Detergents, Micelles and Membranes.
Self-Assembly of Amphiphiles
The hydrophobic aspect of lipids and detergents limits their solubility, as
monomers, in water. However, above their true solubility limit, the need
to minimize the surface area of interaction between water and the
hydrophobic parts leads to the formation of small, aggregated structures,
or micelles, which remain fully dispersed in solution. The point at which
this happens is called the critical micelle concentration, or CMC.
Above this the concentration of monomers stays almost constant and
further added material forms more micelles.
The onset of micelle formation is essentially a phase transition, i.e., it is
cooperative, and the sharpness of the transition reflects the cooperativity
inherent in the process of micelle formation:
N lipid (N monomer) ↔ lipidN (one micelle)
Emulsions form when amphiphilic molecules
reduce the oil-water tension
Salad dressing (vinaigrette) separates into oil and water, despite the superficial increase
in order (decrease in entropy) that such separation entails. Water molecules are
attracted to oil molecules, but not as much as they are attracted to one another: the
oil-water interface disrupts the network of hydrogen bonds, so droplets of water
coalesce (get together, unify) to reduce their total surface area.
Mayonnaise, too, is mostly a mixture of oil and water; yet it does not separate. What is
the difference?
One difference is that mayonnaise contains a small quantity of egg. An egg is a
complicated system, including many large and small molecules. But even very
simple, pure substances can stabilize suspensions of tiny oil droplets in water for
long periods. Such substances are generically called emulsifiers or surfactants; a
suspension stabilized in this way is called an emulsion. Particularly important are a
class of simple molecules called detergents, and the more elaborate phospholipids
found in cell membranes.
Oil-water interface
a) An oil-water interface stabilized by addition of a small amount of
surfactant (detergent). Some surfactant molecules are dissolved in the
bulk oil or water region, but most migrate to the boundary as shown in
the inset.
b) An oil-water emulsion stabilized by surfactant: the situation is the
same as (a), but for a finite droplet of oil.
Two classes of amphiphiles
a) Structure of sodium dodecyl sulfate (SDS), a strong detergent. A nonpolar,
hydrophobic tail (left) is chemically linked to a polar, hydrophilic head (right). In
solution, the Na+ ion dissociates. Molecules from this class form micelles.
b) Structure of a generic phosphatidyl-choline, a class of phospholipid molecule. Two
hydrophobic tails (left) are chemically linked to a hydrophilic head (right). Molecules
from this class form bilayers.
The transition is very sharp for some materials, and is similar to the phase separation
seen for immiscible liquids, or at the solubility limit for any solute. At low
concentrations, the material is soluble and the chemical potential (µi) of the solute (e.g.,
monomers of detergent) increases as more is added. At some point, however, the
chemical potential becomes equal to that of the compound in the pure phase (µi*),
whatever that might be (solid, separated liquid, micelle, etc).
µ = µio + RT ln ci = µi*
Since the chemical potential (free energy per mole) of a pure phase is a constant, the
chemical potential in solution must now also remain constant and any further material
added creates a separate, pure phase. This represents the solubility limit - or the critical
micelle concentration, in the case of amphiphiles.
For amphiphiles, reaching the solubility limit is not straightforwardly solved by a
separation of two bulk phases, as for a simple hydrocarbon and water. The polar
headgroups demand some solvation interactions that are not provided by an apolar
environment such as the hydrophobic tails, and dragging water in to the detergent bulk
phase would be costly. Thus, the phase that detergents and other amphiphiles withdraw
to is a microscopic one, the micelle, that satisfies the needs of the polar heads and the
apolar tails, simultaneously.
Formation of Micelles (Aggregates) from Monomers
(simplified model)
Apply the Mass Action rule to the reaction
(N monomers) ↔ (one aggregate).
N is an unknown parameter, which we will choose to fit the data. It will
turn out to be just a few dozen, justifying our picture of micelles as
objects intermediate in scale between molecules and the macroscopic
world. The concentration c1 of free monomers in solution is related to
that of micelles, cN, by
cN/(c1)N = Keq,
(1)
where Keq is a second unknown parameter of the model. The total
concentration of all monomers is then
ctot = c1 + N·cN = c1·(1 + N·Keq·(c1)N-1).
(2)
This is the relation between the total number of amphiphilic molecules in
solution, ctot and the number that remained unaggregated, c1.
It's more meaningful to express the answer not in terms of Keq, but in
terms of the critical micelle concentration (CMC), ccmc. By definition,
ccmc is the value of ctot at which half the monomers are free and half are
assembled into micelles. In other words, c1 = N·cN = ½·ccmc. Substituting
into Eq. (1) gives
 1
 1

 ccmc     ccmc 

 2N
 2

N
 K eq
We now substitute Keq into Eq. (2), finding
  2c
ctot  c1  1   1
  ccmc




N 1 



(3)
Once we have chosen values for the parameters N and ccmc, we can solve
Eq. (3) to get c1 in terms of the total amount of surfactant ctot stirred into
the solution. Although this equation has no simple analytical solution, we
can understand its limiting behavior.
At low concentrations, ctot << ccmc, the first term dominates and we get
ctot ≈ c1: Essentially all the surfactants are loners. But well above the
CMC, the second term dominates and we instead get ctot ≈ N·cN; now
essentially all the surfactants are accounted for by the micelles.
Osmotic pressure
Historical background. As early as 1913, J. McBain had deduced the existence of
well-defined micelles from his quantitative study of the physical properties of soap
solutions. One of McBain's arguments went as follows.
We know the total number of molecules in a solution just by measuring how much soap
we put in and checking that none of it precipitates out of solution. But we can
independently measure how many independently moving objects the solution contains,
by measuring its osmotic pressure and using the van't Hoff relation. For very dilute
solutions, McBain and others found that the osmotic pressure faithfully tracked the total
number of amphiphilic ions, just as it would for an ordinary salt like KCl. But the
similarity ended at a well-defined point, the critical micelle concentration (CMC).
Beyond this concentration, the ratio of independently moving objects to all ions
dropped sharply. The CMC typically decreases at higher temperature, thus pointing to
the role of the hydrophobic interaction in driving the aggregation (self-assemble).
McBain's results were not immediately accepted. But eventually, several physical
quantities (e.g. electrical conductivity) were all found to undergo sharp changes at the
same crtitical concentration as that for the osmotic pressure, and the chemical
community agreed that he was right.
Calculation of the osmotic pressure. The contribution from the
dissociated Na+ ions is simply ctot.kBT, as usual. The contribution from
the amphiphiles is, however, more sophisticated with one key difference:
each micelle counts as just one object, not as N objects. Thus, the
contribution of the amphiphiles to the osmotic pressure consists of the
monomers (c1) and the micelles (cN). The osmotic pressure relative to the
value 2·ctot·kBT of an ordinary salt like NaCl:
N 1 

 1  1  2c1 


N  ccmc 
ctot  (c1  c N ) 1 

pos (rel ) 
 1 
N 1 
2  ctot
2
 2c 
1   1 


c
 cmc 


(4)
where cN is expressed from Eq. (2) and ctot. from Eq. (3). To use this
formula, solve Eq. (3) numerically for c1 as a function of ctot. Then
substitute into Eq. (4) to get the relative osmotic activity in terms of the
total concentration of amphiphiles. Looking at the experimental data, we
see that we must take ccmc to be around 1 mM; the fit shown used
ccmc = 1.4 mM. Two curves are shown: the best fit (solid line) used N =
30, whereas the poor fit of the dashed line shows that N is greater than 5.
Osmotic pressure
vs. concentrations
of micelle-forming
surfactant
(potassium oleate)
and ordinary salt
(KCl)
Conclusion
We have obtained a qualitative explanation of the very sudden
onset of micelle formation by the hypothesis that geometrical
packing considerations select a narrow distribution of "best"
micelle size N. Indeed, the sharpness of the micelle transition
could not be explained at all if stable aggregates of two, three,
four,... monomers could form as intermediates to full micelles.
In other words, many monomers must cooperate to create a
micelle, and this cooperativity sharpens the transition,
mitigating the effects of random thermal motion. Without
cooperativity, the curve would fall gradually, not suddenly.
Micelle Shape and Bilayer Formation
Micelle structures in water (with one exception) have the polar
headgroups on the outside and the hydrocarbon tails on the inside. The
shapes adopted to achieve this are varied, but fall into the categories of
ellipsoids of revolution (prolate and oblate), cylinders or disks, and
bilayer sheets. The micelle shape can be understood in terms of an
effective “packing shape” of the molecules, which reflects the relative
strengths of interaction between the headgroups and between the tails.
1) Amphiphiles with one tail per headgroup - detergents, soaps and
lysolipids (lipids with one fatty acid missing) – are generally “cone
shaped”, with large repulsion between headgroups, relative to the
tendency for the tails to aggregate, driven by the hydrophobic effect.
They form spheroids or ellipsoids, and sometimes cylinders, which can
be thought of as prolate ellipses with an infinite axial ratio.
Spheres
A sodium dodecyl sulfate
(SDS) micelle, drawn to
scale, with 60 SDS
molecules. The
hydrocarbon chains
pack at liquid hydrocarbon
density in the core, where
they are almost as
disordered as in the bulk
liquid state. Each of the 5
spherical shells (dotted
lines) contain the correct
number of chain segments
to ensure even packing
density throughout, and all
segments spend an
appreciable proportion of
the time near the micelle
surface. Thus, although the
core is devoid of water,
each segment of each chain
samples the hydrophilic
environment. (From:
Israelachvili, 1992).
Cylinders (end caps omitted)
2) Amphiphiles with two tails per headgroup - including natural lipids
- generally form bilayer sheets or, occasionally, disks (exaggerated oblate
ellipses). Bilayers then close up into vesicles to avoid exposure of the
hydrocarbon tails to water at the edges (edge effects). The energy
involved in bending the bilayer is the result of several forces acting in the
plane of the membrane, including headgroup repulsions and interchain
pressure, and the interfacial pressure or surface tension, which tends to
minimize the area of the interface between two phases. The curvature of
the bilayer requires energy, but this is recovered from the hydrophobic
free energy upon sealing up the bilayer edges.
Bilayer
Lecithin (PC) bilayer in the liquid crystalline state, drawn to scale, showing the forces
that determine it and its properties. The lipids diffuse rapidly in the plane of the
membrane, covering about 1 µm in 1 s. They also cross the bilayer (flip-flop), and
exchange with lipids in solution, but much more slowly – on the order of hours (c.f., the
exchange time for a surfactant (detergent) in a micelle is 10-5 - 10-3 s).
A rare micelle form - but indicative of the importance of the balance
between head and tail influences in natural membranes - is the
hexagonal HII phase. This is formed by lipids with small effective
headgroup areas, or large relative tail sizes (width and volume), which
gives them an effective “inverted cone” shape. The small effective size of
the headgroups may be due to small physical size and weak interaction as in the glycolipid, monogalactosyl diglyceride (MGDG) - or it may be
due to attractive forces between them, e.g., by hydrogen bonding in
phosphatidyl ethanolamine (PE), or cationic cross-linking between
negatively charged lipids, as in cardiolipin (diphosphatidyl glycerol,
DPG) or phosphatidyl serine (PS). This leads to salt and pH control of
the shape factor and, hence, membrane curvature.
The HII structure is an inverted micelle, in which the headgroups interact
closely on the inside, with the relatively bulky but hydrophobic tails on
the outside. The unfavorable aspect of the hydrophobic effect causes
aggregation of a large number of the cylindrical, hexagonal micelles,
thereby minimizing the surface area.
Hexagonal (HII) phase
The HII phase is probably not found in
biological membranes, but the inverted cone
shape of PE and other lipids (see below) is
important in allowing and controlling
curvature of natural membranes. These lipids
more favorably occupy the bilayer leaflet on
the inside of a curve. Similarly, MGDG is
thought to be especially important in the very
tight curvature of chloroplast thylakoids, the
functional membranes of plant photosynthetic
energy conversion.
The Principle of Opposing Forces
Quantitation of the opposing forces governing phase separation of amphiphiles requires
estimation of the repulsion between headgroups and of the apparent attraction between
the hydrocarbon tails. Even though it is a fictitious force, the latter is actually more
readily quantified as it is manifested as the surface or interfacial tension between the
hydrocarbon phase and water. This can be measured directly, e.g. for monolayers in a
Langmuir trough, and can also be estimated from empirical relationships such as
between hydrocarbon length or surface area and the free energy of transfer from water
to oil, etc. By contrast, the repulsion between headgroups is complex. Although it is
essentially electrostatic in nature, it includes large effects of solvation shells and
competition between heads for solvent.
The problem is approached semi-quantitatively, by recognizing that there is an optimum
surface area per headgroup, a molecular volume, v, and an effective length, lC, for the
hydrocarbon tails. The optimum area per headgroup, a0, is determined by the maximum
separation (to minimize repulsive interactions between polar headgroups) that will not
allow water molecules to slip between and enter the hydrocarbon region. It is
determined empirically from the results of the analysis, but can be intuitively guessed
from the chemical nature of the headgroup.
The effective length is usually taken to be close to (and obviously not
more than) the maximum length of an extended chain1:
lC < lmax ≈ 1.54 + 1.265 nC
Å
The volume of the chains is taken directly from the molar volumes of
liquid hydrocarbons:
v = 27.4 + 26.9 nC Å3
We can now categorize different amphiphiles according to their
geometric properties, indicated by the dimensionless packing parameter
or molecular shape factor, the ratio of the actual molecular volume to
the volume of a cylinder with the same area per headgroup and same
chain length, v/a0·lC. For a cylinder, v/a0·lC = 1; for a cone, with the fat
part at the headgroup, v/a0·lC = 1/3; and for an inverted cone, v/a0·lC > 1.
1
The value of nC is usually modified (decreased) from the actual number of carbons
because it is considered that at least the first one or two, attached to the headgroup, are
in substantial contact with the solvent and therefore do not contribute to the difference
in free energy between the monomer dispersion and the micelle phase.
The rough order of the shape factor can be determined by comparing the experimental
aggregation number, N - the number of molecules per micelle - with that expected for
certain simple geometric shapes and the values of v and lmax calculated from nC, as
above. Most simply we can calculate what we expect for a sphere, with diameter =
2·lmax, and then see how the estimated aggregation number agrees with the experimental
value. For maximal packing of the hydrocarbon tails in a micelle, with minimal
exposure of the tails to the aqueous phase, at least some of the tails must be fully
extended (see Fig. above) and the radius of a spherical micelle is expected to be close to
lmax. For other geometries, the constraint of no voids in the interior of the micelle
demands that at least one dimension must correspond to this minimum measurement,
e.g., in an ellipsoid, a minor axis of 2·lmax. This is consistent with each molecule
occupying a fixed volume and with the notion that the headgroups cannot be buried in
the hydrocarbon phase.
The aggregation number for a sphere (diameter = 2·lmax) is the minimum possible for a
given lmax (just as the volume is minimum), and experimental values much greater than
the spherical prediction indicate a non-spherical micelle shape. This, in turn, can be
interpreted as the result of the balance of forces acting on the headgroups and tails or,
equivalently, a specific molecular shape factor. A spherical shape implies strong
curvature due to strong headgroup repulsion, or a highly conical molecular shape factor
(<0.5); a highly non-spherical shape implies a correspondingly stronger driving force
for tail aggregation - a less conical molecular shape factor.
Most biological lipids have shape factors close to 1, which favors their
packing in-line. However, a single line or layer would expose the ends of
the tails to the water, so a bilayer sheet is formed and edge effects are
avoided by closing the sheet on itself to form closed vesicles.
The precise value of the shape factor for different lipids is determined by
second order effects, including (i) specific headgroup interactions such as
H-bonding (e.g., PE) or ionic bridging (e.g., DPG), and (ii) specific
chain-chain interactions (as in incomplete fluidization.)2. The variability
in shape factors is crucial in allowing the flexibility of membrane shapes.
Thus, the sharp curvature characteristic of certain (many) natural
membranes requires different shape factors for lipids in the inside and
outside leaflets of the bilayer. For this reason, it is not surprising that the
dominant lipids in animal membranes are PC (v/a0·lC ≈ 1) and PE
(v/a0·lC > 1). In chloroplasts and some other plant membranes, the
equivalent pair are digalactosyl diglyceride, DGDG, and monogalactosyl
diglyceride, MGDG.
This can give rise to “lateral phase separations” in which specific lipids aggregate into patches –
or “rafts” - in the membrane, sometimes forming gel-like regions in an otherwise liquid
membrane - or vice versa.
2
The hydrocarbon interiors of both micelles and bilayers are normally in their fluid state.
Repulsive headgroup forces and attractive interfacial forces determine the optimum headgroup
area, a0, at which the surface free energy per molecule is at a minimum. The chain volume, v, and
chain length, lc, set limits on how the fluid chains pack together, on average, inside an aggregate,
depending on the magnitude of the shape factor, v/(a0·lc).
Mean (dynamic) packing shapes of lipids and the structures they form
Mean (dynamic) packing shapes of lipids and the structures they form
(cont.)
Self-Assembly in Cells
Bilayers self-assemble from two-tailed amphiphiles
Puzzle: How can amphiphilic molecules satisfy their hydrophobic tails in a pure water
environment? The answer is that they can assemble into sphere. This solution,
however, may not always be available due to geometrical constraints.
Suppose that N amphiphiles pack into a spherical micelle of radius R. Find two relations
between ahead, vtail, R and N:
4 R3
N  vtail 
,
4R 2  N  ahead
3
vtail
R
Combine these into a single relation:

ahead
3
Suppose instead that amphiphiles pack into a planar bilayer of thicknes 2d. Find relation
between ahead, vtail, and d:
a
d  v
head
tail
Although some molecules, like SDS, may be comfortable with the spherical
arrangement, it doesn’t work for two-tailed molecules, like the
phosphatidylcholines.
Schematic figure of a biological membrane. The lipid content of different membranes
varies from as little as 25% up to 80% by weight. At highly curved regions the outer
convex face contains mainly cone-shaped lipds while the inner concave face has more
wedge-shaped lipids. Stressed regions may even adopt a locally non-bilayer structure.
Reasons why
the phospholipid bilayer membrane is the most
ubiquitous architectural component of cells
1) The self-assembly of two-chain phospholipids (like PC) into bilayers is even more
avid than that of one-chain surfactants (like SDS) into micelles. The reason is simply
that the hydrophobic cost of exposing two chains to water is twice as great as that
for one chain. This free energy cost ε enters the equilibrium constant and hence the
CMC, a measure of the chemical drive to self-assembly, via its exponential. There’s
a big difference between exp(-ε/kBT) and exp(-2·ε/kBT), so the CMC for
phospholipid formation is tiny. Membranes resist dissolving even in environments
with extremely low phospholipid concentration.
2) Phospholipid membranes automatically form closed bags because any edge to the
planar structure would expose the hydrocarbon chains to the surrounding water.
Such bags, or bilayer vesicles, can be almost unlimited in extent; it is
straightforward to make „giant” vesicles of radius 10 μm, the size of eukaryotic
cells. This is many thousands of times larger than the thickness of the membrane;
giant vesicles are self-assembled structures composed of tens of millions of
individual phospholipid molecules.
3) Phospholipids are not particularly exotic or complex molecules. They
are relatively easy for a cell to synthesize, and phospholipid-like
molecules could even have arisen abiotically (from nonliving processes)
as a step toward the origin of life. In fact, bilayer membranes are even
formed by phospholipid-like molecules that fall to Earth in meteorites.
4) The geometry of phospholipids limits the membrane thickness. This
thickness in turn dictates the permeability of bilayer membranes, their
electrical capacitance, and even their basic mechanical properties.
Choosing the chain length that gives a membrane thickness of a few
nanometers turns out to give useful values for all these membrane
properties; that’s the value Nature has in fact chosen. For example, the
permeability to charged solutes (ions) is very low, because the partition
coefficient of such molecules in oil is low. Thus, bilayer membranes are
thin, tough partitions, scarcely permeable to ions.
5) Bilayer membranes are fluid. No specific chemical bond connects any
phospholipid molecule to any other, just the generic dislike of water for
the hydrophobic tails. Thus, the molecules are free to diffuse around for
membrane-bound cells to change their shape, as, for example, when an
amoeba crawls or a red blodd cell squeezes through a capillary.
6) Again because of the nonspecific nature of the hydrophobic
interaction, membranes readily accept embedded objects; hence they can
serve as the doorway to cells and even as the factory floors inside them.
An object intended to poke through the membrane simply needs to be
designed with two hydrophilic ends and a hydrophobic waist; entropic
forces then automatically take care of inserting it into a nearby
membrane. Understanding this principle also immediately gives us a
technological bonus: a technique to isolate membrane-bound proteins.
Solubilization of integral membrane proteins by
detergent
Mechanical Properties of Membranes:
Bending Stiffness
Flat membrane
The bilayer membrane prefers to be flat, because this state has the lowest
free energy. As the layers are mirror images of each other, there is no
tendency to bend to one side or the other. Because each layer is fluid,
there is no memory of any previous bent configuration (in contrast to
a small patch snipped from a bicycle tire, which remains curved). In
short, although it's not impossible to deform a bilayer to a bent shape
(indeed, it must so deform in order to close onto itself and form a
bag), still bending will entail some free energy cost.
Strictly speaking, the argument for minimum free energy state of planar
surface applies to artificial, pure lipid bilayers only. Real plasma
membranes have significant compositional differences between their
two layers, with a corresponding spontaneous tendency to bend in one
direction.
Energetic cost to bend the planar membrane
Bending a bilayer involves a combination of stretching the outer layer
and squeezing the inner layer. In addition, the bilayer's elasticity also
contains contributions from deformation of the tails (not just the heads)
of the amphiphilic molecules. These elaborations do not change the
general form of the bending elasticity energy established for much more
restricted conditions (only the stretching of the heads of the amphiphilic
molecules in the membrane is taking into account).
With bending one side of the membranes, the polar heads get streched
apart, eventually admitting water into the nonpolar core. In other words,
each polar head group normally occupies a particular geometrical area
ahead; a deviation Δa from this preferred value will incur some free
energy cost. For small (Δa << ahead) bends (Hooke relation):
elastic energy/phospholipid molecule = ½·k(Δa)2
Bending of bilayer membrane
The value of the spring constant, k is an intrinsic property of the
membrane. Suppose that we wrap a small patch of membrane around a
cylinder of radius R much bigger than the membrane's thickness d.
Bending the membrane requires that we stretch the outer layer by
ahead  d
a 
R
Thus, we expect a bending energy cost per head group of the form
½·k(ahead·d/R)2. Because the layer is double, the number of such head
groups per area is 2/ahead. The (specific) free energy cost to bend a
bilayer membrane into a cylinder of radius R:
free energy cost/unit area = ½·κ/R2,
where κ is an intrinsic parameter of the membrane, the bend stiffness (its
dimension is energy):
κ = 2·k·d2·ahead
The cost to bend the membrane into a spherical patch of radius R is four
times as great as that for cylinder, because each head group gets stretched
in two directions, so Δa is twice as great. Thus bending the layer into a
spherical shape with radius of curvature R costs
free energy per unit area = 2·κ/R2.
The total bending energy to wrap a membrane into a spherical vesicle is
total free energy cost (flat → sphere) = 8πκ
This is already an important result: The total bending energy of a sphere
is independent of the sphere’s radius.
Estimate of the numerical value of κ.
Consider a single layer at an oil-water interface. Bending the layer into a
spherical bulge, with radius of curvature R comparable to the length ltail
of the hydrocarbon tails, will spread the heads apart and expose the tails
to water. Such a large distortion will incur a hydrophobic free energy
cost per unit area, Σ, comparable to that at an oil-water interface (surface
tension). The corresponding cost for a bilayer in water will be roughly
twice this value.
We thus have two different expressions for the bending energy of a
spherical patch of bilayer. Equating these expressions
2κ/(ltail)2 = 2·Σ.
lets us estimate κ. Taking typical values: Σ ≈ 0.05 J/m2 and ltail ≈ 1.3 nm
we get κ ≈ 0.8 .10-19 J. Our estimate is crude, but it’s not too far from the
measured value κ = 0.6 .10-19 J = 15· kBT for dimyristoyl phosphatidylcholine (DMPC). The total bending energy 8πκ of a spherical vesicle of
Lessons from the measured value of κ
Suppose that we take a flat membrane of area A and impose on it a
corrugated (washboard) shape, alternating cylindrical segments of radius
R. The free energy cost of this configuration is ½·κA/R2.
Taking A to be 1000 μm2, a value corresponding to a typical 10 μm cell,
we find that the bending energy cost greatly exceeds kBT for any value of
R under 10 μm. Thus, the stiffness of phospholipid bilayer membranes
has been engineered to prevent spontaneous corrugation by thermal
fluctuations.
At the same time, the bending energy needed for gross, overall shape
changes (e.g. those needed for cell crawling) is only a few hundred times
kBT, so such changes require the expenditure of only a few dozen ATP
molecules. (The free energy change of ATP hydrolysis under normal cell
conditions is ΔG = -20 kBT/molecule. The standard free energy change is
ΔG’o = -12.4 kBT/molecule, but the cells are far from standard
conditions.) Phospholipid bilayer membrane stiffness is thus in just the
right range to be biologically useful.
Lessons from the measured value of κ
Not only are cells themselves surrounded by a bilayer plasma membrane
(cell walls). Many of the organelles inside cells are separate
compartments, partitioned from the rest by a bilayer (inner membranes).
- Products synthesized in one part of the cell (the „factory”) are also
shipped to their destinations in special-purpose transport containers,
themselves bilayer vesicles.
- Incoming complex food molecules awaiting digestion to simpler forms
are held in still other vesicles.
- The activation of one neuron by another across a synapse involves the
release of neurotransmitters, which are stored in bilayer vesicles until
needed.
Self-assembled bilayers are ubiquitous in cells.