18Microtubules are highly dynamic polymers that play fundamental roles in all 19 eukaryotes. As the control of microtubule nucleation and regulation is central to 20 their function, there has long been interest in obtaining quantitative descriptions 21 of microtubule polymerization. Textbooks have focused on variations of a 22 nucleation-elongation mechanism: monomers are in rapid equilibrium with an 23 unstable oligomer (nucleus), but once the nucleus forms, the polymer grows by 24 monomer addition. While such mechanisms readily capture the actin assembly 25 process, they are inadequate to describe the physical mechanism by which the 26 much larger and more complex microtubules assemble. Here we develop a new 27 model for microtubule self-assembly that has three key features: i) microtubules 28 initiate via the formation of closed, 2D sheet-like structures which grow faster the 29 larger they become; ii) the dominant pathway proceeds via addition of complete 30 longitudinal or lateral layers; iii) as predicted by structural studies and the lattice 31 model, the formation of lateral interactions requires payment of an energetic 32 penalty for straightening early structures. This model quantitatively fits 33 experimental assembly data, and provides important insights into biochemical 34 determinants and assembly pathways for microtubule nucleation. 35 2017), a process called nucleation. 52
53Microtubules are hollow, cylindrical polymers formed from ab-tubulin 54 heterodimers that interact with each other in two ways: stronger head-to-tail 55 (longitudinal) interactions between ab-tubulins make up the straight 56 protofilaments, and weaker side-to-side (lateral) interactions hold protofilaments 57 together. The mechanisms underlying the dynamic instability of existing 58 microtubules are increasingly well understood (Alushin et al., 2014; Zhang et al., 59 2015;Manka and Moores, 2018; Duellberg et al., 2016; Gardner et al., 2011; 60 Geyer et al., 2015;Piedra et al., 2016; Driver et al., 2017;VanBuren et al., 2002; 61 2005;Grishchuk et al., 2005), but our understanding of spontaneous microtubule 62 nucleation remains relatively primitive (reviewed in (Roostalu and Surrey, 2017)). 63Multiple factors contribute to this difficulty: first, nucleation occurs very rarely, so 64 measuring it directly is much harder than measuring the growing and shrinking of 65 3 existing microtubules. Second, the open, tube-like structure of the microtubule 66 also poses unique challenges to assembly. In most organisms, microtubules 67 contain 13 protofilaments, although there are clear examples of specialized 68 microtubules containing 11 or 15 protofilaments (Chalfie and Thomson, 1982; 69 Davis and Gull, 1983;Kwiatkowska et al., 2006;Burton et al., 1975; Saito and 70 Hama, 1982; Tucker et al., 1992; Chaaban et al., 2018). Regardless of 71 protofilament number, the hollow nature of the microtubule means that it takes 72 many more ab-tubulin subunits to close a tube than it does to make a minimal 73 helical repeat for a simp...