Gen Physiol Biophvs (1998) 17, 349—363 349

Channel-Sizing Experiments in Multichannel Bilayers

0 \ KŔ X.SII NIKO\ ' 2 P G M E R Z L Y A K 1 2 L N YULDASHFVA2 ?

\ND R \ N O G I J E I R A 2

1 Laboratory of Molecular Physiology Institute of Physiology and Biophysics 700095 Tashkent Uzbekistan

2 Laboratory of Membrane Biophysics Department of Biophysics and Radiobiology Federal University of Pernambuco 50670 901 Recife, PE Brazil

3 Departmi nt of Biochemistry, Tashkent Pediatric Medical Institute, 700125 Tashkent Uzbekistan

A b s t r a c t . The possibility of obtaining mfoimation about the radius of high and low conductance states of channels in multichannel membranes was tested expen nu n t a l h In spite of the mteifeience of non elec tiolytes on the numbers of channels that appealed in the membrane the non electiolyte exclusion method was success fully adapted to multichannel bilayers to estimate the radius of the larger opening of the low conductance state of the channel induced by Staphulococcus aurevs alpha-toxin At the pH used, the channel transition to a low conductance s ta te was accompanied bv a decrease of the opening radius horn 1 3 ± 0 2 nm to 0 9 ± 0 1 nm The determination c i i tena foi maximum si/e of a channel opening when using the non electrolyte exclusion method is discussed

K e y words: \ l p h a toxm Planai bilayei — Ion channel size — Conductance states — Multichannel bilayer

I n t r o d u c t i o n

Staphylococcus aureus alpha-toxm (ST) is a single chain protein with molecular mass 33 LDa (Giay and Kehoe 1984) Its ability to foim t iansmembrane ion channels was established moie than 15 years ago (Kiasilmkov et al 1980, 1981) Since t h a t time, the properties of the channel incorporated into lipid bilayers as well as into cell membranes have been under intensive study (for review, see Bhakdi and Tranum Jensen 1991, Krasilmkov et al 1991) Most likely, the channel is ohgomenc,

Coriespondence to Dr Oleg V Krasilmkov Umversidade Federal de Pernambuco Centro de Ciencias Biologicas Depto de Biofisica e Radiobiologia, Av Prof Moraes Rego S/N Cidade Universitana Recife Pernambuco Brazil CEP 50670-901 E mail krasOnpd ufpe br

350 Kiasilmko\ et al

<ontammg 7 molecules of the toxm (Gouaux et al 1994) Diffeient appioaches wen used to establish the appaient laclms of the channel which was found to be m the (J 5 1 4 nm lange in biological membianes and in the 0 5 1 3 nm íange m lipid bilayers (Bhakdi et al 1984, Menestima 1986 krasilmkov et al 1988a, 1992 Sabnoy et al 1991, 1993 Walev et al 1993, Jonas et al 1994 Bezrukoy et al 1996)

Bilayei expcinnents (Kiasilmkoy et al 1988b, 1990a, kasianowicz and Be/-nikoy 1995) hay e demonstrated that at neutral pH, ST fonns ion channels which mainly show a high conductance state Decreasing the pH led to an mclease m the sensitivity of the channel to voltage giadient \ s a result, transitions between a high and a low < onductance state occur more frequently and can be easily observed (kidsihnkoy et al 1988b, 1990a, kor c hey et al 1995) The- nature of the gate is unknown although it was smpiismglv similar to the current fluctuation shown in ion channels piesent m biomeinbranes In some recently published studies (kiasi l-mkoye t a l 1988a, 1991 1992 Sabnoy et al 1991, 1993) on individual ST-channels the appaient radius of the channel was estimated to be 1 3 nm The channel ra­dius m the low conductance state was found to be considerably smaller (~ 0 6 nm kiasrhnkcn et al 1990b) A few years later korchty et al (1995) examined the channel cioss-section rn high and loy\ conductance states and found much smaller changes m the channel ladius (frorrr ~ U 8 nm to ~ 0 64 nm) The dee laied \a lue foi the lachus of the ST-chamrel in high conductance states was considerably smallei (~ 0 8 nm) than the early data (krasrlmkov et al 1988a 1991, 1992, Sabnov et al 1991 1993), although both groups of authors have used non-electrolytes (NE) as molecular probes to srze the channel A resolution of this discrepant u was oiu

of tin aims of the present study

In the original descnption (Sabnoy et al 1991, 1993, krasihnkoy et al 1992), the \ E - exclusion method allows to si/e individual pores bv a technique based on the de e u ase of c onductiy ítj induced by high concentrations of neutral NE applied to both sides of lipid bilayers small NE that enter the pore deciease the conduc­tance wheieas large NE that do not enter rt do not affect the conductance The method is based on obseiyations made on a number of separate single channel cyents, and then the data are ayeraged in ordei to peimit a fair decision about the si/es of both the high and the low conductance states In this respect, a hilaycr

containing many channels seems to he a more appropriate system to study, being

less time < onsuming and especially appropriate for low conductance channels The

domination of the vsi of mvltichannel bilayers to determine channel size was the

second aim of our study Lipid bilayei s modified by S aureus a-toxm yyere chosen as the model This model has advantages as well as disadvantages Information about the channel size (krasilmkov et al 1988a, 1990b, koichev et al 1995) facil­itates the study On the othei hand, the influence of polymer non-electrolytes on the eciuihbrium between high- and low conductance states of the channel and on

Channel-Si/mg Experiments 351

the piocess of poie for matron (opening) has also been demonstrated (Zimmeibeig and Paisegrarr 1986, Bashford et al 1993 korehev et al 1995), a fact that s t iongh complicates the study Hence, if theie is a possibility to establish the channel size for this complicate case the approach could be applied to anv other channel The present study was undertaken to examine tins possibility

M a t e r i a l s and M e t h o d s

S aureus cv-toxm was donated by Dr k D Hungerer (Behrmgweike Labora­tories, Marburg, Germany) Pure1 phosphatidylcholine was prepared according to Bergelson c t al (1981) or purchased from Sigma (St Louis I "S \ ) (Type \ - E ) Chole sterol was purchased from Sigma and used without any modiheatron Glucose was purchased from Merck (Darmstadt, Germany) and suciose from Reagen (Rio ele Janeiro Brazil) Polyethylene glycol (PEG) 1000 and PEG 1450 (Sigma) PEG 2000, PEG 3000, PEG 4000 and PEG 6000 (Loba Chenne, Mumbai, India) were used as non-electrolytes (NEs) When necessary the non-electrolyte polymers weie additionally pmified by amori-exe hange chromatography using stiong alkaline an ion exchangers (III or I \ Merck) to remove anion gioups contarmng contaminants which deeiease the' stability (life time) of bilayei lipid membranes and meiease the probability of ion channel transitions hour open to closed states Othc i chemicals were of analytical grade and weie used without additional pur rhc atron

Tyvice-distilled yvatei yyas used to prepare all buffer solutions The standard solution used in the bilayei experiments contained 100 inmol/1 k C l 5 nimol/1 citiie ae id and the pH was adjusted with Tns to 4 0 In experiments c a m e d out to deter­mine channel size this solution also contained 17Vc oi 20% (w/y) erf an appropriate non-electioly te In all e ases the solutions on both sides of the bilayei weie the same The hydiochnamic radii of non-clectroly tes weie obtained horn recent viscometry stuches (Sabrrov et al 1991, 1993), and were as folloyvs (nm) glycerol, 0 31 ± 0 02 glucose, 0 37 ± 0 02, P E G 1000, 0 94 ± 0 03 P E G 1450, 1 05 ± 0 03 PEG 2000 1 22 ± 0 03, P E G 4000, 1 92 ± 0 03, P E G 6000, 2 5 ± 0 03 The e onduc trvrty of eac h buffer solutron was measured \yrth an HI 9033 (HANNA Instruments, Woonsockct, RI) multi-range conductivity meter at 25°C

Planai lipid bilayers were foimed at loom temperature (25 ± 2°C) by the technique of Montal and Mueller (1972) from a phosphatidylchohne-cholesterol mixture (1 1, w/w) Monolayers were spread from a 10 mg/ml solution of lipids in n-hexane, on the surface of two buffered salt solutrons, separated by a 25 rem thick Teflon partit ion in a Teflon experimental chambei The onhce diameter was about 0 2 mm

Experrments were carrred out under voltage-clamp The current through the bilayer was measuied yvrth Ag/AgCl electrodes connected via salt bridges (3% agar with 3 0 mol/1 k C l ) to the cis- and rrani-compartments of the bilayer chambei

352 Krasilmkov et al

The irans-compaitment was connected to virtual ground through an operational amplifier (K284UD1A) m the current-to-voltage configuiation Voltage pulses were applied to the m-compar tment of the chamber The toxm was also added to the r/A-compaitrnent The solutions m both compartments were magnetically s tn ied The> amphfiei signal was momtoied wrth a storage oscrlloscope and recorded on a s tup chart or tape recorder Basal conductance of non-modrhed'bilayeis was less then 4 pS Moie than 200 ion channels were recorded m each experimental condition (5 7 channels per membrane)

Protein c oncentratron was determined with a Bradfoid reagent (Bio-Rad, Cal­ifornia ISA.) using bovine serum albumin as the s tandaid

Resu l t s and D i s c u s s i o n

\ s published elsewhere (kiasilmken et al 1998), the size of mchyidual poies can be evaluated by measuiing a paiameter which represents the filling (F) of a channel y\ it h NE F c an be e alculated as follows

F = ((<j0-g,)/ejl/((xo-\l)/\l) (1)

yyheie g„ is the single channel conductance m the presence of an nnpeimeable non-eleetroly te oi the single channel conductance m a solution without non-electroly tes g, is the single channel conductance m the presence of a solution containing NE yvith access to the channel mtenoi on both sides \ 0 is the conductivity of the solution without non-electrolytes or the conductivity of the vrrtual volume free of non-electrolytes rn a solution with non-electrolytes \, is the conductivity of the solution containing a given NE

To apply the method for measuring the size of the high and low conductance states of a channel m a multichannel bilayei yye must show the existence of a coirelation between related paiameteis at the single- and multichannel levels This can be done bv comparing the conductance distributions of the single ST-channel at high and low conductance states, on the one hand and the conductance levels obtained m a multichannel bilayei at a low- and high transmembrane potential (when ST-channels are previously in a high and lo\y conductance state (Menestima 1986 kiasilmken et al 1988a, b, 1990a, b, korchev et al 1995) on the other one

As expected when ST yvas added at low concentiations (~ 0 1 /ig/ml) to the aqueous solution bathing a voltage-clamped bilayer the membrane conductance increased m drscrete steps, indicating the mcoiporation of ronrc channels into the lipid bilayei The membiane potential yyas fixed at 20 mV Under these conditions channel openings weie detected as upward current deflections Dowmvaid steps, lepresentmg the closing of the channel, were veiy seldom observed at this low voltage The conductance values for the unitary eyents were calculated and plotted

Channel-Sizing Experiments 353

0.3-0. SÍ = 0.2-r> ro n o L 0.1-

0 , , - •

0 50 100 150 200 250 Coductance, pS

Figure 1. amplitude histogram of conductance fluctuations for the high conductance state of the ST-chaimel The probability, P to obser\e conductance steps like the one shown m the cuirent traces m the inset is represented Standard solution of pH 4 0 was used The record was discarded when any of the open channels temporarily closed ST was added to the ns compartment to a final concentration of ~ 0 1 /ig/ml The bilayei was clamped at 20 mV More than 200 ion channels were íecorded (5 7 channels pei membiane) Bin yvidth was 10 pS All other conditions foi the expenment are described in Matenals and Methods The mean yalue for single channel conductance was obtained using Gaussian distribution for the mam pool of this histogram (g\uei, = 212 ± 9 pS) \ sample of an original single channel refolding is shown m the inset The dashed line indicates /eio current level the arrow indicates the addition of the toxin

m a cumulatiye histogiam (Fig 1) A mean value of 212 ± 9 pS in 100 mmol/1 KCl (pH 4 0) foi single channel conductance (<7illgi,) was obtained by fitting a Gaussian cui ve to the mam pool of this histogiam Hence we found that the high conductanc e state of the ST-e hannel is quite umfoim in size, nr agreement with da ta reported by others (Menestrma 1986, krasilmkov et al 1988b, krasilmkov and Sabrrov 1989)

To study the low conductance state, the brlayers contained only one ST-channel The experrment was started as descrrbed above and when a single channel appeared the t ransmembrane voltage yvas increased to 100 mV Under these con­ditions channel closures were detected as downward current deflectrons, but the cm lent never dropped to zeio value This remaining conductance yvas used to con­struct a histogram and to measure the average low conductance Since ST-channels in the low conductance state change to a high conductance state after applying zero potential (Menestrma 1986, Krasilmkov et al 1988b, 1990a b, korchev et al 1995) we used this pioperty to determme the variations in conductance by observ­ing about 10 transrtrons for a grven channel These conductance values for many individual channels were plotted rn a cumulatrve hrstogram (Frg 2) A mean value (plow ) of 27 ± 13 pS in 100 mmol/1 k C l (pH 4 0) was obtained foi this low con­ductance level by fitting a Gaussian curve to the mam pool of this histogram The

í

I2PA

30S

354 Krasilmkov et al

a. 0 2 J? J5 ta €0.1-O.

/

/

\ \

0 20 40 60 80 100 120 140

Conductance, pS

Figure 2 Amplitude histogram of conductance fluctuations for the low conductance states of the ST-channel The probability P to observe a low value of channel c onductance is lepusented ST was added to the cis compartment to a final concentration of ~ 0 05 //g/ml Standard solution of pH 4 0 was used The analysis of the channel transitions to closed state conductances was done m bilayers containing only one channel The re-cord was stopped when a second channel appeared Data obtained from more than 30 membranes are plotted Bin width was 6 pS For all other experimental conditions see Matenals and Methods and the text The mean value of the low conductance state was obtained by plotting a Gaussian distribution for the main pool of this histogram ({/low = 27 ± 13 pS) An original recording is displayed m the mset The dashed line indicates /eio current level At the beginning the bilayer was clamped at 20 mV When a channel appeared the potential was switched to 100 mV This forced the channel to go to a low conductance state In order to reopen the channel the transmembrane potential v\as transiently switched to 0 mV and then back again to 100 mV

distribution of the low conductance state was found to be1 much widei (in relation

to its mean value) than tha t established foi the high conductance state suggest

mg the existence of different low conductance states, as demonstiated prevrously

(krasilmkov et al 1990a) From this type of experiment, one can see that , under

these conditions the mean value of the conductance of the low state is about 12%

of that of the high state

In multichannel experiments we examined bilayer e onelue tances at two different

t iansmembiane potentials low (10 mV) and high (100 mV) for the high and low

channel conductances respectively The experiment was earned out as follows

after the bilayer was formed and its parameters stabilized, ST was added to the

e is compartment at a relatively high concentration (~ 4 /zg/ml) and voltage was

clamped at 10 mV When the conductance of the bilayei reached approximately

10 nS the toxm-contammg solution was replaced with fresh buffer The increase

in bilayei conductance stopped within a few minutes and the final value (Gingh)

was deteimmed at this point for ST channels m the hrgh conductance state The

t iansmembiane potential was then increased to 100 mV The conductance of the

Channel Sizing Experiments 355

TlOOpA

2 min

1=0

I j l 00 mV

Figure 3 Time course of the cmrent in response to the application of a voltage pulse to a lipid bilayer containing numerous ST-channels m the presence of standard buffer solution pH 4 0 The dashed line on the current trace indicates zero current h and I aie cuntut levels used to calculate Gh,th and Giow The voltage pulse protocol is shown below the emient trace The stepwise increase in transmembrane potential to 100 m\ leads to the large instantaneous value of the current passed through the channels with a subsequent decrease toward a lower steadv state value At least h\ e half times were allowed to pass before steady state conditions with G\ovl conductance were obtained The asterisk with the airows indicates the pei fusion tune interval of the cis compartment of the experimental cell with standard solution without the toxm For other experimental conditions see Materials and Methods and the text

low state Glow was deteimined when the current reached a steady level after the initial transient (Frg 3) A s a i e s u l t the Giow/Ghigh ratio of about 0 12 was found This is equal to the value of <7iow/i/higii obtained from single channel experiments This finding indicates that channels in a multichannel brlayer behave in the same manner as in single channel bilayers

With this in mind, one can apply the NE- exclusion method to estimate the size of the channel using multichannel experiments In this case, Equation (1) which detei mines the filling of the channel with NE in the high conductance as well as in the low conductance states should be written m a slightly different form

F=((Go-Gi)/G,)/((X0-Xl)/x,) (2)

where G0 (Ghigh or Giow for hrgh and low conductance state, respectrvely) rs the brlayer conductance in the presence of an impermeant NE or wrthout any NE at eithei channel openrng, Gt rs G ^ h or GfJ^, and is the bilayer conductance in the presence of a solution containing NE with access to the channel interior on both sides The conductance of non-modrfied brlayer s (~ 4 pS) was negligible in

356 Krasilmkov et al

comparison with tha t of the modified bilayers, and was not taken into account \0

and \ , have the same meaning as m Equation (1)

Equation (2) is only valid if there rs no marked influence of NE on the equi-

hbrmm between high- and low conductance states and on the opening piocess and

the number of channels in the bilayei (N) is kept constant during the expenment

Unfortunately this is not the case foi ST induced channels, since the addition

of some ^ E can change the number of functional ST-channels m the membiane

This phenomenon, noted by Bashfoid et al (1993), takerr togethei with lecent

observations of an increase m the numbers of opeiated ST-channels induced by

a pH shift fiom any value to 5 6 (which is the pH value at which maximal ía te

of ST channel formation is observed (Kiasilmkov et al 1986, 1991)), suggests the

existence of a pie-formed, but not functional ST channel pool in the membrane

Ibis fact precluded the dnect use of Equation (2) to determine the size of the high

and low conductance states of ST channels m a multichannel bilayei snnultanc

ouslv because at least two paiameters (cr, and N) are unknown Thus, we weie

fenced to fust estimate gt foi one of the ST-channel states The high conductance

state of the channel was chosen Values of gl obtained m the presence of drffeient

NE m the bathing bilayei solution aie shown m Table 1 These data can be used

to determine the size of ST channel m the high conductance state by calculating

F (using Equation (1)) and plotting this F against the hydiodynamic íadn (/)

of the NE (Fig 4) The ladms of the channel can be considered to be equal to

the hvdioelvnamie radius (r) of the NE coiiespondmg to the point of t iansition

from the1 falling pai t to the lowei quasi-hoiizontal branch of the relationship of F

Table 1 High conductance state of ST channel in the prese-nee of non electrolytes m the bathing solutions

Non electrolyte g£™ g£™ \ (pS) (pS) (mS/cm)

1 "None 3 Glveeiol 4 Glue ose 5 Sucrose

10 P E G 1000 11 P E G 1500 12 P E G 2000 13 P E G 4000

212 ± 9 124 ± 11 113 ± 8 112 ± 10 134 ± 20 181 ± 22* 213 ± 26* 238 ± 28*

130 ± 11

74 ± 10 97 ± 15

103 ± 18 136 ± 17* 147 ± 2 0 *

12 6 7 8 7 5 7 6 6 6 6 5 6 5 6 5

* and # mark differene es at P > 0 02 (ŕ test) In all other cases, P < 0 005 Standard solution of pH 4 0 and pH 6 0 was used All non electrolytes were used at 20% (w/v) concentration y (mS/cm) is the conductivity of used solutions For other conditions, see the text

Channel-Sizing Experiments 357

1.5

1-

U-

O)

| 0.5 iZ

0

0L5 1 iľŠ 2 ?5 Hydrodynamic radius, nm

Figure 4. Dependence of parameter F on the hydrodynamic radius of the non-electrolvte ioi high (single channel level) and low (multichannel level) conductance state of the ST-chdimel Symbols (o and •) indicate the filling of the high conductance state of the ST channel with NE in single channel experiments at pH 4 0 and pH 6 0 Foi experimental conditions, see legends to Figures 1 and 2, and footnotes to Table 1 Symbol (•) indicates the filling of low conductance states of the ST-channel with NE in multichannel experiments (pH 4 0) As described in text, data analogous to those presented in Figure 5 (Gulf,h. Gi o w , G^h and G ^ , together with values of conductances of the high conductance state of the single channel and the numbers of appaient channels in lelated conditions (Table 1 and Table 2), were used to calculate the apparent values of single channel conductance in the low conductance state and equation (1) was used to evaluate parameter F Lines are best fits to the experimental points The horizontal hue for the low conductanc e state of the ST-channel connects the points measured m the presence of PEG 1000, PEG 2000 and PEG 4000 The horizontal line for the high conductance state of the ST-channel connects the points measured m the presence of PEG 2000, PEG 4000 and PEG 6000 The points foi ladn ranging from 0 31-0 37 to 0 94-1 22 nm were used to draw another linear regiessron The arrows indicate the maximal values of the radius of the ST-channel in the high and low conductance state For types and sizes of used NEs, see Materials and Methods sectron For other experimental conditions, see the text

against r Molecules with this and largei ladii do not enter the channel and do not affect conductance One can see that the value obtained for the channel radius was slightly larger than the hydrodynamic radius of the molecule P E G 2000 (1.22 nm), and equal to ~ 1.3 nm. The same values were found at pH 6.0 and 4.0 (Fig. 4) A srmilar ladius was obtained earlier at pH 7.5 (krasilnikov et al. 1988a, 1991. 1992; Sabnov et al. 1991, 1993), despite t h a t fact that the conductance at acid pH consideiably exceeds that at neutral pH (krasilnikov et al. 1986, 1989, 1991; kasianowicz and Bezrukov 1995).

As shown elsewhere (Krasilnikov et al. 1998), this method allows the maximal

358 Krasilnikov et al

JlOOpA

lOmin

Glycerol

A.

lOOmV

OmV

S T \ x

[lOOpA

lOmin

PEG1000

"u_r 100 m V

OmV

lOOpA

lOmin

PEG4000

C.

lOOmV

OmV

Figure 5. Effec t of NE on integral current flowing through numerous ST channels in the high and lov\ conductance states The result of a sepaiate experiment is presented The- dashed line on the current trae e indi­cates zero current h and Ii are the cur­rent levels used to calculate Gi,,8h, and Giow

while Is and 1\ are the- current levels used to calculate G ^ and G^ i , The voltage-pulse protocol is shown below the current trace Foi other experimental conditions see legend to Fig 3 Materials and Met h ods and the text A Glvcc-rol B PEG 1000 C PEG 4000

size of a channel opening to be established Consequently, the radrus of the laigest opening of ST-channels 111 the high c oneiric tance- state is quite stable, does not depend 011 pH, and is e lose to 1 3 11111 The data obtained aie 111 excellent agreement with the recently established moleculai architecture of the ST-channel (Song et al 1996) and are different from those published by Korcliev et al (1995)

The da ta about ej, for the high c oneluc tane e state allowed us to estimate the size of the low e onductane e state of the ST-e hannel in multichannel bilayei s The exper­iment was s ta i ted as descrrbed above (Fig 3) and the bilayer conductances (Gh,gi,, at 10 mV and G\ov, at 100 111V) foi ST-channels 111 high and low conductance states weie also deteimmed Then, keeping the 100 mV potential, the solutions on both sides of the modified lipid bilayei were replaced with fiesh (ST-free) basic so­lution with 17% (w/v) NE The result obtamed usmg glycerol, PEG 1000 and P E G 1000 is piesented m Fig 5 The conductance of the brlayer (Giow) was changed by substituting a new value (G[^JV, determined by ST-channels in a low ccmductairce state in the presence of NE) Two effects of NE may participate 111 this change 1)

Channel-Sizing Experiments 359

an alteiation in the number of functioning ion channels, and 2) a deciease in the conductance of the low conductance state of the ion channel Only the latter effect should depend on the radius of the low conductance s tate of the ion channels To conect foi such effect we must subtract the influence of the non-electrolyte on the number of functional channels Thus, we decieased the value of the fixed potential from 100 mV to zero for a few seconds and then fixed it at 10 mV This piotocol of voltage pulses is sufficient foi complete tiansition of the ST-channels to then high conductance state (Menestrma 1986 Krasilmkov et al 1988b, 1990a, Korchev et al 1995) \ s a result, we determined the sum of conductances foi all ST-channels (at then high conductance state) m the presence of NE ( G ^ h ) Usmg the values of the single ion channel conductances m basrc solutron without (</iUgh) and with NE (9hit.ii) (which w d s established duimg the single ion channel radrus determination) yye could calculate the number of channels under these conditions (Arl and TV2) as follows A ' = Gingh/cyingi, and A r i = G^J h/ej^h The lesults are piesente-el m lable 2 One can see that addition to solutions bathing the multichannel bilayei of NE actually changes the iiumbei of functional channels Knowing the iiumbei of e hannels allows us to find the mean value of the conductance of a single ST-channel m low conductance- states without {cj\m = Gi„w/A r I) and m the piesence of NE m the solution bathing the membiane {g^ = GK E low/A r 2 ) The ic-sults of this and many snmlai expoiimeiits with PEG 1000 as well as with other NEs were used to obtarn reliable data foi c/iow and eyNI low undei these conditions

Table 2. Influence of non electrolytes on the numbers of ST channels opened m lipid bilaveis

Non-cle-ctiolyte Ar~

1 Glycerol 82 4 ± 18 3 2 Glucose 68 9 ± 10 2 3 Sucrose 75 0 ± 42 2 4 PEG 1000 187 0 ± 69 5 5 PEG 1500 144 2 ± 36 8 6 PEG 2000 103 9 ± 11 9 7 PEG 4000 65 7 ± 23 5

N~ are numbers of channels aftei the addition of the NE to the bathing solution (ex­pressed as % of those in pure buffer) For other conditions, see the text

These findings peimit us to use Equation (1) to calculate parameter F and to

determine the channel radrus of low conductance ST-channel from F against the

hydrodynamic íadius of NE dependence The da ta aie shown m Fig 4 along with

360 Krasilmkov et al

those for the open state of the ion channel One can see that the maximal radrus of the ST-channel openings decieases consideiably upon transition from the high to the low conductance state (fiom 1 3 nm to 0 9 nm)

Using eiystallogiaphic da ta Song et al (1996) demonstrated that the two channel openings have almost the same radius On the other hand the NE-exe lusion method pi ovules mfor matron about the decrease in the maximal size of the channel openings d m m g the channel transition to low conductance state Hence, we can suggest that both openings of the channel are involved (deciease m size) m the voltage-induced channel transition fiom high to low conductance state During this piocess the maximum eioss-sectional aiea of the ion channel openings decieases moie than two times horn ~ 5 4 nm 2 to 2 5 run2 The discrepancy between oui data and those íepoi ted bv others (Korchev et al 1995) who obtained a smaller difference (1 6 times) is certainly a íesult of differences in the evaluation of the channel radrus from the relationship of F and r The size of the smaller NE which do not cntei the channel at all, must be considered to be equal to the maximal size of the channel openings This criterion is irr good agreement with the lecentlv established molecular arclntectuie of the ST channel (Song et al 1996) and was used m the- piesent study whereas korchev et al (1995) took a 50% 'cutoff" size of NE as the size of the channel This lattei assumption has rro clear physical me-amng By applying om ci i tenon to Ivoichov 's data one can obtain ~ 1 3 nm arid 0 9 nm as ladn of the- channel m the high and low conductance state, lespeetively Tins agreement suggests that the multichannel approach may validly be used foi channel size determination (as used for the low conductance state of the ST channel m the present study) Using these da ta the calculated change in the maximum cross section of the ST-channel water pore durrrrg rts transition fiom high to low conductanc e state is c onsideiable, but strll less than expected from the change m the channel conductance It should be pointed out, however, that channel c loss-see tion might conelate with conductance for very large channels only (> 10 nm lachus Pasternak et al 1993) For narrower channels (to which the ST channel belongs) the theoietical conductance data could diffei from experimental conductances by a factoi of 5 (Smait c-t al 1997) Foi these channels conductance should much moie depend on the molecular nature of the surface, i e , charges and dipoles situated at the entrances and along the walls of the channel It should also be mentioned that image (Markin and Clnzmadjev 1974) and faction (Antonov 1982) forces can also mteifeie with the cioss section/conductance relation These explain the deviation of conductance from expected values Tins also accounts for the changes m selectivity and in conductance- at high conductance state observed with a shift m bathing solution pH m using ST-channels (Menestrma 1986, krasilmkov ct al 1986 kiasilmkov and Sabnov 1989, kiasilmkov et al 1991, Beziukov and kasianowicz 1993)

C hannel Sizing Exper iments 3 6 1

A c k n o w l e d g e m e n t s We are grateful to Prof Wamber to A Varanda (Depar tment of Physiology Faculty of Medicine of Rib t i rao Pre to University of Sao Paulo SP Brazil) for valuable help with the manuscr ip t preparat ion We thank Dr S D Aird (Depar tment of Biophysics and Radiobiologv U F P E ) for critically reading the manuscr ip t Research suppor ted by C N P q (Brazil) and C A P E S (Brazil)

R e f e r e n c e s

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Final version accepted October 2, 1998