Order-disorder phenomena in myelinated nerve sheaths

J.

Mol.

BioZ.

(1991) 220, 351-357

Order-Disorder

Phenomena in Myelinated

Nerve Sheaths

III-f-. The Structure of Myelin in Rat Optic Nerves over the Course of Myelinogenesis Leonardo

Mateu’, Vittorio Luzzati’x, Maria Eva Vonasek’ and Rodolfo VaTgas

‘Centro de Biofisica y Bioquimica Apdo 21827, Caracas 1020-A. Venezuela

I VIC, Tentre

Borgo’

de Ge’ne’tique Mole’culaire, Laboratoire Propre du CNRS Associe’ ci 1‘Universite’ Pierre et Marie Curie 91198 Gif-sur- Yvette, France

(Received

18 December 1990; accepted 18 March

1991)

An X-ray scattering study was performed on optic nerves dissected from rats aged from ten days to one year. The spectra were analysed using the procedure described in the previous papers of this series. Each experiment yields the values of a variety of parameters: the average D and the variance rsD of the repeat distance, the average number (N) of motifs per crystallit#e, the fraction alooseof myelin that does not belong to the compact sheaths, the sets the spurious scattering and {i,i,,(hlD)I and {imotif (k/2D)} that suffice to define, respectively, the continuous intensity curve of the elementary membrane pair. A surprising result is that, in the native optic, as previously found in the swollen sciatic nerves, the stacking disorder affects the external space, whereas in native sciatic nerves the disorder affects the cytoplasmic space. An analysis of the evolution of the structure parameters as a function of the age of the animal and a comparison with the results previously obtained with rat sciatic nerves led to the following conclusions: the structure of the elementary membrane pair is constant throughout myelinogenesis; (N) is much smaller in optic than in sciatic nerves: (N) and the degree of myelination increase with age in the two types of nerve; D is smaller in optic than in sciatic nerves; in optic nerves, D decreases slightly with age, but in sciatic nerves it increases; oD is strongly age-dependent in optic nerves, but almost age-independent in sciatic nerves. In contrast to sciatic, the structure of optic nerve myelin was found to be almost insensitive to hypertonic solutions. Finally, a pair of electron density profiles was selected, quite similar to those selected previously in sciatic nerves, one corresponding to Caspar & Kirschner’s the other to Worthington & McIntosh’s proposals, neither of which can be ruled out according to the criteria used in this work. Keywords:

optic

nerve myelia;

1. Introduction In the first paper of this series (Luzzati & Mateu, 1990), we described a novel approach for the study of disordered lamellar systems by X-ray scattering techniques, based upon the following assumptions: (1) the system consists of planar lamellae; (2) the lamellae are stacked into crystallites, with a variable repeat distance whose average and variance are 1) and cr& respectively; (3) within each crystallite, the lamellae are strictly parallel to each other; 7 Paper II in this series is Mateu et ~2. (1990). .I. Mol. Biol. 215, 385-402. $ Author to whom all correspondence should be addressed. 0022~2836~~l~1403,51-07

$03.00/O

structure,;

swelling:

myelinogenesis

different crystallites may be slightly tilted with respect to the direction of the nerve fibre; (4) the structure of the elementary membrane pairs may not be identical throughout the crystallite, provided that the structure of any of the membrane pairs is independent of the distances to the neighbouring pairs; (5) each crystallite contains a finite number of membrane pairs whose average is (N); (6) a fraction, alooser of membrane pairs is not tightly wrapped in the sheaths; (7) a spurious scattering, &r(s), is also present, defined by its values at the lattice points, a,, = h/D. This model led us to elaborate a simple and fast algorithm, which operates on the raw scattering data; the results are the values of the parameters D, gD, (N) and aloose, and

also of the sets {i,,,(h/D)} and {i,,,if(k/211)}. which define the diffuse scattering i,iff(S) and the conGnuous intensity function imotif of the elementary membrane pair. Moreover, knowledge of the set at best, suffice, or, at worst. {irnotif(k/2D)} may, greatly help to select the “best” electron density profile. The algorithm was first applied to X-ray scattering data recorded with the native rat sciatic nerves as a function of the age of the animal or in sciatic nerves swollen in a variety of non-isotonic solutions (Mateu et al., 1990). Here, we present, a similar study of rat optic nerves. X-ray scattering studies of optic nerves from a variety of animals have been reported in the literature (e.g. see, Worthington & Blaurock, 1969; Caspar 8: Kirschner, 1971; Inouye & Kirschner, 1988a,b; Inouye et aE., 1989, and references therein). Most of those studies were focused on electron density profiles, although some authors (Tnouye & Kirschner, 1989, see Section 3(c)) were also concerned with disorder. Our interest’ in myelin st,ems from the expectation that the physical organization of the sheaths may undergo subtle alterations under the influence of parameters related to thtr physiological functions and the pathological dysfunctions of myelin. For this reason, the present study of optic as well as the previous one of sciatic nerves is focused on the parameters that characterize the real, disordered structure, rather than on the ideal structure represented by the electron density profiles.

The swelling experiments were carried out on IPI’VPS from adult rats, superfused with the hyIlotoni(. solutio[r used by Inouye & Kirschner (1988a.6). The X-ray scattering experiments were performed, and the spectra analysed, as described (Mateu rf (11.. 1990). (c) Assr.ssing

the sin&&y between in,tcnsity CI match indu.1

mr~w:

A problem

similarity curves

frequently

of different

met in this work

intensity

are not scaled together

and arr known

and Methods

(a) Notation As a guide to the reader, we define the various parameters used in this work (see Luzzati & Mateu. 1990: Mateu et al.. 1990). II and &, the mean and variance of the repeat, distance. (IV), the average number of lamellae per crystallite. clmye,, the “degree of myelination”. i.e. the myelin content of the sample. as compared to a native adult preparation. tlloose, the fraction of myelin that is not tightly packed in the sheaths. CI~, the variance of the angular spread of the individual nerve fibres in the preparation. i motif(s), the intensity curve of the isolated lamellae. i&s). the diffuse scattering. (b) The samples and the X-ray

.scattering expprriments

Rats aged from 10 days to 1 year were anaesthetized with thiopental (5 mg/lOO g body weight) and decapitated. The optic nerves were dissected, while the connecaCons with the ocular globe and with the brain were preserved. The preparation (brain-optic nervrPocular globe) was mounted on a holder provided with separate (Lompartments for each of the anatomical regions. The nerve was fastened under gentle tension and set parallel to the X-ray beam. During the scattering experiment the nerve was superfused continuously with normal Ringer solution (Mateu et al., 1990).

the

at thr lattice p0int.s .sk= h$?D (D may br different. for each curve), or a.t a set of experimental channels. We assume that the conditions that justify interpolation P~CI Shannon’s algorithm are fulfilled (T,uzzati & Mat,eu. 1990). We introducae a mat)ch index.

either

as a measure of the similarity T:l

~CJ’).

of the pair of funcationsfJj) unscaled and known at t.hr points ., ;V. K is a scaling facstor. h’:e also use thr

notation: L4, = cj”= If&j);

A, = cj”= ,fbfj):

‘4,, = c,“= IfJAfbW

The value of K can be chosen so that

(2)

M,* is minimum.

thus: dM,,/d A trivial

calculation

K = 0.

(3a)

yields: Kz = A,,/ A,,.

Replacing

the expression of A,,

(3b)

(eqn 2) and h’

(eqn

3b)

in eqn (1). M,, takes the form: M,, = (A,, - K-bJ(4,

2. Materials

is to assess the

curvc~s. Xs a ruir,

+ KA,,)

(4)

Note that eqn (4) is symmetric with respect to rr and 6 (namely, M,, = Mb=). If the functions foci) and J,,(j) are identical, then A, is equal t.o KA,, and M,, is zero. If. on the other hand, the functions f,G) and f&j are totally uncorrelated with eac*h other. then t,htJ expressions of il,,, and of M,, take the form: and (k,Juncorr 0’4Ancorr

= (A,,-

KA,A,/,V)/(A,,+

can be used to normalize

KA,d,/S).

(3)

the mat)c*h int1c.x:

~+~,, = wdhlwoh)““corr~

t(j)

The minimum of JI,, is 0. when thr 1 func*tiorls arcs identical. For a pair of unrorrrlatrd functions JI,,, = I. 11’ thr 2 funct.ions displa,y negative correlations. t,hrn N,,, may he larger than I. The choice of the function to which the mat-c+ indrs is applied. the range of s over which it is computed and the density of sampling are matters of convenirnee. Hy way of’ example, the computations shown in Table I werct per(Simotif(s)). formed or1 the functions { imotif f. {I[i,o,if(.s)]“zl} and {.~l[;,,,~~(.s)]‘~*1): the value of ‘\I,, is almost the same in the 4 c*ases.

3. Results A few spectra

examples of raw experimental da.&. of si,S,(s), of’ sets (ai,,,(h/L))) and {s~,,,,,~~(L$D)) and of curves i&s) and imotif (see. Mateu et al., 1990) are presented in Figure 1. AR in

Order-Disorder

in Myelinated

Nerve Sheaths

353

2 c,

i i -

Figure 1. Rat optic nerves: a few examples of X-ray scattering experiments (see Fig. 5 of Mateu et al. (1999)). (a) to (c) Native myelin as a function of the age of the animal; note that the signal-to-noise ratio increases with age and that the function i m,,,&) is barely age-dependent. (d) Adult nerve in hypotonic solution. Note that the spectrum and the curve and the presence of 2 imorir(d) are similar to th ose of the native, except for an inversion of the ratio i,,ir (2/D)/i,,,,(4/D) additional broad and weak bands, centred at approx. 0018 and 0.022 A-‘. Left frames show the raw experimental data, in counts C’(J) at the channel j. Middle frames show the functions sif,,(s) (dots) and sidiff(Slaloose)(continuous lines: see eyns (6) and (14) in Mateu et al., 1990). Right frames show the continuous intensity curve of the isolated motif. si,,,,&s), where filled circles represent {i,,&h/D)} and open circles, {imotif(lC/2D)}kodd. (a) N at’rve 350 days old; (b) native 21 days old; (c) native 11 days old: and (d) adult “swollen”.

the case of sciatic nerves, tackled using optic nerves. (a) Thr structure

three

of adult nerve

problems

were

mydin

The curve si mo,if(C~)of the elementary pair is shown in Figure 2; the curves

membrane of s~,,,~~(s)

relevant to native opt’ic, native and swollen rat sciatic nerves are compared in Figure 3. It is clear from the Figure that the curve si,,&s) of native optic nerves resembles more closely that of swollen sciatic than that of native sciatic nerves. This conclusion is corroborated by the value of the match index (see Table 1).

354

I,. Jfateu -

et al.

pheral myelin. the earl? membrane pairs a pposf’ t,hrir external faces. This rtxsult also supports t ht.

1” .

,’ Q

hypothesis

that

st,ac*king tlisordrr

affects

prt&t~n

t ially,

Rank

R

if not uniquely. ant’ of t hts two spa(‘t’s ittltl that the stacking is more’ ordered wit,hin thy t,arl> formed pairs t,han between late apposed membrant‘s (Mateu rf ~1.. 1990). The intetrsity curve. imotif( consists of 1hretb well-defined lobes. carnt,rrd at s = 0.013 A. ON?6 :I and 0+68 .q ’ (1 ‘8 = 0.1 nm). The intensity, tnore over, slmost reaches zero at the minima. sug@ing



(10-4)

I f 4 5 2048

;

52218 59 2 ,, 59 Z-16 E? 2; 7639

K-CO6 ::p:

3.663

-+++c----++++-----++*++o--+,++-----+++--oi+~---+*++*--~-++*++o ~+++t+----++*--o++r+++ -+++++----++*++a--++++ -+*++-----++++-0 --i+--+++--++--Ok-+++--+*-

+++--a++----

-++ -++ +++

-~-~-

-*+--++ -++

*+--------

Figure 2. Experimental curve irno&~) for an optic nerve from 350 day old rat (see Fig. 1). The circles mark the point’s of the sets { i,O,i~(L$D)} with k even (filled) and odd (open), respectively, and D = 155.18 A. The Table reports the first 7 &sets. as well as the last, from a list sorted in order of increasing R, and also the corresponding values of the parameter ((AP)~). The intensities i,,,,,,(k/ZD), from k = 1 to 26, take the relative values: 950; 1: 11190; 69874: 4607; 49; 11249; 39955: 17922; 6; 11; 16: 4; 1; 0: 0: 8; 3; 84: 221:

113:

3: 0: 0; 0; 2.

We have previously interpreted (Mateu et nl., 1990) the difference between the native and t,he swollen sciatic nerves in terms of a shift of the layer affected by the stacking disorder from the cytnplasmic space (in native nerve) to the external space (in swollen nerves). Using the same arguments, we infer here that, in native rat optic nerves, as in swollen sciatic nerves, the stacking disorder involves the t,he external space. This result corroborates

conclusions of an earlier electron microscope study of the formation of central and peripheral myelin sheaths in rat (Caley & Butler. 1974). In central myelin, early pairs of membranes are formed via the tight apposition of the cytoplasmic faces, followed by spiral wrapping around the nerve fibres. In periTable 1 The match index matrix Optic native

(Mab)

Sciatic swollen

Sciatic native

that the signs of t’he structure

Sciatic

native

0 0230 0615

0230 a 0.615

0615 0.615 0

Each element M,, was computed using eqn (6). for pairs of functions s~~~,&x~), with sj= 4 x 10e4j 8-l and over the range 0 I s i @04 A-‘. The matrix is symmetrical. The curves relrvant to native sciatic and swollen sciatic are computed using Shannon’s interpolation of the points i,,,,(k/ZD) reported in Table 2 of Mateu et al. (1990). A rough estimate of the mean and the variance of the “noise” (namely of the diagonal terms of the matrix) is provided by the cross-comparison of the 74 experiments performed with optic nerves in the course of myelinogenesis: the result is 0+45 and (0031)‘, respectively (see Results, section (b)).

change at t,hese

((AcJ)~) = ((P-)~>I~ (test of consistency; Mateu et al., 1990). In the case of t’he optic and sciatic nerves the ranks of the &sets selected and the values of the parameters R and ((Ap)“) are as follows: Rank

Optic native Sciatic swollen

factor

points. In order to select the “best” electron density map, we used the test of flatness (Mat,eu et ul., 1990): we generated all the sign combinations (the &sets) associated with the observed reflections { i,,,i,(h/lI)} and we evaluate t,heir relative merit using the parameters R (eqn (19) of Mateu et ~1. (1990)). The $-sets (204X) were sorted in the order of inc.reasing R: a few of the &sets of highest merit, and the one of lowest merit, are presented in Figure 2. Note that. the top seven $-sets are almost equivalent (namely R varies little). In the &sets of rank I to 4 t,he sign of the strongest, reflections (h = 2, 4, .i. 6, 10 and 11) are preserved; in the t,wo following &sets t,hr sign of the t’hird lobe (reflections h = 10 and 1 1) is inverted with respect t.o the other lobes. The maps correspending t,o the top &set of each class (namely. those of ranks I and 5) are presented in Figure 4. along with the pair of maps similarly selected in t,he case of rat sciatic nerves (from Fig. 13 of Mat,eu rt al. (1900)). In the two nerves t’hr selec%ed &sets correspond to those advocated by Worthington $ McIntosh (1973. 1974) and by (raspar &, Kirscshner (197 1). respectively. Tt is worthwhile to stress that by virtue> of t,he model and knowledge of the entire curve imotif( the origin of the rnaps is unambiguously set at, the centre of t,he orderly apposed membrane pair (Mateu of al.. 1990). In order t,o compare electron derisity maps of different systems we use t,he parameter

Optic Sciatic Optic Sciatic

I I 35 r 15;

Rx IO- * 51 1153 61 I220

((AP?) 2.18 1.1 I 290 3-28

The agreement of ((Ap)“) in the pairs of @sets (optic l-sciatic 135) and (optic S-sciatic 157) is satisfactory. The wider discrepancy of R is to be ascribed to the presence in the curve imotif of the optic

nerve of much deeper

minima

than in that

of

the sciatic nerves (compare Fig. 2 of this paper with Fig. 11 of Mateu et al., 1990).

Order-Disorder

in iWyelinated

Nerve Sheaths

355

Cytoplosmlc

Cytoplasmic external

external +

+

I

I

i57

135

s (lo-2 A-‘,

Figure 3. Comparison of the curves ~i,,,~~(s) of native optic (continuous thick line) (data from Fig. Z), native sciatic (broken thin line) and swollen sciatic (continuous thin line) (data Fig. 8 of Mateu et al. (1990)). The 3 curves are normalized so that jTz s~,,&s) ds = 1. Note the much closer similarity of native optic with swollen sciatic than with native sciat,ic (see Table 1).

(h) ,%lyelinogenesis Optic nerves were dissected from rats varying in age from ten days to one year old. A few examples are presented in Figure I. The parameters D, CJ~, and c(, are plotted in Figure 5 as a %ose~ (W, %nyel function of age; for the sake of comparison, the results obtained from sciatic nerves (Fig. 6 of Mateu et aE. (1990)) are also presented. Accuracy is higher for the optic nerves because of the large amounts of data (74 experiments in optic nerves, 20 in sciatic nerves). Several comments can be made.

r--

u -+

I 73

-1

I

!b)

ia)

Figure 4. Maps p(r) with the corresponding rank: data from Fig. 2. For comparison, the maps of’rat sciatic nerve (reproduced from Fig. 13 of Mateu et al.. 1990) are also reported. The maps of rank 1 and 5 of optic (and those of rank 135 and 157 of sciatic nerve) belong to the families of profiles put forward by Worthington & McIntosh (1973, 1974) and by Caspar & Kirschner (1971). respectively. The origins arc positioned as discussed in the text. (a) Sciatic nerve: (b) optic nerve.

In optic nerves (as in sciatic nerves, see Fig. 5 of Mateu et aE. (1990)), the function imotif varies lit,tle with age. More precisely, the mean a,nd the variance of the match index computed for all the pairs of functions si mo,il(~) corresponding to the 74 experiments, are: (M) = @045, c& = (O031)2. This

VW (deg.) 6 IO aln”tl 0.5 30 )

I logCN> 0.5

160 D(8) 155 Age (days)

Age (days)

(a)

(b)

Figure 5. (a) Sciatic nerve; (b) optic nerve. Open circles; values of some of the structural parameters determined by the X-ray scattering study, as a function of age. The total number of experiments was 20 for sciatic and 74 for optic nerves. co was measured in each of the experiments performed on optic nerves. In the case of sciatic nerves, a, was measured in only 3 experiments and found to be equal to 6”; that value was adopted in the analysis of all experiments (dotted line in upper frame of (a)). Filled circles; average number ((N)) of membrane pairs per nerve sheath as determined by electron microscopy (m) rat sciatic (Webster, 1971); (0) rat optic (Rawlins, 1973): (A) rat pyramidal track (Sturrock, 1975).

observation suggests that. from the onset of’ myelinogenesis. t)he elementary membrane pairs arc well formed and t,hat their structure is independetit of age. Note tha.t the same parameters (*otrcsponding, respectively, to myelinogenesis of sciatic nerves (Mateu et al., 1990) and to the cross-correlation between the various age-dependent curves of optic and sciatic nerves take t,hr values {(M) = 0.058, r& = (o046)2} for the pairs sciat’ica, sciatic. and {(AZ) = 0.415. CJ$ = (0.162)2j for the pairs optic/sciatic. At all ages, the average number. (X). of membrane pairs per sheath is much smaller in optic. than in sciatic nerves; moreover. (:V) and z,,,~~, increase with age in the two types of nerve. although at a slower rate in optic than in s&tic‘ nerve. Note also (Fig. 5) the excellent agreement of the values of (N) obtained in the X-ray scattering study with those of the previous electron microscope determinations (see the legend to Fig. 5). Hesides, this agreement indicates that’ the formal “crystallite” and the morphological “myelin sheath” are one and the same object. I) is smaller in optic than in sdiatic nerves. With age, moreover, I) increases slightly in sciatic (17.5 to 180 .A) and decreases in optic nerves (15X to 155 x). @D is almost constant (and equal to approximately 2.2 A) in sciatic nerves but strongly age-dependent in optic nerves (5 a at 10 days to 3 A4 in the adult). The fraction, alooSe, of unpacked membrane pairs decreases slightly with age in sciatic nerves (0.3 to 0.15) but more strongly in optic nerves (0.6 to 0.1). Tn optic nerves, the angular spread of the fibres (measured by CJ, seems to remain constant between the ages of 10 and 20 days, and then to decrease. In scaiatic nerves, CT, seems to be less variable, although the data are less complete than in optic nerves. (c) IVwelling

experiments

The response to hypotonic solutions is different in optic and in sciatic nerve myelin. In sciatic nerves. the swelling unit is a pair of membranes apposed by the cytoplasmic space (Mateu et al., 1990, and references therein). In optic nerves, the process is less well understood. Finean & Burge (1963), Lalitha & Worthington (1974, 1975) and McIntosh & Robertson (1976) arrived at the conclusion that the swelling unit consists of two pairs of elementary membranes. Tnouye & Kirschner (1989) and Tnouye et al. (1989) interpreted their X-ray scattering experiments in terms of a unique swollen phase of repeat 228 A. Following Inouye & Kirschner’s procedure (1988a, 1989), freshly dissected optic nerves from adult rats were soaked in normal Ringer solution ate ionic strength 0.06 and pH 8.5. at 4°C and for variable lengths of time. The spectra (Fig. l), which are independent of incubation time from 12 to 48 are almost indistinguishable from that hours, reported by Inouye & Kirschner (1989, see Fig. 2(b) in that paper). The spectra contain two strong and sharp bands, similar in shape and position to those

of native nerves. plus two broad and weak shonhlt~rs at approximately 0.018 and 0.022 A ‘. ‘I%. sirni laritv of the native atid ‘-swolktr” hl)ta(.t rii ih in (vtrtrwsl t 0 t htb clriinial ic, st.riGng, t~specially swelling-ilrduc~rcl rffec2t.s of hypotorric solutions OII scaiatic nerves (see Fig, 7 of hlateu c,f a/. (19!)0)). This remark is further corroboratctl by tht, results of’ thcb analysis of the “swollen“ spectrum: I) = I T,l~!)T, 4. (AT)

= 2’4%.

CJD= 1.57 A

iLIl(i

tilt’

(‘lll’V(’

‘motif(‘Y)

(Fig. 1). are all quite (*lose to those ohtainecl wit 11 native nerves. Therefore. all the observations (‘oncur that t ht. hypotonic. solution usc~l in the rsperirncnt has hut minor effects on t)he structure of optic nerve’ trryelin sheaths (the dramatic alterations rt~ported by Inouye & Kirschnrr (1989) are the consequt’n(‘e of their interpreting the 2 weak shoulders as the 4th and 5t’h order reflections of a latt,ic*c. \vit h n = 228 A). w e also anticipate that caonspicuous swelling phenomena have been observed in rat, olnic nerves under thrs eflect of a local anaesthtbtic* (in preparatjion).

4. Discussion

and Conclusions

Note, from a practical viewpoint, that without resorting to sophisticated cquiprnent and powerful computers each of the experiments reported in t,his paper was performed and analysed in one to four hours: obvious improvemenus could easily cut that time down to minutes or less. The final result is a remarkable wealth of parameters: I). crD, aloose. (iv). and { i,,,i,(k/Z~)}. which %yetr ~0~ (idiff(h/D)} defines t,hr intensity curve. imotil(s), and in favourable cases, t,he electron density profile. Once more, we emphasize that our work is airnrd at exploring the structural disorder of myelin rather than at reviving the old dispute of the electron density maps. Our original purpose was to elaborate a suitable technique to deal with orderdisorder problems in myelin sheaths; we intend now to tackle problems relevant to the physiological and tht pathological aspects of myelin. whose study has been hindered so far by t’echnical limitations. WV can mention, by way of example, the number of membranes per sheath. a parameter of obvious physiologicsal interest. whose determination has generally involved time-consuming elrct~ron microscopy studies and cumbersome statistical analyses (Webster. 197 I ; Rawlins. 1973; Sturroc*k. 1975). Using the novel algorithm the determinat,ion of (~1:) becomes a much faster and easier task. In addition to confirmatory results (U and (IV) are smaller in optic than in sciatic nerves, the electron density profiles of the 2 nerves art: similar), the study of rat optic nerve myelin and the comparison with sciatic nerve myetin led to a wealth of novel observations. One is the remarkable finding (con sistent with previous electron microscopy results: 1974) that stacking disorder Caley Q Hutler, involves the external space in the optic nerve and the cytoplasmic space in t’he sciat,ic* nerve, Other observations bear on the evolut’ion of the structural

Order-Disorder

in Myelinated

parameters in the course of myelinogenesis, a phenomenon barely accessible to traditional X-ray scattering techniques. Within experimental accuracy. the structure of the elementary membrane pair was found to be independent of age, both in optic and in sciatic nerves; D was observed to decrease slightly with age in optic and to increase in sciatic nerves, CS~to decrease substantially in optic and to remain constant in sciatic nerves. Not surprisingly, in the two nerves, (N) and the degree of my&nation, amye,. increase substantially with age. The analogies between the two nerves could not overshadow the differences regarding the space affected by stacking disorder and the swelling effects of hypotonic solutions. An important unanswered question is whether the observations made with rat optic and rat sciatic nerves mirror general properties of the central and of the peripheral nervous systems. The novelty of our approach is to link the X-ray scattering phenomenon to a precise physical model, the degrees of freedom of which are clearly specified. As a consequence. the experimental observations can be expressed as explicit functions of a finite number of unknowns, the values of which are event)ually determined by straightforward mathematical methods. The main virtue of the algorithm, as compared to previous procedures, is to avoid many intermediate. and questionable, manipulations: subjective appreciation of the spurious and the diffuse scattering, subjective identification of the individual reflections (especially when they overlap), integration of the intensity, separate analysis of the electron density profile and of the disorder parameters. We have noted previously that the model used in our work barely differs from the models used by our predecessors. with one exception. Some authors have assumed that both the internal and the cytoplasmic spaces contribute to the stacking disorder, whereas we assume that the wobbling of the repeat distance is localized in one or the other of the two spaces. The point must be stressed that according to our model the stacking across the other space may well be disordered, provided that the disorder is independent of the repeat distance (see Mateu et al., 1990). The main argument supporting the model is internal consistency. In rat sciatic nerves, all the results of the analysis were shown to be consistent with t,he model (Mateu et al., 1990). That, argument is corroborated in this work by a variety of conclusions, which all hinge upon the model involved in the analysis of the data: (1) the age-dependent curves &,,,,&s) are all similar to each other (Fig. 1); (2) the evolution of the structure parameters in the (*ours(l of myelinogenesis is regular (Fig. 2) and is in Edited

Nerve Sheaths

357

with excellent agreement other observations (Webster, 1971; Hildebrand, 1972; Krigman & Hogan, 1976; Rawlins, 1973; Sturrock. 1975); (3) in agreement with previous electron microscopy studies, the space affected by stacking disorder is different in sciatic and in optic nerves (note that this conclusion is critically dependent upon t’he hypothesis that only 1 of the 2 spaces is affected by stacking disorder): (4) the values of (LN) determined by the analysis agree quite well with those determined by electron microscopy. The authors are grateful to Lon Aggerbeck for a critical reading of the manuscript and to AndrC Gabriel for his unfailing assistance regarding data acquisit,ion. This work was supported in part by an excohange grant CRXS-CONICIT and by grants from CONICIT (Sl-1413), the Association Frangaise contre les Myopat,hies and the Association Franpaise pour la Recherche MBdicale. R.V. was supported by a postdoctoral grant, from the Association Franqaise pour la Rechrrchr MBdicale.

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