of different penetration depths with the potential to reconstruct the 3-D volume of the sample. With the ultimate goal to quantify important biological parameters of microtubules, we present a method to reconstruct 3-D position and orientation of microtubules based on multi-angle TIRF data, as well as experimental calibration of the actual decay function of the evanescent field at each angle. We validate our method using computer simulations, by creating a phantom simulating the curvilinear characteristics of microtubules and project the artificially constructed volume into a set of TIRF image for different penetration depth. The reconstructed depth information for the phantom data is shown to be accurate and robust to noise. We apply our method to microtubule TIRF images of PtK(2) cells in vivo. By comparing microtubule curvatures of the reconstruction results and several electron microscopy (EM) images of vertically sliced sample of microtubules, we find that the curvature statistics of our reconstruction agree well with the ground truth (EM data). Quantifying the distribution of microtubule curvature reveals an interesting discovery that microtubules can buckle and form local bendings of considerably small radius of curvature which is also visually spotted on the EM images, while microtubule bendings on a larger scale generally have a much larger radius and cannot bear the stress of a large curvature. The presented method has the potential to provide a reliable tool for 3-D reconstruction and tracking of microtubules.