Strain rate does not affect cortical microtubule orientation in the isolated epidermis of sunflower hypocotyls

A hypothesis exists that external and internal factors affect the orientation of cortical microtubules in as much as these lead to changes in cell elongation rate. Factors that stimulate elongation are proposed to lead to transverse microtubule orientation, whereas factors that inhibit elongation lead to longitudinal orientation. The elongation rate is equal to the rate of longitudinal irreversible strain in cell walls. Incubated epidermis peeled from sunflower hypocotyls does not extend unless it is stretched by loading and the pH of the incubation medium is appropriately low. Thus, peels provide a convenient model to investigate the relationship between longitudinal strain rate and cortical microtubule orientation. In the present study, it was found that peeling affects microtubule orientation. Peels were incubated for several hours in Murashige & Skoog medium (both unbuffered and buffered) to attain a steady state of microtubule orientation before loading. The effects of loading and pH on strain rate and orientation of microtubules under the outer epidermal walls were examined in three portions of peels positioned with respect to the cotyledonary node. Appropriate loading caused longitudinal strain of peels at pH 4.5 but not at pH 6.5. However, no clear effect of strain rate on microtubule orientation in the peels was observed. Independent of applied load and pH of the incubation medium, the microtubule orientation remained unchanged, i.e. orientation was mainly oblique. Our results show that strain rate does not affect cortical microtubule orientation in isolated epidermis of the sunflower hypocotyl model system, although orientation could be changed by white light.     

Interaction of auxin, light, and mechanical stress in orienting microtubules in relation to tropic curvature in the epidermis of maize coleoptiles

Summary Changes in the orientation of cortical microtubules (longitudinal vs. transverse with respect to the long cell axis) at the outer epidermal wall of maize coleoptile segments were induced by auxin, red or blue light, and mechanical stresses (cell extension or compression produced by bending). Immunofluorescent techniques were used for the quantitative determination of frequency distributions of microtubule orientation. Detailed kinetic studies showed that microtubule reorientations are temporally correlated with the simultaneously measured changes in growth rate elicited by auxin, red light, or blue light. Growth inhibition induced by depletion of endogenous auxin produces a longitudinal microtubule pattern that can be changed into a transverse pattern in a dose-dependent manner by applying exogenous auxin. A mid-point pattern with equal frequencies of longitudinal and transverse microtubules was adjusted at 2 mol/1 auxin. Bending stress applied under these conditions adjusts permanent, maximally longitudinal and transverse microtubule orientations at the compressed and extended segment sides, respectively, quantitatively mimicking the responses to differential flank growth during phototropic and gravitropic curvature. During tropic curvature the changes in microtubule pattern reflect the distribution of growth rather than the distribution of auxin. The microtubule pattern responds to auxin-dependent growth changes and mechanical stress in a synergistic manner, confirming the functional equivalence of these factors in affecting microtubule orientation. Similar results were obtained when segment growth was altered by blue or red light instead of auxin in the presence or absence of mechanical stress. It is concluded from these results that growth changes, elicited by auxin, light, etc., and mechanical stress affect microtubule orientation through a common signal perception and transduction chain.Abbreviations IAA indole-3-acetic acid (auxin) - MT cortical microtubule     

Flower stalk segments of Arabidopsis thaliana ecotype Columbia lack the capacity to grow in response to exogenously applied auxin

Exogenously applied IAA stimulated cell elongation of segments excised from flower stalks of Arabidopsis thaliana ecotype Landsberg erecta (Ler) by increasing the cell wall extensibility, but it did not affect that of ecotype Columbia (Col). Treatment with a low pH buffer solution (pH 4.0) or fusicoccin (FC), a reagent activating H(+)-ATPases, significantly increased the cell wall extensibility and promoted elongation growth of flower stalk segments of both ecotypes, indicating that the flower stalk segments of Col possess the capacity to grow under acidic pH conditions. IAA promoted the proton excretion in segments of Ler but not of Col. On the other hand, FC increased the proton excretion in segments of Col as much as that of Ler. These results suggest that IAA activates the plasma membrane H(+)-ATPases in the segments of Ler but not those of Col, while FC activates them in both ecotypes. Flower stalks of Col may lack the mechanisms of activation by IAA of the plasma membrane H(+)-ATPases.     

Auxin-induced longitudinal-to-transverse reorientation of cortical microtubules in nonelongating epidermal cells of azuki bean epicotyls

Summary In epidermal cells of azuki bean (Vigna angularis) epicotyl segments, that were sequentially treated with an auxin-free solution and an auxin solution, cortical microtubules changed their orientation from longitudinal to transverse. Auxin caused the reorientation of microtubules from longitudinal to transverse in segments that were kept under anaerobic conditions and, therefore, showed no elongation, indicating that auxin can regulate the orientation of microtubules by a mechanism that does not involve auxin-induced change in the rate of cell elongation.Abbreviations DMSO dimethylsulfoxide - GA₃ gibberellic acid - IAA indoleacetic acid - MT microtubule - PBS phosphate-buffered saline     

The function of guard cells does not require an intact array of cortical microtubules

The development of stomatal guard cells is known to require cortical microtubules; however, it is not known if microtubules are also required by mature guard cells for stomatal function. To study the role of microtubules in guard cell function, epidermal peels of Vicia faba were subjected to conditions known to open or close stomata in the presence or absence of microtubule inhibitors. To verify the action of the inhibitors, microtubules in appropriately treated epidermal peels were localized by cryofixation followed by freeze substitution and embedding in butyl-methyl methacrylate. Mature guard cells had a radial array of microtubules, focused toward the thick cell wall of the pore, and the appearance of this array was the same for stomata remaining closed in darkness or induced to open by light. Treatment of epidermal peels with 1 mM colchicine for 1 h depolymerized nearly all cortical microtubules. Measurements of stomatal aperture showed that neither 1 mM colchicine nor 20 M taxol affected any of the responses tested: remaining closed in the dark, opening in response to light or fusicoccin, and closing in response to calcium and darkness. We conclude that intact microtubule arrays are not invariably required for guard cell function.     

Luminal flow modulates H+-ATPase activity in the cortical collecting duct (CCD)

Epithelial Na(+) channel (ENaC)-mediated Na(+) absorption and BK channel-mediated K(+) secretion in the cortical collecting duct (CCD) are modulated by flow, the latter requiring an increase in intracellular Ca(2+) concentration ([Ca(2+)](i)), microtubule integrity, and exocytic insertion of preformed channels into the apical membrane. As axial flow modulates HCO(3)(-) reabsorption in the proximal tubule due to changes in both luminal Na(+)/H(+) exchanger 3 and H(+)-ATPase activity (Du Z, Yan Q, Duan Y, Weinbaum S, Weinstein AM, Wang T. Am J Physiol Renal Physiol 290: F289-F296, 2006), we sought to test the hypothesis that flow also regulates H(+)-ATPase activity in the CCD. H(+)-ATPase activity was assayed in individually identified cells in microperfused CCDs isolated from New Zealand White rabbits, loaded with the pH-sensitive dye BCECF, and then subjected to an acute intracellular acid load (NH(4)Cl prepulse technique). H(+)-ATPase activity was defined as the initial rate of bafilomycin-inhibitable cell pH (pH(i)) recovery in the absence of luminal K(+), bilateral Na(+), and CO(2)/HCO(3)(-), from a nadir pH of ～6.2. We found that 1) an increase in luminal flow rate from ～1 to 5 nl·min(-1)·mm(-1) stimulated H(+)-ATPase activity, 2) flow-stimulated H(+) pumping was Ca(2+) dependent and required microtubule integrity, and 3) basal and flow-stimulated pH(i) recovery was detected in cells that labeled with the apical principal cell marker rhodamine Dolichos biflorus agglutinin as well as cells that did not. We conclude that luminal flow modulates H(+)-ATPase activity in the rabbit CCD and that H(+)-ATPases therein are present in both principal and intercalated cells.     

Developmental reorientation of transverse cortical microtubules to longitudinal directions: a role for actomyosin-based streaming and partial microtubule-membrane detachment

Transversely oriented cortical microtubules in elongating cells typically reorient themselves towards longitudinal directions at the end of cell elongation. We have investigated the reorientation mechanism along the outer epidermal wall in maturing leek (Allium porrum L.) leaves using a GFP-MBD microtubule reporter gene and fluorescence microscopy. Incubating leaf segments for 14-18 h with the anti-actin or anti-actomyosin agents, 20 microm cytochalasin D or 20 mM 2,3-butanedione monoxime, inhibited the normal developmental reorientation of microtubules to the longitudinal direction. Observation of living cells revealed a small subpopulation of microtubules with their free ends swinging into oblique or longitudinal directions, before continuing to assemble in the new direction. Electron microscopy confirmed that longitudinal microtubules are partly detached from the plasma membrane. Incubating leaf segments with 0.2% 1 degree-butanol, an activator of phospholipase D, which has been implicated in plasma membrane-microtubule anchoring, promoted the reorientation, presumably by promoting microtubule detachment from the membrane. Stabilizing microtubules with 10 microm taxol also promoted longitudinal orientation, even in the absence of cytoplasmic streaming. These results were consistent with confocal microscopy of live cells before and after drug treatments, which also revealed that the slow (days) global microtubule reorientation is superimposed over short-term (hours) regional cycling in a clockwise and an anti-clockwise direction. We propose that partial detachment of transverse microtubules from the plasma membrane in maturing cells exposes them to hydrodynamic forces of actomyosin-driven cytoplasmic streaming, which bends or shifts pivoting microtubules into longitudinal directions, and thus provides an impetus to push microtubule dynamics in the new direction.     

Interleukin-1 potentiates basal and AVP-stimulated ACTH secretion in vitro--the role of CRH pre-incubation.

The acute-phase cytokine interleukin-1 (IL-1) is known to activate the hypothalamic pituitary adrenal axis, primarily via corticotropin releasing hormone (CRH). The aim of this study was to determine whether IL-1beta could directly stimulate ACTH secretion from perifused equine anterior pituitary cells, and whether CRH pre-incubation affected corticotroph responsiveness. Isolated equine anterior pituitary cells were pre-incubated with media containing 10 nM CRH or vehicle for 20 hours before being loaded onto columns and perifused with 0.02 nM CRH and 100 nM cortisol. Columns were given a 5-minute pulse of arginine vasopressin (AVP, 10 nM), perifused for 4 hours with 0 (control) or 1 nM IL-1beta, then given a further 5-minute pulse of AVP (10nM). ACTH was measured in 5 minute fractions. In the setting of CRH pre-incubation, cells perifused with IL-1beta for 4 hours showed increased basal ACTH secretion compared to control (114 +/- 6 pM vs. 86 +/- 4 pM [means +/- S.E.M.], p < 0.001) and a significantly greater ACTH response to the final AVP pulse (240 +/- 32% vs. 96 +/- 30%, p = 0.009, expressed as % of ACTH response to the initial AVP pulse). The potentiation of AVP-stimulated ACTH release by IL-1 was not observed in cells pre-incubated with vehicle alone. In conclusion, IL-1 increases ACTH release in equine corticotroph cells pre-incubated with CRH and potentiates responsivity to AVP.     

FT-IR study of the Chara corallina cell wall under deformation

Fourier-transform infrared (FT-IR) microspectroscopy was used to investigate both the chemical composition of, and the effects of an applied strain on, the structure of the Chara corallina cell wall. The inner layers of the cell wall are known to have a transverse cellulose orientation with a gradient through the thickness to longitudinal orientation in the older layers. In both the native state and following the removal of various biopolymers by a sequential extraction infrared dichroism was used to examine the orientation of different biopolymers in cell-wall samples subjected to longitudinal strain. In the Chara system, cellulose microfibrils were found to be aligned predominantly transverse to the long axis of the cell and became orientated increasingly transversely as longitudinal strain increased. Simultaneously, the pectic polysaccharide matrix underwent molecular orientation parallel to the direction of strain. Following extraction in CDTA, microfibrils were orientated transversely to the strain direction, and again the degree of transverse orientation increased with increasing strain. However, the pectic polysaccharides of the matrix were not detected in the dichroic difference spectra. After a full sequential extraction, the cellulose microfibrils, now with greatly reduced crystallinity, were detected in a longitudinal direction and they became orientated increasingly parallel to the direction of strain as it increased.     

Effects of ethylene on the orientation of microtubules and cellulose microfibrils of pea epicotyl cells with polylamellate cell walls

Summary Following a 5 hours ethylene treatment, cortical cells of Pea (Pisum sativum L. var Alaska) epicotyl third internode showed a change in the orientation of both microtubules near the plasma membrane and recently deposited cellulose microfibrils. Control cortical cells had mostly transverse microtubules. The ratio of the average frequency of transverse to longitudinal microtubules was 6.0. After 5 hours of ethylene treatment, cortical cells had mostly longitudinal microtubules, with the ratio of transverse to longitudinal microtubules equal to 0.1. Epidermal cells were more variable than cortical cells with regard to the frequency of longitudinal and transverse microtubules. Observation of cortical cell walls in conventionally stained thin sections revealed that recent deposition of microfibrils had been primarily transverse in almost all of the control cortical cells sampled. In contrast, more than half of the ethylene-treated cortical cells had recent deposition oriented primarily longitudinally. This change in microtubule and microfibril orientation may be early enough to constitute the primary effect of ethylene leading to radial cell expansion.Research supported by NSF grant PCM 78-03244, A1, 2 to PBG and by a Research Corporation grant to WRE.     

Gibberellin-induced changes in growth anisotropy precede gibberellin-dependent changes in cortical microtubule orientation in developing epidermal cells of barley leaves. Kinematic and cytological studies on a gibberellin-responsive dwarf mutant, M489

We conducted kinematic and cytological studies on "between vein" epidermal cells of the gibberellin (GA)-deficient M489 dwarf mutant of barley (Hordeum vulgare L. Himalaya). GAs affect radial and axial components of cell expansion and cortical microtubule orientation. Adaxial cells in particular expand radially after leaving the elongation zone (EZ), probably as part of leaf unrolling. Exogenous gibberellic acid corrects the mutant's short, wide blades, short EZ, and slow elongation rate. Cell production rates increase more on the adaxial than on the abaxial surface. Cells spend equal periods of time elongating in dwarf and tall plants, but relative elemental growth rates start to decline sooner in the dwarf. GA increased the rate at which longitudinal wall area increased because the increased axial growth more than compensated for reduced radial growth. In dwarf leaves, increased radial expansion was detected in basal parts of the EZ before cortical microtubules lost transverse orientation in the distal elongation zone. We conclude that loss of microtubule orientation is not required for low GA levels to reduce growth anisotropy.     

The V-ATPase from etiolated barley (Hordeum vulgare L.) shoots is activated by blue light and interacts with 14-3-3 proteins

The vacuolar H(+)-ATPase (V-ATPase) is a key enzyme that controls the electrochemical proton potential across endomembranes. Although evidence suggests that V-ATPase is important for photo-morphogenesis, little is known about short-term regulation of V-ATPase upon initiation of the photo-morphogenetic programme by exposure of dark-grown plants to light. In this study, etiolated coleoptiles were given a short blue light treatment and V-ATPase characteristics were determined. The effectiveness of the light treatment was assessed by means of fusicoccin binding to the plasma membrane; this increased 5-fold. The short light treatment also induced a 2-fold to 3-fold increase in the hydrolytic activity of V-ATPase. Members of the 14-3-3 protein family are involved in both blue light perception and the subsequent activation of the P-type ATPase. We provide evidence that 14-3-3 proteins specifically interact with the catalytic A-subunit of the V-ATPase. First, the isolated V1-part of the V-ATPase co-purifies with 14-3-3 on a gel filtration column. Secondly, in an overlay experiment, 14-3-3 interacts with a 68 kDa band that was identified as the V1 A-subunit by mass spectrometry. Thirdly, in 14-3-3 affinity chromatography, both A- and B-subunits of the catalytic moiety of the V-ATPase were identified by matrix-assisted laser desorption ionization tandem time of flight mass spectrometry (MALDI TOF/TOF MS) as 14-3-3-interacting proteins. It was shown that the A-subunit can be phosphorylated in vitro by a tonoplast-bound kinase, whose properties are affected by blue light. Taken together, the data show that besides the P- and F-type H(+)-ATPases, the V-type H(+)-ATPase also interacts with 14-3-3 proteins.     

Orientation of cortical microtubules correlates with cell shape and division direction

Summary Cortical microtubules in the epidermis of regeneratingGraptopetalum plants were examined by in situ immunofluorescence. Paradermal slices of tissue were prepared by a method that preserves microtubule arrays and also maintains cell junctions. To test the hypothesis that cortical microtubule arrays align perpendicular to the direction of organ growth, arrays were visualized and their orientation quantified. A majority of microtubules are in transverse orientation with respect to the organ axis early in shoot development when the growth habit is uniform. Later in development, when growth habit is non-uniform and the tissue is contoured, cortical microtubules are increasingly longitudinal and oblique in orientation. Microtubules show only a minor change in orientation at the site of greatest curvature, the transition zone of a developing leaf. To assess the role of the division plane on orientation of arrays, the pattern of microtubules was examined in individual cells of common shape. Cells derived from transverse divisions have predominately transverse cortical arrays, whereas cells derived from oblique and longitudinal divisions have non-transverse arrays. The results show that, regardless of the stage of development, microtubules orient with respect to cell shape and plane of division. The results suggest that cytoskeletal function is best considered in small domains of growth within an organ.Abbrevations DMSO dimethylsulfoxide - EGTA ethylene glycol-bis-(ß-aminoethyl ether)-N, N, N, N-tetra acetic acid - FITC fluorescein isothiocyanate - MTSB microtubule stabilizing buffer - PBS phosphate buffered saline     

Root contraction in hyacinth III. Orientation of cortical microtubules visualized by immunofluorescence microscopy

Summary Cortical microtubules (MTs) were visualized in root cortex cells ofHyacinthus orientalis L. using immunofluorescence techniques. Cellular MT orientation was determined adjacent to radial longitudinal and transverse walls of root tip, uncontracted, contracting, and fully contracted regions. As seen in longitudinal views, MTs formed parallel, apparently helical arrays which were oriented transversely, axially or obliquely depending upon the region. Transverse sectional views showed that MTs adjacent to transverse cell walls formed a variety of patterns which varied with developmental stage and cell location. Microtubules were oriented in crisscross or parallel arrays. The parallel arrays were oriented either parallel, perpendicular or oblique to the radius of the root. There was an apparent temporal progression in MT reorientation from outer cortical to inner cortical cell layers. A resultant progression of reoriented cell growth could account for root contraction. These findings corroborate earlier electron microscopic observations of changing MT orientation accompanying root contraction, and provide cytological evidence to test mathematical and biophysical models of the mechanics of cell expansion.Abbreviations MT microtubule - MF microfibril - MTSB microtubule stabilizing buffer - PBS phosphate buffered saline     

Relationship between microtubule orientation and patterns of cell expansion in developing cortical cells of Lemna minor roots

In actively growing cortical cells in the elongation zone of Lemna minor L. roots, both longitudinal (radial and tangential) and transverse walls expand in both length and width. The longitudinal walls of the three types of cortical cells in the root (i.e. outer, middle and inner) showed the largest expansion in the longitudinal axis. In contrast, the inner cortical cells exhibited the least expansion in width, whereas the middle cortical cells displayed the largest expansion in width. Thus, the profiles of the expansion of longitudinal walls were characteristic for the three types of cortical cells. In this study, both the orientation of cortical microtubule (MT) arrays and their dynamic reorientation, and the density of cortical MTs, were documented and correlated to the patterns of cell wall expansion. Significantly, transverse arrays of cortical MTs were most prominent in the radial walls of the inner cortical cells, and least so in those of the middle cortical cells. Toward the base of roots, beyond the elongation zone, the orientation of cortical MTs shifted continuously from transverse to oblique and then to longitudinal. In this case, the rate of shift in the orientation of cortical MTs along the root axis was appreciably faster in the middle cortical cells than in the other two types of cortical cells. Interestingly, the continuous change in cortical MT orientation was not confirmed in the transverse walls which showed much smaller two-dimensional expansion than the radial walls. Additionally, the presence of fragmented or shortened cortical MTs rapidly increased concomitantly with the decrease of transversely oriented cortical MTs. This relationship was especially prominent in the transverse walls of the inner cortical cells, which displayed the least expansion among the three types of cortical cells investigated. In the root elongation zone, the density of cortical MTs in the inner cortical cells was about three times higher than that in the other two cortical cell types. These results indicate that in the early stage of cell expansion, the orientation of cortical MTs determines a preferential direction of cell expansion and both the shifting orientation and density of cortical MTs affect the magnitude of expansion in width of the cell wall.     

Mechano-sensitive orientation of cortical microtubules during gravitropism in azuki bean epicotyls

The orientation of cortical microtubules (cMT) during gravitropism was studied in epidermal cells of azuki epicotyls. The relative proportion of cells with longitudinal cMT increased in the upper epidermis, and those with transverse cMT increased in the lower epidermis. When epicotyls were kept straight during gravistimulation, no change in cMT orientation occurred in either the upper and lower epidermis. When epicotyls were forced to bend downward, cells with transverse cMT increased in the upper epidermis, and those with longitudinal cMT increased in the lower epidermis. When epicotyls were loaded with naphthylphthalamic acid, an inhibitor of auxin transport, both gravitropic bending and change in cMT orientation were inhibited. However, when a change in cMT orientation was induced by forced downward bending, cells with longitudinal cMT increased in the compressed (lower) side and those with transverse cMT increased in the extended (upper) side. It was suggested that cMT orientation was controlled by the bending of the epicotyl and not by a gravity signal per se. Loading with Gd³⁺, an inhibitor of the stretch-activated channel, did not inhibit gravitropic bending. However, it inhibited cMT reorientation induced by gravitropic bending and by forced bending. Involvement of the stretch-activated channel in mechano-sensitive orientation of cMT was suggested.     

A GFP-MAP4 reporter gene for visualizing cortical microtubule rearrangements in living epidermal cells

Microtubules influence morphogenesis by forming distinct geometrical arrays in the cell cortex, which in turn affect the deposition of cellulose microfibrils. Although many chemical and physical factors affect microtubule orientation, it is unclear how cortical microtubules in elongating cells maintain their ordered transverse arrays and how they reorganize into new geometries. To visualize these reorientations in living cells, we constructed a microtubule reporter gene by fusing the microtubule binding domain of the mammalian microtubule-associated protein 4 (MAP4) gene with the green fluorescent protein (GFP) gene, and transient expression of the recombinant protein in epidermal cells of fava bean was induced. The reporter protein decorates microtubules in vivo and binds to microtubules in vitro. Confocal microscopy and time-course analysis of labeled cortical arrays along the outer epidermal wall revealed the lengthening, shortening, and movement of microtubules; localized microtubule reorientations; and global microtubule reorganizations. The global microtubule orientation in some cells fluctuates about the transverse axis and may be a result of a cyclic self-correcting mechanism to maintain a net transverse orientation during cellular elongation.     

Changes in strain and deposition of cuticle in developing sweet cherry fruit

Changes in surface area, deposition and elastic strain of the cuticular membrane (CM) were monitored during development of sweet cherry (Prunus avium L.) fruit. Fruit mass and surface area ('Sam') increased in a sigmoidal pattern between 16 and 85 days after full bloom (DAFB) with maximum rates of 0.35 g day(-1) and 0.62 cm(2) day(-1), respectively. Rates of total area strain, namely the sum of elastic plus plastic strain, were highest in cheek and stem cavity regions followed by stylar and suture regions. Rates of total uniaxial strain were higher in transverse, namely perpendicular to the stem/stylar axis, than in longitudinal direction, namely parallel to the stem/stylar axis. On a whole fruit basis CM mass remained essentially constant during fruit development. Mass of CM, dewaxed CM and wax per unit surface area decreased during development, particularly between 43 and 71 DAFB. There was no change in wax content of isolated CM. Up to 43 DAFB the surface area of isolated CM was similar to the area prior to excision indicating little elastic strain, but markedly decreased thereafter. Calculating elastic and plastic components of total strain of the CM revealed, that initial deformation up to 22 to 43 DAFB was mostly plastic. Thereafter, elastic strain was evident and both, elastic and plastic deformation, increased linearly with an increase in total strain. There was no consistent difference in the relative contribution of elastic strain to total strain between transverse and longitudinal directions, but both total and elastic strain were larger in the transverse direction. Abrading the CM had only little effect on fruit turgor. However, turgor decreased when the exocarp was cut indicating that the exocarp provided a significant structural shell of a mature sweet cherry fruit ('Regina'). Our data demonstrate, that (1) surface area expansion in sweet cherry fruit causes elastic and plastic strain of the CM, and (2) the onset of elastic strain coincided with the cessation of CM formation.     

Viscoelasticity of Tau Proteins Leads to Strain Rate-Dependent Breaking of?Microtubules during Axonal Stretch Injury: Predictions from a Mathematical Model

The unique viscoelastic nature of axons is thought to underlie selective vulnerability to damage during traumatic brain injury. In particular, dynamic loading of axons has been shown to mechanically break microtubules at the time of injury. However, the mechanism of this rate-dependent response has remained elusive. Here, we present a microstructural model of the axonal cytoskeleton to quantitatively elucidate the interaction between microtubules and tau proteins under mechanical loading. Mirroring the axon ultrastructure, the microtubules were arranged in staggered arrays, cross-linked by tau proteins. We found that the viscoelastic behavior specifically of tau proteins leads to mechanical breaking of microtubules at high strain rates, whereas extension of tau allows for reversible sliding of microtubules without any damage at small strain rates. Based on the stiffness and viscosity of tau proteins inferred from single-molecule force spectroscopy studies, we predict the critical strain rate for microtubule breaking to be in the range 22–44 s⁻¹, in excellent agreement with recent experiments on dynamic loading of micropatterned neuronal cultures. We also identified a characteristic length scale for load transfer that depends on microstructural properties and have derived a phase diagram in the parameter space spanned by loading rate and microtubule length that demarcates those regions where axons can be loaded and unloaded reversibly and those where axons are injured due to breaking of the microtubules.     

Viscoelasticity of Tau Proteins Leads to Strain Rate-Dependent Breaking of Microtubules during Axonal Stretch Injury: Predictions from a Mathematical Model

The unique viscoelastic nature of axons is thought to underlie selective vulnerability to damage during traumatic brain injury. In particular, dynamic loading of axons has been shown to mechanically break microtubules at the time of injury. However, the mechanism of this rate-dependent response has remained elusive. Here, we present a microstructural model of the axonal cytoskeleton to quantitatively elucidate the interaction between microtubules and tau proteins under mechanical loading. Mirroring the axon ultrastructure, the microtubules were arranged in staggered arrays, cross-linked by tau proteins. We found that the viscoelastic behavior specifically of tau proteins leads to mechanical breaking of microtubules at high strain rates, whereas extension of tau allows for reversible sliding of microtubules without any damage at small strain rates. Based on the stiffness and viscosity of tau proteins inferred from single-molecule force spectroscopy studies, we predict the critical strain rate for microtubule breaking to be in the range 22–44 s⁻¹, in excellent agreement with recent experiments on dynamic loading of micropatterned neuronal cultures. We also identified a characteristic length scale for load transfer that depends on microstructural properties and have derived a phase diagram in the parameter space spanned by loading rate and microtubule length that demarcates those regions where axons can be loaded and unloaded reversibly and those where axons are injured due to breaking of the microtubules.