Proc. Natl. Acad. Sci. USA
Vol. 75, No. 11, pp. 5669-5673, November 1978 Immunology
Steady-state analysis of tracer exchange across the C5b-9 complement lesion in a biological membrane (immune lysis/membrane channel/erythrocyte ghost)
PETER J. SIMS AND PETER K. LAUFt Department of Physiology, Duke University Medical Center, Durham, North Carolina 27710
Communicated by Hans J. Miller-Eberhard, August 10, 1978
ABSTRACT Resealed erythrocyte ghosts have been used to define the kinetics of tracer exchange across the membrane-bound terminal complex of the complement cascade (C5b-9). Under steady-state conditions and at net chemical equilibrium, C5b-9 ghosts showed no significant lysis above control levels as measured by hemoglobin efflux. In 1 mM sucrose at 370C, [14Cjsucrose isotopic exchange diffusion into CSb-9 ghosts occurred at 4.8 (+0.5, SEM) X 10-20 mol sec1 per
functional lesion, equivalent to an apparent permeability coefficient of 4.8 X 10-14 cm3 sec-1 for the single C5b-9 lesion. No significant uptake of [14C]sucrose above control levels was observed in C5b67 ghosts. The apparent rate of tracer permeation through the complement lesion is one to two orders of magnitude slower than predicted by a model of a transmembrane channel of dimensions permitting free diffusion of sucrose. The data support earlier assertions from this laboratory that diffusion of small molecules across the complement lesion in biological membranes is significantly restricted. The assembly of a single complex of the complement proteins C5b-9 on a cell membrane can result in the transmembrane equilibration of ions, and consequently, colloid osmotic lysis of the cell (1-3). Mayer (4) has proposed that the C5b-9 proteins form a water-filled annular structure inserted into the membrane, providing a diffusional channel (S*) for the dissipation of ionic gradients. The mechanism of solute equilibration across S* is unknown. The apparent activation energy for cell lysis by the assembled C5b-9 complex exceeds that of a free diffusional process, suggesting that some other process is rate limiting to the terminal stages of lysis (5). On the basis of the apparent permeability of the immune-damaged membrane as measured by osmotic flow, Lauf (6, 7) has argued that solute diffusion across S* is restricted and rate limiting to cell lysis, a possibility also raised by Hoffmann (8) in an analysis of the reported (9) rate of efflux of cell solute during immune lysis. Each of these studies, however, failed to distinguish experimentally between the rate of formation of S* and the rate of solute diffusion across S* per se. Consequently, multiorder rate relationships were obtained for the apparent kinetics of diffusion across the complement lesion (8). Definitive analysis of the observed kinetics was also precluded by the inability to maintain cellular steady state due to colloid osmotic lysis. Although measurement of ionic conductance across S* under steady-state conditions has been achieved in artificial membranes (10-12), interpretation of these data required the a priori assumption of free ionic mobility across S*. A precise determination of the rate of diffusion across S* in a biological membrane under steady-state conditions is therefore essential to a clarification of the nature of the membrane lesion generated by the insertion of the C5b-9 complex. The present report describes the measurement of the rate of steady-state exchange diffusion across the C5b-9 lesion in the erythrocyte membrane. The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U. S. C. §1734 solely to indicate this fact.
5669
MATERIALS AND METHODS Solutions. All solutions were freshly prepared in ultrafiltered deionized H2O to which was added 2 mg of chloramphenicol per liter (grade B, Calbiochem). KCIl/Tris: 165 mM KCI/2 mM Tris/1 mM sucrose, pH adjusted to 7.2 (230C) with 1 M HC1. KCI/Trls/EDTA: 1 vol of 0.1 M K3EDTA/1 mM sucrose mixed with 9 vol of KCI/Tris, pH 7.2 (23"C). Albumin buffer: 1 g of fatty-acid-free bovine serum albumin (Sigma) dissolved in 1 liter of KCl/Tris, pH 7.2 (230C). GPS buffer: 1 vol of guinea pig serum (GPS) mixed with 79 vol of KCl/Tris/ EDTA.
Complement Components. C5b6: The C5b6 complex was isolated from zymosan-(Sigma) treated human sera by a modification of the procedures of refs. 13 and 14. Human sera were screened for the "reactor state" (15) and 200-ml volumes were activated by incubation with zymosan (4 mg/ml) for 12 min at 370C. The zymosan was recovered by centrifugation and washed with ice-cold glucose (0.5 g/liter), and the C5b6 activity was eluted from the washed pellet with 0.5 M NaCl at 230C. The eluate was made 0.5 M NaCl, 0.05 M Tris, 1 mM NaN3 (pH 7.8, 40C), concentrated, and applied to a Sephadex G-200 column (1.5 X 90 cm) equilibrated with the sample buffer. Active fractions were eluted at 4"C, pooled, concentrated into KCl/Tris, and stored at -90'C until used. The product was determined to be free of C8 and C9 activity by hemolytic assay, and free of immunoglobulin by immunoelectrophoresis. C7: Human C7 was obtained from Cordis Corp., Miami, FL, and stored at -90'C until used. GPS: The GPS was absorbed three times at 00C with 1/10th vol of pooled human erythrocytes prior to storage at -900C. Preparation of Resealed Erythrocyte Ghosts. Hypotonically lysed and resealed erythrocyte ghosts were prepared by modification of the procedure of refs. 16 and 17. Erythrocytes from healthy human donors were washed and suspended to 40% (vol/vol) in 165 mM KCl and maintained at 00C (+0.50C) in a salted ice bath. One volume of the cell suspension was lysed in 10 vol of a 4 mM MgSO4/2 mM Na2ATP (Sigma) solution maintained at 00C (+ 0.20C). A pH at lysis of 6.0 (+0.1) was maintained by dropwise addition of 0.1 M Tris or 0.1 M HCL. The lysate was stirred 5 min at 0C and then made 165 mM KCl, 2 mM Tris, 1 mM sucrose (pH 7.2, 0°C) by the addition of 1 vol of 1.83 M KCI/25 mM Tris/12 mM sucrose at 0°C. In some experiments, [14C]sucrose (New England Nuclear) was added to the lysate prior to resealing. The lysate was maintained at 0°C for 15 min and then at 37°C for 1 hr. The hemoglobin concentration [Hb] of the lysate was determined spectrophoAbbreviations: C5, C6, etc., refer to individual components of the complement system. C5b6 denotes a stable complex of the "b" fragment of C5, and C6; CMb-9, the complex of C5b, C6, C7, C8, and C9. S*, a functional lesion in the membrane due to the inserted C5b-9; GPS, guinea pig serum; Hb, hemoglobin; r, statistical correlation coefficient. t To whom reprint requests should be addressed.
5670
Immunology: Sims and Lauf
tometrically at 415 nm (range, 9-12 g/liter). The resealed sucrose-impermeable ghosts were isolated by centrifugation on a sucrose cushion (16) and then washed and suspended to 2 X 109/ml in KCl/Tris (40C) for use the same day. The number of ghosts was estimated from the [Hb] in the lysate at resealing, utilizing a mean corpuscular volume of 94.1 fl and cell H20 of 969 g/kg of ghosts (17). Preparation of Cellular Intermediates. C5b67 ghosts: C7 was added to the ghost suspension (100 Cordis units/109 cells), which was placed in a 370C bath. The cells were then mixed with an equal volume of an appropriate dilution of C5b6 (in KCl/Tris) to yield the desired number of potential S*. One unit was defined as the amount of C5b6 required to ultimately cause the release of 63% of trapped [14C]sucrose. After 15 min at 370C the C5b67 ghosts were recovered by centrifugation and washed three times in KCl/Tris/EDTA (40C). C5b-9 ghosts: C5b67 ghosts were made C5b-9 by incubation (1 X 109/ml) in GPS buffer (10 mM EDTA) for 60 min at 37°C. In preliminary experiments, the generation of S* on C5b67 ghosts during incubation in GPS buffer was determined by measuring the release of [14C]sucrose incorporated into ghosts at the time of resealing. Tracer-loaded C5b67 ghosts, and controls not exposed to C5b6 + C7, were each suspended in GPS buffer (10 mM EDTA) at 370C. Aliquots were withdrawn at 15-min intervals and centrifuged, and the radioactivities of the supernatant and cell pellet were determined. Cell lysis was simultaneously determined by the release of initial ghost Hb, measured spectrophotometrically at 415 nm. Additional controls included C5b67 ghosts and complement-free ghosts suspended at 37°C in GPS buffer heat inactivated at 100°C for 2 min. Kinetics of Tracer Influx. C5b-9 ghosts prepared under conditions generating from 0.2 to 0.8 mean S* per cell were utilized to measure the kinetics of [14C]sucrose influx through S* under steady-state conditions. Samples (2 X 109) of C5b-9 ghosts, C5b67 ghosts, and complement-free controls were recovered by centrifugation and washed three times in albumin buffer (4°C). The washed ghost pellets were suspended to approximately 20% (vol/vol) in albumin buffer, capped tightly, and placed in a 370C shaker bath. After a preincubation period of either 5 min or 3 hr. 3 ,uCi (1 Ci = 3.7 X 1010 becquerels) of [14C]sucrose (delivered as 1 mM net sucrose in albumin buffer) was injected into each suspension. At recorded times, 50-pi samples of each suspension were withdrawn, injected into a tube containing 35 ml of albumin buffer at 00C, and immediately centrifuged at 0°C. The pellet was lysed in a fixed aliquot of detergent, and Hb and radioactivity were measured. Elapsed time at 00C was 6-7 min, during which the backflux of tracer was determined to be less than 3%. The specific activity of sucrose in the cell water was calculated and expressed as a ratio to that in the total cell suspension. Percent cell lysis was determined as described above.
Proc. Natl. Acad. Sci. USA 75 (1978) Table 1. Release of [14C]sucrose and Hb as a function of S* assembly on human erythrocyte ghosts Treatment % release (2 hr, 370C) GPS buffer C5b6, Hb C7 (10 mM EDTA) units ['4C]Sucrose 3+2 + 83 5 + 2 2+1 + + 63±9 1 3 1 + 50+7 + 0.5 + 34 3 3± 2 + 0.25 Controls 3+1 + 3i2 Heatinactivated 1 2±1 3 1 + 2± 1 3 i2 Heat inactivated
Ghosts resealed to tracer [14C]sucrose were made C5b67 by incubation (15 min, 370C) in various amounts of C5b6 plus 100 units of C7 (+). Ghosts were then made C5b-9 by suspension (109 per ml, 370C) in GPS buffer (+). Percent release (mean + SEM) of initial radioactivity and Hb was determined at the end of 2-hr incubation in GPS buffer as described in text. Controls: C5b67 ghosts suspended (2 hr, 370C) in GPS buffer that had been heat inactivated (1000C, 2 min) and ghosts not pretreated with C5b6 plus C7 (-) before suspension in either GPS buffer (+) or heat-inactivated GPS buffer. GPS buffer contains 10 mM EDTA.
the cells were pretreated, suggesting conversion of C5b67 sites to S*. No tracer was released from controls incubated-in GPS buffer (10 mM EDTA) alone, confirming that neither the classical nor the alternative pathway was activated. C5b-9 ghosts washed free of GPS buffer after 1 hr and then suspended in albumin buffer showed no lysis above control levels during subsequent incubation at 370C (Fig. 1 upper). However, when suspended in KCl/Tris in the absence of added serum proteins, C5b-9 ghosts underwent a protracted lysis significantly above control levels (not shown). Kinetics of Tracer Exchange. Fig. 1 presents the data of one typical experiment for tracer influx at 370C into C5b-9 ghosts incubated at net chemical steady state (sucrose = 1 mM). Ghosts pretreated under conditions to generate S* on approximately 30% of the population were suspended in albumin buffer at 37O. * 1! 10 1( ._
E l I
CL
a
3
W
N.
I-
N.
RESULTS Assembly of C5b-9 Cells under Nonlytic Conditions. Table 1 summarizes the results obtained after treatment of [14C]sucrose-loaded ghosts with the terminal complement components. In the absence of a source of C8 + C9, ghosts preincubated with C5b6 + C7 and then suspended at 37CC remained impermeable to sucrose and showed no lysis above control levels, as measured by Hb release. During prolonged (>2 hr) incubation at 37°C, all three controls released tracer at 1-2% per hr, entirely accounted for by nonspecific lysis. When C5b67 ghosts were suspended in GPS buffer (10 mM EDTA) as a source of C8 + C9, tracer was released with no lysis detected above control levels. The equilibrium exchange of tracer was directly related to the amount of C5b6 with which
FIG. 1. (Lower)
Hours [14C]Sucrose tracer influx measured for C5b-9
ghosts (e-*) and C5b67 controls (L---A) suspended in albumin buffer at 37°C, sucrose = 1 mM. Tracer additions were made after preincubation period of 3 hr, 370C. Data of single experiment; each point and bar represent mean and SEM of three determinations. The abscissa is elapsed time after tracer addition; the ordinate is the ratio (Y/Y8yp) of the specific activity of sucrose in ghost water to that in the total suspension. (Upper) Lysis of C5b-9 ghosts (-) and C5b67 controls (M) during the same experiment. Lysis was determined from the percent release of initial ghost Hb, as measured at 415 nm.
Immunology:
Proc. Natl. Acad. Sci. USA 75 (1978)
Sims and Lauf
Controls included C5b67 and complement-free ghosts (not shown). After a preincubation period of 3 hr, tracer was added to each flask and the specific activity of the sucrose in the washed ghost pellets was determined. In the experiment shown as well as in eight additional experiments, lysis of C5b-9 and control ghosts did not exceed 2% per hr. Uptake of tracer by C5b67 controls did not significantly differ from tracer uptake by complement-free controls. Analysis. Under conditions of net chemical steady state, bidirectional exchange, and isotopic indistinguishability, the specific activity (Y*) of cells permeable to tracer added extracellularly may be related to a first-order rate constant (k) by 1 - (Y*/y*if) = exp(-kt), [1] in which y*if is the specific activity of sucrose in the permeable cell compartment at equilibrium and t is time (18). Assuming that tracer equilibrates across only those cells with at least one S*, Y* will be related to the observed specific acitivity of sucrose in the cell pellet (Y) by the relationship Y* = Y/F*, in which F* is the fraction of the cell population with at least one lesion. After equilibration of tracer, the specific activity of sucrose in the permeable cells is well approximated by that in the total suspension: Y*inf = Ysusp Substituting for Y* and y*inf, Eq. 1 may be rewritten 1-
*
= exp(-kt).
[2]
In Fig. 2, the data of Fig. 1 for tracer exchange into C5b-9 ghosts are replotted with correction at each time point for nonspecific uptake of sucrose, as determined by the specific activity in the C5b67 controls. The solid lines are generated from Eq. 2 with coefficients F* and k determined by reiterative least squares analysis of the corrected data, utilizing an error minimization routine on 1 - r2. In this, as in all experiments (Table 2), tracer flux into the C5b-9 ghosts was well approximated (IrI > 0.98) by Eq. 2. Permeability to Sucrose of the C5b-9 Lesion. The apparent flux (J) of sucrose due to C5b-9 lesions was calculated from the slope (k) of the semilogarithmic regression plot (Inset, Fig. 2) according to aj
1.0
cf
0.1
0.01
-
0.001
0..
&:
2
1.0
Hours
0.31-
I
Table 2. Steady-state analysis of [14C]sucrose tracer flux across S*
J.
k, F*
0.23 0.31 0.34 0.35 0.55
hr)l
Irl
nmol hr-1
X
N* * 10-7 molecules sec1
Grdup 1. Five-minute preincubation, 370C 3.53 2.49 0.986 6.52 31,000 1.64 0.998 4.36 3.74 20,000 3.59 0.995 10.28 4.13 42,000 1.24 0.996 4.42 5.29 14,000 7.47 6.83 0.996 1.93 18,000 Group 2. Three-hour preincubation, 370C 5.68 2.87 0.998 2.55 3.40 0.982 7.47 2.93 0.997 9.31 4.29 3.02 9.27 5.82 0.996 2.61
33,000 43,000 36,000 27,000 Results of steady-state analysis of data from nine separate experiments, for [14Cjsucrose isotopic exchange diffusion into C5b-9 ghosts suspended at 370C. Each line represents the results obtained from a single experiment, as described for Figs. 1 and 2 (see text). Group 1: experiments in which C5b-9 ghosts and controls were preincubated at 370C for 5 min prior to addition of tracer; group 2: 3-hr preincubation at 371C prior to tracer addition. From data of nine experiments,j* = 29,000 (43000, SEM) molecules sec-1 (4.8 ± Q.5 x 10-20 mol sec-1). Symbols: F*, k, coefficients of least squares regression (from Eq. 2); r, correlation coefficient of least squares regression; J, apparent unidirectional flux calculated from Eq. 3; N*, total number of lesions determined by Poisson analysis, see ref. 4; j*, unidirectional flux per single S* (J/N*). t Denotes experiment depicted in Figs. 1 and 2. 0.19 0.25 0.27t 0.49
J = k * [sucrose] (v* * v,)/(v* + v,), -
[3]
in which v* is the volume of cells exchanging tracer and v,,c is the volume of the extracellular space (18). Assuming that all S* are identical and that tracer exchange at one is independent and kinetically indistinguishable from that at any other, the flux across a single S* (j*) is obtained from J by dividing by the total number of S*. The number of S* is estimated by applying the Poisson distribution to the end point of tracer exchange to predict the mean number of lesions per cell (4) and multiplying by the number of cells in each experiment. In nine experiments (Table 2), j* was determined to be 4.8 (±0.5, SEM) X 10-20 mol sec-1 per single S* at 37°C. On the basis of Student's t test, there was no significant difference (0.80 < P < 0.85) between j* determined in ghosts preincubated 5 min before tracer addition (Group 1 of Table 2) and from those preincubated for 3 hr (Group 2). The unidirectional flux of tracer determined for a single S* per ghost in the presence of 1 ,mol cm-3 of sucrose can be used to calculate an apparent permeability (P*)t of 4.8 X 10-14 cm3 sect for diffusion across S* at 37'C.§
0..1
0.1,u1
II 0.5 Hours
1.0
FIG. 2. Steady-state kinetic analysis of data of Fig. 1, for [14C]flux across S*. 0, Data points for sucrose uptake by C5b-9 ghosts after correction for nonspecific uptake as determined by the specific activity in the C5b67 controls (see Fig. 1). Solid curve was generated by computer from Eq.-2, using a numerical approximation by reiterative least squares analysis to coefficients F* and k. The abscissa is elapsed time after tracer addition; the ordinate is the ratio (YYSUSP) of the corrected specific activity of sucrose in the C5b-9 ghost water to that in the total suspension. (Inset) Semilogarithmic graph of corrected data, plotted according to Eq. 2 with coefficients F* and k determined by least squares analysis; r = 0.99. Numerical approximations to F* and k are given in Table 2. sucrose
5671
t P; (dimensions: cm3 sec'1) represents an apparent permeability for the single S* (P* = j*/[sucrose]) and disregards the effective area (A*) of the C5b-9 lesion, which is unknown. This coefficient permits analysis of transport properties of S$ without introduction of assumptions about the geometry of the putative C5b-9 channel. The apparent permeability per lesion is related to the true permeability (P*) per lesion area (dimensions: cm sec'1) by the relationship P* - P*I/A*. § Under certain conditions, the observed rate of tracer permeation through a biological membrane may be significantly limited by the rate of diffusion across the unstirred layer of solvent at the membrane boundary. In the present experiments, the maximum thickness of this layer (in the absence of stirring) can be estimated to be 2.7 Am; diffusion of tracer across this layer would contribute less than one part in 106 to the observed kinetics of exchange across S* and, therefore, was neglected in the present analysis.
5672
Proc. Natl. Acad. Sci. USA 75 (1978)
Immunology: Sims and Lauf
DISCUSSION Calculation of the rate of solute diffusion across S* from the measured kinetics of tracer exchange depends upon three conditions: (i) C5b-9 ghosts are at chemical steady state with respect to the extracellular compartment. (ii) Tracer entry into C5b-9 ghosts occurs only by the pathway of preformed S*. (iii) The number of S* remains constant during the period of observation. To establish the first condition, net flux of sucrose was precluded by incubation at chemical equilibrium. In the absence of significant lysis of C5b-9 ghosts (Fig. 1), it can be assumed that no significant net water movements occurred. Undetected volume changes to less than the critical hemolytic volume (19) would not have significantly altered the interpretation of the data. In compliance with the second condition, tracer exchange (above small background levels) was observed only after exposure of C5b67 cells to a source of C8 + C9 (Table 1), demonstrating that the generation of the C5b67 site was a necessary but not sufficient step for the assembly of the exchange pathway. The background level of tracer exchange observed for all controls during prolonged incubation at 370C can be entirely accounted for by a slow nonspecific lysis. The third condition required that the assembly and decay of S* were controlled to keep the number of lesions constant during the period of isotopic exchange. The significance of this condition is underscored by the observation (8) that solute exchange prior to immune lysis obeys non-first-order kinetics, suggesting compound rate processes. The use of C5b-9 ghosts washed free of fluid phase components prevented the assembly de novo of C5b-9 sites during incubation in albumin buffer. The rate of tracer entry into ghosts that had been preincubated for 3 hr, a period exceeding any observed time constant (k'1, see Eq. 2) for tracer exchange (groups 2, Table 2), did not significantly differ from the rate of entry into ghosts preincubated only 5 min (group 1). Therefore, S* activation from bound C5b-9 complexes was essentially complete prior to the time of the earliest tracer addition, and could not have been rate limiting to tracer equilibration. The report (20) that S* insertion at 370C is complete within 3 min after assembly of the C5b-9 complex supports this conclusion. Although the decay of S* during prolonged incubation cannot be discounted (5), the data from both experimental groups remained monotonic to the origin and were well fitted (Ir > 0.98) by a first-order function (Eq. 2) throughout the 1-hr sampling period. Hence the data reflect only the kinetics of tracer exchange. Kinetics of Transport Across S*. As revealed by the electron microscope, the lesion associated with the C5b-9 complex displays a central core of approximately 100-A diameter (21, 22). An unrestricted water-filled cylindrical channel of this diameter and sufficient length to span the membrane should permit the free diffusion of small ions with permeability coefficients approaching 25 cm sec-1.1 For example, a single lesion of this dimension on a sheep erythrocyte [for which kinetic data have previously been reported (5, 6, 8, 9)] would lead to the equilibration of cellular ions with an initial rate coeffiPermeability to NaCl and KCI calculated assuming free diffusion through a uniform transmembrane channel of 75-A length. Diffusion coefficients (D) for NaCl and KCI in aqueous solution obtained from ref. 23 and corrected to 300C according to method suggested by ref. 24: P* (300C) = D (300C)/75 A, in which D (NaCl, 300C) = 1.67 X lo-5 cm2 sec-1 and D (KCI, 30'C) = 2.08 X lo-5 cm2 sec1.
cient of 0.9 sec1 at 30'C. 1 Because the rate coefficient reported for Hb release from a sheep erythrocyte due to iysis by a single S* at 300C is less than 0.0004 sec-1 (8, 9), free diffusion of ions across the C5b-9 lesion cannot be rate limiting to lysis. A comparison of the activation energy observed for immune lysis to that for free diffusion also leads to this conclusion (5). The present data, obtained under conditions not rate limited by S* formation, demonstrate that the diffusion of small molecules across S* is significantly restricted. Size of the C5b-9 Channel. In the absence of reliable information about the selectivity of S* to diffusing molecules of various geometries and ionic charge, it would be premature to attempt to deduce the geometry of the C5b-9 lesion from the present data. Nevertheless, the determination of the diffusional kinetics of a nonelectrolyte of known dimension does permit an estimate of the apparent cross sectional area of the lesion, and invites comparison to the data of other reports. If the C5b-9 complex forms a cylindrical channel with an internal diameter of 100 A as suggested by its appearance by electron microscopy (21, 22), the present data (obtained at 370C) suggest that its permeability to sucrose (P* = P*/7.9 X 10-13 cm2) is only 0.06 cm sec-1, two orders of magnitude slower than the permeability to freely diffusing sucrose at 370C (9.2 cm sec'1) as predicted by Fick's Law (23, 24). Thus the effective area available for diffusion across S* must be significantly smaller than the internal dimension of the C5b-9 complex suggested by electron microscopy, and restrictions to free diffusion encountered by solute traversing S* must be considered. As discussed by Renkin (27), the apparent rate of diffusion of nonelectrolytes through inert pores of molecular dimensions can be well approximated by a theoretical formulation that corrects for steric hindrance encountered by the solute at the entrance of the pore and the frictional resistance experienced within the channel. This formulation (equation 11 of ref. 27) permits an estimation of the equivalent pore radius of S* on the basis of the apparent effective area for free diffusion (5.2 X 10-15 cm2), determined from the present data (P*) and the free diffusional permeability to sucrose at 370C (above). This analysis suggests an equivalent pore radius of 11.7 A for SP. Whether solute diffusion in fact occurs across only a small segment of the C5b-9 complex or is restricted by a permeability barrier distributed over its entire area remains to be determined. Recent estimates of the size of S* have been made on the basis of the mean conductance step recorded during C5b-9 assembly on voltage-clamped lipid bilayers (10, 12). Although the dimensions reported are comparable to the dimension suggested by the present analysis, it must be emphasized that they were derived on the basis of the a priori assumption of free ionic (Na+) mobility within the C5b-9 channel, an assumption difficult to reconcile with the present data and other observations upon biological membranes (6-8). For example, a single such lesion on a sheep erythrocyte permitting free transmembrane diffusion of ions would result in the apparent unidirectional flux of Na+ and K+ at 300C with rate coefficients exceeding 0.04 1 Initial first-order rate coefficient calculated for unidirectional flux of solute across a single channel of area [A * = 7r(50 A)21 ssuming P* = 25 cm sec-1. Cell water (v) is that for a sheep erythrocyte (25, 26): k P*A*/v [4] =
= =
(25 cm sec-1) (7.9 X 10-13 cm2)/(2.1 X 10-1" cm3) 0.9
sec .
Immunology:
Sims and Lauf
sec-1,tt as compared to the apparent single-lesion rate coefficient of 0.00085 sec-1 reported for 86Rb efflux from sheep erythrocytes during immune lysis at 300C (8). It has also been reported that conductance increments equivalent to transmembrane channels of 6 A and 12 A were observed upon exposure of black lipid membranes to C5b6 and C5b67, respectively (12). Because this finding also contrasts the demonstrated impermeability of C5b67 ghosts to [14C]sucrose (cf. Table 1 and Fig. 1), and the stability of C5b6- and C5b67-treated erythrocytes (15), it appears premature to directly equate conductance fluctuations observed in lipid bilayers to permeability changes induced in biological membranes by the complement pro-
Proc. Natl. Acad. Sci. USA 75 (1978)
5673
3. Miller-Eberhard, H. J. (1975) Annu. Rev. Biochem. 44, 697724. 4. Mayer, M. M. (1972) Proc. Natl, Acad. Sci. USA 69, 29542958. 5. Li, C. K. N. & Levine, R. P. (1977) Immunochemistry 14, 421-428. 6. Lauf, P. K. (1975) J. Exp. Med. 142,974-988. 7. Lauf, P. K. (1978) in The Physiological Basis for the Disorders of Bio-Membranes, eds. Andreoli, T. E., Fanestil, D. & Hoffman, J. F. (Plenum, New York), pp. 369-398. 8. Hoffmann, L. G. (1969) Immunochemistry 6,309-325. 9. Hingson, D. J., Massengill, R. K. & Mayer, M. M. (1969) Immu-
nochemistry 6,295-307.
teins.
10. Wobschall, D. & McKeon, C. (1975) Biochfm. Blophys. Acta 413,
The present data suggest that the C5b-9 complex in a biological membrane provides a significantly restricted diffusional pathway for solute exchange; alternative models, however, may be suggested. For example, if the C5b-9 lesion exhibited multiple conductance levels, or fluctuated between "open" and "closed" states [compare alamethicin (28) and excitabilityinducing material (29)], the slow permeation of a small molecule such as sucrose could be reconciled with the apparent transport of relatively large molecules such as inulin and ribonuclease (30). In this context, the large variability in the conductance step size (10) and its sensitivity to applied electrical potential (11) as observed during S* activation on lipid bilayers is of interest. The present data do not permit any distinction to be made between models, but suggest that additional insight into the structure of the membrane-bound C5b-9 complex is to be acquired by further characterization of its selectivity and transport kinetics. Accordingly, investigation of the selectivity of S* as a function of the size and chemical structure of the diffusing molecule is called for.
11. Michaels, D. W., Abramovitz, A. S., Hammer, C. H. & Mayer, M. M. (1976) Proc. Nati. Acad. Sci. USA 73,2852-2856. 12. Michaels, D. W., Abramovitz, A. S., Hammer, C. H. & Mayer, M. M. (1978) J. Immunol. 120, 1785 (abstr.). 13. McLeod, B., Baker, P. & Gewurz, H. (1974) Immunology 26, 1145-1157. 14. Baker, P. J., Rubin, L. G., Lint, T. F., McLeod, B. C. & Gewurz, H. (1975) Clin. Exp. Immunol. 20, 113-124. 15. Lachmann, P. J. & Thompson, R. A. (1970) J. Exp. Med. 131,
We thank Dr. P. Baker for her generous assistance in the isolation and purification of C5b6 and M. Johnston for writing the computer programs used in the data analysis. This work was supported in part by U.S. Public Health Service Grants 2-PO1-HL 12157 (to P.K.L.) and S07-RR-07070-12 and Medical Scientists Traineeship GM07171 (to P.J.S). tt Calculated from Eq. 4 assuming P*
= 20 cm sec- and A * that for 11-A-radius pore. P* derived from Fick's law, assuming diffusion coefficient (300C) of 1.5 X 10-5 cm2 sec-1. an
1. Green, H., Barrow, P. & Goldberg, B. (1959) J. Exp. Med. 110, 699-713. 2. Mayer, M. M. (1961) in Immunochemical Approaches to Problems in Microbiology, eds. Heidelberger, M. & Plescia, 0. J. (Rutgers Univ. Press, New Brunswick, NJ), pp. 268-279.
317-321.
643-657. 16. Schwoch, G. & Passow, H. (1973) Molec. Cell. Biochem. 2, 197-218. 17. Funder, J. & Wieth, J. 0. (1976) J. Physiol. 262, 679-698. 18. Gardos, G., Hoffman, J. F. & Passow, H. (1969) in Laboratory Techniques in Membrane Biophysics, eds. Passow, H. & Stamppli, R. (Springer, New York), pp. 9-20. 19. Valet, G. & Opferkuch, W. (1975) J. Immunol. 115, 10281033. 20. Boyle, M. D. P., Langone, J. J. & Borsos, T. (1978) J. Immunol. 120, 1721-1725. 21. Humphrey, J. H. & Dourmashkin, R. R. (1969) Adv. Immunol.
11,75-115. 22. Tranum-Jensen, J., Bhakdi, S., Bhakdi-Lehnen, B., Bjerrum, 0. J. & Speth, V. (1978) Scand. J. Immunol. 7, 45-56. 23. Weast, R. C., ed. (1977) Handbook of Chemistry and Physics (Chemical Rubber Co., Cleveland, OH), 58th Ed., p. F62. 24. Kabat, E. A. & Mayer, M. M. (1961) Experimental Immunochemistry (Thomas, Springfield, IL), 2nd Ed., pp. 675-686. 25. Tosteson, D. C. & Hoffman, J. F. (1960) J. Gen. Physiol. 44, 169-194. 26. Valet, G., Franz, G. & Lauf, P. K. (1978) J. Cell Phys. 94, 215-227. 27. Renkin, E. M. (1955) J. Gen. Physiol. 38,225-243. 28. Eisenberg, M., Hall, J. E. & Mead, C. A. (1973) J. Membr. Biol. 14, 143-176. 29. Ehrenstein, G., Lecar, H. & Nossal, R. (1970) J. Gen. Physiol. 55, 119-133. 30. Giavedoni, E. B. & Dalmasso, A. P. (1978) J. Immunol. 120, 1774-1775 (abstr.).
Vol. 75, No. 11, pp. 5669-5673, November 1978 Immunology
Steady-state analysis of tracer exchange across the C5b-9 complement lesion in a biological membrane (immune lysis/membrane channel/erythrocyte ghost)
PETER J. SIMS AND PETER K. LAUFt Department of Physiology, Duke University Medical Center, Durham, North Carolina 27710
Communicated by Hans J. Miller-Eberhard, August 10, 1978
ABSTRACT Resealed erythrocyte ghosts have been used to define the kinetics of tracer exchange across the membrane-bound terminal complex of the complement cascade (C5b-9). Under steady-state conditions and at net chemical equilibrium, C5b-9 ghosts showed no significant lysis above control levels as measured by hemoglobin efflux. In 1 mM sucrose at 370C, [14Cjsucrose isotopic exchange diffusion into CSb-9 ghosts occurred at 4.8 (+0.5, SEM) X 10-20 mol sec1 per
functional lesion, equivalent to an apparent permeability coefficient of 4.8 X 10-14 cm3 sec-1 for the single C5b-9 lesion. No significant uptake of [14C]sucrose above control levels was observed in C5b67 ghosts. The apparent rate of tracer permeation through the complement lesion is one to two orders of magnitude slower than predicted by a model of a transmembrane channel of dimensions permitting free diffusion of sucrose. The data support earlier assertions from this laboratory that diffusion of small molecules across the complement lesion in biological membranes is significantly restricted. The assembly of a single complex of the complement proteins C5b-9 on a cell membrane can result in the transmembrane equilibration of ions, and consequently, colloid osmotic lysis of the cell (1-3). Mayer (4) has proposed that the C5b-9 proteins form a water-filled annular structure inserted into the membrane, providing a diffusional channel (S*) for the dissipation of ionic gradients. The mechanism of solute equilibration across S* is unknown. The apparent activation energy for cell lysis by the assembled C5b-9 complex exceeds that of a free diffusional process, suggesting that some other process is rate limiting to the terminal stages of lysis (5). On the basis of the apparent permeability of the immune-damaged membrane as measured by osmotic flow, Lauf (6, 7) has argued that solute diffusion across S* is restricted and rate limiting to cell lysis, a possibility also raised by Hoffmann (8) in an analysis of the reported (9) rate of efflux of cell solute during immune lysis. Each of these studies, however, failed to distinguish experimentally between the rate of formation of S* and the rate of solute diffusion across S* per se. Consequently, multiorder rate relationships were obtained for the apparent kinetics of diffusion across the complement lesion (8). Definitive analysis of the observed kinetics was also precluded by the inability to maintain cellular steady state due to colloid osmotic lysis. Although measurement of ionic conductance across S* under steady-state conditions has been achieved in artificial membranes (10-12), interpretation of these data required the a priori assumption of free ionic mobility across S*. A precise determination of the rate of diffusion across S* in a biological membrane under steady-state conditions is therefore essential to a clarification of the nature of the membrane lesion generated by the insertion of the C5b-9 complex. The present report describes the measurement of the rate of steady-state exchange diffusion across the C5b-9 lesion in the erythrocyte membrane. The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U. S. C. §1734 solely to indicate this fact.
5669
MATERIALS AND METHODS Solutions. All solutions were freshly prepared in ultrafiltered deionized H2O to which was added 2 mg of chloramphenicol per liter (grade B, Calbiochem). KCIl/Tris: 165 mM KCI/2 mM Tris/1 mM sucrose, pH adjusted to 7.2 (230C) with 1 M HC1. KCI/Trls/EDTA: 1 vol of 0.1 M K3EDTA/1 mM sucrose mixed with 9 vol of KCI/Tris, pH 7.2 (23"C). Albumin buffer: 1 g of fatty-acid-free bovine serum albumin (Sigma) dissolved in 1 liter of KCl/Tris, pH 7.2 (230C). GPS buffer: 1 vol of guinea pig serum (GPS) mixed with 79 vol of KCl/Tris/ EDTA.
Complement Components. C5b6: The C5b6 complex was isolated from zymosan-(Sigma) treated human sera by a modification of the procedures of refs. 13 and 14. Human sera were screened for the "reactor state" (15) and 200-ml volumes were activated by incubation with zymosan (4 mg/ml) for 12 min at 370C. The zymosan was recovered by centrifugation and washed with ice-cold glucose (0.5 g/liter), and the C5b6 activity was eluted from the washed pellet with 0.5 M NaCl at 230C. The eluate was made 0.5 M NaCl, 0.05 M Tris, 1 mM NaN3 (pH 7.8, 40C), concentrated, and applied to a Sephadex G-200 column (1.5 X 90 cm) equilibrated with the sample buffer. Active fractions were eluted at 4"C, pooled, concentrated into KCl/Tris, and stored at -90'C until used. The product was determined to be free of C8 and C9 activity by hemolytic assay, and free of immunoglobulin by immunoelectrophoresis. C7: Human C7 was obtained from Cordis Corp., Miami, FL, and stored at -90'C until used. GPS: The GPS was absorbed three times at 00C with 1/10th vol of pooled human erythrocytes prior to storage at -900C. Preparation of Resealed Erythrocyte Ghosts. Hypotonically lysed and resealed erythrocyte ghosts were prepared by modification of the procedure of refs. 16 and 17. Erythrocytes from healthy human donors were washed and suspended to 40% (vol/vol) in 165 mM KCl and maintained at 00C (+0.50C) in a salted ice bath. One volume of the cell suspension was lysed in 10 vol of a 4 mM MgSO4/2 mM Na2ATP (Sigma) solution maintained at 00C (+ 0.20C). A pH at lysis of 6.0 (+0.1) was maintained by dropwise addition of 0.1 M Tris or 0.1 M HCL. The lysate was stirred 5 min at 0C and then made 165 mM KCl, 2 mM Tris, 1 mM sucrose (pH 7.2, 0°C) by the addition of 1 vol of 1.83 M KCI/25 mM Tris/12 mM sucrose at 0°C. In some experiments, [14C]sucrose (New England Nuclear) was added to the lysate prior to resealing. The lysate was maintained at 0°C for 15 min and then at 37°C for 1 hr. The hemoglobin concentration [Hb] of the lysate was determined spectrophoAbbreviations: C5, C6, etc., refer to individual components of the complement system. C5b6 denotes a stable complex of the "b" fragment of C5, and C6; CMb-9, the complex of C5b, C6, C7, C8, and C9. S*, a functional lesion in the membrane due to the inserted C5b-9; GPS, guinea pig serum; Hb, hemoglobin; r, statistical correlation coefficient. t To whom reprint requests should be addressed.
5670
Immunology: Sims and Lauf
tometrically at 415 nm (range, 9-12 g/liter). The resealed sucrose-impermeable ghosts were isolated by centrifugation on a sucrose cushion (16) and then washed and suspended to 2 X 109/ml in KCl/Tris (40C) for use the same day. The number of ghosts was estimated from the [Hb] in the lysate at resealing, utilizing a mean corpuscular volume of 94.1 fl and cell H20 of 969 g/kg of ghosts (17). Preparation of Cellular Intermediates. C5b67 ghosts: C7 was added to the ghost suspension (100 Cordis units/109 cells), which was placed in a 370C bath. The cells were then mixed with an equal volume of an appropriate dilution of C5b6 (in KCl/Tris) to yield the desired number of potential S*. One unit was defined as the amount of C5b6 required to ultimately cause the release of 63% of trapped [14C]sucrose. After 15 min at 370C the C5b67 ghosts were recovered by centrifugation and washed three times in KCl/Tris/EDTA (40C). C5b-9 ghosts: C5b67 ghosts were made C5b-9 by incubation (1 X 109/ml) in GPS buffer (10 mM EDTA) for 60 min at 37°C. In preliminary experiments, the generation of S* on C5b67 ghosts during incubation in GPS buffer was determined by measuring the release of [14C]sucrose incorporated into ghosts at the time of resealing. Tracer-loaded C5b67 ghosts, and controls not exposed to C5b6 + C7, were each suspended in GPS buffer (10 mM EDTA) at 370C. Aliquots were withdrawn at 15-min intervals and centrifuged, and the radioactivities of the supernatant and cell pellet were determined. Cell lysis was simultaneously determined by the release of initial ghost Hb, measured spectrophotometrically at 415 nm. Additional controls included C5b67 ghosts and complement-free ghosts suspended at 37°C in GPS buffer heat inactivated at 100°C for 2 min. Kinetics of Tracer Influx. C5b-9 ghosts prepared under conditions generating from 0.2 to 0.8 mean S* per cell were utilized to measure the kinetics of [14C]sucrose influx through S* under steady-state conditions. Samples (2 X 109) of C5b-9 ghosts, C5b67 ghosts, and complement-free controls were recovered by centrifugation and washed three times in albumin buffer (4°C). The washed ghost pellets were suspended to approximately 20% (vol/vol) in albumin buffer, capped tightly, and placed in a 370C shaker bath. After a preincubation period of either 5 min or 3 hr. 3 ,uCi (1 Ci = 3.7 X 1010 becquerels) of [14C]sucrose (delivered as 1 mM net sucrose in albumin buffer) was injected into each suspension. At recorded times, 50-pi samples of each suspension were withdrawn, injected into a tube containing 35 ml of albumin buffer at 00C, and immediately centrifuged at 0°C. The pellet was lysed in a fixed aliquot of detergent, and Hb and radioactivity were measured. Elapsed time at 00C was 6-7 min, during which the backflux of tracer was determined to be less than 3%. The specific activity of sucrose in the cell water was calculated and expressed as a ratio to that in the total cell suspension. Percent cell lysis was determined as described above.
Proc. Natl. Acad. Sci. USA 75 (1978) Table 1. Release of [14C]sucrose and Hb as a function of S* assembly on human erythrocyte ghosts Treatment % release (2 hr, 370C) GPS buffer C5b6, Hb C7 (10 mM EDTA) units ['4C]Sucrose 3+2 + 83 5 + 2 2+1 + + 63±9 1 3 1 + 50+7 + 0.5 + 34 3 3± 2 + 0.25 Controls 3+1 + 3i2 Heatinactivated 1 2±1 3 1 + 2± 1 3 i2 Heat inactivated
Ghosts resealed to tracer [14C]sucrose were made C5b67 by incubation (15 min, 370C) in various amounts of C5b6 plus 100 units of C7 (+). Ghosts were then made C5b-9 by suspension (109 per ml, 370C) in GPS buffer (+). Percent release (mean + SEM) of initial radioactivity and Hb was determined at the end of 2-hr incubation in GPS buffer as described in text. Controls: C5b67 ghosts suspended (2 hr, 370C) in GPS buffer that had been heat inactivated (1000C, 2 min) and ghosts not pretreated with C5b6 plus C7 (-) before suspension in either GPS buffer (+) or heat-inactivated GPS buffer. GPS buffer contains 10 mM EDTA.
the cells were pretreated, suggesting conversion of C5b67 sites to S*. No tracer was released from controls incubated-in GPS buffer (10 mM EDTA) alone, confirming that neither the classical nor the alternative pathway was activated. C5b-9 ghosts washed free of GPS buffer after 1 hr and then suspended in albumin buffer showed no lysis above control levels during subsequent incubation at 370C (Fig. 1 upper). However, when suspended in KCl/Tris in the absence of added serum proteins, C5b-9 ghosts underwent a protracted lysis significantly above control levels (not shown). Kinetics of Tracer Exchange. Fig. 1 presents the data of one typical experiment for tracer influx at 370C into C5b-9 ghosts incubated at net chemical steady state (sucrose = 1 mM). Ghosts pretreated under conditions to generate S* on approximately 30% of the population were suspended in albumin buffer at 37O. * 1! 10 1( ._
E l I
CL
a
3
W
N.
I-
N.
RESULTS Assembly of C5b-9 Cells under Nonlytic Conditions. Table 1 summarizes the results obtained after treatment of [14C]sucrose-loaded ghosts with the terminal complement components. In the absence of a source of C8 + C9, ghosts preincubated with C5b6 + C7 and then suspended at 37CC remained impermeable to sucrose and showed no lysis above control levels, as measured by Hb release. During prolonged (>2 hr) incubation at 37°C, all three controls released tracer at 1-2% per hr, entirely accounted for by nonspecific lysis. When C5b67 ghosts were suspended in GPS buffer (10 mM EDTA) as a source of C8 + C9, tracer was released with no lysis detected above control levels. The equilibrium exchange of tracer was directly related to the amount of C5b6 with which
FIG. 1. (Lower)
Hours [14C]Sucrose tracer influx measured for C5b-9
ghosts (e-*) and C5b67 controls (L---A) suspended in albumin buffer at 37°C, sucrose = 1 mM. Tracer additions were made after preincubation period of 3 hr, 370C. Data of single experiment; each point and bar represent mean and SEM of three determinations. The abscissa is elapsed time after tracer addition; the ordinate is the ratio (Y/Y8yp) of the specific activity of sucrose in ghost water to that in the total suspension. (Upper) Lysis of C5b-9 ghosts (-) and C5b67 controls (M) during the same experiment. Lysis was determined from the percent release of initial ghost Hb, as measured at 415 nm.
Immunology:
Proc. Natl. Acad. Sci. USA 75 (1978)
Sims and Lauf
Controls included C5b67 and complement-free ghosts (not shown). After a preincubation period of 3 hr, tracer was added to each flask and the specific activity of the sucrose in the washed ghost pellets was determined. In the experiment shown as well as in eight additional experiments, lysis of C5b-9 and control ghosts did not exceed 2% per hr. Uptake of tracer by C5b67 controls did not significantly differ from tracer uptake by complement-free controls. Analysis. Under conditions of net chemical steady state, bidirectional exchange, and isotopic indistinguishability, the specific activity (Y*) of cells permeable to tracer added extracellularly may be related to a first-order rate constant (k) by 1 - (Y*/y*if) = exp(-kt), [1] in which y*if is the specific activity of sucrose in the permeable cell compartment at equilibrium and t is time (18). Assuming that tracer equilibrates across only those cells with at least one S*, Y* will be related to the observed specific acitivity of sucrose in the cell pellet (Y) by the relationship Y* = Y/F*, in which F* is the fraction of the cell population with at least one lesion. After equilibration of tracer, the specific activity of sucrose in the permeable cells is well approximated by that in the total suspension: Y*inf = Ysusp Substituting for Y* and y*inf, Eq. 1 may be rewritten 1-
*
= exp(-kt).
[2]
In Fig. 2, the data of Fig. 1 for tracer exchange into C5b-9 ghosts are replotted with correction at each time point for nonspecific uptake of sucrose, as determined by the specific activity in the C5b67 controls. The solid lines are generated from Eq. 2 with coefficients F* and k determined by reiterative least squares analysis of the corrected data, utilizing an error minimization routine on 1 - r2. In this, as in all experiments (Table 2), tracer flux into the C5b-9 ghosts was well approximated (IrI > 0.98) by Eq. 2. Permeability to Sucrose of the C5b-9 Lesion. The apparent flux (J) of sucrose due to C5b-9 lesions was calculated from the slope (k) of the semilogarithmic regression plot (Inset, Fig. 2) according to aj
1.0
cf
0.1
0.01
-
0.001
0..
&:
2
1.0
Hours
0.31-
I
Table 2. Steady-state analysis of [14C]sucrose tracer flux across S*
J.
k, F*
0.23 0.31 0.34 0.35 0.55
hr)l
Irl
nmol hr-1
X
N* * 10-7 molecules sec1
Grdup 1. Five-minute preincubation, 370C 3.53 2.49 0.986 6.52 31,000 1.64 0.998 4.36 3.74 20,000 3.59 0.995 10.28 4.13 42,000 1.24 0.996 4.42 5.29 14,000 7.47 6.83 0.996 1.93 18,000 Group 2. Three-hour preincubation, 370C 5.68 2.87 0.998 2.55 3.40 0.982 7.47 2.93 0.997 9.31 4.29 3.02 9.27 5.82 0.996 2.61
33,000 43,000 36,000 27,000 Results of steady-state analysis of data from nine separate experiments, for [14Cjsucrose isotopic exchange diffusion into C5b-9 ghosts suspended at 370C. Each line represents the results obtained from a single experiment, as described for Figs. 1 and 2 (see text). Group 1: experiments in which C5b-9 ghosts and controls were preincubated at 370C for 5 min prior to addition of tracer; group 2: 3-hr preincubation at 371C prior to tracer addition. From data of nine experiments,j* = 29,000 (43000, SEM) molecules sec-1 (4.8 ± Q.5 x 10-20 mol sec-1). Symbols: F*, k, coefficients of least squares regression (from Eq. 2); r, correlation coefficient of least squares regression; J, apparent unidirectional flux calculated from Eq. 3; N*, total number of lesions determined by Poisson analysis, see ref. 4; j*, unidirectional flux per single S* (J/N*). t Denotes experiment depicted in Figs. 1 and 2. 0.19 0.25 0.27t 0.49
J = k * [sucrose] (v* * v,)/(v* + v,), -
[3]
in which v* is the volume of cells exchanging tracer and v,,c is the volume of the extracellular space (18). Assuming that all S* are identical and that tracer exchange at one is independent and kinetically indistinguishable from that at any other, the flux across a single S* (j*) is obtained from J by dividing by the total number of S*. The number of S* is estimated by applying the Poisson distribution to the end point of tracer exchange to predict the mean number of lesions per cell (4) and multiplying by the number of cells in each experiment. In nine experiments (Table 2), j* was determined to be 4.8 (±0.5, SEM) X 10-20 mol sec-1 per single S* at 37°C. On the basis of Student's t test, there was no significant difference (0.80 < P < 0.85) between j* determined in ghosts preincubated 5 min before tracer addition (Group 1 of Table 2) and from those preincubated for 3 hr (Group 2). The unidirectional flux of tracer determined for a single S* per ghost in the presence of 1 ,mol cm-3 of sucrose can be used to calculate an apparent permeability (P*)t of 4.8 X 10-14 cm3 sect for diffusion across S* at 37'C.§
0..1
0.1,u1
II 0.5 Hours
1.0
FIG. 2. Steady-state kinetic analysis of data of Fig. 1, for [14C]flux across S*. 0, Data points for sucrose uptake by C5b-9 ghosts after correction for nonspecific uptake as determined by the specific activity in the C5b67 controls (see Fig. 1). Solid curve was generated by computer from Eq.-2, using a numerical approximation by reiterative least squares analysis to coefficients F* and k. The abscissa is elapsed time after tracer addition; the ordinate is the ratio (YYSUSP) of the corrected specific activity of sucrose in the C5b-9 ghost water to that in the total suspension. (Inset) Semilogarithmic graph of corrected data, plotted according to Eq. 2 with coefficients F* and k determined by least squares analysis; r = 0.99. Numerical approximations to F* and k are given in Table 2. sucrose
5671
t P; (dimensions: cm3 sec'1) represents an apparent permeability for the single S* (P* = j*/[sucrose]) and disregards the effective area (A*) of the C5b-9 lesion, which is unknown. This coefficient permits analysis of transport properties of S$ without introduction of assumptions about the geometry of the putative C5b-9 channel. The apparent permeability per lesion is related to the true permeability (P*) per lesion area (dimensions: cm sec'1) by the relationship P* - P*I/A*. § Under certain conditions, the observed rate of tracer permeation through a biological membrane may be significantly limited by the rate of diffusion across the unstirred layer of solvent at the membrane boundary. In the present experiments, the maximum thickness of this layer (in the absence of stirring) can be estimated to be 2.7 Am; diffusion of tracer across this layer would contribute less than one part in 106 to the observed kinetics of exchange across S* and, therefore, was neglected in the present analysis.
5672
Proc. Natl. Acad. Sci. USA 75 (1978)
Immunology: Sims and Lauf
DISCUSSION Calculation of the rate of solute diffusion across S* from the measured kinetics of tracer exchange depends upon three conditions: (i) C5b-9 ghosts are at chemical steady state with respect to the extracellular compartment. (ii) Tracer entry into C5b-9 ghosts occurs only by the pathway of preformed S*. (iii) The number of S* remains constant during the period of observation. To establish the first condition, net flux of sucrose was precluded by incubation at chemical equilibrium. In the absence of significant lysis of C5b-9 ghosts (Fig. 1), it can be assumed that no significant net water movements occurred. Undetected volume changes to less than the critical hemolytic volume (19) would not have significantly altered the interpretation of the data. In compliance with the second condition, tracer exchange (above small background levels) was observed only after exposure of C5b67 cells to a source of C8 + C9 (Table 1), demonstrating that the generation of the C5b67 site was a necessary but not sufficient step for the assembly of the exchange pathway. The background level of tracer exchange observed for all controls during prolonged incubation at 370C can be entirely accounted for by a slow nonspecific lysis. The third condition required that the assembly and decay of S* were controlled to keep the number of lesions constant during the period of isotopic exchange. The significance of this condition is underscored by the observation (8) that solute exchange prior to immune lysis obeys non-first-order kinetics, suggesting compound rate processes. The use of C5b-9 ghosts washed free of fluid phase components prevented the assembly de novo of C5b-9 sites during incubation in albumin buffer. The rate of tracer entry into ghosts that had been preincubated for 3 hr, a period exceeding any observed time constant (k'1, see Eq. 2) for tracer exchange (groups 2, Table 2), did not significantly differ from the rate of entry into ghosts preincubated only 5 min (group 1). Therefore, S* activation from bound C5b-9 complexes was essentially complete prior to the time of the earliest tracer addition, and could not have been rate limiting to tracer equilibration. The report (20) that S* insertion at 370C is complete within 3 min after assembly of the C5b-9 complex supports this conclusion. Although the decay of S* during prolonged incubation cannot be discounted (5), the data from both experimental groups remained monotonic to the origin and were well fitted (Ir > 0.98) by a first-order function (Eq. 2) throughout the 1-hr sampling period. Hence the data reflect only the kinetics of tracer exchange. Kinetics of Transport Across S*. As revealed by the electron microscope, the lesion associated with the C5b-9 complex displays a central core of approximately 100-A diameter (21, 22). An unrestricted water-filled cylindrical channel of this diameter and sufficient length to span the membrane should permit the free diffusion of small ions with permeability coefficients approaching 25 cm sec-1.1 For example, a single lesion of this dimension on a sheep erythrocyte [for which kinetic data have previously been reported (5, 6, 8, 9)] would lead to the equilibration of cellular ions with an initial rate coeffiPermeability to NaCl and KCI calculated assuming free diffusion through a uniform transmembrane channel of 75-A length. Diffusion coefficients (D) for NaCl and KCI in aqueous solution obtained from ref. 23 and corrected to 300C according to method suggested by ref. 24: P* (300C) = D (300C)/75 A, in which D (NaCl, 300C) = 1.67 X lo-5 cm2 sec-1 and D (KCI, 30'C) = 2.08 X lo-5 cm2 sec1.
cient of 0.9 sec1 at 30'C. 1 Because the rate coefficient reported for Hb release from a sheep erythrocyte due to iysis by a single S* at 300C is less than 0.0004 sec-1 (8, 9), free diffusion of ions across the C5b-9 lesion cannot be rate limiting to lysis. A comparison of the activation energy observed for immune lysis to that for free diffusion also leads to this conclusion (5). The present data, obtained under conditions not rate limited by S* formation, demonstrate that the diffusion of small molecules across S* is significantly restricted. Size of the C5b-9 Channel. In the absence of reliable information about the selectivity of S* to diffusing molecules of various geometries and ionic charge, it would be premature to attempt to deduce the geometry of the C5b-9 lesion from the present data. Nevertheless, the determination of the diffusional kinetics of a nonelectrolyte of known dimension does permit an estimate of the apparent cross sectional area of the lesion, and invites comparison to the data of other reports. If the C5b-9 complex forms a cylindrical channel with an internal diameter of 100 A as suggested by its appearance by electron microscopy (21, 22), the present data (obtained at 370C) suggest that its permeability to sucrose (P* = P*/7.9 X 10-13 cm2) is only 0.06 cm sec-1, two orders of magnitude slower than the permeability to freely diffusing sucrose at 370C (9.2 cm sec'1) as predicted by Fick's Law (23, 24). Thus the effective area available for diffusion across S* must be significantly smaller than the internal dimension of the C5b-9 complex suggested by electron microscopy, and restrictions to free diffusion encountered by solute traversing S* must be considered. As discussed by Renkin (27), the apparent rate of diffusion of nonelectrolytes through inert pores of molecular dimensions can be well approximated by a theoretical formulation that corrects for steric hindrance encountered by the solute at the entrance of the pore and the frictional resistance experienced within the channel. This formulation (equation 11 of ref. 27) permits an estimation of the equivalent pore radius of S* on the basis of the apparent effective area for free diffusion (5.2 X 10-15 cm2), determined from the present data (P*) and the free diffusional permeability to sucrose at 370C (above). This analysis suggests an equivalent pore radius of 11.7 A for SP. Whether solute diffusion in fact occurs across only a small segment of the C5b-9 complex or is restricted by a permeability barrier distributed over its entire area remains to be determined. Recent estimates of the size of S* have been made on the basis of the mean conductance step recorded during C5b-9 assembly on voltage-clamped lipid bilayers (10, 12). Although the dimensions reported are comparable to the dimension suggested by the present analysis, it must be emphasized that they were derived on the basis of the a priori assumption of free ionic (Na+) mobility within the C5b-9 channel, an assumption difficult to reconcile with the present data and other observations upon biological membranes (6-8). For example, a single such lesion on a sheep erythrocyte permitting free transmembrane diffusion of ions would result in the apparent unidirectional flux of Na+ and K+ at 300C with rate coefficients exceeding 0.04 1 Initial first-order rate coefficient calculated for unidirectional flux of solute across a single channel of area [A * = 7r(50 A)21 ssuming P* = 25 cm sec-1. Cell water (v) is that for a sheep erythrocyte (25, 26): k P*A*/v [4] =
= =
(25 cm sec-1) (7.9 X 10-13 cm2)/(2.1 X 10-1" cm3) 0.9
sec .
Immunology:
Sims and Lauf
sec-1,tt as compared to the apparent single-lesion rate coefficient of 0.00085 sec-1 reported for 86Rb efflux from sheep erythrocytes during immune lysis at 300C (8). It has also been reported that conductance increments equivalent to transmembrane channels of 6 A and 12 A were observed upon exposure of black lipid membranes to C5b6 and C5b67, respectively (12). Because this finding also contrasts the demonstrated impermeability of C5b67 ghosts to [14C]sucrose (cf. Table 1 and Fig. 1), and the stability of C5b6- and C5b67-treated erythrocytes (15), it appears premature to directly equate conductance fluctuations observed in lipid bilayers to permeability changes induced in biological membranes by the complement pro-
Proc. Natl. Acad. Sci. USA 75 (1978)
5673
3. Miller-Eberhard, H. J. (1975) Annu. Rev. Biochem. 44, 697724. 4. Mayer, M. M. (1972) Proc. Natl, Acad. Sci. USA 69, 29542958. 5. Li, C. K. N. & Levine, R. P. (1977) Immunochemistry 14, 421-428. 6. Lauf, P. K. (1975) J. Exp. Med. 142,974-988. 7. Lauf, P. K. (1978) in The Physiological Basis for the Disorders of Bio-Membranes, eds. Andreoli, T. E., Fanestil, D. & Hoffman, J. F. (Plenum, New York), pp. 369-398. 8. Hoffmann, L. G. (1969) Immunochemistry 6,309-325. 9. Hingson, D. J., Massengill, R. K. & Mayer, M. M. (1969) Immu-
nochemistry 6,295-307.
teins.
10. Wobschall, D. & McKeon, C. (1975) Biochfm. Blophys. Acta 413,
The present data suggest that the C5b-9 complex in a biological membrane provides a significantly restricted diffusional pathway for solute exchange; alternative models, however, may be suggested. For example, if the C5b-9 lesion exhibited multiple conductance levels, or fluctuated between "open" and "closed" states [compare alamethicin (28) and excitabilityinducing material (29)], the slow permeation of a small molecule such as sucrose could be reconciled with the apparent transport of relatively large molecules such as inulin and ribonuclease (30). In this context, the large variability in the conductance step size (10) and its sensitivity to applied electrical potential (11) as observed during S* activation on lipid bilayers is of interest. The present data do not permit any distinction to be made between models, but suggest that additional insight into the structure of the membrane-bound C5b-9 complex is to be acquired by further characterization of its selectivity and transport kinetics. Accordingly, investigation of the selectivity of S* as a function of the size and chemical structure of the diffusing molecule is called for.
11. Michaels, D. W., Abramovitz, A. S., Hammer, C. H. & Mayer, M. M. (1976) Proc. Nati. Acad. Sci. USA 73,2852-2856. 12. Michaels, D. W., Abramovitz, A. S., Hammer, C. H. & Mayer, M. M. (1978) J. Immunol. 120, 1785 (abstr.). 13. McLeod, B., Baker, P. & Gewurz, H. (1974) Immunology 26, 1145-1157. 14. Baker, P. J., Rubin, L. G., Lint, T. F., McLeod, B. C. & Gewurz, H. (1975) Clin. Exp. Immunol. 20, 113-124. 15. Lachmann, P. J. & Thompson, R. A. (1970) J. Exp. Med. 131,
We thank Dr. P. Baker for her generous assistance in the isolation and purification of C5b6 and M. Johnston for writing the computer programs used in the data analysis. This work was supported in part by U.S. Public Health Service Grants 2-PO1-HL 12157 (to P.K.L.) and S07-RR-07070-12 and Medical Scientists Traineeship GM07171 (to P.J.S). tt Calculated from Eq. 4 assuming P*
= 20 cm sec- and A * that for 11-A-radius pore. P* derived from Fick's law, assuming diffusion coefficient (300C) of 1.5 X 10-5 cm2 sec-1. an
1. Green, H., Barrow, P. & Goldberg, B. (1959) J. Exp. Med. 110, 699-713. 2. Mayer, M. M. (1961) in Immunochemical Approaches to Problems in Microbiology, eds. Heidelberger, M. & Plescia, 0. J. (Rutgers Univ. Press, New Brunswick, NJ), pp. 268-279.
317-321.
643-657. 16. Schwoch, G. & Passow, H. (1973) Molec. Cell. Biochem. 2, 197-218. 17. Funder, J. & Wieth, J. 0. (1976) J. Physiol. 262, 679-698. 18. Gardos, G., Hoffman, J. F. & Passow, H. (1969) in Laboratory Techniques in Membrane Biophysics, eds. Passow, H. & Stamppli, R. (Springer, New York), pp. 9-20. 19. Valet, G. & Opferkuch, W. (1975) J. Immunol. 115, 10281033. 20. Boyle, M. D. P., Langone, J. J. & Borsos, T. (1978) J. Immunol. 120, 1721-1725. 21. Humphrey, J. H. & Dourmashkin, R. R. (1969) Adv. Immunol.
11,75-115. 22. Tranum-Jensen, J., Bhakdi, S., Bhakdi-Lehnen, B., Bjerrum, 0. J. & Speth, V. (1978) Scand. J. Immunol. 7, 45-56. 23. Weast, R. C., ed. (1977) Handbook of Chemistry and Physics (Chemical Rubber Co., Cleveland, OH), 58th Ed., p. F62. 24. Kabat, E. A. & Mayer, M. M. (1961) Experimental Immunochemistry (Thomas, Springfield, IL), 2nd Ed., pp. 675-686. 25. Tosteson, D. C. & Hoffman, J. F. (1960) J. Gen. Physiol. 44, 169-194. 26. Valet, G., Franz, G. & Lauf, P. K. (1978) J. Cell Phys. 94, 215-227. 27. Renkin, E. M. (1955) J. Gen. Physiol. 38,225-243. 28. Eisenberg, M., Hall, J. E. & Mead, C. A. (1973) J. Membr. Biol. 14, 143-176. 29. Ehrenstein, G., Lecar, H. & Nossal, R. (1970) J. Gen. Physiol. 55, 119-133. 30. Giavedoni, E. B. & Dalmasso, A. P. (1978) J. Immunol. 120, 1774-1775 (abstr.).
