91av

Without liquid crystals there would be no life. Even the simplest single-celled
creature has an outer skin whose fabric is liquid crystalline. It is this
skin that forms the membrane separating the inner workings of the cell from
its surroundings. More complex life forms, such as human beings, use liquid
crystalline membranes for a vast variety of biological processes, for example,
transmitting nerve impulses and digesting fats.

You might be surprised to find out that cell membranes are liquid crystals.
In fact, the first recorded observations of the liquid crystalline phase
were of myelin, the material that coats nerve fibres. In 1855, a German
ophthalmologist called C. Mettenheimer was studying myelin under a polarising
microscope, and noted that, although it flowed like a liquid, it was brightly
coloured, or ‘birefringent’ like a crystal when viewed between crossed polarisers
(see ‘The fourth state of matter’, 91av, 4 May). It was not, however,
until much later that myelin was identified as a liquid crystalline material.

We now know that the liquid crystal structure of myelin consists of
regularly stacked layers of membranes, with each membrane consisting of
molecules that move around freely within it. In the direction of the stacked
membranes it behaves like a crystal, but in the plane of the membrane it
behaves like a liquid. Without exception, all biological membranes behave
simultaneously like a liquid and a solid, so liquid crystallinity must play
an important part in the function of cells. Over the past 20 years there
has been a surge of interest in biological liquid crystals. This has produced
new and exciting ideas about how liquid crystalline behaviour may influence
the way a cell membrane works.

Biological membranes are extremely complex and elaborate structures.
But in 1972, two Californian biologists S. Singer and Garth Nicholson developed
a simple, coherent picture called the fluid mosaic model of the cell membrane
(see Graphic above right). They regarded all biological membranes as consisting
of a two-dimensional fluid in which various globular proteins are embedded.
For simplicity, most of the research into the liquid crystal structure of
the membrane, however, ignores the proteins, and looks only at the idealised
two-dimensional fluid fabric. Research groups around the world, including
our own at Imperial College are now trying to go one step further and apply
our knowledge of these simplified systems to the behaviour of real biological
membranes. We are studying the complex relationships between their liquid
crystalline structures and their effect on the biochemical and physical
behaviour of a living cell.

The molecules that nature chooses as building blocks for the membrane
look like miniature tadpoles. They are made up of two dissimilar portions.
The part of the molecule that looks like the tadpole’s head is strongly
water-loving, or ‘hydrophilic’. The tail, being made up of a chain of carbon
and hydrogen atoms, is oily and, therefore, hates being in contact with
water, it is ‘hydrophobic’. Such molecules are called ‘amphiphiles’-a name
reflecting their two-sided nature. A second, equally important property
of these molecules, is that the hydrocarbon tail (or tails since many amphiphiles
possess more than one) is flexible. These two properties make the amphiphiles
quite different from the stiffer rod-like molecules used in liquid crystal
displays. The more complex structure of amphiphilic molecules means that
they possess an even richer diversity of liquid crystalline structures.

Molecules gather head to head

How do these structures form? In watery surroundings, amphiphilic molecules
will collect together so that the water-loving headgroups form a ‘skin’
that avoids exposing the oily chains to the water. This process is driven
by a force resulting from the hydrophobic tails not wanting to mix with
water-the hydrophobic effect. Amphiphiles that behave in this way are called
surfactants. Soaps and detergents are all surfactant molecules, and every
time you wash your hands or do the dishes liquid crystalline phases form
in the dirty water. One surfactant that is a typical biological amphiphile
is dioleoylphosphatidylcholine, or DOPC for short. DOPC is part of a subclass
of lipids called phospholipids, which are found everywhere in living systems.
They have a backbone of glycerol attached to which are the hydrophilic and
hydrophobic parts of the amphiphile. Two hydrocarbon chains are attached
to the middle and end positions along the backbone, and the headgroup, based
on a phosphate group, is attached to the remaining end of the glycerol.
In DOPC, the phosphate is attached to a choline headgroup and the two hydrocarbon
chains are 18 carbon atoms long.

If you take a dry lump of DOPC and gradually add water, the lipid readily
sucks up the moisture. If you continue to add water, there comes a point
when no more is absorbed and the excess water lies around in a puddle. At
this stage the lipid molecules have arranged themselves into sheets, or
‘lamellae’, in which all their headgroups are on the top and bottom surfaces
of the sheet facing the watery environment and the oily tails are tucked
into the centre of the sheet like a sandwich (see Figure 1a).

Because the lamella is made up of a pair of amphiphile layers placed
back to back, it is called a bilayer. The lamellae are regularly stacked
one above the other with a layer of water in between, rather like molecular
strudel pastry. This is essentially how nerve myelin looks. The overall
structure is ordered like a crystal, but within the bilayers there is no
order at all. In fact, if we attach fluorescent tags to some of the lipids
we can see them moving within the bilayers at speeds up to 1000 nanometres
per second. By contrast, there is only a very slow exchange of molecules
between bilayers.

The bilayer behaves like a liquid because the hydrocarbon tails are
flexible. At the temperatures that living cells operate, the chains are
free to wiggle about, so they collide with the chains of neighbouring molecules.
These collisions are sufficiently energetic to cause the molecules to wander
around in the sheet. But they are restrained from jumping out of the sheets,
because this would expose oil to water.

Unlike nerve myelin, most cells only have a single outer bilayer membrane.
We can form a model membrane with one bilayer from DOPC, by adding yet more
water. Eventually, the stacked bilayers break up and coalesce into small
sacs whose walls are a single bilayer-a primitive cell (see Figure 1b).
The bilayers break up because the thermal undulations that propagate along
them deform the lamellae. When the deformation is large enough, globules
‘bud’ off from the main layer.

Such globular protocells are, of course, very simple compared to a real
cell. However, it seems clear that they must have played a critical role
in the prebiological stages of the Earth’s evolution. The argument is quite
simple, and goes like this. A living cell has to be out of chemical equilibrium
with its surroundings; it is this lack of equilibrium that provides the
driving force that the cell needs to do the work to maintain and replicate
itself. The membrane is, therefore, central to maintaining this chemical
imbalance by selectively allowing molecules in and out of the cell. This,
in turn, means that the membrane must be capable of building itself, because
the cell cannot exist prior to the membrane.

Amphiphilic molecules such as DOPC are obvious candidates for cell membranes.
You can imagine them forming small sacs in the waters of prebiotic Earth.
Occasionally, biologically important molecules would get accidentally trapped
inside to give the first protocells. (Chemists artificial cells called liposomes
to encapsulate biologically active chemicals-see ‘Cells by design’, New
Scientist, 3 June 1989.) The liquid crystalline nature of the cell’s membrane
would also allow it to deform enough to break into two new cells without
the membrane falling apart. Large molecules embedded in the membrane-such
as proteins, which process many of the cells’ most important chemical activities-are
able to wander in the plane of the bilayer. This is essential if a dividing
cell is to retain the same set of proteins in each new cell.

This is the classical view of the importance of liquid crystalline properties
for cell membranes. Now, new research into biological liquid crystals is
giving us some deeper insights. This research started with the pioneering
work of Vittorio Luzzati and his colleagues in Paris in the 1960s on various
amphiphiles dissolved in water. They discovered that biological amphiphiles
can form a host of new liquid crystalline structures that are not layered
but are much more complicated.

One intriguing group of structures they discovered are the so-called
cubic phases which look a bit like sponges with holes and channels where
water can enter (see Figures 2a and 2b). Cubic phases have a topology in
which the lipid bilayer is completely interconnected, forming a single continuous
surface. The structure in Figure 2a looks like a bunch of connected pipes
and is sometimes called the ‘plumber’s nightmare’-although we think of it
more as a topologist’s dream. Another cubic phase is the double diamond
phase (see Figure 2b). Both these structures have two continuous but entirely
separate water channels separated by a somewhat contorted, oily bilayer.

The role of cubic phases

Another slightly less bizarre structure is the hexagonal phase, which
looks like Swiss rolls grouped into hexagonal piles. This time there is
only one layer of lipids, with the oily tails pointing outwards into an
oily phase. Running through the centre of the rolls are water channels (see
Figure 2c).

Do these bizarre phases have any biological importance? Certainly, they
continue to turn up in living systems. For example, in 1962 Walther Stoeckenius
and Vittorio Luzzati showed that phospholipids extracted from the human
brain is in the hexagonal phase. In 1965 B. Gunning found the plumber’s
nightmare cubic phase within the organelles of certain plant cells. In 1979
John Patton and Martin Carey at Harvard University observed the appearance
of what is almost certainly a cubic phase when they observed the digestion
of fats under the microscope. And within the past few years, Luzzati and
his team have also shown that cubic phases appear to form the basis of the
cell membranes of bacteria that live in hot sulphur springs.

Until the mid-1970s, the consensus was that these ‘non-lamellar’ phases
cropped up only in these rather unusual cases. Since then, a growing number
of researchers have found evidence to suggest that non-lamellar phases play
a profound role in regulating the activity and stability in cell membranes.

This hypothesis originated in two observations. The first was made by
Pieter Cullis and his colleagues at the University of British Columbia in
Canada, and Ben Kruijff at the University of Utrecht. They pointed out that
during dynamic processes such as cell division, a non-lamellar structure
formed just around the area in the membrane where the cell was splitting
with another cell. Something similar happened during cell fusion. The researchers
argued that studying how non-lamellar phases form should, therefore, help
us to understand division and fusion in real cells. The second, related
observation is that a real biomembrane contains a wide range of lipids,
of which many-often more than half-form non-lamellar phases when isolated
from the parent membrane.

Indeed, there must be a reason why Nature risks using these lipids in
membranes. After all, as Figure 2 shows, the hexagonal and cubic phases
are porous, and if the lipids in the membrane were to adopt these phases,
you would expect the cell’s innards to fall out. To understand the possible
role of these non-lamellar components in the membrane, we need to examine
their physics and chemistry a little more closely.

The structure of liquid crystalline phases arises from an interplay
between the hydrophobic effect and geometrical constraints on the way the
molecules can pack themselves. The hydrophilic headgroups must spread along
the interface between the water region and their hydrocarbon tails, while
ensuring that there are no gaps between the tails. The preferred structure
will be the one that optimises the packing of the interfacial and hydrocarbon
regions.

Frustrated liquid crystals

This packing is strongly dependent on the chemical structure of the
lipids. Take the example of dioleoylphosphatidylethanolamine (DOPE), which
is identical to DOPC except that the choline headgroup is replaced by ethanolamine.
Ethanolamine has a reduced attraction to water, so fewer water molecules
gather around the headgroup. This reduces the effective size of the headgroup
compared to the hydrocarbon tails. Because the headgroups occupy less space
than the hydrocarbon tails, the two outer sides of the bilayer try to curl
away from the inner hydrocarbon region, producing a ‘frustrated’ state in
which each monolayer is facing in opposite directions (see Figure 3). The
compromise solution for DOPE is to adopt the rolls of the hexagonal phase,
where each monolayer curves tightly round a water channel with the hydrocarbon
tails spread out on the outside.

The molecule monoolein has a single chain of 18 carbon atoms and a glycerol
headgroup. In monoolein, the glycerol headgroup is also less hydrophilic
than that in DOPC, so again each side of the bilayer wants to curve towards
the water, but the single hydrocarbon chains take up less room than the
double chains of DOPE. This time, the physical frustration is resolved by
regions of the bilayer buckling into a saddle shape . In forming these saddle-like
regions, the bilayer must have holes in it. So to ensure that no hydrocarbon
tails are exposed to water, it adopts the double diamond phase built of
interconnecting bilayer tubes.

Non-lamellar phases arise not only because of differences in chemical
structure but also because of changes in the environment of the lipid. For
example, if we cool DOPE from, say 25 °C to 5 °C, its structure
changes from the hexagonal phase to the lamellar phase. This is mainly because
the hydrocarbon tails wiggle about less so that the area occupied by the
headgroup and the tails becomes more equal. This means that the volume occupied
by the headgroup and tails is more equal. There is, therefore, less desire
for each bilayer to curve. Other environmental factors such as pressure,
acidity, and salts and other molecules dissolved in the lipid phase, can
cause structural changes.

The presence of high proportions of lipids akin to DOPE and monoolein
in cell membranes must make the cells extremely susceptible to changes in
their local environment. However, there is a lot of evidence to show that
cells are able to remain stable when their local environment changes, by
adjusting the lipid composition of their membranes. One of the best pieces
of evidence for this was published recently by a group of Swedish researchers
led by Goran Lindblom at Umea University, who grew some primitive bacteria,
Acholeplasma laidlawii, at various temperatures. When they extracted the
membrane bilayer manufactured by the bacteria, they consistently found that
the composition of the membrane adjusted so that the temperature at which
it became non-lamellar-and therefore fell apart-was just a few degrees above
the temperature at which the bacteria were grown. It seems that no matter
how harsh the conditions in which the bacterial cells were grown, the composition
of lipids in the cell membrane was adapted so that the membrane remained
stable but, at the same time, was perilously close to the point of disintegration.

In 1985 Sol Gruner of Princeton University proposed a model of how cells
could stabilise the membrane in the presence of lipids that form non-lamellar
phases. He pointed out that including molecules similar to DOPE and monoolein
in the lamellae leads to stresses across the bilayer wall because they try
to make phases with curved surfaces instead of a simple lamellar structure.
A cell, in placing itself in a state close to the membrane changing its
phase, will cause any protein molecules embedded in the membrane to experience
the build-up of internal stresses across the bilayer. This is liable to
affect its biochemical activity.

Let us consider a cell in which membrane proteins regulate the production
of a specific lipid, you can see how the cell might control the lipid composition
of the membrane by negative feedback. Imagine a really simple cell membrane
made of DOPE and DOPC, with an embedded protein that regulates the production
of DOPE. When the protein is ‘switched’ on, DOPE is produced at full pelt.
As more DOPE is produced, the stresses due to the DOPE wanting to change
phase build up in the membrane, and eventually cause the protein to switch
off. Less DOPE is then made, the stresses reduce, and so once again the
protein switches on.

We can also conclude that by having membranes with structures close
to a phase transition, cells are poised ready to participate in dynamic
processes, in which they meet and interact or divide. As long as the cell’s
local environment changes gradually, the cell wall will survive by the self-regulating
mechanism we have already described. If, however, the environmental changes
are rapid, then the lipids change phase and the bilayer will rupture. This
might happen when two cells fuse, as in sexual reproduction. A channel forms
between the two bilayers at the moment of fusion which is very similar to
the channels found in cubic phases. It is clear that we are only at the
beginning of the exciting quest to understand the subtle strategies that
nature has adapted to exploit the unique properties of liquid crystals.

Richard Templer is Royal Society Research Fellow in the chemistry department
at Imperial College, London. John Seddon is a lecturer in the chemistry
department at the University of Southampton.

* * *

Minimal surfaces and the plumber’s nightmare

Cubic phases such as the plumber’s nightmare will form out of the lamellar
phase if the system’s temperature is raised. Our understanding of how this
happens is still in its infancy. For example, we cannot yet answer simple
questions such as why, under these conditions, the cubic phase appears in
preference to the hexagonal phase. However, a mathematical approach which
describes the geometry of the cubic phases has made great progress over
the past five years, and we are on the verge of being able to make quantitative
predictions about transitions between lamellar and cubic phases.

The mathematics we use is the differential geometry developed a century
ago by the German mathematician Hermann Schwarz. He worked on the problems
of constructing ‘minimal surfaces’ which could be used to form smooth and
continuous repeating structures. Minimal surfaces will form when a wire
loop is dipped in soapy water. The soap film forms the smallest surface
area so as to minimise the energy arising from the film’s total surface
tension.

The conditions for periodically repeating minimal surfaces are more
complex and give rise to some fascinating properties. The simplest property
is that the surface divides space into two equal volumes, and minimises
the area of the surface. This property led L. E. Scriven, a chemical engineer
from the University of Minnesota, in a great imaginative leap, to propose
that such minimal surfaces might be the basis for the structure of liquid
crystalline cubic phases.

A more important and more perplexing property is that these surfaces
have zero mean curvature at all points on their surface. We can find the
curvature at a point P on a surface, by drawing a circle as shown in Figure
4a. The curvature is then defined as 1/r where r is the circle’s radius.
A flat surface, where r is infinite, will have zero curvature. Because a
surface is two-dimensional, you can obtain a mean curvature at a point by
finding the minimum and maximum curvatures at that point and calculating
their mean. In Figure 4b, the mean curvature is zero, because the minimum
and maximum curvatures are equal in magnitude but opposite in sign. So all
points on a minimal surface are either flat or look like this saddle surface.

The simplest example of a periodic minimal surface is made by connecting
up Schwarz’s P-surface (see the Graphic below). This provides the skeletal
frame for the plumber’s nightmare cubic phase. We can think of the phase
as consisting of a continuous surfactant bilayer, ‘draped’ upon the periodic
surface. To be more precise, the minimal surface is where the ends of the
hydrocarbon chains from the back-to-back monolayers lie. Another property
of the minimal surface is that a parallel surface some distance away from
it will always have a smaller surface area. It is this lowering of surface
area as we move away from the hydrocarbon region that solves the problem
of curvature frustration in monoolein.