Critical mixing in monomolecular films : pressure-composition phase diagram of a two-dimensional binary mixture

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Critical mixing in monomolecular films :

pressure-composition phase diagram of a

two-dimensional binary mixture

C.L. Hirshfeld, M. Seul

To cite this version:

Critical

_mixing

in

monomolecular films :

_{pressure-composition}

phase diagram

of

a

two-dimensional

binary

mixture

C. L. Hirshfeld

₍₁₎

and M. Seul

₍₂₎

(1)

Williams

_College,

_{Williamstown, MA, 01267,} U.S.A.

(2)

AT&T Bell Laboratories,

Murray

Hill, NJ _07974, U.S.A.

(Reçu le 17 novembre 1989, révisé le 7

_février

1990,

accepté

le 2

_avril)

Résumé. - Nous

avons mesuré les isothermes

pression-surface

de monocouches mixtes

composées

de

dimyristoyl

lécithine et de cholestérol à 23,5

°C,

et nous les avons

_analysées

afin d’établir le

_diagramme

de

_{phase pression-composition}

de ces

_mélanges

bidimensionnels. Ces mesures sont confirmées par l’observation directe de la

séparation

de

phase.

Nous identifions un intervalle de non-miscibilité des états fluides

qui

se termine _par un

_{point critique,}

accessible à la

température

ambiante. Nous proposons que, dans les

phases

mixtes coexistantes, la lécithine se

trouve dans des états distincts.

Abstract. - The

pressure-composition phase diagram

of mixed

monolayers

of

_dimyristoyl

phosphatidylcholine (DMPC)

and cholesterol at a _temperature of 23.5 °C is derived

by

numerical

analysis

of pressure-area isotherms and corroborated

by

direct fluorescence

microscopic

observations. We

_identify

a fluid-fluid

miscibility

gap, terminated

by

an upper critical

point

which is accessible near room _temperature. We propose that the

coexisting

mixed

phases

of cholesterol

and DMPC contain the

phospholipid

in two distinct states.

Classification

Physics

Abstracts

68.10 - 64.70M - 64.75 - 87.15

,

1. Introduction.

The

_discovery

of domain formation

_{during phase}

coexistence in monomolecular films of

amphiphiles

confined to an air-water interface has

_provided

a

_major

new stimulus to the

investigation

of these

_systems.

A rich

_variety

of domain

_shapes

has been documented

_{[1, 2].}

Recently proposed

phenomenological

theories invoke a

_picture

of

_competing

attractive van

der Waals and

_{long-ranged, repulsive dipolar}

or Coulomb interactions to account for the appearance of domains of finite size

[3, 4].

At the level of the available mean field treatments,

amphiphilic monolayers

are viewed to be

_equivalent

to uniaxial

_{ferromagnets [5, 6],}

ferromagnetic

surface

_{layers [7]}

and thin ferrofluidic films

[8].

Specifically,

the mean field

phase diagram

contains a coexistence

region

characterized

_by

intralayer periodic

modulations

of the relevant order

_parameter

_[3].

Particularly pertinent

in

_ascertaining

the range

of validity

of these theoretical considerations is the

_study

of monomolecular films in the

_vicinity

of a critical

_point.

The existence of critical

points

in several

_single

_component

_monolayer

films at the air-water interface has been

demonstrated in film balance studies

_[9,

10]

and

computer

simulations

_[11].

In

1538

component

monolayers

lateral

_density

and

_temperature

must be varied to reach the critical

point.

As the

_{quantitative analysis}

of

_{configurations}

and

_dynamics

of domain walls

_[12],

recorded

_by

_optical

video

_{microscopy, requires}

extended

_periods

of observation of individual domains in films at the air-water

_interface,

it is

_imperative

to _suppress

_monolayer

flow. We have found this to be a task more

_readily

_accomplished

when

_temperature

is eliminated as an

experimental

variable,

because even small thermal

_{gradients generally}

lead to flow. These

considerations

_suggest

the introduction of

_composition

as a new variable and thus the

study

of

multicomponent

surfactant

_systems.

The isotherms of monomolecular films

_containing

two constituents have been

_investigated

by

several authors. Mixed films of cholesterol and

_{phospholipids}

or

_fatty

acids have been of

particular

interest,

due to the constituents’

_biological

and

_{physiological significance [13-18].}

However,

it was the

_application

of fluorescence

_microscopy

which

_recently

enabled Subramaniam and McConnell

[19]

to

_directly

observe

_{phase separation phenomena}

in mixed films

_containing

the

_phospholipid

_{dimyristoylphosphatidylcholine (DMPC). They interpreted}

their

_intriguing

observations to

_imply

critical

_mixing,

and the existence of an _upper consolute

point,

accessible at or near room

_temperature.

Two

_{important experimental}

considerations render this mixed film

system

particularly

suitable for detailed

_experiments.

At

temperatures

exceeding

the

_postulated

critical

tempera-ture of the

_{liquid-condensed (LC)-liquid-expanded}

(LE ;

for

_{nomenclature,}

see e.g.

[20])

coexistence

_{of DMPC,}

_{approximately}

20 ° C

_[10],

DMPC

_simply

behaves as a two-dimensional

fluid. This

_{greatly simplifies}

the behavior of the cholesterol-DMPC mixture. In

_addition,

the

expected

absence of internal conformational order in DMPC facilitates dissolution of the fluorescent

_{phosphatidylcholine analog}

which is added as an

_impurity

to the host

_phase

and

vénérâtes

the contrast

_enabling

fluorescence

_microscopic

observation of

_{phase separation.}

In

view of the

_desirability

of

_experiments

in the

_vicinity

of a critical

_point,

this

_system

thus offers

itself as a candidate for closer

_inspection.

We have

recently

applied techniques

of

_{digital image analysis}

to establish a detailed

characterization of the domain

_shapes

formed in this mixed

_monolayer

_system

_{by evaluating}

power

spectra

of domain wall

_{configurations.}

This

_{analysis permits}

the identification of several distinct

_regimes

of domain

_{shape stability}

as the

putative

_upper consolute

point

is

approached.

As discussed elsewhere

_[12],

_{the appearance of different stable}

_ground

states of domain wall

_{configurations}

is in

_general

accordance with

_{stability analyses}

based on the model

of

_competing

interactions,

referred to at the outset.

In the

_present

article,

we derive the

pressure-composition phase diagram

for this

binary

mixed film at a

_temperature

of 23.5

° C,

based on the

_analysis

of

_{thermodynamic}

measure-ments, i.e. pressure-area isotherms and the bulk modulus curves derived from them

by

numerical differentiation. We correlate the

_{thermodynamic}

measurements with direct

_optical

observation of

_{phase separation, corroborating}

the determination of the location of a

two-phase

coexistence

_region.

A rather detailed

_picture

of the

_{global phase}

_{behavior may be} deduced. We

_identify

an _{upper critical}

_point

in this mixture

_which,

at 23.5

°C,

is located near a

mole fraction of cholesterol of 0.27 and a surface pressure of 11.5

_dyne/cm.

The

coexisting

phases

emerge at _{very low surface pressure}

_{(ir 5}

0.5

_dynes/cm)

with

_{respective compositions}

of

_{approximately}

10 mole% and 55 mole% cholesterol.

We propose a

_simple

rationale for the

_qualitative

features of observed

_phase

behavior

by

noting

that,

to a

_{good approximation,}

the isobaric increase of cholesterol mole fraction in mixed films is

_equivalent

to an isothermal

compression

of the

lipid

constituent,

DMPC.

Specifically,

this leads us to

_suggest

_that,

in contrast to

_simple

fluid-fluid

_{immiscibility,}

the

miscibility

gap in the

phase diagram

studied here involves a second order

_parameter,

related

the

_distinctly

different

_{compressibilities}

of the two mixtures and related

characteristics,

we

argue that these

configurations

are

_analogous

to those

_{adopted, respectively,}

in the LE and LC

_phases

of

_single

_component

_monolayers

which have been shown to differ

_primarily

with

respect

to the

_degree

of intramolecular chain order

_[21,

_22].

In what

_follows,

we first

_describe,

in section

_2,

our

_experimental

methods and the

digital

filters

_employed

to

_compute

the bulk modulus of the mixed

_monolayer

films. Section 3 contains the results

_leading

to the

_{phase-diagram}

which we discuss and

interpret

in section 4.

We summarize our conclusions in section 5.

2. Materials and

_{expérimental}

methods.

2.1 MATERIALS. - For the measurement of 7T-A isotherms it was crucial that the surfactants

and substrate be as _pure as

_{possible ; impurities produced}

substantial distortions in the

isotherms. In

_particular,

it

proved

difficult to obtain cholesterol free of its oxidation

product(s)

[23],

and difficult to _prevent it from

oxidizing

at the air-water interface

[18].

Cholesterol was

_purchased

from both

_{Sigma (Sigma}

Grade 99

+%,

as well as cell-culture-tested

_grade

99

_{+% ;}

_Sigma

Chem.

_Co.,

St.

Louis,

MO)

and Serva

_{(analytical grade,}

99.9 %

pure ;

Serva,

Westbury, NY),

the latter

_yielding

best results.

_{Recrystallization}

from ethanol removed a substantial fraction of oxidized

_material,

as

_judged

from a characteristic inflection

in the isotherm

_(compare

_e.g.

_{Fig. 2).}

_However,

even careful

_{recrystallization}

of cholesterol in an _argon

_atmosphere

did not

_improve

the

_purity

of a

_{newly opened supply.}

DMPC

(> 99

%

pure)

was obtained from Avanti Polar

_{Lipids (Birmingham, AL)}

and used without further

purification,

since its isotherms indicated sufficient

_purity.

The fluorescent

_probe

C6-NBD-PC

_{(1-Palmitoyl-2-[6-[7-nitro-2-1,3-benzoxadiazol-4-yl)amino]caproyl]PC),}

a

phosphatidyl-choline

_{(PC) analog}

with the NBD

_fluorophore

attached to one

_aliphatic

_chain,

was also

obtained from

Avanti,

and used without further

_{purification.}

Stock solutions of DMPC and of cholesterol were made up in

spectroscopic grade

chloroform,

at

_{approximately}

10 mM

_{(8 mg/ml),}

and diluted to

_{approximately}

1 mM with chloroform to make

_spreading

solutions. 9: 1

_{hexane/ethanol}

was also tried as a

_spreading

solvent,

but seemed to

_aggravate

cholesterol oxidation

_(perhaps

due to water absorbed

_by

the ethanol or due to _{the process of}

_{changing solvents).}

Mixtures of DMPC and cholesterol were

made

_by

_{diluting appropriately}

mixed amounts of the two stocks. A new cholesterol stock had

to be made _up from a fresh bottle of cholesterol every two or three

_days

because of

oxidation,

as

_judged

_by

the isotherms of cholesterol or cholesterol-rich mixtures.

Those mixtures which were studied

_{by epifluorescence microscopy}

were

_prepared

with

2 mole% C6-NBD-PC. This

_dye

was also

_kept

in chloroform stock solution. The inclusion of

the

_dye

caused a small

₍

5

_%)

shift of the isotherm of the 30 mole% cholesterol

mixture,

leaving

its overall

_shape

unaltered.

2.2 PRESSURE-AREA ISOTHERMS. - Pressure-area isotherms

were recorded under

_computer

control on a

_{Langmuir-Blodgett trough}

_system

_(KSV

2200

_{LB ;}

KSV

_{Chemicals, Helsinki,}

Finland).

The entire

_{trough, kept}

in a laminar flow

hood,

was

_placed

in a

_plexiglass

enclosure

to reduce

_monolayer

flow. The area of the teflon

trough

was varied between

_{approximately}

15 x 45

CM2

and 15 x 15

CM2

by adjusting

the

position

of a

_stepping

motor driven

barrier,

machined from white delrin. To reduce thermal

drift,

the

_subphase

_temperature

was held

constant at 23.5 ° C

_{by circulating}

water

_{through glass tubing submerged}

in the

_subphase.

The surface

_temperature

was read with a thermistor

_{(Yellow Springs}

Instrument

Co.,

Yellow

Springs, OH),

while the surface pressure measurement

_employed

a

_{Wilhelmy plate}

of

roughened

platinum, supplied by

KSV.

Isotherms,

usually containing

200-300

_points,

were

1540

Fig.

1. - Schematic

representation

of

experimental

set-up. Not shown is a

_dipping

_well, attached to the KSV

_{Langmuir Blodgett trough, required}

in the

_deposition

of

_monolayer

films onto substrates.

At the

_beginning

of this

_project,

the

_trough

was

_thoroughly

cleaned

_{by allowing purified}

water to stand in it

overnight,

then

_{by rinsing}

it with water and

_organic

_solvents,

and

_{finally by}

running

many isotherms and

repeating

the

_{cleaning operation,}

until a standard isotherm of

the

_{phospholipid dipalmitoyl phosphatidylcholine (DPPC)}

at - 22 ° C was obtained

_[10].

The

glass

tube which carried

_{temperature-controlled}

water

_through

the substrate was cleaned in a mixture of sulfuric acid and

_{hydrogen peroxide.}

The bottom of the

_moving

barrier was

_given

a new surface finish to remove _any

_{irregularities.}

_Thereafter,

the

_only

_cleaning

_{necessary for the}

apparatus

consisted of

_{repeated sweeping}

of the substrate surface after each isotherm. The entire volume of

_{subphase (of approximately 1.51)}

was

_{exchanged weekly ;}

at that time the

trough

was cleaned with ethanol.

The aqueous

subphase

was

_composed

of water of 18 Mfl cm

_resistivity,

obtained from a

water

_purification

unit

_{containing ion-excange,}

carbon and

_{« Organex »}

filters

_(Ultra

_pure

Cartridge

Kit ;

Millipore

Co., Bedford,

MA).

The

_{subphase pH}

drifted to a value of

approximately

5.5 within 2 hrs. Measurements were also made on a

_{subphase containing}

100 mM 1-ascorbic acid

_(Fisher

_Scientific,

_reagent

_grade),

added to minimize cholesterol oxidation at the air-water interface

_[23].

_Here,

the

_{typical subphase pH}

was found to be 3.5. The addition of ascorbic acid to the

_{subphase helped}

to stabilize

cholesterol,

especially

in

monolayers

of

_{Xchol >-}

_0.5,

but had otherwise no effect on the isotherms.

After a

_monolayer

was

_spread

at the air-water

_interface,

the

_spreading

solvent was allowed

compressed

at a rate of

_{approximately}

2

_{Â2/Molecule.min.}

_Compressing

more

_slowly

produced

no

_significant

differences in the

isotherm ;

compressing

much faster introduced substantial noise into the measurement of _{surface pressure}

_(see

Sect.

2.4)

and may have

produced

kinetic effects on the isotherms as well.

2.3 EPIFLUORESCENCE MICROSCOPY. - A small

_{epifluorescence}

microscope,

adapted

from

a beam

_splitter

tube

_{assembly (Rolyn Optics,}

_Covina,

_CA)

in a _way

_previously

described

_[24],

was

employed

to monitor

_monolayer

films while

_recording

their 1T-A isotherms on the KSV

trough.

For these measurements, 2 mole% of a fluorescent

_{lipid (see}

Sect.

2.1 )

were added to

the

_monolayer.

The 457.9 nm line of a 5 W _argon laser

_(Innova

_{90-5 ;}

Coherent,

Palo

Alto,

CA)

was used for illumination. Fluorescence

_images

were collected

through

a 25X

_{(NA 0.45)}

objective, passed through

a 495 nm cut-off filter and recorded

_by

a CCD camera

_(CCD72,

Dage-MTI,

Michigan City, IN).

The camera head’s small

_weight

and size made it

possible

to

attach it

_directly

to the

_microscope

barrel. A _{video processor with} a _gray scale stretch circuit

(Dage-MTI)

was instrumental in

_{obtaining images}

of

_{acceptable signal-to-noise}

_ratio,

_given

the low

_{input light}

levels otherwise found to be insufficient to

_generate

usable

_output.

The

photographs

in

_figures

4 and 5 were taken on a smaller

_trough

with a SIT camera, as described

elsewhere

_[12],

_requiring

the addition of

_only

1 mole% of

_fluorophore.

2.4 ISOTHERM ANALYSIS. - Pressure-area isotherms

were

_{analyzed by application}

of a seven

point least-squares quadratic

or

_{quartic smoothing}

filter

_(chapter

3.3 in

_[25]),

followed

_by

a seven

_point

Lanczos

_{differentiating}

filter

_(chapter

6.4 in

_[25])

to

_compute

the two-dimensional bulk

_modulus,

i.e. the inverse of the isothermal

_{compressibility :}

where à and TT denote mean molecular area and _{surface pressure,}

_{respectively. Building}

vibrations,

which

_coupled

_{into the surface pressure}

_reading

via surface excitations of the

subphase represented

the

_primary

source of noise in the

_recordings.

While of little concern in

the isotherms

_themselves,

these vibrations necessitated the introduction of a

_smoothing

filter

to minimize noise contamination of the

_computed

_{1 / K}

vs. à curves.

_{Digital filtering}

was

implemented numerically by executing

the

_equivalent

convolution

_operation

as a matrix

multiplication (see

e.g.

chapter

3 in

[26])

on a 32 bit

_{floating point}

array processor

(DT7020,

Data

Translation,

Marlborough, MA) residing

in a

_personal

_computer.

3. Results.

A

_typical

set _{of pressure-area}

_isotherms,

_compiled

in

_figure

_2,

reveals the absence of any

obvious characteristic features

_(«

breaks

_»)

_{marking phase}

_{transformations in many other}

monolayer

systems

[9,

10, 14,

20].

It is this observation which motivated a more careful

analysis

based on the

inspection

of the isothermal

compressibility ( K ),

or its

_inverse,

the

two-dimensional bulk modulus.

_Figure

3 contains a

_{representative sample}

of the results. Several features are now

_readily

identified. The first is a discontinuous increase in

_{1 / K}

_indicating

a

drop

of the

_{compressibility}

to a finite value. The

_{corresponding}

mean molecular area which

we refer to as

_in.t

in what follows

_{(see particularly Fig.}

7

_below)

marks the termination of

liquid-vapor

coexistence

_[13].

The

_significant

decrease of

_a-onset

with

_increasing

cholesterol

1542

Fig.

2. - Set of pressure-area isotherms of mixed

monolayers

of

dimyristoylphosphatidylcholine

(DMPC)

and cholesterol, recorded at 23.5 ° C on an aqueous

subphase,

in some cases

containing

100 mM 1-ascorbic acid. The mole fractions are as indicated. The features visible near 20

_dynes/cm

on the

_Xh.1

= 0.5 and

_Xchol

= 0.6 isotherms

signal

the _presence of oxidized cholesterol.

The second characteristic feature in the

_{plots of log}

_{( 1 / K )}

vs. li is a distinct

break,

apparent

from

_figures

_3b,

3c and

_3d,

_{corresponding}

to cholesterol mole fractions

_{of 0.15,}

0.30 and

_0.45,

respectively. Consistently,

this break occurs at the

_junction

of two

_{approximately}

linear

segments

in the

_{semi-logarithmic representation}

of the

_{1 / K}

_{profiles (see Fig. 3)}

and thus

signals

a discontinuous increase in their

_slope.

At the

_{corresponding point}

on the

_isotherm,

the mixed

_monolayer

becomes less

_{compressible. Epifluorescence microscopy}

reveals that this «

_{stiffening »}

of the surface

_layer

coincides with the transition from a

_{phase-separated}

regime,

characterized

_by

a

_{heterogeneous}

distribution of fluorescent label in the

monolayers,

to a

_{homogeneously}

fluorescent state which we

_identify

below with a

_homogeneous

mixture

(see Fig. 8). Figure

4 illustrates this conclusion with a series of

epifluorescence micrographs,

taken

_{during compression}

of a mixed

monolayer

of

_Xh.1

= 0.3 at

_increasing

_pressures.

Figure

5

_presents

_micrographs

of

_monolayers

in the

_{two-phase region}

with

_compositions

fixed

below

_(Xchol

=

0.1)

and above

(Xchol

=

0.45)

the critical value

(see

below).

These

images

provide

direct evidence for the coexistence of two

_phases,

the

_bright

areas

_{corresponding}

to

the

_{phase predominantly containing}

DMPC. We will see below that these

_optical

observations are

_entirely

consistent with the

_analysis

of the

_{thermodynamic}

data.

A third feature

_{characterizing}

the mixed

_monolayer

may be extracted from the

log

( 1 / K )

vs. i curves

_{(of Fig. 3) by plotting}

the value of

_{1 / K ,}

assumed at onset and at several fixed values of the surface _pressure, as a function of

_increasing

cholesterol mole fraction. A selection of such

_plots

is shown in

_figure

6.

_{They permit}

the

_important

observation that the addition of cholesterol to the mixed

_monolayer

does not

_{substantially}

alter the value of

1 / K

from that found for _{pure DMPC} until a threshold value of the cholesterol mole fraction

(Xchol)

is attained. This threshold value was estimated

_{by applying}

a linear

regression analysis

to the low

_{X,,h.1 portion}

of each

_plot,

as indicated

_by

the solid lines in

_figure

6. As many

points,

in order of

_{increasing Xchob}

as

_possible

were

_included,

until this caused a

_significant

deterioration of the

_goodness

of fit

_parameter.

The first value of

_Xchol

defined

by

this

procedure

not to lie on the initial linear

_portion

was identified as the threshold value. These

points

mark the

_{phase boundary,}

shown in

_figure

8

(«

V

_»)

which

_separates

_region

II from the

Fig.

3. - Inverse

compressibility

1 / K - -

il

2013 )

_{(bulk modulus)}

as a function of mean molecular

a

area, for

increasing

values of

_Xchol

= 0.05, 0.15, 0.30, 0.45 and 0.55. Also shown, _as solid lines, _are the

corresponding

isotherms from which the bulk modulus curves were

_{computed by application}

of a seven

point

Lanczos

_{differentiating}

filter

_(see

text, Sect.

2.4). Straight

lines serve as a

_guide

to the eye. The left

hand ordinate shows the surface pressure, the

right

hand ordinate refers to the bulk modulus. The inversion in the

_{1 /K}

curves for

_Xchol

= 0.45 and 0.55 centered at J m 47

Â2/Mol ,

arises from cholesterol

oxidation.

meaningful

test of the functional form

_obeyed

as

_{1 / K}

_approaches

the

_limiting

value measured

for pure cholesterol.

To

_identify

the

_partial

molecular areas of

_{coexisting phases}

in the surface

monolayer

we

follow

_{(in Fig. 7)}

the classical scheme of

_plotting

the mean molecular area, li, at onset

(liquid-vapor

coexistence),

and at several fixed values of the surface pressure, as a function of

cholesterol mole fraction. It is

_readily

_apparent

that,

in contrast to several other

1544

Fig.

4. -

Fluorescence

micrographs

of

DMPC/cholesterol

mixed

_monolayer

_containing

30 mole%

cholesterol, and 1 mole% of the fluorescent

lipid analog

C6-NBD-PC

_(see

Sect.

_{2.1). a)}

Fluorescent and

probe

excluding phases

occupy

approximately equal

area fractions. In the

_regime

of _strong

_segregation

shown here, domains

adopt

a circular

shape.

The

photograph

is taken at a surface pressure of

approximately

5

_dynes/cm.

The bar marks 50 fJ.m.

b) Upon

approaching

the upper consolute

point

the domain wall energy softens and

significant

domain

shape

fluctuations lead to distorted

_{shapes [12].}

The

photograph

is taken at a surface _pressure of

_{approximately}

10

_dynes/cm.

Fluctuations

decay

on time scales consistent with

rapid,

i.e. fluid-like

intralayer

molecular diffusion in both

_{phases. c)}

Further

compression

yields

a

_{homogeneously}

fluorescent _mixture, shown here at a _{surface pressure of}

approximately

14

_dynes/cm.

The appearance of this

homogeneous phase

coincides with the «

_stiffening

»

of the

monolayer

described in connection with

figure

3.

constituents does not obtain : this would

_imply

â =

ADMPC( 7r )

XDMPC

+

_{achol C Tr ) Xchob}

and

thus a

_straight

line

_connecting

_ii(Xchol

=

0)

=

aDMPC and

a(Xchol

=

1.0)

=

achol.

However,

all

plots (certainly

those up to 7r = 15

dynes/cm)

are well

_approximated

_by

a

_{representation}

permitting

the identification of three distinct

_regimes,

each characterized

_by

a linear decrease

of â with

_increasing

mole fraction of cholesterol. Construction of the

_{intercepts (see}

e.g.

chapter

7.4 in

_{[27]) yields}

the

_partial

molecular areas of DMPC and cholesterol. As

implied by

Fig.

5. - Fluorescence

micrographs

of

_{DMPC/cholesterol}

mixed

_{monolayers containing}

1 mole% of the fluorescent

_{lipid analog}

C6-NBD-PC

_{(see Sect. 2.1 )}

and 10 mole%

(Fig. 5a)

and 45 mole%

_{(Fig. 5b)}

cholesterol,

respectively. Photographs

were taken at surface pressures of

approximately

0.5

dyne/cm

and 0.2

dyne/cm, respectively,

at molecular areas close to _jonset- In combination with

figure

4a these

photographs

demonstrate that

_{fluorophore excluding regions}

in the

_monolayer

occupy an

_increasingly

larger

area fraction as

_Xchol

is increased. In section 4 we _suggest these

regions

to be associated with a

DMPC/cholesterol

mixture

_containing

DMPC in an ordered conformation. A

heterogeneous

distri-bution of labelled domains

generally prevails

at

_length

scales

exceeding

500 jim. The bar in

figure

5a marks 50 fJ-m.

three

_regimes.

To extract the

_partial

molecular areas listed in table 1

below,

a linear fit was

applied

to the middle

_portion

of each

plot.

That

is,

beginning

with

_Xehol

= 0.1,

the number of

points,

in order of

_{increasing Xch.1,}

included in the linear

_regression

was increased until this led to a deterioration of the fit. The solid lines shown in the middle

_portion

of the

plots

in

figure

7 were so obtained.

_{Approximate straight}

lines,

indicated dashed in the

_figure,

were

than drawn to obtain

_intercepts

with the ordinates

_Xehol

= 0 and

Xchol

= 1.0. The

scarcity

of

points

for

_{Xchol --}

0.6 is the

_primary

source of the

_uncertainty

in the values for the

_partial

molecular areas listed in the table below. It is also reflected in the error bars

_given

for the

points

marked

_by

« à » in

_figure

8.

The existence of three distinct linear

_regimes

in the

_dependence

of â on

_Xchol

indicates the

existence of two

_phase

_boundaries,

shown in

_figure

8

_(«

à

_»).

The first of these

_separates

region

IV from the rest of the

_{phase diagram.}

As indicated

_{(by « à »),}

the second

_phase

boundary

coincides,

within

_experimental

error, with the

phase

boundary

derived on the basis

of

_figure

6,

which

_separates

_region

II from the rest of the

_{phase diagram.}

The behavior documented in

_figure

7 and in the table is

_analogous

to that observed and

discussed

_by

de Bernard in his careful

_early

film balance

_study

of mixed

_monolayers

_{of egg}

phosphatidylcholine

and cholesterol

[13].

It _may be understood

_{simply by observing}

that the

addition of

cholesterol,

itself

quite incompressible

as demonstrated

_by

the

_shape

of its isotherm in

_figure

2,

induces a « condensation » of DMPC which

_consequently

assumes a

molecular area close to its

_partial

molecular area of 51

A2,

while the

_{corresponding partial}

molecular

area of cholesterol coincides with its actual molecular area

₍₌

38

_A2),

as extracted

from the

_pertinent

isotherm in

_figure

2. We return to this

_point

in section 4 below. The

_findings

described so far lead to the

_phase

_diagram

of

_{DMPC/cholesterol}

mixed

monolayers

at 23.5

_°C,

shown in

_figure

8. Its

_global

features exhibit a remarkable

_similarity

to

1546

Fig. 6. - Examples

of

plots showing

the

_dependence

of

_{1 / K}

on cholesterol mole fraction at fixed ’TT

values. The threshold values of

_Xchol

for a finite increase in

_{1 / K}

over its baseline value were extracted from such

_{plots by}

a

_procedure

described in the text,

_yielding

the solid

straight

lines on the basis of linear fits. These threshold values define the appearance of a state of low

_{compressibility}

of the _mixture,

separating

the

_region

of

_{high X,,h.1 (region}

II in

_{Fig. 8)}

from the rest of the

_{phase diagram}

shown in

figure

8.

Fig.

7. -

Plots of the mean molecular area as a function of mole fraction, at fixed values of

Fig.

8. -

Pressure-composition phase diagram

of mixed

monolayer

of DMPC and cholesterol at 23.5 ° C. The

_phase

boundaries shown here are derived on the basis of

figure

3

_{( 0 »), figure}

6

_{(« V »),}

figure

7

_(«

à

_»),

as discussed in section 3. Where indicated,

they

were confirmed

_by

fluorescence

microscopic

observation of

phase separation («

X »,

(this work),

and « + »

[19]).

All lines serve as

guides

to the _eye. Dashed lines were drawn

_by

hand ; the solid line follows a standard functional form for

_phase

coexistence as discussed in section 3. The three distinct lines

separating regions

III and II are

argued

to coincide within

_experimental

error

_{(Sect. 3) ;}

an indication of

typical

error

_margins

is

given by

horizontal delimiters

_{( 1 - > 1 ).}

The various lines delineate a fluid-fluid

_miscibility

gap

(region III)

bounded

_by

three distinct

_regions

further described in section 3. The

numbering

is consistent with

figure 5

in

_[15].

A

_highly

_compressible

vapor

phase, existing

at all values of

_Xchol

for

a > _aonset and 7T 5 0.5

_{dyne/cm (see}

text and

Fig. 3),

is not shown.

Table I. - Partial Molecular Areas. Listed are

_partial

molecular areas

_(in

Â2 )

derived

_from

figure

7 as discussed in the text. The notations « low », « middle » and «

_{high » refer}

to the 3 linear

_regimes

_of

the

_plots

in

_figure

7. Partial molecular areas

_of

DMPC and

cholesterol,

are

denoted

by

âdmpc

and

_{àchob respectively,}

and are estimated to be accurate to within

:t 3 Á 2.

1548

isotherm

_{(Fig. 5}

in

[10]), suggesting

that small amounts of added cholesterol

_{(Xchol «}

0.1 )

a

_randomly

distributed

impurity,

eliminate the ordered

phases

of DPPC

_[29].

On the basis of our

analysis

we

_identify

_region

III as a coexistence

_regime

of two immiscible fluid

_phases

with an _upper consolute

point

near

_(Xghol

=

0.27,

ir’ =

11.5).

The data

points

( 0 ») delineating

this

_region

were obtained from the breaks in the

_{log ( 1 / K )}

vs.

à curves described in connection with

figure

3 and confirmed in several cases

_{(« X ») by}

epifluorescence

microscopy.

The data

_{points reported}

in the fluorescence

_{microscopic study}

of Subramaniam and McConnell

_[19]

are also indicated

_(«

+

_»).

The solid

line,

little more

than a

_guide

to the eye at this

stage,

follows the standard functional form

with the critical values indicated

above ;

/3

was held fixed at a value of

_{1/3, generally}

observed

for fluid-fluid coexistence

_(see

_e.g.

_[30])

and favored

_by

_comparison

with coexistence curves

computed four 6

=

1/2,

the mean field

_value,

and for

_{f3 = 1/8,}

the value indicated

_by

a

postulated

2d

_{Ising analogy applied}

to

_monolayer

films

_[31].

_However,

our data set is too

small to _{make any}

_meaningful

detailed test ; the value of

_1/3

is

_certainly

not to be taken

literally.

We estimate the critical values to be accurate to within

_dXghol

= ± 0.05 and

Air’ = ± 1

_dyne/cm.

In

_region

1 DMPC and cholesterol form a

_{macroscopically homogeneous}

mixture whose

cholesterol content varies in the range 0.1 _

Xchol S 0.35.

This mixture _appears 1

homogeneously

fluorescent

_(see

_{Fig. 4).}

Characteristic « breaks » in the

_plots

of â as a

function of

_Xchol

in

_figure

7

_suggest

that to the left of the line

_{Xchol S 0.1,}

that

is,

in

_region

IV,

pure DMPC coexists with a

_{DMPC/cholesterol}

mixture of

_Xchol

-- 0.1.

Monolayers

in this

region

of the

_{phase diagram}

_{also appear}

_{optically homogeneous.}

In

_region

_II,

_{pure cholesterol} coexists with a

_{DMPC/cholesterol}

mixture. When

_entering

this

_region,

mixed

_{monolayers undergo}

a transition to a state of low

_{compressibility.}

Points

marking

the

_{phase boundary}

were extracted from

_plots

of the

_type

shown in

figure

3

(«

D

»),

plots

of

_{log ( 1 / K )}

vs.

_{Xchol (Fig.}

_{6 ;}

_{« V »)}

and from those

showing

the

dependence

of

à on

_{Xchol (Fig.}

_{7 ;}

« à

_»).

These different determinations of the location of the

_phase

line

differ

_{by approximately}

0.1

_Xchol.

Given the

_{appreciable uncertainty}

in the data in this

_region,

we cannot _say whether it is this

_uncertainty

which sets the width of the transition

_region,

or

whether the three

procedures

in fact

_capture

_{differing signatures}

associated with the

transition. In _any case, it appears

likely

that the coexistence

boundary

meets the

_phase

boundary

in a

_{triple point}

near

_(Xchol

=

0.35,

’TT = 10

dynes/cm).

This is the scenario favored

by

Albrecht et al. in their

_study

of mixed

_monolayers

of cholesterol and

_dipalmitoyl

phosphatidylcholine (DPPC)

at 24.9 °C

_[15].

_{Epifluorescence microscopy}

reveals that

_layers

composed

of 40 mole% and 45 mole% cholesterol remain

_{inhomogeneous}

when

_compressed

up to surface pressures of 30

dynes/cm, suggesting

a direct

path

between

regions

III and II at

those values of the cholesterol mole fraction.

4. Discussion.

In what

_follows,

we

_suggest

a rationale to account for the

_qualitative

features

_displayed

in the

phase diagram

and discuss the notion that DMPC in fact assumes distinct states in the two

immiscible fluid

_phases

which coexist within the

_miscibility

gap

(region

III in

Fig. 8).

To set the

_stage,

we note that the

_sharp

rise in the isotherm of the pure cholesterol

(7T,

Xcho0 phase diagram

of

_figure

8 _may in fact be understood

_{by explicitly making}

this identification. That

is,

one assumes that cholesterol-cholesterol interactions are

governed

by

a

hard-core

repulsive

potential

with a characteristic scale set

_by

the molecules’ van der Waals

radius,

and one

_regards

the actual molecular area, ah.1

(as opposed

to its

_partial

molecular

area,

àchol),

as constant.

An _{immediate consequence of this}

_assumption

becomes

_apparent

when

_considering

the behavior of the

_binary

mixed

_monolayer

_along

an isobaric

_{trajectory through}

the

(w,

Xchol) diagram.

As the set of isotherms in

_figure

2

_{demonstrates,}

the mean molecular area

à at which a

_given

value of ir is attained decreases with

increasing Xchol. Figure

7

_displays

the

dependence

of â on

_{Xchol explicitly}

for a number of fixed values of 7r. Three linear

_regimes,

readily

identified in the

_plots

at 7r x- 15

_dyne/cm,

indicate that the

corresponding partial

molecular areas

_{( â )}

of both constituents remain constant

_throughout

each

_regime,

but

undergo

an

_{abrupt change}

at the transitions between them

_(see

also Tab.

_I).

A linear

dependence

of â on

_{Xch.1, in conjunction}

with the

_assumption

of the

_{incompressibility}

of

cholesterol,

directly

indicates an effective

_compression

of DMPC

_[13].

_Consider,

for

_example,

the middle

_portion

of the

_plot

for ’TT = 0

dynes/cm.

Here,

àdmpc

= 90

Â2

and

àchol

=

20

Â2

« achob

implying

that for each molecule of cholesterol

(of

actual molecular area

achol = 40

A 2)

added to the

_mixture,

the total molecular area increases

_{by only}

20

Â2.

It is the concomitant

_{compression (or}

« condensation

_»)

of DMPC which balances the

_equation.

We may thus

regard

an increase in

_Xchol

at constant _pressure to be

_{effectively equivalent}

to a

compression

of

(the

remaining)

DMPC.

_{Consequently,}

one

_expects

the conformations exhibited

_by

DMPC

_along

any isobar in the

(ir, Xcho0 diagram

to reflect those of the

equivalent

pure DMPC

monolayer subjected

to isothermal

_compression.

Specifically,

this

_suggests

to us that the

_miscibility

_gap,

_{corresponding}

to

_region

III in the

phase diagram

depicted

in

_figure

_8,

involves

_coexisting

mixed

_phases

in which DMPC

preferentially

assumes two distinct states. One of the two

_mixtures,

_containing

_{predominantly}

DMPC,

exhibits

_bright

fluorescence

_(Figs.

4,

5)

and a

_{compressibility}

which is

_essentially

that of a _pure DMPC

_{monolayer (see Fig. 6).}

In contrast, the second mixture excludes most of the fluorescent

_{lipid analog, consequently appearing}

dark

_(Figs.

4,

5),

and

_develops

a

_markedly

lower

_{compressibility,}

as discussed in connection with

_figures

3 and 6.

Furthermore,

as noted in section 3 in connection with

_figure

_7,

when

_reaching

the

_{phase boundary}

of

_region

II,

the

partial

molecular area of DMPC

_approaches

a value

_{of approximately}

51

Â2

_(see

Tab.

_I).

All these features are

_strongly

reminiscent of the coexistence of the

_{liquid-expanded (LE)}

and

liquid-condensed (LC) phases featuring prominently

in the

_{phase diagram}

_{of the pure}

phospholipid monolayer (see Figs.

2 and 6 in

_[10]

and inset to

_{Fig. 8).}

It is therefore

_tempting

to

_suggest

that DMPC in the two

_coexisting

mixtures assumes

_{configurations}

similar to those it

exhibits in the LE and LC

_{phases, respectively.}

A recent

_report

of

_{experiments probing}

molecular

_{configurations}

in

_monolayers

at an

air-water interface

_[21]

_]

states that the transition into the LE

_phase

is characterized

_by

the excitation of disordered molecular chain conformational states.

_X-ray

measurements have been

_interpreted

to indicate the existence in the

_LC-phase

of

_fully

extended

_aliphatic

chains

adopting

a

_significant

tilt

_{angle [22].}

Monte Carlo simulations based on this mechanism

_[11,

31]

]

reproduce

many of the

experimentally

observed features.

Accepting

this

scenario,

one

would,

in the

_spirit

of Doniach’s

_simple

two-state model

_{of chain-melting [31, 32], picture}

the

predominantly

DMPC

containing phase

as a mixture of cholesterol with DMPC in a disordered chain

_{configuration,}

characterized

_{by « gauche »}

_excitations,

while in the

coexisting

second mixture DMPC

_approaches

an

all-trans,

ordered conformation. A more

1550

In _support of such a model for

lipid/cholesterol

mixtures we observe that in the

_phase

diagram

of pure

phosphatidylcholine

the

_typical

values of the molecular area in the LC

_phase

are indeed close to 50

Â2 [10]. Figure

7 and the

_accompanying

table 1 of

_partial

molecular

areas reveal that

_àdmpc,

the

_partial

molecular area of

_DMPC,

in the

_{high Xchol region}

is in fact

of that

_magnitude,

while

_Jchob

the

_partial

molecular area of

_{cholesterol, approaches}

achol, its actual molecular area of

_{approximately}

40

Â2.

To the extent that

_{à ch.1 me}

achol, as assumed at the outset of the

discussion,

àdmpc

= _ADMPO

placing

DMPC

along

the

phase boundary separating region

II from the rest of the

_diagram,

_{in the range of densities} characteristic of its LC

_phase.

Single

component

lipid monolayers

also exhibit a characteristic

_drop

in

_{compressibility}

when

_entering

their LC

_{phase [10, 20]. By}

_analogy,

one would attribute the sudden increase of

1 / K,

described in connection with the

_log

_{( 1 / K )}

vs.

_{Xchol plots}

ôf

figure

_6,

to _{the appearance}

of the

_equivalent

state of DMPC in the mixed

_monolayers.

This statement

_implies

that the

phase

line

_delineating

the

_high

cholesterol

_{region (region}

II in

_{Fig. 8) signals}

the condensation of the

_lipid

constituent into its all-trans

_{configuration.}

This transition

_persists

to values of the surface pressures far

exceeding

the critical _pressure for

_demixing.

Considerations in accordance with those

_pertinent

to _pure

_{lipid monolayers [11]}

_]

would

_suggest

a continuous

transition to a mixture of cholesterol and all-trans DMPC above the upper consolute

_point

(Fig. 8).

Within the context of the

_proposed

model one would attribute the

inhomogeneous

distribution of

_fluorescent

label within the

_miscibility

_gap to the fact that the

_type

of fluorescent

_{lipid analog employed}

here is

_largely

excluded from the

_{phase containing}

DMPC in its chain-ordered state. It is this _very feature which makes

_possible

the fluorescence

microscopic investigations

of the LE - LC

_phase

coexistence in

_single

_component

_monolayers

[1,

2, 33,

34].

For the same reason, one would

_expect

mixed

_monolayers

to exhibit an

inhomogeneous

fluorescence distribution in

_region

_II,

as we have observed.

As the

_pertinent

isotherm in

_figure

2

_{demonstrates,}

the

ordered,

LC-equivalent

state is inaccessible to _pure DMPC

_monolayers

at the

_temperature

of the

present

experiments,

namely

23.5 ° C. This is the

_frequently

notes «

_{condensing »}

effect of cholesterol

_[13,

_20,

_{35] :}

according

to our

_{phase diagram,}

the

_{LE-equivalent}

conformation of the

_lipid

accommodates

cholesterol _up to

_only

a modest

_composition,

in the

_present

case

_{approximately}

10 mole%.

Further admixture of cholesterol stabilizes the conformation associated with the

_lipid’s

LC

phase.

The new

_phase

_{appears in the}

_{present system}

with a

_composition

of

_{approximately}

55 mole% cholesterol at 7T = 0

dyne/cm.

Compression

of

_single

_component

_{monolayers eventually}

induces a

_positionally

ordered solid

_[36].

_{This appears}

_unlikely

in the _presence of excess cholesterol. One

_possible

scenario in the

_high

cholesterol

_{region might}

be the formation of a

_{glassy DMPC/cholesterol}

_mixture,

coexisting

with pure cholesterol. The characteristic response of such a state to mechanical

perturbations (e.g.

in torsional oscillator

_{measurements)}

should be distinctive and

_interesting

to _pursue.

We believe the

_preceeding

_{interpretation}

of fluid-fluid

_{immiscibility}

in

phospholipid/choles-terol mixed

_monolayers

to be

_plausible.

It

_certainly

lends itself to be tested

_by

an

experimental technique

which is sensitive to the state of

_aliphatic

chain

_{ordering [21].}

However,

irrespective

of

_{specific microscopic}

model one may wish to invoke to characterize

the different states of DMPC in the two

_coexisting

fluid

_phases,

a

_{complete theory}

of mixed

monolayers

would in any case have to consider the

_coupling

between an internal

_degree

of

freedom and the

_macroscopic

order

_parameter,

_e.g.

_{Ycy)l - X(2)chol,}

in contrast to

_{simple binary}

[30].

This

_generic

situation is reminiscent of the nematic to smectic A transition in

thermotropic liquid crystals

and the

_{equivalent phenomenon}

in

_{superconductors [37].}

5. Conclusions.

We have

_investigated

the

phase

behavior of a two-dimensional

_mixture,

a monomôlecular

film confined to an air-water interface

containing

DMPC and cholesterol.

_By

_inspection

of the

dependencies

of bulk modulus and

_partial

molecular areas on cholesterol mole

fraction,

we

have established a

_{phase diagram}

whose

_global

features include a fluid-fluid

_miscibility

_gap,

terminated

by

an _{upper consolute}

_point

near

(X’ 01

=

0.27,

’TTc =

11. 5)

_at 23. 5 ° C. The

location of the

_{phase boundary}

was confirmed

by

direct observation of

_phase

_separation

via

epifluorescence microscopy.

We _propose that DMPC assumes states oi different chain

ordering

in the

_coexisting

fluid

_{phases, corresponding}

to those

_{characterizing}

liquid-condensed and

_{liquid-expanded phase,}

_{in the pure}

_{lipid monolayer.}

This

_hypothesis

may be

readily

tested

_{by experiments}

sensitive to chain conformational order

_[21]

_]

and

_{perhaps by}

those sensitive to chain tilt

_[22].

We

_expect

that the

_possibility

of

_coupling

of the mean-field

order

_parameter

to a second

_degree

of freedom must be examined to obtain a correct

_picture

of the critical

_mixing.

The

_{probed phase diagram}

contains three further

_regions.

These are

_{occupied by : firstly,}

coexisting

pure DMPC and a

_homogeneous,

fluid

_{DMPC/cholesterol}

mixture of

_{Achoi ===}

_{0.1 ;}

secondly,

a

_mixture,

also fluid and

_{homogeneous (0.1 Xchol S}

_0.35,

7r 2:

_{Ir 5}

but

charac-terized

_by

a reduced

_partial

molecular area of

DMPC ;

thirdly,

a

_highly

_{incompressible}

mixture,

coexisting

with pure cholesterol in which DMPC assumes a

_partial

molecular area

coinciding

with that

_marking

_{the appearance of the LC}

_phase

in

_single

_component

_layers.

The latter

region,

with similar

_properties

has also been identified in the

_{phase diagram}

of DPPC and cholesterol

_[10].

The

_{accessibility}

of a critical

_point

in a two-dimensional

_monolayer

film in a convenient

range of

experimental

parameters

has

_already

been

_exploited

in the

study

of a series of

domain

_shape

instabilities in the

_{present system}

[12].

It offers

_{promising possibilities}

for more detailed

_experiments

in the critical

_region.

Acknowledgments.

We would like to thank E. Chin and S.

_Stuczynski

for their advice and the use of their facilities in the

_{recrystallization}

of cholesterol under argon. CLH

acknowledges

support

through

the Summer Research

_Program

for Women and

Minorities,

sponsored by

AT&T Bell Laboratories.

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