Effects of domain connection and disconnection on the yields of in-plane bimolecular reactions in membranes

Effects

of domain connection and

disconnection

on

the

yields

of

in-plane bimolecular reactions in membranes

Eurico C. C. Melo, * Isabel M. G. Lourtie,* Mantripragada B. Sankaram,§Thomas E.Thompson,§ andWinchil L. C.

VazI

*Centro deTecnologia

Quimica

e

Biol6gica-l.S.T.,

Oeiras, Portugal;tCentrodeAn6liseeProcessamentodeSinais,Complexo1, I.S.T., Lisboa, Portugal; §Department of Biochemistry, University ofVirginia,Charlottesville,Virginia22908, USA;and

lUnidadedeCidnciasExactaseHumanas,Universidade doAlgarve,Faro, Portugal

ABSTRACT It hasrecently been shown(Vaz,W. L.C.,E.C.C. Melo,and T. E.Thompson.1989.Biophys.J.56:869-875;1990.Biophys. J. 58:273-275) that in lipid bilayer membranes in which ordered and disordered phases coexist, the ordered phase can form a two-dimensional reticular structure that subdivides the coexisting disordered phaseintoa disconnected domain structure. Herewe

considertheoreticallytheyields ofbimolecular reactions between membrane-localized reactants, whenboth thereactantsandproducts areconfinedtothedisorderedphase.Itis shown thatcompartmentalization ofreactantsin disconnecteddomainscanleadtosignificant reductions in reaction yields. The reduction in yield was calculated for classical bimolecular processesand for enzyme-catalyzed reactions. Theseideas can be used to explain certain experimental observations.

INTRODUCTION

Biological membranes are made up ofa lipid bilayer, andintegralandsurface-attachedproteins.The

lipid

bi-layer is viewed as a quasi-two-dimensional fluid-like

sheet inwhich lateral diffusion and redistribution

ofcom-ponents occurs

(Singer

and

Nicholson,

1972). This

lat-eral diffusion permits molecular reactions and interac-tions ofphysiological importancetooccurintheplane of

amembranesuchasthemitochondrial innermembrane

(Lenaz, 1988; Chazotte and Hackenbrock, 1989;

Rajar-athnam etal., 1989).

The lipidbilayer is a complex mixture of

lipids

that

may varysignificantly from eachotherintheir chemical

and

physical

properties. Insuch

mixtures,

phase

separa-tionsleadingtodomain formationare

possible

(Wuand

McConnell, 1975; Lee, 1977; Tocanne et al., 1989). Phase separation is dependentupon temperature, pres-sure, chemical

composition,

and for membranes with charged

lipids,

alsouponthe pHandionic strength ofthe aqueous medium. Phase

separation implies

nonhomo-geneous componentdistributionsnot only of thelipids but also of the membrane

proteins,

which may

prefer

onephaseoveranother.Forthe caseofreacting protein

or

lipid

species, nonhomogeneous distributionscan sig-nificantly affect reaction yields.

Wehaverecently shown (Vaz etal., 1989, 1990; Bult-mann etal., 1991) that membranes in which ordered and disordered phases coexisthave adomain structure

in whichasmallmassfractionof ordered phase formsa

reticulum that subdividesthedisorderedphaseinto dis-connecteddomains.Ithas beenshown(Vazetal., 1989; Bultmannetal., 1991)that the massfraction ofthe or-deredphaserequiredtoachieve this subdivisioncanbe

aslowas20% of thesystem.

Address correspondenceto Dr.Thomas E.Thompson, Department of

Biochemistry,Box440MedicalCenter,UniversityofVirginia, Charlottesville, VA22908.

Here weconsiderspecificallytheeffects of reticulation

uponthe reactionyieldof bimolecular reactions

involv-ing membrane-boundreactants.Fromthestandpoint of biologicalsystems the effects of reticulation are twofold:

(a) if the existence of reticulation is unknown to the

outside observer, measurements ofthe reaction system can lead toincorrectthermodynamicparameters;(b) if the cell can by metabolic means movethe membrane domain structure back and forth across thepercolation threshold to connect or disconnect a particular phase,

the cell can control the extent of membrane-localized reactionsconfined to that phase. The general problem

concerns reactions occurring in a compartmentalized

spaceandis,inprinciple, alsoapplicabletoreactions in systems with phase separations involving disordered

phases only, butwithanabsolutesolubility preference of the reactants for one phase overthe other(Hatlee and Kozack, 1980).

Recentlywehaveexamined fromatheoretical

stand-point

the effect of

compartmentalization

on a

mem-brane-confined homodimerizationreaction(Thompson

et al., 1992). The ideas developed in this paper have beenappliedinanexperimental analysis ofthe

concen-tration dependence of electron spin resonance (ESR) line shapes ofaphosphatidylcholine spin labelin two-component, two-phase phosphatidylcholine bilayers (Sankarametal., 1992). Inthe present

manuscript,

we

extend thetheoretical

analysis

toincludemorecomplex in-plane reaction systems.

THEORY

In general when reactants are randomly distributed over a compart-mentalized system, the product yieldwillbe lower than when the

reac-tants aredispersed in a continuous system. The yield decreases as the average numberofreactantmolecules per compartment decreases. As

ameasureof theextenttowhich a reaction is hindered by reticulation of the membrane, let us define the expected relative yield,

(1)

1506 0006-3495/92/12/1506/07 $2.00 Biophys. J. ©BiophysicalSociety

Volume63 December 1992 1506-1512

(

(P>

= (Iklet>

(,tcont

>

astheratio oftheyield expectedtobe achieved in the reticulated

mem-brane,(t,,t>,totheyield expectedtobe achieved inacontinuousone,

<D,t>.Theyieldornetyield,

<(>

is definedasthefinal number of product moleculespercompartment/the initial number ofreactant

moleculespercompartment.

Wemodelthe reticulated membraneasapatternoftwo-dimensional fluid domains that,regardless ofshape,have thesame area.Moreover,

weconsider that the barriers between domainscannotbecrossedbythe

reactantmoleculessothat thereisnoexchangeofreactantsbetween

reactioncompartments. Forthe sake ofsimplicity,weassumepoint molecules. We makeafurthersimplifying assumptionthat the

reac-tionsarenotreversible sothat the chemicalprocesseswithina

com-partmentproceeduntilatleastoneof thereactantsisfullyconsumed.

Itmustbe stressed thatwedonotconsider the kineticsof the reactions

butonlytheiryield,sothat neither the dimensionnortheshapeof the

domains (two-dimensional vessels) needstobe taken into account.

The lifetime of disconnecteddomains is assumedtobe muchlonger than the timerequiredtoattaincompletereaction.

Inpractice,wedeal withdispersions of cellsorlipid vesiclesin which

the reaction spaceis the lipid bilayermembrane. Both are apriori

compartmentalizedreaction systems. Reticulation of the membrane

superimposesasecondarycompartment pattern onthisalready

dis-cretereactionspace.Weareconcerned hereonly with the secondary compartmentalizationthat makes thesingle vesicleorcell,whichwe

shallrefertoasthe"unit,"ourpointof reference. We consider that

encountersbetween allreactantmolecules inasinglenonreticulated unitarepossible,whereas in the reticulated unitonlyreactionswithin

singledomains will takeplace.Inbothcases,thenumber,i,ofproduct molecules, P, formedinagivenreactioncompartmentisafunction of

thenumberofreactantmolecules present in that compartment. Itmust

bestressed that all the unitsareassumedequivalent and,intheabsence

ofreticulation,reaction compartments(domains)and unitsare

indis-tinguishable. Since,inourmodel,the reticulum divides each unit into domains ofequalarea, uponreticulation all reactioncompartments

remainequivalent.Inbothcasesthe availablereactantmolecules,R

(R=Rl,R2, * -),aredistributed randomlyinthe reaction

compart-ments.Asaconsequence,theobservedyieldis themeanvalue taken

overthe entiresetofcompartments.

Inthehomogeneousmembrane,aconcentration[P]J,tofproduct molecules results after completion ofthe reaction. For the reticulated

casethe final concentration of theproductis[P],,t.Therefore, Eq. 1 maybe rewritten

=(P I r(2)

[P ]<ont(2)

Letusdenote the unit'Uand the domainbyD. Hence, the expected

concentrationofproduct moleculesisgiven by

[P] =

[O1]

z iPp(i), (3)

i

wherePp(i) stands for the probability of obtainingiproduct molecules

inadomain.Recalling thatinthenonreticulatedsituationthe domain extendsoverthe entireunit,theexpectedrelativeyieldwhen each unit

is divided intoNdom domainsis

E iPp( i,Ndom)

= Ndom iPp(i,Ndom= 1l) Theprobability

Pp(i,Ndom) ...* 2 P(ilnRl, * nRm)

nRI nRm

X PRIo adRm(hRledis nRmi Ndom) (r)

dependsonboth thekind ofreaction and the distribution of the

reac-tantmolecules R(R=Rl,...,Rm)amongthe domains.InEq.5the

conditional probabilityP(iInR1, ..., nRm)accountsfor the

mecha-nism of thereaction,whilePRI .Rm(nRt ... nAm,Nd&m)represents

thejoint probabilityofhavingrespectivelynRI,...,nRmreactant

mole-cules, Rl,...,Rm, inadomain. Forabimolecularreaction,ifthe

distributions of thereactantmolecules(RlandR2),PRI(nR,,Nd,m)

andPR2(nlR2,Nd,m),areassumedtobemutually independent, Eq.5

becomes

sp dom)

= z

flP(ilnR1,

nR2)PR(l(nR,

Ndom)PR2(nR2,

Ndom). (6)

nRI nR2

Provided thatalargenumberofreactantmoleculesaredistributedover alargenumber of units withoutcrowding effects,thedistributionof reactantmoleculesoverthe different units followsaPoisson distribu-tion law

An(n)=-e (7)

Themeannumber ofreactantmoleculesperreactioncompartment,U,

is either g = [R]/['U] for the nonreticulated case or ,u = [RI/

(['U]Ndom)when there is reticulation.

Inthenextsection, theaboveformalism is appliedtofourimportant

reactionmechanisms.

CASE STUDIES

We confine ourselves to the study of four cases: (a) a

Michaelis-Menten type enzymatic reaction, (b) a

con-ventionalbimolecularreaction, (c) adimerization

reac-tion,and

(d)

consecutivereactionsconsisting oftwo se-quential Michaelis-Menten type steps.

Enzymatic

reaction

Weconsiderareaction inwhichanenzyme Ecatalyzes

thetransformation ofasubstrate R intoa

product

P:

E+R -E+P.

While inahomogeneous mediumaminuteamountofE is enoughtocause acomplete conversion of RtoP,ina compartmentalizedmedium the yieldwilldependupon

the probability of having atleast one molecule of E in every compartment. Under certain conditions thiscan lead to a drastic decrease in the yield of P. The condi-tional probability that reaction takes place in a given domain withanetyield of i molecules ofP, given thatnE

molecules ofenzyme and nR molecules ofreactantare

present, is given by i=0 I =nR. (8) nEl=ew

P(ijnE,

nR)= 1 nE* °, O elsewhere

Substitution ofEq. 7 and Eq. 8 in Eq. 6 leads to the

relativeyield exp- [E]N dom, ~~(P> = [E]I I-exp -IVU IJ (9)

Meloetal. Reactionsin Reticulated Membranes 1507W]

It should be notedthat, in this case, the relativeyield,

p>,

doesnot

depend

onthe concentration of

R,

[R].

In

particular, itrepresentsthe ratio between the probabili-ties offindingatleastonemolecule of Einagiven reac-tion compartment for both the reticulated and the nonreticulatedsituations. Since, in thesecompartments,

all Rmolecules thatcancomeincontactwithanE mole-cule are converted, the expected net yield is, in both cases,proportionaltothemeannumberof Rmolecules percompartment.

Fig. 1 presentsaplot of<

p>

versusNdom. As expected,

a sharp decrease in the relative yield of the reaction is

observeduponreticulation when the number ofenzyme moleculesperreactioncompartmentis small. Infact,as a result ofcompartmentalization a large fraction ofR moleculesarenotaccessibletotheenzyme, E.

In additiontotherelative reaction yield, it is also

im-portant toevaluate how thenetyield of Pchanges with [E]inthe reticulated reactionspace. Inthiscasethenet

yield ofPisgiven by (numerator of Eq. 9)

<

(k,,

>

= 1 - exp{-

[EUINdom

(10)

Fig.2presents a plotof

<

¢t>

versus

[E]

/

['U]

forseveral statesofreticulation.Thedifferencebetween the curves

is simply a consequence ofthe change in the average valueof[E]in the reaction compartment resulting from

differences in the degree of compartmentalization.

Hence thecurves in Fig. 2 actually represent the same curveunderdifferent concentration scaling.

-a 75

[EI [ilJ

FIGURE 2 Netyield ofacatalyzed reactionas afunction ofthecatalyst concentrationfor values ofNdom= 1, 2, 10, and 100.

P)1 nRInR2l< nRsIee i

P(ij|nRI,snR2)=41 nRI > nR2, nR2 =i.

LO

elsewhere

(11)

Asinthe previouscase,the relative yield is obtainedas the ratiobetweentwoprobabilities, i.e.,

1 {

[Rl]

[R2] ((p> = [llNdom [U]Ndom I _f [Rl ] [R2] \[W] '

Vu]

(12) where

CONVENTIONAL BIMOLECULAR REACTION

Inthecaseofthe bimolecular reaction

Rl + R2-P

theconditionalprobability P( i nR1,nR2) that describes

the reaction mechanism isnowgivenby

.8

.4

f(ORI, AR2)= exp[-(ARI +AR2)A

oo nRrl nR2 AnRI-I

RI.

X (nR1 -nR2) (13)

nR1o nR2 0 nR2! nRl.

In Eq.

13,f(ARl,

/'R2) stands for theprobability thatno reactiontakes place in the wholesystem.

Fig. 3 shows that fora fixed value of [R2]/[U], the

tXii=20

.8 20 -100~~~~~ra A[~~~~~~~3 NdfO

FIGURE 3 Relativeyieldofaconventionalbimolecularreactionasa

function ofcompartmentalization forafixedconcentration ofoneof thereactants.[RlI/[l]issetas20, while [R2]/[lJ]= 1, 10, 20,30,

50,and 100.

B-p--a ounlVlm ee br19

FIGUREi Relativeyield of product formation for a catalyzed reaction

as afunction ofthe number ofdomains per reaction unit. The different

curvescorrespond tovarying catalystconcentrations, [E]/ [ l]= 1,5, 10,and 100.

decreasein reactionyieldofthesimplebimolecular

reac-tion considered here issomewhatlessthan thatobserved for the enzyme catalyzed reaction considered earlier

(Figs. 1 and2). Another result of the calculation is that

the relative reactionyield isnotamonotonicfunctionof [Rl

].

This effect ismoreclearly visiblewhenweanalyze the evolution of thenetreactionyield

I

[R1]

[R2] if[R] [R2]

[WUNdom [']Ndom' [U]

] 1 _[R2] [R]R] > [R2]

t \[W ] dom [ dom 1 [W] [e ]

(14)

withf(*, *)given in Eq. 13. In Fig. 4 we plot the net

yield,

<k,t>,

withrespect to[Rl1! ['U] foragivenvalue of[R2

]

/ [Ml].Weseethatthenetyieldexhibitsa mini-mumat[Rl] =[R2]. The meaningof thisminimumis easytounderstand ifextremecases,andasimplified sce-nario,areconsidered. Ifthe number ofRl moleculesina unit is much smallerthan the number ofR2 molecules in

it, theprobability thatuponreticulationanRlmolecule is in thepresenceofatleastoneR2molecule in thesame

compartmentisrelatively high. Conversely,ifthe num-ber of Rl molecules per unit is much larger than the

number of R2molecules, uponreticulationalarge

frac-tionof theR2moleculesareexpectedto react.Ifthe unit

ispopulated withanequalnumber ofRl and R2

mole-cules,inthe absenceofreticulationreaction isexpected

togotocompletion.However,reticulationwillresult in

acertain fraction of reaction compartments (domains) which have unequal number of Rl andR2moleculesso that the net result will be a significant fraction of unreactedreactants. -o C) [Rli

[1,1

Dimerization reaction

Herewedealnotonlywiththesimple bimolecular reac-tion

2R R2

butwealsocompareittothemoregeneralcaseof poly-merformation reactions for thecasesof aggregation of3 and 4monomers

Rk (k=2,3,and4).

If,inhomogeneousmedia,adimerizationreaction pro-ceeds until total consumption of the monomer, upon

reticulationeveryunpaired molecule will be lost forthe process,withaconcomitantdecrease in yield. This drop inyieldis stillmoremarked in thecaseoftheformation of trimersortetramers.

The conditional probability that the reaction takes place inagivendomain withanetyield of i molecules of Rk, given thatnRmoleculesarepresent, isgiven by 'P(ilunR) 1 i=nR/k, 1 i=(nR- 1)/k, 1 i=(nR-k+ 1)/k, 0 elsewhere nR

multiple

of k (nR- 1) multipleofk (nR-k + 1) multiple of k (15)

Taking into consideration that, for these reactions, all

theinvolved molecules pertaintothesamereactant,the relative yield is 1_ n( [R] ) (4P>= (16) where oo k-1 (kjl+j2-1 )

f(AR) = exp(-AR) . 12 kji+j2)! ijI-O j2-0 (kj1 +12)!

(17) In Fig. 5 wepresentplots ofthe relative yield of

forma-tion ofdimer, trimer andtetramerforasingle

concentra-tion ofR,

[R]/[UJ]

= 20,as afunction ofthe number of domains. Thedifferences in yield for dimers andhigher aggregation numbersareclearlyobserved.

From the study of the relative yield we canfind the

extentofhindrance resulting from membrane reticula-tion. The primary reticulation effect, which is always

presentinvesiclesorcellsuspensions, is better dealt with through examination of thenetyield of the reaction

(18)

< t

>

= I f

[Rt[]N&m

J)

ReactionsinReticulatedMembranes 1509

FIGURE 4 Netreactionyieldforaconventional bimolecular reaction asafunctionof[RI/[U],for[R2]/[l/J =20,andNd&m=1,5,10,20,

50, and 100.

40 60

Nd,,

FIGURE5 Relativeyieldofadimerizationreaction(k=2)for [R]/ [U]=20 as a functionof the number of domains per unit, Ndom. Plots arealsopresented for thecaseof trimer(k=3) and tetramer(k=4) formation.

withf(*) given in Eq. 17. The netyieldasfunction of

[R]/['U]

for k=2, and 4, is plotted in Figs. 6, A and B.

Consecutive reactions

We consider two cases ofsequential enzyme-catalyzed reactions:(a) the action ofanenzyme on apro-enzyme

to produce a second enzyme that catalyzes the subse-quentreaction inthe sequence, and(b) the product of

thefirstenzymaticreaction is thesubstrateof the second

enzymatic reaction in the sequence. We consider the

formercase first:

El + Rl El + E2 E2+ R2 E2 + P

where El and E2arethe catalysts. Itcanbe shown that, whether thesystemis reticulatedornot,thenetyield of Pis thejoint probability of havingatleast one El and oneRl moleculeinthe smallest reactioncompartment.

Therefore, if the distributions of all reactants are as-sumedtobeindependent, from Eq. 1, the relative yield is

(1-exp{- [ex]N-})(l P{ [R]

(

[El>

1 exp [Rl]

(19)

Notingthatthe concentrations of Rl and E2 areequal whenthe first reactionstepis performed withprobability

one, the above expression is theproduct of the relative yields for both reactions.

In Fig. 7, we comparethe singlestep catalyzed

reac-tion with the consecutive mechanism, for the case of

[El]/[U

] = 10.The consecutive reaction is performed

atthreedifferentmean occupancynumbers for Rl. As expected, when the concentrations of the two starting

reactantsareverydifferent,oneof thestepsbecomes the

bottleneck of theglobal mechanism. But when the

con-centrationsofEl andRlarecomparable, the decrease in yield dependsonthe concentration of both theenzyme and thereactant.

Forthe secondcaseof the consecutive reactions men-tionedabove,weconsiderthefollowingsequence

El + Rl El + P1 E2+ P1 E2+ P2.

Inthiscasethenetyield ofP2is thejoint probability of havingatleastoneElandoneE2 molecule in the

small-estreactioncompartment. Again, recalling that the dis-tributions of all reactantsare independent, from Eq. 1, the relativeyield is given by

[El] I[E2]

1 exp-[- ]Ndom }) 1 exp-[- ]NdO )

-P(>

-expj- [EU]l)(1 eP [E2] 1)

(20)

Both Eqs. 19 and 20areformally identical. The relative yield ofthe final product is, for bothcases,theproduct of

-o a) -o 5: [R1 [RI E1,7

FIGURE 6 Representationof the net yield as a function of the mean numberofRmolecules perunit for different number ofcompartments perunit. (A) thecaseofdimerformation. (B) the case of tetramer formation.

151- ipyia ora oue6 eebr19

.N

-a)

cs

NdO,

FIGURE7 Relative yields for the finalproduct oftwoconsecutive

cata-lyzedreactionsas afunctionof Ndom with [El]/[ l(]= 10.Theyields

shownareidentical fortwodifferent types of reaction sequences(see

textof Eqs. 14and 15).XrepresentsRlinthefirstcase(Eq. 14)and E2in the secondcase(Eq. 15). Curvesaregivenfor[X]/['1]= 1,10,

and100. Forreference,thecorrespondingcurvesforasinglestep

cata-lyzed reactionwith [E]/['U] = 10 and 100 are also shown(broken lines).

two relative yields. However, theyrepresent two physi-cally distinct situations. The relative yield of the final productas afunction of number of domains forafixed meanvalue of Elperdomain is identical for Eqs. 19 and 20, and given inFig. 7.

DISCUSSION

We have demonstrated that the reaction yield of four typesofbimolecular reactions confinedto a membrane

surface is decreased by compartmentalization ofthe

sur-face forarandomdistributionofreactants over the com-partments. Theyield is highlydependent upon both the reactionmechanismand the reactantconcentrations.

Inthe case ofthe enzyme catalyzedreactionit iseasy tounderstandthat, since onlyvery small amountsofthe enzymeneed be present,compartmentalizationcanlead

to a very low average enzyme concentration per com-partment, even ifthesize ofthe compartments is

rela-tively large. This is the situation depicted onthe

right-handsideofthe curvesinFig. 1.Thus,the consequence

ofcompartmentalization foranenzymatically catalyzed reaction inabiologicalmembraneisamarkedinhibition ofthe processregardless ofcompartmentsize.When the average numberofenzyme molecules per compartment

isless thanfivethereactionisessentiallyshutoff. Similar

but more dramatic effectsare seen for consecutive en-zymecatalyzed reactions shown inFig. 7.

For a bimolecular reaction involving two different

reactantstheeffect of compartmentalizationonthe rela-tiveyield,asshown inFig. 3, isnot asgreat asit is foran

enzyme catalyzed reaction. The yield is, however, a

rathercomplexfunctionoftheconcentrationsofthe two reactants, as shown in Fig. 4. In the special case of a

single

homodimerization

reaction,

the decrease in the

relative yield observeduponcompartmentalization

origi-natesonlyinanincrease ofthe number of molecules left over in domains with an odd number of molecules. When theformation ofeither trimersortetramersis con-sidered, themean number of molecules leftoverper

do-mainincreases, leadingtoafurther decrease in the rela-tive yield (see Fig. 5). A similar argument can also be

appliedtotheanalysis ofthenetyield,asdepicted inFig.

6. The fraction of unreacted molecules decreases as a consequence of the increase in the

[R]

/ ['U]. This

be-comes moreevident in thesigmoidal shapeofcurvesin Fig. 6 B. In fact, forverysmall values of

[R]

/ [U

],

the probability of havingatleast k molecules inasingle do-main isverylow, being much smaller for k=4 than for

k=2.Therefore,anearlyzeronetyield is observed when [R]/['U]isverylow.

The arguments presented in this paper have been given in thecontextofcompartmentalizationas aresult ofchanges of the phasestructureofalipidbilayer

mem-brane in which the reactants are confined. It is clear, however, that the conclusions are independent ofthe means of compartmentalization, which in biological membranes could include compartmentalization by meansof proteincomponents(Freire andSnyder, 1982) andcytoskeletalstructures(Saxton, 1990)aswellasfor hypothetical situations in which proteins are separated from each other by preferential solubilizationin phase-separated domainsinthesamemembrane. We havealso limitedourconsiderationstoreactions confinedto

two-dimensionalsystems.Thesametreatmentalsoappliesto

compartmentalized three-dimensional systems and the conclusionsare,in everyaspect,similar.

Recently the basic ideas developed in thispaperhave been usedto understand experimental results obtained in two unrelated studies. In the first of these, the line broadeningofaspin labeledphosphatidylcholine dueto

spin-spin interactions between labels wasexamined by ESRspectroscopy in bilayers formed from mixtures of dimyristoyl phosphatidylcholine and distearoyl phos-phatidylcholine as afunction oftemperatureand com-position(Sankarametal., 1992). The detailednatureof theline broadeningintheregion of coexistence of fluid andgel phasescanbeunderstoodquantitatively only by taking into account the compartmentalization of the spin-labeled phospholipidincertainportions of the

two-phase region. Thisstudy providesadirect experimental

testof thebasicideas outlinedabove. Inthe second, the difference between the apparentequilibrium poise ofa reactionindisconnected, ascomparedtoconnected

sys-tems,hasprovidedanexplanation forananomalous situ-ation observedinphotosyntheticsystems(Lavergne and Joliot, 1991). The anomaly concerns the difference in equilibrium constantdetermined under lowlight inten-sity and theconstants determined using artificial redox

carriers. Lavergne and co-workers explain the difference

as being due to the attainment ofglobal equilibrium

among the subsystems of each chloroplast through the

Melo et al. Reactionsin ReticulatedMembranes

useofartificialredoxmediators,whereasatlow

illumina-tionintensity each globalequilibrium subsystem attains

its own equilibrium. The ideas that lead to thesuccessful resolution of the anomalous behavior ofphotosystems

areconceptuallyanalogous to theideas developedin this paperconcerning the effects of in-plane connectionand

disconnection onmembrane-localized reactions.

Although not directly relevanttotheproblem of

do-mainstructures inbiological membranes,much very

in-teresting workon thestructureofphases has beendone ontwo-componentmonolayersat anair/waterinterface

(for a review, seeMcConnell, 1991). The large dipole

momentassociated with thesemonolayers

gives

rise to

relatively large domains, whichareusually arranged ina regular two-dimensional super lattice. Frequently,

do-main shapes exhibit symmetry properties arising from

the

chirality

ofcomponentmolecules. Structuresof this

typeandsizeareabsent in

bilayers,

presumably because

thereisalmostcompletecompensation ofthedipole mo-mentofoneofthe monolayers bythedipole ofthe other monolayercomprisingthebilayer.Thediscussion ofthe effectsof connection and disconnectionon

bilayer-con-fined reactions outlined above can, of course, be readily

appliedtoreactionsconfinedtomultiphasic monolayers

attheair/water interface.

This research was partially supported by the Junta Nacional de

Ivesti-ga,aoCientifica eTechnologica, Portugal, under contract no. PMCT/ CEN658/90, and by the National Institutes of Health, USA, under

grantsGM-14628andGM-23573.

Receivedfor publication 18 May 1992 and in revisedform 25August 1992.

REFERENCES

Bultmann, T., W. L. C. Vaz, E. C. C. Melo, R. B. Sisk, and T. E. Thompson. 1991. Fluid-phase connectivity and translational diffu-sion in aeutectic, two-component, two-phasephosphatidylcholine bilayer. Biochemistry. 30:5573-5579.

Chazotte, B., and C. R. Hackenbrock. 1989. Lateral diffusion asa

rate-limiting step in ubiquinone-mediated electron transport. J.

Biol. Chem. 264:4978-4985.

Freire, E., and B. Snyder. 1982. Quantitative characterization of the lateraldistribution of membraneproteinswithin thelipidbilayer. Biophys. J. 37:617-624.

Hatlee, M. D., and J. J. Kozak. 1980. Astochastic approachtothe theory ofintramicellar kinetics. I. Masterequationfor irreversible processes. J.Chem.Phys.72:4358-4367.

Lavergne, J., and P. Joliot. 1991.Restricted diffusion in photosynthetic membranes. TrendsBiochem.Sci. 16:129-134.

Lee, A. G. 1977.Lipid phase transitions andphasediagramsI.Lipid

phasetransitions. Biochim.Biophys.Acta.472:237-281.

Lenaz,G. 1988. Roleof mobilityof redox components in the inner mitochondrial membrane.J.Membr. Biol. 104:193-209.

McConnell, H. M. 1991.Structures andtransitions inlipidmonolayers attheair-water interface. Annu. Rev.Phys. Chem. 42:171-195. Rajarathnam, K., J. Hochman, M.Schindler,and S. Ferguson-Miller.

1989. Synthesis, location and lateral mobility offluorescently la-beledubiquinonelOinmitochondrial and artificial membrane.

Bio-chemistry.28:3168-3176.

Sankaram, M.B., D.Marsh, and T.E.Thompson. 1992. Determina-tionof fluid and gel domain sizes in two-component, two-phase lipid

bilayers:AnESRspin label study.Biophys.J.63:340-349. Saxton, M. J. 1990. The membrane skeleton oferythrocytes.A

perco-lation model.Biophys.J.57:1167-1177.

Singer,S. J., and G. L.Nicholson. 1972. Thefluidmosaic modelofthe

structureof cell membranes. Science(Wash. DC). 175:720-731. Thompson,T.E., M. B.Sankaram, and R.L.Biltonen. 1992.

Biologi-cal membrane domains. Functional significance. CommentsMol. Cell.Biophys.8:1-15.

Tocanne, J. F., L.Dupou-Cezanne, A. Lopez, and J. F.Tournier.1989. Lipid lateral diffusion and membrane organization. FEBS (Fed.

Eur.Biochem.Soc.)Lett.257:10-16.

Vaz, W. L. C., E. C. C.Melo, and T. E.Thompson. 1989. Translational diffusion andfluiddomainconnectivityinacomponent, two-phasephospholipidbilayer.Biophys.J. 56:869-876.

Vaz, W. L.C., E. C. C. Melo, and T. E.Thompson. 1990. Fluid phase

connectivityinan isomorphous,two-component, two-phase phos-phatidylcholinebilayer. Biophys.J. 58:273-275.

Wu,S. H., and H. M. McConnell. 1975. Phaseseparations in phospho-lipid membranes.Biochemistry. 14:847-854.