Temperature-dependent elasticity of microtubules

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.

Pulling the springs of a cell by single-molecule force spectroscopy

The fundamental unit of the human body comprises of the cells which remain embedded in a fibrillar network of extracellular matrix proteins which in turn provides necessary anchorage the cells. Tissue repair, regeneration and reprogramming predominantly involve a traction force mediated signalling originating in the ECM and travelling deep into the cell including the nucleus via circuitry of spring-like filamentous proteins like microfilaments or actin, intermediate filaments and microtubules to elicit a response in the form of mechanical movement as well as biochemical changes. The 'springiness' of these proteins is highlighted in their extension-contraction behaviour which is manifested as an effect of differential traction force. Atomic force microscope (AFM) provides the magic eye to visualize and quantify such force-extension/indentation events in these filamentous proteins as well as in whole cells. In this review, we have presented a summary of the current understanding and advancement of such measurements by AFM based single-molecule force spectroscopy in the context of cytoskeletal and nucleoskeletal proteins which act in tandem to facilitate mechanotransduction.

Coarse-Grained Simulation of Mechanical Properties of Single Microtubules With Micrometer Length

Microtubules are one of the most important components in the cytoskeleton and play a vital role in maintaining the shape and function of cells. Because single microtubules are some micrometers long, it is difficult to simulate such a large system using an all-atom model. In this work, we use the newly developed convolutional and K-means coarse-graining (CK-CG) method to establish an ultra-coarse-grained (UCG) model of a single microtubule, on the basis of the low electron microscopy density data of microtubules. We discuss the rationale of the micro-coarse-grained microtubule models of different resolutions and explore microtubule models up to 12-micron length. We use the devised microtubule model to quantify mechanical properties of microtubules of different lengths. Our model allows mesoscopic simulations of micrometer-level biomaterials and can be further used to study important biological processes related to microtubule function.

Soft-Matter Nanotubes: A Platform for Diverse Functions and Applications

Self-assembled organic nanotubes made of single or multiple molecular components can be classified into soft-matter nanotubes (SMNTs) by contrast with hard-matter nanotubes, such as carbon and other inorganic nanotubes. To date, diverse self-assembly processes and elaborate template procedures using rationally designed organic molecules have produced suitable tubular architectures with definite dimensions, structural complexity, and hierarchy for expected functions and applications. Herein, we comprehensively discuss every functions and possible applications of a wide range of SMNTs as bulk materials or single components. This Review highlights valuable contributions mainly in the past decade. Fifteen different families of SMNTs are discussed from the viewpoints of chemical, physical, biological, and medical applications, as well as action fields (e.g., interior, wall, exterior, whole structure, and ensemble of nanotubes). Chemical applications of the SMNTs are associated with encapsulating materials and sensors. SMNTs also behave, while sometimes undergoing morphological transformation, as a catalyst, template, liquid crystal, hydro-/organogel, superhydrophobic surface, and micron size engine. Physical functions pertain to ferro-/piezoelectricity and energy migration/storage, leading to the applications to electrodes or supercapacitors, and mechanical reinforcement. Biological functions involve artificial chaperone, transmembrane transport, nanochannels, and channel reactors. Finally, medical functions range over drug delivery, nonviral gene transfer vector, and virus trap.

Primary cilia have a length-dependent persistence length

The fluctuating position of an optically trapped cilium tip under untreated and Taxol-treated conditions was used to characterize mechanical properties of the cilium axoneme and its basal body by combining experimental, analytical, and computational tools. We provide, for the first time, evidence that the persistence length of a ciliary axoneme is length-dependent; longer cilia are stiffer than shorter cilia. We demonstrate that this apparent length dependence can be understood by a combination of modeling axonemal microtubules as anisotropic elastic shells and including actomyosin-driven stochastic basal body motion. Our results also demonstrate the possibility of using observable ciliary dynamics to probe interior cytoskeletal dynamics. It is hoped that our improved characterization of cilia will result in deeper understanding of the biological function of cellular flow sensing by this organelle.

Microtubule self-healing and defect creation investigated by in-line force measurements during high-speed atomic force microscopy imaging

Microtubules are biopolymers composed of tubulin and play diverse roles in a wide variety of biological processes such as cell division, migration and intracellular transport in eukaryotic cells. To perform their functions, microtubules are mechanically stressed and, thereby, susceptible to structural defects. Local variations in mechanical properties caused by these defects modulate their biological functions, including binding and transportation of microtubule-associated proteins. Therefore, assessing the local mechanical properties of microtubules and analyzing their dynamic response to mechanical stimuli provide insight into fundamental processes. It is, however, not trivial to control defect formation, gather mechanical information at the same time, and subsequently image the result at a high temporal resolution at the molecular level with minimal delay. In this work, we describe the so-called in-line force curve mode based on high-speed atomic force microscopy. This method is directly applied to create defects in microtubules at the level of tubulin dimers and monitor the following dynamic processes around the defects. Furthermore, force curves obtained during defect formation provide quantitative mechanical information to estimate the bonding energy between tubulin dimers.

Integration of intracellular signaling: Biological analogues of wires, processors and memories organized by a centrosome 3D reference system

BACKGROUND

Myriads of signaling pathways in a single cell function to achieve the highest spatio-temporal integration. Data are accumulating on the role of electromechanical soliton-like waves in signal transduction processes. Theoretical studies strongly suggest feasibility of both classical and quantum computing involving microtubules.

AIM

A theoretical study of the role of the complex composed of the plasma membrane and the microtubule-based cytoskeleton as a system that transmits, stores and processes information.

METHODS

Theoretical analysis presented here refers to (i) the Penrose-Hameroff theory of consciousness (Orchestrated Objective Reduction; Orch OR), (ii) the description of the centrosome as a reference system for construction of the 3D map of the cell proposed by Regolini, (iii) the Heimburg-Jackson model of the nerve pulse propagation along axons' lipid bilayer as soliton-like electro-mechanical waves.

RESULTS AND CONCLUSION

The ideas presented in this paper provide a qualitative model for the decision-making processes in a living cell undergoing a differentiation process.

OUTLOOK

This paper paves the way for the real-time live-cell observation of information processing by microtubule-based cytoskeleton and cell fate decision making.

Microtubules dual chemo and thermo-responsive depolymerization

The effects of chemotherapeutic agent vinblastine versus low temperature of 277 K were investigated on the structure of αβ-tubulin heterodimer by means of molecular dynamics simulations. Individual experiments have shown that the vinblastine-bound heterodimer, and its apo structure under low temperature of 277 K, both undergo conformational changes toward destabilization of the dimer as compared to the apo tubulin at 300 K. Both factors exhibited weakening of the longitudinal interactions of tubulin heterodimer through displacing dimer interfacial segments, resulting in dominant electrostatic repulsion at the interface of the subunits. The two independent factors of temperature and anti-mitotic agent facilitate alteration of secondary structure in functional segments such as H1-S2 loop, H3, H10 helices, and T7 loop, which are known to be important in either longitudinal or lateral contacts among αβ-heterodimers in MTs protofilaments and their depolymerization mechanism.

Effects of microtubule mechanics on hydrolysis and catastrophes

We introduce a model for microtubule (MT) mechanics containing lateral bonds between dimers in neighboring protofilaments, bending rigidity of dimers, and repulsive interactions between protofilaments modeling steric constraints to investigate the influence of mechanical forces on hydrolysis and catastrophes. We use the allosteric dimer model, where tubulin dimers are characterized by an equilibrium bending angle, which changes from 0° to 22° by hydrolysis of a dimer. This also affects the lateral interaction and bending energies and, thus, the mechanical equilibrium state of the MT. As hydrolysis gives rise to conformational changes in dimers, mechanical forces also influence the hydrolysis rates by mechanical energy changes modulating the hydrolysis rate. The interaction via the MT mechanics then gives rise to correlation effects in the hydrolysis dynamics, which have not been taken into account before. Assuming a dominant influence of mechanical energies on hydrolysis rates, we investigate the most probable hydrolysis pathways both for vectorial and random hydrolysis. Investigating the stability with respect to lateral bond rupture, we identify initiation configurations for catastrophes along the hydrolysis pathways and values for a lateral bond rupture force. If we allow for rupturing of lateral bonds between dimers in neighboring protofilaments above this threshold force, our model exhibits avalanche-like catastrophe events.

Anomalous flexural behaviors of microtubules

Apparent controversies exist on whether the persistence length of microtubules depends on its contour length. This issue is particularly challenging from a theoretical point of view due to the tubular structure and strongly anisotropic material property of microtubules. Here we adopt a higher order continuum orthotropic thin shell model to study the flexural behavior of microtubules. Our model overcomes some key limitations of a recent study based on a simplified anisotropic shell model and results in a closed-form solution for the contour-length-dependent persistence length of microtubules, with predictions in excellent agreement with experimental measurements. By studying the ratio between their contour and persistence lengths, we find that microtubules with length at ~1.5 μm show the lowest flexural rigidity, whereas those with length at ~15 μm show the highest flexural rigidity. This finding may provide an important theoretical basis for understanding the mechanical structure of mitotic spindles during cell division. Further analysis on the buckling of microtubules indicates that the critical buckling load becomes insensitive to the tube length for relatively short microtubules, in drastic contrast to the classical Euler buckling. These rich flexural behaviors of microtubules are of profound implication for many biological functions and biomimetic molecular devices.

ENGINEERING AND THERAPEUTIC APPLICATIONS OF MICROTUBULES

Living organisms are fascinating systems. The macromolecules that make up a living cell possess equally astounding structural and functional characteristics. By taking simple cues from how these biopolymers organize and work inside the cell, one can draw inspiration to utilize them outside their natural environment for several purposes. Microtubules are example of biopolymers that demonstrate extraordinary properties of hierarchical self-organization, dynamic remodeling and mechanical rigidity. Mimicking the principles and properties of microtubules and improving them have opened novel engineering avenues. In addition, due to the functions that microtubules perform during cell division, they are excellent therapeutic drug targets for anticancer agents. In this work, we describe the biological properties and functions of microtubules, and discuss their engineering and therapeutic applications.

Temperature dependence rigidity of non-taxol stabilized single microtubules

Because microtubules are the structural elements of cells, it is essential to study the mechanical properties of single microtubules under physiological conditions. Previously, we measured the effect of temperature on the flexural rigidity of a single taxol-stabilized microtubule and found that the flexural rigidity is 2.5×10(-24)Nm(2), independent of temperature in the 20-35°C range. Employing the same technique here, we have measured the flexural rigidity of microtubules polymerized in the presence of guanylyl-(a,b)-methylene-diphosphonate (GMPCPP, the slowly hydrolyzable GTP analogue) and in the presence of GTP only; both of the states were taxol-free. The obtained values were approximately 5-fold (for GMPCPP) and three- to 4-fold (for GTP) greater than those of taxol-stabilized microtubules. Interestingly, rigidity decreased as temperature increased, that is, temperature dependence was only observed in taxol-free microtubules. Length dependence was also observed. These results indicate that the transition of microtubule's rigidity is associated with the tubulin conformation change from a GTP-bound state to a GDP-bound state in the α/β subunit. We discuss the relationship of the regulation mechanism of the microtubules in the cell body to the changes in rigidity through hydrolysis.

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.

Flexible magnetic microtubules structured by lipids and magnetic nanoparticles

This study presents a microtubule that responds to a magnetic field. We made such a structure by incorporating iron oxide nanoparticles during the preparation of the microtubule. We found that the microtubule stretches its body when the magnetic field is applied and easily aligns with the direction of the applied magnetic field by rotating its body. When the magnetic field is removed, it loses its orientation and goes back to its original state by contraction. From the analysis of its magnetic response, we estimated that the magnetic microtubule had an elastic modulus of 33 MPa. Further analysis showed that the stretching and contracting of its body are due to its flexibility.