Polymorphism of Ganglioside-Water Systems: a New Class of Micellar Cubic Phases. Freeze-Fracture Electron Microscopy and X-Ray Scattering Studies

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Class of Micellar Cubic Phases. Freeze-Fracture Electron Microscopy and X-Ray Scattering Studies

Annette Gulik, Hervé Delacroix, Günther Kirschner, Vittorio Luzzati

To cite this version:

Annette Gulik, Hervé Delacroix, Günther Kirschner, Vittorio Luzzati. Polymorphism of Ganglioside- Water Systems: a New Class of Micellar Cubic Phases. Freeze-Fracture Electron Microscopy and X-Ray Scattering Studies. Journal de Physique II, EDP Sciences, 1995, 5 (3), pp.445-464.

�10.1051/jp2:1995143�. �jpa-00248172�

Classification

Physics

Abstracts

81.30D 61.30E

Polymorphism of Ganglioside-Water Systems:

_a

New Class of Micellar Cubic Phases, freeze-fracture Electron Microscopy and

X-Ray Scattering Studies

Annette

Gulik(I),

Hervd

Delacroix(I),

Gunther

Kirschner(~)

and Vittorio

Luzzati(1)

(~) Centre de

Gdndtique

Moldculaire,

CNRS,

91198

Gif-sur-Yvette,

France

(~) ^{FIDIA Research}

Laboratories, Department

of

Chemistry,

35031 Abano

Terme,

Italia

(Received

27

July

1994, received in final form 4 November 1994, accepted 15

November1994)

Rdsumd. Le

diagramme

de

phases

de deux

gangliosides,

G Ml et GMT

(ac4tyl),

_a 4t4

explord malgrd

la prdsence d'dtats mdtastables. On _a identifid les

phases

suivantes dans GMT deux

phases lamellaires,

_une

hexagonale,

deux

cubiques (aspects

5 et

13),

_une solution micellaire dans

GMT(acetyl)

deux

phases cubiques (aspects (

8 et

13)

et une solution micellaire. La

structure des

phases

lamellaires et

hexagonale

est triviale. La structure des

phases cubiques

_a

dt4 d4terminde par

l'usage

combin4 de

microscopie 41ectronique

et de diffraction des rayons X.

Les trois

phases cubiques

sont form4es de micelles de type I

(huile

dans

l'eau)

dans deux de

ces

phases

(Q~~~ et Q~~~) les micelles sont toutes

identiques

et de forme _presque

sphdrique.

La

phase

Q~~~ est _connue

,

elle est formde _par deux types ^de

micelles,

les _{unes presque}

sphdriques,

les autres

l4gArement aplaties.

Les rayons des mlcelles d4terminds _sur les cartes de densit4

41ectronique

sont en excellent accord _avec les donn4es

chimiques.

Dans les deux

phases cubiques

la taille des micelles de

GMT(acdtyl)

est

compatible

_{avec une} forme

sphdrique,

tandis _que les micelles de GMT semblent Atre _{un peu} trop

grandes

_par rapport ^{h la}

longueur

des moldcules

: ces observations sont en excellent accord _{avec ce que} l'on _{salt sur} les solutions mlcellaires de

ces deux

lipides.

Cette richesse de

phases cubiques

micellaires est inhabituelle dans les

systAmes lipide-eau.

Abstract, The

(T, c)-dependent phase diagrams

of two

gangliosides,

GM I and GM

I(acetyl),

have been

explored,

in

spite

of the

frequent

_occurrence of metastable _states. In GMT two

lamellar, one

hexagonal

and two cubic

(aspects (

5 and

13) phases

were

identified,

in addition to the

isotropic

micellar solution. In

GMT(acetyl)

two of the

phases

_are cubic

(aspects

8 and

13),

_one is the fluid

isotropic

solution. The structure of the lamellar and the

hexagonal

phases

are trivial. The structure of the cubic

phases

_was ^determined using a combination of freeze- fracture electron

microscope

and X-ray

scattering

experiments. The three cubic

phases

consist of

lipid

micelles of type I

(oil-in-water);

in _two of the

phases

(Q~~~ ^and Q~~~) ^{the micelles} are all

identical and of

quasi-spherical shape.

^Phase Q~~~ was

previously

known to contain two types of

micelles,

_one

quasi-spherical,

the other

slightly

flattened. The radii of the micelles determined from the dimensions of the electron

density troughs

_were consistent with the chemical data. In

keeping

with what is known of the micellar solutions, the size of the micelles of the cubic

phases

of

GMT(acetyl)

is compatible with _a

spherical shape,

whereas the micelles of GMT _seem to be somewhat _too

large

to be

compatible

with the

length

of the molecules and with _a

spherical shape

Such _a wealth of micellar cubic phases is unusual in

lipid-water

systems.

©

Les Editions de

Physique

1995

1. Introduction

Gangliosides

_are sialic acid

containing glycosphingolipids (see Fig. ₁₎

abundant in vertebrate cell membranes and involved in _a

variety

^of

physiological

functions: surface

recognition,

mem-

brane

transduction,

toxin

reception, cytoskeleton protein synthesis,

cell

differentiation,

etc.

(reviewed

in

iii).

The

lipophilic moiety

is a

ceramide, namely

_a

long-chain

amino alcohol

(a sphingosine)

bound to a

fatty

acid

by

_an amine bond. In brain

gangliosides

the

sphingosine

is

predominantly

formed

by

^C18 and C20 chains and the

major fatty

acid is stearic. The

oligosaccharide moiety

is

quite

variable: 3 saccharide residues in

GM3,

7 in GT1b

(reviewed

in

iii).

As

compared

with other

lipid

molecules of

biological membranes,

the

headgroups

of

ganglio-

sides _are

exceptionally bulky;

_{as a} consequence the association

properties,

the

phase diagrams

and the structure of the

phases

_are also

expected

to differ from those of other

lipids.

The

association

properties

of

gangliosides

have been studied

extensively (reviewed

in

[1-3]).

Most of the

gangliosides

form

large

micellar

aggregates

ⁱⁿ

solution,

with the

exception

of GM3 that has been

reported

to

spontaneously

form vesicles

[4j.

^{The size of these micellar}

aggregates

varies with the nature of the

apolar

and the saccharide moieties

[5].

^In

contrast,

little is known

about the _more ordered

phases

that

gangliosides

form in the _presence of water. In this respect it _is worthwhile to mention the remarkable

polymorphism displayed by

the

lipid

extracts from the

thermoacidophilic

archebacterium S.

soifataricw,

that share with

gangliosides

the _presence of saccharidic

headgroups

_[6].

This work deals with the

lipid-water phases

of two

gangliosides,

GMT and its

semisynthetic

derivative

GMT(acetyl),

which share the _same

oligosaccharide headgroup

^and differ

by

the

apolar moiety (Fig. 1),

and is

sharply

focussed _on the structure of the cubic

phases.

As _a

rule,

the

X-ray

structure

analysis

of the cubic

phases hinges

_upon the determination of the

phase-angles

of the

reflections,

and this _may be _a

tricky operation.

In the _recent

study

of other cubic

phases

of

lipid-containing

systems we have tackled the

problem by resorting

to a

procedure

based _upon the axiom that the

histograms

of the electron

density

_maps of different

polar apolar

0H oH

o

0H x

CH3CO-NH

~~

Na00C 0H

CH~OH

~

CH=CH-(CH2)12-CH3

0H

0H NH-COCH~

Fig

I. Chemical structure of the

lipid

molecules studied

m this

work,

with the separation into the

polar

and the

apolar

moieties. In GMT X

corresponds

to _a mixture of

fatty acids,

in

GMT(acetyl)

X represents ^the CH3 _group.

Table I. Partial uohmes

(at

20 °

G).

The

separation of

the

lipid

moiec~ie into _a

"polar"

and

an

"apolar" moiety

is

defined

in

Fig.

1. The uohmes ascribed to the gro~ps

CH3, CH~

and CH _are

respectively 5$.0,

27.0 and 20.

51~ f21/;

the

partial specific

uohmes

of

GMI _is 0.7976

cm~/g f22/.

_n~ and _{u~ are} the n~mber

of

^electrons and the uohme

of

the

moiety

_z:

z=pot for polar,

_z=par

for apoiar,

z=mot

for

the whole moiec~ie.

llPld

f°~fl'lll~

~par Vpar npol _Vpol ~mol

Vmol

el

13

_el

13

_el

13

C72H128N3Na031

264 932 592 165.2 856 2097.2

C

57H98N3Na031

128 473 592 165.2 720 1638.2

phases

_{are more}

dependent

_upon the chemical

composition

of the

phases

than _on their

physical

structure

[7, 8].

^{In the} case of

gangliosides, yet,

the

scanty knowledge

of the

phase diagrams (see

Sect.

3)

thwarted the _use of that

procedure.

We thus had to

adopt

_a different

strategy, heavily d~pendent

_upon freeze-fracture electron

microscopy,

_a

technique traditionally

confined to the

qualitative

identification of the

phases.

A strict control of the effects of the

freezing step

on the _structure of the

samples [9,10]

and the introduction of the

image filtering procedures

so

widespread

in other _areas of electron _microscopy has in fact transformed this

technique

into _a

powerful

and accurate tool for the

crystallographic analysis

of the

lipid phases [11,12].

This paper

provides

_an additional illustration of the _power of this

technique

in the structure

analysis

of the

lipid phases.

2. Materials and Methods

2.1. THE LIPIDS. G~/11

ganglioside

_was

prepared

and

purified according

to

[13]

^and

GMT(acetyl) according

to

[14].

The

acyl

_group of natural GMT

belongs

to stearic acid

(ca. 90%)

and to minor

fatty acids;

in

GMT(acetyl)

to acetic acid. We

report

in

Figure

1 and in Table I the formulae and some

chemical

parameters.

^As it is

customary

ⁱⁿ the field [6], the molecules _are

ideally split

into _a

polar

and _an

apolar moiety (Fig. 1);

the volume concentration cv,~~r

(and

_cv,pal

= 1-

cv,~ar)

is assessed as follows:

Cv,p~r " iCeP0Uparj

/

_{iflmol + Ce (P0Umoj}

nmol)j (1)

where _c~ is the ratio of the number of electrons of the

lipid

to that of

lipid-water _system,

_po is the electron

density

of the low molecular

weight component (respectively

0.334 and 0.360

el/1~

for water and

water/glycerol 2/1),

_umai and _{nmai are} the volume and the number of electrons

of _one

molecule,

_up~r the volume of the

hydrocarbon moiety (see

Tab.

I).

It is worthwhile to

point

out that the results of this work _are

fairly

insensitive to chemical

heterogeneities.

The

samples

for the electron

microscope

and the

X-ray scattering experiments

_were

prepared by mixing lipids

^and water

(or buffer,

_or

water/glycerol).

The

samples

_were

usually kept

at room

temperature;

ⁱⁿ some cases

heating

and

cooling cycles

were used to facilitate the

mixing

of the components

(see

Sect.

3).

2.2. FREEzE-FRACTURE ELECTRON MIcRoscoPY.

Water-glycerol

_was used in order to avoid the formation of ice

crystals.

Before

freezing,

the structure of the

samples

_was tested

by X-ray scattering experiments.

A small fraction of the

sample

was

deposited

_{on a copper}

planchette, rapidly

frozen into

liquid

_propane, fractured and shadowed in _a Balzers ireeze-etch

unit, using

Pt-C _or W-Ta

shadowing.

The

replicas

_were examined in a

Philips

301 electron

microscope.

We call domain

[h

^kii an area of the

replica

that

diplays

_{a coarse} 2-D

periodic order,

whose lattice

corresponds

to _a

planar

section normal to the

crystallographic

direction

[hk ii.

Most often

(see Fig. 3)

_a domain is _a mosaic of

strictly

2-D

periodic mbdomains,

each

corresponding

to _a

single

step of the fracture surface.

Usually, adjacent

subdomains _are shifted with

respect

to each other

by

_a vector related to the structure elements

[12].

v, w, and _{~ are} the vectors and the

angle

^{of the 2-D}

lattice, respectively.

The

procedures

used to

analyze

the

micrographs

_were described in

[11]

^{and need}

only

be summarized here.

Initially, unidirectionally-shadowed replicas

_are

inspected (visual inspection

is indeed easier in

unidirectionally-shadowed

than in

rotatory-shadowed replicas)

in _a search for ordered domains. The

images

oi these domains _are

optically filtered,

the dimensions of the 2-D lattices determined and their relative

frequency

assessed. The

crystallographic

orientation of each domain is

determined,

with the

help

of the

X-ray scattering

information. From this

stage

on all the

operations

_are

performed

_on

rotatory-shadowed replicas.

A few well ordered domains _are

singled out, corresponding

to the

previously

determined orientations. Stereo views _are used to select the domains whose iracture

plane

is

virtually parallel

to the

plane

oi the

image

^Further

processing

is used to

improve

the

signal-to-noise

ratio. A iew selected

images

_are

digitized,

the subdomains _are identified and the cell

parameters

^determined

by

Fourier transformation. Each subdomain is then Fourier-filtered

using

those cell

parameters.

Finally,

_{an area} is selected and

analyzed

_{using a} cross-correlation

averaging

_process. The

relationships

^{between the different subdomains} are

analyzed by cross-correlating

the domain with the

averaged

motif of _one subdomain. It _must be stressed that _no

symmetry operation

is

involved in the entire process.

2 3. X- RAY SCATTERING The

experiments

_were

performed

with _a

temperature-controlled

focussing

Guinier _camera,

using

monochromatic radiation

(Cu Kai)

and linear collimation.

The films _were scanned with _a

Joyce-Loebl

microdensitometer and the intensities measured _as described

previously

_[7].

The

spacings

ratios of the observed reflections

provide

the information

specifying

the

type

of lattice and the space group

(we

_use the notation of

[7]):

1:2:3:4..,

I-D lamellar

(phase L) 1.vi:vi.vl;

2-D

hexagonal (phase H)

/:fi:/:fi;@:/l:@:@:li:4:/l:li:..

_3-D

_cubic,

cubic aspect

Q5 (Possible

space groups

PT3n, Pm3n)

@:fi:fi:@:@:@:/1:...;

_3-D

_cubic,

cubic aspect

Q8 (Possible

_{space groups}

(123, I213), Im3, IT3m, _1432, Im3m)

/;fi:@:/fi:@.li:@:li:/fi:/fl:...;

_3-D

_cubic,

_cubic

_{aspect Q13 (Possible}

space groups

F23, Fm3, F13m, F432, Fm3m).

Once the cubic

aspect

is

known,

the lattice dimension _can be determined.

Also, knowing

the cell

parameter

a of the cubic cell and the number _v of

primitive

cells in the cubic cell

(respectively _1,

2 and 4 in the

primitive, body-centred

and face-centred

lattices),

the

apolar

volume V~ar ^{and the}

aggregation

number

N~gg ii-e-

the number of

lipid

molecules _per

primitive cell)

is assessed:

V~~r ⁼

a~cv,~~~ Iv (2)

i~~agg "

Vpar/Upar (3)

where cv,~~r ^is the volume concentration of the

paraffin moiety

in the

sample

and u~~r ^is the volume of the

paraffin moiety

of _one molecule

(see

Tab.

1).

3. Phase

Diagrams

As _a

rule, thermodynamic equilibrium

is not _a serious issue in

lipid-water systems:

_some mechanical

stirring

and _a little

waiting (rarely exceeding

_a few

days) usually

suffice to attain

equilibrium.

This

rule, yet,

^has _many

exceptions:

^it is

notorious,

for

examples,

that metastable states _are

predominant

in

systems

with stiff and ordered

chains; examples

of

metastability

have also been

reported

in

phase

transitions

involving

cubic

phases [6,15].

In contrast,

ganglioside-water samples prepared

with the

precautions

that in other

systems

suffice _{to ensure}

equilibrium

often

yielded

erratic

X-ray scattering spectra.

This

problem

_was

particularly

acute in the

high

concentration

region beyond

the range of

phase Q13. Frequently

broad bands _were observed that could not be ascribed to well-defined

phases;

with time these bands sometimes gave way ^to

sharp

reflections.

Also,

removal _or addition of water had to be carried out with unusual

precautions

if the results _were to be

reproduced.

For these _{reasons we} had to be content with

outlining

the

general

features of the

phase diagrams

and with

focussing

the structure

analysis

_{on a} few

samples

with weli-defined structure.

Although

the

samples

studied in this work have been stable for

weeks,

_{we are} not at all certain that

genuine thermodynamic equilibrium

has been reached. With this restriction and for the sake of

simplicity

each of the

structures,

be them stable _or

metastable,

will be ascribed to one

phase.

The

problem

of

determining

the chemical

composition

of the

phases

is _{not as} serious _{as one} could fear for _a metastable state. All the

samples

_were indeed

optically

clear and

transparent:

the

samples

would be turbid should the

system

be

heterogeneous.

3.1. GMT. The

position

of the

phases

in the

(T,c)-dependent diagram

is sketched in

Figure

2.

At the

dry

end of the

diagram

a lamellar

phase

_was observed.

According

to the

shape

of the

signal

recorded in the

(4

to 5

1)~l _region

the conformation of the

hydrocarbon

chains _seems to be ordered

(phases Lp

of

Lp,)

at room

temperature

^and to "melt"

(phase L~)

_near 40 °C.

The lamellar

phase

is

followed,

at lower

concentration, by

_a

hexagonal phase.

At lower concentration the

samples

become

optically isotropic;

the

X-ray scattering spectra

consist of _a number of

sharp small-angle reflections,

sometimes

accompanied by

_a few broad bands. This

region

_was not

properly explored; apparently,

it contains two _or more cubic

phases.

At still lower

concentration,

and

especially

above _room

temperature,

a pure

optically isotropic phase

sets

in,

characterized

by

_a

family

of

sharp

small

angle

reflections whose

spacings

ratio

corresponds

to the cubic aspect ⁵

(Tab. II).

This

phase

is followed

by

another

optically isotropic phase,

characterized

by

a set of

sharp small-angle

reflections whose

spacings

ratio

corresponds

to the cubic

aspect

13

(Tab. III).

The very low concentration end of the

phase diagram

is the realm of the micellar solution.

3.2.

GM1(ACETYL).

The

phase diagram

is sketched in

Figure

2.

At _room temperature, and _at all

concentration,

the

samples

_are

optically isotropic

and the

short-range

conformation of the

hydrocarbon

chains is disordered.

At concentrations

higher

than

approximately

0 6 the

X-ray scattering spectra display

_a

number of

sharp

reflections

and,

in _some cases, a few broad bands.

Apparently,

the

system

consists of _more than _one cubic

phase,

that _we have _so far been unable _to

identify.

T°c GMT

60

Q5

La

,

"

H

Q13

Fl

~°

,

0 75 0 25 _c

GMT

(acetyl)

40

Q8 Q13

Fl 20

06 04 _c

Fig

2. Schematic representation of the position of the

"phases"

_m the

(T, c)-dependent diagrams

of the systems ^GM I-water and

GMT(acetyl)-water

_c is the

weight

concentration

[lipid/(lipid+water)].

As discussed in the text, ^the cubic structures may

correspond

to

genuine phases

_in

thermodynamic equilibrium,

_or else to metastable states For the sake of

simplicity

_we call all them

"phases".

The phases _are identified

as follows L~. lamellar with the

hydrocarbon

chains _m the disordered _con-

formation, Lp (Lp<)

^lamellar with stiff chains, H. 2-D

hexagonal; Qs, Q8,

Q131 3-D cubic of cubic aspect 5,8,13

(see text);

FI fluid

isotropic (micellar solution)

The position of the

samples

of well- identified structure _is

marked;

little is known of the

phase composition

of the intermediate

regions.

In GMT the dotted line represents ^the

approximate

position of the borderline of the

low-temperature, high-concentration

_region over which the chains _are stiff

When the concentration reaches

approximately

0.6 _a few

sharp

reflections _{set in} whose

spacing

ratios

correspond

to cubic

aspect

⁸

(Tab. III).

At lower concentration another

family

of reflections

arise,

whose

spacing

ratios

correspond

to cubic aspect ¹³

(Tab. III).

At still lower concentration the micellar solution sets _in.

The _presence in the _sugar

moiety

of ionizable _groups made _us suspect ^that the

phase diagrams

of these

lipids

_may be sensitive to ionic conditions. For this _{reason some} of the

experiments

were

performed using

buffered _water

(experiment D,

_see Tab.

IV) (note, nevertheless,

that

none of the

phases

is observed in

equilibrium

with the

solvent,

and thus that the

pH

is not

buffered)

the results indeed _seem to be different from those obtained with unbuffered water.

Besides,

_some

experiments

_were

performed

in the _presence of

glycerol (B

and

C,

_see Tab.

IV)

in order to mimic the conditions of the electron

microscope experiments.

4. Freeze-Fracture Electron

Microscope Study

Freeze-fracture electron

microscope experiments

were

performed only

on

phase Q13.

The _nar-

row c, T range and the

metastability (see

Sect.

3)

hindered the electron

microscope study

of the other

phases.

We used

X-ray scattering experiments, performed

before

freezing

on the very

samples

used

Table II. The str~ct~re

factors of phase _Q~~~. Amplit~de of

the str~ct~re

factors of phase

Q~~~

of

GMT

(experiment

C

of

Table IV

)

and

of

those

of

the _same

phase of

PLPC

f8/.

The

Ffl1)

_are normalized _{as in} Table III. _a is the cell

parameter,

_cv,p~r is the uoi~me concentration

of

the

hydrocarbon moiety.

GMT PLPC

T(°C)

70 20

c 0.30 0.50

c~p~

^{0.12 0.28}

a(1)

187 136.7

hkl

l10 <12 +22

200 80 -89

210 lls +122

211 l16 -l17

220 49 +53

310 <17 -7

222 82 -66

320 49 -38

321 43 +34

400 78 -69

410 36 -34

411 <22 -28

330 <22 -39

420 12

in the electron

microscopy study,

to test the

phase composition

and to ascertain that

glycerol

does _not have _any drastic effect on the structure of the

phases (see experiments

A and

B,

and also Sect.

5).

4.1.

GMT(ACETYL).

Three main types ^{of fracture} were identified

(Fig. 3).

The filtered

images (Fig. 4)

consist of _a

simple-looking

motif of

quasi-globular shape. Only

_one kind of

filtered

image

was obtained for all the domains of the _same orientation. The most

frequent

domains

display

_a

hexagonal lattice,

the second

frequent

a square

lattice,

the least

frequent

a

rectangular

lattice. The

apparent

2-D lattices of the fracture

planes

indicate that these _are normal to the directions

ill11, [100], [110]

^{of the cubic cell of}

aspect Q13.

The

symmetry

^{of the} filtered motifs

(Fig. 4)

is 3m for the fracture

[iii],

_mm for the other two fractures: of the 5

[1

loco loco

Fig

3. Freeze-fracture electron

micrographs

of the

phases

^of cubic aspect Q13 of GMT

(left frames)

and

GMT(acetyl) (right frames). Rotatory shadowing.

The

images

represent ^three domains

[100], [llo], [III].

Insert.

optical

Fourier transforms of _a selected _area of each domain Note that the

domains _are subdivided into

highly

ordered subdomains; the

fragmentation

_increases from

[III]

to

[100]

^to

[llo].

GMT (acetyl)

-' w

~i v

'j/ j"

I

WL

~

V

--~

" l

w

~

~

v

100 1

Fig.

4 2-D sections of the electron

density

_maps

(left frames)

and cross-correlation

averaged

electron

micrographs (right frames).

The maps

correspond

to experiments B and E of

Figure

6.

The

averaged micrographs correspond

to one subdomain of each of the domains of

Figure

3. The distortions of the electron

micrographs,

with respect ^{to the lattices determined}

by

the

X-ray

scattering

experiments,

_{are on} the average of 8% and 3~

on

respectively

the linear and the

angular

dimensions Note the presence of mirror

planes

in the three sections, and of 3-fold

axes in

[III].

Note also that the structure elements _are compact and

quasi-spherical

in

GMT(acetyl),

_more

spiky

in GMT.

GMT

~

v

) )

w

""

~

,,

'

~

fi fi

t'i' I /

w

~

v

ioo

Fig.

4 continued.

Table III. Str~ct~re

factors of phases

Q~~~ and

Q~~~.

The data _are relevant to the _ex-

periments A, B, D, E,

F

of

Table IV. The str~ct~re

factors

_are normalized

by setting

Zhmhf~(h)

=

1000,

where _{mh is} the

m~ltiplicity factor of

the

reflection

h. In

parenthe-

sis one

half of

the _~pper limit

of Ffl1) for

the

reflections

whose

intensity

is too weak to be observed. The _signs

correspond

to the

spherically symmetric

model

(see Fig. 5).

exper A B D E F.

ph~~~ Q225 Q225 Q225 Q225 Q229

ail)

_{155 147 123 108 85}

hkl hkl

iii 0 -146 -126 -159 l10 -260

200 -70 -145 -160 -192 200 -1 14

220 -252 -203 -193 -191 211 -47

311 -73 -76 -80 -51 220 0

222

(-1 1)

-45 -24 -25 3 lo +32

400 0 0 0 0 222 +50

331 +31 +24 +37 +34 321 +15

420 +33 +25 +41 +35

422 +33 +30 +41 +26

511

(+7)

+11 +5

333 +11 +5

space groups

compatible

with that cubic aspect

(F23, Fm3, F43m, F432, Fm3m) only

Fm3m is consistent with those

symmetry

elements.

Moreover,

the structure _seems to consist of identical

globular objects

located at the vertices and at the centres of the faces of the cube

(position

_a of

space group

Fm3m).

The determination of the _{space group} is confirmed

by

the

displacements

of _one subdomain with

respect

to the

adjacent

_ones.

Indeed,

the

symmetry

elements identified in each subdomain

belong

to the 2-D space of the

image,

^whereas the

apparent displacements

between subdomains _are related to the

symmetry operations

in the 3-D _space

(see

in

ill]

_a

more detailed discussion of this

problem).

4.1.1. Domains

[111).

^{These domains} are the most

frequent

and also the least

fragmented:

fairly

extended subdomains _are

frequently

observed. As

expected,

the dimensions of the 2-D lattice _{are u}

= w =

all,

_~

= 120°. The relative shift between

adjacent

subdomains is

iv /3

+

w/3) (result

not

shown).

4.1.2. Domains

[loo).

These domains _are

fairly frequent,

and often

fragmented

into small

subdomains. The 2-D lattice parameters are u = w =

all,

_~

= 90°. The relative shift between

adjacent

subdomains is

(v/2

₊

w/2).

Jo URNAL DEPHYSIQUE u T5,NO3, MWCH 1995 18

Table IV. Chemical

parameters.

The data _are relevant to the

experiments analyzed

in this work

(see

Tables III and

IV).

_cv,p~r is the uol~me concentmtion

of

the

hydrocarbon moiety,

_v is the n~mber

of

miceiies _per c~bic ~nit

cell, _Vm~,~ar

and

Nagg

are the

hydrocarbon

uoi~me and the

n~mber

o,f lipid

moiec~ies in _one miceiie

(see Eq.s. (1)

to

(3)). _R~ar

=

[3Vmic,~ar/(4ir)jl/~

_is the radi~s

of

the

apoiar

_core

of

the miceiie

(s~pposed

to be

spherical); Smai

₌

4irR(~~/Nagg

^{is the}

area per molec~le at the

poiarlapoiar interface.

In the _case

of phase

_{Q~~~ the} ~nit cell contains 8

miceiies,

2

of

_one

type

^and 6

of another;

the

pammeters

ⁱⁿ italics

refer

to the _auemge micelie.

Glycerol,

when

present, (experiments

B and

C)

_is ass~med to

belong

to the

polar moiety.

A B C D E F.

GMT GMT GMT

GMT(ac.) GMT(ac.) GMT(ac.)

H20 H20-gly H20-gly H20# H20 H20

(°C)

20 20 70 20 20 20

0.33 0.31 0.30 0.53 0.53 0.53

group Fm3m Fm3m Pm3n Fm3m Fm3m Im3m

155 147 187 123 108 85

4 4 8 4 4 2

0.128 0.126 0.122 0.133 0.133 0.133

(10513)

1.192 1.001 0.997 0.619 0.419 0.408

128 107 107 131 88 86

(I)

_{30.5 28.8 28.8 24.5 21.5 21A}

(12/mol)

_{91 97 97 58 66 67}

# In this

experiment

the water was buffered at

pH

7

(cikate

0.

lM).

4.1.3. Domains

(110).

^{These domains} are the rarest and the most

finely fragmented.

The subdomains take the form of _narrow

bands,

_as if the

"persistence length"

of the fracture _was very short in _one direction

(Fig. 3).

The lattice dimensions

(u

₌

all,

w = a, ~ ⁼ 90° and

the translation

iv /2

₊

w/2)

between subdomains _{are as}

expected.

4.2. GMI. The _same results _were obtained with

Pt/C

_or

W/Ta replicas (Fig. 3).

The

orientation,

content and

frequency

of the fracture

planes

_{are very} similar to those observed with

GMT(acetyl) suggesting

that the _{space group} is the _same, Fm3m. The unit cell is

larger

in this

system;

moreover the cell _seems to shrink in the

replicas by

5 to

8~.

The filtered

images

are also similar to those of

GMT(acetyl), although

the

objects

_seem to be less

globular

and

more

spiky (Fig. 4).

5.

X-Ray Scattering Study

As discussed in Section 3

(see Fig. 2)

_we have identified _a lamellar and _a

hexagonal phase,

three cubic

phases

of cubic

aspects Q5, _Q8

_or

Q13

and the micellar solutions. The

phase

_sequence

lamellar, hexagonal, cubic,

micellar

solution,

in the order of

decreasing

concentration

(Fig. ₂₎

clearly

indicates that the structures _are all of

type

I

(oil-in-water).

The

crystallographic analysis

of the lamellar and the

hexagonal phases

is

straightiorward.

In

contrast,

^{in the} case oi the cubic

phases

the

scanty knowledge

oi the

phase diagrams

forced

us to

adopt

_a

_strategy heavily dependent

_upon the freeze-fracture electron

microscope study.

S-I- LAMELLAR _AND HEXAGONAL PHASES. We did not carry out _a

systematic study

of these

phases,

that _we observed

only

in GMT. Therefore _we

only _report

_a iew scattered observations. For

example,

_a

heating

and

cooling cycle

oi _an

anhydrous sample

of GM1

yielded

the

following

results:

Tj°C) aji)

coni.

dparji) Smoi(i~)

1 20 54.0

pip')

23.4 77.8

2 0 54.5 23.2 77.1

3 50 58.1 _a 25.0 72.3

83 60.2 _a 26.1 69.8

s no

6 20 62.2

pip')

26.7 67.6

80 63.9 _o 27.5 65.8

In all these

experiments

the

small-angle

reflections _were

sharp

and the

spacings

consistent with _a I-D lattice. The

short-range

coniormation of the

hydrocarbon

chains

(p

_or

a)

_was

identified

according

to the _presence of _a

sharp

reflection _or of _a diffuse band in the

(4

to 4.5

1)~' region [16j. dp~r

^and

Smai

_are the

partial

thickness of the

hydrocarbon layer

and the

area-per-molecule

at the

polarlapolar

interface. Note that

thermodynamic equilibrium

_was

not attained in this

experiment:

at 20 ^°C the

repeat distance,

that _was 54

I

_{at the}

beginning

of the

experiment,

becomes 62.2

I

_{after the}

sample

is heated _to 110 ^°C and then

brought

back to 20 °C.

The

parameter qf

the

hexagonal phase

observed with GMT at c = 0.75 and 20 °C is 84.0

I,

the radius of the

hydrocarbon

_core is

Rp~r

= 24

I

_{and the}

area

Smoi

_per molecule at the

polar lapolar

interface is 75

i~.

_{Note that the value of}

_Smoi

_is

slightly larger

in the

hexagonal

than in the lamellar

phase,

in

keeping

with the

increasing hydration.

5.2. CUBIC PHASE

Q~~~.

The

spacing

ratios oi the observed reflections _are consistent with the cubic

aspect Q13.

4 out of the 5 space groups

compatible

with this

aspect

are ruled out

by

the electron

microscope

evidence

(Sect. 4).

The space group is thus

unambiguously

determined to be

Fm3m,

^{and the}

phase

called

Q~~~.

^The

analysis

of the electron

micrographs

also shows that the structure contains _one

type

^of

disjointed

elements. It _may thus be inferred that the structure consists of identical micelles of

type

^{I centred} at the

point (0, 0, 0)

and

that,

in

keeping

with the

symmetry

of this

point,

the

symmetry

of the micelles is

quasi-spherical (at

A

F(s)

B

a

D

E

o.i~.

F

x

0.02

0.04(I-I)

s

Fig

5 The _curves represent ^the structure factor

Fmod(8)

of the

spherical

model

[p(r)

= pa for

r < _ra,

p(r)

= pb for _ra < _r <

rb),

convoluted by _a Gaussian function

(Eq. (4)).

The dots represent the observed

amplitude

of the structure

factors;

the

signs

_are those of the function

Fmod(s~).

^The

bar indicates the limits of

uncertainty

of the weakest, unobserved reflections. The parameters ^{of the} model _were determined

by fitting

the

Fmod(s~)

to the structure factors

F(h)

The values _are:

experiment

A B D E F

ra(I)

29.3 26.2 23.4 20.0 20.3

rb(I)

_50.4 45.2 40.2 34.3 35.6

p~ -1.046 -0.270 -0.890 -0.276 0

pa +1.464 +0.811 +1.484 +0.827 +0.433

p2 (i~)

986 986 506 416 306

least in the

vicinity

of their

centre).

As _a consequence, the structure factors of the reflections should

sample

the

positive

and the

negative

^{lobes of the Fourier transform of the}

spherically symmetric

micelle. The trend observed in

Figure 5,

and

especially

the _presence of _a node in the

vicinity

of _{s =}

41a,

fulfill this

expectation. If,

_moreover, the structure of the micelle _can be

satisfactorily modelled,

then the _{test can} be refined and the

signs

of the reflections determined.

We

adopted

for this purpose a

two-density

model in which the electron

densiy p(r)

is

equal

to p~ for _r < ra and to pb for _r~ < r < rbi we smoothed this

object by convoluting

with _a Gaussian function. The structure factor takes the form:

Fmod(s)

₌

[(p~ pb)

4l

(x~)

+

pb4l (xb))

_exp

(-fl~s~) (4a)

4l(x)

=

3(sinx xcosx)/x~ (4b)

x~ = 2irr~s _{xb "}

2irrbs (4c)

Using

_a crude trial-and-error

procedure

we fitted this model to the observed

(F(h))

and thus determined _an

approximate

set of

parameters (r~,rb,

_{Pa, Pb,}

fl~).

^We

applied

this

procedure

to the 4

examples

of

phase

_Q~~~

(experiments A,B,D,E,

_see

legend

of

Fig. 5).

The excellent

agreement

^{of the}

experimental points

with the functions

Fmod(s)

and the reasonable values of the

parameters (ra,

_{rb, Pa, Pb,}

_fl~ prompted

_us to ascribe the

signs

of

Fmod(s)

to the observed

llf(h)11.

We _were thus

ready

to

compute

the electron

density

_maps. Three sections of the 3-D _maps

are

plotted

in

Figure

6. The

agreement

^with the model _is excellent: _a

deep quasi- spherically- symmetric trough

is

observed,

^centred at the

origin,

surrounded

by

_a

high density spherical

shell. In order to

inspect

^the

shape

of the low

density

_{core we}

computed

the

spherically averaged

_maps

[8j:

pjr)

_=<

pjr)

_>=

(I/I')Zhfjh)

sin

j27rrsh)/(27rrsh) (5)

These _{maps are}

plotted

in

Figure

7.

Knowing

the chemical

composition

of the

system,

^the

partial specific

volumes and the _pa- rameter of the cubic

cell,

_one can also determine the number

N~gg

^of

lipid

molecules _per micelle

(and

the radius

Rp~r

^{of the}

hydrocarbon

_core if the micelles _are

supposed

to be

spherical) (see Eqs. (2)

and

(3)),

this determination is

independent

of the

intensity

of the reflections. The

values of these

parameters

are

reported

in Table

IV;

_{an arrow} in

Figure

7 also

points

at the value of

R~ar.

^{Note the excellent}

agreement

^of

Rp~r

^{with the size of the low}

density trough

of the _map.

Note that in the

procedure adopted here,

and

commonly

used to solve and refine struc- tures, the initial model

plays

its role

only

at the very

beginning

of the

phasing

_process and

becomes obsolete _{as soon as an} electron

density

_map is available. This is the _reason

why

_we contented ourselves with the

qualitative consistency

^{of the model and did} not

attempt

to refine its

parameters.

5.3. CUBIC PHASE

Q~~~.

A

phase

of cubic

aspect Q8

_was observed with

GMT(acetyl).

In

the absence of electron

microscope

^{evidence the} structure

analysis

had to

rely

_on the

crystallo- graphic

^and on the chemical evidence. Six space groups are

compatible

with this cubic

aspect:

we

presumed,

ⁱⁿ

keeping

with

previous

studies of

lipid-water phases

_[7j that the

symmetry

^is the

highest compatible

with the cubic aspect. ^{We thus}

adopt

_{space group} Im3m

(Q~~~).

On the other hand the number of molecules _per micelle is very close in this

phase

and in

phase

q225 (experiments

E and F in Tab.

IV).

It _may also be noted

(Fig. 5)

that the

agreement

of the

(F(h))

with the continuous transform of _a

spherical

micelle is _as

good

in this _{cwe as}

Q Q

B

cJ cJ

o

~j:];.i'O"" ~'""' ^~~$~$'

~.~' _"" '~~. O'#O _'O

fl@fl

,;.,, ,[. _,,.,

©~@'.? ^~

.@flfi+ j;j,~,;,j~.j~

ffO~fO

.J '" I.,j: ..j.,

~

a O O

~ ~

@,

^,,

^{~, ~O ~}

°Q° ^ffi

_I,"

^lfi /~Q/~ F

e°o e°o _{j..:j tfl}

I"% n ~ ~n

U

U,.

~ ~

ioo

Fig.

6. Sections

through

the

origin

of the _map

Ap(r)

=

[p(r) (p)] / ([p(r) (p)]~))"~ ((pi

is the _average of the function

p(r)

_over the volume of the unit

cell), parallel

to the

planes [loo], [llo]

an

[III].

The maps were

computed

with the structure factors of Table III. The interval between the

isoden#ity

tines is

o.5;

the o and the

positive

lines _are

full,

the

negative

_{ones are} dotted.

«p(r)» A

,

B

D

E

F

20

40(I)

r

Fig

7.

Spherically averaged

_maps «

p(r)

» centred at the

origin (Eq. (5)).

The structure factors

are

given

_in Table III. The full lines

correspond

to the _maps

computed

with the observed

(and truncated)

structure factors, the dotted lines _to the _maps obtained

by extrapolating

the _structure factors with the function

Fmod(h) (Eq (4))

and to the parameters

reported

in the

legend

of

Figure

5. The _arrows

point

at the radius

Rp«r

of the virtual

paraffin

_core of the micelles,

supposed

to be

spherical (Tab. IV).

In

experiment

B

(dotted arrow)

the

glycerol

_is assumed to

partition entirely

in the

polar region.

in the

examples

of

phase Q~~~.

All these observations indicate that the structure is micellar.

We thus

proceeded

to

compute

the 3-D and the

spherically-averaged

_maps

(see Figs.

6 and

7) using

the _same

procedure

_as for

phase Q~~~.

The

consistency

with the results obtained with

phase

Q~~~ and the

agreement

^{of the}

spherically averaged

_map with the value of

Rpar (Fig. 7)

confirm that the structure is indeed

micellar,

and that the

shape

of the micelles is similar to that of the micelles of

phase Q~~~.

5.4. CUBIC PHASE

Q~~~.

^A

phase

of cubic

aspect Q5

^{has been}

reported

in a

variety

of

lipid-

water

systems,

^{in the low} concentration

region

of the

phase diagram,

between the

hexagonal

phase

^and the micellar solution

[8j.

^A combination of freeze-fracture electron

microscopy III]

and

X-ray scattering

studies has shown that the space group is Pm3n

(phase Q~~~)

and that the structure consists of two

types

^{of micelles} of

type I,

_one

quasi-spherical

in

shape,

the other somewhat flattened

[8j.

This structure, reminescent of _{a structure}

commonly

observed in water

clathrates,

_can be described in terms of the

space-filling packing

of _two

types

^of distorted 12- and 14-hedra

ii?]

and references

therein).

The number of14-hedra is twice _as

large

as that of the 12-hedra. In the _case of the

phase Q5

of GMT _two observations

strongly suggest

^that the structure is also micellar and _very similar to that of the

phase

Q~~~

Previously

described

in other systems. One is the average number of molecule per micelle

(namely

the number of molecules divided

by

the number

(8)

of micelles in _one unit

cell):

this

figure

is very close to the number of molecules per micelle of

phase

Q~~~

(experiments

B and C in Tab.

IV).

The other observation

(see

Tab.

II)

is that the

amplitude

of the reflections of

phase Q22~

of GMT is very similar to that of

phase

Q~~~ of PLPC. We thus conclude

that,

at least at the

resolution of _our

X-ray scattering study,

the structure of the

phases

Q~~~ of ^GMT and of PLPC

are

mathematically

similar to each other.

The presence in the structure of two

types

^{of micelles}

hinders,

in this _case, the

analysis

of the structure in terms of

quasi spherical micelles,

_as carried out in

phases

_Q~~~ and

Q~~~.

6. Discussion

The wealth of micellar cubic

phases

_seems to be _a

peculiar

feature of

gangliosides, although

3 cubic

phases

^whose

scattering

data _are consistent with the cubic aspects

5,

8 and 13 have also been

reported by

Mirkin

[18j

^{in the}

system, C12EO12-water (C12EO12

is _a

polyethylene glycol surfactant).

Phase Q~~~ ^is

widespread

in

lipid-water

_systems,

always

in the

vicinity

of the micellar

solution;

its structure, ^solved

by X-ray scattering

and freeze-fracture electron

microscope techniques,

has been shown to be micellar

[8,11j.

On the other hand

phase

_Q~~~

is _one of the most

widely quoted

cubic

phase

of

lipids;

its structure is

generally presented

as a

periodic

minimal surfaces of type ^P

(the popular "plumber's nightmare" cartoon),

_a

claim that still lacks firm

experimental support [7,17].

Phase Q~~~ ^is mentioned

by

Barois et al.

jig],

without further discussion of its structure, ⁱⁿ the ternary system

(didodecyl dimethyl

ammonium

bromide)-water-hexene,

_{over a narrow}

region

of the

phase diagram

and in the

vicinity

of the

phases

Q~~~ and

Q~3°.

Identifying

the

phases

and

laying

out the

(T, c)-dependent phase diagrams

have been

painful operations

^{in the}

systems

studied in this work. This

problem,

unusual in

lipid-water systems,

seems to be related to the _presence in _a small

region

of the

phase diagram

of _a

variety

of

phases,

all formed

by

the _same micelles

differently packed

in the different

phases,

and to the

presumably

small free _energy differences of the different

packing

modes. The contrast is indeed

striking

between the mild structural transformations involved in these cubic

/cubic phase

transitions and the dramatic

morphological upheaval

that takes

place

at other

phase

transitions

(lamellar/hexagonal, hexagonal /cubic, etc.).

Another _cause of the

thermodynamic equilibrium being

ill defined _may well be the _presence of electrical

charges,

that in other

systems

have been

found to

promote metastability (unpublished observations).

The _poor

knowledge

of the

phase diagrams

^{hindered in} this work the

implementation

of the pattern

recognition

that _we have advocated in the

study

of other

lipid _systems

_[8j and Refs

therein).

We thus had to resort to a different

strategy, heavily dependent

_upon the electron

microscope study. First,

we used the

X-ray scattering

data to

identify

the

phases

and determine their cubic aspect.

Second,

in the _case of

phases (Q~~~)

we relied _upon the electron

microscope study

to confirm the cubic

aspect,

to determine the _{space group} and to show that the _structure consists of identical and

quasi-spherically-symmetric

micelles centred