Polymerization of microtubules begins with nucleation (Roostalu and Surrey, 2017). In cells, microtubules are nucleated and anchored at specialized organelles such as centrosomes and spindle pole bodies that serve as microtubule-organizing centers (MTOCs) (Wu and Akhmanova, 2017; Paz and Lüders, 2018). It is now apparent that not all microtubules are nucleated from conventional MTOCs (Petry and Vale, 2015; Basnet et al., 2018; Yi and Goshima, 2018; Lüders, 2021). For example, nucleation has been observed on ‘acentrosomal’ sites which include chromatin, nuclear membranes and golgi in animal cells, and plastids and plasma membranes in plant cells (Lee and Liu, 2019; Lüders and Stearns, 2007). A well-studied non-MTOC-based mechanism is branching microtubule nucleation, where new microtubules are generated from the lattice of a pre-existing ‘parent’ microtubule.

Since its first report in the alga Nitella tasmanica, branching nucleation has been observed to generate new microtubules at distinct orientation to the parent tubule in diverse cell types (O. WASTENEYS and E. WILLIAMSON, 1989). For example, newly nucleated microtubules are parallel to the parent in the spindle and neuronal axons, anti-parallel in arrays in yeast interphase cells and Arabidopsis pavement cells, and oriented at an angle of 40° with respect to the parent microtubule in plant cortical arrays (Janson et al., 2005; Murata et al., 2005; Petry et al., 2013; Sánchez-Huertas et al., 2016; Yagi et al., 2018). In this section, we discuss how pre-existing microtubules together with the γ-tubulin ring complex (γ-TuRC) direct the generation of new microtubules, and influence the polarity, orientation, and density of microtubules within an array (Figure 1).

Plant cortical arrays are characterized by the coalignment of microtubules with mixed polarity (Dixit et al., 2006; Wasteneys and Ambrose, 2009). These microtubules are nucleated from dispersed sites in the cortex and are initially oriented randomly to each other. To form the cortical array, longitudinally aligned microtubules need to be stabilized, and ‘discordant’ microtubules that grow at steep contact angles to the longitudinal array need to be removed. Dixit and Cyr, 2004 proposed that the contact angle a growing microtubule makes when it encounters another microtubule can determine its stability, to specify its eventual fate. Microtubules that intersect at shallow contact angles (<40°) are selectively cross-linked by MAPs such as members of the MAP65 family to form coaligned bundles. While the individual filaments within a bundle may be dynamic and exhibit tubulin turnover, the bundle as a whole has higher positional stability arising from the increased likelihood that at least one of its filaments is present at a given position (Wasteneys and Ambrose, 2009; Wightman and Turner, 2007; Ehrhardt and Shaw, 2006). In contrast, a steep contact angle (>40°) between a growing end and a pre-existing microtubule lattice generates a pushing force on the growing tip (Chi and Ambrose, 2016). Such forces can induce catastrophes, likely through a reduction in the rate of tubulin addition at plus-ends (Janson et al., 2003). Another consequence of the increase in contact angle is the altered accessibility of MAPs (Deinum et al., 2017). Together, force-induced catastrophe and differential MAP accessibility lead to the destabilization and eventual loss of discordant microtubules (Figure 2(i)). Thus, the selective modification of microtubule dynamics specified by a simple geometric feature such as contact angle between microtubules can generate an array with coaligned polymers.

The function of certain arrays relies on coaligned microtubules with specific polarity, such as parallel microtubule arrays in epithelial cells and invertebrate neurons (Bacallao et al., 1989; Stone et al., 2008). A mechanism that can align two microtubules parallel to each other is microtubule tip guidance or steering. Here, coalignment occurs through the bending and guiding of a growing microtubule tip along the lattice of a microtubule it encounters (hereafter referred to as the rail), by motor proteins. For example, in branched neurons, the interaction between the motor kinesin-2 and the plus-tip tracking proteins adenomatous polyposis coli (APC) and end-binding protein 1 (EB1) promote the parallel alignment of a growing microtubule with a pre-existing bundle following the point of encounter (Mattie et al., 2010).

Reconstitution of tip guidance starting from randomly oriented dynamic microtubules and chimeric kinesins modified to bind to the plus-tip tracking EB1 have revealed that the probability of coalignment depends on the microtubule-binding affinities and tip occupancy of the MAPs (Chen et al., 2014). The occurrence of tip guidance events also depends on the contact angle between the two microtubules (Figure 2(ii)). Tip guidance is found to be more probable at very low angles and close to 90°, but less so at intermediate (40°−85°) and high obtuse angles (Doodhi et al., 2014). Modeling the microtubule as a rod bending under load predicts that the forces required for bending microtubules would permit guidance at low angles and limit it at high obtuse angles. However, it does not explain the decrease in frequency of guiding at intermediate angles. Experiments reveal frequent slippage of the growing microtubule along the rail in the intermediate angle regime as a probable mechanism. Slippage occurs because steering a tip along a rail at intermediate contact angles requires both tubulin polymerization and kinesin-mediated guiding at the tip. The need for continuous kinesin occupancy at the newly grown tip, in order to maintain contact with the rail, thus limits effective tip guiding. Slippage is not a limiting factor at higher angles where guidance is dominated by polymer bending (Figure 2(ii)).

The examples in this section illustrate that the encounter angle is a key variable that regulates polymer dynamics, MAP accessibility, and cross-linking probability. Thus, the initial orientation of polymers and the angles at which growing microtubules intersect one another are important determinants of structural features such as the organization and polarity of microtubules in the final array.

The lengths of individual microtubules are determined by protein regulators of microtubule dynamic instability (Howard and Hyman, 2007). Several studies have uncovered the existence of feedback loops between regulator activity and microtubule length. For example, in budding yeast astral and kinetochore microtubules, the rate of tubulin disassembly by the kinesin-5 motor Cin8p increases with microtubule length (Gardner et al., 2008). Similarly in vitro studies reveal that the rate of microtubule depolymerization by kinesin-8 family members Kip3p and Kif18A and the rate of microtubule polymerization by the budding yeast kinesin Kip2p are proportional to microtubule length (Figure 3(i); Gupta et al., 2006; Varga et al., 2006; Mayr et al., 2007; Varga et al., 2009; Hibbel et al., 2015).

The microtubule length-dependent regulation of microtubule dynamics has been best studied in the context of Kip3p and explained by a mechanism called the ‘antenna model’ (Varga et al., 2006). Here, motor molecules land stochastically all along the lattice and step toward microtubule plus-ends. For highly processive motors with a slow dissociation rate from the microtubule end, such as in the case of Kip3p, the number of motors accumulated on the plus-ends is proportional to microtubule length (Figure 3(i)). Consequently, the rate of polymerization or depolymerization at the tip, which is mediated by motors, scales with microtubule length. An increase in depolymerization activity at the plus-end shortens microtubules, thereby providing negative feedback by reducing further motor accumulation and depolymerization rates. The antenna model thus illuminates the biophysical principles by which highly processive motors or motor complexes can alter microtubule dynamics in a microtubule length-dependent manner [(Subramanian et al., 2013; Leduc et al., 2012 Varga et al., 2006).].

Somewhat counterintuitively, studies in animal cells have shown that damage to microtubule lattices can result in an increase in the length and stability of microtubules (Aumeier et al., 2016). Several lines of experimental evidence indicate that sites of damage in the middle of a microtubule can incorporate GTP-tubulin dimers, as observed in live cells (Dimitrov et al., 2008; de Forges et al., 2016) and in microtubules polymerized in vitro (Schaedel et al., 2015; Schaedel et al., 2019; Rai et al., 2020). These ‘GTP-islands’ promote microtubule growth in two ways: (i) by serving as rescue points for re-initiation of growth during subsequent catastrophe events (Dimitrov et al., 2008; Tropini et al., 2012; Aumeier et al., 2016) and (ii) through the recruitment of growth-promoting MAPs that specifically recognize and bind to GTP-tubulin over GDP-tubulin, such as the rescue factors cytoplasmic linker protein of 170 kDa (CLIP-170) and CLIP-associating protein (CLASP) (Figure 4(i); Folker et al., 2005; de Forges et al., 2016; Aher et al., 2020). Consequently, as demonstrated by in vitro studies, sites of damage can result in microtubules that have significantly longer lifetimes, lengths, and rescue frequencies compared to microtubules undergoing stochastic polymerization and depolymerization (Aumeier et al., 2016). Thus, the repair of damaged lattices can infuse a fresh lease of life into a dynamic microtubule. This is advantageous in a crowded environment, where microtubules have a high probability of crossing over each other, which can result in lattice damage (de Forges et al., 2016). Repair at a site of damage increases the rescue frequency, resulting in an increase in the average length of polymers in the network. This further enhances the likelihood of microtubule crossovers, lattice damage, and rescue, thus increasing the overall density and lifetime of microtubules in the array.

Pre-existing microtubules can change the total microtubule number by recruiting severing enzymes which catalyze the removal of tubulin subunits to break the microtubule into shorter polymers (McNally and Roll-Mecak, 2018). Some severing enzymes like katanin have been predicted to preferentially bind to sites of lattice damage on microtubules, based on in vitro experiments and simulations (Davis et al., 2002; Díaz-Valencia et al., 2011). Severing activity can counterintuitively also lead to an increase in the overall microtubule mass (Figure 4(ii); Roll-Mecak and Vale, 2006; Srayko et al., 2006). For example, in Caenorhabditis elegans meiotic spindles, the severing of microtubules by katanin leads to a steep decrease in microtubule density near the poles and an increase in microtubule density at the cell center (Srayko et al., 2006; McNally et al., 2006). It is proposed that short microtubules generated by severing are redistributed to the cell center and organized into a bipolar array. Curiously, instead of conserving the total microtubule mass, the activity of katanin in this system was found to cause an increase in the overall cellular microtubule mass. In vitro studies on the severing enzymes katanin and spastin have provided an explanation, showing that the activity of severing enzymes leads to the removal of tubulin dimers and causes lattice damage (Vemu et al., 2018; Kuo et al., 2019). Repair of these sites through incorporation of GTP-tubulin dimers from solution leads to an increase in total microtubule mass and number through a combination of two mechanisms: (i) When the rate of GTP-tubulin incorporation exceeds rate of enzyme-catalyzed tubulin removal, the lattice acquires GTP-islands which increase rescue probability and decrease shrinkage rates during subsequent depolymerization events. (ii) When the rate of tubulin removal is higher than tubulin addition, enzyme activity severs the lattice. However, the newly created plus-ends contain GTP-tubulin dimers which increase their stability, and polymerization can be re-initiated from the severed microtubule ends. In vitro, it has also been shown that soluble tubulin itself can bind katanin and inhibit its activity, thus setting up a feedback loop for the control of microtubule length and density (Bailey et al., 2015).

Together, these examples show that the inter-dependence between structural features of microtubule lattices, such as defects, and the activity of MAPs including severing enzymes and rescue factors can modulate polymer length and dynamics. This interplay serves to change microtubule density in an array through the disassembly, redistribution, stabilization, or amplification of microtubules.

Stimulation of plant cells by blue light results in a dramatic reorientation of their cortical microtubules by ~90°, to specify a new cell elongation axis (Zandomeni and Schopfer, 1993; Paredez et al., 2006; Chen et al., 2016). In this section, we refer to the initial array as the longitudinal array, and the final arrangement, which is perpendicular to the original array, as the transverse array (Figure 5(i)). The microtubules of the longitudinal array play a critical role in directing array reorientation (Lindeboom et al., 2013). The process begins with γ-TuRC-mediated branching microtubule nucleation, from the microtubules in the longitudinal array. This results in new microtubules which grow at angles close to ±40° (hereafter referred to as diagonal microtubules) to the longitudinal array. Subsequent branching nucleation from diagonal microtubules generates a subset of new microtubules that grow perpendicular to the longitudinal array and are oriented correctly to form the transverse array. However, to establish an array that is reoriented by 90°, the selective amplification of transverse microtubules and destabilization of longitudinal and diagonal microtubules is required. For this, the severing enzyme katanin is specifically recruited to sites where two microtubules cross over (Zhang et al., 2013; Deinum et al., 2017; Wang et al., 2017). At these sites, the frequency of katanin severing is higher on the new microtubule compared to microtubules of the original array, although the precise mechanism for selective severing is currently unknown. Katanin severing of a new microtubule generates two microtubules, doubling the number of transverse and diagonal microtubules that continue to grow (Nakamura et al., 2018). How does this mechanism preferentially amplify transverse over diagonal microtubules? A new microtubule forms the maximum number of cross-overs, when the distance between the pre-existing microtubules that it encounters is the least. Basic geometry dictates that this condition is satisfied when the new microtubule grows perpendicular to the original array, compared to all other orientations, thereby selectively amplifying the transverse microtubules. Once the transverse array is established, there is a reduction in branching nucleation rates by mechanisms such as phototropin signaling, and a reduction in severing at cross-overs by mechanisms that remain unclear. This halts both generation and amplification of new microtubules, and a stable transverse array is e. Thus, the longitudinal array serves as a patterned template for the preferential amplification of microtubules that grow at right angles to it, to form the transverse array (Figure 5(i)).

The spindle midzone is an inter-digitating array of anti-parallel microtubules at the cell center. (Mastronarde et al., 1993; Figure 5(ii)). The precise cellular location and size of the spindle midzone determine the site of cell cleavage during cytokinesis and ensure error-free genome propagation (Eggert et al., 2006; Scholey et al., 2016). The specification of both these parameters relies on several microtubule-regulated mechanisms. The formation of the spindle midzone first requires an increase in microtubule density at the cell center. For this, microtubules growing radially outward from the centrosomes serve as platforms for γ-TuRC and augmin-mediated branching nucleation resulting in new microtubules that grow with their plus-ends oriented toward the cell center (Uehara and Goshima, 2010; Uehara et al., 2016; Pamula et al., 2019). Here, they form overlaps with microtubules of the opposite polarity, through the action of cross-linking motors and non-motor MAPs. The location of this overlap must be maintained at the cell center even as the lengths of the constituent microtubules change as cell division progresses. The scaling of microtubule depolymerization rates with polymer length through the action of depolymerizing kinesins such as Kip3p is proposed to play an important role. Length-dependent depolymerization ensures that microtubules have uniform length, and overlaps between anti-parallel microtubules are formed at the center of the cell (Varga et al., 2006; Varga et al., 2009; Rizk et al., 2014). How is the overlap length of the array precisely specified? The initial overlap length between two microtubules is proposed to be a key determinant. This is because microtubule overlap length regulates microtubule polymerization dynamics and relative sliding of microtubules by several midzone kinesins. These include kinesin-5, kinesin-6, kinesin-14,, and the Kif4A-PRC1 complex (Glotzer, 2009; Bieling et al., 2010; Subramanian and Kapoor, 2012; Scholey et al., 2016; Wijeratne and Subramanian, 2018; Shimamoto et al., 2015; Hannabuss et al., 2019; Krüger et al., 2019). As sliding progresses, overlap length-dependent braking forces generated by motor and non-motor MAPs increase, while the rate of sliding decreases, to establish a stable midzone of defined length (Braun et al., 2011; Braun et al., 2017). In addition to the initial overlap length, relative microtubule polarity can also regulate sliding forces generated by midzone motors (Shimamoto et al., 2015). Thus, while the activity of MAPs alters the dimensions of the array, the changes in geometrical parametersthat define crosslinked microtubules in turn provide instantaneous feedback to regulate MAP activity. This interdependence between MAP activity and array geometry ensures that a stable spindle midzone array is formed at a fixed location in the cell, even as its constituent dynamic microtubules undergo growth, depolymerization, and relative sliding (Figure 5(ii)).

The self-organization of microtubules into specialized micron-sized arrays has been extensively studied from the perspective of motor and non-motor MAPs that shape arrays. It is now evident that microtubules themselves provide cues to regulate MAP activity, both at the nanometer scale through a tubulin code and at the micron scale via geometrical features of the lattice. The interplay between microtubules and MAP activity directs the self-organization process, by specifying microtubule density, array architecture, and stability (Figure 6). This ‘DIY’ (Do It Yourself) approach adopted by microtubules toward their organization has far-reaching consequences in the cell. First, members of the different cytoskeletal families are known to engage in extensive crosstalk. (Dogterom and Koenderink, 2019; Logan and Menko, 2019; Seetharaman and Etienne-Manneville, 2020). For example, microtubules have been shown to regulate the nucleation, polymerization, and dynamics of the actin network in migrating cells, neuronal growth cones, and dendritic spines. In dividing cells, the position and geometry of the acto-myosin contractile ring at the cell center are determined by astral and spindle midzone microtubules (Pollard and O'Shaughnessy, 2019). Further, microtubule-based transport is also important for the assembly of intermediate filaments (Hookway et al., 2015). Second, microtubule networks are important in creating and maintaining biochemical concentration gradients in the cytosol. For instance, spindle microtubules are known to play a role in creating spatial gradients of Aurora B kinase activity and components of the Ran-GTP pathway (Noujaim et al., 2014; Oh et al., 2016). Thus, beyond directing the assembly of microtubules into arrays, micron-sized features of microtubule networks contribute to the larger-scale spatial organization of the eukaryotic cell by directing the organization of other cytoskeletal networks and signaling gradients.

Polymeric proteins that self-organize into micron-sized arrays are not exclusive to eukaryotic cells, but are found across all kingdoms of life. In bacteria and archaea, homologs of tubulin, actin, and intermediate filaments form filamentous assemblies, with the assistance of conserved proteins (Busiek and Margolin, 2015; Fink et al., 2016; Stairs and Ettema, 2020). Future studies will reveal if the mechanisms invoking the regulation of microtubule array assembly by geometrical features of microtubules could have emerged in prokaryotic ancestors. In addition to the assembly of protein-based structures, these principles may also apply to the self-organization of nucleic acids and other cellular polymeric arrays.