Molecular recognition and processing of periodic signals in cells: study of activation of membrane ATPases by alternating electric fields

Biochimica et Biophysica Acta, I ! 13 (1992) 5 3 - 7 0

53

~-~ Iqq2 El~vier Science Publishe~, B.V. All rights rescmved 0304-4157/92/$05.00

BBAREV 853t,~

Molecular recognition and processing of periodic signals in cells: study of activation of membrane ATPases by alternating electric fields Tian Y. Tsong Department of Biochemistry. Unit.ersity o[ Minnesota College of Biological &'ien('es, St. Paul, MN (USA) and In.ttitute of Biomedical Sciences, Academia Sintca, Taipei ( Taiwan) (Recewed 27 August 1991) tRevised manuscript received 2 December lUql)

Contents |.

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

II.

Intrc~luctJon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

I!1.

Chemical reactions in isotropic and aniu)tropic media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

IV.

T h c r n ~ I v n a m i c basis o f molecular interaction with a periodic potential . . . . . . . . . . . . . . . . .

55

V.

Some characteristics of Iranm)cmbrane proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5f,

VI.

Activation u2 membrane ATPascs by dynamic electric ticlds . . . . . . . . . . . . . . . . . . . . . . . . . A. ATP synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Cation pumpings by Na.K-ATPas¢ of hun~an erythrocyte . . . . . . . . . . . . . . . . . . . . . . . . . C. ATP hydrolysis actwily of EcIo-ATPase ~'rom chicken oviduct . . . . . . . . . . . . . . . . . . . . . . D. ATP hydrolysis activity o[ rai~bit kidney Na.K-ATPase . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Calcium pumping by the C a - A T P a ~ ol human eqtthrtv..'yles . . . . . . . . . . . . . . . . . . . . .

57 57 5~ 58 fi0 Ol

VII.

Eleclroconfi)rmational coupling in medium and high level electric fields . . . . . . . . . . . . . . . . A. Entorccd and synchronized oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Energy flow during a conformalional oscillalion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Maximal efficiency Ior energy coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Winch)ws for electroconformational coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E Rec:ificatieu of charged ligands and other Iranspuft sy~tcm~ . . . . . . . . . . . . . . . . . . . . . . . F. Fluctuating membrane potentia; and ,:;¢c':Jc s;gna'. . . . . . . . . . . . . . . . . . . . . . . . . . . . G. Electnvonforma6tmal coupling in a channel enzyme . . . . . . . . . . . . . . . . . . . . H. Piezoconformational coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61 61 61 63 63 64 65 66 66

VIII.

Transduction of hv,v level "-q¢ctric signals

6";

IX.

Channels, transporters, receptors, growth factors and enzymes . . . . . . . . . . . . . . . . . . . . . . . .

..................................

6~

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

09

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

b'~

Correspondence: T.Y. Tsong, Department of Biochemistry., University of Minnesota College of Biological Sciences, St. Paul. MN 551C,8, USA.

54 I. Summary A molecule which is immob;ilzcd, uJicmcd o, tumbling more slowly than the frequency of a pcriodic field, may interact v,ith the field to producc chemical effects that are uncommon in a homogeneous solution. Among these effects arc the alteration of the rate of :'. chemical reaction and the exchan.,e of energ' between the oscillating field and the conformation of the molecule. When certain coaditioas are satisfied, this exchange allows the molect~le to absorb and couple tn.: energy of the field to drive an endergonic reaction. The efficiency of energy coupling depends on field strength and frequency and on the ligand concentration. There are windows of these parameters to achieve efficient coupling. These windows can be expre.~sed in terms of the rate constants and equilibrium constants of the catalytic reactions, and the amplitude and frequency of the periodic field. This mcehani.~-n allows cells to receive, process and transmit energy of high and medium level periodic potentials by mtans of membrane enzymes or receptors. A theory for the tran.~luction of electric energy, electroconformational coupling (ECC) will be discussed. Th? electric field induccd cation puil~pi.2g activities of Na,K-ATPasc and Ca-ATPa.~ of human erythrocytes and the ATP synthctie activity of beef heart mitochondrial ATPase will then be used to test an ECC mcmbrane transport model. For the processing of low level periodic signals, a theo:y of an oscillatory activation barrier (OAB). which considers resonance transduction between an oscillating field and the activation barrier of the rate limiting step in an enzymic reaction, will be discussed. The OAB m~:chanism successfully interprets the AC stimulated ATP rlydrolysis activity of Ecto-ATPase from chicken oviduct and F.F,-ATPase from beef heart. We propose that mechanisms similar to an OAB model are adopted by cells to sense weak electric, acoustic, mechanical, concentration (i.e., chemical potential) and other types of signals, and to communicate with other cells by these signals. The experimental data and mechanistic information presented in this communication give us a glimpse of the molecular electronic designs in living cells. This information is also relevant with respect to environmental issues. Em'ironmental electromagnetic fields and sonic pollutants may interfere with normal communications of cells and organisms. Their bcncfit, if any. and detrimental effects can be asses~d and dealt with only if we fully understand mechanisms of cellular interactions with these fields and pollutants, at the molecular level.

I!. Introduction Cells or organisms must Ix able to detect both gradual and abrupt .:hanges in their environment in

order to survive. They must also be able to coorzlinate with other cells, organs or organisms in order to engage in, and regulate iheir ~,idc ~,alictiL.s of activitics. After millions of years of evolution and adaptation, they have acquired the ability to sense, decipher, process and generate periodic signals, such as electric, sonic, thermal and chemical att,'actant signals. Sharks, skates and rays are able to pcrce~,,e nV per cm electric signals [I]. and electric fishes use very weak EOD (clcctric organ discharge) to warn or track their p r e ~ i:i. t~,,.=.,, na~ngatc with the earth magnetic fields. Sonic communication am,,ng organisms is a vide spread pbenomcnon. Cells can also transmit information through oseillation of transmembrane potentials and Ca 2÷ concentration, as in /]-cells of pancreatic islets [3-6], or oseillation of cAMP, as in slime molds [7]. This ability of cells implies that molecules of the cell are capable of producing and responding to thc.;c periodic signals. Many of these oscillatory reactions are quite unique and their analysis demands new ideas and fresh aoproache,~ [8,';]. A cell may Ix: considered a miniature electronic device, capable of not only signal transducrio,1 b::t of decision making as well [10]. The molecular aor, aratus for accomplishing these tasks is ~mong the most fascinating sub.iccts of sludy in cell bio.ogy.

!11. Chemica! reactions in isotropic and anisotropic media A chemical reaction that takes phce in ~alution or in gas has no directionality. The reaction space is isotropic. A driving force originated internally or externally will be evenly distributet~ to the entire reaction space, it is like the space in~;idc a balloon. / pressure applied to any part of the b~lloon will be tl-.:..,.'.":" to all o~hcr parts, and will be .2xpericnced equally by all moleo~les inside the balloon. The equilibrium property c;f a rt:action in such an isotropic medium is described by the law of the mass action. For a reaction on a cell membrane, there is certain directionality. A reaction will occur only if the reactants approach each other f~,~m the right direction. Reactants that approa~.h from the wrong direction or the wrong side will not react. The space, or medium, in this case is anisotropic. Most chemical reactions in a living cell take place in an anisotropic medium. We kr.ow very little concerning thermodynam!c principles governing chemical reactions of an anisotropic system. Much less is known when a driving force of a reaction is also a vector quantity. Biochemists have for many years been studying mr:r,I-,~,m,, transport phenomena. They have recognized the vectoria~ characteristic of membrane transport and the importance of this characteristic for the energy coupling in cells. However, mechanisms of energy coupling in an anisotropic medium and the vectorial interaction of biological molecules remain for the

55 most part unknown [9]. The chemiosmotic hypothesis of Mhchell [11] and Williams [12]. which postulates that the gradient of an ton, e.g., proton, is an intermediate for coupling a source energy to an energy consummg reaction, continues to be popular. Although the chemiesmotic hypothesis has survivt;d many years of scrutiny and testing to my kno~vled.7,-e, no .serious attempts have been made to understand how the transmission of energy from a proton gradient to a chemical reaction can be accomplished at the molecular level, in this article, i will r( view experiments, by others as well as our own, of the past 10 years on the electric stimulations of cation tran ~ports, A T P synthetic and hydrolytic activities of several membrane ATPases. ! will then present two theories, electroconformational coupling (ECC) [9,13-,17] and oscillatory activation barrier (OAB) [18,19], and enzyme model.~ based on the two theories, to interpret experimental results. In these mode!s, interactions occur at the level of conformational equilibria or rates .;f the catal)tic cycle of a Michaelis-Menten enzyme system. In the ECC mechanisms, a molecule utilizes energy of a high or medium level periodic field to drive a reaction away from chemical equilibrium. Whereas, in the OAB mechanisms, the rate, but not the equilibrium, of a spontaneous reaction is modified by a low level periodic field. Some fundamental concepls, which the two theories are based on, are briefly reviewed. IV. Thermodynamic basis of molecular interaction w';h a periodic potential

an increase in temperature will shift the equilibrium toward the left and if it ;s ~:c~,ative, or exothermic, an increase in temperature will shift the equilibrium !oward the right. In other words, the extent of change depends on the value ar, d the direction of change depends on the sign of the A H . Similarly, for a reaction having a change in the molar volume. AV. the pressure will change the equilibrium according to 1~ In

K /,~PIr

=

- At" / R T

(31

Again, depending on the value and the sign of the AV, the shift in equilibrium by a pressure or an acoustic

signal will be towards the :ighr or towards the left. A change in chemical poter.tial or concentration of a compound will also shift an equilibrium. Since this article deals mainly with the proce,,,.',ititt of electric signals, we will focus on effects of the electric field [9,13.231. The relevant equation for molecular interaction with an electric field is [,~ In K /aE]~,.r.r

=

..IM/RT

(4)

Here A M denotes the difference in the molar electric moments of the two conformers, A and B. in Eqn. 1. The main contributions to A M are charge displacements ( ~ z , e o A d t, e o being the elementary, charge). changes in permanent dipole moment (A/z) and changes in polarizability or the induced dipole moment ( A a L , a oeing the polarizab;l;:.y) of ~he molecule. A M ~ N , , - ~"~z.e.dd. + Air "* A a E

(5)

A biological molecule can interact with a force field and change its conformation (see e.g., Refs. 9, 20-22). ,ii,. ,,i,~st familiar example is the conformational change induced by heat. DNA has a double helical structure at a low temperature, e.g., 25"C, and becomes a single stranded randoi~ ~ i l at a higher temperature, e.g., 80"C. Likewise, a protein may have one confor, aalion at one teraperature and a different one at another temperature. Conformational change of a molecule involves a change in its internal energy. Consider a simple reaction which denotes the conformational change of a molecule,

N. is the Avogadro's number and Ad, are distances between charges. The equilibrium constant. K. and the two rate constants, k~ and k_ ~, depend on the effective field strength, E for a molecule in solution, and E~mh~ for a transmembrane integrated protein (E~mb, being the effective field stre.".gth across the lipid bilayer given in Eqn. 9). In Eqn. 4, the induced dipole term is usually sinai! :.:,J may ~.~ neglected. In such a case, the integral forms ,~f Eqn. 4 for a membrane protein when E = E,,~mh, are approximated by [13,14], K - K" cxp[ - .1M"E,,~mh,//¢ r )

(~)

/,i Ac*B /, i

k 2" tel' expl r i M . E,.~,.h,/RT]

(7)

k _ I ~ '~ ° l ~Xl)[I. r -- I ) A ~ "

(8)

(I)

Wizen pressure and volume are held constant, the effect of temperature on the , hemical equilibrium is described b', the van 't H o f f equation [21,22]. [a ',n K / a T t]e.r = - . t H / R

t2)

where the eq,,ilibrium constant K = [ B 1 / [ A } = k l / k _ i. i f the A H is positive, i.e., the reaction is endothermic.

E.:cmhf / R T ]

where the su.nerscript '0' denotes zero field and r is an

apportionment ,:onstant. r has a value ranging from 0 to ! depending on the structure ui the transition state [23]. The closer ;he transition state is to the product state the closer the value is to unity. For the differen" types of potentials just mci4iuned, the electric field is p.-~icalarly interesting because it is

56 TABLE + I ,5+o~?lrpdlrl'd Ih('rl~lodtt+tltlttt i~tratH( I(.r~ /or I'?lt'l~'t. Irllll'*dlI< [Itlll

2

I)aircti ,,r,,;~,: rtic,,

S:, mbol,

l-xample,,

[ Jcclrlt mt'~nlt.'nt/t'leL'li',t" h~'ld

.3 .~,f/ J L

C h a r g e / t l c c t r t c field :'~t~.,,,;~.~ ~tenll,ll,/¢oflft'lllralfOl|

Aq / J 1; tu/.1("

l)l~-,,,ure/,plume

ll'/Jl" 37 ,'3.4

m e m b r a n e A T P a ~ s 129,35] c l c d r o r e c e p t i o n 12] neural i m p u l ~ 13q] m e m b r a n e A ' I ' P a ~ . [ ~,6,37] [cAMP]. It'a: " } o~.ci!l:dkm,, [5.7] r c c c p t o r / l i g ~ n d interaction o,,rm~lic sensitive channel,, [55] acoustic transduction I54.56] stretch .~nsitive channels 154.5~} mechanosensitive channels [54.55l thermal t r a n ~ u c t i o n f;botos~.,nt hems

4 5

Surfac e lenMon/artra

6 7 8 9

Mechanical t o r t e / d i s p l a c e m e n t |ical/tempt'raturc Phot.)n/intern~d cAcrgy ('ombinations of Ihc~e parameters

J k~ a L A II.IJT t .V,,hv/..I l',m

Note: ...lq and N . art" the m(n, inl2 chalet;., ~lnJ the .'~vogadro',, number, rc.,pcetr.cly. I:,nt denotes the hlternal energ~ o! the phl)tt)ret:eptor protein. Item., I. 3. J. 7. and 8 art' cxprc,.~,ed m molar quantttic',. 1.¢ .rg', 2. 5. and v ',~.' *7 ...... :d In unit,, per molecule.

a vector quantity. Mechanical force also has some vector characteristics. However, temperature and pressure are not vector quantities. A scalar driving force may also interact with a molecule in an anisotropic mediarn to produce a vectorial reaction. However. distinction between vector and scalar driving forces, and i.sotropic and anisotropic reactants is essential for understanding the ECC and the O A B mechanisms. "1able 1 lists .several pair,, of thermodynamic quantities which can ,nteraet according to the general rules dc,,.q,),~ed and discusmd in this article. O.~illations of any one quantity of a pair will give a molecule in an anisotropic medium the ability to convert energy from one form to another (see below). Examples !L, each type of oscillation are also given. The osciUations of Ca-" and c A M P conecntratitms have drawn much attention in the past scvc,al years [3-71. V. Some characteristics of transmembrane proteins A transmembrane protein has several propertics which characterize a signal or ene gy transducing sy~,tern. First, a transmcmbrane prote,,t i% fixed in orientation with respect to the membrane surface. While an~ular rotation around the normal to the membrane is allowed but it is relatively slow ( # s to ms) compared to the rotation in an aqueous pha~ : (ns). Lateral ,tifiusion is also two orders of magnitude slower than that in water and flip-flop across the lipid bilaycr is not permissible, in othe, words, a transmembrane protein is an anisotropic reactant. Second, the reactivity of a transmembrane protein is different on the two sides of the membrane. For t.xan.ple, Na,K-ATPase of human erythrocyte has two principal coni'ormat.ional states. E~ and E 2. T h e cntion bindir, g sites of E t are inward facing and those ol E 2 .';r.' oatw:,rd facing. The ouabain

binding site is outward facing. The compartmentalizati, m of chemical reactions by a membrane is another manifestation of an anita)tropic reactant. Third. an electric field is greatly amplified m a cell membrane according to the equation. I:.,, .,., = ..l~',.,, .,,.,/'
(91

where the transmembrane electric field strength E,.cmhr is shown +'.) depend on the radius of the cell R,.,., and th,. thi,'kn~,~+ of the lipid bilayer ¢sce e.g.. Rcf. 9). The ratio, l:m,.mh,/E = 1.51¢,,.+jJdh,zj>+ ,, iS the amplification factor. In a big cell. this factor is large, which means thai a transmembrane protein will experience E~mb,, a much stronger electric field than the applied field E which the protein in solution would experience. For example, the En,,.m,, experienced by the Na.K-ATPase of the human erythrtmyte would be I(MMgfold more intense than the applied field, E. This field focusing effect of the plasma membrane confers to a t,t:ll the ability to sense and process weak electric signals. Fourth, the dielectric constant of c~ll membranes is typically 8-10 ;:o..pared to 80 for water [24.25]. The smaller dielectrw constant meatus that coulombic intt:tactions between charges or dipoles are much stronger in a membrane compared to that in an aqueous phase. One should note that in an AC fh;Id, the dielectric ¢onstat.i of a ntembrane dcimnds 0 , the frequency. This would influence the electrostatic interactions. However, its effl.ct on optimal frequency of electric interaction, to be discussed later, is small. And. finally, the plasma membrane of ~ cell is the first site of contact for a cell with its environment. ~'it|t these characteristics, m,:ny laboratories have chosen to study effects of pulsed, or o~illatory electric fields on membrane A'FPase~ [26.31].

57 VI. Activation of membrane ATPases by dynamic electric fields

VI-A. A TP ,~'nt;ie~i,~ ATP synthesis under physiological conditions requires 10-15 kcal t o o l ~ of energy, in the mitochondrion, this energy is supplied by the electron transport supported by the oxidation of food stuff. In chloroplast, the required energy comes from photons emitting from the sun. in both cams the final form of energy before conversion into the y-phosphodiester bond of ATP is thv proton electrochemical potential energy, according to the Mitchell's hypothesis, or the electric potential energy, according to the ECC mechanism. A strong electric fic'd is required to produce this magnitude of energy by either concept. The tr'msmembrahe [x)tcntial, Agm,.m,, of the mitochondrial inner membrane i- approx. 21~ mV in the energized state, which gives an /"=~.m,, of 4(X'HXX) V cm-~ across the lipid bilayer (d,.~,,>,., = 5 nm). Experimentally. exlx~sing submitochondrial particles, l'scherichia colt, or thylacolds to electric pulses of kV per cm and of u s to ms duration resulted in the synthesis of ATP [2~-2~.31]. In most of these ::xi'crimcnts the elec,,ron transport chain of mitochondria was inhibited or the thylacoids were kept in the dark. Therefore, energy sources from the normal channels were depleted, and any de novo ATP synthesis must derive energy from the applied electric field, tk~ever, the level of electric potential required for ATP synthesis depends on the phosphor3'lation potential of :~ ,;ample suspension. Higher phosphorylation ~)tcntial requires higher e!ectric field in-

(3.

40

"

E

A

tensity for ATP synthesis. Experimentally, the two methods for the determination ~f ATP, one by the phosphorescence intensity of the luciferase/lucifcrin system and the other by ihc radioactive labelling of ATP, allow adjustment of the phosphorylation potential. The former retains a relatively high concentration of ATP while new ATP is synthesized and the phosph,)rylation potential is high, thus, mimicking conditions of in vivo ATP synthesis. For the latter, hexokinase may bc used to rapidly convert newly formed ATP into gluco~ 6-pho,;phate (G6P). Radioactive G6P is then extracted and quantified. The phosphorylation potential in this case would be low and ATP synthesis should not reqt, ire much input energy. In the high field experiment, wc have used up to 30 kV c m ~ of short electric pulses (I(X) p,.'; decay time) to trigger ATP synthesis in rat liver submitochondrial particles. The ATP yield in the best of conditions was less than one per enzyme per electric pulse, i.e., the enzyme did not turnover with a single pulse. Evidence of enzyme turnover is crucial for ,lemonstrating conversion of electric energy into the chemical bond energy tff ATP. However, when 5 mM dithiothreitol (D'VI') was present, the ATP yield was gr;:atly increased to 5-8 ATP per enzyme per pulse (30 kV cm ~, 1(8) p.s decay constant). Apparently, certain SH groups of the ATPase were essential fl~r the enzyme tat.over [3~i. this conclusion is supported by the observation that .V-ethylmaleimide, a sulfhydryl-modifying reagent, inhibited the electric field induced ATP synthesis. The electric field induced ATP synthesis was abolished by inhibltors o r the F.Ft-ATPasc, oligomycin.

E

B

3

o

o

E

Q. c

/

20

"10 ¢

/

t° O

E u

o,. i.-. ,<

l 0

10

20 E in k V ! c m

J

30

0

~

J

J

I

0

2

4

b

[O1r]

in mM

Fig. I. ATP ,)nthc,,i, reduced by it.tcn,,e pul~'d electric fidd,, (Pr-'F). (A) Field .~Irength dependence of ATP ,,ynthe.~is in rat hvcr submi;ochondrial particles v, hich v.ere ,..xix),,cd to one PEF with an CXl~'mential decay constant of hO p,, Newly s'ynthesised ATP wa~, assayed by the incorl~'~ration of ~:P,. Beyond 3(I kV em ~. there wa- :~ -:- ...... ;,m in ATP ~;c;d duc to ¢Icctroporation of the ~,ubmil~x'hondrial particles. The maximal ATP ~icld v.as Ic~,~,than one A T P per enz~'mc [..:; i;i:,t ! hc 5ul',mitoehondrial .;,J,.pr'n,~i(m comained :' mM Na(:'N to inhibit the elc,:tmn transl~)rt. Data from Teis~,ic c t a l . [27J. (El) Dependence ~ff AI'P ~icid ot beef heart submitochondrial p a r , k " ~ .m the diihiolh.:i~,! ( D T T ) concentration. [:ach ~mple v~a~exp(~,cd to a 2~ kV cm t PEF ~ith a decay time com, k , l t of IIl~ ps. A T P yield incrca~,~d ~,dh IDTTi. At the maximal level. ATP yield wa.~ 5- II) ATP per enz~jmc per PEF. Data from Chauvin el al. 13.~.65J.

58 N,N'di,=yclohcxylcarl'x~liimide (DCCD), venturicidin and aur,'~"ertin, but was not .sensitive to inhibitors of electron transport. NaCN and rotenone. Membrane tightness was found to be critical for eificient synthesis. lonophores, valinomycin, sodium nitrate and carbonylcyanide p-trifluoromethoxyphenylhydrazonc (FCCP) effectively bkx:ked the synthesis. These observations suggest that the electric field induced ATP synthesis was by mechanisms similar or identical to those for in vivo ATP synthesis [331. Experiments also showed that when the phosphorylation potential was high, there was a threshold field of 10-15 kV c m - J , which would generate a ,~l,~nu:mbr of about 100-150 mV, or a E m c m b r of 200 to 300 ~'1 c m - ~, for the .,,ynthcsis. Fig. IA gives the high field induced ATP synthesis in rat liver submitochondrial particles and Fig. IB gives the effect of D'UI" on the ATP yield of beef heart submitochondrial particles. In the low field experiment, we have used up to 611 V era ~ of alternating electric fields (AC). ATP yield was low, less than I l l ~ ATP per enzyme per cycle of A C [34]. However, because the JouI,: heating was much less ~ , ' r e than that of the hi.:,t" c!._,!~ c:;p~rim:nt electric stimulation could be continued fi)r a long pc. riod of time, e.g., 10 min to I h. and the accumulated ATP yield was more than l(I per c~izyme. It was al~) found that ATP yield was dependent on the frequency of the AC field. An optimal frequency was found around I11 Hz. ATP yield diminished to zero fiw frequencies greater than 10 kHz. Effects of various types of inhibitors on the AC stimulated .,i,athesis wcrc similar to those of the high ficld experiment. Fig. 2A shows the frequency, dependence of the AC stimulated ATP synthesis by ,q 6(I V c m i AC field. In this c~.~c, the ..~l,~/mcmh ~. geaerated would be a mere 11.4 mV (diame~.or of submitochondrial particles 80 nm). Fig. 2B shows the field dependence (~f the ATP synthesis.

VI-R Cation pumpmgs hy Na.K-ATPasc ¢~f human ervth,of')'te Under physiological conditions, the enzyme hydrolyzes an ATP to pump 3 N a ' out of. and 2 K" into the erythng'ytc. The K* influx is believed to be an elcctrogenic transport. At 4°C. when erythrocytes in ig)tonic suspension were exposed to an A C field of 20 V cm '. a net influx of K ÷ or R b ' was dctec:ed at I kHz. and when an 1 kHz A C field was u.~d. the maximal influx was found to be at 2() V c m - t . Thus, the A C stimulated K ÷ and Rb ÷ influx exhibited an optimal frequency and an optimal field strength. According to Eqn. 9, a 20 V c m - i field will generate a maximal A~,,~,,h, of 12 inV. or an E,,~mhr of 24 kV c m - I . Activation of Na+ effiux was also accomplished by using a 20 V c m - J AC field with a frequency at ! MHz. Fig. 3 presents the dependence of Rb + influx and Na"

A

150 0 ¢L

O

z

511

<

0

I

I

I

I

1

2

3

4

LOG (FREQUENCY) (HT)

Z

4OO

l

l

3OO

B

a. w -r pz>.

100

n p0

I

l

25

50

75

APPLIED VOLTAGE (V/cm)

Fig. 2. A T P ~,ynthcst*, o! b e e t heart submitt,chondJi:d particles induced I~. ahcrnating electric ficld~. ( A , F r c q u c n o ' dependence. Net ficltl induced A T P synthesis i,, plotted against the frequerg'y of the A ( ' field ( ~ 1 V cm i ). The A C stimulation wax continued for I0 rain. {B; Dcp,cnd,:ncc (,f A T P yield on field ,,trength. Data from Chauvin

ct al. [3 ~1. cfflux on the frequency and field stre-qth of the stimulating AC [35]. The AC .,,timulatcd c:,'! .i pumping ~as shown to be an active process (i.,.'., pumping up the concentration gradients). Yct thcsc activities were independent of ATP concentration in the range l0 /,tM to i mM [31|.35]. Apparently, ATP hydrolysis was not required for the A C stir~ulated activity and the energy, for this aetiwty was derived from the applied field. These activities were judged to be relevant to the in vivo mcchanb, ms , f f the °,n~,,,,,,, actkm because t h e y w e r e completely inhibited by ouabain, a specific inhibitor of the enzyme. Other inhibitors, such as oligomycin, euabageni;: and vapadate a l ~ inhibited the A C stimulated ;tctivitics. Our data on the Na,K-ATPasc arc more detailed ;:nd complete than data o n other enzymes. Con~quentty, our development of membrane transport models based on the ECC will largely rely on the data presented in Fig. 3.

VI-C A TP hydrolysis actirity of Ecto-ATPase from chicken oriduct Ecto-ATPase from chicken oviduct (molecular weight 80 000) was purified to homogeneity by a mono-

59 T A B L E II Electric actwation of mcmhra~w ,4 TPa~('.~" Enzyme

Activity

Optimal amplitude (pcak-to-p~.ak)

Na,K-ATPa~e (human cq,lhr(x'ytc)

Rh" pumping Na " pumping

20 V cm 20 V cm

~ ~

K ' pumping ('a:" pumping

20 V cm 30 V cm

i 1

A T P hydrolysis

not determined 5 V cm I

201) Hz

A T P hydroly~i~

Ill kllz

[IS,19]

A T P ,,yn~hcsis

not determined

Ill Hz

[34]

Ca-ATPa~ ( h u m a n cryt hn~=ylc) Na,K-ATPa.~ (ral~it kindncy)

Eclo-ATPase (chickcn m'iduct, dclcrgcnl .~duhilizcd I F.F,-ATPa~ (beef heart. • uhmit~cl~mdria )

clonal antibody affinity column and was .~duhilizcd in 0.1t'/c non-ionic detergent NP40
n-

¢)gtim;~l frequent3 ~! I~)

Reference

1.0 k i l z 1.0 M I I z

(29,3l).35] [3.~]

III kH7 Illl) kltz

[2')]

13~l [3h..~?J

with a frequency window at 10 kHz and an amplitude window at 5 V cm ~(peak-to-peak). Fig. 4 summarizes lhc results of these experiments [18.1¢#]. Because the size of the enzyme/detergent micc[le was only 20 nm. the enzyme will cxperic,,ce only a l0 ,u.V potential drop. Thus. the electric stimulation of the ATP hydrol-

6O

A

3O

so

2o 11 IS

3o

.,_.i._,....i... J - , . t . , - J . 3

4

S

$

0

7

1

2

Log (Freq. in Hz) ¢, 3o -y.

7O

4; ¢.) m er m

C

6O

(J

m m

SO

i

40

.~

3o

3

4

S

6

7

8

Log (Freq. in Hz)

D

25

$

n-

cii 0

,

S

i 10

,

i iS

Stlmul.

.

,

.

20 Voltage.

I 2$

.

, 30 V/cm

.

. $

.

$

|

.

10 Slimut.

• ls

.

I

i

20 Voltage,

i 2S

-

J 30

S

V/cm

Fig. 3. Electric field induced cat~n pumping r,y N a , K - A T P a ~ o f human e~thr¢~/les. ( A and B) Frequency dependence of N a ' - c f f l u x and R b ' - i n l l u x with an A C held of 20 V cm t t (pcak-to-I~'ak). Symlxds used: O. sat,lple not stimulated by A C field: ~ . ~ m p l c stimulated hy A C field; O. ~ m p l c ~,limulaled with A C field in the presence o f I).2 m M nuahain: II. sample not .~limulaled with A C field in the prc~:ncc of(I 2 m M ouabain (C and D) Fic:ld slrenglh dependenceof the cation pumping acliviW. For N a ' - e f f l u x the frequency of the A C was 1.0 M l t z and for Rh "-influx it was I kHz. Syml'~)ls u~cd are the .,,am¢ as II~)s¢ in A and B. The Idmix'ralure was 4°C. A C stimulation wa~, continued for I h. Taken from Liu et al. [35]

60

E E

=: _e O E

a~ooi

I

A

I

2eoo t"

2~

2~o L

•

0

!

\

,


I,-

found that ;in AC current c. n either stimulate or inhibit the /~,TP hydroiysls activity of =he cnz3'me depending ~n tl~c dcgrcc of ion activation, i.¢.. the Na " /

(

1

i

1

i

i

4

1

2

3

4

S

6

7

10

.--r

I

I.og [AC Frequency, Hz] i

t

E

-=

I

!

3

a2oo

Log [Freq in HZ]

j-.. I

E

2soo

16

e

I

!

B

-2. ~ • ~ <

n

o

o

E=k

1600

_C 0

5

10

15

20

Electric Field Strength, V cm" |:lit. 4 J:i,.,',,;.+ [;¢]~ ~',!uL,t¢+.i A ' ) i ' rl+',drol.'~',l', ~It'll~il% i l l iA.l~'" Al"Pase o f chicken o+.iduct. The I-clo-A'l'Pa,,c ,~.a', ,,,~lubd~/t.d in I L l ' ; nt,l-ionw detergem Ni)-411. (A) | q c q u e n t 3 delx:nde,k.c. An optimal field ,,trength of 5 V cm i ",~,dSI.l~+td. [);ll.I in open ",qtl;irc~ tire for the control ,,~lmple+, (un,,hmulated) and d,llll ~n lilt' t h .el| cil¢le~, :ire Ior the +,timuL~led ,,~mp]¢,,. r h e t'ttr~'e tlrav.n th~oJgh the Mlmulatud ~l:t!:: I~)ints ~,a,,. a ximulatcd +.:Ul~e u,+ing the o'~.',l',Mi ", ;icli'+';lll,,n b;,rr~er mt,,J:2! ~(,~,~.11~ .~+;.,.~'u,+.,ed in Ihc It.'xt. "l'hc tcml'~.,,llure of the cxr, erimcnt v,~v, 37' (" {l{) l ) e l ~ n d e n c e tin held ,.trcn.clh. An A ( ' field of ~'l k ; l " v,a+, uxcd in the experiment. Svmb<,!,, it',cd .,to the ..amc ;P. lho~,e in ( H ) T h e e u ~ c drav, n ...'r,:~..~, Ihc qtnmh~l~.d dul. Ix,~.", v.a,, ,,imulated b~, the ():X)'I m,~h..I. Taken trom P'.l~irkm ct id.

ysis fall:: in the range of ,~c~lk field ellcots. ;,,,ill, dl: classified as environmental fici,: cfl('cts. This st~dy is a!,+,~ re!,'vant fi~r the dlscu~,sion of d:'" ccltular ,,ignal tran~htction, as ~c shall ,,ec later. Data i,, Fig. t will form the basis for our fl)rmulation of an enzyme modci for the theory of OAB.

F'I-D. ,'IT/" hydrolvsi.~ actirity o]" rahhit ki, ncy Na.K,4 TPase Blank and Stxl h;,~, im,'csligatcd effects of ~cak AC fields (mV per cm}. on the ATP hydrolysis activity ol Na,K-ATPase from rabbit kidn¢~ [36.37]. They have

J

-AL-- 1

~

I

4

20

--"

i

I

30

40

~0

E in Vlcm 300

!

=o0L 0 I 0

|

I

05

[Ca"]

10

,n mM

Fig. 5. Elcclric field ~tlmulawco (.'~-"-efflux ~,i human ery.lhrt~.'y'les if'a"-efflux at 4('). rhc conlrob, (un,,timulal~.d) arc given in lhe ~lo~d cl~¢les and lhc ~limulalcd ~aml'dc~, arc gi~:n in lhc op
K " ratio. Under normal conditions, the cn~.. me in A(" currents showed a decreased ability to split ATP. Convcrsely, at lowered activity, the cn~'me showed ;:n enhanced ability to split A'rP !~6 371. Maximal cffccls of At" were around ;,,()-2(X) ttz [3fi.37]. I/7-E. C a k f l , , pumpiw,, hy the ('a-.4Tl'ase +~f human erythrr;.O't,'s Calcium efflux was ai.',..) fl)und to h¢ stimulated by the A C field. The optim;:l frequency was found to h: Ill0 kHz. optimal field st:ength to be 30 V cm ~. An optimal ligand concentrat:.+n fie :hi~ .+etivil~y w a s also foun~ at [ C a : ' ] = (I.8 raM. The AC stimulated Ca+" pumping activity was approx. 15 p m o l per liter of cell,, per h. These results ;are .,,hown in Fig. 5 [38]. The window fi~r the ligand ct)ncenlration is partic+,larly interesting because the existence of much a window was first predicted by an EL'(, n a v e l (scc below) [16]. Table II summarizes data obtained with several ATPases.

VII. Eledrocunformational coupling in medium and high level electric fields

chtonized conl+ormatit+0;al o,,e+lhiti(,n at abe macroscopic level 18.q]. ()l+viously. if the frequency of an A(" field dge~, not |;;,it...-h with the relaxation prt~.'css of the molecuics, there will b,,." ilit.+'ic~ate m.decular micra+Liens leading to complex chemical kinetics flea :he reactions. "ThcsL" effects on r-.tes arc omside the ~cop¢ of this article. Whal is important is Io recognize the clcctr(vconformati(mal chan~e and the enft)recd c o n t o f mational oscillali,)n by a periodic field. One shoubt point out that in a ccll. the o~illation ta! an enzyme is by no means synchronize,,+. Htwvever, m)mc degree of synchronizatiL)n is crucial to generate chemical wave. e.g.+ the propagation of Ca -'+ and c A M P concentraiium, in cells [3-71. Synchronization is not a necessary, condition fi)r signal transductvm. Each molccule may respond k, a locally oscillatia[; eleclric lm~',ential and funeti,m independent of other molccule~,, as in the punlpnlg ol cations by Na.K-A'fl)asc or A i i: sylatlac.,,ix by F.FrATPa.-,e. in vivo. Nonethelcss, each molecule is enfl)rced by the local transmembranc electric fields to oscillate. SynGtronlzed :lectr(~:onb~rmational changes t)cc..r an s u c h C V C I I t S ~-JS t~C gencrallo~ ,)f the evoked potential or the firing of a neural intpulsc 13+]. FTI-II. l;m'r~' ~+m' +lurmq a t on[ormali+ma/ owdlalion

I'71-A. I:+nh~rce, i uml synchnmized ux('illatums Any Michaelis-Mcnle.n type of enzyme will turnover aflcr converting a substratc to a product. Enz3'mc turnover means enzyme re¢3,cling. Micro+opically. each enzyme molecule oscil+ates f,+llowing its cataly:ic c~cle W+t~ t; frcqucn-~., ' t'~t":.ling Ihe turnover numbc . When an ensemble of enzyme molecuh:s is consider¢,3, icy, molecules will I~, in phase. Because of the lack of synchronization, no macro~opic oscillation,, will be discernible. Instead, the slam of catalysis by the whole ensemble of molccules will be measured and exl, ressed am the rate. Howevea. if a chcmical ,,peci¢.s ha.-, two confl)rmational states ia equilibrium (F4n. I). and if the two stales have different molar electric moments, then the equilibrium ol +Eqn. I can be +;hif,c,+ :-"~'nrding to Eqn. 4. This b, true only if a molecet," ;, oriented and fixed in an anisotropic medium Whet+ ::n oscilhning electric Eel,! (,+,.,~...... ? y,xt ) of the itnm ~)f E(In. It| i~, applied. II,e moh:cule will oscillate between the ;wo confl)rmati(+,ml state.,, A and B. If thc cm, emble nf molecules is oriented and their motions restricted in an anisotropic medium, thc field will cnfl)rcc these molecules to oscillate simultancously. E = E~< sint2~'/A( I )

The oscillation ot Eqn. I i.jw)lv,_'s the absorption and the release of energy in each cycle. Theoreticaliy. flw a membrane protein with a high affir;',~,' for a substrate, the maximal amount of encrg3, that can be translerred from an applied field to the pr,.;t-in is A M . E ...... Ior ...~ch nc-ind (,me half c~,,.Ic) which is then returned Io the field or rcl,:~.,,cd to the :,k'dlum at Ihc pninl where I:,,~,,,,, : 0 [~}. Conversu;y. for : [ a r g e amplitude At" field, thc maximal energy :ransduccd pet cycle is determined by the affinity o; the tran,~~ , r t c r fl)r the ligand [1~;.16.40]. To utili.'e thi,, cnerg,.. [-~qn. I must he coupled h) an energy, reccptiv¢ rea:'tk)n, e.g.. pumping a substrate, either neutral or charged, up its c<)n¢cntration gradienL c!r s!'nthcsi~, of .~-rP from AL)P and P, [~.14]. A simplc prot,,:in pump repaesentcd by the fi)ur sl;,,e kinetic ,¢chcme. [-~qn. t I. will Ix: u~,cd fl,r ana;ysis.

All

kH

l:,

k ,

(Ilk

+II))

At first, most molecules arc out of phase. But because of the dependence t>f rate on the e.h:utric ficld (Eqns. 7 and 8). soon they will be all in phase and synchronized. This pheaomenon is knowr as thc enforced and syn-

,,

|

Ps,, 4

In Eqn, I | , an integral membrane ~ranN~rtcr P is considered. Pt,.f, P,,=m, SJ~.~t and S,.,~,, ;ire the tran,x-

62 ra,,tu.t .vilh its subs[rate b i n d i n g site facing th¢ Iefl C(:,'l";f~arlmCnl. facing It',. right Loff;,parlmcRI. stlb, tral¢ in the left c o m p a r t m e n t , and in the right (.-t)ml)artmcnt. rcspeclivel.v. F,~r the e';planali~m of (.'~mcepl ~mly. v.c x+ill cho~,sc it c o n d i t i o n [S,,.~,] - [S,,,.,,,] - I ,~:'d,.= v.mch the on and (~fl raft". : q lh,." ',,uh'qral,' ;ire equal It) flit' rail: C,~llP,,tai1t',, gi~,en ill the ~chem¢ w i t h o u t lhe nccd l,=r includ~tlg [S,,.,.] and [S,,,.,,J iu rate equalioi~n, l [ q u i l i h rium t',mslanls are d e f i n e d to be K,, -, k,,/l:,, ~ [ i j / [ I} ( i , , r j :: I. 2, 3 or 4).

'°I-; I! I~

- , 0

"?[

/

Pl '- "

i g_ ~-

I

,-,J 081

P2

"-r - ' - - - j

' "

0

0.~

_

0.111

Ii1: 7 Numer=t',d denl=~llstrall, lns *d Ih¢ enlorcu'd conh~rmalional os~.'lllaIl*~ns id ,2to/.xmu" sl)L'~.'l¢, ('.Nil ] I ) has+,'d llll I]1¢ theory of clt'+:;r(g.'Imlt~1"malioi.al cl~llpling. ~A) The Stilll? (g.'cup2.~.;~ ,re ~ormal-

i,":d ,.om:,.'~ h~llon ,~: ; i ( .......... ). p: ( . . . . . . . ). IPS)~ ( . . . . . . I. and (PSI+ (' '-) ;tr*.' .~,,;.~l~ h, ,,,~llld¢ V,llh the applied At" .';old I~'ufxc in ll). (B) Inleglaled Iran,,illon*, of P, to :. ( - -) .md~l)~.~ ,,,(p~=I . . . . . . k lak~'n Irom ~,¢~tcrhoffct al. I41l.

~al-t1. (~I the field induced fluxes of suhstral¢ was not

zero. This implies thai l'qn. II would not he symmetric. Several fach)rs characterizing it simple fo,~r state transporl ,,ystem of Eqn. I I to transduce energy of an (~s¢illating field ha~,c bccn examine,l [15.!6.4!1-42]. An ob~.ious and crucial factor b, lha! art applied field must retain a ccrtairl dc~ree of a u t o n o m o u s character;sues. i i l a t is. the v.avcl~)rm of the applied field should m~( t~e altered by the interaction with the tlansp,;rtcr or substr;.tl¢ ['+31. Anoth1.'r crucia: attribute is th;,t the bhtdln+. 1.+.111.+.ilhls i)I the; ti,,Ii",lJtlltUl I+.,I ~'Jl++jl ,uid ~r,+hl are diH..:rcnt 1t).14.21'.I I.~21. g , = = K.,~

I IR IL J-',rsl 111llnCllg I d~.'tlltHl,+Ir iIIOI~ iii l ht+" pli1111': ,i~.I.'+ii), ,~I t i|11. I I ILI+,~+',' ~'!I th+: lh~.'~l~ ol lh" .'ll:l.'I[O-.on orln,iIlonilJ ~.'oupJln¢. "|~ikl..ll 11 ,,11 1,,,tllg ;I111 t.,quml.lll It+:']

04O5 TIME

,I

ily assign~.d ,, value of l)..~. Pumpin,. ~+. ;, ncutrai ~iubslral~: g a s used Io demonsllal1." lhal ¢lire¢l inleraclion of an cl,:ctric field v, ilh "~ suhslr;~l¢ v, o u l d sol bc r e q u i r e d for lhc spc,.:ial effects of lhc I-.('(' modal. A l t c r numerous uuy.u~.'t.'es'~fl;l illlCrltpls, a,'¢,.!n'+Ul;lliOrl o! a suhnlratc in a hypoth¢liu'al c¢11 was d c n l o n s t r a t c d in Fig. E [I.11 This w;~,. ,,,., :rl, .';;m~ d,. ~ ~l,r , * , . I v ,d"

fwld. elralil: fhlx~..,, t)l sub,,irah" v+elt? obscrxed hul 11o net accumt,l'tli,ms v,.cre d1.'t¢cu'd [ ! .-1] T h e n¢l cIock~vln¢ or c,~untercloekwis¢ r e v o l u i i t m ot lhe catalytic ,~heel of Eqn. I I all,)~cd the Iranst'r~rter to utilize: the electric ~:nergy Io i,u.ld up it chemical potential. ~t cono:r, tration gradient ia tile p t " . c n l c,tse. This enforced .-onlorii+l;.itit":': f ~,,:-,u.,ti~r, ~,.~,, ~h¢ b;,,ds ~)I ~he ~.'ncrg_v coupling, l-q.,.. 7A gives im cx"mpi1." ~,i large a m p l i t u d e oscillali~n,, ~I lh~.' enzyme: c o n l o r m ; i lion;, Stilt¢s itlld l.ig. 71] show:, illt~,.'griltcd numbers ,)i th1.' it,,, It) P,,+,,, and the l)3,,+h, to I'S,.., trar~sitio,ls [ a l i . 1111.' tii.i¢ a'.,.:r:~t,, + li,,hl ,,Ir,.nt,lh l)l a b l p t d a r t)s(:illaling el¢~:lrt~: l i c l d x~as ,,crt). l l o w c ' . c r , th1.' lira1.' a~,c,agc

'

g

A set of four r:ltc equalions Ior Eqn. I I was an;ilyzcd by the matrix computation method and hi- direct numerical in'cgrati, ms [14.35]. Kinelic behavior ol Eqn. II when exlx)sed t,~ an oscillating electric field hits been investigated. As information on the transili(m st:'.tc was not available, r of Eqns. 7 and ~ v, as a t b i ' r a r -

the l'('(" mechanism. W h e n th,' choi='¢ of kinetic paras+clefs d l d ~It'! match the ir+:quen~.)' of II1¢ a p p l i e d

I

(12)

~g'ucn these tcquircnlerd', are met. tht: L.ffi¢ien~'~,.. of cnclg~, Iransdu¢lion. "r/n,.,,. depend,, on E,.,~,,b,..t/I.l. In K,I. m d In ,,,':~ [15.16.44]. If E,,,.n,h, is a square v, av¢ of very large umplilude, and both (k ~: + k i l l wild (~.= +/~l~) ate much bigger than i.he frequ,'ncy of thc .&C. fat. then the amplitude o q" the c~:nfc, rmatlonal oscillation v, ill he large (Fig. 7) 1 hc e m o r e e d oscillalien nf :m ~n:.cl~tl,;~ o~ cnz,,me n, fi,.,:u~cs ,.,,..:!J h~ an

h3 imp~irtant aspect of the sign il tran.,;ductinn in cells (as in the ease of slime mold).

iw //

In(K.~ + 1) ,.f. ..........

VII-(; Ma.rmlal efJTcil'm'yfor em'O,'Ycoupling

In k~/

When the intensity of a per!ndic field i,~ hlrge, eimformational oscillations will achieve :heir maximally allowed limits. Use of a square wave electric field ,,,,ill maximize the field effect. Combining these cnnditions, the energy coupling for a reaction will reach the maximal efficiency if the inequalities Eqns. 13 and 14 are al.~) sat isfied [ 15-17.411.44]. k~,

- " [a("

(13t

[,.,. :l k , . m

In(I + K~) .

.

.

.

.

.

.

,.. pS t

/

/

If

(I-11

v, hcic I,,,,,,i ,,,d ~,hvm dui,ote rates of the e(mft,rmational changes and chemical reaction, respectively. For Eqn. II. k,,,n , is oI the same order of ( k t c + k ~ ) or t k , + ~.~D and k,,.:m is of the same order of(k:~ + k32) c,r ,~k41 + kl,). Note that [S,,,,,I and [Sk.. ] are assumed It, be uqity (for mor,: general cases see Refs. 15-16 and 44). The inequality Eqn. 13 ensures that the conh)rmational coupling is , e a r equ,librium at all time and fu!ly reversible. r h c inequality Eqn. 14 maximizes the energy transfer from the field (o ~he chemical reaction, in this case. :he ',igand ;,s,~ociation/dissociation reaction. The energy absorbed from the electric field is utilized to it,,, utmost level and the efficiency of energy eouplin~ is d o s e to the theoretical maximum of IIX)%. Fig. 8A pre~'nts maximal work done by the system per t.'y,-te and Fig. XB prc.,,ent's the accumulated work

I40,441. For an asymmetric tran:,porter, defined by Eqn. 15, the highest level of a chemical gradient thai can be sustained by the ECC model, o'.:lled the static head. is K~.~. or the square of the affinity ,m Ihe left hand side, if K , , ..-K.., [16.44]. In tiffs case. lb,: suh,;tratc is transported from the left compartment to ~he right compartment of th," membrane. If K,~ >> K~:. pumping wouid be in the rc 'cr,,cd direction, i.e., pu:nFinl, trom the right Io the left. and accordingly the ..,ratio head v,uuld [,c K~,. ~'14 =" ~ ,.'; f I! - "~2;

and Kl: = K,~ =

/ "--,r/

K:t

= h,~

At other iweresting prnpeHy of the sy..,tcm is tidal en.-r.t¢ transfer may be oblained both ways [16.44]. Whe,, ihe ~;radient exeeeds t;,c static head. energy of the gradient ~:an bc t:,,nverted to an electric field.

/ _. ~s.

, In Ka4

._ j \

%:, ! ~-.--.~--

4

¥

Fi.. X l..ncrg~, tra.~,duction by the electr(~.'onfo, maliona; coupling with a larqe amplitude A(" field. ]'he inequalities Eqns. 13 and 14 arc ~:ttiMe.:d. (A~ Wh.m the m e m b r a n e potential is allnwcd to (~eilhoe the ,,y..tem o*" Eqn. I I will perform u.~rk (pumping J ~,ul'~',trate up its concentration grz.:!i:'qt). The amount nf work pcrh)rmed by the sy~,tem =.,, cxpre~,s,:d in certain equilibrium constanls n f Ihe ,',ystem, (ID Accumulated work done by m e r,,y~'-,lemin reH'x)nr,,e Io coqlinuou~,, pcri*~tic pcrlurbalions. Taken from Markin ¢t al. 115..~:1].

Al;.hou~.h, dli.~ ha.', bccn shown to be therrnooynamitally plausible, mechanistic details for perferming such a task have not yet been worked out. Experimental!:,, activation of Na.K-A'IPasc has been shown to generate local electric fields.

i,, lld. ) . Windo,cs ]or ('k',tr()conl}mnJti~ ~t,~f , o,/,lim,, Another fa~,~inaling property ,~! the fclor sla~e ECC mt~.lcl (Eqn. I11 is the presence of windows for the frequency of the AC field and the concentration of the ligand [16.44J. l'h:'~': v,ind,.;w:~ define par,,mc[cl s for an ~(ficient caergy coup'ing under a particular set of experhnentai conditions. The relationships l'~r these wind(~ws ,:xpresscd m ra~e constanls, equilibrium conslants and applied field s:rength have been derived. In a wide rang,: of ,uhstraee coneentralion,~, the frequency windows are broad. The heil~ht of the flux on the iow frequency end :~ccur.~ :'.t. fl,,,, = k1~/4; and the height on the hi~,h frequency end (x:curs at. fh,g,=0.14 (k~..k,i)'~ exlAEr,,.mh,/ 2RTJ (Table IV). Like~.; .... the concentration window i,, ;~ comp!ex func',itm o! the field strength and frequency Fig. 9A gives a H,r,:c

64 J / k,,

region in the c e n c c n t r a t i o h / f r c q u e n c y plane, the higher the field induced f l u x ) [ 1 6 ] . T h e E ( C m o d e l o f l~qii II hi,., been u,,;cd to sin:ulate e x p e r i m e n t a l data ol the cation transport fl;, N a . K - A T P a s e [ I h l and CaA T P a : c [38] of h u m a n en,.'thn~rytes. Hov,'ever. in these simuh~tinn-, charges of ligands were al~o i n c l u d e d in the f o r m u l a t i o n (see bclov,).

i'II-E. Rectt[ication o[" ,,'tmrged liga,l,l.~ and otlwr tranx-2

I~

- I

I H)I

(:dli¢+ k141)

'

.~.~.~let H h

A

!.

j,

Z

t

-t

-Z

.

-t

-0.s

0".

o++~

t

t:~,

z.

z 5

l'~(l~/k,O

II F'm q. Windows for the CfII:¢IIV¢'Iran,~lu¢lion Ot en..'rg~, b:. l.qn. I I acet,rding Io the I I l ¢ o r y ol the ¢leClr(~ollhlllllalllln,li couphng. IAI I)imen',ionle~ flu~ of ~.ubsll'al¢ P, phoned vcr,,u,~subMriHc conccntratitm and .~rcquent'i tit the A(" flckl. (B) Th,.- pump :tcttxil~, in dilh'rent tcgion,, i,, cxpr¢,,,cd in diflcrcnt dcgtccs of e,,.y'.had¢', h, mimic the tran,,oarcmT ol v.indov.,,. Taken from Matkin and l'~mg '~e,I

dimcn.,,ioflal ph)t o f the electric =icid induc.:d tran.~l-a,i llt~x as function.~ of the A C ficqt, cncy :rod the c o n c c n :talk n o f the ,,ub~tralc, and ll,. 9P, p . , ' , , ' n t - !he :+; ,no data in dfi'fc.,c.n! -!,_'grccs o f , h a d i n g tt~ mimic the : ansparent3' t)f a w i n d o w Ilhc p;ore Iran*,parc,.lt Ih.:

Until now o u r dis~:ussion has b e e n limited to t h e t r a n s p o r t o f a n e u t r a l ligand by t h e E C C mechanism. If a ligand i+ c h a r g e d , t h e electric field wil! also act directly o n t h e ligand ;.,r..d the efficiency o f the e n e r g y c o u p l i n g may be q u i t e d i f f e r e n t . T h e i n t r o d u c t i o n o f charge,, m l o a ligand would makt, )he system m u c h m o r e comT,!!:::: : _! ' .... '."c "~! :h,. :.;gn oi" c h a r g e s , v, hich m a y cancel or a d d to the c h a r g e s ol the t r a n s p o r t e r protein. For the analysis ba~,cd on t h e E C C m e c h a nisms, all c o m b i n a t i o n s o f t r a n s l ~ r t e r / l i g a n d pairs may bc classified into o n e ot the six c a t e g o r i e s w i t h o u t e x c e p t i o n [441. Syslem I): "l'r;In~+~r~,'r w i t h o u t gating c h a r g e s and hcutrai iigand, i.e....'p = 0. ~,, ~ 0. System I; T r a n s l m r l e r with gali~=g charges ,rod neut r d lig;md, e.g.. : t ' ~ ;, z~ = O. ,~ystem 2: I r a : ~ p ~ , , ; ' r w a h n u t gating charges and charged ligand, e.g.. ,.-p = O, . s = I. S,'stem 3: T r a n s p o r t e r wilt= gating c h a r g e s but neutralized by hgand, e . g . r e = - I. :~, = I. System 4: T r a n s l ~ r t e t a n d c o m p l e x having gating cLargcs o f tile o p p o s i t e signs, e.g.. :o, = - I . -:s = 2. : v,; - 1. S,,~,tem :~: I'ran,~porter ;mu ct~mplex having g a t n g charges o f thc '~ame sigq, e.g.. = ,, - ~ - 1, :t,~, - 2. System 0 is electrically inert -m..l an electric field can not have any effect on its function. Sy,,tem ! has be "n

'I AI+I.I III I,~'ltlhrllHt'

Irtlll+lN~ll

+~. ~l¢*ltl', I l l '1",4 I l h l ! l t l L + t ll't I ' l l

,~ J,,xmlal ¢lliclcnc2,. 1'; )

,~,|illll a'lll.'t+l

-: •

1)

II

!I

t|

II

]

()

I

I

IlPll

.~c~

IX'("

2

i

it

I

~

no

| ,"'("

I

I

II

N 7

lh~

|:.( t.', l;:C

2 I

• I ;

~

511

nll

[ i~.'!.

"

11141

~,¢s

t'('(

++

-" I",

Rt.",~.'r',l.'d Irall..du,.tlt01t 1%t.',, n i l )

,~,',h.'m

4

"I'

ti+'l~l I I d . l l + /

..... (I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Note. ('ondm.n~ /, :,..... t~t ", ,~.,,,., , ~d I..t:t" ampl.udc A(" Itcld ;.

nt'l L!hl[t.l.'~ On '~ll|l~ll~lll"

:I+ F'il|Ink* L'lhlll~l."~ Ot l|ll.' If.ll1~p, l r t { r . '1'~ ~,llln~.' ~;h,ll~l.'~ '~l I h c slll~*,lr;lll.' I o a d c . ! Ir;in~,rn~rtL'r. RL'Vt'I~L" |Ir,ln~dllCilllll L'Oil~¢[~lOI10l l:n~'Ig) t~| ;l ~rilt;l¢lli 0 t'l¢clrl¢ | { ( ' ( ' t..lll-lg) lldll~,dUClllWl b~. ~:h'Lllt~'t~nlolnlilllOtlal .ou+~ n~ r*.'i'l crl~.l~d~, l l d n ~ d l l , : l i , ~ b~ t:leL.'Ifll: r¢~:lilic,tllon ,~I !t'l'~

field

"e,.'t

65 discussed at great length. A systematic ,audy has bccn done to compare the properties of systems I to 5 i44]. Some main difference,: arc s-mmarized. First, Systems I and 5 arc similar a , d theoretically the most efficient mechanisms for transdociag cncrD', the maximal cfficioncy being 10@5,;. Reverse transduction of energy from a concentra:ior: gradient to electric energy is also permissible. The transduction ot energy is purely by the ECC mechanism. Second. sy ;tern 4 can reach 50C~efficiency and ~hc tr=,'::;d::c;J,,n i~ .~,i~iy by h",,. icctification of ions. Reverse energy tr;msduction is not permissible. Systems 2 and 3 have very low efficiency, a mere 8.7% at the highest, and reverse transduction is not allowed. Both the rectification and the ECC mechanism contribute to the e n e r ~ transduction in these two cases. T h e ~ behaviors of the six transport categories are summarized in Table Iil [44]. Interestingly, except for system 0 which is electrically silent, all other systems exhibit frequency windows for optimal energy transduction. The positions of windows are dif:'erent for these systems. The static head, maximal flux and other properties are also different. Table IV compares some prominent features of the live electrically active membrane transport systems in an oscillating electric field [44].

VI.F. Fluctuating membrane polenlml and clec!ric sfgnal The anisotropic interactions leading to the transfer of energy from one chemical species to another and the conversion of encr,~ f ' o m one form to another are theoretically interestins but are they biologically relevant. The main concern is that the ECC mechanism demonstrate~ that only an oscillating field can facil;tate

the ;arnover of an enzyme or transporter, whereas, in cells a transmcmbranc eleclric potential is believed t,,

be stationary, i.e., non-oscillatory. The spatial and time ave= tgc transmcmbraac potential of a cell may have a constant value, hut at higher spatial and time resolutions, local electric fields of a mcmbran,: are more likely o~illatory [9.10,43.45]. The amplitudes of these oscillations can a l ~ be large. Even at the whole cell level, slow coordinated oscillations of electric potentials, conccntratior,:~ of calcium and cAMP, and supramolecular structures have been reported and new c a ~ s are continuously being found [.3-7]. For the ECC mechanism to work, oscillations of electric fields at the local level are essential [9.14]. On a membrane surface, transport of electrons, ions and charged molecules, and modifications of proteins and Iipids with charges, such as phosphorv, lation and dephosphorylation and conformational changes leading to changes in the pK~ of titratable groups, opening/closing of membranc channels. etc. can all lead to modulation,; of local cl,:ct-ic potentials. Fo subanit of F . F : - A T P a ~ has %:en suggested to function as a potenliidl vnodulator for the ECC synthesL.: of A T P [9,14]. These considerations lead to another crucial qu,:slion. Are regularly oscillating potentials required for the ECC mechanism to work.'? Local electric potenti,Js of a cell membrane arc unlikely to be regularly oscillatory because of me h e a w traffic of electrons and ions from different sources of biochemical reactions. Astumian et a!. have addressed this question using computer analyses of Eqn. II [43]. E l c c t . c field: with lifetimes, or amplitude, or b o t h flu, tuating ar(,.nd certain values were applied to Eqn. I I. A'~m,m, , or Era.,.,, and !if,2.fir..:s '.:~:.: 3i'~c- ihc I,,rm of a ,,tandard

T A B L E Iv

ComPurL.,;r. :~f fit e m e m b r a n e tea~,3Ix~r~ .~) ~lc,n~ m o~cWatu~g e h c t r w field/44.4h/ v i,,i-.;'r'.:"

~:a~:lor

~ys~cln 2

:,y~,lcm .s

I !,,~ Window (right b o u n d a r y )

J / ( 0 . 2 5 k 14)

l

~ K41

4 K~l

1

!

f h, /(0.25 k ~ ~

I

oK ,

~ K Jt

II

I

Windov, (left boundary)

lh,~hl[ ',~ i4.~((:i.,k:~) I ' ]

I

ll.'~5 K~':'

0.35 K l . i :

I

0.71

R~ctific~,!i:~a ~~J,~, R c c t i f i c a t . m practical r [:lllclenc~ Efflcicnc~

.~yMcm l

~I (, (max) qc~,: (max)

liKff.; IiXF;

[(I. I ] 0.3 ~, ',;.'.'~ ;. IY ;

lit.I J 0.33 ~.7~,; 0"~

.%~,~[cm 4

I ~ll' ~ O:;

.'~ystcm

It I(~)G lifO' ;

Notes: I. Conditions: k~.h~.n, < fA(" "=: /(~.n: and large ampl;tu,:le AC" fieh! 2. I-or rows I to 3. all qaantiti:s o f the five ffa v,porl s)slca~s, d~fi.~cd in lal~iu ; i l ::re h, bc muhip~icd by Ihc t ,c,o~., ~,, 7. !':..::'.:..::.1 2. 3 The ,'wo equilibrium ~.ou~anis acr defined: t:.= - k la "k~t ~ K~I I. This convention is *:;~.hi;x d d l c r c n t from l h ) l usc~ ;;; |(¢b,: ~ a . o .s. ~l.(~ (max) mean~, [he Ih,:orcticaiiy alk)wcd 0"naximal ¢|l-icien(T of ¢qc."gy ~t'Jnsfer from ¢lcclric field to gradicnl % . ~,nl,.,,O mcan~, th~ maximal efficiency ol reverse enerL, y trans/,er f r o m gradien! to electric fiel(J. 5. ,', = e~P[zel:d%crnh , / ( 2 Ri-)]. v, here F is I:ne Faraday constan[ m d ~m,.,,,h, is tl',e Iransmcmbrane I~)lcalial. Fo; '.lcfi,.tions ~,f other

s)mbols scc Rely. 44 a n d le.

66 A

/, . =/,*'~ cxpl

1

I .2

-

:~,'.l:.~m,.,/4RT]

(17)

The channel cnz3,m¢ has been .,hown t:J produce an • t t I¢"fl optimum for thc amplitude of the applied f,~.,u t-,,,. However, a detailed investigation of properties of the channel enzyme remains to be done. One should also point out thai a similar model, the access channel model, has been investigated in great detail, with respect to effects of long lasting potential changes on the act,vity, the ion 3n'2I- ~hFtrate. hindings, and i o n / i o n exchange properties ot A l ' ? a s e s [48-53]. VI-H. P~ezoconformational coupling

J I Fig. IlL Model ~'f a channel-enzyme. (A) T h e c h a n n e l - e n ~ m e o p e n s Ior ~,ubMri~l¢ one '~idt at a lime. (B) [:nergy profil¢.,~ for ion Iran~,l~rt. T a k e n Irom M a r k m t:t al. 117].

error function. In all three cases, net pumping of subs(rat( was o;rscrved after :~ ,~hort latent period. This was a great surprise to us because one should not be able to harvest energy from ¢lcctlic noises. It .,,uon became clear to us that energy could only be harvested from autonomously fluctuating electric signals not from equilibrium electric noises [43]. In other words, these electric signals were sustained by energy of the metal'olic reactions. When the autonomous nature of fluctcati~,g electric field was removed, no energy could b~: h,,vc.,,'~:¢ 'o d : i w a I~h'lt:culdl pump. Mtu~h. Cad,) simulation co~dirmcd these results [43].

VI-G Electroconformathmal coupling it: a channel en2ylq['

The ECC mechanism developed .',t~ far could not explain the amplitude optimum observed in th~ experiments (scc Pigs. 3,4 and 5~ This deficiency can be :c~.olved if wc considcr t h e ~ ATP.,..,c.-, ;o have ~ome characteristics of a membrane channcl [46,47]. Fig. 10 illustrates mar, features of a channel-entyt,e. The enzyme or ~ra'l;oortcr is depicted as a h:.,If-ch;innel which can open ,'lther on the lef! side or :he right side of the membrane bat ,lot on both sides at ,me time. In thi:; system, the con'~rmational change of the enz'~Tne and the m ~ c m e n t (,f lig-.nd are Ixlth sensitive to electric : ,_,!,.', ,i.~i. Site equilibrium and late constant.,, for the :onf ~rmational changes depend o n Emcmh, as arc give~3 in Eqn.',. 6,7 an3 o,. The ralcs of the llt~a,'~d association and d/s:;t,ciation reacl'.'on depend till Emcmt., as

k, = / ~ '.Apl : s ' .E,, ,.~,,/4RT]

(16)

As mentioned earlier, any periodic potcntial which can induce catalytically relevant conformational changes of an enzyme, a transporter, a channel, or a receptor should be able to perform energy and signal transduction [8,9]. To demonstrate that this is the case, we ha~,.- examined how a pressure sensitive membrane tr:wspultcr may resr~nd to a periodic pressure perturbation or an acoustic signal to pump an ion, thus, converting acoustic energy into an electric potential energy [17,4;']. Piezoelectric transduction of energy in hair cells of the CUdl|Ca for hearing is an example [54-56]. in the analysis, Eqn. 11 was ;:sed, although the i.tcraction enelgy in Eqns. 6, 7 and 8~ A M . E was substituted with PAV (P being pressure and AV being ct:~nge in the molar volume of the transporter) or "),AA (3' being surface tension and ,IA be;ng change in the area occupied by the transporter m the membrane). The former is called PV-coupling and the latter "/Acoupling• The t l a . s p o r t e r is assumed m have a gating charge ol zee,. It was found that the PCC mode! behavcd very similarly to systems I and 5 of the ECC model. T;teJ(: were windows for the frequency, of the oscillating pressure and the concentration (,f the ligand. However. ~ , u c differences were also found. The most unusual property is that thi~ ~::mp can distinguish the two :ompon,'nts (concentration grad(era and electric potential) of the electrochemical potcntiai of the transported ior~. The latter component can serve as a ocrmlss,vc switch to open or close the pump when the ~-,,~:enl::t '~'achcs the threshold value [17]. The PCC model wa,~ used to inte~orc, active ion pumping and em:ssion ot sounds in the r0c,:hapoelectric transduction of hair cells. Simple estimates suggested that PV-ompling may not be practical in cells because dV required for energy coupling would be too large, approx. 40 nm 3, three ot'det's of magnitude greater than the volume change of a typLeal pressure ~cnsitive membrane cha'mei. However, 7A-coug,'.i;..g ".'.,.~J bc a plal;~ibl¢ mcchawsm (_t A of aoprox. 3 nm 2). With a yA-coupling membrane pump. building up a 100 -nV AOn~mb, would take roughly 10 ms if there were 100(J pumps in a ce~l. if

~7 there were I'J0 0(XIpumps, it would take only 0.1 ms to build up the same potential. A concept similar to the PCC model has previously been explored by Post fi~r Na,K-ATPase [57] VIH. Transeuction of low level ¢ l e c t H c signals The weak field induced A'IP synthesis of FoF tATPase under a low phosphorylation potential (Fig. 2) and ATP hydrolysis of Ecto-AYPase (Fig. 4) and of Na,K-ATPa,e from rabbit kidne:/(Table !!)can not be explained by the ECC mechanism because the applied AC fields were weak and the sizes o! the submitochondrial particles and micelles were also small. Thus, the aO,,,,=~ produced by these fields would be too small to give sufficien: interaction energies, ,aM. E,~=,, for the stimulation of the t;nzyme activity (see Eqn. 6). Em,:=b, generated by these AC fields were only up to 800 V cm-J in the submitochondrial particles and a mere 5 V e r a t ,n the micclle. Experimentally, electric fields weaker than these fields have been siaown to stimulate or inhibit enzyme activity, DNA, RNA and protein i'iosyntheses and induce many other cellular responses [12,36-38,58-60]. Apparently, the ion activation phenomenon observed for the AC stimulation of the Na,K-ATi:ase of rabbit kidney is also not a feature of the ECC mechanisms [36]. Blank has p~oposed the surface compartmental model (YCM) which considers the current produced in the vicinity of the cell mere brane as the origin of the field effect [61]. Sir,,vle relationships have been derived to interpret their data on the AC stimulation and inhibition :~f thc ATP hydrolysis activity of Na,K ATPa~e The ~C'M model can also prot4uce frequency optima of Serpcrsu and T ~ n g [29,30] and Liu etal. [35]. Another mechansism, the oscillai,,ry act.;vat!on barrier model (nAB), has been considered by Markin et al. [1847]. For a molecule to recognize a weak r~e"icldic signal, the signal must be able to invoke a resonance response of the molecule. For macromolecules, such as DNA or ~,ruteh., there a,'e many modes of motion within their structures: vibration, stretching and rotation of chemical bonds, local and delocalized covtormational dynamic,, ~'hese confnrmational dynamics most likely i n "ions of charges and electric dipoles, a.,,, hobic residues E~zyme snbstrate inter: vitably be influenced by these modes of inte~ .. mot,on. Conscqt.,t-r:tl;,. rates of reactions within the catalytic cycle of at, enzyme will be affected by these conformationai dynamics Macroscopically, ttais means that activation barriers of these reactions fluctuate with the fluctuation of the conformation of an enzyme. This concept was extended to formulate the n A B mechanism for the r~.sonance transductien of weak electric signal by the Ecto-ATPase [18,19].

The basic postulate of the n A B mechanism is that the activation barrier of the rate-limiting step of an enzyme is oscillatory,, in pri,cloal, many activation barriers in the catalytic cycle are likely oscillatory, but tb': -verall rate will be mainly determined by the rate nf the rate-limiting step. A Michaelis-Menten enzyme mechanism is then represented oy a two step chemical reaction. ,~. /t I •

t, I

~i21

I12

Substrate+ ~') ~(~) g/Q) + Pr~luct

(18)

k ,2 and k:t are rate constants for the rate-limiting step and r a and rt, are rates of the sum of all of the fast reactions. When [S]:*,K m (Michaelis-Meoten constant), the overall rate, A 0, of such a sys;.cm i'.. [6_9] (Igy

A o = ( k 12r2l - k , i r l 2 ) / ( k 12 + k :1 + ri2 + r2l )

We assume that the rate-limiting step on the substrate side is oscillatory, with the height of the barrier X k T and a characteristic frequen~ fo "=¢ao/2~r. We lurther assume that the activation barrier is electrogenie. When an applied AC field F_.xln.}0 is imposed, there ~ill be a resonance between the barrier and the AC field if .f^c---f0. The amplitude of the AC induce..t resonance of the barrier. 6X~c, depends on the model of an enzyme omillator. For a simple resonator it may take the form .... , .o I[0,,,, o,..^,.: ~,o^<.E.A< Here

-,<<., " , d z]

g a n d /3 ~re, r e s p c c t i v e l y ,

I~l) a proportionality

constant and a damping constant due, e.g., to iriction. The mean rate constants per period welt: ubtaincti from the probabilities of the enzyme in ",he states ! and 2. Effects of an AC field on the rate were calculated by replacing kl2 and kzl with the mean val te,~ ."f the two rate e,.m~!ants over lime, i.e., ( k l , ) and (k21), respectively. Fwo assumptions were made. First, f.t. :*-kl, or k2i. This condition simplified m:,thematieal procedures. Sccona, the barrier oscillation dJe to therr,lal fluctuation~ was symmetrical. And sir,,': thermal flactuatl-~n~ did net have a characteristic ,-equency, their effect on AC induced balricr o.,cillation .vould be small. Thus. 5A~c could be a'~x~;ed in0et:,endcntly ot thermal fluctuaUons. The mean rate cgnstan.s w e r e expressed frequ,:n~,

in t e r m s o f the a m p l i t u d e , o~,w , o f the A C field.

<#<,:'=kT,.F(~;~,.<~,<):

~.- ,%('= ant~ the

,: k.,~ > = k'_.',~ ( K~,. ,,,,.,,. )

~21~

Th : mean o eerall rate, ( A AC), became (A.lc.)

=

I

v2~t I - ~'.'l R~2 ) R l ,"i l l k , " F( E^( -i^~-- )J"

+ '(>i. 4- r 1 2 ( I ..

122S

68 i

where K,~ = kz=,/k~, :rod R~: = r~:/r:~. An integrated fl~rm ol /"( L..~ ''" , ~ox~ ) wa~ obtained ,t~, ,~ • -91 function of ,'iA .~. Fitting the rer, ults of the A t ' stmmlatcd A T P hydrolysis td I::,cto A'I'P;|~¢ to k-.qn. 22 (Fig. 4) gave the amplitude of the maximal barrier o.~illa=ion ;iX,~', at 2.5 k T . As was mentioned, the electric I~)tcntial drop experienced by Kcto ,Vl'P:tsc in a detergent rnicclle was approximately 10 /z~/. ! ~" ;.| ,,ingle charge was involved in the A C c n h a n c e m c m of rate, the interaction energy would be 10/.teV or an equivale=,t of 4 . 1 0 -4 k T , roughly 6(XJ0-fold smaller than ~.hc amplitude of the barrier oscillation 2.5 kT. T h e free cr, ergy of ATP hydroiysis ix approx. _,,'~'~~.T and would be sufficiont I t propel a barrier ost.~ll,tlio~ ,~f 2.5 /~,~'. The At" field was to facilitate ,rnergy Iransfcr Irom a catalyzed re:to=ion to the kinetic barrier of a fluctuating cn,.ymc via the rc.,amancc tram, duction m c t h a n i s m . The inertia or the Irletton ol a=t cnz~mc osciilator is expected to be small In such a c;,sc. =be cffcct of an A t " field on rate will I,e rapid. IIoit tilt o t h e r hand, the inertia =s in Ihc /(7' range it m;~y take a ilcriod of time for the AC' field to induce a steady-st;=to o,~cillat;on. Fig. 4 show,~ tha! the optimal At" freque,~t3' for stim.ulating A T P hydrolysis was I0 kltz. If the transfer of energy from the AC were 5(1'7.,;. it v.ould take 121111(I t3'c~es of the At" field to induce u ste~dy ,~t-~tc Icvt:l. or 2 5 k T . of barrier o~illation. With a Itl kHz AC. the lull impact of the resonance tram,d',tction could be r~.a,.|,~.u in approx. I s. Fig. Ii qualitatively cxpkJns how :~n A t ' r;,!~ ,. . . . . . . ~,....... ,h,. r.,~,. |ff at~ enzyme catalytic reaction through the O A B m e c h a n i s m "/he .~nsitivity of dctecti:m by the O A B mechanism :s not limited to a potcnt=al dtl*erential of It| HV. The optimal I'~tential differential lot detection in a p:~rticuI,tr ',yslcnl d~'p,~nds c n the property of the system. Au |'n,,ymc could be many orders of magnttudc p)orc st~ccptib~c I t Ihc pt'rlttlbali~m of ;~ periodic sig~al. If the: activation barrier of the r;::e-limitin~ re,teflon involvc~ it~c,al sub~.I-,:,~, ..ff structures, ils rate =~,'illb," fast a~d it,, sensitivity of dctection is likely high. If a more glob:d structural chang,.: is in',olvcd :he reaction will be slow and the sensitivity of dct,:~:tion ma~., bc lov,. For a tell the size of the h u m a n erythrt~'yte, a field of :; mV cm ~ is .,,uffitient to produce I1| /aV potential drop ;~cro~,~ Ihc lil,iJ bilaycr. An external field a; smltll :~s 5 nV cm ~ may be easily a c c o m m o d a t e d by the O A B |aechani~,m. Thus, molccuhtr recognition of a iiu~,v level AC field (nV per cm) is fca.,,iblc and may ind~:ed I c an adopted mecha,i:~m of ~ign:d tr:msducti~m in ,'cll~. If this ix the case, envirtmmental clcctrom;~gneti,~ fic~d,; or sonic I~dlul,mt,,, wt,uld interfere with in vr, o commurotation ol cells ant: ot~.a~isms. Their ell'cots on health mu,,t bc examined in light ol e~nerim,.'ntal data on th|" elect=it acti,'ation ,~f m e m b r a n e ATPascs. With rega~d to the tran',dcution of ELF :,ignals (extremely low level low frcqucnc3' eh:ctrom;~ncltc held) by cell,,. W,'avcr

t

X ÷ t~,X~,,,.c X-~'~

,u

~

s Reaction Coordm~e

/ i i i

+/$X

X

.&X

Rate

c

/'1 .

.

.

.

.

.

.

.



-,~

Fig. I I | : n h a m . ' c f n e n l o f t h e r a t e o ! an e n l , ) r n e cataly,,i~, by t h e o.,cill,dor2,, acli~,,lli.,,~,n halli~.'[ mechani~,m. I A ) Acliv;Jtion b a r r i e r of a n

cnO.mc c:tt~d,,'/edreaction X. i~, induced It t~¢ill;Jle by an AC fidd. '~ilh the amplitude of o~.'illalion A ,Y"..~,~ . ( B ) T h e a o n - h n e a r d e p c , • . d c l l t c ,,11 I d l e t,l! the.' ~ctiv;ttk~n e n e r g y (Arrh~:niu~ acti~,ationL ( ( ' ) "1 h¢ ,rn,t'l'all r a t e o,,cilt:Jlc,, ;1~, t h e h;~rrier ~scillate,,. ] ' h e m e a n t n e r a l l r a t e . ~ .4 ~,,t ~', i,, g r e a t e r =10an t h e r;d¢ "~ilhoul barrlt'~ ~a.'illatitm. ,4 o, r~ccau',e lit t h e ilonlint'arit~, ol r a t e on th,2 acliV;.lllOl= enert:~, S a n d P = l e n t • ".tlhMr,lte .Hid pr~,~lu,:t, re',,pt'cliv¢l~,.

an,I A,,lumian [63] have con.,,idcrcd the J o h n s o n / Nytlulst t l c r m a l electric noises as the limit of detcctkm. In this case. clectrcc,~n:"t,rm;ttional coupling is the m:6n ,,n~r,c ol field intcractiem with a col!. App-lrcntly, the tr:m'.dueti.~n ot .,.i,~n,ti~, by tnc ( l A B n~echanism~, ;,ould not hc circumvented by the thermal noise. IX. Channels, transporters, z~eceptors, growth factors and en ome'~ [-ncrgy may 13c teml~)rarily ,,¢ored in the fl)rm of ct,.r'fical bonds. -'=sin the phosphodie:;:cr L,~md of A'I P, G T P or l)hosphcrylmed amino acids, in cono'nt,,ati,,,n gratlicnts, ;is in , ! " and Na gi.,di~.nt,, t,- ,n suDratu,.dccular ,aructurcs. i.ikcw;sL, the received signal must hc convcrt,,-d int,~ more pcrman,.'qt chemic-"-! records so that its instruc'ton c,,~ ~,...~r ;,_',1out with biochemical reactions. T h e r e ca,= bc ',vide varieties of ~ays with ,Ahiqb these tasks are accomplished. Howevez-. the initial events of the signal ;:nd ent.rgy transduction are performed by the c o m m o n m e m b r a n e channels, transporters, rccepto;s growth factors, and cnz3'mcs. T h e

69 c h e m i c a l p r i n c i p l e s e n a b l i n g t h e s e m o l e c u l e s to t r a n s duce energy or sigqals arc the laws of anisotropic c h e m i c a l r e a c t i o n s . F o r m u l a t i o n for m e m b r a n e e n z y m e r e a d i - n , , , ill a n o s c d l a t i n g pt~lctttial h a v e b c c n im.,,:',,;g a t e d [9,[email protected]"9]. R e l a x a t i o n a n a l y s i s h a s I - c c n done to extract kinetic infl)rmation which otherwise can not be obtained by the conventional kinetic metho d s [68,~9]. U n t i l n o w , t h e s e s t u d i e s h a v e b e e n c o n fined to understanding general principles. Future study s h o u l d u . ~ '~pecific e x a m p l e s t o e x a m i n e t h e i r m e c h a n i s m s in m o l e c u l a r d e t a i l .

Acknowledgements I thank my colleagues and collaborators, Drs. R.D. A s , u r n , a n , V.S. M a r k i n . E . H . S e r p e r s u , B . E . K n o x . J. T e i s s i e , F. C h a u v i n a n d M r D.-S. L i u for t h e i r c o n t r , but!on.,, to t h i s p r o j e c t . T h a n k s a r c a l s o d u e t o C a r o l J. G r o s s for h o l d i n g m c p r e p a r e t h e m a n u s c r i p t , a n d t,) Dr. Chem,-Wen W u , D i r e c t o r (:f t h e I n s t i t u t e o f B i o m t : d , c a l S c i e n c e s a n d f r i e n d s in t h e i n s t i ! , , t e : o r t h e i r h o s p i t a l i t y . It w a s d u r i n g m y visit t o t h e in.stitu~c. in t h e s u m m e r o f 1991, w r i t i n g o f t h i s a r t i c l e w a s i n i t i a t e d . T h i s w o r k wits s u p l ~ * r t e d by a g r a n t f r o m t h e U.S. O f f i c e o f N a v a l R e s e a r c h .

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