The free energy,enthalpy and entropy of hydration of phospholipid bilayer membranes and their difference on the interfacial separation

Volume 91. number 3

CHEMICAL

PHYSICS LETTERS

10 September 1982

THE FREE ENERGY, ENTHALPY, AND ENTROPY OF HYDRATION OF PHOSPHOLIPID BILAYER MEMBRANES AND THEIR DEPENDENCE ON THE INTERFACLAL SEPARATION Cregor CEVC Max-Phck Instsrrtu~ liir btopliynAaltsclreClfemre, Abt. Spektroskopre. Nlkohuberg, D-3400 Girtingen. Fedeml Republtc of Germany

and Rudi PODGORNIK and BoSt)an &KS Inrhtutefor Bi~pfrytics,hfedtcal Faculty, and Insntute J. Stefart. UniversityE, Kordelf of Lfubl/ottn, YU-61000 LJub/Jana, Yugoslovta Recerved 6 Aprd 1982.1” final form 3 July 1982

The phcnomcnological theory of water bmdmg to non-charged phosphohpid bdayer mcmbrancs IS prcscnted and the free energy, enthalpy, and entropy of hydrahon are calculated as a functron of rnterfacwl sepamtron. Thcsc cstrmated hydration quantiues agree with our expenmental data provided the mterfanal effects arc descnbcd m terms of the surface wnter-onentmg field of constant strength.

It IS now agreed that the structuring of water plays an important role tn deterrninmg the propertres and behaviour of aqueous solutrons of inorganrc and organic compounds (ions, bromolecules, membranes, cell aggregates) [I]. But whilst the hydration of simple molecules has been experimentally well explored and can be described wAun the framework of standard quantum chemical physics, hardly any relevant expertmental data [2,3] and hardly any suitable theories of hydratron of larger, more complex systems have been available. Here we report results of the first measurements of the enthalpy, entropy and free energy of hydration of multibilayer membranes (from the noncharged phosphohpid phosphatidylethanolamme) as a function of the interfacial separation down to 0.2 nm, i.e. to the lipid monohydrate. We describe a simple phenomenological theory of the water interactions with a polar or non-polar interface which bears no net charge, based on the concept of the interfacial water-orienting fields and show that such a model provides a correct description for the interfacial water binding beginning with the mono-

0 009.2614/82/0000-0000~8

02.75 Q 1982 North-Holland

hydrate. Wrthin the framework of thus theory, we derive expresstons for the free energy, enthalpy, and entropy of hydratron of two drssimdar, opposmg interfaces as a functton of then separation. WCalso detemune the right boundary condition for the water order induced by the presence of neutral mterfaces. The ercellen t agreement between our c3lonmetnc or X-ray data and the theoretical predictions indicates that the model is adequate for descrrbing both the microscopic and macroscopic bdayer hydration

parameters down to the smallest experunentally achtevable mterfacial separattons. The enthalpy and entropy of hydration,@vd and Shyd, were determmed calonmetrically as a functron of the water content in multllayer dispersions of the noncharged lipid, phosphatidylethanolamine. The inter-bitayer separatton d was estunated from the relative water concentratron by using the lipid molecular areas (determined separately in X-ray experiments) and the molar volume of water. The free energy of hydratton, Chyd, was calculated from Hhyd and Shyd and is thus subject to somewhat larger expen-

193

Volume

91, number 3

00

01

02

CHChllCAL

03

OL

05

06

07

08

09

05d [ nm] Tlg. I The inverse hypcrbohc tangent of the ctionmctncally determtned wlues of the cnthalpy (X = H, 0). entropy (X = S, n) and free energy (X = G, A) of hydration of multlbdaycr phosphattdylclhanolammc dtsperaons In water relattvc to the valurs of thcsc quantmes at ma..lmal y ahon, I c. at v-2 , Gb?d),and ma\lrnal mterbtlaycr scpantton, (/&fd, Ly asa function of the half-distance between the mtcrfaces, 0 Sd. The solid hne denotes the calculated depcndcncc ac-

cordlng to the present theory and E the water-order cocrclation length The uucrt shows the correspondmg cvpertmcntal tatlo sb’d(d)/&Yd as a funcuon of the toter mtcrbdPycr separntlond. together wrth the calculated dependence assummg a lixcd value of the surface water polanzahon (cIJ-2) or a lived value of the surface oricnbng field strength (-th) and E = 0 26 run Ghyd(d)/G>d and t&‘d(d)/ifhYd

also behave slmtlarly

errors. The details of these experiments wtll be grven elsewhere 141. Our main interest was to study the dependence of the thermodynamic membrane hydration parameters on the interbdayer separation, In excess water, when

mental

the molar water/lipid ratio29, @‘d(d), flyd(d), and Ghsd(d), as well as the mterlamellar water layer th1ckness.d

= d,,

cez~~e to depend

on the water

con-

centration. In the insert to fig. I we present the inverse ratlo of the absolute value of shYd(d,) = $JYd (Hh2d and GkYd behave similarly) and the correspondmg

quantities

measured for d -Cd_,. These

data mdicate that whenever d + 0, fiyd(d),. Shyd(d), and Ghyd(d) tend to zero approximately as the hyperbohc tangent. In fig. 1 we have therefore also plotted ath(A?yd($ d)/fl_Yd), where X = S, H, C and found that all the experimental pomts fall roughly onto one straight line which goes through the o&n

194

and

has slope 5:= 0.26 (1 f 0.13) NIL

10 September

PHYSICS LETTERS

1982

The only theory of membrane hydration proposed so far is due to MarEelJa and co-workers. These authors assumed that the water structuring caused by an mterface can be described by an average water order parameter which they have shown to fall-off as the hyperbolic sure wrth the distance from the interface. By using the fued value of this parameter at the surface as a free parameter they successfully explained the nature of the water-mediated interlamelfar repulsion [5,6]. However, because of the assumption that the surface order parameter has a futed value, the validity of their approach remamed confined to large mterfacial separations. Moreover, the question as to the right chorce of the boundary condition was raised [I 1. For these reasons, and also because of the lack of unambiguous experimental venfication [3,7], therr ideas have been less widely acknowledged than they deserve IS]. Here we generalize their concept, to become apphcable for the descriptron of the hydratron of arbrtrary, noncharged, polar or non-polar Interfaces and for the calculation of the hydration energies at all separations >.$. We represent the order of the water molecules withm the interlamellar space by an onentational order parameter p(x), which is a function of the distancex measured from the midpoint between the two interfacial planes, wluch are located at g/2. In order to make the problem of determining P(x) reasonably tractable, we neglect the discrete ongin of the water binding rites.. Instead, we replace their onenting field by Its effective average F(x). The changes of the free energy caused by the partral orientation (polarizatron) of the interbdayer water, Ghyd(d), can now first be wntten in terms ofP(x), its derivatives, and F(x)GhYd(r.f)= (1/2A)S -tiF(x)

[P’(x) + .$2(dP(x)/d#

P(x)] d V .

(0

where A = A(T) and .&the water-order correlation length, is a parameter with lesser, by assumptibn neghgible, temperature dependence. It can be shown that Ghyd(d) written UIsuch form includes all the free-energy terms neglecting the fourth and h@er orders [9]. The requirement for Chyd(d) to be mini-

mum then leads to the Euler-Lagrange equatron r;2[d2P(x)/dx21 -P(x)=

--/IF(x),

(2)

Volume 9 I. number 3

We confirm

CIIIXICAL

ourselves

all the sources of F(x)

to the most sunple case when are located

solely on both mter.

faces or F(x)=f$(x

+d/2)

where j;

andf,

denote

fields atx

= -$2

the delta

function.

tlons forP(x)

-_f$(x

-d/2),

(3)

the strengths

andx

= d/2,

of the orienting

respectively,

The appropnate

can be found

and 6 is

boundary

by mtegratmg

atx

pectively.

Assummg

that P is bite

for -d/2
and identsally

zero outslde

thus Interval,


= -d/2

conch-

eq (2)

across the boundary

and atx

= d/2,

IO Scptcnlbcr 1982

PHYSICS LL-fTlIRS II-,,

‘/I

Ghyd(d)

=/,

cq (5) sunphfics

= -(AS”/~)

th(d/?$)

to

= Gkyd

th(d/?.$)

(7)

,

wluch IS prcctscly the dependence on the mtcrfacial separation found m our eupcruncnt.

The MarrelJa

model [S] on the other hand, prcdlcts the free energy of hydratron x, -th

to mcreasc

as cth(d/2[).

x = cth x - 2 = 2 eup(-2x)

-

For large I

.md the devrations between the concept of the fiixcd res-

surface

watcrordcr

orlentmg

polarrzatlon

field IS Immatcrral

when d + 0, the model

one

becomes

obtams

madequatc

and fuccd surface

(Insert

m fig. I). But

usmg P(ti/2)

as a panmctcr

since It does not account

for the

mutual disturbance of the surface water order caused by the approaching non-physical

mterfaces.

singulanty

hcncc

It leads to the

of the free energy

Ghyd

X cth(d + 0/2t) + 00. Moreover,

because

of the sample form

(1) can be arranged (dp/dx)2

(by mtegratlon

term) to consist

Ghyd(d)= -;Sv,f’(x where

of F(x),

of only surface tf?P(x

=-d/2)

S is the boundmg

surface

The use of the appropnate

From

eq.

by parts of the

=d/T)] -

7

(4)

with eq (4) fmally lcads to the evprcsslon for the total free energy of hydratlon of two mutually Interacting, dissmuJar mterfaces as a function off,, iz and d.

- (ilG”yd/a 7.) th(d/?t) m

S”yd(d) = -X’l”d(d)/H-”

and the enthalpy of hydration fiyd

(4

= (&‘d

+ T@‘)

th(d/Zt)

to see that In both cases the dependcncc on the mtcr-

It seems that the discreteness sites and the precise nature

(5)

csch(dMl the selfenergy

Ghyd = -(AS/20 self

&$O=

agrcemcnt

-L4S/2E)

(fig.

2

and the correspondmg

interactton energy {U; +I.;,

MW~

We note that these expressions

- 1I

[E/Qd=m)] interfacial

despite

their

This is so because

(dp(x)/b)x=djz - 1 *d+O due to the couplmg. The conditions for the valirhty

of the series expansion

lmphclt

fulftied even when the hydrated ly together.

in eq. (1) are thus surfaces

III

th(d/ZQ. binding

surface

play

the case of phosphatldylby the evcellcnt

our experiment

and the theory

tits to

I) and also by the fact that our model

molecula.~

may also be used m

separations

character.

of the bilayer

This IS Indicated between

by

of the water

error 4%) the phosphatidyl-

ethanolamtne bdayer hydration data obtained In the klontc Carlo simularion procedure when the detailed

(6)

the case of small interfacral

role, at least

wIthin 11% (average

- V-,f2c~cW/S)~ .

phenomenological

only a mmor ethanolamme.

terms

(fz + f') 1

,

facial separation IS grven approummately

Ghyd(d) = l (AS/25) [(f; +I;) cth(d&)

and Includes

of

= &“d th(d/l<)

of eq. (2)

together

- 2ftf2

the entropy

terms

area. solution

eq. (7) we can also calculate

hydration,Shyd(d).

come closc-

(Because

structure

was taken

the bdayer-bdayer

ected m the Monte

Carlo

k IS m this case somewhat phenomenolo@cal tlon proposed quite accurate. eral apphcability

into account tnteractlons

study,

the optimal

larger,

0.35

description

nm.)

value

the prereqmslte

of such a theory

for

The

of the interfaclal

in this work and in ref. [S] However,

[ 101. were II@

IS

hydra-

thus

for the gen-

IS that the presence

IS described by Its onenting field, rather than by the surface value of the water polanzaof the mterfacc

[Ion. The fact that such a model

agrees with both

the 195

Volume 91. number 3

CHEMICAL

PHYSICS LETTERS

microscopic and the macroscopic experimental data can be seen by comparing the waterorder correlation length determined m our caIonmetnc measurements, 4 = 0 26 nm and m the X-ray experiments, 5 i= 0.25 nm (see also refs. [3,7,8]). It is worth restatmg that our results also provide an extension into the regron of small bilayer-btlayer separations of the previous studies of the interlamellar forces smce the interbilayer repulsave pressure is given simply by S-t [aGhyd(d)/adj. In summary, we have determined the entropy, enthalpy and free energy of hydratron of noncharged polar phosphohpld bllayers as a functron of the interlamellar separation. By generahzing the recent theory we have developed a simple phenomenlogical desctiption of the interfacial hydratron, based on the use of the surface onenting field dens@ which can be used even m the case of small interfacial separations. We have clarrfied the queshon of the appropriate boundary conltion for the water-order parameter (m case of membranes with no net charge) and shown that good agreement between both the mrcroscoptc and macroscopic experimental data and the theory can

196

10 September 1982

be obtained provided the Interracial orienting fields are taken to be surface distributed.

References [ I] B.W. Ninham. J. Phys Chcm. 84 (1980) 1423 (21 J 8. Hasted, Aqueous dielectrics (Chapman and Halt, London, 1973). ]3] R P Rand, AM. Rev. Btophys Broeng 10 (1981) 277. 141 G. Cevc and D. Marsh, rn preparatron. [ 5] S hfmEelJa and N. Radrc, Chem. Phys Letters 42 (1976) 129 [6] S. hf&elJa, D J hlrtchcll. B.W. Nmham and hl 5. ScuBey, J. Chem. Sot Faraday II 73 (1977) 630. 17) D.hl LeNeveu, R P. Rand and V A Parscgian, Nature 259 (1976) 601. V A Parscfpm, N. Fuller and R.P Rand, Proc Natl Acad SCI US 76 (1979) 2750_ [9] R Podgorntk, C Cwc and B Zek? to be pubhshed. [IO] H fruchlcder, In: Proceedrngs of the 6th School on Btophyacs of Membrane Transport, Part I. eds J Kucaera.C. Grygorczyk and S. Pnestalskt. Wroclaw, Poland (1981) p. 55

[ 81