Neurons play a central role in receiving and distributing information and depend on long, slender axons and dendrites for their function. Vertebrate peripheral neurons can be meters long and less than 1 μm in diameter: the peripheral neurons of Cetaceans have aspect ratios exceeding a factor of 10,000,000 (Wedel, 2012). Despite their slender construction, peripheral neurons have axons that bend without breaking—that is they are robust enough to withstand the mechanical deformations generated during body movements under most conditions. Conversely, injuries that lead to compression of the longest human nerve, the sciatic nerve, can cause severe back pain and palsy. The neurons of the central nervous system are also subject to mechanical deformations during contact sports or other activities, despite the protection afforded by the skull (e.g. Broglio et al., 2011). In all neurons, mechanical trauma can disrupt the cytoskeleton and trigger axonal degeneration (reviewed by Gaetz, 2004). Thus, it is of central importance to understand how neurons maintain their shape and function in the mechanically active environment of our bodies.

Axons harbor bundles of microtubules (MT), which are known to be important for neuronal architecture, growth, and organelle transport (Tyler, 2012). MTs are needed for resistance to compressive loads in fibroblasts and cardiac myocytes, especially when the MTs are laterally constrained (Brangwynne et al., 2006). Considering this, it is likely that MTs also affect how axons respond to mechanical loads. For instance, Tang-Schomer et al. (2010) showed that rapid mechanical stretch deforms cortical axons grown on elastic substrates and that the observed deformations were enhanced by treatment with the MT stabilizing drug, taxol, and suppressed by treatment with the MT stabilizing drug, nocodazole. Taxol slowed and nocodazole accelerated stretch-induced axonal degeneration, suggesting that intact MTs are needed to protect neurons from mechanical strain-induced damage

Microtubules are not the only components of the neuronal cytoskeleton. Actin and spectrin assemble into a subcortical lattice with a ~200 nm periodicity in neurons and glial cells (D'Este et al., 2016, 2015; He et al., 2016; Xu et al., 2013; Zhong et al., 2014). Spectrin filaments are composed of α and β subunits, which associate head to head to form tetramers: the N-terminal end of each α-subunit associates with the C-terminus of each β-subunit. In axons and dendrites, spectrin filaments have an estimated length of 200 nm, a value larger than expected from the their resting contour length (Boal, 1999). Genetic defects leading to a reduction of tension in the actin-spectrin networks cause C. elegans neurons to buckle and deform during body movements, leading to axon damage (Hammarlund et al., 2007; Krieg et al., 2014).

Here, we use C. elegans to study how neurons maintain stable shapes even under the large mechanical strains generated by body movements. We focused on the six touch receptor neurons (TRNs) required for sensing gentle touch (Chalfie et al., 1985) because they are among the best characterized neurons in the C. elegans nervous system. TRNs have a simple morphology and long neurites that emanate from the cell body and tile the body into anterior/posterior and ventral/lateral dermatomes. The anatomy of C. elegans TRNs has been studied intensively through light- and electron microscopy and their neurites contain >60 MT cross-linked into a coherent bundle (Chalfie and Thomson, 1979; Cueva et al., 2007). The TRN microtubules depend on expression of mec-7 β-tubulin and mec-12 α-tubulin and together these genes account for more than 90% of the tubulin transcripts expressed in these neurons (Lockhead et al., 2016). TRNs also contain an actin-spectrin network, in which spectrin is under constitutive mechanical tension and has been implicated in mechano-protection (Krieg et al., 2014).

Here, we examine how the mechanical interplay between these two cytoskeletal elements influences neuronal shape dynamics and resistance to mechanical stress by leveraging mutations in UNC-70 β-spectrin, MEC-7 β-tubulin, and in PTL-1 tau, the sole C. elegans homolog of MAP2/tau proteins. Our observations indicate that mechanical neuroprotection depends on spectrin-dependent longitudinal tension, MT-dependent bending stiffness, and MT-binding proteins such as PTL-1 that act to dissipate torsional forces that would otherwise destabilize MTs and the neuron (Grason, 2015; Grason and Bruinsma, 2007). Because spectrin, β-tubulin, and tau are highly conserved from C. elegans to humans and constitute the major protein content in the mammalian central nervous system, our results provide a mechanistic framework for understanding how neurons remain resilient in the face of mechanical stress.

Mechanical stability is one of several vital functions provided by the neuronal cytoskeleton, which includes both actin-spectrin networks linked to the plasma membrane and bundles of microtubules (MTs) that fill the cytoplasm. To understand how these structures interact to protect axons and dendrites from mechanical stress in living animals, we examined axon shape in mutants carrying genetic defects in the constituents of actin-spectrin networks and MT bundles. Our study builds on prior work in this area: Genetic defects in UNC-70 β-spectrin have been linked to movement-dependent axon fracture (Hammarlund et al., 2007) and buckling (Krieg et al., 2014) in C. elegans motor neurons and TRNs, respectively. Additionally, morphological distortions in the TRNs such as bends and kinks have been described in animals carrying loss-of-function alleles of mec-17 α-tubulin acetyltransferase (Topalidou et al., 2012) and missense alleles of mec-12 α-tubulin (Hsu et al., 2014). No such shape distortions appear in mutants lacking MT bundles in the TRNs (Chalfie and Thomson, 1982; Hsu et al., 2014; this study—Figure 1A), suggesting that defects in MT bundles, but not their absence, cause shape distortions

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To learn more about the interaction between the spectrin and the microtubule cytoskeleton, we analyzed TRN shape in mutants affecting the microtubule cytoskeleton and asked whether or not these mutations could enhance shape defects in unc-70(e524) missense mutants. The e524 allele encodes a missense mutation, E2008K, affecting the linker region between the tetramerization domain and the 16th spectrin repeat of β-spectrin (Krieg et al., 2014). To enable quantitative comparisons, we devised a method to quantify the neurite’s deviation from the straightest possible path. In brief, we measured the deviation perpendicular to the long (anterior-posterior) axis of the animal and the axon at all positions and reduced these measures to a single value, D, which describes the displacement of the neurite about this axis on a pixel-by-pixel basis. In this computation, D has a value of zero for a perfectly straight neuron and any deviations from straightness increase D, regardless of the nature of the morphological defect (see Materials and methods). Using this approach, we examined a novel allele of mec-7 β-tubulin, wy116, and a null allele of ptl-1 tau, ok621.

The wy116 allele replaces threonine 409 with an isoleucine (Figure 1—figure supplement 1) and maps to a region in the C-terminal tail of MEC-7 β-tubulin thought to form the interface between α and β tubulins (Figure 1—figure supplement 2). The wy116[T409I] allele was isolated in a genetic screen for defects in synaptic vesicle transport (Materials and methods) and has a mild defect in touch sensation (Table 1). As in wild type, TRNs in young-adult mec-7(wy116) animals were straight and lacked local bends and shape distortions (Figure 1A and B). The TRNs in mec-7(wy116);unc-70(e524) double mutants displayed large bends and kinks that were not found in either single mutant. Such shape defects were largely absent in mec-12(e1607); unc-70(e524) double mutants (Figure 1A and B) that lack MEC-12 α-tubulin and fail to form 15pf MTs in TRNs (Chalfie and Thomson, 1982). This finding and the fact that wy116 affects a region implicated in binding MT-associated proteins (MAPs) including tau (Al-Bassam et al., 2002; Littauer et al., 1986) led us to examine mutants lacking PTL-1, the sole tau homolog in the C. elegans genome (Goedert et al., 1996; Gordon et al., 2008).

As found in mec-7(wy116), TRNs in ptl-1(ok621) null mutants were straight, lacked obvious shape distortions, and had D values close to zero (Figure 1A and B). In ptl-1(ok621);unc-70(e524) double mutants, by contrast, the TRN axons exhibited large bends and localized helices, loops, and plectonemes (Figure 1A, Video 1). Given that rescue of β-spectrin in epidermal cells reduced but did not eliminate buckling instabilities in AVM neurons (Krieg et al., 2014), we examined ptl-1(ok621);unc-70(e524) double mutants expressing wild-type UNC-70 β-spectrin in the epidermis from the oxIs95[epi::UNC-70] transgene. This manipulation resulted in a less pronounced phenotype but did not obviously alter the displacement metric, D (Figure 1A). The defects in ptl-1;unc-70 mutants appeared at roughly regular intervals of 13 ± 0.5 µm (mean ± s.e.m., n = 121 intervals in 10 neurons) along the axon (Figure 1) and were dynamic. Figure 1C is a series of images illustrating the dynamic nature of the shape defects seen in ptl-1;unc-70 double mutant axons (see also Video 1 and Video 2). The shape defects in ptl-1;unc-70 double mutants were qualitatively similar, but more pronounced than those observed in mec-7(wy116);unc-70 double mutants (Figure 1A).

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The defects we observed in living animals are reminiscent of what happens following the partial release of tension in an elastic rope that is twisted and held under tension. The dynamics of this situation are familiar to anyone handling twisted ropes or threads (Video 3) and are well-described by a physical model in which the formation of coils and plectonemes is the result of an imbalance between torque, tension, and bending stiffness (Coyne, 1990). This physical model also predicts that no coils form in the absence of twist (Video 4). Based on these observations, we hypothesized that the shape defects observed in mutant axons reflected the same physical process. If the analogy holds, then releasing axial tension in mutant axons via in vivo laser axotomy is expected to cause rotation along the axon’s long axis and conversion of twist into writhe evident in the formation of new coils and plectonemes. Consistent with this prediction, releasing axial tension via in vivo laser axotomy readily drove reorganization of coils and plectonemes (Figure 1D, Video 5). In some cases, we also found evidence of rotation following axotomy (Video 6), indicative of a release from a preexisting, twisted state.

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The position of axons within tissues determines their exposure to mechanical stress

Mechanical stresses generated by tissue movement are not expected to be uniform throughout the tissue. The worm’s cylindrical body and the differential position of the lateral (ALML, ALMR, PLML, PLMR) and ventral (AVM, PVM) TRNs provide an opportunity to investigate this question. Given that C. elegans crawl on their sides and bend primarily along their dorsal-ventral axis, the lateral midline constitutes the animal’s neutral bending axis (Figure 2A). Euler beam bending theory (Bauchau and Craig, 2009) predicts that strain, ε, within the worm’s cylindrical body is the product of the curvature, c, of the neutral bending axis and the displacement, z. away from the neutral bending axis: ε=cz. In wild-type control animals (Figure 2A), the AVM axon is located along the ventral midline at a distance of z = 21.1 ± 6.5 µm (mean ± s.d., n = 32 worms) and the ALM axons lie much closer to the neutral bending axis at z = 5.5 ± 1.7 µm (n = 15 worms). If Euler’s simple theory of mechanical stress in a bending cylindrical beam holds for C. elegans, then the body bends that occur during movement are expected to deform the AVM axon four-fold more than the ALM axon.

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Consistent with this idea and prior work (Krieg et al., 2014), wild-type AVM axons undergo local contractions and extensions with up to 50% strain observed during normal locomotion (Figure 2B and C, Figure 2—figure supplement 1; Video 7). The ALM axons, by contrast, show only modest changes in strain during movement (Figure 2B and C; Figure 2—figure supplement 1; Video 8). As an additional test of the idea that the larger displacement of AVM from the neutral bending axis is responsible for the larger change in strain, we took advantage of a mutation in him-4 hemicentin that displaces the ALM away from the neutral bending axis and toward the dorsal side of the animal (Figure 2D) but has little effect on AVM’s position (Vogel and Hedgecock, 2001). Thus, in him-4 mutants AVM lies along the ventral midline and ALM lies near the dorsal midline at z = 17 ± 2.6 µm (mean ± s.d., n = 9 worms, Figure 2D and E). Measuring the relationship between neuron strain and body strain in him-4 mutants, we found that both AVM and ALM axons generate similar local contractions and extensions during locomotion (Figure 2E and F; Figure 2—figure supplement 1; Video 9, Video 10). These findings suggest that AVM and ALM axons have similar mechanical properties and that axon position has dramatic effects on bending-induced mechanical stresses.

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Next, we sought to elucidate the interplay of axon position and the tension born by the spectrin cytoskeleton. Previously (Krieg et al., 2014), we showed that unc-70 β-spectrin mutant neurons have reduced axial tension and that the axons of AVM neurons in unc-70 mutants undergo buckling instability under movement-induced compressive, but not tensile stress (Figure 3A,B and C; Video 11). However, similar defects are not observed in the axons of ALM neurons in these mutants (Figure 3A,B and C, Video 12). The simplest explanation for this discrepancy is that because the ALM axons are positioned close to the animal’s neutral bending axis, they are exposed to significantly smaller compressive stresses during body bending. We exploited the fact that the ALM axons are displaced away from the neutral bending axis in him-4 mutants (Figure 3D) to test this model. Indeed, both AVM and ALM exhibited buckling during locomotion-induced compression in him-4;unc-70 double mutants, consistent with the large strains experienced by both neurons in this animal (Figure 3E and F; Figure 3—figure supplement 1; Video 13, Video 14). Collectively, these findings support the idea that peripheral axons are subjected to mechanical stresses in a manner that depends on their anatomical position within the tissue.

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A balance of tension and torque governs axonal resilience to mechanical stress

We sought to develop a quantitative model describing how mechanical stability of neuronal processes might arise in vivo. To do so, we applied Euler-Kirchhoff theory describing the time and space evolution of a filament subjected to bending, stretching and twisting stresses (Bergou et al., 2010; Goyal et al., 2005; Nizette and Goriely, 1999; Purohit, 2008; Van der Heijden and Thompson, 2000). The key factors in the model, which we implemented by modeling axons as discrete elastic rods (DER model), are mechanical parameters that measure the energetic cost of bending, stretching, and twisting the axon. They are bending stiffness B (Equation 1), axial stiffness k (Equation 2), and twist rigidity C (Equation 3):

(1) ${\displaystyle B=EI}$

(2) ${\displaystyle k=EA/L}$

(3) ${\displaystyle C=2GI}$

where E is the Young’s modulus, I is the second moment of area of the cross section, A is the cross-sectional area, L is the length, and G is the shear modulus. The twist rigidity C depends on the shear modulus G (Equation 4), because twisting generates shear stresses when two neighboring cross-sections are rotated in respect to another. The relation between G and E is set by the Poisson’s ratio ν:

(4) $G= \frac{E}{2(1+\nu )}$

To obtain initial values for the relevant mechanical parameters, we estimated the Young’s modulus from elasticity measurements of cultured, GFP-tagged TRNs by indenting them with an atomic force microscope (Figure 4—figure supplement 1). In parallel, we used genetic and pharmacological perturbations to evaluate the predicted contributions of the actin-spectrin and microtubule cytoskeleton to Young’s modulus, E. Using this approach, we found that wild-type axons were stiffer (E = 6.3 ± 0.7 kPa, mean ± sem, n = 5) than those treated with the actin depolymerizing agent Latrunculin A (E = 4.9 ± 1 kPa, n = 5; p=5$\bullet$10⁻⁴, Mann-Whitney U-test, Figure 4—figure supplement 2). Similar results have been reported for mammalian sensory neurons (Magdesian et al., 2012; Ouyang et al., 2013), underscoring the conservation of material properties among neurons. Estimated values for E in unc-70(e524) β-spectrin mutant axons (3 ± 1.1 kPa, mean ± sem, n = 4, p=2$\bullet$10⁻³) were lower than untreated wild-type axons and indistinguishable from Latrunculin A-treated wild-type axons (p=0.28). We repeated these measurements and compared wild-type axons (E = 6.1 ± 0.3 kPa, mean ± sem, n = 11) to those of ptl-1(ok621) (E = 4.6 ± 0.6 kPa, mean ± sem, n = 18) and mec-7(wy116) neurons (E = 4.3 ± 0.4 kPa, mean ± sem, n = 17) and found that both classes of mutant axons had significantly lower Young’s moduli, in agreement with our hypothesis that mutations affecting the microtubule cytoskeleton lead to decreases in bending rigidity. Collectively, these results demonstrate that axonal stiffness depends on both the actin-spectrin cytoskeleton and MT bundles.

We next used the DER model to simulate TRN responses to mechanical stress as we varied the tension, bending stiffness, and twist rigidity around the initial values that we measured [tension (Krieg et al., 2014); stiffness (this study); or estimated (twist rigidity)]. The simulations revealed three shape classes for a neuron twisted around its longitudinal axis: straight axons, axons with localized helices, and plectonemes reminiscent of the ones created with in a twisted, elastic thread (Figure 4A, Video 15, Video 3). For a given shear modulus, the presence or absence of these shapes depended on the parameters of bending stiffness and tension for a given shear modulus (Figure 4B), axial stiffness (Figure 4C), and bending stiffness (Figure 4D). Similar to our experimental findings, simulated axons displayed multiple plectonemes at intervals of ~10–20 µm (Figure 4E, Figure 4—figure supplement 3). By exploring a larger parameter space, we found that plectonemes could also co-exist with less localized bends for a given shear modulus. The separation between these two phases depended on the values for tension and bending stiffness. These simulations predict that TRN axons will appear straight even when highly twisted, provided they have a sufficiently high bending stiffness and are held under axial stiffness. In this scenario, the generated torque is not strong enough to bend the neuron. Reducing either bending stiffness or end-to-end axial stiffness leads to the formation of localized helices for small values of twist and plectoneme-like supercoils at high levels of twist (see Nizette and Goriely, 1999).

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A reduction of either bending stiffness or tension alone (in absence of torque or low shear modulus) was not sufficient to induce the formation of coils or plectonemes for 10-fold variations around the experimentally determined input moduli (Figure 4B, C and D). An increase in torque leads to the formation of localized, solitary plectonemes and further increases in torque induce multiple plectonemes. These results are consistent with analytical solutions (Goriely and Tabor, 1998) that specify a buckling stability criterion, ${\tau }_{crit}$ (Equation 5). The analytical expression for ${\tau }_{crit}$ underscores the interdependence of bending stiffness, B (Equation 1), axial stiffness, k (Equation 2), and twist rigidity (Equation 3).

(5) ${\tau }_{crit}=2\raisebox{1ex}{$\sqrt{kB}$}\!\left/ \!\raisebox{-1ex}{$C$}\right.$

For torques that exceed ${\tau }_{crit}$, the rod collapses into structural instabilities. Rearranging Equation 5, yields k_crit, which is inversely proportional to B:

(6) $k_{crit}=\frac{C^2 {\tau }^2}{4B}$

This indicates the boundary (Figure 4B,C and D, green lines) separating areas that lack bends from those that contain bends and plectonemes. This boundary shifts to the left on each plot with lower τ and C.

In the classical description of rods, the mechanical parameters B, C, and k all depend on Young’s modulus, E, and the rod’s cross-sectional area, A (Equations 1–4). However, it is possible that bending stiffness, B, stretch stiffness, k, and twist rigidity, C, depart substantially from their predicted values. One source of variation is Poisson’s ratio, which varies between 0 and 0.5 for most materials and is known to deviate from this range for biological materials (e.g. Reese et al., 2010). Modeling the axon as an inhomogeneous material might also predict mechanical parameters that differ substantially from those resulting from our measurements. For instance, the bending stiffness estimated from the measured E (Figure 4—figure supplement 2) using Equation 1 yields B = 1.5 $\bullet {10}^{-23}$ N m. However, estimates of B based on the number (N) of MTs yields a bending stiffness of 1.26 $\bullet {10}^{-21}$ N m for a completely loose bundle $(B_{bundle}=N\bullet B_{MT})$ and $7.6\bullet {10}^{-20}$ N m in the limit of a completely crosslinked bundle $(B_{bundle}=N^2\bullet B_{MT};$ Guo et al., 2007), with the assumption that the bending stiffness for a single MT $B_{MT}$= 2.1 $\bullet {10}^{-23}$N m (Gittes et al., 1993). This yields a 100-fold difference between the classical description (Gittes et al., 1993) and the microscopic model (Bathe et al., 2008; Guo et al., 2007). Similar arguments can be made for shear modulus and tension, justifying the large parameter space explored in our simulations (Figure 4).

In summary, these simulations provide a conceptual framework for analyzing the physical properties responsible for mechanical neuroprotection. In this model, neurons are stabilized against the effects of mechanical stress by high bending stiffness, end-to-end axial tension, or a combination of both factors. In particular, the simulations predict that the appearance of periodic loops is caused by an imbalance in axonal bending stiffness, axial tension, and torque. Furthermore, they suggest that shape distortions we observed in mec-7(wy116);unc-70 and ptl-1;unc-70 double mutants (Figure 1) and those reported in mec-17 (Topalidou et al., 2012) and mec-12(gm379) (Hsu et al., 2014) might arise from a confluence of factors such as decreased bending stiffness, decreased axial tension, and/or an increase in the effective axonal shear modulus (torque).

Spectrin forms a periodic, helical lattice in C. elegans axons and dendrites

To examine the architecture of actin-spectrin networks, we used super-resolution microscopy (stimulated emission depletion; STED) to visualize SPC-1 α-spectrin and UNC-70 β-spectrin in transgenic animals carrying fluorescent proteins fused to their C- and N-termini, respectively (Figure 5—figure supplement 1). In agreement with studies of actin-spectrin networks in mammalian and invertebrate axons and dendrites (D'Este et al., 2016, 2015; He et al., 2016; Pielage et al., 2008; Xu et al., 2013; Zhong et al., 2014), α– and β-spectrin formed periodic structures in wild-type C. elegans TRNs in vitro (Figure 5, Video 16) with an average spacing of 197 ± 13 nm and 199 ± 10 nm, respectively (p=0.64, Mann-Whitney test), suggesting that the spectrin tetramer resides at its fully extended contour length in these cells.

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Periodic spectrin structures observed in GFP::SPC-1 α-spectrin transgenic neurons in vitro were eliminated upon addition of the actin depolymerizing agent Latrunculin A (Figure 5c) and by loss of UNC-70 β-spectrin (Figure 5D). Interestingly, α-spectrin remained organized into periodic structures in unc-70(e524) mutants (Figure 5E), but displayed a slightly shorter period of 188 ± 13 nm (p=0.003, Mann-Whitney U-test; Figure 5F). The 5% shorter period in unc-70(e524) neurons is consistent with the decreased axial tension found in these mutants in vivo (Krieg et al., 2015). Loss of ptl-1 expression, by contrast, had no obvious effect on the distribution of α-spectrin (Figure 5—figure supplement 2), which still formed periodic structures with a period similar to that observed in wild-type neurons: 195 ± 10 nm (n = 10, U-test, p=0.42). Taken together, these observations indicate spectrin forms a periodic structure sensitive to axial tension, but not defects in the microtubule cytoskeleton.

Microtubule bundles are disrupted in mec-7(wy116) β-tubulin and ptl-1(ok621) tau mutants

A bundle of long, 15-protofilament MTs overlap to fill the TRN cytoplasm (Chalfie and Thomson, 1982). We used serial-section transmission electron microscopy (ssTEM) to determine how genetic defects in the microtubule and spectrin cytoskeleton affect these MTs and their organization within the bundle. The distribution of edge-to-edge distances between adjacent microtubules are well described by a log-normal distribution with a geometric mean of 9.8 nm for wild-type TRNs (Figure 6Aii). The MTs are organized into an approximately hexagonal bundle, as demonstrated by 60°, 120°, and 180° being the dominant angles between three adjacent MTs (Figure 6Aiii, Figure 6—figure supplement 1). In mec-7(wy116) TRNs, by contrast, the distribution of edge-to-edge distances was altered such that the geometric mean decreased to 4 nm, or about half the value in wild-type (Figure 6Bii). The variance in this distribution was nearly three-fold that found in wild-type (σ² = 32 and 89 nm² in wild-type and mec-7(wy116) respectively). Despite this, a hexagonal arrangement of MTs was also detected in mec-7(wy116) axons (Figure 6Biii) with similar distribution of inter-MT angles to wild type (p=0.2; Watson U² for radially distributed data), although the 120° and 180° peaks seemed collapsed together in the histograms. However, individual MTs often separated from the main bundle and adjacent MTs often contacted one another in these mutants (Figure 6Bi), situations that we have seldom if ever observed in wild-type TRNs (Bellanger et al., 2012; Cueva et al., 2012, 2007, 2007; Hueston et al., 2008; Richardson et al., 2014). Qualitatively similar structural phenotypes were found in some but not all samples taken from mec-7(wy116); unc-70(e524) double mutants (Figure 6C). This variable phenotype likely accounts for the bimodal distribution of edge-to-edge microtubule distances that we observed (Figure 6Cii).

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Similar to mec-7(wy116) missense mutants, MTs were closer together in ptl-1(ok621) null mutants than in wild-type axons (Figure 6Di, Dii). The distribution of edge-to-edge distances had a geometric mean of 6.7 nm and a variance of 81 nm². Meanwhile, the hexagonal geometry of MT cross-sections was largely unaffected (Figure 6Diii) despite our observation that adjacent MTs often collapsed onto one another (Figure 6Di). In ptl-1(ok621);unc-70(e524) double mutants (Figure 6E), the distribution of edge-to-edge distances was similar to that observed in the ptl-1(ok621) single mutant (Figure 6Eii): the geometric mean was 6.9 nm and its variance was 114 nm².

This analysis also revealed that mec-7 β-tubulin and ptl-1 tau mutants had fewer and shorter microtubules than wild type (Figure 6F and G; Figure 6—figure supplement 2). Given that bundle stiffness is expected to be proportional to the number of filaments in the bundle (Bathe et al., 2008; Guo et al., 2007), this finding suggests that bending stiffness is decreased in both of these mutants. This is not the only structural feature that suggests a decrease in bending stiffness: The fact that neighboring MTs contact one another in mutant but not wild-type axons suggests that mutants lack a spacer or linker molecule leading to a reduction in its cross-sectional area. A decrease in area and in the number of cross-links is expected to decrease the bending stiffness of the bundle (Bathe et al., 2008; Tolomeo and Holley, 1997). Thus, we propose that defects that reduce MT length, number, and inter-microtubule spacing also decrease the axon’s bending stiffness.

Not all MT profiles in ptl-1 and ptl-1;unc-70 axons conformed to those expected from the cross-section of a cylindrical MT. Some cross-sections appeared to be oblique or nearly longitudinal (Figure 6—figure supplement 3A). Rarely, we captured TRN profiles in mec-7(wy116);unc-70 mutants consistent with having sectioned a local coil within the TRN axon (Figure 6—figure supplement 3B–D). One of the most striking and consistent observations in the ssTEM datasets from ptl-1 and ptl-1;unc-70 mutants was that outer MTs rotated and tilted away from the central axis of the bundle (Video 17) in manner that generated a twist of the entire MT bundle. We applied particle image velocimetry (PIV) techniques to adjacent thin sections to quantifying this structural phenomenon (Figure 7A, B and C). This approach yields an estimate of the pitch of the helical twist in the entire bundle and showed that the pitch angle was small near the center and increased linearly with across the bundle’s radius (Figure 7D). Notably, we also observed helical perversions in twisted bundles, in which the MT bundle reverses between clockwise and counter-clockwise twists (Figure 7D, Video 17). Thus, ptl-1 loss of function resulted in fewer, shorter MTs that were organized into a twisted bundle, findings consistent with the idea that ptl-1 mutant axons have both decreased bending stiffness and increased torque.

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C. elegans tau protein binds MTs in vivo and contributes to mechanical neuroprotection

Based on our observation that mec-7(wy116) and ptl-1(ok621) mutants exhibit similar defects in MT bundle structure, we hypothesized that wy116 disrupted the association between the PTL-1 protein and microtubules. To test this idea in living animals, we used CRISPR/Cas9-based genome editing (Dickinson et al., 2015) to create a PTL-1::mNeonGreen (PTL-1::mNG) fusion protein and performed a FRAP assay in wild-type and mec-7 β-tubulin mutants (Figure 8). In agreement with prior work (Konzack et al., 2007) and consistent with the idea that PTL-1 protein diffuses along microtubules (Hinrichs et al., 2012), we observed rapid but incomplete recovery of PTL-1::mNG fluorescence in control axons. On average, the apparent diffusion constant for PTL-1 in living axons was 0.12 ± 0.1 µm² s⁻¹ (mean ± s.d., n= 47), which agrees with values reported for mammalian tau in vitro (0.17 ± 0.03 µm² s⁻¹; Hinrichs et al., 2012). Both the recovery rate and the mobile fraction increased in mec-7(ok2152) β-tubulin null mutants and in mec-7(wy116) β-tubulin missense mutants. By comparison, PTL-1 mobility was unaffected in unc-70(e524) mutants (Figure 8). In principle, the increased PTL-1 mobility found in mec-7(wy116) could reflect a decrease in the number of MTs (Figure 6), a decrease in the affinity of PTL-1 for mutant MTs, or a combination of both factors. We favor the idea that the wy116 allele affects the affinity for PTL-1 since unc-70(e524) had no detectable effect on PTL-1 mobility (Figure 8D and E) despite having fewer MTs (Table 2). Together, these results support the idea that PTL-1 binds to MTs in vivo and that the T409I mutation in MEC-7 β tubulin interferes with PTL-1 binding to MTs.

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Table 2

	Genotype		Neuron		Number		Length, µm		Source
	N2 (Bristol)		AVM		12.8 ± 3.3 (8)		9.40 ± 0.4 (3)		Chalfie and Thomson (1979)
	control, uIs31 [mec-17p::GFP]		AVM		7 ± 3.6 (3)		4.1 ± 0.6 (3)		This study
	unc-70(e524); uIs31		AVM		8 ± 2 (3)		3.8 ± 0.4 (3)		This study
	unc-70(s1502); uIs31		AVM		23 ± 10 (5)		2.7 ± 0.7 (2)		This study
	N2 (Bristol)		ALM		28.6 ± 4.1 (9)		22.2 ± 3.6 (5)		Chalfie and Thomson (1979)
	N2 (Bristol)		ALM		57 ± 11 (3)		14 ± 4.3 (3)		This study
	control, uIs31		ALM		31 ± 2 (4)		16 ± 4.5 (4)		This study
	unc-70(e524); uIs31		ALM		17.9 ± 3.4 (4)*		5.3 ± 1.3 (4)		This study
	unc-70(s1502); uIs31		ALM		24 ± 11 (5)		2.8 ± 0.9 (5)*		This study
	mec-7(wy116);wyIs97; uIs31		ALM		27 ± 13 (4)		11 ± 6 (4)		This study
	ptl-1(ok621); uIs31		ALM		20 ± 10 (5)		6.95 ± 6.6 (5)		This study
	ptl-1(ok621);unc-70(e524); uIs31		ALM		32 ± 0.8 (2)		8.9 ± 3.5 (2)		This study
	mec-7(wy116);unc-70(e524); uIs31		ALM		44 ± 4 (3)		8.9 ± 3 (3)		This study

The spectrin network stabilizes TRN microtubules against fracture

To address the question of how loss or disruption of the periodic spectrin network affects MTs, we compared MTs in unc-70(e524) mutants, which retain a periodic spectrin cytoskeleton, and unc-70(s1502) mutants, in which the spectrin network is disrupted (Figure 9A,B and C). Given the differential sensitivity of AVM and ALM neurons to mechanical stress in unc-70 mutants (Figure 3), we examined MTs in both cell types. In accord with prior studies of wild-type animals, we found that MTs were shorter in AVM neurons than in the ALM neurons, on average (Figure 9D; Figure 9—figure supplement 1; Table 2). Thus, mechanical stress may be a factor that limits MT length in wild-type axons, since AVM neurons undergo more extreme cycles of compression and extension than do the ALM neurons (Figure 2).

Figure 9 with 2 supplements see all

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Neither the e524 partial loss-of-function nor the s1502 null allele of unc-70 caused a further reduction in MT length or number in AVM neurons, but both alleles were associated with a decrease in MT length in the ALM neurons (Figure 9D and E). This differential sensitivity to unc-70 mutation likely arises from the fact that MTs are already shorter in AVM and do not shorten further. Moreover, MT length in AVM is similar to the buckling wavelength observed under compression in unc-70 mutants (Figure 9—figure supplement 2). The variance in the number of MTs was higher in unc-70(s1502) mutant ALM neurons than that in either wild-type (F-test p=0.01) or unc-70(e524) (F-test p=0.05; Figure 9F. Figure 9—figure supplement 1), but no difference in average values was detected (Figure 9E). Related to the expected mechanical stresses generated in these animals, e524 animals have a loopy and uncoordinated locomotion phenotype and s1502 animals are paralyzed (Hammarlund et al., 2000). As a result, e524 animals are expected to generate more intense movement-induced mechanical stresses than s1502 animals. In light of these differences, we interpret the increased variance in MT as an indication that some long MTs persist in s1502 mutants because mechanical stresses are decreased in this genetic background and other MTs are shortened due to the loss of actin-spectrin networks.

To further examine the possibility that the shorter MTs in the β-spectrin mutants might result from mechanically enhanced fracture and/or disassembly, we generated unc-70(e542);oxIs95[epi::UNC-70] and unc-70(s1502);oxIs95[epi::UNC-70] animals in which wild-type UNC-70 β-spectrin was expressed in the epidermal cells that engulf the ALM neurons. We found that MT length and number in unc-70(e542);oxIs95[epi::UNC-70] transgenic animals were similar to those of unc-70(e542) mutants (Table 2; Figure 9D and E). However, the epi::UNC-70 transgene appeared to restore MT length to nearly wild-type levels in unc-70(s1502) mutants (Figure 9D). One plausible explanation for this result is that the mutant β-spectrin present in unc-70(e524) animals acts in a dominant fashion and interferes with the mechanical stabilization that would otherwise result from the expression of wild-type UNC-70 β-spectrin in the epidermis.

Together, these findings suggest that the longer ALM MTs are more susceptible to bending-induced fracture than the shorter AVM MTs. In addition, an analysis of MT length and number in β-spectrin mutants suggests that the actin-spectrin network provides a lateral support that protects the MT bundle against deformation via both cell-autonomous and non-autonomous mechanical stabilization.

The MT bundle can account for the torque build-up in ptl-1;unc-70 mutants

Experimental measurement and simulations support the hypothesis that supercoils and plectonemes are revealed when axons experience a combination of high torque, low bending stiffness, and reduced axial stiffness (Figure 4). The discovery of twisted MT bundles in ptl-1 single mutants and ptl-1;unc-70 double mutants (Figures 6 and 7) points toward the MT bundle as the source of torque. To investigate this possibility, we created a ptl-1;unc-70;mec-7(e1434) triple mutant. e1434 is a temperature-sensitive, semi-dominant, missense allele that encodes a P171I mutation in MEC-7 β-tubulin (Savage et al., 1989). This allele is linked to a reduction in MT number and length in animals grown at restrictive temperatures but is not known to display any clear shape defects (Chalfie and Thomson, 1982). Control experiments revealed that shape defects in the TRNs of ptl-1;unc-70 double mutants were more pronounced for growth at 20°C than at 15°C (Figure 10A). When ptl-1;unc-70;mec-7(e1434) triple mutants were cultivated at a permissive temperature (15°C) that allows for nearly wild-type MT assembly (Chalfie and Thomson, 1982), the TRN axons contained loops, twists, and plectonemes. Strikingly, axons were smooth in the triple mutant following growth at 20°C, where MT assembly is defective (Figure 10B). In summary, these findings indicate that the formation of loops, twists, and plectonemes in mutant axons depends on intact microtubules, likely due to the induction of torque resulting from their assembly into twisted bundles.

Figure 10

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In this study, we combined experiment and theory to reveal how axial tension and bending stiffness balance torque to protect long, thin TRN axons from mechanical deformation. The picture emerging from this work is that actin-spectrin networks provide tension, MT bundles confer stiffness, and microtubule-associate proteins like tau minimize torque within MT bundles. Together, these factors combine to protect axons from mechanical damage. Simulations based on Euler-Kirchhoff theory revealed that the balance of tension and torque stabilizes axons and dendrites and show that plectonemes result when torque overcomes tension (e.g. Figure 4A.). Experimental observations show that UNC-70 β-spectrin forms an extended cytoskeleton similar to that in mammalian neurons (this study and D'Este et al., 2016; Xu et al., 2013) and is essential for maintaining proper axial tension (Krieg et al., 2014). Changes in tension have also been linked to pearling, a phenomenon in which tubes under tension form bulges that resemble pearls on a string (Bar-Ziv et al., 1999; Pullarkat et al., 2006). Although pearling is driven by a competition between membrane tension and actin rigidity (Bar-Ziv et al., 1999), the periodic defects we found in tau-spectrin double mutants occur due to an unbalanced torque-tension coupling.

The shape defects seen in tau-spectrin double mutant axons were associated with dramatic rearrangements of the MT bundle. Whereas wild-type axons contain a regularly spaced array of MTs, axons lacking PTL-1 tau have MTs that contact one another and spiral around each other. How might PTL-1 tau oppose contact between adjacent MTs? Like other tau proteins, PTL-1 has a MT-binding domain in its C-terminus and an intrinsically disordered N-terminal projection domain harboring dozens of glutamate/proline repeats (Chung et al., 2015). These repeats have been proposed to function as a polyelectrolyte brush (Wegmann et al., 2013), to regulate the spacing between MTs in bundles and confer steric stabilization against aggregation (Chung et al., 2015; Goedert et al., 1996). Our data are likewise consistent with the idea that PTL-1 tau and related MAP2 proteins enable MTs to glide past one another during mechanical stress-induced compression and elongation. We infer that PTL-1 allows sliding of MTs in a bundle by preventing MT-MT contact during locomotion and thus friction and the generation of torque within the bundle that would otherwise impart torsion to the neurite as a whole. It is tempting to speculate that these functions for tau are essential for mechanical neuroprotection throughout the nervous system.

How does loss of PTL-1 cause MTs to spiral around one another? The MT bundles structures we observe in ptl-1 mutants are strikingly similar to bundles of twisted filaments predicted to assemble from chiral biological polymers (Grason and Bruinsma, 2007), suggesting similar physical mechanisms account for formation of twisted MTs bundles in neurons. We propose that the observed torque is an emergent property of MT assembly that appears in the absence of PTL-1, which normally mediates long-range repulsion between adjacent MTs. In the absence of such repulsion, MTs twist around one another so as to maximize the cohesive energy of a chiral bundle. The gain in binding energy per unit length comes in expense of an energy cost to bend individual MT around the central, longitudinal axis. This manifests as an external torque that twists the bundle. This argument applies both to bundles of chiral filaments like MTs and bundles of achiral filaments, since the binding energy gained as filaments come together is sufficient to deform individual filaments (Cajamarca and Grason, 2014). Axial compression of this twisted bundle, as occurs during locomotion, could potentially deform the whole axon (as seen in the elastic thread of Video 3) via cross-links to the plasma membrane. Although all microtubules possess a helical surface lattice (Hunyadi et al., 2007), this mechanism is expected to be independent of the number of protofilaments per microtubule, and to apply to both the unusual 15-protofilament MTs present in C. elegans TRNs, and also to the more common 13-protofilament MTs found in mammalian neurons. Consistent with this idea, neurons containing 13-protofilament MTs bend and deform into similar defects (as observed by us in TRNs) under compressive forces in cultured hippocampal neurons (Roland et al., 2014) and form twisted, hexagonal bundles in certain in vitro preparations (Needleman et al., 2004). In summary, we propose that MT bundles and actin-spectrin networks act synergistically to prevent shape defects, as a deficiency in both structures was required for the appearance of plectonemes. These structures and their molecular constituents ensure that axial tension, bending stiffness, and torque are balanced in manner sufficient to stabilize axons against mechanical deformations.

Spectrin, microtubules, and tau are among the most abundant components of the neuronal cytoskeletal and these proteins are conserved in all animals, from C. elegans to humans (Baines, 2009; Findeisen et al., 2014). The same mechanisms that protect C. elegans peripheral neurons against mechanical deformation may also protect axons in the mammalian central nervous system from damage caused by mechanical stress during daily life or during traumatic brain injuries. Intriguingly, mechanical stress has also been implicated in neurodegenerative disease (Levy Nogueira et al., 2016; Wostyn et al., 2010). Thus, it may not be surprising that pathological biomarkers such as loss of tau function (Puvenna et al., 2016) and spectrin degradation are shared between mechanical stress-based brain disease and aging-related neurodegeneration (Cai et al., 2012). Indeed, this work suggests the intriguing possibility that defects in the genes encoding tau, spectrin, and microtubule isoforms expressed in the nervous system sensitize axons to mechanical stress and function as risk factors in traumatic brain injury or neurodegenerative disease.

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Author details

1. Michael Krieg

   1. Department of Molecular and Cellular Physiology, Stanford University, Stanford, United States
   2. Department of Chemical Engineering, Stanford University, Stanford, United States

   Present address

   ICFO, Institute of Photonic Sciences, Barcelona, Spain

   Contribution

   MK, Conceptualization, Formal analysis, Supervision, Funding acquisition, Validation, Investigation, Visualization, Methodology, Writing—original draft, Writing—review and editing

   Competing interests

   No competing interests declared.

   "This ORCID iD identifies the author of this article:" 0000-0003-0501-5036

2. Jan Stühmer

   Department of Informatics, Technical University of Munich, Germany

   Contribution

   JS, Software, Formal analysis, Investigation, Visualization, Methodology, Writing—original draft, Writing—review and editing

   Competing interests

   No competing interests declared.

3. Juan G Cueva

   Department of Molecular and Cellular Physiology, Stanford University, Stanford, United States

   Contribution

   JGC, Formal analysis, Validation, Investigation, Visualization, Methodology

   Competing interests

   No competing interests declared.

4. Richard Fetter

   Department of Molecular and Cellular Physiology, Stanford University, Stanford, United States

   Contribution

   RF, Data curation, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing—original draft, Writing—review and editing

   Competing interests

   No competing interests declared.

5. Kerri Spilker

   Department of Biology, Stanford University, Stanford, United States

   Present address

   Biogen, Cambridge, United States

   Contribution

   KSp, Resources, Investigation

   Competing interests

   No competing interests declared.

6. Daniel Cremers

   Department of Informatics, Technical University of Munich, Germany

   Contribution

   DC, Resources, Software, Supervision, Funding acquisition, Writing—review and editing

   Competing interests

   No competing interests declared.

7. Kang Shen

   Department of Biology, Stanford University, Stanford, United States

   Contribution

   KSh, Resources, Funding acquisition, Investigation, Writing—review and editing

   Competing interests

   KSh: Reviewing editor, eLife

   "This ORCID iD identifies the author of this article:" 0000-0003-4059-8249

8. Alexander R Dunn

   Department of Chemical Engineering, Stanford University, Stanford, United States

   Contribution

   ARD, Conceptualization, Supervision, Funding acquisition, Validation, Visualization, Project administration, Writing—review and editing

   Competing interests

   No competing interests declared.

   "This ORCID iD identifies the author of this article:" 0000-0001-6096-4600

9. Miriam B Goodman

   Department of Molecular and Cellular Physiology, Stanford University, Stanford, United States

   Contribution

   MBG, Conceptualization, Resources, Data curation, Formal analysis, Supervision, Funding acquisition, Validation, Visualization, Methodology, Writing—original draft, Project administration, Writing—review and editing

   For correspondence

   mbgoodmn@stanford.edu

   Competing interests

   No competing interests declared.

   "This ORCID iD identifies the author of this article:" 0000-0002-5810-1272

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