Why Microtubules Run in Circles: Mechanical Hysteresis of the Tubulin Lattice

Abstract

The fate of every eukaryotic cell subtly relies on the exceptional mechanical properties of microtubules. Despite significant efforts, understanding their unusual mechanics remains elusive. One persistent, unresolved mystery is the formation of long-lived arcs and rings, e.g. in kinesin-driven gliding assays. To elucidate their physical origin we develop a model of the inner workings of the microtubule's lattice, based on recent experimental evidence for a conformational switch of the tubulin dimer. We show that the microtubule lattice itself coexists in discrete polymorphic states. Curved states can be induced via a mechanical hysteresis involving torques and forces typical of few molecular motors acting in unison. This lattice switch renders microtubules not only virtually unbreakable under typical cellular forces, but moreover provides them with a tunable response integrating mechanical and chemical stimuli.PACS numbers: 87.16. Ka, 82.35.Pq, Microtubules (MTs) are the stiffest cytoskeletal component and play many versatile and indispensable roles in living cells. As 'cellular bones', they define to a large part cell mechanics, and are crucial for cellular transport and cell division [1][2][3][4]. Beyond their biological importance, MTs have been used as molecular sensors for intracellular forces, as biotemplates for nanopatterning, and as building blocks for hybrid materials and active systems like artificial cilia and self-propelled droplets [5][6][7][8][9][10]. The MT's structure is well known [11]: the elementary building blocks, tubulin dimers, polymerize head to tail into linear protofilaments, that associate side by side to form the hollow tube structure known as the MT.Despite of the MTs' importance, widespread use, the knowledge of its structure, and numerous experiments probing their elastic properties [13][14][15][16][17], understanding their basic mechanics still poses challenging problems. A remarkable one is found in MT gliding assays [18][19][20][21], see Fig. 1: already two decades ago, Amos & Amos [19] observed that MTs driven by kinesin motors on a glass surface can form arcs which continue gliding for significant time intervals before suddenly straightening out. They remarked with quite some foresight that these circular MT states could be explained by the existence of alternative tubulin dimer conformations [22]. The observation remained without wider public notice despite the frequent reoccurrence of MT arcs in the gliding dynamics of single filaments [23][24][25], bundles [26][27][28] and in collective (high density) gliding [29]. Force-induced circular arcs on the same scale, but rather dissimilar to classical buckling, have been found in numerous other situations [20,30], also in vivo [31][32][33]. While the lifetime of MT rings varies, their characteristic size of about one micron is preserved in single filament experiments [19,[23][24][25], indicating a robust mechanism at work. The importance of internal degrees of freedom of the MT lattice (e.g. interprotofilament shear [34,35] and ...

Mechanical splitting of microtubules into protofilament bundles by surface-bound kinesin-1

“…It has recently been proposed by Ziebert et al . that these arcs are caused by a conformational change in tubulin rearrangement of the tubulin lattice in the MT to a curved configuration35. However, our work offers an alternative explanation: the arcs might be caused by PFBs at the leading end of the MT.…”

Invited review: Microtubule severing enzymes couple atpase activity with tubulin GTPase spring loading

“…Starting from the hypothesis that the GDP‐tubulin dimer is a conformationally bistable molecule, able to switch rapidly between a curved and a straight state, Kulic and collaborators developed a model for polymorphic dynamics of the microtubule lattice . This theoretical model explains the unusual dynamic fluctuations seen in microtubules and formation of helical loops by microtubules . One limitation of this model is that it does not take into account the findings of atomistic simulations in solution that in short protofilaments interdimer and intradimer contacts in both GDP and GTP‐bound tubulin dimers and protofilaments bend .…”

“…54 This theoretical model explains the unusual dynamic fluctuations seen in microtubules and formation of helical loops by microtubules. 55 One limitation of this model is that it does not take into account the findings of atomistic simulations in solution that in short protofilaments interdimer and intradimer contacts in both GDP and GTP-bound tubulin dimers and protofilaments bend. 9,56 In these simulations, there were no observable differences between the mesoscopic properties of the contacts in GTP and GDP-bound dimers, in accord with the recent structural information on microtubule states.…”

Single microtubules and small networks become significantly stiffer on short time-scales upon mechanical stimulation

“…40 introduced an additional internal friction term to explain deviations of their measured MT drag coefficients when microtubules were shorter than ≈ 5 µm, attributed to dissipation during conformational changes or liquid flow passing through narrow pores in the MT lattice as introduced by 41 . Polymorphic conformational states of the tubulin lattice and non-equilibrium filaments dynamics have also been studied in motor based microtubule gliding assays, recently 42, 43 . Irrespective of the effects found here, the plateau value G ′( ω  = 0) is directly related to the conventional, frequency independent persistence length l p ( ω  = 0), which increases with the contour length of the MTs according to l p ( ω  = 0, L ) ~ 1/(1 +  l c 2 / L 2 ) 38 .…”