INTRODUCTION

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The antibiotic A23187 (calcimycin, or CAL) has been extensively used in biochemical research because of its ability to facilitate transmembrane Ca²⁺ ion transport. Initially, this ionophore was thought to be specific for divalent metal ions (Reed and Lardy, 1972). However, there is now ample experimental evidence for CAL-mediated monovalent metal ion (M⁺) transport, such as that of K⁺ ion also (Pfeiffer and Lardy, 1976; Ben-Hayyim and Krause, 1980; Nakashima and Garlid, 1982; Garlid et al., 1986; Krishnamoorthy and Ahmed, 1992; Ortiz-Carranza et al., 1997). Presumably, such a transport is responsible for CAL-mediated K⁺/H⁺ exchange and 2K⁺/Ca²⁺ exchange across membranes. In the literature, there have been suggestions that CAL-mediated K⁺/H⁺ exchange is similar to that by nigericin and that the dimeric species Cal₂MH is dominantly responsible for the transmembrane M⁺ transport (Pfeiffer and Lardy, 1976). The species Cal₂M have also been suggested to be transporting M⁺ across the membrane (Krishnamoorthy and Ahmed, 1992). In the present work we have tested such hypotheses by kinetic measurements using M⁺ = Li⁺, Na⁺, K⁺, and Cs⁺. A recent controversy about the existence of CAL oligomers and the channel mechanism in CAL facilitated transmembrane H⁺/M⁺ transport (Balasubramanian et al., 1992; Jyoti et al., 1994; Prabhananda and Kombrabail, 1994; Thomas et al., 1997) has also been examined. Our experimental strategy is based on the following.

In liposomes transmembrane H⁺ transport can be driven by a pH difference across the membrane (pH). However, a net H⁺ transport in one direction generates electric potential across the membrane that opposes further H⁺ transport. Therefore, for continued H⁺ conduction leading to pH decay in liposomes, it is necessary to abolish this electric potential by a compensating charge flux such as that from alkali metal ion transport in the opposite direction (Henderson et al., 1969). From a study of the dependence of pH decay rate on various concentrations we can identify the rate-limiting species. For example, when the rate-limiting step involves CAL-species the pH decay rate will show a dependence on the concentration of CAL. When the H⁺ transport step is sufficiently fast and the pH decay rate is limited by the M⁺ transport step, the CAL-species transporting M⁺ across the membrane can be identified by the above procedure. In our experiments, soybean phospholipid (SBPL) vesicles were used as model membranes for reasons mentioned elsewhere, and temperature jump (T-jump) was used to create pH across the vesicular membrane (Krishnamoorthy, 1986; Prabhananda and Ugrankar, 1991).

	MATERIALS AND METHODS

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The SBPL vesicle solutions with 2 mM pyranine inside and other concentration conditions as given in the figure legends were prepared from asolectin (Sigma, St. Louis, MO), following the procedure described elsewhere (Krishnamoorthy, 1986; Prabhananda and Ugrankar, 1991). In our experiments MCl (M⁺ = Li⁺, Na⁺, K⁺, and Cs⁺) were used to regulate concentrations of M⁺ in the SBPL vesicle solutions. Concentrated HCl and MOH were used to adjust the pH of the N-(acetamido)-2-aminoethanesulfonic acid (ACES) and tris(hydroxymethyl)aminomethane (TRIS) + ACES buffers. Stock solutions of 5 mM CAL (Sigma) in ethanol were added in microliter amounts to vesicle solutions with vortex stirring. T-jump was used to create pH (~0.02) and the pH decay was observed at 23 ± 1.5°C by monitoring the fluorescence from the pH indicator pyranine entrapped inside vesicles (Prabhananda and Ugrankar, 1991). The observed pH decay traces were single exponentials. The pH relaxation times  were measured by comparing the observed trace with those obtained from a calibrated exponential generator (Prabhananda and Ugrankar, 1991).

	RESULTS

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Dependence of pH relaxation rate on CAL concentration

The CAL added to SBPL vesicle solutions is predominantly partitioned to the vesicular membrane. Therefore, in the absence of oligomer formation its concentration in the inner layer of the membrane, [Cal_t]_il, can be related to lipid concentration ([lip]) and the concentration [Cal]₀ estimated with respect to vesicle solution volume (Prabhananda and Ugrankar, 1991).

(1)

When a specific step of the H⁺/M⁺ transport cycle dominantly limits the pH decay rate in vesicle solutions, the pH relaxation rate 1/ is linearly related to the concentration of the rate-limiting species (Prabhananda and Ugrankar, 1991; Prabhananda and Kombrabail, 1996):

(2)

where k is the rate constant and b_i is the internal buffer capacity of vesicles.

(3)

where C₁ and K_H1 are the concentration and proton dissociation constant of the buffers entrapped inside vesicles. C₂ = 30 mM, K_H2 = 10^6.9 M, C₃ = 45 mM, and K_H3 = 10^7.8 M are associated with the endogenous groups in SBPL vesicles (Prabhananda and Kombrabail, 1992).

In view of Eq. 2 we can say that the nature of the CAL-species participating in the rate-limiting step of pH decay for different choices of M⁺ can be inferred from the dependence of 1/ on [Cal]₀ and pH. From the observed near-linear increase of 1/ with [Cal]₀² (Fig. 1) we can infer that the concentration of the rate-limiting species is nearly proportional to [Cal]₀² or [Cal_t]_il². Such a situation can be envisaged only if 1) the rate-limiting species is made up of two CAL molecules, 2) [rate-limiting species]_il  [Cal_t]_il, and 3) the dimeric rate-limiting species is in a dynamic equilibrium with the monomeric CAL-species. The dependence of the slopes of the plots in Fig. 1 on the specific choice of M⁺ suggests the involvement of the metal ion in the constitution of the rate-limiting species. The dynamic equilibria of the two possible dimeric species in the membrane showing such features are given below.

(4)

(5)

The magnitudes of the dissociation constants K_MH and K_MM of the above equilibria are such that the concentrations of the dimeric species [Cal₂MH] and [Cal₂MM] are very much less than [Cal_t]_il, as mentioned above. The apparent dissociation constants K_H and K_M of the following equilibria refer to those determined with concentrations of the CAL-species in the membrane and [H⁺] and [M⁺] in the aqueous medium. [H⁺ and M⁺ bind to CAL competitively; see Eq. 5 of Pfeiffer and Lardy (1976)].

(6)

(7)

Therefore, the concentrations of the above-mentioned candidates for the rate-limiting species of pH decay can be calculated using the following expressions.

(8)

(9)

(10)

View larger version (14K): [in this window] [in a new window]   FIGURE 1   Dependence of pH relaxation rate 1/ on A23187 concentration, [Cal]0, in SBPL vesicle solutions containing 100 mM MCl at pH 7. M+ = (a) Li+, ; Na+, ; (b) K+, ; Cs+, . Inside vesicles 0.25 mM ACES buffer. Outside vesicles 7 mM ACES for Li+, Na+, and K+; 7 mM ACES + 10 mM TRIS for Cs+. Lipid concentrations were (a) 3.5 mM for Li+ and Na+, and (b) 3.3 mM for K+ and 3.2 mM for Cs+.

Dependence of  on pH

The dependence of 1/ on pH comes from 1) b_i (Eq. 3), and 2) concentration of the rate-limiting species (Eqs. 8 or 9) occurring in the expression for 1/ (Eq. 2). Since the variation of the concentrations with [H⁺] predicted by Eqs. 8 and 9 are distinctly different, we should be able to identify the rate-limiting species as either Cal₂MH or Cal₂MM from the pH dependence of 1/. The estimate of K_H in typical phospholipid vesicles is ~10^7.8 M (Kauffman et al., 1982). Therefore, for a given vesicle preparation in the pH range of our study (especially in the lower pH region) the "shape" of the 1/ against pH plots is mainly decided by the magnitude of K_H/K_M and the nature of the rate-limiting species (Eqs. 2, 8, and 9). The parameters k/K_MH or k/K_MM can be suitably chosen to match the magnitudes of the observed  with the calculated .

Fig. 2 shows the variation of CAL-facilitated 1/ with pH. The "shape" of the plot for the data obtained with Li⁺ as the alkali metal ion in vesicle solutions is close to that of 0.5/b_i against pH (Fig. 2 a). Such an observation implies only a small variation of the concentration of rate-limiting species with pH (in our pH range) and helps us identify Cal₂LiLi as the rate-limiting species in this system (see Eq. 2). The experimental "shape" of the data obtained with Li⁺ as the metal ion (Fig. 2 a) could be reproduced using Eqs. 2 and 9 for K_H/K_Li = 10^4.4, a value close to that expected from the dissociation constants determined by Kauffman et al. (1982) and Taylor et al. (1985). The 1/ data obtained with Na⁺ as the metal ion (shown in Fig. 2 a) does not show significant variation with pH. Such a "shape" could be explained by identifying the Cal₂NaNa as the rate-limiting species with K_H/K_Na = 10⁵. The ratio of the apparent dissociation constants K_Na/K_Li (=10^0.6) in SBPL vesicles determined from these estimates is close to that in aqueous methanol reported in the literature (Taylor et al., 1985). However, this estimate is an order of magnitude smaller than in L--Dimyristoylphosphatidylcholine (DMPC) vesicles, presumably due to differences in the lipid composition (Taylor et al., 1985). (Calculations using K_H/K_Na < 10^5.5 predicted a substantial increase in 1/ with pH quite different from the observed shape. Such a trend can also be seen in the broken line of Fig. 2 b obtained from such a calculation.) However, the data obtained with K⁺ and Cs⁺ could be reproduced only in the lower pH regions if Cal₂KK or Cal₂CsCs is assumed to be the rate-limiting species (see the broken line simulated using K_H/K_M = 10^5.2 and other constants appropriately chosen to fit the lower pH region of the M⁺ = K⁺ data in Fig. 2 b). The shapes of the plots in Fig. 2 b could be reproduced only by identifying Cal₂KH and Cal₂CsH as the rate-limiting species and using K_H/K_M comparable to that given in Table 1.

View larger version (14K): [in this window] [in a new window]   FIGURE 2   pH dependence of 1/ observed in SBPL vesicle solutions containing 100 mM MCl for different choices of monovalent metal ions. M+ = (a) Li+, ; Na+, ; (b) K+, ; Cs+, . The concentrations [Cal]0 were (a) 33 µM and 17 µM, and (b) 17 µM and 12.5 µM, respectively. Buffers and lipid concentrations were the same as those used in obtaining the data of Fig. 1. The broken line in (a) corresponds to 1/ = 0.5/bi plotted against pH; the broken line in (b) corresponds to calculated pH dependence, fitting the data at lower pH conditions using KH/KM = 105.2 and assuming Cal2KK to be the rate-limiting species. Solid lines were calculated using Eq. A7 and the parameters given in Table 1 with rate-limiting species as identified in the text.

View this table: [in this window] [in a new window]   TABLE 1   Parameters determined from the observed dependence of 1/ on [Cal]0 and on pH using Eqs. 8, 9, and A7 with fx = 1 for Li+ and Na+ and fx = 0 for K+ and Cs+

Confirmation of the rate-limiting species from experiments in a mixture of metal ions

If the dimeric species Cal₂MM can exist, as inferred above, species of the type Cal₂M1M2 can also be expected to exist with dissociation constant K_M1M2 in the membrane when two types of metal ions M1⁺ and M2⁺ are in vesicle solutions.

(11)

The concentrations of Cal-M1 and Cal-H in this case are given by the following expressions.

(12)

(13)

A similar expression can be written for [Cal-M2]_il. Thus, if our identification of the rate-limiting species is correct, in vesicle solutions containing M1⁺ = Li⁺ and M2⁺ = Na⁺ the CAL-facilitated 1/ should include contributions from [Cal₂M1M2]_il in addition to that from [Cal₂M1M1]_il (=1/_M1) and [Cal₂M2M2]_il (=1/_M2). 1/_M1 and 1/_M2 can be calculated with A* instead of A (Eq. 13) in Eqs. 2 and 9 using the parameters given in Table 1. Since [Cal₂M1M2]_il is proportional to the product [Cal-M1]_il × [Cal-M2]_il it should be possible to express the above-mentioned additional contribution to 1/ using an equation similar to Eq. 2,

(14)

with a constant value for F_ext (proportional to the rate constant). The significant and near-constant F_ext for M1⁺ = Li⁺ and M2⁺ = Na⁺ seen in Table 2 confirm this prediction.

View this table: [in this window] [in a new window]   TABLE 2   data and concentration of monomeric CAL-species in SBPL vesicle solutions containing a mixture of M1Cl and M2Cl such that [M1Cl] + [M2Cl] = 0.1 M

Cal₂MH has been identified to be the rate-limiting species for M⁺ = K⁺ or Cs⁺. Therefore, in vesicle solutions containing a mixture of K⁺ and Cs⁺ we can expect dominant contributions to CAL-facilitated 1/ to come from [Cal₂KH]_il (=1/_K) and [Cal₂CsH]_il (=1/_Cs) and negligible contributions to come from [Cal₂M1M2] (M1⁺, M2⁺ = K⁺ and Cs⁺). (In the calculations of these contributions using Eqs. 2 and 8 one must use A* instead of A.) The data given in Table 2 for the K⁺ and Cs⁺ mixed ion system also confirm this prediction.

Identification of the rate-limiting step

The relaxation rates 1/_b associated with the equilibration of the bimolecular reactions X + Y  W + Z or X + Y  X  Y, with rate constants k_f and k_r in the forward and reverse directions, depend on the concentrations of the reactants (Eigen and DeMayer, 1963).

(15)

The transfers of H⁺/M⁺ between the aqueous medium and the CAL-species in the membrane can be considered to be bimolecular reactions at the interface. The equilibration rate for this step should not show a significant dependence on [Cal]₀, since at the interface it is mainly determined by the concentrations of the buffer species and M⁺, which are large compared to [Cal]₀. Thus, the observed  is not associated with this fast step.

If the translocation of the M⁺ carriers Cal₂MM or Cal₂MH is the rate-limiting step it must be possible to increase the translocation rates (and 1/) by disturbing the membrane order such as by adding valinomycin at sufficiently high concentrations (Prabhananda and Kombrabail, 1995). The pH relaxation traces shown in Fig. 3 a with M⁺ = Li⁺ and in Fig. 3 b with M⁺ = K⁺ confirm this prediction. The following two observations show that the increase of 1/ was not due to increased M⁺ transport by valinomycin. 1) Similar magnitudes of changes were observed with both M⁺ = Li⁺ and K⁺ even though the selectivity of valinomycin to K⁺ transport is relatively high. 2) There was no increase in 1/ on increasing M⁺ transport by forming gramicidin channels in the membrane.

View larger version (19K): [in this window] [in a new window]   FIGURE 3   (a) A23187-mediated pH relaxation traces observed with 100 mM LiCl in 3.5 mM SBPL vesicle solutions at pH ~ 7 and [Cal]0 = 25 µM. (i) [Valinomycin]0 = 0,  = 135 ms, and (ii) [valinomycin]0 = 84 µM,  = 70 ms. (b) pH relaxation traces observed with 100 mM KCl in 3.5 mM SBPL vesicle solutions at pH ~ 6.35 and [Cal]0 = 17 µM. (i) [Valinomycin]0 = 0,  = 36 ms, and (ii) [valinomycin]0 = 84 µM,  = 18 ms. Buffer details are similar to those given for Fig. 1.

	DISCUSSION

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CAL-mediated transmembrane H⁺/M⁺ transport scheme

The CAL-species inferred above and the conclusions given above suggest the ion transport scheme of Fig. 4 for the CAL-facilitated pH decay. In this scheme the Cal₂MH could be considered as H⁺ carrier if the dominant reaction of this species at the "interface" is the fast H⁺/M⁺ exchange leading to the formation of Cal₂MM:

(16)

with dissociation of Cal₂MM given by Eq. 5. However, Cal₂MH could be considered as M⁺ carrier if instead of Eq. 16 the dominant reaction of Cal₂MH at the interface is the fast M⁺/H⁺ exchange leading to the formation of Cal₂HH, which dissociates into monomers.

(17)

(18)

The expression for 1/ has been derived in the Appendix (Eq. A7) using the transport scheme of Fig. 4 and taking note of the aforementioned uncertainty with the help of the factor f_x: f_x is the probability of the reaction given in Eq. 16. Eq. A7 is consistent with the observed behaviors of  since it reduces to Eq. 2, with [rate-limiting species]_il given by Eq. 8 or 9 depending on the choice of M⁺. With the stronger binding metal ions Li⁺ and Na⁺, the dissociation of M⁺ from Cal₂MH may be more difficult than that of H⁺ making Eq. 16 more probable and f_x = 1. Similarly, with weaker binding metal ions K⁺ and Cs⁺, Eq. 17 and f_x = 0 may be appropriate. When M⁺ = Li⁺ or Na⁺ we have inferred that the H⁺ translocation is not rate-limiting. Thus, in Eq. A7 the term involving k₂ (associated with M⁺ translocation) should be negligible compared to the terms involving k₀ and k₁ (associated with H⁺ translocation). Therefore, [H⁺]_i{k₀ + 2k₁[Cal_t]_il/A)([M⁺]/K_MH)(K_H/K_M)}  2(k₂/K_MM)[Cal_t]_il/A)([M⁺]K_H/K_M)². Also, we can use Eq. 12 with K_H/K_M given in Table 1 to show that the concentration of H⁺ translocating species [Cal-H]_il in the experiments with M⁺ = K⁺ or Cs⁺ are much greater than that with Li⁺ or Na⁺. Thus, if H⁺ translocation is not limiting the rate of pH decay for M⁺ = Li⁺ or Na⁺ it must be a even faster step and F₄  k₀ × [H⁺]_il in Eq. A7 when M⁺ = K⁺ or Cs⁺. Estimates of k₂/K_MM and k₁/K_MH which reproduce the observed magnitudes of 1/ on using the above conditions in Eq. A7 are given in Table 1.

View larger version (18K): [in this window] [in a new window]   FIGURE 4   Suggested transport scheme for the dominant mode of A23187-mediated pH decay with monovalent metal ion transport participation.

It is possible to choose f_x slightly different from (but close to) 1 and 0 and yet obtain calculated  in agreement with the observed  within the limits of errors for M⁺ = Na⁺ and K⁺ ions. Typical sets of parameters used for obtaining such  are given in the footnote of Table 1.

Estimates of translocation rate constants and dimer dissociation constants

Equation A7 and the 1/ data are not adequate to determine unique estimates of the translocation rate constants of the transport scheme (Fig. 4) and the dimer dissociation constants of the reactions given in Eqs. 4 and 5. However, we can get the limits to their magnitudes using the following criteria. 1) To get the linear behaviors seen in Fig. 1 within the limits of experimental errors, [Cal₂MM]_il and [Cal₂MH]_il should be <10% of the [Cal_t]_il even at the highest [Cal_t]_il. Using this restriction in Eq. 9 we get K_MM > 0.15 M and > 0.2 M along with k₂ > 5 × 10² s¹ and > 10³ s¹ for M⁺ = Li⁺ and Na⁺, respectively. Similarly, we can use Eq. 8 to conclude that K_MH > 0.02 M and k₁ > 2 × 10³ s¹ for M⁺ = K⁺ and Cs⁺. 2) The translocation rate constants of Cal₂MH and Cal₂MM are unlikely to be much different from those of other electroneutral molecules of similar molecular weight and size, such as the metal ion-bound monensin (Prabhananda and Kombrabail, 1992) or nigericin (Prabhananda and Ugrankar, 1991). Using this criterion we get 10⁴ s¹ as the upper limit for k₁ and k₂. Choosing k₁ = k₂ ~ 5 × 10³ s¹ between the two limits given above, we get K_MM ~ 4 M and 1 M for M⁺ = Li⁺ and Na⁺. Also, K_MH ~ 0.05 M and 0.04 M for K⁺ and Cs⁺. 3) The CAL-mediated H⁺ translocation step (as Cal-H translocation) is sufficiently faster than the M⁺ translocation step. This condition is satisfied if k₀  k₂ (say k₀ ~ 10⁵ s¹). Such an estimate is consistent with the inequality k₀  28 s¹ given by Kolber and Haynes (1981). They had observed that when a solution of vesicles loaded with Ca²⁺ is mixed with a solution containing CAL and ethylenediaminetetraacetic acid (EDTA) the ionophore fluorescence increase with time is biexponential. The fast phase of this change could be attributed to the overall process in which CAL is incorporated into the membrane from the aqueous medium and is equilibrated across the two layers of the membrane. In view of our estimate of k₀ given above we can say that the incorporation of CAL from the aqueous medium into the membrane (which could involve a fast binding to the surface followed by a slower step of distortion of the membrane structure at the interface to accommodate the ionophore) is slow compared to the translocation of CAL-H involved in the equilibration across the membrane. 4) The data for M⁺ = K⁺ and Cs⁺ (Fig. 2) require the dominant M⁺ translocation term in the expression for 1/ to be proportional to [Cal₂MH]_il even though Cal₂MM can also translocate M⁺. Therefore, in these situations we should have [Cal₂MH]_il  [Cal₂MM]_il since k₁  k₂. Substituting the smallest [H⁺] of our experiments and setting the detectable limit of the less dominant term as 10% of the dominant term in Eq. A7 (and with f_x = 0 and F₄  k₀ [H⁺]_i) we get 0.05 K_MM > K_MH. Thus, K_KK and K_CsCs > 1 M. 5) With intermolecular interactions contributing to the dominant stability of the dimeric species we should not expect large differences in the magnitudes of K_MM for different choices of M⁺. The estimates given above are consistent with such an expectation. The differences between K_MH and K_MM could be the result of structural differences, steric factors, and hydrogen bond bridges favoring the stability of Cal₂MH. 6) In our transport scheme the dominant fast step of H⁺ translocation is by Cal-H translocation. The possibility of a dominant H⁺ translocation by the dimeric Cal₂HH with translocation rate constant k^*₀ (k₁ in view of the similarity in the sizes of dimeric species) is not compatible with the requirement on the relative concentrations of monomeric and dimeric species. (See Discussion about modification of Eqs. A7 and A8 in the Appendix). 7) A paradoxical feature of the transport scheme (Fig. 4) is that to explain the 1/ data we require the translocation rate constant of monomeric Cal-M to be negligible even though the translocation rate constant of the monomeric Cal-H is high. This paradox can be understood if the M⁺ dissociation rate constant of Cal-M in the membrane is so high that it dissociates even before its translocation across the membrane, unlike the situations with the dimeric Cal₂MH and Cal₂MM. 8) In Fig. 4, the rate of pH decay involves H⁺ translocation by the monomeric Cal-H and the M⁺ translocation is by the dimeric species. Therefore, it follows that the rate of equilibration between the monomeric and dimeric species in the membrane must be faster than 1/. Also, for the efficient translocation of M⁺, the dimer dissociation rate constant should be  k₁, k₂.

CAL species inferred from experiments

The monomeric species Cal, Cal-H, and Cal-M invoked for the above discussion of the kinetic data have been inferred from optical absorption or fluorescent studies (Kauffman et al., 1982; Pfeiffer et al., 1974; Taylor et al., 1985) and using two phase extraction technique (Pfeiffer and Lardy, 1976). The dimeric species Cal₂MH invoked to explain the data of the latter studies could not be inferred from the two phase extraction data obtained with M⁺ = Li⁺, Na⁺, K⁺, and Cs⁺ by Mimouni et al. (1992) even though they had used a higher concentration of CAL (~2 mM in the organic phase). Our conclusions about the "dimeric species" can be reconciled with the two-phase extraction data as explained below: in our experiments the total concentration of CAL in the lipid membrane (estimated using Eq. 1) was 3-10 mM. Even though we invoke the dimeric species to explain the kinetic data, we require their concentrations to be considerably smaller than those of monomeric species to explain the linear plots of Fig. 1. Presumably, the errors in the two-phase extraction data make it difficult to detect the dimeric species at small concentrations in the presence of monomeric species at large concentrations. However, on using M = Ag and Hg (for which the selectivity of CAL is quite high) Mimouni et al. (1992) also could infer the formation of dimeric species of the type Cal₂MM from two phase extraction data, confirming the existence of such species. The differences in the equilibrium constant estimates given above and those reported in the literature perhaps reflect the importance of the medium in deciding the magnitude of these constants (Taylor et al., 1985). The species Cal₂HH, undetected in steady-state observations (Thomas et al., 1997), have not been detected from our kinetic data also. However, they could exist in membranes at small concentrations, as suggested in the undetected kinetic steps (Eqs. 17 and 18). Their stabilization could come from intermolecular hydrogen bond bridges (Deber and Pfeiffer, 1976).

Comparison with mechanisms of CAL-mediated monovalent metal ion and H⁺ transport suggested in the literature

Species of the type Cal₂MH had been invoked in the literature to explain the "two-phase extraction" equilibrium data at different concentrations of H⁺ and M⁺ (Pfeiffer and Lardy, 1976). It had also been suggested that the CAL-mediated M⁺/H⁺ exchange could be similar to that by nigericin. The kinetic data discussed above support the hypothesis that Cal₂MH can be the dominant species responsible for M⁺ transport when M⁺ = K⁺ and Cs⁺. However, the pH-dependent 1/ obtained with M⁺ = Li⁺ and Na⁺ are not consistent with such a hypothesis and suggest the involvement of Cal₂MM for M⁺ transport in these systems. Also, unlike in the nigericin-mediated M⁺/H⁺ exchange (Prabhananda and Ugrankar, 1991) where only monomeric species are involved, in the CAL-mediated M⁺/H⁺ exchange the dimeric species translocate M⁺ and the monomeric Cal-H translocate H⁺ (Fig. 4).

Two more kinetic studies on CAL-mediated H⁺ transport in SBPL vesicle solutions containing K⁺ with conclusions different from ours have appeared in the literature. Krishnamoorthy and Ahmed (1992) created pH by T-jump and observed a pH relaxation rate proportional to [Cal]₀² similar to that in Fig. 1. Even though they have suggested the translocation of M⁺ carrying CAL-dimeric species to be rate-limiting, they have not been able to characterize the dimeric species as Cal₂KH since their studies were restricted to pH ~ 7.5.

In the second kinetic study, the pH was created by mixing vesicle solutions at pH ~ 7.5 with a buffer of slightly different pH in a stopped-flow instrument (Jyoti et al., 1994). In this work, the rate-limiting step of pH decay was not identified and the observed nonlinear dependence of pH decay rate on [Cal]₀ was used to argue that the ion transport is through channels formed by CAL aggregates in the membrane. This study suffers from severe infirmities:

1.	As shown in Eq. A11, in the channel mechanism the slope of log(transport rate) against log([A23187]) plot should progressively decrease with increase in [A23187]. In the limit when almost all the CAL aggregate into channels the slope should tend toward a constant value = 1. The plot in Fig. 3 of Jyoti et al. (1994) shows quite the opposite behavior. Thus, contrary to the claim made by Jyoti et al. (1994), even their data do not support the channel mechanism.
2.	In the decay traces shown in Fig. 1 a of Jyoti et al (1994) the "base lines" [the value of a0exp(kappt) at infinitely long time t] are uncertain since the data have not been recorded at longer intervals of time. The drift in the amplifiers used for recording the data could also cause base line errors. The errors in the base line of exponentials could lead to large errors in the estimates of kapp when plots similar to Fig. 1 b of Jyoti et al. (1994) are used. Estimates of "initial rates" from the initial region of the decay traces also have large uncertainties. Within the limits of such errors, the data given in Fig. 2 of Jyoti et al. (1994) also show transport rates proportional to [Cal]02 similar to those reported by Krishnamoorthy and Ahmed (1992) and in the data given above. However, the "dimeric rate-limiting species" invoked to explain such data have to be at concentrations very much smaller than [Cal]0 to account for the "quadratic dependence." Also, the dimeric species (without further aggregation) are not adequate to form channels.
3.	Other independent evidence against the channel mechanism given in the literature includes the following. 1) CAL-polymeric species are at negligible concentrations in chloroform solutions (Thomas et al., 1997). 2) The model of the divalent metal ion-CAL complex does not favor channel formation (Deber and Pfeiffer, 1976). Such a model has the support from electron paramagnetic resonance data, which have helped the identification of the ligand atoms coordinating to the metal ion (Prabhananda and Kombrabail, 1994).

Rate-limiting step of CAL-mediated divalent metal ion transport

Kolber and Haynes (1981) have studied the kinetics of CAL-mediated divalent metal ion (DM²⁺) transport across vesicular membranes by monitoring the time dependence of depletion of the divalent metal ion-bound CAL in the membrane, from fluorescence measurements. They have analyzed the data using a transport scheme with the following assumptions. 1) The Ca²⁺-CAL complex dissociation-formation reactions and formation of Ca²⁺-EDTA complex at the aqueous medium-membrane interface are not rate-limiting. 2) Cal₂-DM translocation across the membrane is the rate-limiting step. Therefore, the validity of their estimate of Cal₂-Ca translocation rate constant (~0.1-0.3 s¹) depends on the validity of these two assumptions. The experimental observations discussed below show that both the aforementioned assumptions are not valid.

Grell and co-workers (Krause et al., 1983, Grell et al., 1984) have noted a correlation between the relative magnitudes of dissociation rate constants of the Ca²⁺ and Mg²⁺ complexes of CAL (determined from stopped-flow and T-jump relaxation studies in methanol and 30% water-methanol mixtures) and the turnover numbers for CAL-mediated Ca²⁺ and Mg²⁺ transports (Pfeiffer et al., 1978). In the "two phase extraction kinetic studies," Jeminet and co-workers (Bolte et al., 1985; Prudhomme et al., 1986) have observed large Ca²⁺/Mg²⁺ selectivity in the rate of release of DM²⁺ into the aqueous phase by the dissociation of Cal₂-DM dissolved in the organic phase. Similar observations have been made even when calcimycin analogs were used. In these experiments the translocations within the organic phase could not have contributed to the Ca²⁺/Mg²⁺ selectivity, since the diffusion rates of Cal₂-DM (which depend on the sizes of the complexes) are expected to be similar for both DM²⁺ = Ca²⁺ and Mg²⁺. Therefore, we conclude that the dissociation of the complex is the rate-limiting step.

From the kinetic study of Cal₂-DM formation and dissociation in methanol it was possible to conclude that the rate-limiting steps of formation and dissociation mechanisms are associated with the charged complex Cal-DM⁺ (Krause et al., 1983; Albrecht-Gary et al., 1989) and the coordination and dissociation of the second CAL is a fast step. The observation that the dissociation rate constant of the 1:1 complex is sensitive to the polarity of the medium (Krause et al., 1983) can be used to predict that the CAL-mediated Ca²⁺ transport rate should be lipid composition-dependent if the dissociation of this complex at the interface is the rate-limiting step. The kinetic data are consistent with this prediction (Kolber and Haynes, 1981).

Furthermore, the translocation rate constants of the electroneutral complexes Cal₂-DM and Cal₂MM can be expected to be of similar magnitude (~5 × 10³ s¹ determined in the present work) in view of the expected similarity in the sizes of the dimeric CAL-species. Compared to this estimate the turnover number of CAL-mediated Ca²⁺ transport (~45 s¹) is much smaller (Pfeiffer et al., 1978). Therefore, we conclude that the translocation of Cal₂-DM is not the rate-limiting step of CAL-mediated Ca²⁺ transport across the membrane, contrary to the assumption of Kolber and Haynes (1981).

In the mechanism of Fig. 4 the transfer of M⁺ between Cal₂MM or Cal₂MH and the aqueous medium is a fast step. This is in contrast with the transfer of DM²⁺ to the aqueous medium by the slow dissociation of Cal-DM⁺ at the interface, suggested above. Stabilization of the charged species Cal-DM⁺ by coulombic interactions with the polar region of the bilayer membrane could also have contributed to such a difference in the rates at the interface.