Biomembrane Electrochemistry - American Chemical Society

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18 Laser Doppler Scattering for the Determination of Ionic Velocity Distributions in Channels and Membranes Felipe Macias and Michael E . Starzak Department of Chemistry, State University of New York at Binghamton, Binghamton, NY 13902-6000

The Doppler shift of light scattered from a moving particle provides a direct measure of the velocity of the particle. Laser Doppler velocimetry is applied to the observation of the velocity distribution of potential-driven ions in gramicidin channels in bilayer membranes. The membrane-channel system constrains the ions to a limited range of directions. Because the length of the channel (2.6 nm) is small relative to the wavelength of the scattering light (632.8 nm), the scattering in the channels is constructive and produces a net observable signal as the sum of scattering from multiple, intrachannel ions. The frequency, or velocity, distribution is unimodal, which indicates that the intrachannel velocity is roughly constant as it traverses the channel. Potential binding sites within the channel produce small variations in the intrachannel velocity that are reflected in the width of the velocity-Doppler frequency distribution. For transmembrane potentials from 10 to 150 mV, the intrachannel average velocities range from 0.0375 to 0.238 m/s.

COMPLETE CHARACTERZ IATO IN OF THE KINETICS

o f m e m b r a n e channels requires a detailed understanding o f channel gating, selectivity, a n d i o n permeation. I o n permeation, the most basic o f the three phenomena, has b e e n described w i t h a n u m b e r o f distinct models. Discrete state models postulate one o r m o r e b i n d i n g sites w i t h i n the channel. T h e i o n then p e r 0065-2393/94/0235-0401$08.00/0 © 1994 American Chemical Society

In Biomembrane Electrochemistry; Blank, M., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1994.


402

BIOMEMBRANE ELECTROCHEMISTRY

meates through the channel i n a series o f discrete kinetic steps. Rate parameters describe m o t i o n f r o m b i n d i n g site to b i n d i n g site u n t i l the i o n appears o n the opposite side o f the m e m b r a n e ( I ) . Mathematically similar models postulate i o n - c h a n n e l states (e.g., two ions i n a single channel) and develop kinetics for the transitions between such stochastic states ( 2 ) . I n such formulations, the transition f r o m a state that defines a c h a n n e l w i t h a single i o n to a second state that defines a c h a n n e l w i t h two ions is a first-order kinetic process. A d d i t i o n a l states might be c h a n n e l states m o d i f i e d by the action o f some b i n d i n g external to the channels (3, 4). T h e total n u m b e r o f stochastic states can increase rapidly for c o m p l i c a t e d systems, a n d it becomes progressively m o r e difficult to determine w h e t h e r a g o o d fit o f the experi mental data using a large n u m b e r o f adjustable rate constants signifies an accurate mechanism for the permeation process. F o r multistep intrachannel i o n - b i n d i n g models, the formulation o f the rate constants for i n d i v i d u a l transitions is c o m p l i c a t e d b y the existence o f two parameters i n the flux expression. P a r l i n a n d E y r i n g ( 5 ) a n d Starzak (6) developed a flux expression for i o n flow through membranes or channels that used transition-state theory w h e r e the rate constant was characterized b y an activation energy barrier. F o r d i m e n s i o n a l consistency, this rate constant, k , appeared i n conjunction w i t h a length, X the distance i n the channel that the i o n must move to cross the energy barrier. {

i 5

T h e net flux, /, for ions w i t h concentration c at an intrachannel b i n d i n g site h is p r o p o r t i o n a l to the velocity w i t h w h i c h these ions progress to the next b i n d i n g site: {

{

/ = ι>Λ

F o r consistency, the E y r i n g - P a r l i n parameters, \ and k must be c o m b i n e d into a single local velocity, v for the transition f r o m state b to the next state. T h e flux is {

i9

i7

i

T h i s local velocity, rather than the rate constant, is the parameter o f interest. H o w e v e r , the magnitude o f the local velocity can still be described b y an energy barrier f o r m a l i s m :

w h e r e E is the barrier height, R is the gas constant, a n d Τ is the temperature. A determination o f all local velocities for an i o n w i t h i n a channel t h e n provides a complete description o f the i o n permeation. Stochas tic models that focus o n stochastic states, w h i c h i n c l u d e b o t h the channel a n d {


18.

M A C I A S A N D STARZAK

403

Laser Doppler Scattering

the i o n , must still b e formulated using rate constants or transition p r o b a b i l i ties a n d are less amenable to a local velocity analysis. I f i o n permeation involves a discrete binding-site mechanism, the n u m b e r o f distinct local velocities that must be d e t e r m i n e d w i l l increase w i t h the n u m b e r o f b i n d i n g sites. F o r example, the permeation o f a single i o n through a channel w i t h two discrete b i n d i n g sites requires six local velocities: three Downloaded by UNIV OF CALIFORNIA SAN FRANCISCO on December 9, 2014 | http://pubs.acs.org Publication Date: May 5, 1994 | doi: 10.1021/ba-1994-0235.ch018

that lead the i o n through the channel to the opposite bath and three that describe the i o n m o t i o n i n the opposite direction. U n d e r conditions w h e r e the reverse velocities make a negligible c o n t r i b u t i o n to the total flux (e.g., i n a large electric

field

that drives the ions to the opposite bath), a velocity

distribution for the i o n c o u l d consist o f three separate peaks for (1) the local velocity f r o m the solution to the first b i n d i n g site, (2) the local velocity f r o m the first intrachannel b i n d i n g site to the second site, and (3) a final local velocity for the i o n as it moves f r o m the second b i n d i n g site to the opposite bath. I f all local velocities for this two-binding-site case are identical, the velocity distribution w i l l coalesce to a single peak. Discrete

state models w i t h b i n d i n g sites suggest

that the i o n may

physically b i n d at the intrachannel b i n d i n g sites. I f b i n d i n g does occur, the velocity distribution can be significantly b r o a d e n e d because o f deceleration and acceleration as the i o n approaches a n d leaves the b i n d i n g site. T h e local velocity f o r m u l a t i o n for permeation is more forgiving because it assumes that these accelerations a n d decelerations are far shorter than the net transit time; that is, the i o n is i n a steady velocity state for each leg o f its journey. T h e i o n approaches the site w i t h one steady local velocity a n d rapidly assumes the second velocity as it passes the b i n d i n g site. T h e r e is no " b i n d i n g " , m e r e l y an abrupt change i n velocity. A l t h o u g h many permeation processes can be described effectively b y discrete state b i n d i n g sites w i t h i n the channel, they are not the only possible permeation mechanisms. T h e i o n may diffuse through the channel to reach the opposite bath. T h i s diffusional flow can be considered the l i m i t

of

discrete site diffusion because the n u m b e r o f discrete sites increases. I n such a m o d e l , the i o n cannot make the abrupt changes i n velocity that c o u l d characterize the finite site, discrete state m o d e l . T h e velocity, however, can change continuously as the i o n moves t h r o u g h the channel. A discrete state velocity distribution w o u l d evolve naturally to a continuous velocity distribu tion, w h e r e the relative numbers o f ions at each velocity i n the c o n t i n u u m o f velocities c o u l d be established. C o n t i n u u m models have b e e n

studied theoretically (7,

8)

a n d are

amenable to c o m p u t e r simulations ( 9 ) . I n addition, c o n t i n u u m models may be more consistent w i t h physical evidence that indicates that each prermeating i o n is accompanied b y a p l u g o f water molecules (10). These water molecules must also move through the channel w i t h local velocities a n d may act to ensure a more steady continuous i o n flow i n the channel.



404


A l t h o u g h the discrete state a n d c o n t i n u u m models are analyzed i n different ways, b o t h models must p r o d u c e a local velocity distribution for the ions w i t h i n the channel. A c o n t i n u u m velocity distribution might b e charac terized b y a single peak o f finite b a n d w i d t h that reflects velocity fluctuations w i t h i n the channel, whereas a discrete state m o d e l might consist o f several different peaks i n the distribution. S u c h velocity distributions have b e e n generated f r o m the models used because electrochemical experiments do not y i e l d detailed i n f o r m a t i o n o n the internal kinetic parameters. T h e s e parame ters are d e d u c e d f r o m the experimental data, w h i c h are generally the net currents observed for a series o f transmembrane potentials for a variety o f bath i o n i c components a n d concentrations. M o r e detailed i n f o r m a t i o n o n the nature o f intrachannel kinetics becomes accessible i f it is experimentally possible to deduce the velocity distribution o f the ions i n the channel. T h e g r a m i c i d i n channel is the ideal m e m b r a n e channel for a detailed study o f i o n permeation. T w o g r a m i c i d i n molecules d i m e r i z e i n a bilayer m e m b r a n e to f o r m an o p e n channel; potential-dependent gating processes to generate an o p e n channel are absent. R a n d o m current fluctuations can be observed, however, a n d have b e e n attributed to changes i n the c h a n n e l itself. These changes i n c l u d e conformation fluctuations o f the channel p r o t e i n ( I I ) , channel block (12), a n d i o n entry (13). A l t h o u g h most univalent ions are permeable i n the g r a m i c i d i n channel, the channel has some conductance properties that suggest that the p e r m e ation process may be more c o m p l i c a t e d than i o n motion d o w n a narrow " t u b e " . C h a n n e l " b l o c k " b y divalent cations is mechanistically complicated (14). A l s o , w h e n T l i o n is present as the sole permeant i o n , it is an excellent permeant i o n that retains linear behavior to very large transmembrane potentials (15). H o w e v e r , w h e n this i o n is present as the m i n o r i t y cation i n variable mole fraction solutions o f T l a n d N a , T l i o n severely limits set channel currents (16). S u c h anomalous behavior can b e elucidated i f the local velocity o f a specific i o n (e.g., T l ion) can be d e t e r m i n e d experimentally. I n fact, the laser D o p p l e r scattering technique produces a detectable scatter only w i t h the T l so that i o n motions w i t h i n the g r a m i c i d i n channels can be differentiated. +

+

+

+

+

+

Laser Doppler Velocimetry T h e elucidation o f a mechanism for the permeation o f cations i n g r a m i c i d i n channels requires a complete velocity distribution for these cations i n the channels. T h e distribution describes the fractional concentration or p r o b a b i l ity o f finding an i o n at a specific local velocity i n the channel. A n i o n that m o v e d t h r o u g h the channel at constant velocity w o u l d give an extremely narrow distribution; 1 0 0 % o f the ions are m o v i n g at that single local velocity. F o r a discrete state m o d e l w i t h two b i n d i n g sites, the distributions c o u l d


18.

MACIAS A N D STARZAK


405

involve three separate peaks i n the distribution i f the three forward local velocities dominate a n d are a l l different. T h e amplitudes o f the distribution peaks provide a direct measure o f the probability that the i o n moves w i t h a specific velocity; that is, the amplitudes are a measure o f the concentrations o f ions w i t h i n an ensemble o f channels that have a specific velocity. S u c h distributions give the full range o f local velocities f o r each set o f bath Downloaded by UNIV OF CALIFORNIA SAN FRANCISCO on December 9, 2014 | http://pubs.acs.org Publication Date: May 5, 1994 | doi: 10.1021/ba-1994-0235.ch018

concentrations, potentials, a n d other experimentally modifiable conditions. W h e n light is scattered f r o m a m o v i n g particle, the i n c o m i n g light o f frequency / is D o p p l e r - s h i f t e d to a n e w scattering frequency / ' . T h i s f r e q u e n c y / ' is directly proportional to the relative velocity, υ, o f the m o v i n g particle relative to the speed o f light, c:

f -A 1

7)

A l t h o u g h the frequency shift

Α/-Ι/-/Ί is small, it can be detected

as a difference

frequency w h e n the i n p u t

frequency, /, a n d Doppler-scattered frequency, / ' , are m i x e d i n a nonlinear detector. T h e observed difference frequency, Δ / , is υ

υ

c

λ

where λ is the wavelength o f the input light b e a m . Because a range o f i n p u t light wavelengths w o u l d generate a range o f frequency differences, such D o p p l e r scattering experiments are o p t i m i z e d w i t h narrow b a n d w i d t h laser excitation. F o r experiments w i t h a reference light b e a m a n d the D o p p l e r - s h i f t e d scattered light b e a m , the signal is o p t i m i z e d w h e n the amplitudes o f these two signals have approximately equal amplitudes a n d traverse equal o r in-phase path lengths (17), Because balanced amplitudes f o r the two signals can be difficult to establish experimentally, an alternative experimental c o n figuration is preferable. T h e laser b e a m is split into t w o equal amplitude halves that are t h e n displaced equal distances f r o m the optical axes. These displaced beams are then directed parallel to the optical axis a n d passed through a lens that refocuses t h e m onto the optical axis at a c o m m o n point ( F i g u r e 1). I f the b e a m angles relative to the optical axis are each a , the t w o optical beams give positive a n d negative projections o f υ sin α



406


Figure 1. The velocity components required for a net Doppler frequency difference for a crossed-beam system with reference angle a. The net velocity difference 2 ν sin a gives a Doppler shift Av = 2\sin ak~ . 1

A nonlinear detector w i l l detect the net frequency difference p r o d u c e d b y the difference o f these two velocity components as 2v sin α —

—

As illustrated i n F i g u r e 1, the frequency difference w i l l b e generated b y velocity components that are p e r p e n d i c u l a r to the optical axis o f the system. W h e n a h e l i u m - n e o n ( H e N e ) laser w i t h X = 632.8 n m is used as the input beams a n d the two e q u a l beams are separated a n d refocused to give a n intersection angle α = 10.72° f o r each b e a m , the relative velocity o f the scattering particles relates to the observed difference frequency as ν = 1.7 Χ 10~~ Δ ν m/s 6

Because a n o r m a l f o r the planar bilayer must b e oriented at some angle θ relative to the optical axis, o n l y a component o f the actual velocity is observed. T h i s component, w h i c h is perpendicular to the optical axis o f the system, c a n b e converted into the total velocity, v , as t

*

sin θ

sin θ

F o r observations at the standard orientation o f 4 5 ° f o r the H e N e laser, the total velocity is related to the observed frequency difference as v = 2.4 Χ 1 0 ~ Δ / m/s t

6


18.


407



Instrumentation A crossed-beam scattering system ( F i g u r e 2) was the p r e f e r r e d m e t h o d for low-intensity scattering because scattered light b a c k g r o u n d or pedestal ( 1 7 ) can be r e d u c e d . T h e b e a m f r o m a 2 0 - m W H e N e laser (Jodon) was separated into two equal beams that were displaced 25 m m f r o m the optical axis i n opposite directions i n the horizontal plane using a b e a m s p l i t t e r - d i s p l a c e r ( T S I , Inc.). T h e beams were reflected parallel to the m a i n optical axis i n the b e a m s p l i t t e r - d i s p l a c e r . A 5 0 - m m lens refocused these beams to a c o m m o n point o n the m a i n optical axis approximately 120 m m f r o m the lens. Because the intersecting beams diverged after the intersection point, they c o u l d be masked so that only scattered light was observed o n the optical axis. T h i s forward-scattered light was collected w i t h a telephoto lens a n d focused o n a pinhole. T h e light through the p i n h o l e was detected b y a p h o t o m u l t i p l i e r (1P21). Because the p h o t o m u l t i p l i e r acts as a nonlinear detector, the differ ence frequency between the two frequency components o f light scattered b y the two displaced beams appeared as a difference frequency i n the p h o t o m u l tiplier output. T h i s signal was d i r e c t e d to a M o h e r t z frequency spectrum analyzer ( H e w l e t t - P a c k a r d 3561A). A l t h o u g h a current-to-voltage converter was also used between the p h o t o m u l t i p l i e r a n d analyzer, this device d i d not improve the signal-to-noise ratio. T h e optical a n d electronic systems w e r e calibrated using flowing water seeded w i t h colloidal spheres ( D u p o n t L u d o x ) . T h e constant velocity solution flow was inserted into the b e a m intersection region w i t h the water flow perpendicular to the optical axis for direct detection of the total velocity for a

Phot.o- . multiplier! ens

Spectrum Analyzer

Figure 2. Block diagram of the laser Doppler gramicidin channel system.


408



single colloidal particle. A s each colloidal particle entered the b e a m intersec t i o n region, it p r o d u c e d a " t o n e b u r s t " spectrum that was captured o n a storage oscilloscope (Tektronix). T h e frequency w i t h i n each tone burst gave the D o p p l e r difference frequency and the velocity o f the colloidal particle that correlated w i t h the k n o w n flow velocity o f the water. Because laser D o p p l e r velocimetry has b e e n u s e d extensively to deter m i n e the velocity o f large charged particles i n electrophoresis (18-20), the velocities o f charged particles i n an a p p l i e d electric field were studied for further calibration o f the experimental configuration. T h e intersecting beams irradiated a water solution seeded w i t h charged latex microspheres (Interfacial D y n a m i c s ) . A field was a p p l i e d to move the microspheres i n a direction perpendicular to the m a i n optical axis. T h e velocity increased linearly w i t h the a p p l i e d field, w h i c h signaled a constant microsphere m o b i l i t y over the range o f fields studied. T h e s e test systems i n v o l v e d large single particles that serve as effective scattering centers. T h e scattering centers for i o n flows i n g r a m i c i d i n channels are the ions themselves. A l t h o u g h individual ions cannot scatter as effectively as a large colloidal sphere o r very large p r o t e i n , these ions w i l l all experience homogeneous, d i r e c t e d velocities w h e n they permeate the g r a m i c i d i n chan nels. T h e m e m b r a n e constitutes a region o f spatial a n d electrical homogene ity. T h e channel length is small relative to the wavelength o f the light so that scattered light f r o m ions i n a l l parts o f the c h a n n e l is essentially i n phase; that is, it interferes constructively. A channel transmits approximately 1 0 ions p e r second to p r o d u c e a large n u m b e r o f scattering centers i n a small spatial v o l u m e . T h i s scattering amplitude enhancement b y a large n u m b e r o f scatter i n g centers generates an observable i o n scattering signal. 7

Planar bilayer scattering experiments w e r e initially c o n d u c t e d i n a rectan gular c h a m b e r w i t h quartz w i n d o w s for b o t h the intersecting i n p u t beams a n d the Doppler-scattered light. T h e windows a n d bilayer n o r m a l were oriented at different angles relative to the optical axis b y p l a c i n g the c e l l o n a rotating base. T h e rectangular cell was replaced b y a cylindrical c e l l to p e r m i t a greater range o f orientation angles. I n b o t h cases, the m e m b r a n e was f o r m e d at a pinhole i n a support that separated the two solutions. M i c r o m e t e r - c o n t r o l l e d syringes that contained glycerin w e r e used to orient the m e m b r a n e exactly o n the optical axis o f the system. F i n e adjustment was obtained b y maximization o f the scattering signal that reached a photodiode that was inserted into the c h a m b e r b e h i n d the bilayer a n d support a n d lay along the optical axis. W h e n alignment was optimal, this photodiode was r e m o v e d a n d replaced b y a p l a t i n i z e d p l a t i n u m electrode for current measurements. A second electrode i n the opposite bath was used to apply the transmembrane potential. Planar bilayer membranes were f o r m e d f r o m solutions o f 25 m g o f glycerolmonooleate (Sigma C h e m i c a l ) i n 0.9 m L o f decane ( W i l e y ) . I n b o t h chambers, 0 . 1 - M solutions o f thallous acetate ( T l A c ) w i t h a trace of T l C l were


18.

MACA IS AND STARZAK Laser Doppler

409 Scattering

used. A l t h o u g h other univalent ions were used as permeant ions, T l gave the only observable signal w i t h b o t h membrane chambers. A potential r a m p was used to verify the presence o f the bilayer m e m b r a n e a n d the i n c o r p o r a tion o f gramicidin channels. T h e experiments w e r e p e r f o r m e d w i t h a constant transmembrane potential p r o d u c e d b y a b a t t e r y - p o t e n t i o m e t e r arrangement. Currents were r e c o r d e d using a current-to-voltage converter a n d were slightly Downloaded by UNIV OF CALIFORNIA SAN FRANCISCO on December 9, 2014 | http://pubs.acs.org Publication Date: May 5, 1994 | doi: 10.1021/ba-1994-0235.ch018

+

smaller than the currents generated b y the r a m p potentials. Some electrode polarization may have resulted f r o m the l o n g times at constant potential ( 1 0 - 1 5 m i n ) r e q u i r e d for spectral analysis o f the scattered light signal. T l i o n w i t h the largest atomic n u m b e r ( Z = 81) was the only i o n that gave consistent observable D o p p l e r scattering. M a r g i n a l signals were ob served for C s w i t h the rectangular cell but were not observed w i t h the cylindrical cell. N o D o p p l e r scattering was observed for R b , A g , or K . T h e T l spectrum was also observed using a 1 0 - M H z b a n d w i d t h spectrum analyzer (Tektronix) to verify the absence o f additional high-frequency bands. T h e 1 0 - M H z b a n d w i d t h encompassed all frequencies possible for the ions at the maximal electric field strength. +

+

+

+

+

+

Because m e m b r a n e surface waves can also p r o d u c e a D o p p l e r scattering signal (21), the frequency distribution for T l was observed w i t h the c e l l at a series o f angles relative to the optical axis. Because surface waves a n d i o n motions i n the channel move i n mutually p e r p e n d i c u l a r directions, it is possible to discern the direction o f m o t i o n that produces the D o p p l e r shift b y observing the change i n observed frequency difference w i t h a change i n the angle o f orientation. A s shown i n F i g u r e 3, the D o p p l e r frequency increased linearly w i t h the sine o f the angle o f orientation ( Φ ) between the optical axis a n d the membrane n o r m a l . T h e scattering is p r o d u c e d b y particle motions n o r m a l to the m e m b r a n e surface; that is, consistent w i t h the motions o f ions through channels. +

T h e frequency distributions for each potential constituted a single, connected spectrum. Some o f these difference spectra are shown i n F i g u r e 4. T h e average frequencies for these spectra are d e t e r m i n e d b y the spectrum analyzer for the 0 . 1 - M T l solutions w i t h the chamber oriented at 45° a n d are tabulated i n T a b l e I along w i t h their corresponding average velocities. T h e single spectral region suggests that the ions move through the c h a n n e l u n d e r a given transmembrane potential at a steady l i m i t i n g velocity w i t h m i n i m a l acceleration a n d deceleration. T h e bandwidths o f the single spectral regions for each potential ranged f r o m 200 to 1500 H z , w h i c h indicates some velocity fluctuations w i t h i n the channel. H o w e v e r , these fluctuations appear to be perturbations o f a dominant single permeation velocity. If b i n d i n g sites are present i n the region of the channel where the ions p r o d u c e the observed D o p p l e r scattering, these sites only serve to produce perturbations i n the steady velocity o f the permeating i o n . N o distinct spectral regions that indicate different velocities between different b i n d i n g sites w i t h i n the chan n e l are observed. +



410

6.500

ο χ

5.500Η


ο

φ

ν

4.500

ω

1

ϋ

c φ ID

σ

3.500Η

Φ

2.5000.450

0.525

τ 0.900

0.600

sin

Γ 0.975

φ

Figure 3. Variation in Doppler frequency with orientation angle of the membrane system. Doppler frequency and ion velocity increase as the motion becomes more perpendicular to the optical axis.

150 mV 99. khz

120 m V

85 mV

89.2 khz

7l.7khz

/y-

w~A^ V Δϋ

50mV 44.5khz

40mV 4l.7khz

25 m V 30.1 khz

l5mV 19.5 khz

Figure 4. Some typical Doppler spectra for Tl ions in gramicidin channels at different applied potentials. V is the applied constant potential, and Av is the average Doppler difference frequency. +

a

The

interior o f t h e g r a m i c i d i n c h a n n e l is postulated to serve as a

" w a t e r l i k e " environment for b o t h the permeant i o n a n d other water molecules i n the channel. I f the channel interior is similar to b u l k water, a permeant i o n is expected to have permeability properties similar to those o f t h e i o n i n water. T h i s c o n d i t i o n permits a n estimate o f the u p p e r limits o f i o n velocity


18.

M A C I A S A N D STARZAK


411

Table I. Velocities and Transit Frequencies for Tl(l) Ion in Gramicidin Channels


Potential (mV)

Observations

Doppler Shift (kHz)

Velocity (m /s Χ 10 )

Transit Frequency (s' X 10- ) 1.44

1

1

7

10

2

15.6 ± 0.19

0.375

15

1

19.5

0.469

1.80

20

2

24.2 ± 1.0

0.582

2.24

25

1

30.1

0.724

2.79

30

2

32.8 ± 0.8

0.788

3.03

40

3

40.8 ± 1.3

0.981

3.78

50

2

44.5 ± 1.4

1.09

4.21

60

2

54.3 + 0.1

1.31

5.01

70

2

61.2 ± 0.2

1.47

5.68

80

3

67.5 ± 0.5

1.64

6.30

90

3

73.5 ± 1.3

1.77

6.78

100

3

78.3 ± 0.6

1.88

7.21

110

3

83.8 ± 1.4

2.01

7.72

120

3

87.4 ± 1.2

2.10

8.10

130

3

92.3 ± 0.5

2.22

8.53

140

3

96.4 + 0.6

2.32

8.93

150

1

99.0

2.38

9.14

w i t h i n the channel. T h e maximal electric field is the field generated w h e n the m e m b r a n e acts solely as a n insulating barrier. I n this case, the maximal electric field is the transmembrane potential d i v i d e d b y the bilayer thickness. I f this field is m u l t i p l i e d b y the aqueous m o b i l i t y o f the permeant i o n (22), the resultant velocity w i l l b e a measure o f the maximal possible velocity for the i o n i n the m e m b r a n e . These velocities range f r o m 0.3 to 4.5 m/s f o r transmembrane potentials o f 10 a n d 150 m V , respectively. These maximal velocities are clearly an order o f magnitude larger than the observed v e l o c i ties for the channels, so channel permeation is probably m o r e c o m p l i c a t e d than simple aqueous diffusion. O f course, this hypothesis can only b e tested w i t h an accurate determination o f the electric field w i t h i n the channels. T h e velocity distribution observations d o n o t determine t h e i o n mobility i n t h e channel, w h i c h w o u l d p e r m i t a direct comparison o f the m o t i o n o f the i o n i n aqueous solution a n d w i t h i n the c o n d u c t i n g channel. T h e intrachannel velocities o f the ions are experimentally observable parameters and, as such, can b e used to determine other system parameters. Because t h e detailed velocities o f ions w i t h i n t h e channels have not b e e n d e t e r m i n e d using electrochemical techniques, estimates o f the motions o f ions through channels utilize other parameters such as the transit frequency, the n u m b e r o f ions that pass t h r o u g h a single channel at a given transmem brane potential each second (23, 24). Because t h e m o t i o n through t h e channels is essentially a constant velocity m o t i o n , the transit frequency can b e estimated f r o m t h e observed velocity a n d t h e distance traveled d u r i n g t h e


412


observation. F o r example, i f the observed velocity carries the i o n the entire w i d t h o f the m e m b r a n e , d, an i o n transit frequency, υ

ν

is defined as

υ


Vt

=

l

T h e transit frequencies are estimated a n d tabulated i n T a b l e I for a channel length o f 2.6 n m . T h e transit frequencies range f r o m 1.4 Χ 1 0 to 9.1 Χ 1 0 for a p p l i e d potentials f r o m 10 to 150 m V , respectively. T h e results are comparable to those obtained by A n d e r s e n a n d P r o c o p i o (23) for large transmembrane potentials. H o w e v e r , it is important to note that the actual distance covered at the observed velocity is not k n o w n w i t h certainty. Shorter distances o f steady velocity m o t i o n w i l l p r o d u c e a higher transit frequency. A t the same time, however, a delay t i m e near the c h a n n e l m o u t h w h i l e the i o n loses some waters o f hydration may significantly reduce the net transit frequency. T h e experiments detect only motions i n a region w h e r e the i o n moves w i t h a constant, d i r e c t e d velocity. 7

7

Discussion L a s e r D o p p l e r velocimetry permits observation o f a velocity distribution for T l ions w i t h i n the g r a m i c i d i n channel. T h e l i m i t e d velocity range observed for a given transmembrane potential indicates that the i o n probably moves through the channel at a constant velocity. T h e instrument is ideal for such measurements because it monitors the motions o f a large n u m b e r o f ions m o v i n g i n the same direction i n a l i m i t e d v o l u m e o f space. Ions i n solution or i n the interfacial region undergo a general direction m o t i o n as w e l l as other velocity a n d directional variations. D o p p l e r spectra f r o m such ions cannot p r o d u c e the constructive interference necessary for observable scattering. T h e technique has the ability to focus only o n those ions that are located w i t h i n the m e m b r a n e channels. +

Techniques that increase scattering amplitude can be used to increase the intensity o f the Doppler-scattered signal. F o r example, replacement o f the H e N e laser w i t h an argon-ion laser o f shorter wavelength w i l l p r o d u c e approximately a threefold increase i n the scattering amplitude. S u c h tech niques may make it possible to detect scattering f r o m smaller ions i n the channels (e.g., K or N a ) . H o w e v e r , the ability o f the system to detect only scattering f r o m T l ions constitutes an advantage i n some cases. T h e total n u m b e r o f ions i n a channel each second can be estimated v i a electrochemi cal measurements. Because the n u m b e r o f these ions that are T l can be d e t e r m i n e d using laser D o p p l e r velocimetry, it is possible to determine the fraction o f current carried b y each i o n i n studies w i t h m i x e d univalent ions. Because velocities w i t h i n the channels are the fundamental kinetic parameters, such studies to generate the velocity distribution for these ions +

+

+

+


18.



413


makes it possible to establish the best kinetic mechanism for the permeation of a n i o n through the channel a n d the kinetic parameters f o r this mechanism. Such detailed information c a n b e obtained for m o r e complicated ion-specific channels as w e l l . I n each case, the experiments provide detailed n e w i n f o r m a tion o n the permeation o f ions through the channels u n d e r the influence o f an a p p l i e d transmembrane potential.

Acknowledgment T h e support o f the office o f N a v a l Research ( G r a n t 1 4 8 7 K 0 3 0 1 ) is gratefully acknowledged.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

Lauger, P. Biochim. Biphys. Acta 1973, 311, 423-441. Finkelstein, Α.; Andersen, O . S. J. Member. Biol. 1981, 59, 155-171. Sandblom, J.; Eisenman, G . ; Neher, E . J. Membr. Biol. 1977, 31, 383-417. Sandblom, J.; Eisenman, G . ; Neher, E . In Metal Ligand Interactions in Organic and Biochemistry; Pullman, B., E d . ; Reidel: Dordrecht, Netherlands, 1977. Parlin, R.; Eyring, H. In Ion Transport in Membranes; Clarke, H. T., E d . ; Wiley: New York, 1954. Starzak, M. E . The Physical Chemistry of Membranes; Academic: Orlando, FL, 1984; pp 230-234. Helfrich, P.; Jordan, P. Biophys. J. 1990, 57, 1075-1084. Lauger, P. Biochim. Biophys. Acta 1976, 455, 493-509. Turano, B.; Chen, I., Busath, D . Biophys. J. 1989, 55, 503a. Rosenberg, P. Α.; Finkelstein, A . J. Gen. Physiol. 1978, 72, 327-335. Sigworth, F . J. Biophys. J. 1985, 47, 709-720. Heinemann, S. H.; Sigworth, F . J. Biophys. J. 1988, 54, 757-764. Heinemann, S. H.; Sigworth, F . J. Biophys. J. 1990, 57, 499-514. Bamberg, E.; Lauger, P. J. Membr. Biol. 1977, 35, 351-376. Andersen, O . S. In Renal Function; Giebisch, G . ; Purcell, E . , Eds.; Independent Publishing Group: Port Washington, N Y , 1977. Neher, E . Biochim. Biophys. Acta 1975, 401, 540-544. Drain, L. E. The Laser Doppler Technique; Wiley: Chichester, England, 1980; pp 85-118. Haas, D.; Ware, B. R. Anal. Biochem. 1976, 70, 506-525. Mohan, R.; Steiner, R.; Kaufmann, R. Anal. Biochem. 1976, 70, 506-525. Uzgiris, Ε . E. Rev. Sci. Instrum. 1974, 45, 74-80. Byrne, D.; Earnshaw, J. C . J. Phys. D 1979, 12, 1145-1157. Robinson, R. Α.; Stokes, R. H. Electrolytic Solutions; Butterworth: London, 1959; p 463. Andersen, O . S.; Procopio, J. Acta Physiol. Scand. Suppl. 1980, 481, 27-35. Andersen, O . S. Annu. Rev. Physiol. 1984, 46, 531-548.

RECEIVED 17,

for review M a r c h

14, 1 9 9 1 . A C C E P T E D

revised manuscript N o v e m b e r

1992.


Biomembrane Electrochemistry - American Chemical Society

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