Temperature dependence of the flexural rigidity of single microtubules

Mechanics of Single Cytoskeletal Filaments

The cytoskeleton comprises networks of different biopolymers, which serve various cellular functions. To accomplish these tasks, their mechanical properties are of particular importance. Understanding them requires detailed knowledge of the mechanical properties of the individual filaments that make up these networks, in particular, microtubules, actin filaments, and intermediate filaments. Far from being homogeneous beams, cytoskeletal filaments have complex mechanical properties, which are directly related to the specific structural arrangement of their subunits. They are also versatile, as the filaments' mechanics and biochemistry are tightly coupled, and their properties can vary with the cellular context. In this review, we summarize decades of research on cytoskeletal filament mechanics, highlighting their most salient features and discussing recent insights from this active field of research.

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.

Cell mechanical properties of human breast carcinoma cells depend on temperature

The knowledge of cell mechanics is required to understand cellular processes and functions, such as the movement of cells, and the development of tissue engineering in cancer therapy. Cell mechanical properties depend on a variety of factors, such as cellular environments, and may also rely on external factors, such as the ambient temperature. The impact of temperature on cell mechanics is not clearly understood. To explore the effect of temperature on cell mechanics, we employed magnetic tweezers to apply a force of 1 nN to 4.5 µm superparamagnetic beads. The beads were coated with fibronectin and coupled to human epithelial breast cancer cells, in particular MCF-7 and MDA-MB-231 cells. Cells were measured in a temperature range between 25 and 45 °C. The creep response of both cell types followed a weak power law. At all temperatures, the MDA-MB-231 cells were pronouncedly softer compared to the MCF-7 cells, whereas their fluidity was increased. However, with increasing temperature, the cells became significantly softer and more fluid. Since mechanical properties are manifested in the cell's cytoskeletal structure and the paramagnetic beads are coupled through cell surface receptors linked to cytoskeletal structures, such as actin and myosin filaments as well as microtubules, the cells were probed with pharmacological drugs impacting the actin filament polymerization, such as Latrunculin A, the myosin filaments, such as Blebbistatin, and the microtubules, such as Demecolcine, during the magnetic tweezer measurements in the specific temperature range. Irrespective of pharmacological interventions, the creep response of cells followed a weak power law at all temperatures. Inhibition of the actin polymerization resulted in increased softness in both cell types and decreased fluidity exclusively in MDA-MB-231 cells. Blebbistatin had an effect on the compliance of MDA-MB-231 cells at lower temperatures, which was minor on the compliance MCF-7 cells. Microtubule inhibition affected the fluidity of MCF-7 cells but did not have a significant effect on the compliance of MCF-7 and MDA-MB-231 cells. In summary, with increasing temperature, the cells became significant softer with specific differences between the investigated drugs and cell lines.

Molecular swarm robots: recent progress and future challenges

Recent advancements in molecular robotics have been greatly contributed by the progress in various fields of science and technology, particularly in supramolecular chemistry, bio- and nanotechnology, and informatics. Yet one of the biggest challenges in molecular robotics has been controlling a large number of robots at a time and employing the robots for any specific task as flocks in order to harness emergent functions. Swarming of molecular robots has emerged as a new paradigm with potentials to overcome this hurdle in molecular robotics. In this review article, we comprehensively discuss the latest developments in swarm molecular robotics, particularly emphasizing the effective utilization of bio- and nanotechnology in swarming of molecular robots. Importance of tuning the mutual interaction among the molecular robots in regulation of their swarming is introduced. Successful utilization of DNA, photoresponsive molecules, and natural molecular machines in swarming of molecular robots to provide them with processing, sensing, and actuating ability is highlighted. The potentials of molecular swarm robots for practical applications by means of their ability to participate in logical operations and molecular computations are also discussed. Prospects of the molecular swarm robots in utilizing the emergent functions through swarming are also emphasized together with their future perspectives.

Synchronous operation of biomolecular engines

Biomolecular motor systems are the smallest natural machines with an ability to convert chemical energy into mechanical work with remarkably high efficiency. Such attractive features enabled biomolecular motors to become classic tools in soft matter research over the past decade. For designing suitably engineered biomimetic systems, the biomolecular motors can potentially be used as molecular engines that can transform energy and ensure great advantages for the construction of bio-nanodevices and molecular robots. From the optimization of their prolonged lifetime to coordinate them into highly complex and ordered structures, enormous efforts have been devoted to make them useful in the synthetic environment. Synchronous operation of the biomolecular engines is one of the key criteria to coordinate them into certain different patterns, which depends on the local interaction of biomolecular motors. Utilizing chemical and physical stimuli, synchronization of biomolecular motor systems has become possible, which allows them to coordinate into different higher ordered patterns with different modes of functionality. Recently, programmed synchronous operation of the biomolecular engines has also been demonstrated, using a smart biomaterial to build up swarms reminiscent of nature. Here, we review the recent progress in the synchronized operation of biomolecular motors in engineered systems to explicitly program their interaction and further their applications. Such developments in the coordination of biomolecular motors have opened a broad way to explore the construction of future autonomous molecular machines and robots based on synchronization of biomolecular engines.

Effects of the cross-linkers on the buckling of microtubules in cells

In cells, the protein cross-linkers lead to a distinct buckling behavior of microtubules (MTs) different from the buckling of individual MTs. This paper thus aims to examine this issue via the molecular structural mechanics (MSM) simulations. The transition of buckling responses was captured as the two-dimensional-linkers were replaced by the three-dimensional (3D) ones. Then, the effects of the radial orientation and the axial density of the 3D-linkers were examined, showing that more uniform distribution of the radial orientation leads to the higher critical load with 3D buckling modes, while the inhomogeneity of the axial density results in the localized buckling patterns. The results demonstrated the important role of the cross-linker in regulating MT stiffness, revealed the physics of the experimentally observed localized buckling and these results will pave the way to a new multi-component mechanics model for whole cells.

Mechanisms of kinetic stabilization by the drugs paclitaxel and vinblastine

Chemotherapeutic agents that target microtubule dynamics promote a universal phenotype of kinetic stabilization. Integrated computational modeling and fluorescence microscopy identify the fundamental kinetic and thermodynamic mechanisms that result in kinetic stabilization, specifically by the drugs paclitaxel and vinblastine.

Microtubule-targeting agents (MTAs), widely used as biological probes and chemotherapeutic drugs, bind directly to tubulin subunits and “kinetically stabilize” microtubules, suppressing the characteristic self-assembly process of dynamic instability. However, the molecular-level mechanisms of kinetic stabilization are unclear, and the fundamental thermodynamic and kinetic requirements for dynamic instability and its elimination by MTAs have yet to be defined. Here we integrate a computational model for microtubule assembly with nanometer-scale fluorescence microscopy measurements to identify the kinetic and thermodynamic basis of kinetic stabilization by the MTAs paclitaxel, an assembly promoter, and vinblastine, a disassembly promoter. We identify two distinct modes of kinetic stabilization in live cells, one that truly suppresses on-off kinetics, characteristic of vinblastine, and the other a “pseudo” kinetic stabilization, characteristic of paclitaxel, that nearly eliminates the energy difference between the GTP- and GDP-tubulin thermodynamic states. By either mechanism, the main effect of both MTAs is to effectively stabilize the microtubule against disassembly in the absence of a robust GTP cap.

X-ray fiber diffraction analysis shows dynamic changes in axial tubulin repeats in native microtubules depending on paclitaxel content, temperature and GTP-hydrolysis

Microtubules are key components of the cytoskeleton in eukaryotic cells. The dynamics between assembled microtubules and free tubulin dimers in the cytoplasm is closely related to the active shape changes of microtubule networks. One of the most fundamental questions is the association of microtubule dynamics with the molecular conformation of tubulin within microtubules. To address this issue, we applied a new technique for the rapid shear-flow alignment of biological filaments, enabling us to acquire the structural periodicity data of microtubules by X-ray fiber diffraction under various physiological conditions. We classified microtubules into three main groups on the basis of distinct axial tubulin periodicities and mean microtubule diameters that varied depending on GTP hydrolysis and the content of paclitaxel, a microtubule stabilizer. Paclitaxel induced rapid changes in tubulin axial repeats in a cooperative manner. This is the first demonstration of dynamic changes of axial tubulin repeats within native microtubules without fixation. We also found extraordinary features of negative thermal expansion of axial tubulin repeats in both paclitaxel-stabilized and GMPCPP-containing microtubules. Our results suggest that even in assembled microtubules, both GTP- and GDP-tubulin dimers can undergo dynamic conversion between at least two different states: short and long configurations.

Intrinsic bending of microtubule protofilaments

The complex polymerization dynamics of the microtubule (MT) plus end are closely linked to the hydrolysis of the GTP nucleotide bound to the β-tubulin. The destabilization is thought to be associated with the conformational change of the tubulin dimers from the straight conformation in the MT lattice to a curved conformation. It remains under debate whether this transformation is directly related to the nucleotide state, or a consequence of the longitudinal or lateral contacts in the MT lattice. Here, we present large-scale atomistic simulations of short tubulin protofilaments with both nucleotide states, starting from both extreme conformations. Our simulations indicate that both interdimer and intradimer contacts in both GDP and GTP-bound tubulin dimers and protofilaments in solution bend. There are no observable differences between the mesoscopic properties of the contacts in GTP and GDP-bound tubulin or the intradime and interdimer interfaces.

Wave propagation in protein microtubules modeled as orthotropic elastic shells including transverse shear deformations

Wave propagation along the microtubules is one of the issues of major concern in various microtubule cellular functions. In this study, the general wave propagation behavior in protein microtubules is investigated based on a first-order shear deformation shell theory for orthotropic materials, with particular emphasis on the role of strongly anisotropic elastic properties of microtubules. According to experimental observation, the first-order shear deformation theory is used for the modeling of microtubule walls. A general displacement representation is introduced and a type of coupled polynomial eigenvalue problem is developed. Numerical examples describe the effects of shear deformation and rotary inertia on wave velocities in orthotropic microtubules. Finally, the influences of the microtubule shear modulus, axial external force, effective thickness and material temperature dependency on wave velocities along the microtubule protofilaments, helical pathway and radial directions are elucidated. Most results presented in the present investigation have been absent from the literature for the wave propagation in microtubules.

Microtubule elasticity: connecting all-atom simulations with continuum mechanics

The mechanical properties of microtubules have been extensively studied using a wide range of biophysical techniques, seeking to understand the mechanics of these cylindrical polymers. Here we develop a method for connecting all-atom molecular dynamics simulations with continuum mechanics and show how this can be applied to understand microtubule mechanics. Our coarse-graining technique applied to the microscopic simulation system yields consistent predictions for the Young's modulus and persistence length of microtubules, while clearly demonstrating how binding of the drug Taxol decreases the stiffness of microtubules. The techniques we develop should be widely applicable to other macromolecular systems.

Mechanics of microtubules

Microtubules are rigid cytoskeletal filaments, and their mechanics affect cell morphology and cellular processes. For instance, microtubules for the support structures for extended morphologies, such as axons and cilia. Further, microtubules act as tension rods to pull apart chromosomes during cellular division. Unlike other cytoskeletal filaments (e.g., actin) that work as large networks, microtubules work individually or in small groups, so their individual mechanical properties are quite important to their cellular function. In this review, we explore the past work on the mechanics of individual microtubules, which have been studied for over a quarter of a century. We also present some prospective on future endeavors to determine the molecular mechanisms that control microtubule rigidity.