Microtubule mechanics and the implications for their assembly

Microtubules are cytoskeletal protein polymers relevant to a wide range of cell functions. In order to polymerize, the constituent tubulin subunits need to bind the nucleotide GTP, but its subsequent hydrolysis to GDP in the microtubule lattice induces depolymerization. The resulting behaviour of stochastic switching between growth and shrinkage is called dynamic instability. Both dynamic instability and microtubule mechanical properties are integral to many cell functions, yet are poorly understood. The present study uses thermal fluctuation measurements of grafted microtubules with different nucleotide contents to extract stiffnesses, relaxation times, and drag coefficients with an unprecedented precision. Both the stiffness and the relaxation time data indicate that stiffness is a function of length for GDP microtubules stabilized with the chemotherapy drug taxol. By contrast, measurements on microtubules polymerized with the non-hydrolizable GTP-analogue GMPCPP show a significantly higher, but constant, stiffness. The addition of taxol is shown to not significantly affect the properties of these microtubules, but a lowering of the GMPCPP content restores the length-dependent stiffness seen for taxol microtubules. The data are interpreted on the basis of a recent biopolymer model that takes into account the anisotropic architecture of microtubules which consist of loosely coupled protofilaments arranged in a tube. Using taxol microtubules and GMPCPP microtubules as the respective analogues of the GDP and GTP state of microtubules, evidence is presented that shear coupling between neighbouring protofilaments is at least two orders of magnitude stiffer in the GTP state than in the GDP state. Previous studies of nucleotide effects on tubulin have focussed on protofilament bending, and the present study is the first to be able to show a dramatic effect on interprotofilament bonds. The finding’s profound implications for dynamic instability are discussed. In addition, internal friction is found to dominate over hydrodynamic drag for microtubules shorter than ∼ 4 μm and, like stiffness, to be affected by the bound nucleotide, but not by taxol. Furthermore, the thermal shape fluctuations of free microtubules are imaged, and the intrinsic curvatures of microtubules are shown for the first time to follow a spectrum reminiscent of thermal bending. Regarding the extraction of mechanical data, this assay, though previously described in the literature, is shown to suffer from systematic flaws

Microtubule dynamics depart from wormlike chain model

Thermal shape fluctuations of grafted microtubules were studied using high resolution particle tracking of attached fluorescent beads. First mode relaxation times were extracted from the mean square displacement in the transverse coordinate. For microtubules shorter than 10 um, the relaxation times were found to follow an L^2 dependence instead of L^4 as expected from the standard wormlike chain model. This length dependence is shown to result from a complex length dependence of the bending stiffness which can be understood as a result of the molecular architecture of microtubules. For microtubules shorter than 5 um, high drag coefficients indicate contributions from internal friction to the fluctuation dynamics.Comment: 4 pages, 4 figures. Updated content, added reference, corrected typo

Microtubule mechanics and the implications for their assembly

Microtubules are cytoskeletal protein polymers relevant to a wide range of cell functions. In order to polymerize, the constituent tubulin subunits need to bind the nucleotide GTP, but its subsequent hydrolysis to GDP in the microtubule lattice induces depolymerization. The resulting behaviour of stochastic switching between growth and shrinkage is called dynamic instability. Both dynamic instability and microtubule mechanical properties are integral to many cell functions, yet are poorly understood. The present study uses thermal fluctuation measurements of grafted microtubules with different nucleotide contents to extract stiffnesses, relaxation times, and drag coefficients with an unprecedented precision. Both the stiffness and the relaxation time data indicate that stiffness is a function of length for GDP microtubules stabilized with the chemotherapy drug taxol. By contrast, measurements on microtubules polymerized with the non-hydrolizable GTP-analogue GMPCPP show a significantly higher, but constant, stiffness. The addition of taxol is shown to not significantly affect the properties of these microtubules, but a lowering of the GMPCPP content restores the length-dependent stiffness seen for taxol microtubules. The data are interpreted on the basis of a recent biopolymer model that takes into account the anisotropic architecture of microtubules which consist of loosely coupled protofilaments arranged in a tube. Using taxol microtubules and GMPCPP microtubules as the respective analogues of the GDP and GTP state of microtubules, evidence is presented that shear coupling between neighbouring protofilaments is at least two orders of magnitude stiffer in the GTP state than in the GDP state. Previous studies of nucleotide effects on tubulin have focussed on protofilament bending, and the present study is the first to be able to show a dramatic effect on interprotofilament bonds. The finding’s profound implications for dynamic instability are discussed. In addition, internal friction is found to dominate over hydrodynamic drag for microtubules shorter than ∼ 4 μm and, like stiffness, to be affected by the bound nucleotide, but not by taxol. Furthermore, the thermal shape fluctuations of free microtubules are imaged, and the intrinsic curvatures of microtubules are shown for the first time to follow a spectrum reminiscent of thermal bending. Regarding the extraction of mechanical data, this assay, though previously described in the literature, is shown to suffer from systematic flaws

Microtubule mechanics and the implications for their assembly

Microtubules are cytoskeletal protein polymers relevant to a wide range of cell functions. In order to polymerize, the constituent tubulin subunits need to bind the nucleotide GTP, but its subsequent hydrolysis to GDP in the microtubule lattice induces depolymerization. The resulting behaviour of stochastic switching between growth and shrinkage is called dynamic instability. Both dynamic instability and microtubule mechanical properties are integral to many cell functions, yet are poorly understood. The present study uses thermal fluctuation measurements of grafted microtubules with different nucleotide contents to extract stiffnesses, relaxation times, and drag coefficients with an unprecedented precision. Both the stiffness and the relaxation time data indicate that stiffness is a function of length for GDP microtubules stabilized with the chemotherapy drug taxol. By contrast, measurements on microtubules polymerized with the non-hydrolizable GTP-analogue GMPCPP show a significantly higher, but constant, stiffness. The addition of taxol is shown to not significantly affect the properties of these microtubules, but a lowering of the GMPCPP content restores the length-dependent stiffness seen for taxol microtubules. The data are interpreted on the basis of a recent biopolymer model that takes into account the anisotropic architecture of microtubules which consist of loosely coupled protofilaments arranged in a tube. Using taxol microtubules and GMPCPP microtubules as the respective analogues of the GDP and GTP state of microtubules, evidence is presented that shear coupling between neighbouring protofilaments is at least two orders of magnitude stiffer in the GTP state than in the GDP state. Previous studies of nucleotide effects on tubulin have focussed on protofilament bending, and the present study is the first to be able to show a dramatic effect on interprotofilament bonds. The finding’s profound implications for dynamic instability are discussed. In addition, internal friction is found to dominate over hydrodynamic drag for microtubules shorter than ∼ 4 μm and, like stiffness, to be affected by the bound nucleotide, but not by taxol. Furthermore, the thermal shape fluctuations of free microtubules are imaged, and the intrinsic curvatures of microtubules are shown for the first time to follow a spectrum reminiscent of thermal bending. Regarding the extraction of mechanical data, this assay, though previously described in the literature, is shown to suffer from systematic flaws

Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid

At timescales once deemed immeasurably small by Einstein, the random movement of Brownian particles in a liquid is expected to be replaced by ballistic motion. So far, an experimental verification of this prediction has been out of reach due to a lack of instrumentation fast and precise enough to capture this motion. Here we report the observation of the Brownian motion of a single particle in an optical trap with 75 MHz bandwidth and sub-angstrom spatial precision and the determination of the particle's velocity autocorrelation function. Our observation is the first measurement of ballistic Brownian motion of a particle in a liquid. The data are in excellent agreement with theoretical predictions taking into account the inertia of the particle and hydrodynamic memory effects

Motility pattern with two turning events.

<p>During each run, the speed of the cell <i>v</i>₀ is constant. Motion is nearly straight and is affected by the rotational diffusion <i>D</i>_<i>r</i>. The cell changes the direction of its motion during turning events (black dots), where turning angles Δ<i>φ</i>_1,2 are allowed to have two different probability distributions. Importantly, the cell strictly alternates the two types of turning events. When swimming in the gradient of signaling chemicals ∇<i>c</i>, the cell can bias its motion and respond with a drift speed <i>v</i>_<i>d</i> in the direction of the gradient, which we want to calculate.</p

Drift speed as a function of the chemoattractant gradient strength.

<p>Analytically obtained predictions (curve) agree with numerical results (symbols) up to the gradient values of ⋍ 0.5 <i>μm</i>⁻⁴ (<i>D</i>_<i>r</i> = 0.2 rad²s⁻¹, λ = 3.3 s⁻¹, <i>α</i> ≈ −0.34, <i>β</i> = −1).</p

Drift speed without rotational diffusion.

<p>(a) Analytically obtained function <i>v</i>_<i>d</i>(<i>α</i>, <i>β</i>), see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0190434#pone.0190434.e020" target="_blank">Eq (11)</a> is shown as a green surface and numerically obtained results as symbols for <i>D</i>_<i>r</i> = 0.0 rad²s⁻¹, |∇<i>c</i>| = 0.05 <i>μm</i>⁻⁴ and <i>W</i> = 0.0458 <i>μ</i>m³. (b) Comparison of analytically (lines) and numerically (symbols) obtained drift speed dependences on the parameter <i>α</i> for four values of <i>β</i>: <i>β</i> = 1.0 (yellow), <i>β</i> = <i>α</i> (red), <i>β</i> = −1.0 (blue), <i>β</i> = 0.0 (purple).</p

Drift speed with rotational diffusion.

<p>(a) Analytically obtained function <i>v</i>_<i>d</i>(<i>α</i>, <i>β</i>), shown as surface, and numerically obtained result as points for <i>D</i>_<i>r</i> = 0.2 rad²s⁻¹, |∇<i>c</i>| = 0.05 <i>μm</i>⁻⁴ and <i>W</i> = 0.0458 <i>μ</i>m³. (b) Comparison of analytically (lines) and numerically (symbols) obtained drift speed dependences on the parameter <i>α</i> for four values of <i>β</i>: <i>β</i> = 1.0 (yellow), <i>β</i> = <i>α</i> (red), <i>β</i> = −1.0 (blue), <i>β</i> = 0.0 (purple).</p