Non Stationary Ionic Current through Polymer Charged Membrane

Transcription

1 Non Stationay Ionic unt though Poym hagd Mmban Bu. Koan hm. Soc. 2003, Vo. 24, No Non Stationay Ionic unt though Poym hagd Mmban Sunghyun Jong, Wonchu L, and Wongkang Yang * og of Ointa Mdicin, Dongguk Univsity, Gyongju , Koa * Dpatmnt of hmisty, og of Natua Scinc, Dongguk Univsity, Gyongju , Koa Rcivd May 20, 2003 Th axation phnomna of ionic cunts though th chagd mmban und th constant appid potntias has bn studid. Th fomuation was obtaind fo th non stationay cunt by assuming that th ion mobiity is indpndnt of concntation and th potntia gadint is a constant within mmban, and it was appid to th xpimnta suts with th sufonatd poystyn coodion bas mmban. It has bn shown that th initia ion distibutions in th mmban pay a pdominant o in th axation phnomna. Ky Wods : Raxation phnomna, Ionic cunt, Potntia gadint, oodion mmban, Ion distibution Intoduction Th tim cous of ionic cunts though th xcitab mmbans hav bn w dscibd by vsib changs in sodium and potassium conductancs. Mo infomation concning th chang in th ionic conductanc w obtaind by th tchniqus of intcua pfusion and th bhavio of vaious ions oth than sodium ion and potassium ion w discussd. 2 Sinc th atation in th ion conductancs may attibutd to th chang of ion concntation in th composit chagd mmban, th axation of ionic cunts duing votag camp woud b intptd by th tim dpndnt distibution of ions within mmban povidd that th passiv ion movmnts govn th pocsss. 3 Thfo, it is of impotant to find out th ssntia fatu of non-stady ion cunt und a constant votag with th atificia mmban ctoyts systm Though th xact dsciption fo th non-stationay stat of th mmban ctoyt systm w givn by Kikwood, 4 it is gnay impossib to stimat th ionic cunt as th function of appid votag and ionic concntation without th knowdg of th dtaid stuctu of th systm. Hnc, it is ncssay to mak simp assumption in od to xpss th non-stady cunt in tms of th simp masuab quantitis such as th appid votag and th sat concntation of xtio sids of mmban. In this study, th assumption of a constant ctic fid was appid to th non-stationay pobm. Additiona assumptions a that th ionic mobiitis a indpndnt of ionic concntation and th is no coss tm in diffusion cofficint. On th basis of ths assumption, an xpssion fo th non-stady ionic cunt was divd and was appid to th xpimnta data obtaind with atificia systms. thicknss of mmban was 0.03 mm. Th masumnts of mmban conductanc w mad by d.c. mthod using th c dvisd by Laksminaayanaiah. 6 Aft th mmban was quiibatd with xtio ctoyt soutions, a potntia was appid acoss mmban with th cunt caying siv-siv choid ctod. Th appid potntia was kpt constant by using a vaiab sisto and siv-siv choid pobs opatd to th dtct th mmban potntia. Th chang in th cunts with tim w codd as th potntia dpssion btwn a standad sistanc. Th caom ctods w usd to dtmind th sting potntia. Th xpimnts w caid at 25 o without a pfusion of ctoyt soutions. Rsuts and Discussion Th typica tim cous of non-stady cunts with a vaious appid votags fo th systm which consists of th mmban fixd btwn th 0.0 N-K soution and th 0.0 N-a 2 soution a iustatd in Figu. This systm has th sting potntia of 35.6 mv. Th cunts dcasd with tim whn th initia appid potntia was dispacd to th anoda diction, and th axation tims as w as th amount of vaiation in th cunt incasd as th appid potntias bcom ag. On th oth hand, th cunt incasd duing th cous of th cod whn th potntia dviations fom th sting vau w ngativ. In Expimnta Sction Th mmban was did typ sufonatd poystyn coodion bas mmban ppad fom 3.5% coodion soution containing 0.85%/L sufonatd poystyn. 5 Th Figu. A schmatic appaatus fo ionic conductivity masumnt.

2 938 Bu. Koan hm. Soc. 2003, Vo. 24, No. 7 Sunghyun Jong t a. Tab. Th mmban potntia, mmban conductanc, and mmban pmabiity at sting stat though composit chagd mmban and systm no.: 0.0 N-K/0.00 N-K, 2: 0.0 N-K/0.00 N-a 2, 3: 0.0 N-K/0.0 N-a 2, 4: 0.0 N-K/0. N- a 2 Systm no. V 0 (mv) G (mho/cm 2 ) G + (mho/cm 2 ) G (mho/cm 2 ) P K 0 5 (cm/sc) P a 0 6 (cm/sc) P 0 7 (cm/sc) this cas, th tim constants w sma than thos fo th anoda cunts. Whn ony th K soution was usd th xtio ctoyt and th concntation of ctoyt of th on sid mmban was diffnt fom th oth, th systm gav ssntiay th sam suts as thos mntiond abov xcpt fo th sma changs of cunt causd by th ngativ dispacmnt of mmban potntias. Sinc th constant votags masud with siv-siv choid pobs w affctd by th votag dpssion du to th ctica sistanc of th soutions btwn th pobs, th nt mmban potntias by masuing th soution sistancs as a function of th distanc btwn th pobs. 6,7,8 Th ffct of th concntation poaization na th mmban sufacs woud b ignod sinc a suddn mova of th appid potntia causd a ngigib poaization potntia as compad with th sting potntia. In addition, th tim sca adoptd fo coding th cunt was so ag that th capacity cunt was not invovd in masumnt. Fo th initia sting stat of vaious systms, th mmban conductanc, th potntias and mmban pmabiity of ach componnt a givn in Tab. Th quation fo cacuation pmabiitis w divd by using th fomuations givn by Kimizuka as foows. 9 Fo th concntation c of K soution; P + K = RT RT Wh PΚ and P c dnot th mmban pmabiitis to potassium ion and choid ion, spctivy; 0 and, concntations of K soution on th both sid of mmban; G± is mmban conductanc; V0, mmban potntia at th sting stat; F, Faaday constant; R, is gas constant; T, absout tmpatu. Simiay, th mmban pmabiitis of componnts fo th bi-ionic systm composd of K and a 2 w wittn in th fom; P = RT RT + G = ( G + G ) 2 FV = n G RT G + () (2) (3) (4) RT P K xp( 2 0 ) RT RT P a = RT xp = RT RT xp( 0 ) 0 = FV 0 0 RT 0 and G +, G a cacuatd accoding to quations (3) and (4). If th foowing condition was maintaind q 2 >> p 3 P 0 P 3P = a, 2q = P K 0 + P P K 0 + P (5) (6) (7) (8) (9) (0) and Pa indicats th mmban pmabiity to cacium; and, th concntations of K and a 2 in noma, spctivy. Th Tab indicats that th mmban pmabiity to choid ion was ngigib as compad with thos of sodium and cacium ions and hnc th mmban usd in this study is of th high pmsctivity fo cations. In th subsqunt tatmnt of non stady cunt, it is assumd that th mmban is unifom ov its thicknss, and th ion fuxs a dpndnt upon position and tim. Th ion fux, j, of componnt ion fo isothma systm is givn by th Nnst-Panck quation; j = D d z F dψ () dx RT dx Wh is th concntation of ion within th mmban; z, its chag; D, its diffusion cofficint; ψ, th mmban potntia; and x dnots coodinat noma to th mmban. Fo th sak of simpicity, th diffusion cofficint, D, was assumd to b indpndnt of th concntations athough it, in gna, considd to b a compicatd function of th concntation of a componnts. This was usuay assumd by many invstigatos fo dscibing th stady stat of th mmban and ctoyt soution systms. 0 Accoding to Godmam, th futh simpification of th pobm might b possib in th cas wh th assumption concning with ith th potntia distibution o th

3 Non Stationay Ionic unt though Poym hagd Mmban Bu. Koan hm. Soc. 2003, Vo. 24, No concntation distibution of ion within mmban w poposd. Th fom assums th micoscopic ctonutaity at any position within th mmban, and th att assums that th potntia gadint in th mmban is a constant. Th fom cas was studid xcusivy by Tho 2 and th att was pfd by Godman and Hodgkin. 3 Howv th is no thotica ason fo confiming which situation dscibs th chaactistics of systm mo xacty. In viw of th fact that th cunt votag ations obtaind with th non-stady cunts at constant tims can b poducd by th xpssion basd on th assumption of constant ctica fid, it sms asonab to appy this assumption fo th non stationay systms. 4 Dnoting x ant t fo th coodinat noma to th mmban and tim, spctivy, th quation of continuity is givn by j = (2) x t which psnts th consvation of mass fo th componnt. With th assumption of constant ctica fid and by quation (2), th quation of fux xpssd by Nnst- Panck quation is ducd to j = T x x wh and T a givn by foowing quations; 2 = z F dψ RT dx T = D dt' (3) (4) (5) in which is indpndnt of position owing to th psnt assumption. Th gnaizd diffusion quation psntd by quation (3) coud b sovd with th initia condition; j 0 And with th bounday condition; t 0 ( x, 0) = D 2 0 D 0 xp ( 20 x) 0 x (6) ( 0, T) = 0 (, T) = j (7) (8) wh 0, th concntation of ion at x = 0, and T = 0; j 0 and j, th fuxs at T = 0 and T =, spctivy and cosponds to givn by quation (4) at th initia sting stat. Th soution fo quation (3) was obtaind in th poynomia fom as foows; j 0 j D 2 D 0 xp ( 2 ) 0 T ( x, T) = 2 j + 2π x j D 2 D 0 n = j 0 nπx n sin ζ n η n [ D ( η ζ ) n n {η j 0 j n D 2 D j x + η n ζn 2 D D ( 2 0) }( ) n ] ζ nt (9) in which th foowing abbviations w usd; ζ n = { 2 + nπ } (20) η n = ζ n + 4( ) (2) and η dnots positiv intgs. Fo ag T, th quation (9) may b xpssd by th tm with n =. Hnc, w obtain j (22) wh ζ and η a qua to thos of quations (20) and (2) at n =, spctivy. By th substituting th quation (22) to quation () it is possib to psnt th fux quation as th xpicit function of tim and position; (23) Equation (23) indicats that th non stady fow of ion can b dscibd compty povidd th initia and fina stady stats, th diffusion cofficint of th ion and appid potntia a givn. Th summation of th fuxs fo th a constitunt ions th tota cunts; j 0 ( x, T) = j ( D 2 D 0 ) 2 x π ζ T x sin( πx -----) 2 [ j { ζ j 0 j D 2 0 D 2 D j j 0 +( ) } ( 2 D η ) 2 0 D ( { + 2 0) }] j = j 2πD ζ T x { 2 sin( πx -----) + π -- cos ( πx -----)} [ j { ζ j 0 j D 2 0 D 2 D j j 0 +( ) } ( 2 D η ) 2 0 D ( { + 2 0) }]

4 940 Bu. Koan hm. Soc. 2003, Vo. 24, No. 7 Sunghyun Jong t a. I = z Fj, I 0 = z Fj 0, I = z Fj, (24) wh I, I 0 and I a th tota cunts at th finit, zo and infinit tims, spctivy. ombining th quation (24) with th quation (23) and iminating I, w hav th tim dpndnc of th non stady cunt at th mmban bounday, x = 0, as foows; I I 0 = π F z ( j j )( + ) + (2D j )( + ) π 2 unity, is ducd to D P --- η /RT D (29) wh η indicats xcss f ngy of th ion. Insting quation (29) into quation (27), w obtain th nxt quation (30) j 0 = D z ( 0 G z G + ) G z (30) Thus th fuxs at st and th diffusion cofficints coud b stimatd fom th data shown in Tab. Th tim couss ( ) } (2D 0 + j ){ ( 2 0 ) π 2 [ { 2 + ( π --)2 }D t ] (25) aft substituting th quations (5), (20) and (2) fo T, ζ and η, spctivy. Th sting potntia, V0 and th appid potntia, V a intoducd into quation (25) though th foowing ations; 0 = z F V , (26) 2RT = z F V 2RT --, In quation (25) th axation of cunt is xpssd as th dviation fom th initia cunt and th diffnc btwn th initia and fina stady cunts a dtmind by th xtapoation to th infinit tim. It was obvious that th tim constant fo th axation of cunt was paa to th appid potntia and popotiona to th diffusion cofficint as w as th cipoca of mmban thicknss. On th oth hand th amount of vaiation in th cunt was found to b dpnd on th many factos, such as appid potntia, diffusion cofficint, initia concntation of componnts within mmban, th sting potntia and th initia and fina stady fuxs, in mo compicatd mann. 5 In od to stimat th fux at sting stat, th foowing quation coud b avaiab; 6 j 0 = P z ( 0 G z G + ) G z (27) wh 0 and a buk concntations of ion on th both sids of mmban and P is th mmban pmabiity to th ion. Assuming that in th mmban, th potntia gadint is a constant and th diffusion cofficint, D is a constant indpndnt of concntation P may b ducd to P = z FV/2RT D η /RT sinhz FV/2RT (28) which, povidd zfv /2RT, is sma as compad with Figu 2. Rcods of non stady cunt und a constant appid votag fo systm no. 3. Th dispacmnt of mmban potntia is givn in miivots by th numb attachd to ach cods. Figu 3. Th cods psnt an appid potntia; soid in, xpimnta vau and dashd in, cacuatd usd.

5 Non Stationay Ionic unt though Poym hagd Mmban Bu. Koan hm. Soc. 2003, Vo. 24, No Figu 4. Tim cous of non stady cunt fo th ctoyt soution systm no.2. Soid ins a xpimnta vau and dashd ins a cacuatd vau accoding to quation (23). Figu 5. Tim cous of non stady cunt fo systm no.3 and th numbs attachd to th cods psnt an appid potntia; soid ins a xpimnta data, dashd ins a cacuatd vau. of th non-stady cunts masud at vaious appid votags a iustatd in Figus 2, 3, 4 and 5 fo th diffnt systms, spctivy. Th cacuatd diffusion cofficints fom ths suts w sma than thos stimatd by quation (29) fo th pmabiitis in Tab. This fact sms to b du to th diffnt tatmnt fom th pvious on which was dtmind without th constant fid assumption. Howv, th pmabiity atio fo a givn systm shoud b pfd that dtmind with th mthod of Kimizuka 7,8 ath than that accoding to Hodgkin and Katz. Thfo, it was possib to cacuat th diffusion cofficints with th tim constants and quation (25), povidd th atio of diffusion cofficints is accoding to quation (29). Ths diffusion cofficints and fuxs of potassium and cacium at st w shown in Tab 2 fo th vaious systms. Th cosponding quantitis of choid ion w so sma that thy coud not cacuat xacty. As 0 is th concntation of ion at mmban bounday in th initia stady stat, it is uniky asonab to stimat 0 by assuming Donnan quiibium. In th Figus 3, 4 and 5, it was found that th fina cunt, J coud not b stimatd fo cas of th ngativ appid potntias. onsqunty, th vaus of 0 and J a ncssay to dtmin so that thy coud poduc th xpimnta data. Th vaus of 0 and J stimatd in such way a givn in Tab 3 to 6. Thus th tim couss of th axation cunt fo th vaious appid potntia cacuatd accoding to quation (25) coud poduc th xpimnta suts as shown in Figus 2 to 5. Ths Tab 3. Th ion fux and mmban potntia of potassium ion fo th 0 N-K vs N-K soution systm though composit chagd mmban V (mv) j K 0 2 (mo/cm 2 sc ) Tab 2. Th diffusion cofficint, ionic concntation and ionic fux vau at sting stat fo potassium ion and cacium ion though composit chagd mmban and systm no. : 0.0 N-K/0.00 N-K, 2: 0.0 N-K/0.00 N-a 2, 3: 0.0 N-K/0.0 N-a 2, 4: 0.0 N-K/0. N-a 2 Systm no. D K 0 9 ( cm 2 sc ) D a 0 0 ( cm 2 sc ) K 0 2 ( mo / ) a 0 3 ( mo / ) j K 0 2 (mo/cm 2 sc ) j a 0 5 (mo/cm 2 sc )

6 942 Bu. Koan hm. Soc. 2003, Vo. 24, No. 7 Sunghyun Jong t a. Tab 4. Th fuxs of potassium ion and cacium ion at and mmban potntia fo 0.0 N-K vs N-a 2 soution systm though composit chagd mmban V (mv) jk 0 2 (mo/cm 2 sc ) ja 0 4 (mo/cm 2 sc ) Tab 5. Th fuxs of potassium and cacium ion at t = against mmban potntia vau fo 0.0 N-K vs. 0.0N-a 2 soution systm though composit chagd mmban V (mv) jk 0 2 (mo/cm 2 sc ) ja 0 3 (mo/cm 2 sc ) Tab 6. Th fuxs of potassium ion and cacium ion against mmban potntia fo 0.0 N-K vs. 0. N-a 2 soution systm though chagd mmban V (mv) jk 0 2 (mo/cm 2 sc ) ja 0 2 (mo/cm 2 sc ) suts indicat that th quation (25) dscibs th ssntia fatu of th axation phnomna. Th 0c w found to b popotiona to th buk concntations of cacium ion. Though th buk concntation of th on sid of th mmban was constant, th ion concntation within th mmban smd to dpnd on th cacium ion concntation psnt in th od sid. This can b dducd in tms of th vaiation of 0Κ shown in Tab 2. oncusions It is notd in mmban quation that th vau contibut to th amount of th axation cunt considaby and it may b concudd that th axation of cunt w contod by th ion tanspots fom th intio of th mmban to th xtna soution. Fo th K-a 2 Figu 6. Th tim cous of non stady cunt fo systm no.4 and th numbs attachd to th cods psnt an appid potntia and soids a xpimnta data and dashd a cacuatd vau. systms, th tim cous of cunt was mainy govnd by potassium ion tanspot whn th a 2 soution sid was positivy poaizd and vic vsa. Acknowdgmnt. This wok was suppotd by th Dongguk Univsity Rsach Fund. Rfncs. Hodgkin, A. L.; Huxy, A. F. J. Physio. 952, 7, Bak, P. E.; Hodgkin, A. L.; Shaw, T. I. J. Physio. 962, 64, hand, W. K.; Mvs, H. J.Physio. 965, 80, 788 & Kikwood, J. G. Ion Tanspot Acoss Mmban; ak, H.T., Ed; Acadmic pss: 954; p Nihof, R. J. Phys. hm. 954, 58, Lakshiminaayanaiah, N. J. Poym Sci. 960, 46, Lakshiminaayanaiah, N. Subc, Biochm. 979, 6, Lakshiminaayanaiah, N. Tanspot Phnomna in Mmban; Acadmic pss: N.Y., 969; hap Kimizuka, H. J. Thot. Bio. 966, 3, Nagata, Y.; Kohaa, K.; Yang, W.; Yamauchi, A.; Kimizuka, H. Bu. hm. Soc. Jpn. 988, 6, Godman, D. E. J. Gn. Physio. 944, 27, To, T. Pog. Biophys. 953, 3, Hodgkin, A. L.; Katz, B. J. Physio. 949, 08, Kdm, O.; Katchasky, A. Tans. Faaday Soc. 963, 59, Schutz, S. G. Basic Pincip of Mmban Tanspot; ambidg Univ. pss: 980; hap 4, Siddiqi, F. A.; Avi, N. I. J. Mmban Sci. 989, 46, Yang, W.; Yamauchi, A.; Kimizuka, H. J. Mmban Sci. 992, 70, Hiata, Y.; Dguchi, S.; Yamauchi, A.; Kimizuka, H. Nippon Kagaku Kaishi 988, 536.