Statistical mechanics provides novel insights into microtubule stability and mechanism of shrinkage

Electrical behaviour and evolutionary computation in thin films of bovine brain microtubules

We report on the electrical behaviour of thin films of bovine brain microtubules (MTs). For samples in both their dried and hydrated states, the measured currents reveal a power law dependence on the applied DC voltage. We attribute this to the injection of space-charge from the metallic electrode(s). The MTs are thought to form a complex electrical network, which can be manipulated with an applied voltage. This feature has been exploited to undertake some experiments on the use of the MT mesh as a medium for computation. We show that it is possible to evolve MT films into binary classifiers following an evolution in materio approach. The accuracy of the system is, on average, similar to that of early carbon nanotube classifiers developed using the same methodology.

Extensions of the worm-like-chain model to tethered active filaments under tension

Intracellular elastic filaments such as microtubules are subject to thermal Brownian noise and active noise generated by molecular motors that convert chemical energy into mechanical work. Similarly, polymers in living fluids such as bacterial suspensions and swarms suffer bending deformations as they interact with single bacteria or with cell clusters. Often, these filaments perform mechanical functions and interact with their networked environment through cross-links or have other similar constraints placed on them. Here, we examine the mechanical properties-under tension-of such constrained active filaments under canonical boundary conditions motivated by experiments. Fluctuations in the filament shape are a consequence of two types of random forces-thermal Brownian forces and activity derived forces with specified time and space correlation functions. We derive force-extension relationships and expressions for the mean square deflections for tethered filaments under various boundary conditions including hinged and clamped constraints. The expressions for hinged-hinged boundary conditions are reminiscent of the worm-like-chain model and feature effective bending moduli and mode-dependent non-thermodynamic effective temperatures controlled by the imposed force and by the activity. Our results provide methods to estimate the activity by measurements of the force-extension relation of the filaments or their mean square deflections, which can be routinely performed using optical traps, tethered particle experiments, or other single molecule techniques.

Mechanics and kinetics of dynamic instability

During dynamic instability, self-assembling microtubules (MTs) stochastically alternate between phases of growth and shrinkage. This process is driven by the presence of two distinct states of MT subunits, GTP- and GDP-bound tubulin dimers, that have different structural properties. Here, we use a combination of analysis and computer simulations to study the mechanical and kinetic regulation of dynamic instability in three-dimensional (3D) self-assembling MTs. Our model quantifies how the 3D structure and kinetics of the distinct states of tubulin dimers determine the mechanical stability of MTs. We further show that dynamic instability is influenced by the presence of quenched disorder in the state of the tubulin subunit as reflected in the fraction of non-hydrolysed tubulin. Our results connect the 3D geometry, kinetics and statistical mechanics of these tubular assemblies within a single framework, and may be applicable to other self-assembled systems where these same processes are at play.

Microtubule Simulations Provide Insight into the Molecular Mechanism Underlying Dynamic Instability

The dynamic instability of microtubules (MTs), which refers to their ability to switch between polymerization and depolymerization states, is crucial for their function. It has been proposed that the growing MT ends are protected by a "GTP cap" that consists of GTP-bound tubulin dimers. When the speed of GTP hydrolysis is faster than dimer recruitment, the loss of this GTP cap will lead the MT to undergo rapid disassembly. However, the underlying atomistic mechanistic details of the dynamic instability remains unclear. In this study, we have performed long-time atomistic molecular dynamics simulations (1 μs for each system) for MT patches as well as a short segment of a closed MT in both GTP- and GDP-bound states. Our results confirmed that MTs in the GDP state generally have weaker lateral interactions between neighboring protofilaments (PFs) and less cooperative outward bending conformational change, where the difference between bending angles of neighboring PFs tends to be larger compared with GTP ones. As a result, when the GDP state tubulin dimer is exposed at the growing MT end, these factors will be more likely to cause the MT to undergo rapid disassembly. We also compared simulation results between the special MT seam region and the remaining material and found that the lateral interactions between MT PFs at the seam region were comparatively much weaker. This finding is consistent with the experimental suggestion that the seam region tends to separate during the disassembly process of an MT.

Regulation of microtubule disassembly by spatially heterogeneous patterns of acetylation

Microtubules (MTs) are bio-polymers, composed of tubulin proteins, involved in several functions such as cell division, transport of cargoes within cells, maintaining cellular structures etc. Their kinetics are often affected by chemical modifications on the filament known as Post Translational Modifications (PTMs). Acetylation is a PTM which occurs on the luminal surface of the MT lattice and has been observed to reduce the lateral interaction between tubulins on adjacent protofilaments. Depending on the properties of the acetylase enzyme αTAT1 and the structural features of MTs, the patterns of acetylation formed on MTs are observed to be quite diverse. In this study, we present a multi-protofilament model with spatially heterogeneous patterns of acetylation, and investigate how the local kinetic differences arising from heterogeneity affect the global kinetics of MT filaments. From the computational study we conclude that a filament with spatially uniform acetylation is least stable against disassembly, while ones with more clustered acetylation patterns may provide better resistance against disassembly. The increase in disassembly times for clustered pattern as compared to uniform pattern can be up to fifty percent for identical amounts of acetylation. Given that acetylated MTs affect several cellular functions as well as diseases such as cancer, our study indicates that spatial patterns of acetylation need to be focused on, apart from the overall amount of acetylation.

Spatio-temporal correlations between catastrophe events in a microtubule bundle: a computational study

We explore correlations between dynamics of different microtubules in a bundle, via numerical simulations, using a one-dimensional stochastic model of a microtubule. The guanosine triphosphate (GTP)-bound tubulins undergo diffusion-limited binding to the tip. Random hydrolysis events take place along the microtubule and converts the bound GTP in tubulin to guanosine diphosphate (GDP). The microtubule starts depolymerising when the monomer at the tip becomes GDP-bound; in this case, detachment of GDP-tubulin ensues and continues until either GTP-bound tubulin is exposed or complete depolymerisation is achieved. In the latter case, the microtubule is defined to have undergone a "catastrophe". Our results show that, in general, the dynamics of growth and catastrophe in different microtubules are coupled to each other; the closer the microtubules are, the stronger the coupling. In particular, all microtubules grow slower, on average, when brought closer together. The reduction in growth velocity also leads to more frequent catastrophes. More dramatically, catastrophe events in the different microtubules forming a bundle are found to be correlated; a catastrophe event in one microtubule is more likely to be followed by a similar event in the same microtubule. This propensity of bunching disappears when the microtubules move farther apart.

Signatures of a macroscopic switching transition for a dynamic microtubule

Characterising complex kinetics of non-equilibrium self-assembly of bio-filaments is of general interest. Dynamic instability in microtubules, consisting of successive catastrophes and rescues, is observed to occur as a result of the non-equilibrium conversion of GTP-tubulin to GDP-tubulin. We study this phenomenon using a model for microtubule kinetics with GTP/GDP state-dependent polymerisation, depolymerisation and hydrolysis of subunits. Our results reveal a sharp switch-like transition in the mean velocity of the filaments, from a growth phase to a shrinkage phase, with an associated co-existence of the two phases. This transition is reminiscent of the discontinuous phase transition across the liquid-gas boundary. We probe the extent of discontinuity in the transition quantitatively using characteristic signatures such as bimodality in velocity distribution, variance and Binder cumulant, and also hysteresis behaviour of the system. We further investigate ageing behaviour in catastrophes of the filament, and find that the multi-step nature of catastrophes is intensified in the vicinity of the switching transition. This assumes importance in the context of Microtubule Associated Proteins which have the potential of altering kinetic parameter values.

Embryo as an active granular fluid: stress-coordinated cellular constriction chains

Mechanical stress plays an intricate role in gene expression in individual cells and sculpting of developing tissues. However, systematic methods of studying how mechanical stress and feedback help to harmonize cellular activities within a tissue have yet to be developed. Motivated by our observation of the cellular constriction chains (CCCs) during the initial phase of ventral furrow formation in the Drosophila melanogaster embryo, we propose an active granular fluid (AGF) model that provides valuable insights into cellular coordination in the apical constriction process. In our model, cells are treated as circular particles connected by a predefined force network, and they undergo a random constriction process in which the particle constriction probability P is a function of the stress exerted on the particle by its neighbors. We find that when P favors tensile stress, constricted particles tend to form chain-like structures. In contrast, constricted particles tend to form compact clusters when P favors compression. A remarkable similarity of constricted-particle chains and CCCs observed in vivo provides indirect evidence that tensile-stress feedback coordinates the apical constriction activity. Our particle-based AGF model will be useful in analyzing mechanical feedback effects in a wide variety of morphogenesis and organogenesis phenomena.

Detection of Temperature Difference in Neuronal Cells

For a better understanding of the mechanisms behind cellular functions, quantification of the heterogeneity in an organism or cells is essential. Recently, the importance of quantifying temperature has been highlighted, as it correlates with biochemical reaction rates. Several methods for detecting intracellular temperature have recently been established. Here we develop a novel method for sensing temperature in living cells based on the imaging technique of fluorescence of quantum dots. We apply the method to quantify the temperature difference in a human derived neuronal cell line, SH-SY5Y. Our results show that temperatures in the cell body and neurites are different and thus suggest that inhomogeneous heat production and dissipation happen in a cell. We estimate that heterogeneous heat dissipation results from the characteristic shape of neuronal cells, which consist of several compartments formed with different surface-volume ratios. Inhomogeneous heat production is attributable to the localization of specific organelles as the heat source.