Molecular friction and epitactic coupling between monolayers in supported bilayers

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Submitted on 1 Jan 1989

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Molecular friction and epitactic coupling between

monolayers in supported bilayers

R. Merkel, E. Sackmann, E. Evans

To cite this version:

Molecular friction and

_{epitactic coupling}

between

_monolayers

in

_{supported bilayers}

R. Merkel

_(1),

E. Sackmann

₍₁₎

and E. Evans

₍₂₎

(1)

Physik

Department

(Biophysics

Group

E22),

Technische Universität München, D-8046

Garching,

F. R. G.

(2)

Departments

of

_Pathology

and

Physics, University

of British Columbia, Vancouver, B.C.

Canada, V6T 1W5

(Reçu

le 2

_février

_1989,

_accepté

le 8 mars

1989)

Résumé. 2014 On

_présente

des résultats

_{expérimentaux}

_{pour la diffusion latérale de}

_lipides

fluorescents dans des bicouches

déposées

sur des substrats vitreux. A l’aide d’une récente théorie

phénoménologique

pour la diffusion sur un substrat de membrane

couplée

(Evans

et Sackmann,

1988),

on détermine la friction moléculaire

_intrinsèque

entre les deux couches

_qui

forment la bicouche et entre la bicouche et le substrat. On mesure les coefficients de friction entre les couches en fixant la couche mononucléaire

proximale

sur _{le substrat par des liaisons Si-O}

_(en

utilisant des

_silanes)

ou par des ponts

ioniques (arachidate

de

_cadmium).

On trouve un coefficient de friction

_{( =}

rapport entre force de cisaillement et vitesse

_{instantanée)}

entre deux monocouches de fluide

_(DMPC

dans le

_{silane) bs}

_{égal à}

3 x

105 dyne s/cm3

et entre le fluide et la monocouche solide

_(DOPC

sur arachidate de

_Cd)

égal

à 5

_{107 dyne s/cm3.}

Dans le

_premier

cas,

bs

augmente avec le

_{degré d’interdigitation}

entre les chaînes

_{d’hydrocarbure.}

Afin d’étudier la friction entre la bicouche et le substrat, cette dernière est _{bombardée par de}

_l’argon,

ce

_qui

provoque la

séparation

du substrat et _{de la monocouche par} un film d’eau lubrifiant ultrafin

(épaisseur

de l’ordre du

_nm).

On trouve un coefficient de friction entre la bicouche et le substrat

bs

= 6

104 dyne

s/cm3,

d’où on déduit une

_épaisseur

du film d’eau

_égale

à 10

Å.

Le second

aspect de cette étude concerne les transitions de

phase

et le

_couplage

monocouche-monocouche. Des bicouches

_symétriques

_séparées

_{du substrat par} un film d’eau

_présentent

des transitions de

phase

abruptes

à peu

près à

la même

_température

_{que des bicouches libres}

_{(vésicules).}

La

température

de transition de bicouches

_{asymétriques}

se trouve entre les valeurs

correspondant

à chacune des _composantes. Les bicouches formées de

_{phospholipides}

dans les silanes

_présentent

une transition de

_phase

continue à cause des contraintes

imposées

par une surface totale fixée. En

perturbant

les monocouches par

l’adjonction

de marqueurs fluorescents

(NBD

et Texas

_Red),

on

démontre que la couche

proximale

dans un solide ou dans un état de coexistence fluide-solide induit une transition de

_phase

dans la couche distale

_(par

_exemple,

DMPC)

même si elle est

déposée

à

_partir

de l’état fluide. Les monocouches de

_lipides

insaturés sous forme cristalline

compacte

peuvent subir une transition de

phase

indépendante.

Abstract. 2014 Microfluorescence methods were used to examine

monolayer-monolayer

and

bilayer-substrate coupling

in

_bilayers

_deposited

on

_glass

substrates. In the first part, lateral

diffusion of

_lipid

_probes

in individual

_lipid

_layers

was measured

_by

the fluorescence recovery after

photobleach technique.

The aim was to evaluate viscous molecular friction

(i)

between Classification

Physics

Abstracts

87.20Eq

monolayers

that form a

_{single bilayer}

and

(ii)

between a

_bilayer

and an

_adjacent

substrate based

on a recent

_{phenomenological theory}

for

_{particle mobility}

in

_{substrate-coupled}

membranes

(Evans

and Sackmann, J. Fluid Mech. 194

₍₁₉₈₈₎

553

_[1]).

To obtain coefficients for friction between

monolayers,

a

_bilayer

was formed with the first

_(proximal)

_monolayer

fixed to the

_glass

substrate

_by

Si-O-bonds

_{(using silanes)}

or

_by

ion

_bridges

(using

cadmium

arachidate) ;

_then,

probe

diffusion was measured in the second

_(distal)

_monolayer

formed

by phospholipids.

The

coefficient for viscous friction

_(defined

by

bs-interfacial

shear stress/interfacial «

_{slip »}

velocity)

between

_monolayers

with fluid chains

_(DMPC

or DOPC on

silane)

was calculated to be in the range

bs

=

106-107

dyn-sec/cm3 ;

between _a fluid and _a solid

monolayer

(DOPC

_on

Cd-arachi-date),

the frictional coefficient was much

larger,

i.e.

_bs

= 1-5

108

dyn-sec/cm3.

For _two

opposing monolayers

with

_liquid

chains, it was found that

_bs

increased with the

_degree

of

interdigitation

between the

_hydrocarbon

chains. To

_investigate

the effect of lubrication

_by

a water

film between a fluid

bilayer

and the substrate, the substrate was first

_Argon

_sputtered

which acted

to _separate the

_{proximal monolayer}

from the substrate

_by

a thin

_lubricating

water film

_(thickness

in nm

_region).

The frictional coefficient between the

_bilayer

and the substrate was measured to be in the

_{range bs}

= 2 _x

103-3

105

dyn-sec/cm3

which

implied

that the film thickness _was from

1-50 nm. In the second _part, we studied the effect of

_{monolayer-monolayer}

and

_{bilayer-substrate}

coupling

on the

acyl-chain

crystallization

transitions in

_monolayers

of

supported bilayers.

Symmetric bilayers

(separated

from the substrate

_by

a water

_film)

exhibited

_{sharp phase}

transitions at about the same transition _temperature as the free

_bilayers.

The transition

temperature for

_{asymmetric bilayers}

was between the transition temperatures for the individual

monolayer

components.

Bilayers

formed

by phospholipid monolayers

on silanes showed a

concerted but continuous

_phase

transition which

_appeared

to be due to the constraint of fixed total area and

interdigitation

of the two

_{monoalayers. By doping}

the

monolayers

with different fluorescent

probes

(NBD

and Texas Red

_lipid

_analogs),

it was demonstrated that, when the

proximal layer

was in a solid or

_liquid-solid

coexistence state, a

_phase

transition was induced in

the

superficial monolayer

even if this

layer

was

_deposited

from the fluid state. It was also observed that the _patterns of fluid and solid domains in both

_layers

were in

_{complete register.}

On the other

hand, a fluid

_monolayer

of unsaturated

_lipids

on

_{tightly-packed crystalline proximal monolayer}

was able to

_undergo

a _separate

_phase

transition.

1. Introduction.

Stable

_{lipid bilayers supported}

on solid substrates are of

_practical

and scientific interest.

Examples

of

_{practical applications}

are the

_development

of biosensors

_{[2, 3]}

and the simulation of cell surfaces

_[4].

From the scientific

_point

of

view,

lipid bilayers

on solids become of

growing

interest because of new

_{opportunities}

to

_study

fundamental

_properties

of

_symmetric

and

_{asymmetric bilayers ;}

in

_particular

since this

_arrangement

facilitates the

_application

of surface-sensitive

_optical

_techniques

such as

_ellipsometry

or evanescent-field fluorescence

microscopy.

Application

of these

_techniques

was made

_possible

when it was discovered that a

bilayer

could be

_separated

from the

_glass

substrate

_(by

a thin -

many nm thick - water

film)

following sputtering

of the substrate in an _argon

_atmosphere

[5].

The

present

study

was

_organized

into two

_parts

both

_designed

to examine

monolayer-monolayer

and

_{bilayer-substrate coupling.}

In the first

_part,

lateral diffusion coefficients of fluorescent

_probes

were measured

_by

fluorescence after

photobleach-recovery

methods in

supported bilayers.

This first

_aspect

was motivated

by

a recent fluid mechanical

_theory

_[1]

for

particle mobility

in

_{substrate-coupled}

membranes where it was shown that molecular

diffusivity

in the membrane can be

strongly

affected

_{by drag}

exerted at an interface

(represented

by

a

_{phenomenological}

coefficient for viscous

friction).

In order to derive interfacial friction

coefficients,

comparative

measurements of

_probe

diffusion were made in

the substrate

_(referred

to as the

_{proximal layer)}

was fixed to the substrate either

_by

covalent

linkage

with silanes or

_by

salt

_bridges

with cadmium arachidate. In the second

_type

of

_bilayer,

the

_proximal

_layer

was

_separated

from the substrate

_by

a thin

_lubricating

water film. The

water _gap was

_{produced by}

an electrostatic

_disjoining

_{pressure which} was created

_by

first

charging

the substrate

_{through Argon sputtering.}

For both

types

of

_bilayers,

the outer

monolayer

(referred

to as distal in the

following)

was

_made-up

of

_{phospholipids.}

With the first

type

of

_{bilayer assembly,}

measurements of

_{probe diffusivity}

in the distal

_{monolayer yielded}

estimates of viscous coefficients

_{characterizing}

the molecular friction between

_monolayers.

With the sécond

type

of

_bilayer

_arrangement,

measurements of

_{probe diffusivity}

were used to

measure frictional coefficients between the membrane and substrate

_(or

between molecules in the

_{proximal layer}

and the substrate

_{respectively).}

This

_analysis

was also used to estimate the

water _{gap thickness.}

In the second

_part

of this

_work,

_properties

of

_phase

transitions in

_{substrate-coupled lipid}

bilayers

were examined. Similiar to the above studies of interfacial friction both

_types

of

bilayer

configurations

were

_employed.

Observations of

pronounced changes

in diffusion

coefficient were used to

_identify

fluid-solid

_{phase changes}

_(i.e.

_acyl-chain

conformational

transitions)

as a function of

_temperature.

In addition to these measurements of

_probe

diffusivity,

static observations of fluorescence

_patterns

were used to evaluate the

_microscopic

organization

of fluid-solid coexistence

_patterns

_(due

to

_{non-homogeneous}

_partitioning

of the fluorescent

_probe

into fluid and solid

_domains).

In order to evaluate

_coupling

effects between

monolayers

and between

_bilayers

and

_substrates,

_respectively

the two

_types

of

_bilayers

described above

_(with

fixed and

_decoupled

_{proximal leaflets)}

were assembled. The

_coupling

of fluid-solid coexistence

_patterns

between

_monolayers

was evaluated

_{by doping}

the two

opposing

monomolecular leaflets with different

_types

of fluorescent

_probes.

2. Materials and methods. 2.1 LIPIDS

_(1).

-

Phospholipds - L-a-dilauroylphosphatidylethanolamine

(DLPE),

L-a-dimyristoylphosphatidylcholine

(DMPC),

L-a-dimyristoylphosphatidylethanolamine

(DMPE),

1-a-dioleylphosphatidylcholine

(DOPC) -

were obtained as commercial

_products

and used as

_purchased.

The trichlorosilanes with

_hexadecyl

_(HTS)

and

_octadecyl

_(OTS)

chains were

_products

of Petrarch

_System

Inc.

_(Pristol,

Penn.

_U.S.A.).

The fluorescent

_probes

-

synthetic posphatidylethanolamines

of various chain structures

_(DPPE,

DMPE &

_DOPE)

with

7-nitro-benz-2-oxa-1,3

diazol-4-yl

(abbreviated

as NBD

₍₁₎₎

attached to _{the head groups}

-

2.2 PURIFICATION AND PREPARATION OF GLASS SUBSTRATES. - All substrates were

carefully

cleaned before use

_by

the

_following

_{procedure :}

stored in

_Millipore

water for several

days ;

sonified in cuvette cleaner in a bath sonifier for 45

_{min ;}

Rinsed 20 times with

_Millipore

water ; ultrasonified in

_Millipor

water ; rinsed 20 times with

_Millipore

_{water ; ultrasonified} in

methanol ;

dried in a microwave oven. If

_{required prior}

to the

_monolayer

_transfer,

the

_glass

plates

were

_sputtered

in an

_{Argon atmosphere}

_(99.996

%

purity)

which was

_performed

in a

plasma

cleaner

_{(Harric PDC-3XG).}

2.3 SILANIZATION OF THE GLASS SUBSTRATES

_{(COVERGLASSES}

OF 25 X 25 X 0.1

mm 3).

-The

_procedure

of

_Nagiv

et al.

_[6]

was used.

_Clean,

_{non-sputtered}

_{coverglass-plates}

were

dipped

into a 0.1 vol. % solution of silane in a solvent

_consisting

of 80 vol. %

n-hexadecane,

8 vol. % chloroform and 12 vol. % tetrachlorocarbon. The

_plates

were left for 1.5 min

_(except

for one case of

_only

0.5

min)

in the solution.

_Longer

incubation led to

_multiple

_layers

of silane

on the substrate.

_Surplus

silane was washed-off the substrate

by

rinsing

with chloroform. In one case, the substrate was

subsequently

annealed at 250 °C for 14 hours.

2.4 BILAYER DEPOSITION AND SAMPLE PREPARATION. - A film balance

(described

previously,

cf.

_[7])

was used for

_monolayer

transfer. To

_deposit

the first

_(proximal)

monolayer,

the

_{coverglass-substrate}

was

_pulled

out of _{the aqueous}

_phase

_through

a surface

monolayer

kept

at constant

_(proximal)

_pressure

_7rp

at a

_{pulling speed}

of 3.5 mm/min.

_During

this process

monolayer

pressure was held constant

_by

electronic feedback-control of film area.

To

_deposit

the second

_(distal)

_monolayer,

the

_procedure

of McConneff and Tamm

_[8]

was

applied.

The

_monolayer

covered substrate was

_{carefully placed}

onto the

_{monolayer deposited}

onto the film balance which was set at a

_preselected

_pressure

_(transfer

_pressure

7rd of distal

monolayer).

Then,

the substrate was

_{rapidly pressed through}

the surface

monolayer

into the water

_subphase.

In

_preparation

for the

_assembly

of the

_measuring

cell a

microslide with a shallow well

(spherical cap-shaped,

diameter 16 mm,

depth

1

_mm)

has been

placed

in the _aqueous

_subphase.

The

_{bilayer-coated coverglass}

was

_placed

_{(below water)}

on

the microslide with the

_deposited

_{bilayer facing}

the well. The water

_subphase

was

_aspirated

out of the film

balance ;

residual water on the sandwiched

_{glass plates}

was

_{removed ;}

and then

the

_coverglass

was sealed to the slide with nail varnish.

2.5 PHOTOBLEACH-RECOVERY EXPERIMENT. - Fluorescence _{recovery after}

_photobleach

experiments

(FRAP)

were

_performed

with a

_{specially configured}

fluorescence

_microscope

(derived

from a Zeiss Axiomat

_{microscope [9]).}

The beam of an

_Argon

Ion Laser

_(Spectra

Physics

2020-05)

was divided into bleach and observation beams. The

_intensity

of the latter

was attenuated to less than

10-3

x the

_intensity

of the bleach beam. This was achieved

_by

proper

positioning

of two

_{semitransparent}

univers with 10 %

_reflectivity

and a neutral

_density

filter. Both beams were focussed

_by

the

_microscope

_objective

(an

oil immersion Zeiss

_Planapo

Ph3 100 x

oil)

at the same

_spot

on the surface of the

_{bilayer-çovered}

substrate. A

computer-controlled shutter allowed

_{rapid switching}

between observation and bleach beams. A set of interference filters and a dichroic mirror allowed

only

fluorescence emitted from the surface to _pass to the

_{Photomultiplier (RCA 31034-04).}

For visual

observation,

fluorescent

_light

was

diverted

_by

a removable mirror to a SIT camera

_(Hamamatsu

_{Photonics, C1000,}

_Type

_12).

The

_spot

_{bleaching technique}

was used to facilitate

Iocal measurement

of lateral

_diffusivity

in order to detect variations introduced

_by

_{inhomogeneities}

in the fluorescent

_{lipid layer.}

To achieve the

_pattern,

_only

the central

_part

of the laser beam was focused onto the

_sample

_by

placing

an

_aperture

_(0.4

mm inner

_diameter).

in the intermediate

_{image plane}

of the

microscope.

With this

_approach,

a

_{rectangular intensity}

_profile

for the bleach and observation

Prior to the diffusion measurement, the beam focus was controlled with the SIT camera.

Then,

the

_prebleach

fluorescence

_light

excited

_by

the observation beam was

_guided

to the

photomultiplier.

For the initial

_bleach,

the bleach beam was

pulsed-on

for a short time

interval

_t81

which was set to be smaller than 0.1 times the half-time of the fluorescence recovery

t1/2.

To avoid

_{photobleaching}

_(during

observations of fluorescence

_recovery),

the observation beam was switched-on for

_only

24 short time intervals

_ATOB

where

_ATOB

was

chosen to be

_{0-1 tl/2.}

The count rate of the

_{photomultiplier}

was recorded

_during

these

intervals. The total measurement time could be varied from 5 seconds to 3 hours. The values of lateral

_diffusivity

D were derived from the half-time of fluorescence recovery

_t1/2

with the

following

relation :

D = 0.224

r 2/tl/2

where r is the radius of the bleach

_spot

_(usually

r = 9

um)

and

_t1/2

is the fluorescence _recovery

half-time defined as

_by

Axelrod et al.

_[10].

The

_{glass sample plates}

were fixed onto a _copper

heat

_exchange

stage

and the

_objective

was surrounded

_by

a heat

_exchange

collar. The

temperature

of the

sample

was controlled

_by

a water bath. This ensured a constant

equilibrium

temperature

of the immersion oil between the

_objective

and the

_sample

and thus

a constant

_temperature

of the

_{bilayer-substrate assembly. Temperature}

was measured with

thermistors,

one on

_top

of the microslide and one on the _copper

_stage.

3. Latéral diffusion measurements and

_apparent

_phase

transitions.

3.1 DIFFUSION IN SUPPORTED DMPC-BILAYERS VERSUS TEMPERATURE. -

_Figure

1

_presents

the results for

_probe

diffusion measured as a function of

_temperature

in a

_symmetric

supported bilayer

of DMPC

_(on

_sputtered

_glass)

with the fluorescent

_probe

_(NBD-DMPE)

in the distal

_monolayer.

The

_monolayers

were transferred at _{different pressures}

_(17.2

_dyn/cm

for the

_{proximal layer}

and 29.7

_dyn/cm

for the distal

_monolayer).

The

_significant

features in

figure

1 are

_recognized

as :

(i)

the

_{supported bilayer clearly}

exhibited a

_liquid

_crystal-to

solid transition at a

temperature

(Tt

=

20 °C ) slightly

lower than the chain

melting

transition

temperature

of free

bilayers

in DMPC vesicles

_(Tt

=

24 °C ) ;

Fig.

1. - Left :

temperature

dependence

of the diffusion _coefficient, D

_(on

a

_logarithmic

_scale),

of the NBD-DMPE

_probe

in the

_{distal layer}

of a

_{supported bilayer}

of DMPC. _{Transfer pressures of distal film}

30 mN/m and and of

_proximal

17 mN/m. The transfer was

_performed

at 25 °C. Several measurements

(indicated

by

the

_squares)

are

_given

for each _temperature which show the variance of the measurement.

(ii)

above

_T,,

_log

D increased

_linearly

with

_temperature

where the

_slope

dln

_{(D)/d(l/F) =}

_{(6.5 ± 1.0)}

x

103

K was somewhat

_larger

than that found for isolated

DMPC

_bilayers,

i.e.

_{(3.5 ± 0.5)}

x

103

K

[11, 12].

Note : this

_{slope corresponds}

to an

_apparent

_{activation energy of}

_AEapp

=

(54 ± 10 )

kJ/M

whereas that for free DMPC

_bilayers

was found to be

_l1Eapp

=

2(9 ± 5)

kJ/M

[12] ;

(iii)

the value of D at

_temperature

well-below

_T,

_{(at 10 °C)}

was D = 0.05

f.Lm2/sec

which

was much

_higher

than the value characteristic for the

_LJ3

_phase

of

_bilayers

(D :

10- 3

_Jl.m2/sec).

This

_point

will be discussed later in terms of defect structures in

supported bilayers.

In another

_experiment,

the diffusion coefficient was determined in

_symmetric

DMPC

bilayers

where both

_layers

were formed at 20.0

_dyn/cm.

In this

_experiment,

measurements of

probe

(NBD-DMPE)

diffusion were made

_separately

in both distal and

_{proximal layers.}

At a

temperature

of

25 °C,

the diffusion coefficient was found to be D = 1.

(30 ± 20 )

f.Lm2/sec

in

the distal

_layer

and D = 1.

(26 ± 20 )

Jl.m2/sec

in the

proximal layer,

i.e.

equivalent

within

experimental

error. This result demonstrated that the

_monolayers

were

_{strongly coupled}

vis a

vis the weak interaction with the substrate

_(across

the

_lubricating

film of

_water).

3.2 DIFFUSION IN DISTAL _{(SUPERFICIAL)} MONOLAYERS ON SUBSTRATE-FIXED MONOLAYERS

OF VARIABLE PACKING DENSITY. - In

figures

2 and

3,

results are

_presented

for measurements

of

_{probe diffusivity}

in DOPC and DMPC

_{monolayers deposited}

on several

types

of

_proximal

monolayers

which were fixed to the substrate.

Figure

2 summarizes data for the case of a distal DOPC

_monolayer

with NBD-DOPE as

molecular

_probe.

The

_pertinent

features

_apparent

in

_figure

2 are

(i)

breaks or

_{abrupt changes}

in the D-versus-T

_plots

were observed in all cases. These

provided

evidences for weak conformational

_changes

in all cases which were associated with substantial reductions in the

_probe

mobilities with

_decreasing

temperature

(see

also

_[13]).

These reductions were,

however,

much smaller than in case of the chain

_{crystallization}

of DMPC

_bilayers

_(cf.

_Fig.

_1).

_Comparison

of

_figures

2a to 2d shows that the conformational

changes

started at about the same

_temperature

(25 °C)

in all cases

_suggesting

that it is a

characteristic feature of the

_{DOPC-lipid ;}

(ü)

in all tests of

_figure

2 the fluorescence recoveries were

_high

(> 80 % )

and were

essentially

constant over the whole

_temperature

_{range and} are therefore not shown. This

suggests

that the DOPC

_monolayer

was in a fluid-like state at all

_temperatures

_(both

above and below the conformational

_change)

and/or that the solidified islands formed at the transitions were much smaller than the bleach

_spot

diameter ;

(iii)

the

_mobility

of the

_probe

_appeared

to decrease with

_increasing

chain

_length

of the silanes above the conformational transitions

_(cf.

_Figs.

2a to

_2c).

The

_diffusivity

of DOPC on

the Cd-arachidate

_monolayer

was much smaller than on the silanised substrates

indicating

that D decreases with

_{increasing packing density}

of the

_{proximal monolayer.}

_(Note

that an

increase in

_{packing density}

reduces the chain

_mobility).

In

_figure

3,

the results for DMPC

_(with

an NBD-DMPE

probe)

above

hexadecyltrichlorosi-lane

_(HTS)

are shown. Conformational transitions

_(apparent

as

_changes

in

diffusivity)

were

again

found in distal DMPC

_monolayers.

The reduction in lateral

_mobility

across the

_apparent

transition was much less than that observed for

_symmetric

DMPC

bilayers separated

from the

substrate

_by

a

_lubricating

water film

_{(Fig. 1).}

To evaluate the influence of the

_{packing density}

on

_{probe diffusivity}

in the distal

_monolayer,

both the transfer _{pressure of the distal}

Fig.

2. -

Temperature dependence

of the diffusion coefficient of NBD-DOPE in

_{DOPC-monolayers}

on

monomolecular films which are fixed to the substrate.

_a)

_{Hexadecyltrichlorosilane}

_(HTS)

_deposited

from solution for 1.5 min.

_b)

Same as in

_a),

but after

annealing

of the silane

_layer

at 250 °C for 14 hs.

c) Octadecyltrichlorosilane (OTS)

deposited

from solution for 1.5 min.

_d)

Cadmium arachidate

deposited

at a _{pressure of 30 mN/m. DOPC} was in all cases

_deposited

at 20 mN/m and 25 °C.

accomplished through

reduction of the time for

_adsorption

in the silane solution from 1.5 to

0.5 min

_(cf.

_{Fig. 3d).}

The

_significant

features

_apparent

in

_fgure

3

_(and

related

_experiments,

not

_shown)

are as follows :

(i)

in all _cases, broad conformational transitions were indicated

_{by major}

reductions in lateral

_mobility

of

_probes

as the

_temperature

was

_{lowered ;}

(ü)

the nature of these transitions

_{depended critically}

on the relative

_packing

densities of the two

_layers.

The

_change

in

_diffusivity

was

_{comparatively sharp}

in the case of

_figure

3b where DMPC had been transferred at a _{pressure of 20}

_dyn/cm.

However for other cases

where DMPC had been transferred at

_higher

_(31.4

_{dyn/cm, Fig.}

_3a)

and lower

₍₁₀

_dyn/cm,

Fig.

3c)

pressures, the diffusion coefficients showed more continuous

_{transitions ;}

(üi)

the fluorescence recovery also showed a

_{sharp drop}

in the case of DMPC transferred at

20

_dyn/cm

_{(Fig. 3b)}

but remained

_essentially

constant for the cases where transitions were

continuous. These results showed that

_coupling

between

_monolayers

of the

_bilayers

was

_quite

different for each case ;

(iv)

comparison

of

_figure

3d and 3c shows a

_surprising

result. For the

(supposedly)

Fig.

3. -

Temperature

dependence

of the diffusion coefficients, D,

(left side)

and fluorescence

recoveries, R

_{(right side)}

of NBD-DMPE in DMPC

_{monolayers swimming}

on

_{hexadecyltrichlorosilane}

(HTS)

monomolecular

_layers.

a to c :

_HTS-layer

_deposited

from solution

(with

1.5 min

equilibration-time)

with DMPC transferred from 31.4 mN/m

(a),

20 mN/m

_(b)

and 10 mN/m

_(c).

HTS

layer

deposited

hom solution with

_only

0.5 min of

_{equilibration}

and distal DMPC

_layer

transferred at 10 mN/m

_(d).

The

decreasing

temperature

than for the case of the

_tightly

_packed

HTS film

_{(Fig. 3c).}

_Again,

the

packing density

of the silane film was assumed to increase with

_increasing

time for

_adsorption

to the

_glass

in the

_silanising

_{solution ;}

(v)

by

comparison,

the conformational

_change

in a DMPC

_monolayer

_deposited

on an

OTS

_{layer appeared}

to occur at a much

_higher

_temperature

(cf.

curve added to

_Fig.

_{3b) ;}

(vi)

a continuous transition was also observed in the case of DMPC

_(transferred

from

20

_dyn/cm)

on to a 1 : 1 mixture of HTS and OTS.

As will be discussed in the next

_section,

kinetic models indicate that the diffusion coefficient in free

_bilayers

should decrease

_{exponentially}

with

_increasing

surface

_density.

However for

substrate-coupled bilayers,

frictional effects at

_{monolayer-monolayer}

and

_{bilayer-substrate}

interfaces are also

_expected

to be affected

_{by packing density}

and

_monolayer

_{pressure ; if}

sufficiently

strong,

frictional effects _may dominate the

_diffusivity.

Thus,

systematic

measure-ments of the diffusion coefficient as a function of the transfer _pressure were carried out to

distinguish

intrinsic

_monolayer

_packing

_density

effects from

_{intermo.olayer}

friction,

to

evaluate the influence of

_lipid

_{packing density}

on interlamellar

friction,

and to test whether

changes

in

_{packing density}

occurred

_{during monolayer}

transfer.

3.3 EFFECT OF TRANSFER PRESSURE ON DIFFUSIVITY. - Additional

measurements for

symmetric

DLPE

_bilayers

in

_figure

4a show how the diffusion coefficient in the

_{proximal layer}

was effected

by

its transfer pressure whereas data in

figure

4b show the influence of transfer

pressure in the distal

monolayer

on

_diffusivity.

The results demonstrate the

_following

important

features :

(i)

probe

diffusion in the

_{proximal layer}

_{(Fig. 4a)}

decreased with

_increasing

transfer pressure which indicated that no drastic alteration in the surface

_density

occurred

_during

monolayer

transfer.

However,

the increase in

_diffusivity

with

_decreasing

_{transfer pressure} was

much less than

_expected

from the molecular « free » volume model

(discussed

in the next

section).

This

_{discrepancy plus}

the

_large

reduction observed for

_{probe mobility}

_(compared

to

free

_bilayers)

_suggested

that a frictional effect was

_present

which

_depended

on

_packing

density.

(Note :

the measured value of

_{d(D)/d( 1T)}

=== -11

_JLm2

_sec/kg,

whereas the free volume model

_predicts

_{d (D)ld (M)}

: - 22

_itm2

_{sec/kg) ;}

(ii)

the

_unexpected

result was that

_probe

_diffusivity

in the distal

_monolayer

_{(Fig. 4b)}

increased with

_increasing

_{transfer pressure ;}

(iii)

for _{fixed transfer pressure in the distal}

_{layer, probe diffusivity}

in the distal

_layer

decreased when the transfer _pressure was lowered for the

_{proximal layer}

(compare

data in

Fig.

4b).

It should be noted that the diffusion coefficients in the test of

_figure

4 were measured at two

temperatures :

25 °C and 35 °C. The measured D values in the

_{proximal layer}

exhibited a

larger

variance at 25 °C than at 35 °C.

However,

at all

_temperatures

the diffusion coefficients of

_probes

in the

_{proximal monolayer}

were about

_equal

to or rather

_larger

than in the distal

monolayer.

We therefore conclude that both

_monolayers

are

_{strongly coupled together}

but

are

_separated

from the

_glass

surface

_by

a water

_layer.

3.4 THEORETICAL ASPECTS OF DIFFUSION.

3.4.1 Membrane-substrate

_{frictional effects.}

- The

_{experiments just}

described were motivated

by

a recent

_analysis

_[1]

of

_{particle mobility}

in a

_liquid

membrane

_coupled

to a

_rigid

substrate.

The

_development

was an extension of the

_{phenomenological theory}

for diffusion in free

_liquid

Fig.

4. _{- Effect of the variation of the transfer pressures of}

_proximal

and distal

_monolayer

on its diffusion coefficient for the case of

_{supported bilayers}

of DLPE.

_a)

_Dependence

of the diffusion coefficient in the

_{proximal monolayer}

on _{its transfer pressure in all} cases measured at 25 °C. The distal DLPE

layer

is

_deposited

from 17.6 mN/m, b and

_c)

_Dependence

of the diffusion coefficient in the outer

monolayer

on _{its transfer pressure for} two values

_(17.5

mN/m

_(b)

and 20 mN/m

_(c))

of

_deposition

pressure of the

proximal monolayer

(Diffusion

measured at 35°

_C).

[15].

For the

_{substrate-coupled}

membrane

_(cf.

_Fig.

_5),

the transfer of momentum from the membrane flow field

_(created

_{by particle}

_motion)

to the third dimension is dominated

_by

the presence of the substrate at

_large

distances from the

_particle.

For a

_particle

of radius

ap

(which

spans the

membrane) moving

with instantaneous surface

_{velocity vp, particle drag}

is

produced by

two

_effects,

i.e.

_FD

=

(Àm

+ Àp) vp.

The first term accounts for the viscous

dissipation

in the membrane

_plus

friction between the fluid membrane and the substrate whereas the second term is the direct friction between the

_probe

and the

_rigid

_{surface ;}

À m

and

_{À p}

are the

_{corresponding drag}

coefficients in

_{dyne-sec/cm. According}

to kinetic

theory,

the diffusion coefficient D is determined

_through

the Einstein

_relation,

D =

kT/(Àm

+ Àp).

To determine the

_drag

created

_by

membrane

flow,

the 2-dimensional

equation

of motion was solved

_including

the effect of interfacial

drag

on the membrane caused

by adjacent

immobile substrates-or-across a

_lubricating

_liquid

_layer

to the substrate. Interfacial friction was modeled

_{by assuming}

that the interfacial shear stress _Us was

proportional

to the local membrane

_velocity,

_{i.e. Us} =

bs

_v. For a

purely

lubricative

layer

of

Fig.

5. - Schematic illustration of _a

lipid probe

in the

_proximal

or distal

_monolayer

of a

_(in

_general

asymmetric)

bilayer coupled

to a solid substrate. Two

_limiting

situations are

_{possible :}

_{tightly coupled}

monolayers

( vd

=

-Vp)

(this

case is realised at

_lipid

_{bilayers swimming}

on a thin water

_film)

and fixed

proximal monolayer

vp = 0

(realised

in

lipid monolayers

on silane- or Cd-arachidate-covered

substrates).

velocity gradient

and _{the relation os} = IL

(v /h f ).

For direct frictional interactions

(e.g.

between

_monolayers

or between

_monolayer

and

substrate),

the

_liquid

continuum model for

shear stress across a

lubricating layer

is

replaced by

the

phenomenological proportionality

of

bs

=

o-g/tv ;

bs

becomes _an intrinsic

property

of the interface. With this model for interfacial

friction,

the

_{particle drag}

_{coefficient À fi}

for membrane flow was found to be

_{given by}

membrane surface

_viscosity

times a universal function

_{f ( e )}

of the dimensionless

_particle

radius

_[1].

where Tlm

= ’qBl is

the intrinsic

_{2-D-viscosity}

of the free

_bilayer

_(or

_Tlm =

TlBI/2

for _a

monolayer)

in an infinite aqueous

médium ;

_Ko

_{and Kl}

are modified Bessel functions of zero

and first

order ;

the

_argument

e is the dimensionless

_particle

radius

_given

_{by 8}

=

ap(br,/nm)"2

where 17M = 77Bl

or _{nm =}

_{TI BI/2}

as

_required.

It should be noted that membrane surface

viscosity

nm is

formally equivalent

to a 3-D

_{viscosity um}

times the membrane thickness

hm (i. e.

Tlm =

IL m

hm).

Similarly,

it was

_anticipated

that the

_probe

_may exhibit a

_separate

«

_{self-drag »}

characteristic for interaction with the substrate.

_Hence,

another continuum

approximation

was introduced into the

_analysis

to

_represent

_{particle-substrate}

_friction,

i. e.

Fp

=

7ra)

bp

vp.

Therefore,

the

82 term

in the universal function

f (e)

is

simply

augmented by

a factor

(1

+

_bp/bs)

to include this

_possibility.

Since the

_{diffusing particle}

_(probe)

is often an

analogue

of membrane

_{constituents,}

the ratio

_bp/bs

can be taken as

_{approximately}

_unity.

Additional

_drag

due to an exterior

_bathing

solution above the membrane is not

_large

and

can be treated with a

_{simple approximation.}

_Here,

the dimensionless

_particle

radius

fluid

_phase

above the

_bilayer,

i.e. 6 =

ap[(bs

+

boo)/l1m]1/2.

It was found that the effect of the

semi-infinite

_bathing

fluid

_adjacent

to the membrane is

_{well-approximated}

_by

where 1£ .

is the 3-D

_viscosity

of the exterior _aqueous

_phase

and where 6 is a

_length

which characterizes the

_penetration

of the membrane flow field into the third dimension

(S = n BI/2 /-L 00 )

or

_{equivalently,}

where Eoo = 2

ap 1£ oo/’q Bl

is the dimensionless

_particle

radius for

_probe

motion in a free

bilayer. Again,

the surface

_viscosity

_nm is to _{be chosen as nB1}

_{or ’Tl BI/2}

_appropriate

to the

particular

membrane-substrate

_assembly.

Let us consider now two cases.

1)

When the

_probe

is

_moving

in the distal

_monolayer

_adjacent

to a fixed

_proximal

monolayer,

then ’q. = ’qBl/2

and the dimensionless

_particle

radius

_(to

be used in the

_drag

coefficient

_equation)

_becomes,

2)

When the

_probe

is

_moving

in either

_monolayer

of a

_bilayer

_weakly

_coupled

to the substrate

_(e.g.

_by

a thin

_lubricating

film of

_water),

then

_{intermonolayer}

friction

_strongly

couples

the

_probe

motion in one

_monolayer

to the

_adjacent

_monolayer

as if the

_probe

was a

transbilayer particle.

Consequently,

the dimensionless

_particle

radius is

_specified

with n m = 71 Bl

For a

_lubricating

water film of thickness

_{h f, b,}

=

u00,/hf

and we obtain

This

_equation

is valid for

_{h f}

8 and has the obvious _{self-consistent limit EB1} =

£00 for

hf =

S.

In order to determine frictional

_properties

of

_{substrate-coupled}

_membranes,

the

_following

procedure

is

_required.

The first

_step

is to establish the intrinsic viscous

_properties

of the constituents as a free

_bilayer.

This establishes the surface

_{viscosity nB1}

and

_(with

the

_particle

size

_ap)

the value of the dimensionless

_particle

radius _£00 for the free

_bilayer

which are the

parameters

required

in the

_particle

_drag

relations.

_Clearly,

the surface

_{viscosity nm (and}

thus

e(oo) depend

on

_temperature

and surface

density

which also must be established

_{a priori.}

Hence,

probe diffusivity

is measured in free

_bilayers

as a function of

_temperature

_(surface

density

is

_uniquely

determined

_by

_temperature

for a free

_bilayer

in a

_large

_aqueous

_phase).

Using

the fluid mechanical relation for

_drag

coefficient

_(reciprocal

of

_mobility)

and the Einstein kinetic

_equation

for

_diffusivity,

measurements of lateral diffusion in free

_bilayers

are

converted to values _{of 11 m} and _{£ 00 .}

The next

_step

is to measure

_{probe diffusivity}

in

substrate-coupled layers

where the state of

bilayer

system.

In this _case, the surface

_viscosity

and

_prefactor

_eoo are taken from the values

determined for the free

_bilayer.

To derive estimates of viscous coefficients for interfacial

friction,

the

_appropriate

relation for dimensionless

_particle

radius is chosen

_(either

EB1 or _Em, as described

previously)

which

_represents

the

_{bilayer-substrate assembly}

_{process ;}

then,

the universal

_drag

relation

_{f ( E )}

is used to convert the measured value of

_diffusivity

(arranged

as 4 7r

_Dn

_./k7)

to the

_{corresponding}

value of the

_{phenomenological}

coefficient

bs.

3.4.2

_Temperature

and

_{monolayer packing}

_effects.

The variation of the

_diffusivity

in a free

liquid

membrane with lateral pressure can be understood in terms of a molecular « free »

volume

_(or

molecular « free »

_area)

model which relates D to the surface

_density

of the

bilayer.

The model is based on the Cohen-Tumbull model for diffusion in

_glasses

which was

extended to fluid membranes

_[11].

The model

_predicts

that the sensitive

_temperature

dependence

of the diffusion coefficient in fluid

_bilayers

is due to

_changes

in « free » volume

caused

_{by bilayer}

thermal

_expansion

in contrast to a rate-reaction _{activated process. The} molecular « free » volume

_{(or area)}

is the excess volume

_(area)

_{per molecule} at a

_given

temperature

above the volume

_(area)

for the ultimate «

hard-packed

» state

_(usually

taken as

the

_crystalline

_state).

The model

_specifies

that the

_diffusivity

_{depends exponentially}

on the

surface

_density

which has been well verified

_by

measurements in

_monolayers

at air/water interfaces

_[16].

3.5 DETERMINATION OF VISCOUS COEFFICIENTS FOR INTERFACIAL FRICTION. - Two

problems

arise in calculations of frictional coefficients from measurements of

_probe

diffusivity.

First,

the diffusion coefficient

_depends

on two unknown

_parameters,

i.e. the frictional coefficient

_b,

and the membrane surface

_{viscosity q..}

Further,

according

to the

predictions

of the molecular « free » volume model

just

outlined,

surface

viscosity depends

on

surface

_density

of the

_{bilayer (or monolayer)}

which is

_clearly

variable. The second

_problem

concerns the

_{assumptions employed}

in the fluid mechanical

_analysis

of

_particle

_drag

in

substrate-coupled

membranes. In the

_{original analysis}

_[1],

the

_equation

of motion was solved

for a

_particle

_moving

in a

_single

membrane

_{layer coupled}

to a

_rigid

substrate

_(either

_directly

or across a

_lubricating

film of 3-D

liquid).

As

_such,

this treatment is

_appropriate

for

_probe

motion in a

_superficial

_monolayer

_adjacent

to a

_{proximal monolayer}

that has been

immobilized

_by

fixation to the solid

_substrate,

_e.g. DOPC and DMPC on fixed

_proximal

monolayers

of silanes or Cd-arachidate

(Figs.

2 and

3).

Therefore,

we have used the relation for dimensionless

_particle

_{radius £Ml and} nm =

’TlBl/2 in

the

prescription

for

drag

coefficient

to estimate the viscous coefficient

_bs

for

_{intermonolayer}

friction from these data. However for

supported bilayers

separated

from the substrate

_by

a thin film of water

_(e.g.

_symmetric

DMPC

_bilayers

on

_glass),

the

_analysis

would appear to be

_applicable

_only

if the

_probe

spanned

both

_monolayers

so that the

_bilayer

could be considered as a

_{single layer.}

Even

though

the

_{probe only spanned}

one

_layer,

it is reasonable to treat this case as if the

_probe

spanned

both

_layers.

The rationale is that the frictional

_coupling

between distal and

_proximal

monolayers

greatly

exceeds the interfacial

_drag

of the

_lubricating

water film on the underside

of the

_bilayer,

so the surface flow fields created

_by

particle

motion will be

nearly

the same in

either

_layer.

Thus,

the ad hoc

_assumption

is that the

_monolayers

are

_{strongly coupled}

vis a vis

coupling

to the substrate across the

_lubricating

water film. This

_assumption

is

_{supported by}

the

_experimental

observation that

_probe

diffusion measured

_separately

in distal and

_proximal

monolayers

of

_symmetric

DMPC

_bilayers

_(separated

from the

_glass

substrate

_by

a water

_film)

was found to be the same

(cf.

discussion of

_Fig.

1).

Therefore in this case, we have used the

and q .

= _q

Bl in order to derive estimates of the viscous coefficient for the

lubricating

water

film and the film thickness.

The method of calculation described above was

_applied

to data for DOPC and DMPC

monolayers supported by

fixed

_monolayers

_(Figs.

2 and

_3).

Here,

diffusion coefficients for

probes

in free

_bilayers

of

_synthetic

lecithins

_[12]

were used to

_{establish n B1}

and the

_prefactor

£00 at 45 °C. These values were

_expected

to be the same for both DMPC and DOPC at 45 °C because Galla et al.

_[11]

_{measured diffusion for pyrene}

_probes

in both DMPC and DOPC

bilayer

vesicles and found

_nearly

the same values at 45 °C. Values for

_diffusivity

and

_viscosity

at lower

_temperatures

were derived from the

_temperature

_dependence

of

_diffusivity

found for free

_bilayers

_[12].

The crucial

_assumption

_(which

is

_implicit

in the use of these

_values)

is that

monolayers

transferred at 20

_dyn/cm

_pressure

represent

the fluid state in free

_bilayers.

Particle radii

_ap

were taken as 4

Â

for DMPC and

5 Â

for DOPC as estimated from the area

per molecule in film balance

experiments.

Table 1 outlines the

properties

of free

bilayers

used in the calculations of viscous coefficients for interfacial friction. Table II

_presents

measure-ments of

_probe

diffusion in distal DOPC and DMPC

_monolayers

_supported

_by

fixed

_proximal

monolayers

and the values calculated for viscous coefficient

_b,

which

_represent

friction between

_monolayers.

An additional calculation was

_performed.

The viscous coefficient for

the

_lubricating

water film between a DMPC

_bilayer

and

sputtered glass

was estimated

_along

with the film thickness.

_Here,

values for

_probe

diffusion were found to be 5.7

>m2/sec

for a

transfer pressure of 15

dyn/cm

at 25 °C. Since

_precise

surface densities for

_monolayers

were

not

_known,

we have assumed that free DMPC

_bilayers

at the same _{pressure would be}

characterized

_by

diffusivities form 6 to 11

_um2/sec

_(the

_{range of}

_diffusivity

for free DMPC

bilayers

between 25 °C-45

_°C).

With this

_assumption,

the viscous coefficient for interfacial

drag

was estimated to be between 2 x

103

and 3 x

105

dyn-sec/cm 3.

Further,

the

drag

coefficient for the

_lubricating

water film was converted to an estimate of the film thickness

hf,

i.e. 1-50 nm.

Table I. - Kinetic and viscous

_{properties of}

_free

_bilayers.

(1)

A value of

_b,

_{= 103 dyn-s/cm corresponds}

to a characteristic

_depth

d =

10- 5 cm

for

_penetration

of the _{surface flow field into the exterior aqueous}

_phase.

3.6 DISCUSSION OF DIFFUSION DATA AND CALCULATIONS OF VISCOUS PROPERTIES. - As shown in tables 1 and

_II,

most measurements of

_{probe diffusivity}

were characterized

_by

dimensionless

_particle

radii e on the order of one or less. For values of e «

_1,

the relation for

Table II. - Viscous

_properties

_{for interfacial drag}

between

_fluid

and immobilized

_monolayers.

A. Distal

_{Layer :}

DOPC with NBD-DOPE

_probe

_(Transfer

pressure 20

dyn/cm)

(1)

Note that the values of D at _{10 °C may be reduced}

_by

the formation of solid domains

_exhibiting

diameters small

_compared

to the bleach _spot diameter

_(cf.

reference

_[20]).

B. Distal

_{Layer :}

DMPC with NBD-DMPE Probe

_(Transfer

Pressure 20