Address editorial correspondence to Roger E. Koeppe II, Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville, AR 72701. Fax: (479) 575-4049; E-mail: rk2{at}uark.edu
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ABSTRACT |
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Key Words: gramicidin channels bilayer mechanics hydrophobic coupling lateral association
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INTRODUCTION |
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Integral membrane protein folding depends on the association of bilayer-spanning -helices, which is due to more favorable helixhelix, as compared with helixlipid, interactions (e.g., Popot and Engelman, 1990
; Lemmon and Engelman, 1994
; White and Wimley, 1999
). The clustering of membrane proteins often is mediated by cytoskeletal proteins, such as the PDZ family of proteins (Fanning and Anderson, 1999
). Similarly, extracellular ligand binding to growth factor receptors can induce receptor dimerization, which precedes the autophosphorylation that initiates the signal-transduction cascade (Ullrich and Schlessinger, 1990
). The lipid bilayer component also can promote membrane protein clustering when there is a significant mismatch between the proteins' hydrophobic length and the thickness of the bilayer hydrophobic core (Kusumi and Hyde, 1982
; Lewis and Engelman, 1983
; Pearson et al., 1983
; Cornea and Thomas, 1994
). Similar changes in bilayer thickness also alter the function of imbedded proteins (Baldwin and Hubbell, 1985
; Brown, 1994
; Starling et al., 1995
; Cornelius, 2001
). In some cases, e.g., the sarcoplasmic Ca2+-ATPase (Starling et al., 1995
), the bilayer-dependent changes in protein function are not dependent on aggregation or clustering. In other cases, e.g., the nicotinic acetylcholine receptor (Young and Poo, 1983
) and the cyclic lipodepsipeptide syringomycin E (Kaulin et al., 1998
), the changes in protein function result from the clustering itself; and in some cases of heterologously expressed ion channels, e.g., CFTR (Larsen et al., 1996
), cooperative channel openings are suggestive of channel clustering. In yet other cases, e.g., the ryanodine receptor (Marx et al., 1998
), the functional coupling (dimerization) is favored by the presence of an accessory protein FKBP12 but can occur even in its absence. It is not clear, however, whether clustering alters protein function because of proteinprotein interactions or because of bilayer-mediated interactions. In fact, even though bilayer-mediated interactions between membrane proteins have been proposed (e.g., Young and Poo, 1983
; Manivannan et al., 1992
), there is little direct evidence for such interactions. Moreover, within the confines of the "standard" fluid-mosaic membrane model (Singer and Nicolson, 1972
), which often is assumed to equate the bilayer with a thin sheet of liquid hydrocarbon, there is no obvious physical basis such for bilayer-mediated protein interactions.
Simply extending the fluid-mosaic model to incorporate the fact that lipid bilayers are elastic bodies with well-defined material properties (Evans and Hochmuth, 1978; Mouritsen and Bloom, 1984
; Huang, 1986
; Evans and Needham, 1987
) provides a physical basis for such interactions. Because lipid bilayers are elastic bodies, a mismatch between a protein's hydrophobic length and the bilayer hydrophobic thickness will cause a local bilayer deformation. This deformation not only incurs an energetic cost, it also extends 23 nm into the surrounding bilayer (Aranda-Espinoza et al., 1996
; Huang, 1986
; Nielsen et al., 1998
; Partenskii and Jordan, 2002
), which could lead to protein clustering (Aranda-Espinoza et al., 1996
; Harroun et al., 1999b
). Experimental evidence for such a hydrophobic mismatch-driven clustering was, in fact, provided for gramicidin channels incorporated into bilayers of different thickness (Harroun et al., 1999a
), but the functional significance of this clustering has not been established.
Gramicidin A (gA) from Bacillus brevis forms monovalent cationselective channels in which each 15amino-acid ß-helical subunit is inserted in one of the lipid bilayer leaflets (Koeppe and Andersen, 1996; Andersen et al., 1999
). Usually, the hydrophobic length of an assembled dimeric gramicidin channel is less than the host bilayer's hydrophobic thickness (Elliott et al., 1983
), and the formation of a gA channel is expected to compress and bend the monolayers toward each other (Huang, 1986
; Andersen et al., 1999
; Nielsen and Andersen, 2000
). This is indeed the case, as X-ray diffraction measurements show that the peak-to-peak distance in the electron density profile of dimyristoylphosphatidylcholine (DMPC)* bilayers decreases form 35.3 to 32.7 Å upon the incorporation of gA at a 1:10 gA/DMPC molar ratio (Harroun et al., 1999a
). Moreover, the radial distribution function suggests that the bilayer-spanning gA channels tend to cluster. In dilute systems, the average thinning would be less, but the lipids near each embedded entity nevertheless could experience a similar relative deformation. This bilayer deformation, with its associated deformation energy, could provide the means for coupling two channels together. Moreover, given the structure of gramicidin channels, which are fully imbedded within the bilayer (Olah et al., 1991
), any coupling between channels would be bilayer-mediated.
The aim of the present experiments therefore was to examine whether a local thinning of the lipid bilayer, caused by the formation of a gramicidin channel, could influence the properties (e.g., the channel formation rate, single-channel conductance, or lifetime) of a nearby channel? The typical single-channel experiment cannot answer this question because the systems are extremely dilute, one subunit per 106 or 107 lipid molecules (Durkin et al., 1990; Sawyer et al., 1990
). To overcome this limitation, we joined two gA monomers via a flexible, hydrophilic extra-membrane peptide linker at their carboxy terminals. One anticipates that the pair of subunits of such a carboxy-linked dimer potentially could join with equivalent subunits from another linked dimer to facilitate side-by-side channel formation (Fig. 1).
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Some of these results have appeared in preliminary form (Goforth et al., 2002).
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MATERIALS AND METHODS |
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The analogues with single-ended tails were synthesized and purified using standard solid-phase procedures (Greathouse et al., 1999).
The linked analogues were synthesized by the addition of Fmoc-protected amino acids to a low-loaded (0.25 mmole/g) Sasrin®-Ala resin (Mergler et al., 1988). For these analogues, the synthetic procedures were modified from those used for the analogues with single-ended tails, so as to allow for 3050 min deprotection times and 12 h coupling times using a 25-fold excess of the incoming Fmoc amino acid. To minimize unwanted side reactions, each coupling was followed by extensive wash cycles and extra solvation volumes. As a critical step in the synthesis, the bifunctional Lys, denoted K* in Table I, was coupled to the resin after a COOH-terminal Gly-Pro-Ala sequence. This "spacer" was necessary for efficient formation of both of the peptide chains that grew out from the bifunctional Lys. This coupling sequence serves no other purpose in terms of channel formation or channel connections. The bifunctional di-Fmoc-lysine (K*), which constitutes the actual link, was dually deprotected and derivatized at both the
- and
-amino groups, such that both amino groups could be used as starting points for the synthesis of an identical linker-gA sequence. The resulting peptide products were released from the Sasrin® resin using 1% trifluoroacetic acid in dichloromethane for 3 min at 24°C and purified by reversed phase high pressure liquid chromatography (RP-HPLC) on a Zorbax C-8 Column (Greathouse et al., 1999
). The linked analogues were eluted as a single broad peak using a gradient of 8099% methanol (and 201% water) with 0.1% trifluoroacetic acid (Fig. 2 A).
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The quality of the synthetic products was verified by matrix-assisted laser desorption ionization (MALDI) analysis (performed by Mass Consortium). Fig. 2 B shows results for the 15-residuelinked tandem gA. For the 23-residuelinked tandem gA, the spectrum depicts a series of Na+ adduct peaks of a 5,580 molecular weight moiety, indicating that the peptide has the correct molecular weight.
Circular Dichroism Spectroscopy
The secondary structure of the bilayer-imbedded analogues was determined by circular dichroism spectroscopy at room temperature of the analogues incorporated into DMPC vesicles (Greathouse et al., 1999).
Electrophysiology
Planar bilayers were formed from n-decane solutions (2.5% wt/vol) of diphytanoylphosphatidylcholine (DPhPC) across a hole (1.6-mm diameter) in a Teflon® partition that separates two aqueous solutions of unbuffered salt solution, usually 1.0 M CsCl, which was prepared fresh each day. Single-channel experiments were done at 25 ± 1°C using the bilayer punch technique with pipet tip diameters
30 µm (Andersen, 1983a
) and a Dagan 3900 patch clamp amplifier (Dagan Instruments) or an AxoPatch 1C patch clamp amplifier (Axon Instruments, Inc.). The gramicidins were added from ethanolic stock solutions to the electrolyte solution on either side of the bilayer. For most experiments, the gramicidin analogues were added to both sides of the bilayer. In some cases, two analogues were added asymmetricallyone analogue to one side and the other analogue to the other side. Single-channel current transitions usually were detected using a PC/AT-compatible computer using AxoBasic (Axon Instruments, Inc.) and using the algorithm described by (Andersen, 1983a
); in some cases the current transitions were tabulated by hand. Single-channel current transition amplitude histograms and lifetime histograms were constructed as described previously (Andersen, 1983a
; Sawyer et al., 1989
). The lifetime histograms were transformed into survivor distributions, and the average channel lifetimes (
) were determined by fitting a single exponential distribution: N(t) = N(0) · exp{t/
}, where N(t) denotes the number of channels with a lifetime longer than time t, to each histogram (Sawyer et al., 1989
; Durkin et al., 1990
).
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RESULTS |
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Fig. 4 shows single-channel current traces obtained with standard gA (Fig. 4 A), the gA analogue with a 7-residue single-ended eda tail (Fig. 4 B), as well as the two tandem gramicidin analogues, with the shorter 15-residue linker (Fig. 4 C) or the longer 23-residue linker (Fig. 4, D and E). (The results obtained with other analogues with single-ended tails were similar to those illustrated in Fig. 4 B; they are summarized in Table II.)
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Characteristics of Double-Barreled gA Channels
A quite different result is observed in the case of gA subunits that are coupled by the longer 23-residue linker (Fig. 4, D and E). In this case, the channels' lifetimes are much longer than was the case for any of the other analogues, and at the resolution of the figure, the current transition amplitudes in Fig. 4 D appear to be almost twofold higher than was the case for the gA subunits with single-ended tail segments; but, there is evidence for transitions to intermediate current levels when the channels appear and disappear, as well as in the middle of the trace. The current transition amplitude and lifetime histograms for the channels formed by these four gramicidins are shown in Fig. 5; the results for all analogues, as well as gA, are summarized in Table II.
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The 23-residuelinked tandem analogue (Figs. 4 D and 5 D), however, forms channels that differ qualitatively from the channels formed by the other analogues. The full current transitions are about twofold higher than those observed for the channels formed by the analogue with the single-ended tail and the 15-residuelinked tandem analogue, there are transitions to intermediate current levels, and the lifetimes are 200-fold longer. As can be seen in Fig. 4, the 23-residuelinked tandem gA forms two, qualitatively rather different, channel types. The predominant type is that shown in Fig. 4 D. Infrequently (
5% of the observed events), the channels exhibit the behavior shown in Fig. 4 E, in which the transition pattern is distinctly different from that in Fig. 4 Das the intermediate conducting state, which is barely visible in Fig. 4 D, now has a lifetime that may be many seconds. Given the rarity of these events, we did not investigate them in any detail, and the quantitative analysis that follows is based only on channel events of the type shown in Fig. 4 D.
The differences between the channels formed by the 23-residuelinked tandem analogue and the channels formed by gA or the analogues with a single-ended tail or the 15-residue linker become more pronounced when the channels formed by the 23-residuelinked tandem analogue are examined at higher time resolution (Fig. 6). The larger current transitions in Fig. 4 D now are seen to be composite events, in which there is an initial bursting channel activity that is followed by a two-step increase of the current to a new level, which is maintained for up to several minutes.
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Closer inspection of the current traces in Fig. 6 shows that the bursting channel activity represents transitions within a bilayer-spanning pore because the lower of the two current levels within the burst is above the baseline currentwhere no channel is conducting. This is quantified in detail for the case of bursting channels in the current level histograms at the bottom of Fig. 6. Similar results were also obtained for the channel appearances and disappearances; the results are summarized in Table III. Due to difficulties in identifying a 0.2-pA transition from the baseline to (or from) the low-conductance current level in the bursting events, it is not clear if the channel appearances always are from the baseline to the 6-pA intermediate current level, and vice versa for the disappearances. To minimize ambiguities, we identify the channel appearances and disappearances to begin (or terminate) with the first (or last) transition to (or from) the 6-pA current level.
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Given the two-state behavior of the bursting channels, as well as the appearance and disappearance events of the double-barreled, one would expect the lifetime distributions to deviate from single exponential distributions. Somewhat surprisingly, the lifetimes of the appearance and disappearance steps are quite well fit by single exponential distributions (Fig. 7), and so is the lifetime distribution for the flickery events (unpublished data). The bursting events, however, had a lifetime distribution that was not well fit by either a single- or a double-exponential distribution, and we estimate the average lifetime as a simple average of the observed lifetimes. Another surprise is that the average lifetime of the bursting channels is twofold longer than those for the three types of brief channel events, which are indistinguishable. We discuss the implications of this finding in the DISCUSSION. (Because of the very long lifetimes of the double-barreled channels, the experiments had to be done at very low channel appearance rates, and the total number of observed channel events was insufficient for a more detailed analysis of the lifetime distributions.)
Though we did not examine the channels with the appearance pattern in Fig. 4 E in any detail, we noted that the intermediate current level invariably was higher than was the case for the bursting events or the intermediate current level during "normal" appearances/disappearancesand that there were transitions between this higher level and a current level similar to that usually observed (compare Fig. 4 E). The molecular basis for these transitions remains unclear.
Heterodimer Experiments
What is the basis for the different current transition amplitudes in the double-barreled channels? The CD spectra (Fig. 3) show that the tandem analogues form both ß6.3-helical and non-ß6.3-helical structures; but, the rather modest differences in single-channel current and lifetime between the channels formed by gA and the analogues with a single-ended tail suggest that the structure of the bilayer-spanning channel is not altered by attaching an extension at Trp15. Nevertheless, could there be an intrinsic asymmetry between the channel subunit that is linked to the NH group, as opposed to the
NH group? These questions were addressed in heterodimer formation experiments, which constitute a sensitive test for whether a given sequence modification alters the channel structure (Durkin et al., 1990
). Basically, if a gramicidin analogue forms only one type of channel, and if heterodimeric channels can form between the analogue and a reference gramicidin of known structure (e.g., gA), we may conclude that the analogue can fold such as to adapt to the structure of the reference subunit. (Ideally, one should examine the relative distribution between the two homodimers and the corresponding heterodimers, which in the case of structural invariance is described by the binomial distribution [Durkin et al., 1990
; Durkin et al., 1993
]. In practice, the long lifetimes of the 23-residuelinked tandem gA channels preclude this measurement.)
Therefore, we did heterodimer experiments with gA as the reference subunit opposite an analogue with a 7-residue single-ended eda tail, as well as the 15-residuelinked or 23-residuelinked tandem analogues. In each case, we observed heterodimeric channelsformed between the reference gA and the analogue. The experiments were done using asymmetric addition of the two analogues, with the reference gA being present at only one side of the bilayer and the analogue on the other side, such that there is only a single orientation of the heterodimeric channels. Fig. 8 shows the current traces and current transition amplitude histograms obtained with gA and the 23-residuelinked tandem analogue at ±200 mV; the results for the other experiments are summarized in Table IV.
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Moreover, the current transition amplitudes at the two polarities differ: for all the heterodimers, the transitions are larger at negative potentials, when the net ion movement is from the gA subunit to the analogue subunit with a single-ended tail or a linker (Fig. 8 and Table III). The linker residues thus appear to constrain ion entry into the pore. Examination of the -200 mV current trace in Fig, 8 shows that the channels again occur in bursts, in which the current switches between a high-conductance state (i 8 pA) and a low-conductance state (i
0.2 pA). We did not pursue this further,1 but concluded that the two barrels of the tandem gramicidins have intrinsic permeability properties that are indistinguishable.
We also did asymmetric heterodimer experiments with the 15- and the 23-residue lined tandem gramicidin analogues, where we (again) added the two analogues to opposite of the bilayers. In this case, there was no asymmetry between the currents at ±200 mV, both of which were 6.2 pA, again indicating that the linked subunits have indistinguishable permeability characteristics.
Basis for the Unequal Current Transitions
What could be the mechanistic basis for the different current transition amplitudes from the baseline to the intermediate current level (corresponding to just one conducting channel), as compared with the transition from the intermediate to the composite current level (corresponding to two conducting channels)? The difference is unlikely to result from structural differences between the two channels, as we observe only a single population of current transition amplitudes for the heterodimers formed between gA and the 23-residuelinked analogue (Fig. 7). It also is unlikely that it always would be the same variant of two different channel types that formed the first channel in the double-barreled construct.
Accepting that the unequal current steps do not result from chemically dissimilar "barrels," we need to consider two possible explanations for the observation. First, if the linker partially occluded the first barrel of a pair, this steric hindrance could be removed (in part) when the second channel opened. Second, and mechanistically more interesting, the energetic barrier for ion movement through each of the pores could be lower for a pair of channels, as compared with an isolated channel. It is well established that the energy barrier for ion movement through a channel is a function of the dielectric constant of the surrounding bilayer (Parsegian, 1969; Levitt, 1978
; Jordan, 1986
), and a bilayer-spanning channel constitutes a more polar environment than the bilayer hydrophobic core. So, if the two barrels were sufficiently close together the electrostatic barrier for moving an ion through each pore would be reduced because some of the acyl chains surrounding each channel have been replaced by the other bilayer-spanning barrel.
To distinguish between these two possibilities, we did experiments using 0.1 M CsCl, where aqueous diffusion limitations would be more pronounced (compare Andersen, 1983a), and 1.0 M NaCl, in which the currents (in gA channels) are similar to that in 0.1 M CsCl, but where the barrier for ion movement through the pore would be relatively more important than the entrance barrier. The basic pattern of composite channel appearances/disappearances is seen also under each of these ionic conditions. The results on current transition amplitudes are summarized in Table V, which also summarizes the results obtained in 1.0 M CsCl.
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DISCUSSION |
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We first discuss the evidence that the long-lived events indeed are double-barreled channels. Next, we discuss the significance of the different amplitudes of the current transition from the baseline to the intermediate current level, as compared with the transition from the intermediate to the high-conductance level, and conclude that the two barrels are in very close, side-by-side contact. Then, we address the mechanistic basis for the stability of the double-barreled channels, and conclude that the stability results because the elastic force imposed by the bilayer deformation acts on both barrels, such that the force/barrel is less than for the standard, single-barreled gA channel. Finally, we discuss some implications of these results.
Evidence for Double-barreled Channels
In principle, the composite channel events could form either between two 23-residuelinked analogues (one on each side of the bilayer) or between three such analogues (one on one side and two on the other side of the bilayer). Two lines of evidence indicate that the composite channels predominantly are double-barreled channelsformed between two 23-residuelinked analogues. First, we observe no such composite events with the 15-residuelinked analoguesat least not under conditions that allow for single-channel experiments. Second, the experiments were done under conditions where the bursting and composite channel events occur at a rate <10-2 s-1 (compare Figs. 4, D and E, and 7), whereas the transition from the first to the second current level occurs at a rate >1 s-1 (Fig. 7 and Table III). Thus, only a small fraction of the composite events will form as daisy chains between three of the linked analogues. We conclude that the composite events indeed are double-barreled channels. Rokitskaya et al. (2003) similarly conclude that gA channels that are coupled using a biotin-streptavidininduced cross-linking also are double-barreled channels.
Origin of the Unequal Current Transitions
Given the single population of current transition amplitudes in the heterodimer experiments with gA and both the 15- and 23-residuelinked analogues (Fig. 8 and Table III), the pattern of current transitions in the composite events becomes striking. Not only are the two current transition amplitudes distinct; but, the first transition is (almost) invariably the smaller of the two. This pattern differs qualitatively from the one that usually is expected to occur, namely that channel clustering decreases the current amplitude due to local depletion of permeant ions (e.g., Neumcke and Stämpfli, 1983). (The present situation is similar to that observed for alamethicin, which forms multistate channels where the conductance of every next step is higher than that of the preceding step [Gordon and Haydon, 1972
; Eisenberg et al., 1973
], but with little change in pore radiusas deduced from polymer partitioning [Bezrukov and Vodyanoy, 1993
].) The different current transition amplitudes in the composite events somehow must reflect local interactions between the two barrels in the double-barreled channels, which could occur for two reasons. First, the dynamics of the linker close to the pore entrance could be constrained in the double-barreled channels so as to reduce the restrictions on ion access to the pore. Second, electrostatic interactions between the two pores could reduce the electrostatic barrier for ion movement through the pore.
Though the linker most likely reduces the rate constant for (diffusional) ion access to the pore, the results in Table V exclude the possibility that the difference between the two current transition amplitudes results from relative changes in access. Importantly, compared with 1.0 M CsCl or NaCl, the difference between the two current transition amplitudes is decreased in 0.1 M CsCl, where diffusion-controlled ion access is more important (Andersen, 1983b)and more so at 200 mV where ion access will be most important. We also note that Rokitskaya et al. (2003)
, using a completely different linker strategy, observe a similar difference between the first and second transition amplitude as we do, which would tend to exclude a specific action of the linker. Moreover, even in the case of channels formed by the analogue with the 7-residue single-ended eda tail (Fig. 4 A, Table II), there is no evidence for fast transitions between two current levels, similar to those observed by Woolley et al. (1997)
using a shorter linker. That is, the positive charge at the end of the linker seems to move rather freely.
In the next section we conclude that the linker seems to be sufficiently flexible to impose little restriction on the formation of the second barrel, which also would tend to exclude local effects on ion access. We therefore conclude that the pattern of current transition amplitudes results from changes in the barrier for ion movement through the pore itself. It is difficult to envisage how this coupling could arise unless the two barrels were in quite close apposition. If the two barrels, for example, were separated by only one phospholipid molecule, the effective dielectric constant of their surroundings would be increased over that of the bilayer core, which will lower the energy barrier for ion movement through the pore (Parsegian, 1969; Levitt, 1978
; Jordan, 1986
). In addition to this effect, the different current transitions also could result from changes in the average orientation of one or more of the tryptophan residues at the channel entrance, which again would alter the barrier for ion movement through the pore (Becker et al., 1991
; Andersen et al., 1998
).
Formation and Stability of Double-barreled Channels
Standard gA channels usually form in a single stepalthough composite transitions also are observed (Busath and Szabo, 1981; Sigworth and Shenkel, 1988
; Mobashery et al., 1997
), where the intermediate current levels usually are of brief duration. The pattern of channel appearances observed with the 23-residuelinked tandem analogue is quite different from that usually observed with gA, as the first pore does not form in a single, "clean" step to a well-defined current level, but rather presents itself as a series of rapid transitions between two current levels. This bursting channel behavior usually lasts <1 s, and it ceases when the second pore forms (Fig. 5). Similar behavior was observed by Rokitskaya et al. (2003)
, who used a biotin/streptavidin strategy to form double-barreled channels, although in their case the bursting behavior could last many seconds. Somewhat surprisingly, we did not observe double-barreled heterodimeric channels between the 15- and the 23-residuelinked tandem gAs. This most likely reflects that subunit folding is compromised when the linker is too short, as the 15-residuelinked tandem gA has a much more negative ellipticity at 230 nM, which is indicative of a larger fraction of non-ß6.3-helical subunits, than the other analogues (Fig. 3). It also could indicate that a critical linker length is necessary in order for double-barreled channels to form, e.g., because the two monomeric subunits in a single-barreled channel formed by the 15-residuelinked tandem gA are held at positions that do not allow for dimerization.
The question remains, why does the 23-residuelinked tandem analogue form bursting channels? Mobashery et al. (1997) showed that the kinetics of gA channel formation changes qualitatively, with the appearance of bursting events, when the difference between bilayer thickness and channel length exceeds some critical value. These bursting events occur at gramicidin concentrations that are
100-fold higher than the ones normally used (in DPhPC bilayers). The presence of monomers in relatively close proximity may alter the kinetics of dimerization; we do not understand why.
Though their kinetics are complex, the average lifetime of the (single-barreled) bursting channels formed between two 23-residuelinked tandem analogues is twofold larger than the lifetimes for the double-barreled appearance/disappearance transitions. This was unexpected because the initial formation of a single-bilayer-spanning channel between two 23-residuelinked tandem gAs will terminate either because the conducting dimer dissociates (with rate constant k-1) or because the second bilayer-spanning channel forms (with rate constant k+2). (In the discussion that follows we will not consider the two-state nature of the single-barreled, bursting channels.) The same two rate constants would describe the kinetics of channel appearances, flickers from the double-barreled state, and disappearances. One thus would expect that the lifetimes of the bursting channels, the appearance transitions, the flickery transitions, and the disappearance transitions should have identical lifetimes (1 = (k-1 + k+2)-1). The results in Table III show that to be the case for the latter three types of transitions, but not for the bursting channels. The parsimonious explanation for this "discrepancy" is that some tandem gramicidins may have one subunit that is not folded as a ß6.3-helix, as the CD spectra (Fig. 3) show that a significant fraction of not only the 15- but also the 23-residuelinked tandem gAs fold into non-ß6.3-helical structures. If, for example, only 50% of the gA subunit in the 23-residuelinked tandem gA were ß6.3-helices, it would account for the observed differences between the lifetimes for the different types of transitions. (It also could account for the kinetic complexity of the lifetime distribution for the bursting channels.) The relative partitioning between subunit dissociation and double-barreled channel formation is k+2/k-1, or
3, which means that
k+2 is the pseudo-first order rate constant for the formation of the second barrel in the double-barreled channel. To a first approximation, for a flexible linker, where k+1 is the rate constant for gA dimerization, and [gA] is the (local) concentration of gA monomers around the first barrel. Taking the extended length of the linker,
14 nm, as a measure of how far the single, uncoupled subunit can move, [gA]
10-3 molecules/nm2. In DPhPC/n-decane bilayers k+1
104 nm2/(s·molecule) (Rokitskaya et al., 1996
), so assuming no interactions between the subunits, k+2 is expected to be
10 s-1. This estimate is in good agreement with the experimental estimate of 3 s-1 (Table III); we conclude that the linker is unlikely to impose significant stress on the subunit interactions.
For single-barreled gramicidin channels, the channel formation/disappearances are described by Scheme I
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where M and D denote the mole-fractions of nonconducting monomers and conducting dimers in the bilayer. The standard free energy of dimerization, , is given by
![]() | (1) |
![]() | (2) |
For double-barreled gramicidin channels, the channel formation/disappearances are described by Scheme II
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where M-M denotes the linked monomeric subunits, M-D-M the single-barreled channel with two linked subunits, and D-D the linked double-barreled channel. In this case, the standard free energies of dimerization for the single-barreled (M-D-M) and double-barreled (D-D) channels, and
, are given by,
![]() | (3) |
![]() | (4) |
To a first approximation the formation of a single-barreled channel should not be significantly affected by the presence of the other subunit in the tandem gramicidin, in which case ,
, and
.
To evaluate the relative stabilization of the double-barreled channels we note that gA channels obey Poissonian statistics (Hladky and Haydon, 1972; Andersen, 1978
), such that the probability of observing one and two conducting channels (W(1) and W(2), respectively) is given by
· exp{-
} and (
2/2) · exp{-
}, where
is the average number of conducting channels:
= f ·
, where f is the channel appearance rate and
is the channel lifetime. That is, if there were no interactions among the bilayer-spanning channels, the relative distribution between two-channel and one-channel events, W(2)/W(1), would be given by
/2. The stabilization of the double-barreled channels thus can be described as the ratio between the observed and expected distribution between double-barreled [D-D] and single-barreled [M-D-M] channels. The observed distribution is [D-D]/[M-D-M] and, according to Poisson statistics, the expected distribution is [M-D-M]/2. The relative stabilization thus becomes
![]() | (5) |
![]() | (6) |
In Eqs. 36, the Gprot contributions to
Gtot reflect both the hydrogen bond organization at the subunit interfaces, which should be invariant, and the increased monomer concentration around the single-barreled M-D-M channels (Jencks, 1981
; Creighton, 1993
), which means that
. If the linker is flexible, such that it does not impede monomer association:
; if the linker impedes monomer association:
, and the local concentration could, in principle, be zero if the linkers forced the monomers apart to preclude the formation of the second barrel. Similarly, the
Gdef contributions will not be additive because
Gdef varies as a function of channel radius (circumference) (Nielsen et al., 1998
) such that
.
To evaluate G0, we note that the experiments were done at a channel appearance rate of 0.01 s-1 (or less), that the average lifetime of the single-barreled events is
0.25 s, that
75% of the single-barreled channels convert into double-barreled channels, and that the lifetime of the double-barreled channels is
100 s. That is 2 · [D-D]/[M-D-M]2
2 · 0.75 · 0.01 · 100/(0.01 · 0.25)2
2 · 105, or =
G0
30 kJ/mole. For comparison, we note that the making or breaking of one hydrogen bond corresponds to 1015 kJ/mole (Schulz and Schirmer, 1979
; Fersht, 1987
).
Some of the stabilization results from the increased local monomer concentration that is associated with formation of the first barrel (e.g., Jencks, 1981), and some results from bilayer-mediated interactions between the two barrels in the double-barreled channels. The increased local concentration will be reflected primarily in the relative appearance rate of the double-barreled channels, which is
400-fold higher than expected; the bilayer-mediated interactions will be reflected primarily in the relative lifetimes of the double- and single-barreled channels, which is 2 · (
400)-fold higher than expected for a simple Poisson process. That is, one can reasonably attribute about half of the increased stabilization, or
15 kJ/mole, to bilayer-mediated interactions.
Based on HB 20 kJ/(mole · nm2) and (d0 - l)
2 nm,
for a single-barreled channel in DPhPC/n-decane bilayers is
80 kJ/mole. The bilayer-mediated contribution to the energetic stabilization of the double-barreled channels thus may be
10% of the bilayer deformation energy associated with having two independent (noninteracting) bilayer-spanning channels. This result is at the same time comforting, because the relative stabilization is rather modest, and surprising, because even this relatively modest stabilization has so dramatic effects on channel function. As noted previously (Durkin et al., 1992
), the energetic window for useful perturbations of membrane protein function may be remarkably narrow.
The above analysis leads to the following scheme for the formation of double-barreled channels (Fig. 9).
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Why are these interactions seen only in the linked gramicidins? gA single-channel experiments usually are done at gA/lipid ratios 10-7 (compare Durkin et al., 1990
; Sawyer et al., 1990
), corresponding to a subunit density of
10-1 µm-2 where there is no evidence for interactions between two bilayer-spanning dimers (Cifu et al., 1992
). In contrast, the local gA/lipid ratio around a bilayer-spanning channel formed by one of the two subunits in two linked gramicidins would be 24 x 10-3, more than four orders of magnitude larger than the average subunit density, which would tend to increase the likelihood of subunit interactions. At sufficiently high monomer densities similar interactions should occur if the linked gramicidin were present on only one side of the bilayer and gA on the other, but the unavoidable "leak" of gA across the bilayer (see the histograms in Fig. 8) complicates the detection of these interactions at the single-molecular level. Using macroscopic current relaxations after phtalocyanine-induced photoinactivation, however, Rokitskaya et al. (2003)
found that the relaxation time constant indeed increases as the gA concentration increasedconsistent with what would be expected at higher gA surface densities.
Together, the results of Rokitskaya et al. (2003) and those of this study provide strong support for the notion that bilayer-spanning inclusions can couple, both structurally and functionally, through the bilayer. The basis for this interaction is likely the bilayer's elastic properties, and the associated bilayer deformation energy, which could be important for the organization (clustering) of membrane proteins.
Implications for Integral Membrane Proteins
The functions of many membrane proteins depend on the bilayer lipid composition, but usually with only modest chemical specificity in the proteinlipid interactions (Devaux and Seigneuret, 1985; Bienvenüe and Saint-Marie, 1994
; Dowhan, 1997
; Marsh and Horvath, 1998
). Because of the strength of the hydrophobic interactions between the protein's transmembrane domain and the bilayer core, any mismatch between the protein's hydrophobic length and the thickness of the bilayer core will incur an energetic cost that not only may serve to modulate protein function (Brown, 1994
; Lundbæk et al., 1996
), but also could redistribute/cluster proteins within the bilayer (Pearson et al., 1983
; Mouritsen and Bloom, 1984
; Gil et al., 1998
). This clustering serves to increase the local protein density, which can alter the protein's thermodynamic activity (Ryan et al., 1988
) and build up a local stress in the bilayer (Bezrukov, 2000
), and thereby modify protein function by altering the energetics, and thus the kinetics, of the cycle of conformational changes associated with protein function.
In any case, the present results demonstrate that adjacent integral membrane proteins can be coupled functionally by the lipid bilayer. The most likely basis for this functional coupling is that the hydrophobic channelbilayer coupling causes protein conformational changes to perturb the surrounding bilayer, which in turn will later the energetics of conformational changes in neighboring proteins. This shift in the balance between the "intrinsic" energetics of the proteins' conformational changes and the proteins' interactions with their environment, in casu the host bilayer, can alter protein function. To what extent the bilayer-mediated coupling among integral membrane proteins is important for protein function remains to be determined. But 30% of the cell surface area is occupied by the bilayer-spanning segments of integral membrane proteins, so the local protein density is high, which will facilitate bilayer-mediated protein interactions. In fact, growth factor receptor activation and tyrosine autophosphorylation involve receptor aggregation in the cell membrane (Ullrich and Schlessinger, 1990
; Alberts et al., 2002
), and caspase-8-dependent apoptosis, which is mediated by death receptors (Saikumar et al., 1999
), is activated by amphipathic compounds (Borner et al., 1994
; Strupp et al., 2000
) that are known to alter bilayer elastic properties (Sawyer et al., 1989
). As shown by Rokitskaya et al. (2003)
, ligand binding can cause gA channels to dimerize, which together with the present results suggest that the hydrophobic coupling between the bilayer and the imbedded proteins may be an important mechanism for regulating the organization and dynamics of membrane proteins.
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FOOTNOTES |
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ACKNOWLEDGMENTS |
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This work was supported by NIH grants GM21342, RR15569, and GM34968, and NSF grant MCB 9816063.
Edward Moczydlowski served as guest editor.
Submitted: 13 January 2003
Revised: 28 March 2003
Accepted: 2 April 2003
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REFERENCES |
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