From immunofluorescence microscopy it has been suggested that cortical microtubules form whole-cell arrays. This has been most clearly seen in cylindrical hairs where the existence of helical arrays testifies to the continuity of the array around the side walls of the cell. It is not, however, clear how microtubules pack in ‘typical’ polyhedral cells with multiple, angled facets. In addressing this problem, elongated and isodiametric cells in the epidermis of Datura stramonium L. were subjected to anti-tubulin immunofluorescence avoiding distortion by cellulase treatment and air-drying. Serial focal sections were then deblurred by computer, the information being digitized, reconstructed and then rotated in order to observe the arrangement of microtubules along the anticlinal walls (in the z-axis). This established several things. Microtubules tend to be parallel upon any one cell face; they form transverse, oblique or longitudinal arrays except that some walls bear a crisscross arrangement. In subepidermal cells, microtubules clearly form helices. In the elongated epidermal cells, transversely wound microtubules are confirmed by rotation to be continuous from one face to another and probably, therefore, also constitute helices. Microtubules on oblique end walls can be seen to continue onto the side walls and do not form a separate set. Although microtubules can be ordered upon two adjacent facets, the orientation with respect to the stem’s axis need not necessarily be identical on both facets, i.e. overall alignment can change at the cell edge.

In isodiametric epidermal cells, microtubules can similarly be traced from one cell facet to another. However, where microtubules from two anticlinal walls spill over onto a periclinal wall at divergent angles, a crisscross arrangement is set up. This is attributed to the geometrical problem of fitting parallel lines around irregular polyhedra. Despite crossing over one another, the microtubules on these walls are nevertheless continuous with MTs on the side walls.

In conclusion, in elongated cells the arrays still approximate helices of various pitch: in isodiametric cells (where the walls subtend variable non-orthogonal angles to one another) the integrity of the array appears to be preserved by microtubules crossing over each other upon what is termed a ‘sacrificial’ face. The overriding tendency is for microtubules to form an integral array regardless of cell shape.

Cell shape is considered to depend upon parallelism between cortical microtubules and cellulose microfibrils (Robinson & Quader, 1982), but this does not explain the larger problem of how microtubules are packed in irregular polyhedra. How, for instance, are microtubules organized on the inner surface of the typical 14sided plant cell (Lewis, 1923) whose adjacent facets can subtend a variety of angles to one another? Do microtubules reflect or refract around cell edges or does each cell facet bear its own, separate MT array?

Ledbetter & Porter (1963) described MTs as joining up to form hundreds of hoops at right angles to the cell’s long axis. Later, immunofluorescence studies (Lloyd, 1983; Seagull, 1986) established that the microtubule array is an integral unit, since individual microtubules can be seen in cylindrical hairs to form helices rather than separate hoops. Transversely wound microtubules in tissue cells are probably also part of an integral array since ethylene treatment is capable of unwinding this conformation to form oblique helices (Roberts et al. 1985).

How does a microtubule array form? Immunolocalization studies with human scleroderma sera (Clayton et al. 1985; Wick, 1985) have shown that amorphous microtubule nucleation sites exist around the nucleus. In the onion meristematic cells, there is a discrete phase, following cytokinesis (Wick & Duniec, 1984; Clayton et al. 1985) when microtubules radiate from the nucleus before forming organized mature arrays upon the plasma membrane. Organization of the array therefore seems to evolve out of interactions at the cortex. Some cortical microtubules of carrot protoplasts reach lengths of 25 μm (Lloyd, 1984) and microtubules of at least 35 μm length have been observed underlying helical cellulose thickenings in seed hairs (Quader et al. 1986). It is clear that microtubules can increase their effective length by crossbridging to one another. One hypothesis (Lloyd, 1984,1986) is that outgrowth of such long microtubules -especially as they crossbridge the plasma membrane as well as neighbours -will tend to generate helices. Indeed, Hogetsu (1987) has observed that as MTs in cylindrical filaments of Spirogyra recover from drug treatment, they progressively sort out helical patterns from initially disorganized short elements.

A major problem is that not all cells are as regular as the free-growing, cylindrical hairs in which the integral helical arrays have been most clearly demonstrated. Cells embedded in tissue have an average of 14 facets shared with neighbours (Lewis, 1923). Epidermal cells with no outer neighbours have an average of 11 facets (Lewis, 1936). The paths that microtubules take as they wind around the multiple facets of a complex polyhedron might be expected to be considerably more complex than around a cylinder.

Resolution of this problem will not only contribute to the understanding of cell morphology, but also to the understanding of tissue morphogenesis. The selected tissue, epidermis, is reasoned to have a strong influence on the formation of an axis and on the pattern of leaf emergence (Green, 1984). The outer epidermal walls, unabutted by neighbours, represent an external restrainingjacket against the internal pressures generated by growth (Green & Brooks, 1978; Green & Lang, 1981; Lang-Selker & Green, 1984). Outer epidermal walls can bear crisscross rather than ordered microtubules, and can have patterns not shared by the periclinal inner epidermal walls and by the anticfinal walls (Takeda & Shibaoka, 1981; Bergfeld et al. 1988). Cases such as these represent a major challenge since it is unclear whether coordinating principles of array construction either do not exist or have been broken.

In this study, we have subjected epidermis to wholecell immunofluorescence in a way that avoids distortion by air-drying and avoids separating cells with enzymes. To record information in the anticlinal, z, axis in these deep, vacuolated cells, serial optical sections have been deblurred by computer, recombined and either rotated on the screen or projected as stereo pairs. Seeing the way in which microtubules pack in irregular, multifaceted cells has revealed basic principles of array formation.

Material

Plants of Datura stramonium L. were grown in a glasshouse on a day/night temperature regime of 25/20°C with supplementary lighting in the winter. Six to eight weeks after germination, strips of outer tissue were removed from the two internodes below the crotch (the point at which the stem bifurcates) using a flexible razor blade. Sections of this curved material encompassed a range of tissue from outer epidermal wall, through whole epidermal cells to cut and whole collenchyma cells.

Fixation

Fixation was carried out either after cutting the epidermal strips or before, in which case half sections of internode, approximately 1 cm long, were taken. Tissue was fixed for 4 h, initially aided by vacuum infiltration, in freshly prepared and membrane filtered (0·22 pm. Millipore Corp) 4% (w/v) formaldehyde in extraction buffer (50mm-PIPES, 5mm-EGTA, 5 mm-MgSO4, 1% (v/v) DMSO, 0·05% (v/v) Noni-det NP-40, pH6·9). After several 15min rinses in microtubule-stabilizing buffer (as above, minus DMSO and NP40), the strips were scored with a razor blade from the internal face through to the outer epidermal wall. (With this method, only cut cells stain, but it avoids the distortions of air drying and separation by enzymes). The strips were then gently placed into chamber slides using a fine paint brush. Chamber slides were made by glueing coverslip shims onto a microscope slide to form an open square. By using shims of different thickness (i.e., number 0 to 3 coverslips) the thickness of the epidermal strip could be matched to the depth of the chamber.

Immunofluorescence

Anti-tubulin (YOL 1/34, Kilmartin et al. 1982) was added for a minimum of 4h, followed by FTTC-conjugated anti-rat secondary antibody. After the final rinse, the strips were mounted in anti-fade (C1T1FLUOR AF1, City University, Chemistry Department, London) and a coverslip glued on top of the chamber using nail varnish. Specimens were observed with a Zeiss photomicroscope using epifluorescence optics. A Zeiss ×40 planapo objective was used; it had a relatively long working distance and its iris diaphragm allowed the depth of field to be increased for 35 mm photography. Micrographs were taken using Kodak TMAX400 rated at 800 and developed in D:76 or TMAX developer.

Contour staining of epidermis

To show the outline of epidermal cells, stems were painted with a solution of ink from a marker pen as described by Green (1984). Examination and photography (Ilford FP4 film) was performed using a Zeiss Tessovar photomacroscope.

Data collection and image processing

The equipment and methods used for 3-dimensional image data collection have been described in detail elsewhere (Rawlins & Shaw, 1988; Traas et al. 1987; Lloyd et al. 1987). Briefly, the image from a Zeiss universal microscope is relayed to an ISIT video camera and the video image is digitized into a framestore interfaced to a VAX 11/750 computer. The fine focus of the microscope is under computer control via a microstepping motor drive. Optical sections are collected at regularly spaced focus levels (in this study spaced at 2 gm) through the specimen. Video frame averaging (generally over 256 frames) is used to reduce video camera noise.

Each plane consisted of 512×512 pixels, with an interpixel spacing of 0·14μm. At the end of the collection of the data stack, one further image, taken a long way from the focal plane of the specimen, was recorded. This image plane was used as a background correction and was subtracted from each image in the data stack before further processing. Removal of out-of-focus information (deblurring) was carried out using the simple nearest neighbour algorithm described by Castleman (1979) and Agard et al. (1989). In order to visualize the microtubules from all sections simultaneously (i.e. to reconstruct the whole-cell microtubule array) series of related projections of the 3-dimensional reconstruction were calculated in small angular increments between + and — 24 degrees using the program described by Agard et al. (1989). To give the effect of rotation of the reconstructed array, the projections were displayed in rapid sequence. In addition, stereo pairs were produced by displaying two projections side by side on the monitor. Finally, the stereo pairs themselves could be ‘rotated’ on the screen. The images shown in this paper were obtained by a Ramtek 4500 videofilm recorder (Ramtek Corp. Santa Clara, CA 95050, USA) using Kodak Panatomic-X film.

Elongated and isodiametric epidermal cells -overall morphology

The epidermis of D. stramonium can be classified into two broad categories depending upon location on the stem. Fig. 1 shows these two groupings, juxtaposed, where a petiole meets the stem. Along the petiole, and on the stem below and above its junction with the petiole, the cells are elongated. They occur in clearly defined files, their long axis parallel to that of the stem; in surface view the cells are rectangular. Between files, the transverse cross walls are staggered, avoiding 4-way junctions, and this provides a texture resembling a path of bonded bricks. By contrast, to the right (in Fig. 1), the cells form a polygonal mosaic, rather like crazy paving, in which it is difficult to trace the cells in files. They are generally broad polygons with 5, 6 or 7 neighbouring epidermal cells. Although the elongated cells are also surrounded by similar numbers of epidermal cells, the preponderance of transverse (and to a lesser extent, longitudinal) orthogonal cross walls maintains the rectangular pattern whereas in the isodiametric cells, oblique cross walls occur, and adjacent facets are non-orthogonal.

Fig. 1.

Figs 1-6. The organization of epidermal cells and microtubules on the outer walls. Epidermis of D. stramonium stained with ink. Cells to the left, beneath a petiole (not shown), are elongated, occur in files and tend to have transverse cross walls. To the right there is a mosaic of isodiametric cells whose cross walls occur at a variety of angles to the stem’s axis (up and down the page). Scale bar, 100 μm.

Fig. 1.

Figs 1-6. The organization of epidermal cells and microtubules on the outer walls. Epidermis of D. stramonium stained with ink. Cells to the left, beneath a petiole (not shown), are elongated, occur in files and tend to have transverse cross walls. To the right there is a mosaic of isodiametric cells whose cross walls occur at a variety of angles to the stem’s axis (up and down the page). Scale bar, 100 μm.

Concerning terminology, Lewis’s (1926) ‘hexagonal’ epithelial cells are here described as isodiametric in order to distinguish them from the elongated cells which are rectangular hexagons and, similarly, share an average of six neighbours.

Cortical microtubules on the outer wall of elongated and isodiametric epidermal cells

The cortical microtubules in the majority of elongated cells are either oblique, longitudinal (Fig. 2), or transverse (Fig. 3). In the majority of these cells, microtubules are seen to obey the common alignment. This, however, is a net rather than a precise alignment for, in some cells, a subpopulation of microtubules can be seen to diverge more greatly from the mean orientation (arrowed in 2). Alignment is not necessarily common across a field of cells. Fig. 2 contains, for example, a mixture of longitudinal and oblique arrays, Fig. 3 contains oblique and transverse.

Fig. 2.

Anti-tubulin-stained elongated cells containing regular arrays of oblique and axial microtubules. A subpopulation of divergent microtubules can be seen in the lower right cell (arrow). Scale bar for Figs 2, 3, 4 and 6, 10 μm.

Fig. 2.

Anti-tubulin-stained elongated cells containing regular arrays of oblique and axial microtubules. A subpopulation of divergent microtubules can be seen in the lower right cell (arrow). Scale bar for Figs 2, 3, 4 and 6, 10 μm.

Fig. 3.

Regular arrays of transverse and oblique microtubules in elongated cells. Crisscross microtubules can be seen in the central, polyhedral cell (arrow).

Fig. 3.

Regular arrays of transverse and oblique microtubules in elongated cells. Crisscross microtubules can be seen in the central, polyhedral cell (arrow).

Elongated cells possess either oblique or orthogonal end walls. Oblique cross walls are inserted where an orthogonal wall would otherwise tend to form a fourway junction with a cross wall in the adjacent file. Examples can be found where the oblique microtubules run parallel to the oblique cross wall. Alternatively, they can abut the oblique cell edge at about 90° (see Fig. 4).

Fig. 4.

Separated by an oblique division plane, the microtubules in the upper cell are parallel to the cross wall whereas microtubules in the lower cell are at right angles to that wall.

Fig. 4.

Separated by an oblique division plane, the microtubules in the upper cell are parallel to the cross wall whereas microtubules in the lower cell are at right angles to that wall.

Insertion of non-oblique end walls can introduce irregularity into fields of elongated cells (Fig. 3). The elongated cell (arrowed) is abutted to its six neighbours via angled rather than orthogonal facets and the microtubules are apparently randomly organized upon the outer epidermal wall. A further example of apparently random MT organization -this time in an isodiametric cell -is presented in Fig. 5.

Fig. 5.

An isodiametric epidermal cell in which microtubules crisscross the outer epidermal cell. Scale bar, 10μm.

Fig. 5.

An isodiametric epidermal cell in which microtubules crisscross the outer epidermal cell. Scale bar, 10μm.

In epidermal mosaics composed of isodiametric cells (Fig. 6), microtubule parallelism is less conspicuous than in elongated cells; even the most regular looking cells have MTs showing some degree of crisscrossing and, in the arrowed cells, this is particularly pronounced.

Fig. 6.

Montage of a mosaic of isodiametric cells.

Microtubules tend to be less regular than in the elongated cells. Several cells contain crisscross microtubules (e.g. arrows)

Fig. 6.

Montage of a mosaic of isodiametric cells.

Microtubules tend to be less regular than in the elongated cells. Several cells contain crisscross microtubules (e.g. arrows)

Three-dimensional reconstruction of entire microtubule arrays

The foregoing establishes for epidermis of D. stramonium that microtubules pass across the outer epidermal wall in various more- or-less coaligned arrays, or else crisscross one another. To trace the arrays as they move from the outer periclinal face to the subtending anticfinal walls, through-focal series of images were reconstructed from deblurred sections by projection. 28 cells were selected for image reconstruction. A group of three elongated cells as well as two separate isodiametric cells are presented in detail since they illustrate the general principles.

Helical arrays in elongated subepidermal cells

Previous whole-cell immunofluorescence studies have established that microtubules can wind around the cell cortex in helices. The significance of these figures is that they are traceable, continuous arrays. This is known for hairs (Lloyd, 1983; Seagull, 1986) and for elongated pea and mung bean epidermal cells (Roberts et al. 1985). The depth of D. stramonium epidermal cells prevents the potential helicity of those with oblique MT arrays from being seen, but this is not the case for the subepidermal cells. A reconstructed series of one such cell is shown in Fig. 7. It can be seen that microtubules pass across one cell face from bottom right to top left, and on the opposite face from bottom left to top right. Rotation of the reconstructed whole-cell image on the screen clearly shows that the MTs pass around the cell as a series of multistart, oblique helices (Fig. 7A). Motion parallax increases the impression of separation between near and far cell faces. To compensate partially for lack of movement in the still images, 3-D reconstructions are presented for two different stages in rotation. In Fig. 7B, the cell has been rotated further right to show that the oblique MTs in the upper pair do continue around the left side.

Fig. 7.

Stereo pairs of an anti-tubulin-stained subepidermal cell. Sections were deblurred, reconstituted and projected as stereo pairs that were rotated on the screen. Both A and B show that microtubules pass around the cortex as oblique helices. The lower pair (B) has been rotated further to show that the microtubules pass around the cell edges.

Fig. 7.

Stereo pairs of an anti-tubulin-stained subepidermal cell. Sections were deblurred, reconstituted and projected as stereo pairs that were rotated on the screen. Both A and B show that microtubules pass around the cortex as oblique helices. The lower pair (B) has been rotated further to show that the microtubules pass around the cell edges.

Continuity of microtubule array between anticlinal and periclinal walls in elongated cells

Fig. 8 shows a triptych of elongated cells containing microtubules aligned obliquely upon their outer epidermal faces. By rotating the reconstructed image through the y-axis, the microtubule array on the anticlinal wall is revealed (Fig. 8A). To the upper left-hand side of the whole cell to the left (arrow), the array is seen to pass transversely across an anticlinal wall and to be continuous with the slightly oblique array on the outer periclinal face, The array is therefore continuous, rather than discontinuous, around this edge. Next, in order to rotate this reconstruction through the x-axis, the projections were first turned on their axis through 90°. The same three cells are therefore shown in Fig. 8B, but now the MTs along the shared middle two walls are revealed. This indicates that the MTs on these anticlinal walls are, like those on the outer periclinal wall (Fig. 8A) transverse to the cell’s long axis. Not all of the focal sections are projected in Fig. 8A and B. In Fig. 8C, sections including the cut, inner, periclinal epidermal wall are shown. These, too, establish that MTs pass across this face transversely. In the upper of the three cells, the MTs on the anticlinal walls are favourably presented and are continuous with those of the inner epidermal wall. MTs therefore pass trans versely around the cells from inner to anticlinal, and from anticlinal to outer epidermal walls.

Fig. 8.

A triptych of epidermal cells in various rotations.

(A) Rotation in the y-axis: microtubules pass slightly obliquely across the outer epidermal wall. Rotation of this reconstructed image through the y-axis demonstrates (to the top centre) that microtubules along the canted anticlinal wall (arrow) are continuous with those upon the outer periclinal wall. (B) Rotation through the x-axis: the same three cells moved 90° clockwise in the plane of the page prior to rotation in the x-axis. (C) Inner epidermal wall: in A and B, sections including the inner epidermal wall were omitted for the sake of clarity, but this other half is presented here. All three cells have been cut with a razor on the inner face only. By comparing with the upper cell in B (outer and anticlinal wall), it can be seen that MTs pass around the entire cell in a transverse manner.

Fig. 8.

A triptych of epidermal cells in various rotations.

(A) Rotation in the y-axis: microtubules pass slightly obliquely across the outer epidermal wall. Rotation of this reconstructed image through the y-axis demonstrates (to the top centre) that microtubules along the canted anticlinal wall (arrow) are continuous with those upon the outer periclinal wall. (B) Rotation through the x-axis: the same three cells moved 90° clockwise in the plane of the page prior to rotation in the x-axis. (C) Inner epidermal wall: in A and B, sections including the inner epidermal wall were omitted for the sake of clarity, but this other half is presented here. All three cells have been cut with a razor on the inner face only. By comparing with the upper cell in B (outer and anticlinal wall), it can be seen that MTs pass around the entire cell in a transverse manner.

Microtubules in isodiametric epidermal cells

As shown, microtubules in the more regular elongated cells, can be traced from wall to wall, maintaining the continuity of the array. In the isodiametric cells (for example, Fig. 5) microtubules can be random upon the outer epidermal wall. To see whether continuity of the array between anticlinal and periclinal walls is still preserved, several such cells were reconstructed and rotated.

An entire isodiametric cell is presented in two forms in Figs 9 and 10. The deblurred but unprojected serial sections (Fig. 9) indicate that microtubules are criss-cross and apparently random upon the outer epidermal face (bottom of figure) but pass in a more- or-less parallel transverse swirl across the inner periclinal face (top of figure). The sections in the middle of the series contain MTs, seen either obliquely or end on, passing down the connecting anticlinal walls. The domed nature of the outer epidermal wall (bottom) is illustrated by the fact that it takes several sections to focus from the MTs at its edge to those in the middle.

Fig. 9.

Deblurred but unprojected serial sections used for reconstructing Fig. 10. Sections are displayed from left to right, top to bottom, from the inner epidermal wall to the outer. On the inner epidermal wall (upper sections) MTs swirl from lower left to centre right. Microtubules continue down the anticlinal walls as dots or oblique bars (central sections) and emerge upon the outer epidermal wall. On this wall, MTs enter from different directions and cross over each other in numerous places.

Fig. 9.

Deblurred but unprojected serial sections used for reconstructing Fig. 10. Sections are displayed from left to right, top to bottom, from the inner epidermal wall to the outer. On the inner epidermal wall (upper sections) MTs swirl from lower left to centre right. Microtubules continue down the anticlinal walls as dots or oblique bars (central sections) and emerge upon the outer epidermal wall. On this wall, MTs enter from different directions and cross over each other in numerous places.

Fig. 10.

Reconstruction of an entire isodiametric cell. Rotation of the reconstructed image shows that the inner and outer epidermal MT arrays are connected by MTs that pass between them along the anticlinal walls. In the still image presented here, MTs can be seen looping over the upper cell edge, from one face to another.

Fig. 10.

Reconstruction of an entire isodiametric cell. Rotation of the reconstructed image shows that the inner and outer epidermal MT arrays are connected by MTs that pass between them along the anticlinal walls. In the still image presented here, MTs can be seen looping over the upper cell edge, from one face to another.

By rotating the reconstructed whole cell array on screen, it can be seen that MTs on the inner and outer epidermal walls (in the plane of the page) are connected by MTs that pass between them along the anticlinal walls (in the plane between the viewer and the page). Clearly, this is more difficult to present in isolated still images but in Fig. 10, the inner and outer periclinal walls are well separated and MTs are observed to loop over the upper edge from one face to another. However, such complex images are difficult to comprehend as stills, without the benefit of motion parallax. Accordingly, Fig. 11 shows another outer (periclinal) epidermal wall, with all except a few sections of the adjacent anticlinal walls edited out. Microtubules are seen to pass from the anticlinal wall to the left, horizontally across the outer epidermal face, which runs across the page. On the opposite right-hand edge of that face, MTs also pass across but at a slightly different angle. A third set of MTs passes across the same cell face from the upper edge, approximately at right angles to the horizontal MTs. This supports both that MTs pass across the edges between anticlinal and periclinal walls, and that crisscrossing is produced by overlapping of microtubules entering the field from different anticlinal walls.

Fig. 11.

Microtubules on the outer ‘sacrificial’ epidermal wall of an isodiametric cell. A few sections of the anticlinal walls have been included to demonstrate the relationship of their MTs with those on the outer wall. Microtubules on anticlinal walls plunge from viewer to page, along the left, upper and right hand side of the cell. The microtubules continue across the outer epidermal wall where the sets of differing origin converge or crisscross.

Fig. 11.

Microtubules on the outer ‘sacrificial’ epidermal wall of an isodiametric cell. A few sections of the anticlinal walls have been included to demonstrate the relationship of their MTs with those on the outer wall. Microtubules on anticlinal walls plunge from viewer to page, along the left, upper and right hand side of the cell. The microtubules continue across the outer epidermal wall where the sets of differing origin converge or crisscross.

Requirement for a new description of the microtubule array

At the molecular level, microtubules are believed to influence the alignment of nascent cellulose microfibrils (reviewed in Robinson & Quader, 1982). This does not, however, explain cell shape, because it does not account for how (or even, if) this microtubuleμicrofibril parallelism is coordinated over the entire cell, from wall to wall to wall. The early description of transverse microtubules as hundreds of hoops around the cell (Ledbetter & Porter, 1963) was an important milestone although it did not address the question of coordination at the whole-cell level. Immunofluorescence studies subsequently established that cortical MTs can form helices around the side walls of elongated cells (Lloyd, . The significance of this figure is that microtubules, regardless of their individual length, are clearly seen to constitute a continuous device which has the advantage over separate hoops of accounting for higher order coordination of cellulose alignment (Lloyd, . Although larger scale, it still does not provide a global picture of how microtubules wind around the entire cell. Does the insertion of an angled end wall affect array behaviour? In cells without a dominant axis of elongation, adjacent facets form angles greater than 90°; can an integrated array form in such prismatic cells?

If there are rules governing the way in which microtubules wind around the cell cortex, they could help explain how the new interphase array forms immediately following division, and perhaps how the array shifts its alignment during development (Takeda & Shibaoka, 1981; Hardham et al. 1980), during the cell cycle (Takeda & Shibaoka, 1978) and in response to plant growth regulators (Mita & Shibaoka, 1984; Roberts et al. 1985).

The microtubule array in elongated cells

In elongated anti-tubulin stained sufeepidermal cells of D. stramonium, oblique helical arrays are conspicuous. Rotation of deblurred, reconstructed images establishes that microtubules wind from the outer to the inner cell face. This resembles, therefore, the situation in cylindrical hairs (Lloyd, 1983; Seagull, 1986) in which, when air-dried flat, the microtubules are seen unambiguously to zigzag from one cell face to another.

The underlying importance of the helical figure is that it establishes the continuity of its components. The fact that helices occur in the highly elongated subepidermal cells of D. stramonium means that contact with neighbours to form angled facets (contrast with free hairs) does not break the unitary nature of the array, i.e. it is not composed of separate sets of microtubules upon adjacent facets.

In elongated epidermal cells of D. stramonium, although oblique microtubules can be seen, the predominant figure in young tissue is the transverse array. Using the unaided microscope, it is virtually impossible -even in these undried, uncollapsed cells -to trace microtubules around various walls when the elements are so closely packed. Rotating the reconstructed image, however, confirms that microtubules pass continuously from one facet to another; the separation of a long anticlinal wall into two gently angled facets appears to be no barrier to the continuity of the array. Previously it was shown that the proportion of oblique helices in epidermis could be increased at the expense of transverse arrays by ethylene treatment (Roberts et al. 1985), from which it was inferred that the transverse array consisted of tightly compressed helices capable of unwinding. Since microtubules pass around cell edges in D. stramonium epidermal cells, from one facet to another, it is similarly inferred that transverse microtubules are tightly wound helices.

Microtubules can be aligned differently on adjacent facets

In tracing the array from one facet of a cell to another, it becomes apparent that overall alignment -with respect to the cell’s long axis -can change at the common edge. In an electron microscopic study of the root of the water fem Azolla, Busby & Gunning (1983) also noted that individual cells can have microtubules in different orientations on different cell faces.

Arrangement of MTs in isodiametric cells

Korn (1974) concluded that cells which are growing in three dimensions, without a dominant long axis, have adjacent walls forming angles greater than 90°. The angles between the walls in such polygonal cells are therefore different from those in elongated cells where angles tend to be orthogonal. In the isodiametric cells, we have noted that microtubules on the outer periclinal wall can be either transverse, oblique, or longitudinal relative to the stem, but there is a fourth category in which the microtubules appear to be random, i.e. they crisscross. Akashi & Shibaoka (1987) in their EM study of epidermal cells previously reported that they could classify cells on a ‘one cell: one microtubule alignment’ basis. They, too, described cells as transverse, oblique or longitudinal and, notably, ‘random’ since a proportion of cells had crisscross MTs. Others (e.g. Hardham et al. 1980) have also seen crisscross MTs upon a cell facet by electron microscopy. In the present study, ‘random’ MTs were seen on outer epidermal walls, to a lesser extent on inner walls, but not as far as we can judge on anticlinal walls. (In discussing the different ways in which MTs pack upon different faces, it may be significant that the outer epidermal wall is domed, rather than faceted, since it has no external neighbours). Rotation of the reconstructed images establishes that, as for the elongated cells, microtubules on the outer epidermal wall are not a separate set, but are continuous with organized microtubules upon the adjacent anticlinal walls. Therefore, despite apparent disorganization, the array maintains its continuity from one face to another. It seems that where adjacent anticlinal walls subtend an angle to each other approximating 180° (i.e. the two facets constituting the long anticlinal wall of an elongated cell), their transverse microtubules are in harmony with the transverse alignment of the outer epidermal wall as they pass from one cell face to the other (A). But where, in isodiametric cells, adjacent anticlinal walls are ‘hinged’ at an angle much less than 180° (B), the transverse MTs on these anticlinal walls evidently spill over onto the outer periclinal wall in a crisscross manner. It is interesting that the inner periclinal wall in Fig. 10 receives virtually the same sets of microtubules from the common, adjacent anticlinal walls as does the outer wall, except that in this case the array on the inner wall ‘smooths out’ the discordant angles, producing a swirling, but nevertheless essentially parallel, array. We refer to the crisscross orgnaization of MTs as ‘sacrificial’ in order to describe the loss of parallelism on such faces. This seems to be an example of the general problem of arranging a system of parallel lines on a closed surface: in the absence of poles, or other discontinuities, there must be areas where several directionalities are expressed.

In a study of the outer epidermal wall of maize coleoptile cells during auxin-mediated growth, Bergfeld et al. (1988) observed that recently deposited cellulose microfibrils could be ordered or crisscross. They also reported that the microfibrillar organization of the outer epidermal wall could differ radically from that of the anticlinal walls, from which they concluded that a simple helical arrangement of MTs and wall microfibrils would be inappropriate for such cells. Present observations now show how the organization of the outer walls can differ from the inner walls without breaking the continuity of the array: the array’s integrity, rather than helicity per se, being the keynote of MT organization.

Observed rules of microtubule organization

In considering ways in which microtubules are organized upon the cortex, it would appear from this and other studies that their behaviour can be classified according to a set of rules.

  1. Microtubules tend to parallel one another. This influences the pattern that microtubules can form upon any one cell face.

  2. Microtubules form transverse, oblique, longitudinal and ‘random’ patterns upon a face.

  3. Within the same cell, microtubules can form different patterns upon different faces, but…

  4. Microtubules do not stop at cell edges; they are continuous from one cell face to another.

  5. The actual form of the entire array is strongly influenced by the angles between the various facets, and therefore by the geometry, of the cell.

  6. In certain irregular polyhedra, microtubules from different faces can overlap upon another face. Despite local disorder, the overriding principle appears to be that the array maintains its unity.

[Microtubules are considered here as combinable elements rather than as individuals].

Implications for array formation

Deployment of microtubules in different orientations upon different cell faces, has been taken to support the idea of separately controlled MT nucleation sites at selected cell edges (Busby & Gunning, 1983). This does not, however, explain how helices are generated in cells, such as hairs, which have no cell edges. (Microtubule nucleation sites are hypothesized to lie along cell edges, Gunning et al. 1978). Indeed, subsequent studies using human autoantibodies to amorphous MT nucleation sites (Clayton et al. 1985; Wick, 1985) indicated that such sites exist around the nucleus and not at the cortex. This, in turn, is consistent with observations from anti-tubulin studies identifying a discrete postcytokinetic phase in which MTs are seen to radiate from the nucleus prior to forming the cortical array (Wick & Duniec, 1984; Wick, 1985; Clayton et al. 1985). For this reason, microtubules are considered to form from nucleation sites and not organizing centres since array organization appears to be a later process that occurs upon the plasma membrane (see Hogetsu, 1987).

Microtubules up to 25 μm have been observed on discs of plasma membrane tom out of carrot protoplasts (Lloyd, 1984) and up to 35 μm in Cobaea seed hairs (Quader et al. 1986). In view of the length of some (not necessarily all) plant microtubules it has been hypothesized that in growing out over the cortex, their observed capacity to crossbridge each other and the plasma membrane (i.e. to form monolayers) should generate helices (Lloyd, 1984). As demonstrated by the columnar D. stramonium cells, distortion of a cylindrical section by the presence of facets presents no barrier to the smooth, transverse winding of cortical microtubules. This is further supported by the ability of helices to form in the multifaceted subepidermal cells of D. stramonium and in the elongated epidermal and cortical parenchyma cells of pea and mung bean (Roberts et al. 1985). In these elongated cells, the side walls are essentially parallel to the cell’s long axis, but in isodiametric cells the angled facets are canted with respect to the stem’s axis, forming deflecting surfaces. Passage of microtubules onto a common wall from two anticlinal walls at an angle to each other evidently sets up conflicting paths, too disparate to allow coalignment by crossbridging and resulting in a crisscross arrangement.

In addition to the precept that microtubules influence cell shape, the foregoing observations also seem to suggest that that cell shape influences the pattern that microtubules can adopt. Expanding cells are under strain, which is believed to ‘rectify’ or align microtubules transversely (Green, 1984). Gibberellic acid (Akashi & Shibaoka, 1987 and references therein) is one naturally occurring growth regulator which stimulates cell elongation and switches variable MT alignment to the transverse. In such tissue the division plane tends to be transverse to the direction of expansion (Korn, 1974; Green, 1984), but in cells without a dominant axis of expansion, division planes diverge from the transverse, creating (in epidermis) the mosaic tissue in which cells cannot be traced, end-to-end, in files. Lack of uniaxial expansion and insertion of oblique cross walls appear to be conditions that favour a cellular geometry in which ‘sacrificial’/crisscross microtubule arrays can form on periclinal walls.

The present paper concentrates on microtubules in interphase cells, but it is clear that another strong influence on cell, and tissue morphology occurs during division: namely, the plane in which the new cross wall is deposited. In a following paper, we describe how the shape of the interphase cell influences the division plane.

This work was supported by The Agricultural and Food Research Council by way of a grant-in-aid to The John Innes Institute (DJF, DJR, PJS). CWL was supported by The Royal Society. Sara Wilkinson is thanked for secretarial assistance, and Peter Scott, Andrew Davies and Nigel Hannant for photography.

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