Microtubule Elasticity: Connecting All-Atom Simulations with Continuum Mechanics

Abstract

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. DOI: 10.1103/PhysRevLett.104.018101 PACS numbers: 87.16.Ka, 83.10.Ày, 87.15.AÀ, 87.15.La Microtubules are essential players in a wide range of cellular functions. The protein tubulin polymerizes to form these filaments resulting in a hollow cylinder with a diameter of about 25 nm and lengths that range from tens of nanometers to tens of microns. Microtubules are the most rigid structures within the cell and their mechanical stability is particularly important for the role that microtubules play in cell division, cellular transport, and their basic ability to help provide cell shape. The mechanical properties of purified microtubules have been studied extensively using many biophysical techniques, including atomic force microscopy, thermal bending, and single molecule techniques [1][2][3][4][5][6][7][8][9][10][11]. Since microtubules are dynamic polymers and have intrinsic instability, many of these experimental studies have been performed on Taxol-stabilized microtubules, although the mechanical consequences of the drug Taxol for microtubule mechanics remains unclear. The majority of studies have found that the addition of Taxol results in ''softer'' microtubules with a shorter persistence length and lower Young's modulus [1][2][3][4][5], while one published study had found the opposite result [6]. Recently, even the standard elastic model of microtubules characterized by a single elastic bending constant has been called into question by reports of length-dependent stiffness [12]. Thus, in spite of decades of experimental study, many basic questions and puzzles remain concerning the mechanics of even individual microtubules in vitro, let alone in vivo.Here, we combine all-atom simulations and continuum elastic modeling in order to determine both the elastic parameters of persistence length and Young's modulus, as well as to test the applicability of simple, continuum shell elasticity for microtubules. Based on a molecular dynamics simulation of a small section of six tubulin monomers [13], we show that the observed fluctuations of this section are consistent with linear elastic constants for both bending and stretching along the microtubule axis.From these measurements, we determine the effective elastic properties for the microtubule wall, treated as an elastic sheet. With the addition of Taxol, we find in...

Modeling semiflexible polymer networks

“…Interestingly, it has been reported that microtubules have a length-or wavelength-dependent stiffness (Pampaloni et al, 2006;Taute et al, 2008), and the elastic anisotropy of their structure has been implicated as the cause of this (Heussinger et al, 2010). However, it was also noted that the degree of anisotropic elasticity required to account for the reported length dependence is extremely large, and much larger than recent detailed simulations found (Sept and MacKintosh, 2010). Moreover, AFM experiments probing the response of microtubules to radial forces have not shown evidence for significant anisotropy (de Pablo et al, 2003).…”

Effects of microtubule mechanics on hydrolysis and catastrophes

“…The much larger values of κ that have been obtained in [25,27] as discussed above would lead to a ratio k/κ close to the lower bound (10).…”

“…The other estimates κ ∼ 3000k B T from [25] and κ ∼ 300k B T from [27], however, violate this constraint. If κ-values violating the upper bound (14) are confirmed experimentally in the future, this can be a hint that the allosteric model itself, i.e., the assumption that GTP hydrolysis changes the tubulin dimer angle, is inconsistent.…”

“…This means that we will not include catastrophes as explicit stochastic events but obtain catastrophes as emerging events from hydrolysis coupled to mechanics within the MT. Our description will be microscopic on the level of tubulin dimers (i.e., not on the level of all-atom simulations as in [25,27,28]). …”

Mechanotransduction of Ultrasound is Frequency Dependent Below the Cavitation Threshold

“…For microtubules (one of the main load-bearing structures in cells), K s has been reported to lie anywhere from 1 MPa to 10 GPa, with values being strongly dependent on experimental conditions and interpretation of data (Kasas et al 2004). Recent atomistic simulations place the K s of microtubules between 100 MPa and 1 GPa, depending on the specific structure (Sept and MacKintosh 2010). Similarly, organelles display vastly different compressibility.…”