Are microtubules tension sensors?

Abstract

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

Fig. 1

Microtubule self-organization properties lead to their cortical localization by default. a Dynamic instability and self-organizing properties of microtubules. Bundling occurs for collision angles inferior to 40°; for larger angles, induced catastrophes or crossover occur. b Microtubules are cortical by default in silico (adapted from ref. ). c Upon centrosome disorganization, microtubules can become cortical in differentiated animal cells (adapted from ref. )

Fig. 2

Microtubules are sensitive to cell geometry. a In silico, microtubule-bending stiffness weakly influences their final alignment towards the longitudinal axis of the cell; cell geometry also prescribes maximal tension along the transverse direction of the cell, which may in turn counteract the effect of confinement on the final microtubule configuration (adapted from ref. ). b In vitro, microtubules can align with the longitudinal axis of confined spaces. In the present study, most (71%), rhodamine-labeled microtubules aligned along the longitudinal axis of confined space in vitro after 1 h of incubation at room temperature (adapted from ref. ). c. Left division pattern in the glandular trichome of Dionaea muscipula; right: predicted maximal tension directions in the membranes (deformed circles) matching division planes (adapted from ref. )

Fig. 3

In vitro microtubules under mechanical stress. a Schematic diagram of an in vitro system to apply tension and compression to gliding microtubules on a kinesin-coated elastomer substrate (adapted from ref. ). b Microtubules driven by surface immobilized kinesins align along maximal tension in vitro and conversely align against compression direction (adapted from ref. ). c Fragmentation and buckling of microtubules at a stationary state induced by external tension and compression (adapted from ref. ). e Using optical tweezer, growth of single microtubule is promoted when under tension along the direction of protofilaments (adapted from ref. , not to scale). d Microtubule aligns toward the direction that minimizes accumulated bending energy in silico (adapted from ref. )

Fig. 4

An energy-based mathematical model of tension sensing in a single microtubule. The model is based on a one-dimensional two-state mechanical model of tubulin protofilament alignment, through GTP hydrolysis a or external pulling force b, as illustrated. State variables are: the real-valued actual length $l\in \mathbb{R}$ of a stretchable segment of MT (e.g., anchor point to  plus end); a binary-valued indicator variable s ∈ {0,1} for the mechanical state of the lengthwise protofilaments at the  plus end cap (s = 0⇒splayed, s = 1⇒ aligned); and optionally a binary-valued indicator variable σ ∈ {0,1} for internal biochemical sensing of the mechanical state s. Principal exogenous parameters are $\lambda \in {\mathbb{R}}^{\ge 0}$, the length of the splayable subregion; $l_0\in {\mathbb{R}}^{\ge \lambda }$, the segment resting length when aligned (so l₀–λ is the resting length when splayed); τ = externally applied tension; μ_s = energy bias in favor of (or, if negative, against) alignment s = 1; μ_σ= energy bias in favor of σ = 1; α = energetic reward for agreement of s = 1 and σ = 1. Given this notation, a Hooke’s law mechanical spring energy with two states can be written as: E_mech = (k/2)[s(l–l₀)²+(1–s)(l–(l₀–λ))²]–τ(l–(l₀–λ)). Additional energy terms specific to discrete end cap state and sensing are: $E_{discrete}=-{\mu }_{s}s-{\mu }_{\sigma }\sigma -\alpha s\sigma$; then the total energy is E(l,s,σ) = E_mech+E_discrete. State probability follows the Boltzmann distribution, exp(–βE)/Z(β,params) where Z normalizes the distribution. Even ignoring σ (case α small) one obtains a double-well potential in the free energy F(τ) = −(1/β)logZ with two minima as a function of tension, one of them near τ = 0. This indicates that nonzero tension can be stabilized by the s = 1 mechanical protofilament alignment state which is in turn correlated (for α ≠ 0) with σ = 1 tension sensing. The readout state σ = 1 could in turn be amplified biochemically by, e.g., a phosphorylation/dephosphorylation cycle as in ref. , assuming that σ affects such enzymatic activity

Fig. 5

CMTs align along maximal tensile stress in plants. a Left: pattern of cortical microtubules at the shoot apical meristem (CZ: central zone, B: organ–meristem boundary, O: organ). Cell contours (red) and microtubules (green). Right: finite element model where local pattern of stress is predicted, with an emerging co-alignment of tensile stress directions (red bars) at the organ–meristem boundary domain (adapted from ref. ). b Predicted pattern of mechanical stress at the shoot apical meristem (using a continuous model based on pressure vessel analogy), and matching supracellular microtubule pattern (adapted from ref. ). c Pattern of cortical microtubules in light-grown hypocotyls before (left) and after (right) controlled compression along the axis of the hypocotyl (adapted from ref. ). d Correlation between tension pattern derived from adhesion defects (bright propidium staining and cracks) in the qua1 mutant in stems and basal region of dark-grown hypocotyls (left) and cortical microtubule orientation in a wild-type background (right). Microtubules are revealed by a GFP-Microtubule Binding Domain fusion (GFP-MBD) (adapted from ref. )

Fig. 6

A role of wall heterogeneities to explain how microtubules distinguish maximal strain from maximal tensile stress. a Wall heterogeneities may induce strain discontinuities, destabilizing microtubules, whereas wall homogeneities (e.g., along or between cellulose microfibrils) may stabilize microtubules. b Assuming that wall heterogeneities would affect the roughness of the inner face of the wall, the smoother/straighter part of the wall may be parallel to maximal tensile stress direction, along which microtubules (green) would align. c Wall heterogeneity may arise from mechanical differences between cellulose microfibrils and the matrix; the delivery of component of the matrix is also heterogeneous in space and time, as shown by click chemistry with alkynylated fucose analogs in roots (left: late differentiation zone, right: early differentiation zone; adapted from ref. )

Fig. 7

Integrating the microtubule-tension module in morphogenesis. Plant morphogenesis would emerge from the coupling between inputs from the gene regulatory network and an autonomous microtubule-tension amplifier. In that scenario, the microtubule lattice would be at the crossroad of the biochemical and mechanical control of growth. For instance, GTP hydrolysis within the protofilament leads to the compaction of the tubulin dimer (GTP in orange, GDP in pink—adapted from ref. ) and this step may either be modulated by mechanical signals or mimicked by the impact of tension on the protofilament