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JOURNAL OF BIOELECTRICITY, 4 ( 2 ) , 317-348 (1985)

DIELECTRIC SPECTROSCOPY AND MEMBRANE ORGANISATION

Douglas B. Kell and Christine M. Harris Department of Botany and Microbiology

University College of Wales, Aberystwyth, Dyfed SY23 3DA, U . Y .

ABSTRACT

The possible bases fo r field-mediated e f f e c t s on ce l lu l a r processes a re re f lec ted i n the passive e l e c t r i c a l p roper t ies of b io logica l systems. The h i s t o r i c a l , present and prospective u t i l i t y of d i e l e c t r i c spectroscopy i n assess ing the s t a t i c and dynamic organisation of biological membranes i s reviewed within t h i s context. The basis f o r the view tha t the s t a t i c capacitance of biomembranes is as gceat as 1 )IF/cm2 is doubted; cont r ibu t ions from the ( p a r t i a l l y r e s t r i c t e d ) motions of membrane components, and of double- layer ions, probably cont r ibu te t o t h i s apparent value in biomembrane ves i c l e suspensions. The importance of improving our knowledge of the s t a t i c e l e c t r i c a l capacitance of energy coupling membranes is s t ressed . Theoretical and experimental procedures fo r assessing the contribution of ro ta t iona l and t r ans l a t iona l motions of membrane components, and of double-layer/membrane in t e rac t ions , t o d i e l e c t r i c spec t ra in the approximate frequency range 10 t o lo7 Hz a r e described. F ina l ly , three outstanding and generally unsolved problems requiring fu r the r work a re de ta i led .

INTRODUCTION

In t h i s a r t i c l e , we wish t o address ourselves t o the following r e l a t ed

ques t ions : (1) can d i e l e c t r i c measurements te l l us anything new or

s ign i f i can t about the organization and dynamics of biological membranes. when

the measurements a re made with macroscopic, ex t raves icu lar electrodes in

suspensions of closed ves i c l e s ; (2) can modern ideas concerning the s t ruc tu re

and organization of such membranes contribute to the in t e rp re t a t ion or

r e in t e rp re t a t ion of the d i e l e c t r i c spec t ra obtained in such systems? For

reasons of space, and because f ine discussions a re ava i lab le elsewhere, we

317

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318 KELL AND HARRIS

w i l l n o t i n c l u d e s t u d i e s performed a t f r e q u e n c i e s e x c e e d i n g 100 MHz, nor

s t u d i e s of n e u r o p h y s i o l o g i c a l sys t ems , nor of o t h e r non- l inea r b i o l o g i c a l

sys t ems .

However, n o t i n g t h e need f o r a m e c h a n i s t i c e x p l a n a t i o n of t h e many

e x c i t i n g , thought-provoking and i m p o r t a n t s t u d t e s c o n c e r n i n g t h e a l t e r a t i o n of

p h y s i o l o g i c a l p r o c e s s e s by r a t h e r weak e l e c t r o m a g n e t i c (EM) f i e l d s (1-8), and

n o t i n g f u r t h e r t h a t t o a c t u a l l y have a n e f f e c t , EM f i e l d s must f i r s t be

a b s o r b e d , we s h a l l aim for a rather Eundamental and m o l e c u l a r d i s c u s s t o n of

t h e p o s s i b l e means by which such e f f e c t s may be med ia t ed ( a t least i n p a r t ) by

membrane-located enzymes. We beg in w i t h a v e r y b r i e f d i s c u s s i o n of t h e

s a l i e n t E e a t u r e s of e a r l y h i s t o r i c a l c o n t r i b u t i o n s of d i e l e c t r i c s p e c t r o s c o p y

t o the s t u d y of membrane o r g a n i s a t i o n .

14 I S'PORI CAL

"It t s found t h a t Co t s i ndependen t OE t h e f r e q u e n c y up t o 4.5 m i l l t o n

c y c l e s , and i t is a l s o independen t of t h e suspend ing l i q u i d . These r e s u l t s

f u r n i s h c o n s i d e r a b l e e v i d e n c e of t h e v a l i d i t y of t h e t h e o r y , t h a t Co

r e p r e s e n t s t h e s t a t t c c a p a c i t y of a c o r p u s c l e ' s membrane. On this as sumpt ion ,

and u s i n g a p r o b a b l e v a l u e f o r t h e d i e l e c t r i c c o n s t a n t of t h e membrane, t h e

t h i c k n e s s of t h e membrane is c a l c u l a t e d t o be 3.3 x cm."

U i t h t h e s e words, F r i c k e ( 9 ) concluded his classic p a p e r , i n which it w a s

i ndeed shown for t h e f i r s t t i m e t h a t t h e c e l l - d e l i m i t i n g l l p o i d a l membrane

r e q u i r e d by t h e Overton (10) t h e o r y must be of m o l e c u l a r t h i c k n e s s . As

d i s c u s s e d i n a number of e x c e l l e n t t e x t s and monographs, subsequen t work on

the f requency-dependence of t h e d i e l e c t r i c p r o p e r t i e s of a great number of

c e l l s and v e s i c l e s has i n d i c a t e d t h a t t h e y all possess a pronounced (p-) d i s p e r s i o n which r e f l e c t s , OK may be a s c r i b e d t o , t h e p re sence of a cell

membrane v i t h a ( s t a t i c ) c a p a c i t a n c e of 1.2 5 0.7 MF/cm2 (11-35) . The f a c t

t h a t t h i s f i n d i n g s t i l l s t a n d s a f t e r s i x t y y e a r s may be rega rded as a


DIELECTRIC SPECTROSCOPY AND MEMBRANES 319

testament t o Fricke's i n s igh t and t o the power of d i e l e c t r i c spectroscopy i n

assess ing the s t ruc tu re of biological membranes. Since the concept of the

e t a t i c membrane capacitance forms the background t o de ta i led discussion of the

frequency-dependent d i e l e c t r i c properties of membrane vesicle suspensions, we

must theref ore describe the so-called suspension equations tha t a re per t inent

t o the simplest type of biomembrane-bounded ves ic le , the spher ica l s h e l l

membrane (Figure 1).

THE SUSPENSION EQUATIONS FOR SPHERICAL MEMBRANE VESICLES

A s the frequency of an a l t e rna t ing f i e l d is increased through the

radlof requency range, the pe rmi t t i v i ty and conductivity o f a typ ica l

(microbial or other) c e l l suspension are respec t ive ly decreased and increased

(Figure 1B). This can be in te rpre ted as a progressive shor t -c i rcu i t ing of the

cytoplasmic membrane capacitance, v ia a Maxwell-Wagner type of mechanism

(Figure 1). If we model the c e l l s a s t den t i ca l spheres present at a t o t a l

volume f rac t ion (P) of P < 0.2, with a bulk, i n t e rna l conductivity of Ui ,

surrounded by a membrane with a s t a t i c capacitance of C, ( fa rads /uni t a r e a ) ,

and immersed i n a medium of conductivity 'Jo (Figure I A ) , the following

equations express the high- and low-frequency permi t t iv i ty ( E', ~ 1 ' ) and

conducttvity ( 01, Ul') and the re laxa t ion time T (11):


320 KELL AND HARRIS

FIGURE 1A

Spherical model of a biomeinbrane-bounded c e l l suspension: bulk ex terna l and i n t e r n a l c o n d u c t t v i t i e s r e s p e c t i v e l y .

r , rad ius ; u,,, u i ,

I OC IRLOUENCY ( H r )

FIGURE IR

Frequency dependence of the d i e l e c t r i c proper t i e s of the model system.



f c )

FIGURE 1C

In t e rp re t a t ion of the d i e l e c t r i c data; ( f r w l e f t t o r igh t ) there is a progressive shor t -c i rcu i t ing of the membrane capacitance by the applied f i e l d .

I .ACCESS A D M I JJANCE

SPrC,

4 Er

EX IRA CELL UL A R RESISiANCE

FIGURE 1D

The equivalent c i r c u i t of the system.

where c r is the permi t t iv i ty of f r ee space (8.854 x lO-I4 F/cm). These

equations assume tha t the membrane conductivity (G,,,) is zero. Since the

conductivity of the majority of bac te r i a l membranes does not exceed S/cmz

( 3 6 ) , and since G, must exceed 1 S/cmz t o be detected by means of measurements

on suspensions with macroscopic e lec t rodes ( 3 2 ) , t h i s assumption is

acceptable. It is pa r t i cu la r ly in s t ruc t ive to examine equations 1 t o 4 in

some d e t a i l , and we note f i r s t tha t we accept, fo r the ana lys i s of t h i s type


322 KELL AND H A R R I S

of system, the superpos i t ion p r i n c i p l e , which s t a t e s , among other t h i n g s , t h a t

t h e c o n t r i b u t i o n t o a d i e l e c t r i c d i s p e r s i o n of any ind tv idua l v e s i c l e i s

independent of t h a t of any o ther v e s i c l e s which may be present .

The c o n t r i b u t i o n of any ( s i z e c l a s s of ) v e s i c l e t o the overa l l d i e l e c t r i c

p r o p e r t i e s will be a sum of Debye-like d i s p e r s i o n s , with a d i e l e c t r i c

increment and r e l a x a t i o n t i m e appropr ia te t o the rad ius and i n t e r n a l and

e x t e r n a l c o n d u c t i v i t i e s i n ques t ion , g iven t h a t the volume f r a c t i o n is j u s t a

f u n c t i o n of the c e l l r a d i u s and number. Thus, one may s imulate the behaviour

expected on the hasis of a d i s t r i b u t i o n i n the c e l l s i z e (18) from which i t is

found (F igure 2) t h a t only a small d i f f e r e n c e e x i s t s between the d i s p e r s i o n s

s imulated on the basis of ( a ) a superpos t t ion of s i z e c l a s s e s of v e s i c l e s with

d i f f e r e n t r a d i i , ( b ) a suspension of equiva len t volume f r a c t i o n but of mean

f o u r t h power oE the rad ius T, (r = ( ( x n r 4 ) / N ) l / 4 ) , where n is the number of

c e l l s in each s i z e f r a c t i o n , and N the t o t a l number of c e l l s ) , and ( c ) t h e

same, but using the mean cube radius ( r = ( ( z h ~ ~ ) / N ) l / ~ ) . Note a l s o the

predominant tendency f o r E ' 1 (but not E,) t o favor c e l l s i z e f r a c t i o n s with a

somewhat g r e a t e r than average r a d i u s , due t o t h e dependence of E ' 1 upon volume

f r a c t i o n and rad ius ( i . e . i t increases a s a func t ion of r4) . Thus, the

conclusion from t h i s type of s imula t ion 1s t h a t a s u b s t a n t i a l value €or the

Cole/Cole a c a n n o t be ascr ibed in genera l t o the s i z e d i s t r t b u t i o n of ( say

microbia l ) c e l l s , and hence, €or e l l i p s o i d s of a reasonably low a x i a l r a t i o ,

t o any r e a l i s t i c shape-d is t r ibu t ion . S i m i l a r l y , the e l e c t r i c a l an iso t ropy

t h a t one may invoke i n t h e case of condensed mitochondria (18) i s a l s o

i n a p p l i c a b l e t o microbia l c e l l s .

I n t h i s type of s imula t ion , one assumes t h a t the volume f r a c t i o n is known

(from microscopic observa t ion) or may be determined ( f o r the sum) by methods

such a s i so tope d i l u t i o n or from measurements based upon conductimetry

according t o equat ion 2. Thus, the membrane capac i tance , which is a f r e e

v a r i a b l e , may be c a l c u l a t e d d i r e c t l y €ran t h e measured d i e l e c t r i c increment

(equat ion 1). It is t h i s type of measurement (37 ) t h a t has led t o the view


9

5 - x10

- < 4 - In

w V

[L w

i 3 -

2 -

m 3 l - z

0 0.2 0.4 0.6 0.8 1.0 1.2 ( a ) RADIUS ( y m )

2 c e r . . . . . . . . , . . . . . . . . , . . . . . . . . , . . . . . . .

LOG FREQUENCY (Hz)

FIGURE 2

Simulation of the e€ fec t of a heterogeneous s i z e d i s t r ibu t ion on the d i e l e c t r i c proper t ies of spher ica l she l l ves ic les of the type described i n Figure 1. ( A ) The s i ze d i s t r ibu t ion considered, which, although a r b i t r a r y , r ay be construed a s representa t ive of a typ ica l bac t e r i a l population. To obtain a numerical so lu t ion ( in terms of equations 1 and 4), the 12 s i ze c l a s ses indicated a r e used. ( 8 ) Effect of s i z e heterogeneity on p-dispersion. The Debye-like d i e l e c t r i c behaviour of the system, s iau la ted according t o equations 1 and 4, ( a ) by assuming the 12 s i z e c lasses , (b ) by assuming the same t o t a l number of cells but assuming the mean fourth root of the radius ( see tex t ) and (c) by assuming the same t o t a l number of c e l l s but using the mean cube of the radius (see t ex t ) . It is evident tha t (i) the breadth of the dispersions a re almost exactly Debye-like, and (ii) q u i t e a s ign i f i can t s ize-d is t r ibu t ion has r e l a t ive ly l i t t l e e f f ec t upon e i t h e r the mean re laxa t ion time or i ts d i s t r ibu t ion .


3 2 4 KELL A N D HARRIS

t h a t biomembranes have a s t a t i c e lectr ical c a p a c i t a n c e of roughly 1 2 0.5

uF/cm2. S t m i l a r l y , e s t t m a t i o n s of the i n t e r n a l c o n d u c t i v i t y of t y p i c a l ce l l

suspens ions by means of e q u a t i o n 3 have g iven r e a l i s t i c v a l u e s , which are

n e v e r t h e l e s s lower by a f a c t o r of 2-3 than those t o be expected on the basis

of t h e t o n i c c o n t e n t of t h e cel ls ( 2 1 , 3 8 , 3 9 ) . Although new methods are

becoming a v a i l a b l e , by which a n independent measurement of the long-range

d t f f u s i v i t y of bulk cy toplasmic i o n s may be obta ined ( 4 0 - 4 3 ) , we do not a s y e t

know the p r e c i s i o n wi th which the value of U i , c a l c u l a t e d from e q u a t i o n s 2 o r

3 a c t u a l l y r e f l e c t s t h e t r u e , bu lk , i n t e r n a l c o n d u c t i v i t y of t h e cells. In

o t h e r words, a l though t h e r e i s a r e a s o n a b l e , and a t least s e m i - q u a n t i t a t i v e ,

agreement between exper imenta l r e s u l t s and the p r e d i c t i o n s of q u a t l o n s 1 t o 4

( 1 8 , 2 8 , 2 9 , 2 7 , 3 5 ) , t h e a v a i l a b l e d a t a do not permit us t o d i s p o s e of t h e view

t h a t o t h e r p r o c e s s e s , wi th c h a r a c t e r i s t i c f r e q u e n c i e s ( f c = 1 / 2 a ~ ) i n t h e

range of 0.5-5 MHz might make a s i g n t f i c a n t c o n t r i b u t i o n t o t h e RF observed

rad iof requency d i s p e r s i o n s . (Note a l s o t h a t because of t h e c e l l

radius-dependence of both r e l a x a t i o n time and d i e l e c t r i c increment f o r t h i s

type of r e l a x a t i o n , the ease of o b s e r v a t t o n of o t h e r processes will i t s e l f

depend on c e l l s i z e . ) We wish t o stress i n p a r t t c u l a r t h a t t h e b r e a d t h of t h e

P-d ispers ions observed i n b a c t e r i a l suspens ions ( 2 6 , 3 2 , 3 3 , 4 4 - 4 6 ) , as judged by

t h e Cole/Cole p l o t ( 4 7 ) seems t o r e q u i r e t h a t one invoke a h e t e r o g e n e i t y i n r ,

C, or 01 f a r g r e a t e r than i s r e a l i s t i c i f one were t o c la im t h a t the

d i e l e c t r i c d i s p e r s i o n s observable i n t h i s f requency range may be a s c r i b e d

s o l e l y t o a Ftaxwell-Wagner type of mechanism. I n o t h e r words, the f a c t t h a t

C, and 01 are f r e e v a r i a b l e s i n c a l c u l a t i o n s based upon e q u a t i o n s 1 t o 4

a l l o w s us t o invoke c o n t r i b u t i o n s t o t h e 1 - d i s p e r s i o n due t o o t h e r p r o p e r t i e s

of c e l l u l a r , and i n p a r t i c u l a r of energy c o u p l i n g , membranes a d d i t i o n a l t o

t h e i r possess ion of a s t a t i c e lectr ical capac i tance .

According t o t h e now wide ly accepted f l u i d - m o s a i c model of b t o l o g i a l

membranes (48) (Figure 3 ) , biomembranes c o n s i s t of phosphol ip id b i l a y e r s in , on

and through which are l o c a t e d p r o t e i n s and p r o t e i n complexes, and both l i p i d s



I r I

F L ii 1 D MOSA 1 C MEMBRANE MODEL

FIGURE 3

The s a l i e n t f e a t u r e s of a f l u i d mosaic membrane model. The model c o n s i s t s of an a r r a y of po ly topic , i n t e g r a l p r o t e i n complexes, which a r e f r e e t o r o t a t e ( w i t h a r o t a t i o n a l d i f f u s i o n c o e f f i c i e n t D p ~ ) and t o move l a t e r a l l y and independent ly ( w i t h a t r a n s l a t i o n a l d i f f u s i o n c o e f f i c i e n t Dp,) in a "sea" of phosphol ipids . Free r o t a t i o n and t r a n s l a t i o n of the phosphol ipids is also permi t ted , with t h e d i f f u s i o n c o e f f i c i e n t s i n d i c a t e d . The merllbrane is arranged as a v e s i c l e of rad ius r , v e s i c u l a r r o t a t i o n ( o r i e n t a t i o n ) being p o s s i b l e with a r o t a t i o n a l d i f f u s i o n c o e f f i c i e n t DV~. I f p r o t e i n t r a n s l a t i o n a l motion is r e s t r i c t e d in some way, the average d i s t a n c e moved before a " b a r r i e r " is encountered is given by r' ( s e e 88). The "bulk" v i s c o s i t i e s of the membranous and aqueous phases a r e given by q and 17' r e s p e c t i v e l y .

and p r o t e i n s can d i s p l a y thermal (and metabol ica l ly) induced r o t a t i o n a l and

t r a n s l a t i o n a l d t f f u s i o n a l motions i n t h e plane of t h e membrane (49) .

Undoubtedly the s t a t i c capac i tance measured i n p lanar phospholipid b i l a y e r

" b l a c k l i p i d membranes which l a c k p r o t e i n , o r that measured a t high

f requencies with transmembrane e l e c t r o d e s , is smaller by a s much a s a f a c t o r

of 2 than the widely quoted value of 1 ~ F / c m 2 c a l c u l a t e d f o r biomembrane

v e s i c l e suspensions (20,50-64). C e r t a i n l y the f a c t t h a t biomembranes conta in

p r o t e i n s which poss ib ly possess a higher s t a t i c d i e l e c t r i c p e r m i t t i v i t y than

do pure phospholipid b i l a y e r s , may c o n t r i b u t e t o the explana t ion of t h i s f a c t


325 KELL AND HARRIS

(though we a r e not aware of any d i r e c t i n d i c a t i o n of t h i s under

phys io logica l ly meaningful condi t tons) . However, f o r reasons given above, i t

is e q u a l l y p l a u s i b l e i n many cases t h a t o t h e r f a c t o r s c o n t r i b u t e s i g n i f i c a n t l y

t o the frequency-dependent d i e l e c t r i c p r o p e r t i e s of membrane v e s i c l e

suspensions, and we must broaden our d i s c u s s i o n t o enqui re more c l o s e l y i n t o

what Is known of the s t r u c t u r e , and more p a r t i c u l a r l y of the dynamics, of

charged biomeabranes and t h e i r ad jacent e l e c t r i c a l double- layers . We begin by

d iscuss ing e x a c t l y why i t is so important t o improve the p r e c i s i o n of mr

knowledge of t h e s t a t i c capac i tance of b i o l o g i c a l membranes, e s p e c i a l l y a s it

r e l a t e s t o so-cal led energy coupl ing membranes.

WHY SHOULD WE WISH ACCURATELY TO KNOW THE "STATIC" ELECTRICAL CAPACITANCE OF BIOLOGICAL MEMBRANES?

Modelling the membrane a s a s t a t i c e l e c t r i c a l c a p a c i t o r of th ickness d ,

conta in ing a s l a b of d i e l e c t r i c of a uniform p e r m i t t i v i t y E m ( s e e F igure 5 ) ,

we have:

where C, is the capac i tance per u n i t a rea . "Is, a s d id F r i c k e , we may o b t a i n

an e s t i m a t e of d f r m e s t i m a t i o n s of C, and assumptions concerning em, or vice versa. Fur ther , s i n c e i n mst cases t h e membrane capac i tance is d m i n a t e d by

t h a t due t o the hydrophobic phosphol ipid core (55a,65,66, but cf . 67) , and

s i n c e i n any case the value of d is reasonably well e s t a b l i s h e d Erom X-ray atid

neutron d i f f r a c t i o n measurement, or from molecular models, a value f o r E, of

2.0-2.2 has become accepted f o r t h e b i l a y e r membrane (BLM)(50,55,65,67,68).

S i m i l a r l y , s i n c e it is necessary t o p o s t u l a t e t h a t only a r e l a t i v e l y small

f r a c t i o n of t h e s u r f a c e of a phosphol ipid b i l a y e r membrane is penet ra ted by

aqueous pores with a d i e l e c t r i c p e r m i t t i v i t y of between 10 (bound water ) and

80 ( f r e e water) t o o b t a i n va lues of C, t y p i c a l of bianembranes, t h e r e is a

g e n e r a l s a t i s f a t i o n with the present theory. A t least with respec t t o energy

-


D I E L E C T R I C SPECTROSCOPY AND MEMBRANES 3 2 7

coupling membranes in genera l , and the bac te r i a l cytoplasmic membrane in

p a r t i c u l a r , we submit t h a t , fo r three reasons, t h i s is not a s a t i s f ac to ry

s t a t e of a f f a i r s . These reasons per ta in t o our ignorance of ( a ) the mechanism

of ac t ion of the ionophoric types of uncoupler, (b ) the r a t e and extent of the

l a t e r a l mobili ty of the f r e e energy-conserving protein complexes of such

membranes, and ( c ) the degree of e lec t rogenic i ty of redox-linked proton

pumping t o the bulk phase. However, it is f i r s t necessary b r i e f ly t o

summarize, for the benefit of readers who a re not involved i n these i ssues ,

the outstanding area of controversy in membrane bioenergetics.

THE PROBLEM OF ENERGY COUPLING I N ELECTRON TRANSPORT PHOSPHORYLATION

A s is now axiomatic (69), the exergonic reactions of biological e lec t ron

t ranspor t may be coupled t o the otherwise endergonic synthesis of ATP, the two

sets of reactions being catalyzed by s p a t i a l l y separate enzymes, embedded i n

an ion-impermeable phospholipid membrane (Figure 4 ) . The coupling may be

decreased, u l t imate ly t o zero, by the addi t ion of so-called uncoupler

molecules, many of which have the a b i l i t y to t ranspor t protons across both

a r t i f i c i a l BLM and natural biomembranes (68,70)(Figure 5 ) , a fac t cons is ten t

with, and widely in te rpre ted as strongly supportive of, the delocalised

chemiosmotic coupling theory elaborated by Mitchell (71). However, t h i s

general s e t of ideas (69) has some shortcomings (72-75), and one would l i k e t o

know t o what extent there is quan t i t a t ive agreement between the protonophoric

a c t i v i t y induced by uncouplers in BLM and tha t calculated as necessary to

account €or t h e i r uncoupling a c t i v i t y .

A s discussed by McLaughlin and Dilger ( a s ) , while there is an exce l len t

co r re l a t ion between the protonophoric a c t i v i t y of d i f f e ren t uncoupler

molecules in BLM and t h e i r uncoupling e f fec t iveness in r a t l i v e r mitochondria,

a paradox e x i s t s i n tha t it is necessary t o assume tha t the molecules are 100

times more potent a s protonophores in the l a t t e r case, to account fo r t h e i r


328 KELL AND HARRIS

A 6 C

I I

I I

el synthose

I I

FIGURE 4

The problem of energy coupl ing i n e l e c t r o n t r a n s p o r t phosphorylat ion. In such systems, a membrane ( v e s i c l e ) conta ins pro te inaceous e l e c t r o n t r a n s p o r t (ETC) and ATP synthase complexes, whose mutual g e m e t r i c r e l a t i o n s h i p is p r e s e n t l y unspeciEied, and the problem r e l a t e s t o the means by h i c h f r e e energy is t r a n s f e r r e d between t h e exergonic r e a c t i o n s of e l e c t r o n t r a n s p o r t and t h e o therwise endergonic process of ATP s y n t h e s i s . ( A ) In a chemiosmotic model, f r e e energy t r a n s f e r is a f f e c t e d by the product ion and consumption of a proton e lec t rochemica l p o t e n t i a l d i f f e r e n c e ("protonmotive force") a c r o s s the energy- coupl ing membrane; i n t h i s c a s e , no s p e c i a l t o p o l o g i c a l r e l a t i o n s h i p is requi red between ETC and ATP synthase complexes, and t h e i r m o b i l i t i e s and d i s p o s t t i o n s a r e thus i n t h i s sense unimportant. A l t e r n a t i v e l y , (B,C), f r e e energy t r a n s f e r might be a f f e c t e d by an intra-membranal r o u t e , e i t h e r by a d i r e c t (C) OK more long-range (B) i n t e r a c t i o n between t h e complexes. I n t h e case of a long-range i n t e r a c t i o n , a d d i t i o n a l p r o t e i n s (X) may be involved. Although t h e f ree-energy- t ransfer r ing s t e p i n B and C only occurs when an a p p r o p r i a t e geometr ica l r e l a t i o n s h i p e x i s t s between the r e l e v a n t (and mobile) complexes, t h e arrangement i n C sugges ts a much g r e a t e r degree of randan, long-range m o b i l i t y than that i n B.

a b i l i t y t o uncouple oxida t ive phosphorylat ion i n chemiosmotic terms by means

of a purely passive protonophoric a c t i v i t y a lone . These workers pointed cut

(59,68,76) t h a t t h e Born charging energy requi red f o r t h e t r a n s f e r of a

nonpolar i sab le , s p h e r i c a l , monovalent ion from an aqueous phase i n t o the

c e n t e r of t h e b i l a y e r is a c t u a l l y an extremely s e n s i t i v e f u n c t i o n of t h e

membrane p e r m i t t i v i t y , such t h a t increas ing t h a t of a BLM by a f a c t o r of two,

by us ing I-chlorodecane (Em = 4.5) i n the membrane-forming mixture , led t o an

i n c r e a s e of 2-3 o r d e r s of Mgni tude i n the ion permeabi l i ty of the BLM. It


D I E L E C T R I C SPECTROSCOPY AND MEMBRANES 329

H ++ A-

f A-

FIGURE 5

The protonophoric a c t i v i t y of a l i p o p h i l i c weak a c i d in a black l i p i d membrane. The protonophore a c t s by v i r t u e of i ts a b i l i t y t o c ross the membrane in both charged (A-) and uncharged (HA) forms. As discussed in t h e t e x t , the r a t e of transmembrane movement of A- is dependent on the value of E m , and it is t h e r e f o r e important to know t h i s value in a s s e s s i n g whether a protonnotive-force-drtven a c t i v i t y of the present type adequately expla ins the a b i l i t y of protonophores t o uncouple e l e c t r o n t r a n s p o r t phosphorylat ion.

was taken, t h e r e f o r e , t h a t s i n c e mitochondria conta in p r o t e i n s , which might be

expected t o have a much g r e a t e r p e r m i t t i v i t y than t h a t of phosphol ipids , an

explana t ion f o r t h e aforementioned paradox based on E m va lues might be

poss ib le . Thus, a l though the fact t h a t mitochondria a r e not s l a b d i e l e c t r i c s

with a p e r m i t t i v i t y twice t h a t of pure phospholipid BLM, a f a c t t h a t s e r v e s

r a t h e r t o s t rengthen the oppos i te conclusion t o the fol lowing ( 7 4 ) , t h e

conclusion was d r a m by Di lger , McLaughlin and co l leagues ( 5 9 , 6 8 , 7 6 ) t h a t t h e

above observa t ions were f u l l y c o n s i s t e n t with a chemiosmotic view t h a t

uncoupler a c t i o n could be explained s o l e l y in terms of t h e d i s s i p a t i o n of t h e

protonmotive f o r c e , by protonophoric a c t i o n in b i l a y e r a r e a s of the

mitochondria1 membrane via a mechanism of the type diagrammed in Figure 5. It


330 KELL AND HARRIS

is thus obvious t h a t a much better knowledge of t h e s t a t i c p e r m i t t i v i t y of

himembranes than we have a t p r e s e n t w i l l be r e q u i r e d t o g i v e any type of

q u a n t i t a t i v e account of uncoupler a c t i o n i n vivo. S i m i l a r l y , we would mention

c h a t a knowledge of t h e s t a t i c membrane c a p a c i t a n c e is of importance i n

dec id ing between a l t e r n a t l v e e x p l a n a t i o n s of t h e non-appearance of a p p r o p r i a t e

numbers of pro tons i n t h e o u t e r aqueous phase in suspens ions of microorganisms

i n “02-pulse” exper iments i n t h e absence of added ‘permeant’ ions (77-79).

I n t h i s type of measurement (77-80) a smal l volume of a i r - s a t u r a t e d KC1

is added t o an dnoxic suspens ion of r e s p i r a t o r y microorganisms, any r e s u l t a n t

pll changes i n the e x t r a v e s i c u l a r phase being conver ted t o numbers of pro tons

appear ing , such numbers u s u a l l y be ing r e l a t e d t o the amount of oxygen

consumed. and expressed as t h e + H + / O r a t i o . (We c o n s i d e r h e r e only

v e c t o r i a l pH changes, s c a l a r ones i n any event being a b s e n t under the

c o n d i t i o n s d e s c r i b e d , a s may be confirmed by f i n d i n g s obta ined i n the presence

of uncoupler . ) I n p r a c t t c e , i t is found t h a t c e r t a i n t r e a t m e n t s , such as t h e

a d d i t i o n of r a t h e r h igh c o n c e n t r a t i o n s of KSCN. g r e a t l y enhance t h e - + / O

r a t i o measured. The chemiosmotic e x p l a n a t i o n f o r t h e low +*/O r a t i o

observed i n the absence of KSCN relates t o the e l e c t r o g e n i c i t y of H+ pumping

and t h e r e l a t i v e l y low s t a t i c e lectr ical c a p a c i t a n c e of t h e c e l l u l a r

membrane. I n t h i s view, t h e low -+H+/O r a t i o is caused by the build-up of a

l a r g e , d e l o c a l i s e d membrane p o t e n t i a l , caused by the e l e c t c o g e n i c t r a n s f e r of

H+ from the i n n e r t o t h e o u t e r phase.

Using the s imple e l e c t r o s t a t i c equat ion (Q = CV) t h a t r e l a t e s t h e v o l t a g e

(V v o l t s ) a c r o s s a c a p a c i t o r of C f a r a d s when I t is charged by the passage of

Q coulombs of charge , w have, for cells or v e s i c l e s , A$,, = en/C, where e

is t h e e lementary e l e c t r i c a l charge (1.6 x IO-l9C), n is t h e number of €I+

t r a n s l o c a t e d ( e l e c t r o g e n i c a l l y ) a c r o s s a s i n g l e c e l l of c a p a c i t a n c e C, and

A’4max is the maximum orrmbrane p o t e n t i a l t h a t such protonmotive a c t i v i t y can

create. If we t rea t t h e cel ls a s s p h e r i c a l s h e l l c a p a c i t o r s (no membrane

i n v a g i n a t i o n s ) of c a p a c i t a n c e 1 uF/cmz, a t y p i c a l bacter ium of r a d i u s 500 nm



has a capacitance of 3 x F (77,79,81). If we measure the t o t a l number

of ~ t rans loca ted , and assume tha t a l l are e lec t rogenic , then n m y be

ca lcu la ted €ran a knowledge of the c e l l numbers. By using small oxygen pulses

and la rge c e l l concentrations, the maximum bulk-to-bulk phase transmembrane

po ten t i a l which may theo re t i ca l ly be b u i l t up, A$max, may thus be made

a r b i t r a r i l y small, so t h a t , according t o chemiosmotic considerations, the

K'/O r a t i o should now be as g rea t in the absence of KSCN as in i ts presence

(KSCN being taken t o act by d iss ipa t ing a chemiosmotic membrane po ten t i a l ) .

In prac t ice , however, such behaviour is not observed (77,79,81), suggesting

t h a t the non-appearance of most of the protons in the cuter bulk phase in the

absence of KSCN is not due t o the build-up of a chemiosmotic membrane

po ten t i a l but t o the f ac t tha t the protons never entered t h i s phase

e lec t rogenica l ly . Since t h i s conclusion would not necessarily be cor rec t i f

the static roembrane capacitance were only, say, 0.02 !JF/cm2, i t is important

t o know i ts ac tua l magnitude. However, da ta ava i lab le concerning the

P-dispersion of Paracoccus den i t r i f i cans s t rongly suggest tha t the s t a t i c

membrane capacitance is a t l e a s t 0.5 pF/cmZ ( 3 2 , 3 3 ) .

Thus, we have seen tha t a knowledge of the values of even the s t a t l c

e l e c t r i c a l capacitance of energy coupling biomembranes is of c ruc ia l

importance in assess ing the verac i ty of the chemiosmotic and other coupling

hypotheses in a t l ea s t three areas: the mode of ac t ion of uncouplers, the

e l ec t rogen ic i ty of bulk-to-bulk phase proton pumping catalyzed by redox-linked

proton pumps, and t h e i r l a t e r a l mobility r e l a t ive t o tha t of ATP synthase

enzymes (Figure 4).

DIELECTRIC SPECTROSCOPY AND THE DYNAMIC

ORGANIZATION OF BIOMEMBRANES

In the foregoing, we have concentrated mainly upon the s t a t i c e l e c t r i c a l

capacitance of the membrane. However, as depicted in Figures 3 and 4, curren t


332 KELL AND HARRIS

t h i n k i n g c o n c e i v e s of t h e long-range, hydrodynamica l ly -cons t r a ined , la teral

m o b i l i t y of l i p i d and p r o t e i n complexes i n t h e p l a n e of t h e membrane,

a c c o r d i n g t o t h e f lu id -mosa ic p i c t u r e . It was w n t i o n e d by S inge r and

Nicolson ( 4 8 ) . s t r e s s e d by J a f f e (82 ,83) and conEirmed ( 8 4 - 8 6 ) , that t h e

a p p l i c a t t o n of a s t e a d y electric f i e l d t o a biomembrane-bounded ce l l o r

v e s i c l e s u s p e n s i o n s h o u l d r e s u l t i n t h e lateral r e d i s t r i b u t i o n ( " l a t e r a l

e l e c t r o p h o r e s i s " ) of c h a r g e d , i n t e g r a l membrane p r o t e i n c m p l e x e s . S i m i l a r

e f f e c t s shou ld f o l l o w f r a n t h e a p p l i c a t i o n of any s i n u s o i d a l l y v a r y i n g f i e l d

whose f r equency is less t h a n t h e C h a r a c t e r i s t i c f r equency of t h e Maxwell-

Wagner-type d i s p e r s i o n of the v e s i c l e s in q u e s t i o n . As f i r s t p o i n t e d o u t , t o

o u r knowledge, by K e l l (87 ) , such f i e ld -dependen t motions shou ld n e c e s s a r i l y

be accompanied by a frequency-dependence of t h e d i e l e c t r i c p r o p e r t i e s of s u c h

a system. They shou ld be r e f l e c t e d as a d i e l e c t r t c d i s p e r s i o n , t h e d i e l e c t r i c

i nc remen t and r e l a x a t i o n time of which may i n p r i n c i p l e be used t o g a i n

i m p o r t a n t i n f o r m a t i o n c o n c e r n i n g t h e r a t e and e x t e n t ( r a n d a a n e s s ) of such

l i p i d and p r o t e i n motions.

Because of t h e p r o p e r t i e s of t h e Langevin f u n c t i o n ( 2 4 , 3 0 , 8 3 , 8 8 ) , the

r e l a t i o n s h i p between t h e v i s u a l and d i e l e c t r i c o b s e r v a b i l t t y of such motions

i s dependen t upon t h e ce l l r a d i u s ( i f such mot ions are r e s t r i c t e d by

hydrodynamic f o r c e s a l o n e ) . F u r t h e r , t h e r e are good r e a s o n s t o b e l i e v e t h a t

t h e r e is a s t r o n g c o u p l i n g between t h e motions of p r o t e i n s and l i p i d s i n t h e

membrane, on t h e one hand, and of t h e ions and s o l v e n t molecu le s i n t h e

a d j a c e n t d o u b l e l a y e r s , on t h e o t h e r (32,88-90). Thus, t h e s i t u a t i o n i s

compl i ca t ed . and our purpose i n t h e remainder of t h i s s e c t i o n is t o a t t l i n e

t h e p o s s i b l e c o n t r i b u t i o n s of s u c h mot ions t o d i e l e c t r i c s p e c t r a g e n e r a l l y . A

f u l l e r d i s c u s s i o n of t h e s e and r e l a t e d matters is g i v e n e l s e w h e r e (88)

t o g e t h e r u i t h a r a t h e r e x t e n s i v e set of measurements c a r r i e d o u t on a number

of m i c r o b i a l c e l l s , p r o t o p l a s t s and membrane v e s i c l e s (32) .

With r e f e r e n c e t o F i g u r e 3, the characteristic f r equency ( f c = 1 / 2 n r , where r is t h e r e l a x a t i o n t i m e i n seconds ) f o r t h e r o t a t i o n a l d i f f u s i o n of a



membrane protein may be derived f r an the Stokes-Einstein r e l a t ion , and is

given by

f c = k T j 8 n 2 a 2 q h ( 6 )

where q is the membrane v iscos i ty , k is Boltzmann's constant, T the absolute

temperature and the other symbols a re as i n Figure 3 . Using typica l values of

7 (1-10 P), a (4 nm) and h ( 5 nm) , it is found tha t t yp ica l ly fc is

1-10 KHz (88). The advantage of the d i e l e c t r i c method is tha t the

c h a r a c t e r i s t i c frequency is readi ly obtained, and the values of f c as

ca lcu la ted from equation (6) might be expected t o equal the values obtained

d i e l e c t r i c a l l y .

For ca lcu la t ing the t r ans l a t iona l d i f fus ion c w f f l c i e n t s of membrane

pro te ins , i t has become conventional to use an equation f i r s t derived by

Saffman and Lklbruck (91), which fo r our purpose may be modified (88) t o give

the cha rac t e r i s t i c frequency fo r t r ans l a t iona l motional relaxation i n a closed

membrane ves ic le :

f c = (kTK/4r2qr2h) [ln(qh/q'a)- Y ] (7)

where y is Euler 's constant (0.5772), and we consider e i t h e r random

(throughout the ves ic le ) or r e s t r i c t e d 2-dimensional diffusion. In the former

case, K = 1 and r - r , the ves i c l e radius (Figure 3), while in the l a t t e r

case , K = 2 and r = r' (Figure 3 ) , the average distance moved before a

b a r r i e r , of whatever nature, is encountered. P lo ts of equation (7 ) ind ica te

(88) t h a t values of fc f o r t h i s type of relaxation depend c r i t i c a l l y upon the

ex ten t of t r ans l a t iona l randomness (i .e. degree of long-range mobili ty) of the

p ro te in ( s ) , given the r e l a t ive (order of magnitude) constancy of biomembrane

v i scos i t i e s . Some of the values obtained, however (32,92) gtve cause t o doubt

the app l i cab i l i t y of the s i m p l e s t type of f l u i d mosaic model to the bac te r i a l

cytoplasmic membrane (74,93,94). Problems of t h i s type raised by experiments

of a more biochemical nature in animal c e l l s (95) may a t least p a r t i a l l y be

expl icable in terms of membrane protein-cytoskeleton in t e rac t ions ; however,

bac t e r i a a re not thought t o possess a cytoskeleton of the type found in


'334 KELL AND HARRIS

eukaryotes , and t h e exac t mechanis t ic explana t ion f o r t h e apparent ly

non-randm d i s t r i b u t i o n of membrane p r o t e i n s i n many microorganisms remains a

mat ter f o r present concern and f u t u r e research . These more g e n e r a l

c o n s i d e r a t i o n s l i e o u t s i d e our present scope, but have r e c e n t l y been discussed

(74,88,93,94).

A d i e l e c t r i c r e l a x a t i o n is c h a r a c t e r t z e d not only by i t s r e l a x a t i o n time

but a l s o by its magnitude. This i n tu rn depends upon the concent ra t ion of

e f f e c t i v e d i p o l a r p a r t i c l e s , t h e i r e f f e c t i v e molecular d ipole moments and t h e

degree of r e s t r i c t i o n on t h e i r motions. It is usual t o r e l a t e the observable

d i e l e c t r i c increment Ac' due t o the r o t a t i o n of a g lobular p r o t e i n i n an

aqueous s o l u t i o n t o its molecular d i p o l e mment p according t o t h e r e l a t i o n :

(22,96), where c is the nolar p r o t e i n concent ra t ion . N Avogadro's number and H

is an empir ica l cons tan t which is usua l ly taken (from a comparison between

c a l c u l a t i o n and experimental d a t a f o r g l y c i n e ) t o have the va lue 5.8. Note

t h a t t n equat ion ( 8 ) P I s i n Debyes, bu t s i n c e two u n i t charges of oppos i te

s i g n separa ted by 10-lo~ possess a d ipole moment of 4.8 D, w m y express

t h e e f f e c t i v e d i p o l e moment of any p o t e n t i a l l y mobile d i s t r i b u t i o n of charged

p a r t i c l e s i n u n i t s of charge-Angstran by d i v i d i n g the v a l u e f ran equat ion ( 8 )

by 4.8. P l o t s of q u a t i o n (8) i n d i c a t e t h a t e x c e p t i o n a l l y l a r g e d i e l e c t r i c

increments may indeed be exhib i ted by systems in which t h e ex ten t of d i f f u s i o n

of the charged p a r t i c l e i n q u e s t t o n is l a r g e (88).

Tne c l a s s i c a l explana t ion of t h e a - d i s p e r s i o n is t h a t i t r e f l e c t s ( a t

l e a s t p a r t i a l l y ) t h e r e l a x a t i o n , t a n g e n t i a l t o the charged membrane s u r f a c e ,

of t h e ions c o n s t i t u t i n g t h e d i f f u s e double-layer (97-100). However, i n t h e

case of t y p i c a l biomembranes, the o r g a n i z a t i o n of t h e p r o t e i n s in t h e

phosphol ipid m a t r i x is such t h a t t h e i r s u r f a c e s extend s u b s t a n t i a l l y beyond

t h e s u r f a c e d e l i n e a t e d by the phosphol ipid head-groups (F igure 6)(101). Thus,

t h e r e l a x a t i o n times f o r t h e t a n g e n t i a l motions of double l a y e r ions will



1

c

FIGURE 6

The molecular roughness of the s u r f a c e of a protein-containing biomembrane v e s i c l e can l ead t o a s u b s t a n t i a l broadening of the r e l a x a t t o n t ime(s) of double-layer ions moving " t a n g e n t i a l l y " t o t h e charged membrane s u r f a c e s . In p a r t i c u l a r , " f r e e , t a n g e n t i a l " i o n i c r e l a x a t i o n wfll be stopped at the poin ts marked "A" and "B" i n systems of the present type. For f u r t h e r d i s c u s s i o n , see t e x t .

depend not only upon t h e v e s i c u l a r r a d i i but a l s o upon the molecular roughness

of the sur face of ind iv idua l v e s i c l e s , the e f f e c t being t o cause d i e l e c t r i c

r e l a x a t i o n s a t f requencies g r e a t e r than those otherwise t o be expected, i n a

fash ion which w i l l be upaf fec ted by the presence of in te rmolecular cross-

l i n k i n g reagents ( 3 2 , 8 8 1 . Fur ther , any e lec t roosmot ic i n t e r a c t i o n s between

t h e d i f f u s e double l a y e r and the motions of the p r o t e i n s of the membrane

( 8 9 , 9 0 ) w i l l a l s o s e r v e t o broaden such d i s p e r s i o n s , by an uncer ta in amount.

The foregoing d iscuss ion a p p l i e s equal ly , for r o t a t i o n , t r a n s l a t i o n and

e l e c t r o o s a o t i c behaviour , t o t h e charged l i p i d s of the membranes, while even


336 KELL AND HARRIS

n e u t r a l ( z w i t t e r i o n i c ) l i p i d s may be expected t o e x h i b i t a d i e l e c t r i c

d i s p e r s i o n due t o t h e i r r o t a t i o n a l r e l a x a t i o n (102).

F i n a l l y , a d i e l e c t r i c d i s p e r s i o n due t o the r o t a t i o n ( i . e . o r i e n t a t i o n )

of the e n t i r e v e s i c l e might a l s o be a n c i c i p a t e d , i ts c h a r a c t e r i s t i c f requency

being given from the Stokes-Einstein r e l a t t o n a s :

For t y p i c a l va lues of q u e o u s v i s c o s i t i e s (0.01-0.015 P) and c e l l ( v e s i c l e )

r a d i i , c a l c u l a t i o n s based on equat ion (9) i n d i c a t e t h a t d i e l e c t r i c d i s p e r s i o n s

due t o c e l l u l a r r o t a t i o n a r e not t o be observed in the Prequency range above

10 Hz, except f o r e x c e p t i o n a l l y small p a r t i c l e s .

Thus, t h e conclusion from these l a r g e l y t h e o r e t i c a l cons idera t tons is:

any motional c h a r a c t e r i s t i c s of the l i p i d s and p r o t e i n s of biomeinbranes, and

of the ad jacent double l a y e r s , can u n d e r l i e or give r i s e to a d i e l e c t r i c

d i s p e r s i o n . Since t h e s i g n i f i c a n c e of t h i s s ta tement t o d i e l e c t r i c s t u d i e s O E

biomembrane organiza t ion has on ly r e c e n t l y became a p p r e c i a t e d , we next d i s c u s s

t h r e e p a r t i c u l a r exper imenta l manipulat ions t h a t may be or have been used t o

ga in information about the c o n t r i b u t i o n s of such mottons t o d i e l e c t r t c

s p e c t r a .

EXPERIMENTAL NANIPULATIONS OF RELEVANCE TO DIELECTRIC STUDIES OF MEMBRANE ORGANIZATION AND DYNAMICS

The more c l a s s i c a l explana t ions of the a- and !-dispersions i n charged

membrane v e s i c l e suspensions depend e s s e n t i a l l y only upon the r a d i u s , c losed

n a t u r e , s u r f a c e charge d e n s i t y and s u r f a c e p o t e n t i a l of the v e s i c l e s , and on

t h e m o b i l i t y and c o n c e n t r a t i o n of t h e ions of t h e d i f f u s e double l a y e r

Thus , a s s t r e s s e d elsewhere

( 3 2 , 5 7 , 8 8 , 9 2 , 1 0 3 ) , they should be unchanged, o t h e r c i rcumstances being e q u a l ,

by the a d d i t i o n of chemical c ross - l ink ing reagents t o the membrane v e s i c l e

suspension. In other vords, any change i n the d i e l e c t r i c p r o p e r t i e s caused by

a - d i s p e r s i o n ) and bulk phases (?-dispers ion) .



t h e a d d i t i o n of chemical cross- l inking reagents such as g lu ta ra ldehyde or

dimethyl suberimidate , which do not change the s u r f a c e charge d e n s i t y (104) or

hulk phase c o n d u c t t v i t i e s , should be d i a g n o s t i c of a cont r thu t ion of the

l a t e r a l ( t r a n s l a t i o n a l and r o t a t i o n a l ) motions of charged membrane components

t o the observed d i e l e c t r i c spectra, al though c a r e should be taken t o exclude

( o r d i f f e r e n t i a t e ) =-vesicular cross- l inking, a d i a g n o s t i c of a

c o n t r i b u t i o n from v e s i c l e o r i e n t a t i o n . S i m i l a r l y , t h e a v a i l a b i l i t y of

photopolymerizable phosphol ipids (105,106) presents a favourable experimental

oppor tuni ty of t h i s type (87,88).

Since the v i s c o s i t y of biomembranes exceeds t h a t of the t y p i c a l aqueous

s o l u t i o n s t o which they are adjacent by 2-3 orders of magnitude (107),

i n c r e a s i n g t h e aqueous v i s c o s i t y by s a y a f a c t o r of 10, f o r ins tance with

g l y c e r o l , will have an e s s e n t i a l l y 10-fold e f f e c t upon the r a t e of v e s i c l e

o r i e n t a t i o n , o r on r e l a x a t t o n s due t o double l a y e r i o n i c motions, bu t a

n e g l i g i b l e e f f e c t on r e l a x a t i o n s due t o the motions of membrane canponents,

provided t h a t t h e membrane:water p a r t i t i o n c o e f f i c i e n t of g lycero l does not

s i g n i f i c a n t l y exceed 1. Thus, s t u d i e s of the dependence of d i e l e c t r i c s p e c t r a

on both the v i s c o s i t y and the temperature may shed l i g h t on the r e l a t i v e

c o n t r i b u t i o n s of i n t r a - and extra-membranal d ipole r e l a x a t i o n s , a s occurred in

s t u d i e s of q u e o u s g lobular p r o t e i n s (22,108,109).

The time cons tan t and magnitude of d i e l e c t r i c r e l a x a t i o n s due t o t h e

mechanisms of the c l a s s i c a l a- and ?-dispers ions have a d i f f e r e n t dependence

upon t h e v e s i c l e r a d i u s in t h e two cases; s i m i l a r l y , r e l a x a t i o n s due t o

mechanisms of the type p r e s e n t l y under cons idera t ion e x h i b i t d e f i n i t e and

d l f f e r e n t v e s i c l e radius-dependencies, and indeed i t was the s h i f t i n g of t h e

a- and p-dispers ions t o high f requencies i n b a c t e r i a l chrmatophores (87)

which f i r s t drew a t t e n t i o n t o t h e s e p o s s i b i l i t i e s . Thus, at l e a s t t h r e e types

of experimental manipulat ions (c ross - l ink ing , v i s c o s i t y changes, and

s o n i c a t i o n t o change t h e v e s i c l e r a d i u s ) may be used t o a i d the experimenter


KELL AND H A R R I S 338

who seeks t o unrave l the v a r i o u s c o n t r i b u t i o n s of the type under d i s c u s s i o n t o

d i e l e c t r i c s p e c t r a .

I f w accept t h a t fteld-membrane-protein/lipid i n t e r a c t i o n s can e x p l a i n

some of t h e d i e l e c t r i c p r o p e r t i e s of membrane v e s i c l e s , I s l t p o s s i b l e

t h a t they may also u n d e r l i e some of t h e observed e f E e c t s OE low-level

e l e c t r i c a l f i e l d s upon c e l l u l a r physiology?

MODULArION BY ELECTRICAL F I E L D S OF REACTIONS CAT4LYSED BY MEMBRANE-BOUND ENZYMES

The i m p o s t t i o n of a macroscopic , s i n u s o l d a l l y a l t e r n a t i n g , electric f t e L d

wi th a f t e l d s t r e n g t h (peak-to-peak) of Eo (V/cm) and a f requency of

w r a d i a n s / s a c r o s s a suspens ion of s p h e r i c a l membrane v e s i c l e s of r a d i u s r ,

induces a transmembrane p o t e n t i a l of a magnitude given by:

1.30), where 0 Ls t h e a n g l e between a p o r t i o n of t h e b i l a y e r and the f i e l d

d i r e c t i o n , and 7 is t h e r e l a x a t i o n time f o r t h e c l a s s i c a l Yaxwell-Wagner

d i s p e r s i o n . Thus, w i t h c e l l s of a modera te ly l a r g e s i z e , quLte modest

e x c i t t n g f i e l d s can induce p h y s i o l o g i c a l l y s i g n i f i c a n t membrane p o t e n t l a l s .

Such p o t e n t i a l s can have both thermodynamic e f f e c t s on p u t a t i v e l y (quasi-)

r e v e r s i b l e r e a c t i o n s sltch a6 ton uptake (7,110-112) and A T P s y n t h e s i s (113) ,

and even i f they are of i n s u f f i c i e n t magnitude t o a c t as a f r e e energy tenn in

+ r i v i n g e n z y e a t i c a l l y c a t a l y s e d r e a c t i o n s , t h e l a r g e d i p o l e moments (114) and

f l e x i b i l i t y (1 15,116) of such p r o t e i n s can lead t o f te ld- induced modulat ion of

t h e k i n e t i c p r o p e r t i e s of such membrane-bound enzymes by a l t e r i n g t h e i r

conformat iona l s t a t u s o r t h e i r dynamics (116a) . Thus, f i e l d - p r o t e i n

i n t e r a c t t o n s in a p lane normal t o t h e b i l a y e r ioembrane might a l s o cause small

but s i g n i f i c a n t d i e l e c t r i c d i s p e r s i o n under c e r t a i n c i rcumstances ( 8 8 ) .



Another case in which a c l ea r mechanism oi f ie ld-pro te in in t e rac t ion

leading t o a modulation of membrane enzyme a c t i v i t y has been e l i c i t e d comes

from the observations of Young and Po0 (117), who showed tha t l a t e r a l

e lec t rophores i s may lead to protein aggregation and in t u r n to an a l t e r a t i o n

of the k ine t i c s of ion channels (118). Thus, these (and other) s tud ies show

q u i t e c l ea r ly tha t simple, d i r e c t field-enzyme in te rac t ions can lead to a

modulation of enzymatic a c t i v i t y , and hence to biological e f f ec t s . In the

s p i r i t of t h i s a r t i c l e , therefore , we would argue i n harmony, for ins tance ,

with P i l l a (7,111,119), tha t d i e l e c t r i c s tud ies provide a potent mans of

determining the mechanisms of such processes, provided tha t the l a t t e r a r e

l i nea r (see next sec t ion) .

PROBLEMS AND PROSPECTS

The recent commercial a v a i l a b i l i t y of rapid, d i g i t a l , impedimetric

apparatus has been fo r us, and will no doubt continue generally to be, a

potent means and motivation €or advancing the theory and practice of membrane

(and other) d i e l e c t r i c spectroscopy. However, we should l i ke to end by

out l in ing what we perceive t o cons t i t u t e the three major general problems,

both theore t ica l and experimental, slowing the rate a t which cur co l l ec t ive

understanding of the e l e c t r i c a l organization of biomembranes may be improved

by d i e l e c t r c spectroscopy using modern apparatus i n the range 101-107 Hz. ( 1 )

The development of computer programs fo r the automated correction of the

cont r ibu t ion of e lec t rode polar iza t ion to the observed d i e l e c t r i c spectra

would be a grea t boon, and would g rea t ly extend the range of frequencies and

conduct iv i t ies ava i lab le ; ( 2 ) more objective and f l ex ib l e means of f i t t i n g

d i e l e c t r i c data t o sums of individual (mechanisms of) d i e l e c t r i c d i spers ion ,

i.e. of deconvoluting d i e l e c t r i c spec t ra , need to be developed -- we have

tended t o assume tha t d i e l e c t r i c dispersions a re best modelled by a Cole/Cole-

type d i s t r ibu t ion function, an assumption that is at best un jus t i f ied and most


340 KELL A N D HARRIS

l i k e l y i n c o r r e c t (120); ( 3 ) we need more e x p l i c i t l y t o a t t a c k t h e problem of

d e c i d i n g e x a c t l y what a method which is by d e f i n i t l o n measuring l i n e a r

p r o p e r t i e s is a c t u a l l y t e l l i n g us about t h e p r o p e r t i e s and hehaviour of

systems which may be expected t o be, and i n some cases demonstrably a r e

( 6 , 7 4 ) , s t ronAly non-l inear and far f r m e q u i l i b r i u m in vivo . The s c i e n t i f i c ,

and b i o a n a l y t i c a l (121) p o s s i b i l i t i e s embodied i n t h i s a r e a i n p a r t i c u l a r

would seem t o us t o c o n s t i t u t e some of the most e x c i t i n g l i n e s of progress t o

be expected i n the ensuing years .

ACKNOWLEDGEMENTS

We a r e indebted t o t h e Science and Engineer ing Research Council and t o

I(:[ A g r i c u l t u r a l D i v i s i o n f o r f i n a n c i a l suppor t . We should a l s o l i k e wanoly

t o e x p r e s s our deep thanks t o t h e many d i e l e c t r i c s p e c t r o s c o p l s t s who have

generous ly shared t h e i r e x p e r t i s e with us i n encouraging our approaches t o

t h e s e i n t e r d i s c i p l i n a r y problems €ran a b i o l o g i c a l p e r s p e c t i v e . We thank

Anthony Pugh for photographic a s s i s t a n c e and Sian Evans f o r typing the

n a n u s c r i p t .

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