Self-organization is a recurrent theme in biology, evident across multiple length scales ranging from the oscillations of nanometer-sized signaling molecules in the cytoplasm to the formation of micron-sized cellular organelles and the patterning of millimeter-sized tissues. One of the best cellular systems for elucidating the principles of self-organization is the microtubule cytoskeleton, where dynamic microtubule polymers are organized into micron-sized arrays (Karsenti, 2008). Every microtubule filament within a multi-microtubule array is a polymer of tubulin subunits, polymerized with a specific polarity. Despite being assembled from the same microtubule building block, microtubule-based arrays display considerable diversity in their overall dimensions, shape, and polarity, in a manner that is intricately linked to their function. For instance, the orientation of coaligned, overlapping microtubules in the cortex of plant cells specifies the axis of cell elongation, and the polarity of long microtubule bundles in neurons distinguishes axons from dendrites (Chen et al., 2016; Kelliher et al., 2019). Understanding the mechanisms that direct the formation of distinct cellular arrays and specify their architecture will bring to light the general design principles underlying self-organization.

Building a multi-microtubule array of defined architecture requires the regulation of dimensions of individual polymers, as well as organizing them into higher-order structures. Microtubules are characterized by their inherent dynamic instability and cycle between phases of polymerization and depolymerization (Mitchison and Kirschner, 1984). The parameters governing dynamic instability therefore specify the stability, length, and density of microtubules within an array. There are broadly two ways in which dynamic instability is thought to be regulated. First, polymerization dynamics of individual microtubule filaments are sensitive to the concentration of soluble tubulin heterodimers which constitute their building blocks (Walker et al., 1988). In cells, tubulin levels are in turn autoregulated through translational control by tubulin itself (Cleveland, 1988; Lin et al., 2020). Second, the dynamics of microtubule polymers are regulated by the activity of microtubule-associated proteins (MAPs), which include both motor and non-motor proteins. In addition to polymer length and stability, MAPs also mediate the organization of microtubules into arrays through activities such as lattice severing, cross-linking, and sliding of microtubule pairs (Watanabe et al., 2005; Subramanian and Kapoor, 2012; Gardiner, 2013; Kapitein and Hoogenraad, 2015; Bodakuntla et al., 2019). For these reasons, tubulin heterodimers and MAPs have traditionally been the focal point in understanding the mechanisms that determine the assembly and overall architecture of an array. Microtubules themselves are largely viewed as passive building blocks in this process. A notable exception is the ‘tubulin code’, which is generated through the diversity in tubulin isotypes and post-translational modifications on the microtubule lattice. These chemical modifications of tubulin at the amino acid level can affect the inherent physical properties of the polymer and also regulate MAP activity (Alper et al., 2014; Kaul et al., 2014; Sirajuddin et al., 2014; Leo et al., 2015; Valenstein and Roll-Mecak, 2016; Bailey et al., 2015; Schwarz et al., 1998; Robison et al., 2016; Portran et al., 2017). An in-depth discussion of the tubulin code hypothesis can be found in several excellent reviews and will not be discussed further (Janke and Kneussel, 2010; Song and Brady, 2015; Gadadhar et al., 2017; Wloga et al., 2017; Janke and Magiera, 2020; Verhey and Gaertig, 2007). In recent years, an exciting concept that has emerged is that microtubules can encode information on the micron-scale to direct the self-organization of arrays. The features of the microtubule lattice that provide this information fall into two categories: (i) structural defects on the microtubule lattice such as missing tubulin subunits or changes in protofilament arrangement and (ii) size and relative arrangement of polymers, specified by parameters such as microtubule length, and the overlap length or contact angle between two adjacent polymers. Together, these micron-scale geometrical features along with the nanometer-scale tubulin code modulate the dynamics of individual polymers and regulate the activity of associated MAPs. In the following sections, we discuss how regulation by geometrical features of lattices is central to several processes involved in building a multi-microtubule array and determining its architecture. Overall, these mechanisms highlight the role of microtubules - as master architects directing their assembly and organization into cellular arrays.

• ‘Would you tell me, please, which way I ought to go from here?’

• ‘That depends a good deal on where you want to get to’

• – Alice’s Adventures in Wonderland, Lewis Carroll

Microtubules in cells are organized into specialized arrays. Upon close inspection, arrays are seen to contain recurring motifs or arrangements of microtubules A frequently observed motif is one where two polymers are coaligned. This can result in networks where adjacent microtubules are parallel to each other such as in ciliary axonemes and neuronal axons, anti-parallel as in the midzone of the mitotic spindle, or form arrays of mixed polarity such as plant cortical arrays (Subramanian and Kapoor, 2012). In some cases, these aligned arrays emerge from microtubules that are initially randomly oriented relative to each other. How are randomly oriented microtubules coaligned? Several studies highlight the importance of a geometrical parameter, the contact angle, as an important determinant in mechanisms promoting microtubule coalignment. For clarity, we define the contact angle as the angle between the lines joining the point where two microtubules encounter each other and their respective minus-ends (Figure 2).

Figure 2

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• ‘Oh, I'm not particular as to size, only one doesn't like changing so often, you know’

• – Alice’s Adventures in Wonderland, Lewis Carroll

An army of diverse Microtubule Associated Proteins MAPs serve as ‘builders’ to determine the size and shape of arrays through functions such as regulating microtubule dynamics, severing, cross-linking, and relative sliding between microtubules (van de Willige et al., 2016; Elliott and Shaw, 2018; Conkar and Firat-Karalar, 2021). The activity of MAPs, in turn, is found to be modulated by the geometrical parameters that specify array dimensions. On a single microtubule, the relevant parameter is polymer length. For pairs of microtubules, additional geometrical parameters that arise include the relative polarity, ‘overlap length’ over which two adjacent microtubules are cross-linked, the ‘overlap width’, which is the perpendicular distance between their lattices, and contact angle at their site of encounter. In the following section, we discuss the mechanisms by which these geometrical features regulate MAPs, and highlight how the interplay between geometrical parameters and MAP activity sculpt cellular arrays.

Part 1: Microtubule length as a regulator of microtubule dynamic instability

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).

Figure 3

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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).].

• ‘I know who I was when I got up this morning, but I think I must have been changed several times since then.’

• – Alice’s Adventures in Wonderland, Lewis Carroll

In the crowded cellular volume, growing microtubules encounter physical obstacles such as other cytoskeletal arrays, cell membranes, and chromosomes, which can cause the filaments to undergo bending, buckling, or bundling (Odde et al., 1999; Waterman-Storer and Salmon, 1997). The stepping of motor proteins and the action of severing enzymes can also physically damage the lattice (Srayko et al., 2006; Dumont et al., 2015). As a result, both in vitro and in cells, microtubules display ‘lattice defects’, which are disruptions in the ordered arrangement of tubulin subunits in a polymer, extending over length scales ranging from 0.1 to 1 μm (Chrétien et al., 1992; Atherton et al., 2018). These defects manifest as vacancies in the lattice caused by missing tubulin heterodimers, sharp edges on the tubule due to abrupt shifts in protofilament number, or as regions of structural heterogeneity. Despite being localized to discrete sites along the microtubule lattice, defects have been shown to affect plus-end dynamics. For instance, a mismatch in protofilament number on the lattice can lead to an increase in catastrophe frequency (Rai et al., 2021). Sites of microtubule damage can also recruit MAPs whose activity changes the total density of microtubules in cellular arrays through the following known mechanisms.

Lattice repair increases microtubule lifetimes

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.

Figure 4

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• ‘Begin at the beginning,’ the King said gravely, ‘and go on till you come to the end: then stop.’

• – Alice’s Adventures in Wonderland, Lewis Carroll

Microtubule arrays are dynamically assembled, remodeled, and disassembled over the lifetime of a cell. For example, the organization of the spindle constantly changes during cell division, plant cortical arrays are reoriented en masse to specify a new cell elongation axis in response to external stimuli, the polarities of microtubule bundles in neurons change as minor neurites grow into axons and dendrites, and the ciliary axoneme is built and disassembled each cell cycle (Sánchez and Dynlacht, 2016; van Beuningen and Hoogenraad, 2016). The assembly and remodeling of cellular arrays involves the integration of the various microtubule-regulated mechanisms discussed above such as microtubule nucleation, coalignment, MAP regulation, lattice severing, and repair. These processes do not occur in a discrete or sequential manner, but in fact occur concurrently, as illustrated by the two examples below.

Reorganization of plant cortical arrays

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)).

Figure 5

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Conclusion

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.

Figure 6

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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.

• Multiple nucleation pathways co-exist in cells in addition to microtubule-templated microtubule nucleation, each yielding new filaments that grow at specific orientation and polarity with respect to their organizing centers. For instance, centrosome-nucleated microtubules grow out radially, golgi-nucleated microtubules are tangential to the golgi, and nuclear membrane-associated microtubules form longitudinal arrays (Miller et al., 2009; Lüders and Stearns, 2007; Musa et al., 2003). Whether there are specialized geometrical cues that dictate the organization of these arrays relative to pre-existing microtubule networks presents an exciting research direction.

• Several mechanisms facilitate the close packing of microtubules to form bundles, ranging from those that occur in the absence of all MAPs to others which utilize cross-linking proteins of varying lengths (Peterman and Scholey, 2009; Needleman et al., 2004b). Thus far, our understanding of the self-organization and function of microtubule bundles have largely come from studies on coaligned microtubules cross-linked by members of the Ase1p/PRC1 family and a few cross-linking motor proteins of the kinesin family. Physical mechanisms such as osmotic forces induced by macromolecules and formation of liquid crystalline domains also result in the bundling of microtubules (Hitt et al., 1990; Needleman et al., 2004a; Guo et al., 2008). Remarkably, the shape of microtubule bundles formed by these mechanisms and the motility of motor proteins within them are found to be different when compared to bundles formed with protein cross-linkers (Edozie et al., 2019; Conway et al., 2014). Whether the close packing of microtubules in the absence of all MAPs generates geometrical cues similar to those observed with protein cross-linkers is still under-explored. Extending this line of research to diverse protein and non-protein cross-linkers will expand our understanding of geometrical parameters in array organization.

• The role of geometrical parameters in the organization of microtubules into radial, polar arrays such as asters remains poorly understood (Needleman and Dogic, 2017; Rickman et al., 2019). Intriguingly, in vitro studies show that motor proteins belonging to the kinesin-5 or kinesin-14 families can promote either nematic (linear bundles) or polar (radial arrays) organization of microtubules, depending on motor velocity and number, soluble tubulin concentration, microtubule number, and growth rates (Roostalu et al., 2018; Norris et al., 2018). Whether geometric features of microtubules direct the formation of polar arrays by kinesin and dynein motors (Tan et al., 2018; Khetan et al., 2021), and mediate the switch between nematic and polar self-organization remains an open question.

• In addition to overlap length and intersection angles, a fundamental geometrical parameter that defines the relative placement of two microtubules within a close-packed network is the overlap width or the spacing between their lattices. The observation that cross-linking motors and MAPs are characterized by a range of molecular dimensions suggests that the overlap width parameter could (i) regulate selective access of MAPs to the microtubules in an array, which in turn can modulate bundle dynamics and structure (Conway et al., 2014), (ii) determine the 2D and 3D organization of polymers in an array, by varying the nearest-neighbor distances (Nixon et al., 2015; Needleman et al., 2004b). Reconstitution studies that systematically vary the overlap width are likely to provide more insights. The effect of overlap width and the size of the molecular cross-linkers is particularly interesting in the context of asters where the overlap width would vary along the lattice in a radial assembly of microtubules.

• Lattice defects such as bends and breaks in the microtubule wall have been shown in vitro to serve as entry points into the microtubule lumen for the enzyme αTAT1 where it acetylates tubulin on a residue facing the lumen (Coombes et al., 2016). This mechanism raises the exciting possibility that regions of missing tubulin subunits could serve as ‘sieves’, allowing for selective lumen entry of proteins based on size. In addition, a break in the ordered arrangement of tubulin subunits could also hinder motor motility. Precise measurements of the dimensions of lattice defects, including the number of tubulin dimers they span, number of protofilaments they extend over, and their effect on microtubule stability, motor motility, cross-linking, and severing probability will provide insights into how microtubule defects regulate microtubule organization.

• Microtubules serve as platforms to couple the activity of associated motors and non-motor MAPs. The best understood coupling mechanisms arise from short-range interactions such as steric effects and cooperativity or crowding (Vilfan et al., 2001; Leduc et al., 2012). Can the linear structure of microtubules mediate the coupling of MAP molecules over distances in the micron length scale? Prior literature raises the intriguing possibility that microtubules can act as a micron-scale coupling medium to influence microtubule-binding kinetics of MAPs and motile propertiesof motors (Muto et al., 2005; Wijeratne et al., 2020). For example, microtubule-bound kinesin-1 motors have been shown to increase the axial pitch of the microtubule lattice, an alteration that is thought to promote the cooperative binding of other kinesin-1 molecules (Peet et al., 2018; Shima et al., 2018). Similarly, the straightening of tips of protofilaments by EB1 is proposed to mediate the synergistic increase in microtubule growth rates in the presence of Xenopus microtubule-associated protein (XMAP215) and EB1 (Zanic et al., 2013). In addition to MAP binding and activity, long-range effects on the microtubule lattice can also modulate the dynamics of the polymer itself. For instance, the presence of a lattice defect site corresponding to protofilament number mismatch has been shown to affect the dynamics of the polymer’s plus-end which can be several microns away (Rai et al., 2021). Elucidating conditions for micron-scale coupling and uncovering new mechanisms by which the microtubule lattice facilitates long-range communication and allosteric regulation of MAPs promises to be an exciting new research direction.

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Author details

1. Nandini Mani

   1. Department of Molecular Biology, Massachusetts General Hospital, Boston, United States
   2. Department of Genetics, Harvard Medical School, Boston, United States

   Contribution

   Conceptualization, Visualization, Writing - original draft, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-2025-9103

2. Sithara S Wijeratne

   1. Department of Molecular Biology, Massachusetts General Hospital, Boston, United States
   2. Department of Genetics, Harvard Medical School, Boston, United States

   Contribution

   Visualization, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-3935-926X

3. Radhika Subramanian

   1. Department of Molecular Biology, Massachusetts General Hospital, Boston, United States
   2. Department of Genetics, Harvard Medical School, Boston, United States

   Contribution

   Conceptualization, Funding acquisition, Writing - original draft, Writing - review and editing

   For correspondence

   radhika@molbio.mgh.harvard.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-3011-9403

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