.I. Mol. Rid. (1990)

212, 775-786

Characterization

of Microtubule

Protofilament

Numbers

How Does the Surface Lattice Accommodate? R. H. Wade, D. ChrCtien Laboratoire

de Biologic

&ructurale,

C’EA et URA

1333 CNRS

and D. Job I!nitP

244, Institut National de la Sank! et de la Recherche Me’dicale Fe’de’ration des Laboratoires de Biologic DRFIG, CENG. 85 X, 38041 Chnoble Ce’dex, France (Received 24 October 19X9: awepkd

21 Dewrnbw

1989)

Frozen-hydrat,ed specimens of mirrotubules assembled irk r+trrj were observed by c*ryoelectron microscopy. Specimens were of both pure tubulin. and of microtubule protein isolated by three cycles of assembly and disassembly. It is shown that the characteristic. image contrast of individual microt,ubules allows the microtubule protofilament number to be determined unambiguously. Microtubules with 13. 14 and 15 protofilaments are observed to coexist in specimens prepared under various assembly conditions. Confirmation of t,hese results is obt ainrd by observations of thin sections of pelleted samples fixed and stJained using t ht. glutaraldehydeltannic acid technique. Images of individual microtubules sho\s both characterist’ica contrast profiles across t,heir width and typical variations of these profiles a,long their lengt,h. The profiles across t,he images indicate the protofilament number of the microtubule. The lengthwise variations indicat,e how the prot’ofilaments are aligned with respect t,o the microtubule axis giving what has previously been called a supertwist 1n 13 prototilament microtubules the protofilaments are paraxial. ln 14 and 15 protofilament microtubules. t’he prototilaments are skewed with respect t,o the microtubule axis. The ske\\ is greater for t)he 15 protofilament case t.han for 14 prototilarnents, The skew allows t,hr extra protofilaments t,o be accommodated by t,he surface latt8ice. These results should also b(B relevant to situations in z~i1~0.

1. Introduction YVlicrotubules are filamentary structures in t’hc cytoplasm of eukaryotic cells where. t)ogether with act in filaments, they form the major components of the cvtoskelet,on. They have a remarkable range of fut&ons (I)ustin. 1984) and can show different levels of structural complexity as wit.nessed by the singlet. doublet and t.riplet st.ructures involved in the archit)ecture of the cyt’oskeleton. of centrioles. basal bodies. cilia and flag&a. The lowresolution st’ructure of microtubules was first rt~vraled by elecbtron microscopy of negatively stained a.nd of t bin sectioned material (And& & Thirrry. 1963; Pease, 1963; Ledbetter & Porter, 1964; (brimstone R: Klug, 19%). Present. knowledge of microtubule structure is based in part on t,hese two methods, combined with information available from t tiree-dinicnsional recotistruct,ions of electron 775 OWL 2x:~~~/%H)/oxo775 I:! $K3.00,‘~)

micrographs of axoneme microtubules (.\mos R Klug. 1974) and various sheet forms Of tubulin ((~?epeau c~fnl., 1977. 197X; Arnos B Baker. 1979: Tamm of 01.. 197!): Mandelkow et CL/..1984) and. in part. on X-ray fibre diffraction (Mandelkow- cl 01.. 1977: lk?se et al.. 1987). On t,tie basis of all these invrstigat ions. a commonly accepted microtubule model consists of a hollow tubc,.some 250 x in diameter (I :f = 0.1 rim). whose w,all contains 13 juxtaposed prototilaments parallel to the tube axis. Each prototilament is made up of a string of aligned tubulin dimcrs (Amos. 1979: I)ust,in, 1984). In this model. adjacent prototi1ament.s have a slight longitudinal shift with respect IO each other. with the result that t)he x and /j subunits of the tubulin dimers follow a t hr.ct>-start helix wit.h a longitudinal repeat of 120 .‘i (Amos C$ Klug. 1974: Amos. 1979). The dimer packing most probably corresponds to a latt.ice in whicfl the 2 and

\

(‘

IWO

i\c;rtlr~~lw

I’IIW

I,irnit*~~l

1 tubulin subunits alternnt,e along each 1%~LApit ~11 helix; this is called the A lattice. There is some evidence that in the case of microtubules assembled in vitro there may be an alternative packing in which the c( subunits make up one helix, the /3 subunits the next, and so forth: this is called the B lattice. Some authors propose that a mixed lattice may occur (Erickson, 1974: McEwen hz Edelstrin. 1980). Whatever the details of t’he subunit packing, it is now clear that the number of protofilaments built into t’he microtubule wall can vary significantly. since protofilament numbers in the range from I:! tjo 16 have been observed both in cellular material (Tilney et al., 1973: Burton et al.. 1975: Saito & Hama, 1982; Eichenlaub-Ritter 8 Tucker, 1984: Eichenlaub-Ritter, 1985) and in microtubules assembled in c&o (Pierson et al., 197X; Burton & Himes, 1978: Linck & Langevin, 1981; Kcheele et al.. 1982). (‘onseyuently. t,he microtubule surface latt,ice must have the capacity to adapt itself to these different numbers of protofilaments. There are many reasons why it is important to under&and the mechanism by which the surface lattice adjusts it’self. This could ultimately lead to a bett’er understanding of microtubule stability. This stability is thought to be of central importance in cell morphogenesis and motility. The detailed organization of t,he surface lattice may be important for the st.rictly defined anterograde and retrograde intracellular rnovpments of organelles along microt’ubules. Yet’ another unanswered question concerns the control of protofilament number during elongation of a microtubule after nucleation in the region of a microtubulr organizing centre. The experimental determination of microtubule prot’ofilament numbers has always been based on the examination of thin sections (Tilney et al., 1973: Pierson e:t al.. 1978). We have used cryo-electron microscopy of frozen-hydrated specimens t,o investigate the structural aspect of oscillat’ing microtubule assembly (Mandelkow & Mandelkow. 1985: Pirollet et al., 1987; Carlier et al., 1987: Wade ef al.. 1989). We found that, as was first shown by Mandelkow and collaborators (Mandelkow & Mandelkow, 1985; Mandelkow et al., 1986), useful informat’ion concerning the microtubule protofilament number could be obtained from the details of the image contrast in the electron micrographs. This is an attractive possibility, since quick freezing followed by cryo-electron microscopy could allow a rapid microtubule protofilament determination of numbers of unstained and unfixed specimens GILvitro and perhaps irk viva. Meaningful statistical investigations would become possible without’ introducing any bias related to unequal resistance of different microtubule structures to complex chemical fixation and staining procedures. An additional advantage of working with frozen-hvdrated specimens is that they offer longitudinal &ews in which structural variations along the length of the microtubule can be detected. Our observations and interpretation differ in

some significant a,spects f’rom t.hcs c~onc~lusic,tisof Mlandelkow & Mandelkow ( 1985). in part i(,ular a+ concerns the 13 prot,ofilament rnicrot,ubuIrs. \\‘r have therefore re-examined in some detail the cluestion of image interpretation and have (aornyared 0111 results on frozen-hydrated material wit II those, obtained with thin sections of similar specimt~ns. PPYl:r establish unambiguous rules relating t tit> image contrast to the number of 1)rotofilarnr.r~t.s in the corresponding microtubule. We show how the charaoterist~ic caontrast variations along t,he microtubule images are relat,ed to a skew mrc+ha.nism by which the surfact, latt)ice accommodates extra protofilarnents. ilr csonsistent picture emerges. In 13 protofilament rnicrotubules. the protofilaments are essentially parallel to the microtubule axis. The protofilarnent skew will vary with the number of protofilaments added 01’) subtracted from the basic 13 protofilamrnt st)ruc,ture. r\n additional aspect is t’hat \vr (San make reasonable predictions about the surface lat tic:rl COP figurations. and hence image contrast, of microtubule types, for example 12 and 16 protofilaments. which are known to exist, both in ,uivo and in vitro but which, to date. have not been observed by cryoelectron microscopy of frozen-hydrated specimens. Finally, the accommodation of extra protofilaments via the proposed skew mechanism clearly implies that the CIand p subunits have very similar. if not, completely identical, lateral int’eractions.

2. Materials and Methods otherwisch all c>hcmicals were Unless indicated purchased from Sigma Chemical (:o. (St Louis. MO). Phosphocellulose Pi 1 was supplied by Whatman Inc. (Clifton. EJ). MME buffer was used for protein purification 1 mm-NiTA (pH 675)). For (100 mM-Mes. 1 miv-?ulgU,, assays. the prot,ein was exchanged into PME buffer, which had the same constitution as MME buffer except that Pipes was used in place of Mcs. The sucrose-MME buffer was constructed by addition of 5Oy;, (w/v) sucrose to previously prepared MME buffer. Sucleotidrts. acetate kinase and acrtgl phosphate were purchased from Hoehringer-Mannheim Hiorhemic.als (Indianapolis. IN).

(11)Microtubulr

protein

i.wlulion

Cold labile microtubule prot,ein from beef brain was isolated by 3 cycles of assembly and disassembly in MME: buffer. according to published procedures (Asnes & Wilson. 1979; ,Job et al.. 1985). with t,he following modification. For the 3rd cycle, protein was resuspended from pelleted microtubules and centrifuged in MME buffer for fraction was 30 min, 12O,OOOg,,, at 4°C. The supernatant reassembled in 2 mM-GTP at 30°C for 45 min, layered on

sucrose-MME buffer, and centrifuged for 2 h in a fixedangle rotor (120,000 g,,) at 30°C. Pellets (referred to as 3X-tubulin) were stored at -80°C. Pure tubulin (PCtubulin) was isolated from microtubule-associated protein by phosphocellulose column chromatography in MME buffer, from which pure tubulin elutes in the flow-through et al., 1975) and was concentrated fraction (Weingarten further by ultrafiltration. This protein was exchanged by

Microtubule

a centrifugation-filtration method on Biogel P6 (Biorad, Richmond, CA) column into PME buffer (Penefsky, 1977). It was adjusted to final concentrations of 7.5 mg tubuphosphate, 10 mm-acetyl lin/ml , 10 mM-MgCl,, 1 mM-GTP. 5 x 10m4 mg acetate kinase/ml, left on ice for 35 min, then divided into small portions and stored at - 80 “C.

(c) Turbidimetric

assay

Protein samples were thawed immediately before use and assembly was initiated by warming the samples to 37 “C in the spectrophotometer. Changes in absorbance at 350 nm were followed (Gaskin et al., 1974) by using Uvikon 810 or Uvikon 930 recording spectrophotometers equipped with constant-temperature chambers and cell programmers. (d) Preparation

and observation of frozen-hydrated specimens

All the preparation steps were carried out in a room heated to 37°C. The PC-tubulin and 3X-tubulin were assembled in microcuvettes and the state of polymerization was followed by measurements of absorbance as described above. Samples (4~1) were removed from the cuvettes using a micropipette and placed on an electron microscope grid held vertically by a pair of tweezers attached to a guillotine device suspended over a small stainless-steel cup containing liquid ethane. The ethane was continuously agitated using magnetic stirring. The liquid ethane was itself cooled in a liquid nitrogen bath covered by a Plexiglass lid. A small port in the lid could be opened at the last moment to allow the blotted grid to fall freely into the liquid ethane. The exact time of freezing was marked on the absorbance plot. The frozen specimen grids were stored under liquid nitrogen. The holey carbon-covered plastic film technique was used with the aim of forming a thin layer of vitreous ice spanning the holes (Dubochet et al., 1985). The microtubular structures are embedded in this vitreous ice layer, eliminating the need for a specimen supporting film. The frozen grids were mounted under liquid nitrogen into the specimen holder of a Zeiss 10 C microscope and transferred to the cryostage within the microscope via a modified airlock constructed in our laboratory. The stage of the microscope was set at 108 K and the surrounding cold trap to 98 K: an additional cold trap was placed in the observation chamber above the film camera. The grid was searched at a magnification of 2500 x under very low dose rate cxonditions (estimated to be about @05 e/AZ per s). Selected zones were recorded at 20,000 x magnification. Focusing was usually carried out directly on the region to be imaged, at the same dose rate used for scanning. using a television camera pickup, viewing in transmission, a 3 cm diameter phosphor on a fibre optics base. Noise redu&on in the image observed on the television monitor was obtained using a frame-store memory to give a running average of the video signal. The total electron dose received by the specimen during focusing was less than that required to record a single image, Two or 3 images were recorded in the underfocus range of 1 to 3pm on Kodak 163 film, which was subsequently developed for 12 min in D 19 developer. (e) Preparation

777

Protofilament Number Characterization

and observation of thzn eections

A ZOO-p1 sample of microtubule protein (3-X tubulin and PC-tubulin) was polymerized in microcuvettes

(Helma 105. 201. QS) at 37°C and assembly was monitored at 350 nm as described above. The fixation procedure was adapted from Burton & Himes (1978). At 10 min and 60 min of polymerization, 80 ~1 of material was removed from the cuvette with pre-warmed truncated tips and mixed with 32 ~1 of 25% (v/v) glutaraldehyde to give a final fixative concentration of 1%. After 5 min of fixation at 3O”C, 1 ml of 8 y. (w/v) tannic acid (Merck Chemical Div., Merck & Co., Inc., Rahway, NI), 075% (v/v) glutaraldehyde in 005 m-sodium phosphate buffer (pH 6.75) was added. After 30 min of tannic acid staining, the material was pelleted at 26,000 g for 30 min at 25°C (Sigma 3 M-K centrifuge, rotor 12.053). The supernatant was discarded and the pellets were washed twice for 5 min in @05 M-sodium phosphate buffel (pH 6.75) at room temperature. Then 1 ml of 0~0, in @05 M-sodium phosphate buffer (pH 675) was added. Pellets were teased into suspension. This postfixation step lasts for 30 min at room temperature. The pellets werr dehydrated through a rapid acetone/water series (30/70. 60/40. SO/lo, 100/O, 100/O (v/v), 3 min each step), then impregnated in an Epon/acetone series (l/l: 3/l, l/O (v/v). 10 min each step), and embedded in Epon. The resin was polymerized at 60°C for 48 h and left to cool at room temperature for a minimum of 1 day. Silver to gra3 sections (40 to 60 nm) were obtained with glass knives using a Sorvall MT 6000 XL ultramicrotome. and collected on holey plastic/carbon-coated 400-mesh copper grids. Sections were stained with 5% (w/v) aqueous uranyl acetate at 50°C for 30 min, rinsed with deionized water, fogll;;vd by &4O/& (w/v) lead citrate in 0.1 M-NaOH for at room temperature, and rinsed with @02 M-NaOH followed by deionized water before drying. Observations of sections were made with an EM 10 (’ ZEISS electron microscope operating at 100 kV. at a magnification of 25,000 x Electron micrographs were taken at a magnification of either 25,000 x or 40,000 x Protofilament counts were made on photographic enlargements (final magnification, 400,000 x ). (f ) Image processing Selected micrographs, magnification 20,OOOx , were digitized on an OPTRONICS rotating drum microdensitometer using 25 pm steps. This corresponds to steps of 12.5 A at the specimen. Sub-images were extracted and manipulated so as to align a selected portion of a microtubule image parallel to the vertical axis, the microtubule image was then centred using cross-correlation techniques. Image segments some 40 to 80 pixels wide and of varying height were extracted and projected along the length of the microtubule image to give averaged profiles of the type shown in Fig. 3. The same regions were padded up to 256 x 256 pixels, Fourier-transformed, the equatorial amplitude and phase values were output and plotted as shown in Fig. 5. The digitization and processing were carried out at the EMBL outstation in Grenoble. The processing involved use of Semper V software.

3. Results (a) Thin

sections

Although the microtubules are randomly oriented in the pellet, sufficient transverse views are available in thin sections to allow direct counts of the protofilaments to be made in the case of suitably oriented and stained microtubles. Figure 1 shows an

Figure 1. Thin section of a 3X-microtubule pellet, fixed and stained using._ the Rlutaraldehvde/t,arlIli(, acaid method. ., with t)hr number of protofilaments Below are shown typical mirrotuhule structures preseni in t,he pqarations, indicated. overall view of a typical section obtained from assembled 3X-tubulin (see Materials and Methods. section (b)). Enlarged views of individual microtubule cross-sections (Fig. 1 inset) show that the population of singlet microtubules contains structures with 13, 14 and 15 protofilaments. Similar results are obtained with PC-tubulin, except that the relative proportion of the different microtubule types changes (not shown). Other structures that are commonly observed include hook structures and various double microtubular structures. (b) Frozen-hydrated

sample,s

In the underfocused images shown here, the image contrast is the opposite to that in negative stain. This is due to the fact that the protein density is greater than the density of the vitreous ice. Protein-rich regions are therefore imaged dark

compared to the ice background but with a lower inherent contrast than when using negative stain (Stewart & Vigers, 1986). Typical images of frozen-hydrated microtubule struct’ures show that three distinct types of contrast, marked A, K and C in Figure 2, are commonly observed for both PC-tuhulin and 3Xtubulin. With respect to the contrast in the microtubule images, there is no difference between specimens prepared using different assembly conditions nor between the two types of tubulin. So image shows any direct evidence of incorporation of microtubule-associated proteins into the microtubule structures. Major differences in the relative proportions of t,he three main types of microtubule images were found for the different assembly conditions. The dependence of the microtubule populations on the tubulin purity and on the assembly conditions will be reported elsewhere.

Microtubule

Protojilament Number Characterization

779

Table 1 Data concerning the diferent

types of microtubule images

Image type Diameter

(A)

SnRr, Compatible 71values Parity of 12: (1) Image symmetry (2) Equatorial phase behaviour Fringe sequence periodicity (A)

A

247f56 145 12 or 13 Odd Odd

I3

C

269 + I.0 15.5 13 or 14

289 + 49 17.2 15

Even Even 41OOf240

Odd Odd

223Ok72

Summary of data obtained from the different types of images observed in frozen-hydrated of microtubules assembled in vitro.

The interpretation of the images made in the following section shows that the fringe contrast of individual microtubule images depends in a very distinctive way on the number of protofilaments comprising the microtubule wall. Within the dark outer bands that delimit all the images, the type A microtubule images show two fringes slightly offset towards one of the edges. The image profile, Figure 3(a), shows that the edge away from the fringe offset (far-side edge) is broader than that of the near side, that it often has a slight inner hump and that it has a lower contrast than the narrower near-side edge. Both edges have a stronger contrast than the inner fringes. As can be seen in Figure 2: the fringes run continuously over considerable distances, usually well over 1 pm. The fringe pair sometimes switches its offset from one side of the microtubule image to the other, usually after a long stretch within which no fringes are visible. Image profiles obtained in this blurred region show that both edges have the same width and contrast. As shown in Table 1, the type A images have an average width of 247 A. The type B images show three regions of different contrast: three dark fringes, two fringes and no fringes. These regions are marked respectively 3, 2 and 0 in Figure 2 and alternate in a regular pattern along the image with the sequence three fringes, blur, two fringes, blur. This sequence has an average periodic&y of 4100( ,240) A. The profiles of the three-fringe and two-fringe regions, shown in Figure 3(b) and (c), are always centrosymmetric. The three-fringe zone (Fig. 3(b)), has a dark central fringe, whilst, the strongly contrasted bands at the edges both have the same width and contrast. The two-fringe zone (Fig. 3(c)) has a bright central fringe; the edges both have the same width and contrast, and are considerably broader than in the three-fringe region. In the blurred region, the edges also have the same width and contrast (profile not’ shown). Table 1 shows that the type B images have an average width of 269 A. The type C images show two regions of different contrast with three dark fringes or no fringes. The fringes are offset towards one or other of the edges. The contrast alternates along the microtubule image with the sequence three offset fringes, blur, three fringes offset towards the other edge, blur and

specimens

so on. The sequence repeats over a distance of 2230( +72) A. The antisymmetry of the fringe profile can be seen clearly in Figure 3(d); in addition, the edge away from the fringe offset is broader and has a lower contrast than the other edge. In the blurred regions, the edges have the same width and contrast (not shown). Table 1 shows that the average width of the type C images is 289 A. Another microtubule structure that is commonly seen is marked D in Figure 2. This structure shows three edge-type fringes, implying that it might have three walls. There are several possible explanations of these images. In the light of the thin section results, they are probably due to various double microtubule forms.

4. Image Interpretation We need to devote some attention to the question of image interpretation, since the possibility of unambiguously characterizing each individual microtubule image in terms of the number of protofilaments is an essential feature of the observation of frozen-hydrated specimens of assembled tubulin. In this section we consider general features of the local contrast profile across the width of an image. The characteristic periodic changes in the profiles as we move along a microtubule image will be dealt with laber. We assume that the frozen-hydrat*ed rnicrotubules are preserved well and retain bheir native cylindrical cross-sections. Bearing in mind that, t’o a good approximation. the electIron micrograph can be considered as being a defocused projection of the potential distribution within the object. we will consider. as an aid to image interpretation, the possible projections of various numbers of small circular units equally spaced around a circle of a diameter proportional to that of the microtubule. We suppose that’ this represents a reasonable, albeit simplified model of the cross-section of a microtubule at an arbitrary position along its length, and that its projection corresponds to the local projected structure of the model microtubule. Figure 4 indicates that the projected density distribution will depend on the number of units and on t.he angular orientation 0 of the cross-section. The amplitude dist)ribution along the equat’or of the diffraction

K. FI. Wade

et al.

(0)

Fig. 2. pattern of the two-dimensional projection is shown, theorem since, according to the projection (Crowther et al., 1970), this can correspond to the averaged crossFourier transform of a locally section along the microtubule structure. We first make some general remarks about the possible projected structures of such cross-sections. It can be shown easily that if there are an even number of units uniformly distributed around the annulus, the projected structure must always be centrosymmetric whatever the orientation angle 0. It’ follows that a defocused image of the projection must also be centrosymmetric. For an odd number of units, the image may or may not be centrosymmetric, depending on the projection angle. This implies that an image that is not centrosymmetric can be produced only by a structure having an odd number of units. Consequently, symmetry will be an extremely important element in determining the protofilament numbers from the microtubule images. The interpretation of the images will be

aided by examining in parallel both t)he electron micrographs and the amplitude and phase information obtained from their numerically cbalculated Fourier transforms. Since we are concerned here with relatively low-resolution image detail. and specifically with the protofilament arrangement. the lies along the diffraction information of interest equator of the Fourier transforms and concerns t’hr two Bessel function terms: JO(271RTO)+ i”J,(27cRr,)

cos n.(f#J- H).

(1)

where J,(&RrO) is an nth order Bessel function, y0 is the radius of the circle around which n units are disposed, R and 4 are the cylindrical co-ordinates in reciprocal space and 8 gives the orientation of the n-unit structure, see Figure 4. Both Kessel functions oscillate in dist’inctive ways; see, for example, Janhke & Emde (1945). The J, term comes from t,he average circular structure and shows phase oscillations from 0” to 180”. The second term depends directly on the number of units and is real for n even

Microtubule

Protojilament Number Characterization

781

(b)

Figure 2. Frozen-hydrated specimens of microtubules assembled in rfitro from 3X-tubulin. Three distinct t,yprs ot microtubule images are observed, these are marked A. B and C. and are referred to as such in the text. (a) This overview shows that each intact microtubule can be identified positively as type A. R or C. (b) The typical fringe contrasts of t,he :( tgpps of image. The clontrast variations along each microtubule are typical of each image type.

and imaginary for n odd. In other words, it has phases of 0” or 180” for n even and of 90” or 270” for nj odd; through the cosine term, the amplitude of its oscillations depends on the angle of project,ion 8. For relatively low values of n, overlap occurs between t,he J,(X) and J,,(X) terms, in which case their amplit’udes are added vectorially. When n. is even, the resulting phases are confined to 0” or 180” but when IL is odd, the two terms add in quadrature and, as a result, the overall phase will vary as the relative va,lurs of the amplitudes of t,he t,wo terms vary. Figure 5 shows the amplitude and phase distributions along the equator of the computed Fourier transforms of short regions, 50 to 100 nm in length, extracted from experimental microtubule images. It can be seen that in the region where J,(X) and J,(X) overlap, there is a distinct difference in the phase behaviour of the two-fringe and three-fringe segments of the type B images compared to the type A and C images. The phases of the type B images behave as expected for n even, while those of the A and C images are only compatible with n odd. In summary, the image symmetry gives a clear indicat,ion of whether n is even or odd. This information can be confirmed by examining the phase

variations along the equat)or of the calculated diffractogram. Moreover. possible values of n call be identified from measurements of the radius T,, of the microtubule and of the position R, of the main peak associated with the JJ27cRr,,) term. Data on the type A, 13 and (’ images are summarized in Table 1.

5. Discussion (a) Protqfilament

nu,mbers

The thin sections of fixed and stained microtubule pellets show that microtubules assembled in vitro from 3X-tubulin or PC-tubulin can have 13. 14 or 15 protofilaments. This result is completely consistent with previous investigations (Pierson et al.. 1978; Burton & Himes, 1978). The data obtained from the images of frozenhydrated samples are summarized in Table 1. It is clear that the different image types can be classified unambiguously as follows: Type Type Type

A: 13 prototilaments I!%: 14 prot,ofilaments (‘: 1.5 protofilament)s

R. II.

Wade et al.

Figure 4. A section through a model microtubule structure consisting of 72units set on a circle of radius r and oriented at an arbitrary azimuthal angle 0 with respect to the projection direction. The profile of the projected structure is schematized below. Such profiles will show strong edge bands where several units project slightly out of register. The inner fringes will be observed when upper and lower units are in register along the projection dirertion. To the right, we show the amplitude distribution along half of the equator in the diffraction patt)ern. This corresponds to the Fourier transform of the projected structure and contains, in the low-resolution range, the 2 Bessel function terms (------) J,(X) and (- - -) J,(X). The exact form of the projected structure depends on the contribution of the J, term: for n even, the projection is centrosymmetric for all projection angles 0.

Cd)

Figure 3. Computed average profiles across the 3 image types, These profiles are averages of short segments some 50 to 100 nm in length. The 12.5 A sampling steps account for the angular form of the profiles, since only 20 t,o 25 points are included across an image. The profiles are quite characteristic of the image types and show both inner fringes and more strongly contrasted edge bands. The peaks correspond to the darker regions in the images in Fig. 2. The fringe positions show typical symmetry for each image type. In principle, the fringe heights should all be the same, the differences are due to noise. (a) Type A image, 2-fringe region; (b) type B image, 3-fringe region: (c)type B image, 2-fringe region; (d) type C image. 3-fringe region.

It should be noted that, the measured diameters of the type B and C microtubules correspond well with the addition of one and two protolilaments. respectively. to the 13 protofilament’ t’ypc A rnicrotubule. on the basis of a 60 A separation between protofilaments around the microtubule circumference. A consequence of this classification is that direct scrutiny of the images of frozen-hydrated microtubule structures allows the numbers of protofilaments in each microtubule to be deduced from the characteristic and easily recognized image contrast. Bearing the above classification in mind, the longitudinal variations in the image contrast can now be interpreted directly wit,h the aid of Figure 6. In all cases, the projected st,ruct~uras should show strong bands along their edges. where scvcral protofilaments superpose in projection. 1)istinct fringes of lower contrast will be observed between these bands if the orientation of the cross-section is such that the protofilaments from above and below cxactlq superpose along the line of projection. In the projection of the 13 prototila~ment model of Figure 6(a), depending on the orientation angle 0. two fringes will be observed offset t,o the right or to the left, with an associated disyrnrnetry in the edge band widths due t,o the diflerent number of proto laments contributing to each of the two bands. These general features correspond to those seen in the profile of t#he type A images shown in Figure 3(a). Since the tot,al number of prot’ofilaments is odd, it is possible for the projected structure to bc symmetric. but in t,his case the prOtOfilamentS from ahOW anti k)ehJw &I’? interCalated in projection and only the edgt: contrast subsists. as can be seen on some regions of t)he type

Microtubule

Protojilament Number C’huracterization

783

r 2

.*.

t

(a)

I

(a 1

..*a.

360

g,80-g:i ---....,.-

.*.

I

-*.:

,” 0

a

i/80;

it

.

(b) .

o-

.

Figure 6. LModel cross-sections and projec+d structures.

. . ...*

(b)

i-i!; D 0 :

I

. . . . . ..

.

. . . . . . .* .* l/80 ;1

I

a

. . 0

*. . . . . . . -*

1 Cc)

360

.

-

. ._

.

. . -a..... Ol-

* *.

.*

.-

.a*

(d)

Figure 5. Equatorial amplitude (----- ) and phase (a**) distribut,ions of comput,ed Fourier transforms of short segments of t,ype A, B and C images, see Fig. 2. In all cases, the phases corresponding to the 1st 3 amplitude peaks have phases close to 0” or 180”. Beyond l/80 A, the phase of the type B images, (a) 2-fringe segment and (1~)3-fringe segment, remains close to 0” or 180”. This indicates t,hat n is even. The phase of (c) the “-fringe

The sections are drawn to give projected widths in scale with t,he measured values of 247 A and 269 A, respectively. for 13 and 14 protofilament strurtures; the circular unit,s are scaled at 35 .!L (a) Thirteen protofilamrnt microtubule, showing 3 identical cross-sections, which are rotated progressively clockwise from left t,o right acaross the Figure. They each give bhe typical projected strurture profiles show-n below. The observed image int,ensity profiles (Figs 2 and 3) show similar symmetry to these model projections. (b) Fourteen protofilament microtubule model, same procedure as in (a). Again the observed profiles behave similarly to the models.

,4 images in Figure 2(a). This corresponds t,o thta situation where cos n(4-0) = 0 in equation (1). In the case of t,he 14 protofilament. model. Figure 6(b) shows how either two or three centrosymmetric fringes should be observed in the imagca depending on the local angular orientation of the microtubule: when the protofilaments mismatch in projection, no fringe contrast will be observed. However, whatever the orientation, the projection, including the edge bands, will always be centrosymmetric. When two fringes are observed. the edge bands will he broader than in the three-fringe case. since an extra prot,ofilament corit)rihutcs to each edge projection. These features can Irmaseen clearly in the local contrast across the typt> 1%images in Figure 2 and in Figure 3(b) and (c), which shows profiles from the type B microtubule images. Another feature quite characteristic of the type B images is to be seen in the alternating stretches of the two and three fringes that run along the image and that are separated by blurred regions showing just the edge bands. This indicates that the protoregion of a type A image and of(d) the 3-fringe region of a type (’ image shows a continuous variation bevond ’ l/SO .r\ This behaviour indicates that n is odd.

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Wade et, al

filaments do not run exactly parallel to the micro tubule axis but must be skewed so that the orientation angle 8 of the cross-sections varies along the length of the microtubule. Applying the same argument to the case of the 15 protofilament model shows that three fringes may be observed offset’ to the left or to the right. with a narrow edge band on the offset side and a broader, band on the other side. These features can be seen in the type C images in Figure 2 and in Figure 3(d), which shows the profile of a segment of a type (y image. Since the type (1 images also show a more rapidly alternating contrast along their length, the prot’ofilaments in the 15 protofilament microtubules must be more &ongly skewed than in t,he 14 protofilament case. (b) Relationship between the observed image contrast and structural models of ,microt,ubules According to the structural model described by Amos & Klug (1974), 13 protofilament microtubules have a characteristic surface lattice in which adjacent protofilaments, made up of a string of t)he aJ tubulin heterodimers, are longitudinally staggered to give a three-start 120 A pitch helix when the plane surface lattice is rolled up to form a cylinder. This pitch ensures that the geomet’rical fit between the first and 13th protofilaments is identical to that between the other profilaments, and that the correct packing sequence of the dimer lattice is maintained across the “seam”. In the case of 14 protofilaments that maintain the same inter-protofilament stagger, it is impossible t’o obtain a fit between the first and 14th protofilament of the t’hree-start’ helices at the seam between the two edges of the plane lattice for two reasons: ( 1) there is a slight, longitudinal mismatch of about 9 A between protofilaments 1 and 14 (see Fig. 7, top left); (2) the dimer lattice does not have the correct packing sequence between protofilaments 1 a,nd 14. The longitudinal mismatch problem is accentuated in the case of 15 protofilament microtubules but, due to the odd number of protofilaments, the three-start helical lattice has the correct packing sequence bet,ween protofilament,s 1 and 15. If the basic three-start helix ntruct’ure is maint,ained, then, in t’he case of 14 and 15 protofilament longitudinal microtubules, correction of the mismatch requires that the three-start helix pitch be brought back down to 120 A, the same value as for 13 protofilaments, since t’his value is set’ by the dimer packing along the protofilaments. One way to reduce the pitch would be to reduce, by the appropriate increment, the longitudinal stagger between protofilaments. This mechanism, of course, implies that the protofilaments remain parallel to the microtubule axis but with a modified lateral binding between the dimers of adjacent protofilaments. There is another possibility that would allow the lateral binding geometry between protofilaments to stay the same as that, for 13 protofilaments. As shown in Figure 7. the idea is to let, the nth proto-

t

’

Seam

Seam

/

t

I

Surface

lattice

j

/

Figure 7. Showing at the top right a view from the outside of unrolled surface lattice of a 14 protofilament microtubule drawn on the basis of the Amos & Klug (1974) left-handed 3-start helix model of 13 protofilament microtubules. The letters a and b represent the subunits of the tubulin heterodimer. When the lat,tice is rolled up to form a cylinder. shown to the left. a mismatch occurs both in the packing and in the geometry of the lattice along the seam between the 1st and the 14th protofilaments. Below, we show that the same surface lattice can be rotated anticlockwise to slightly lower the units on the 14 prot,ofilament side and then be rolled up around t,hr same vertical axis as above to give a cylinder in which the 3-start helices now match geometrically (but still not in packing sequence). The result is that the protofilaments are now skewed left relative to the cylinder axis.

filament (n = 14 or 15) side of the seam slip down along the other side (protofilament 1) until the two sides mat,ch. This operation maint,ains bot,h the longitudinal contacts along the protofilaments and the lateral intermolecular interactions between all the other protofilaments and adjusts, to the same geometry. the contact between protofilaments M and 1. The djmer packing sequence across the seam is, of course. perturbed for n even. A consequence of the slip is that, the protofilaments become skewed with respect Taot,he microtubule axis (see the lower panel in Fig. 7). The required skew angle is about 0%” and 1.6”, respect,ively, for the 14 and 15 proMlament cases; this means that t,he cross-section view will rotate from point t,o point along the length of the microtubule and, as a result,, the projected struct~ure will vary slowly along the microtubule. What, briefly, are the consequences of this model in terms of the image contrast of the different t,ypes of microtubules 1 Type A, 13 protofilament microtubules: the protofilaments are parallel to the microtubule axis, consequently, offset fringes (2 fringes in the model in Fig. 6), or a blur, depending on the local orientation angle 8, should run uniformly along the image. Type R, 14 protofilament microtubules: the skew will produce t,he repetition three fringes/blur/two

Microtubule fringes/blur/three

ProtoJilament Number Characterization

fringes, etc. The repeat distance

will be about 4100 8. The image contrast will be centrosymmetric, since n is even. Type C, 15 protofilament microtubules: the offset fringes (n odd) will have the repeat three fringes/ blur/three fringes (opposite offset)/blur/three fringes, etc. with a repeat distance of 2050 A. Our experimental results are in close accord with t,hese features and imply that the microtubule surface lattice does indeed adapt to extra protofilaments via the protofilament skew mechanism. A protofilament skew model was put forward by Langford (1980) to explain a longitudinal moirB pattern that he observed in negatively stained 14 protofilament microtubules reassembled from dogfish brain tubulin. The details of the fringe contrast were completely different from those we have observed. This is almost certainly due to the considerable degree of flattening inherent in the negative stain technique applied to this material. With hindsight, it is clear that a longitudinal fringe periodicity has often been visible in published electron micrographs of negatasr: in the work presented here it becomes clear t)hat these are due to 15 protofilament microtubules and that. it is the type A images that arise from 13 prot &lament microtubules. In fact 1 each of the t hrchr c*ont,rast ty-pes t’hat we have observed can be seen in Figure 1 of Mandelkow & Mandelkow (1985).

6. Conclusions It is in many ways surprising that the fringe contrast in the images of the frozen-hydrat)ed microtubules should be such a rich source of information. We have shown that, with care, the number of prot,ofilaments can be deduced unambiguously for all the intact mic*rot)ubules visible in a correctly defocused micrograph (Fig. 2(a)). The repetitive contrast variations along the microtubule images indicate how the surface lattice may adjust to extra protofilaments: 13 protofilaments being taken as the reference structure. We suggest that, within the three&art helix model, a protofilament skew results from the geometric accommodation of the lattice to extra protofilament~s. The interpretation presented hrre essentially treats thfl protofilament)s as corltinuous strands: only the rquatorial region of the Fourier transform is involved. Naturally, full three dimensional reconstructions are now required to confirm this model.

785

The protofilament skew mechanism allows us to predict the surface lattices, and hence the image contrast, of microtubules with arbitrary numbers of prot’ofilaments. Take the case of 12 or 16 protofilament microtubules that are known to occur both in vitro (Pierson et ab., 1978) and in Gvo (Burton et.al., 1975; Saito & Hama, 1982; Eichenlaub-Ritter & Tucker, 1984) but which, to date. we have not observed in our frozen-hydrated samples. Tn the 12 protofilament case, the protofilament skew should have the opposite hand to the 14 protofilament case (we cannot directly determine the hand, however). The image contrast will be centrosymmetric, it will show a longitudinal repeat close to the 14 protofilamerit, case and it will most probably consist of the sequence 1 fringe/blur/two fringes/blur, etc. The 16 protofilament case is interesting in that, the addition of three extra protofilaments to the three-start 13 protfofilament surface latt$ice implies that, thtl shift, along the seam required to give a geometric lattice fit, is considerably smaller if the lattice adapts to a four-start helix. If this occurs, the hand of the resulting protofilament skew will be opposite to the 14 protofilament case. The image contrast will again be centrosymmetric, sincae n is even, the longitudinal repeat ~111 be close to the 14 protofilament value (it will be 3 times smaller if the lattice should adapt to the S-start helix) and the predicted sequence will be three fringes/blur/four fringes/ blur, etc. We would expect’ that t’he surface lattice rnodifications reported and predicted should also be rehvant to the situation in vivo since it is now clear thst rnicrot’ubules wit’h more than 13 prot,ofitaments can occur bot,h in unic~rtlular organisms (Eichenlauh-RBitt’er. 1984) and in animal phyla (Burt,on et ~1.. 1975). The skew mechanism that we propose allows the microtubule surface lattice to adapt, with minor modifications, to a wide range of protofilament numbers. It’ implies that the lateral interprotofilament binding can involve c1to j3. CYto c1and B to fi subunits. that these lat*eral interactions are, to all intents and purposes, equivalent and give a fixed bonding angle between neighbouring protofilaments. In t.his. our results strongly support previous results in which discontinuous dimer lattices were proposed (McEwen & F:drlst,rin, 1980; Langford, 1980).

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Wade et al. Mar&lko\r. K.. S;c*hultheisb. I