Molecular Studies of Voltage-gated Potassium Channels

Molecular Studies of Voltage-gated Potassium Channels E. ISACOFF, D. PAPAZIAN,* L. TIMPE, Y.-N. JAN, AND L.-Y. JAN The Howard Hughes Medical Institute and the Departments of Physiology and Biochemistry, University of California, San Francisco, California 94143; *Department of Physiology, University of California, Los Angeles, California 90072 Excitability and synaptic efficacy in the nervous system are regulated by a variety of potassium channels. Transmitter-induced alterations in the behavior of these channels are capable of effecting the short- and long-term modulation of synaptic transmission that may underlie some forms of memory and learning. These potassium channels are diverse pharmacologically and can be broken down into several subgroups on the basis of whether they are activated by voltage or second messengers and on whether they inactivate. The differences in gating among channels with similar ion selectivity suggest that there exist certain common pore-forming domains in diverse potassium channels that otherwise possess specialized regions specific for gating. Studies of the molecular nature of potassium channels have been made possible by the cloning of the voltage-activated Shaker potassium channel in Drosophila and of related genes in invertebrates and vertebrates. The Shaker Phenotype Shaker mutations were first isolated decades ago on the basis of the leg-shaking phenotype induced under ether anesthesia (Catsch 1944; Kaplan and Trout 1969). The first indication of a potassium channel defect emerged in a study of neuromuscular transmission in Shaker mutant larvae (Jan et al. 1977). Abnormally large and prolonged postsynaptic potentials were recorded in these larval muscles that could be accounted for by prolonged transmitter release from the nerve terminals (Jan et al. 1977). Since the mutant phenotype could be mimicked by treating the wild-type larval preparation with a potassium channel blocker, 4- aminopyridine (4-AP), it appeared likely that Shaker mutations affected a 4-AP-sensitive potassium channel. Subsequent voltage-clamp and single-channel analyses have shown that Shaker mutations affect a rapidly inactivating voltage-gated potassium channel, the A channel, in larval and pupal muscles (Salkoff 1983; Wu and Haugland 1985; Solc et al. 1987; Timpe and Jan 1987). A similar defect in the central neurons has also been reported (Baker and Salkoff 1990). This defect in potassium channel function is likely responsible for the prolonged transmitter release from the larval nerve terminals, since it also prolongs the axonal action potential recorded intracellularly from the cervical giant fibers of adult Shaker mutant flies (Tanouye et al. 1981). EXPERIMENTAL PROCEDURES The molecular and electrophysiological methods employed in the studies reported here have been described previously (Timpe et al. 1988a,b; Isacoff et al. 1990). Briefly, Xenopus oocytes were injected with transcripts of Shaker cdnas. A two-electrode voltage clamp was used to record macroscopic currents (11~ and patch clamping in the outside-out configuration was done to record single-channel activity (22~ RESULTS The Shaker Gene Gives Rise to Different A Channel Subtypes by Alternative Splicing The cloning of the Shaker gene (Baumann et al. 1987; Kamb et al. 1987: Papazian et al. 1987; Tempel et al. 1987) revealed that it is alternatively spliced, giving rise to a number of different protein-coding sequences (Papazian et al. 1987; Tempel et al. 1987; Kamb et al. 1988, Pongs et al. 1988; Schwarz et al. 1988). Each of the five full-length Shaker cdnas resembles one quarter of the a subunit of sodium and calcium channels (Fig. 1). Shaker transcripts produce functional inactivating potassium channels when expressed in Xenopus oocytes (Iverson et al. 1988~ Timpe et al. 1988a,b). These Shaker variants have a potassium selectivity, voltage dependence, and 4-AP sensitivity that are similar not only to each other, but also to the Shaker channels recorded in Drosophila muscles. The different Shaker products differ, however, in their inactivation kinetics. Macroscopic inactivation of Shaker currents has both fast and slow components (Fig. 2). The alternatively spliced products differ in the time constants of both components and in the magnitude of the slower component. With large depolarization, the channels open briefly and synchronously, soon after the membrane potential is stepped to the depolarized level, producing the fast component of macroscopic inactivation (Figs. 2 and 3) (Solc et al. 1987). The slower component is due to reopenings later in the step (Zagotta et al. 1989: Zagotta and Aldrich 1989), which progressively decrease in frequency with time (Fig. 3). A comparison of channels induced by naturally occurring, chimeric, and mutant Shaker variants that differ only at their amino- or carboxy-terminal regions (Figs. 2, 3, and 4) indicates the importance that these Cold Spring Harbor Symposia on Quantitative Biology, Volume LX( 9 1990 Cold Spring Harbor Laboratory 0-87969-059-3/90 $1.00 9

I0 + Na channel ISACOFF ET AL. $4 $4 $4 $4 2+ Ca channel $4 $4 $4 $4 --f HI IU m H Ill H I III + S4 K channel (A channel) H37 ~ [~ [~[~ I [~ ~Jt*~[~ ShC I ShA B ShB S4 NH 2 - -COOH Figure 1. Schematic representation of the primary structure of voltage-sensitive ion channels. The a subunits of sodium and calcium channels are large and are composed of four internally homologous domains. Each of the five alternatively spliced products of the Shaker potassium channel gene that have been isolated resembles a single one of these four domains. Each domain of the sodium and calcium channels, and each alternatively spliced Shaker product, contains multiple stretches of 19 or more predominantly hydrophobic residues that are potentially membrane spanning (crosshatched) and one $4 segment (labeled above) that has a basic residue at every third position. (Adapted from Jan and Jan 1989.) alternative ends have in determining inactivation gating. Variants containing the carboxy-terminal region of ShA inactivate to completion rapidly (Fig. 2, left panels), whereas those containing the carboxy-terminal region of ShB require considerably longer to decay to baseline (Fig. 2, right panels); this decay time is 40-50 times longer for ShB and ShB(A17-25) than for ShA and ShA(A17-25), respectively. These differences in macroscopic currents are due to differences in the probability of reopening between variants containing the two carbo regions. For example, whereas ShB channels reopen several times during the depolarization, ShA channels open at the beginning of the step but reopen rarely and only early in the step (Fig. 3). In addition to inactivating rapidly, channels containing the carboxy-terminal region of ShA recover from inactivation much more slowly (e.g., ShA requires 30-60 times longer to recover than ShB (Fig. 4) (Timpe et al. 1988b). These observations suggest that there are two inactive states that Shaker channels enter: a first inactivated state from which they recover rapidly, even during sustained depolarization, and a second, more stable inactive state from which they recover only during repolarization. Apparently, channels encoded by Shaker products containing the carboxy-terminal region of ShA rapidly enter a very stable inactive state, whereas those encoded by products containing the carboxy-terminal region of ShB enter the stable inactive state far more slowly. The amino-terminal region also appears to play a critical role in inactivation. Constructs differing in the amino-terminal region produce channels that inactivate and recover from inactivation at different rates (Figs. 2 and 4). Comprehensive mutagenesis of the alternative amino-terminal region common to ShA and ShB has shown directly that it plays an important role in inactivation gating, with deletions in the first 20 amino acids strongly slowing inactivation of ShB (Hoshi et al. 1989;

VOLTAGE-GATED POTASSIUM CHANNELS ShC ~ShCB 11 ShDA ShA ShA(AI 7-25) ShB(zxl 7-25) 0.5 sec she I ~!!1 i ~'//A shcb SnDA /1 g$$~ I::ii ~/~ ShD ShA I ~ II V//A shb Figure 2, Kinetics of A channels induced in Xenopus oocytes by alternatively spliced products of the Shaker gene. Both the amino- and carboxy-terminal regions play a role in determining the rate of the fast component of inactivation and the magnitude of the slow component of inactivation. The role of the amino terminus can be seen by comparing the kinetics of channels encoded by variants displayed in the left panels as a group (ShC, ShDA, ShA, and ShA[A17-25]) and by comparing those in the right panels as a group (ShCB, ShD, ShB, and ShB[AI7-25]). The role of the carboxy-terminal region can be seen by examining horizontal pairs. ShCB and ShDA are chimeric cdna constructs (E. Isacoff, unpubl.) that have not been found in flies. Note the slowing of inactivation in the mutants ShB(A17 25) (Isacoff et al. 199{)) and ShA(A17-25) (E. Isacoff, unpubl.) in which amino acids 17-25 were deleted from the amino terminus common to ShB and ShA. Currents were evoked by 2-sec depolarizations from 100 mv to +40 mv. Aldrich et al., this volume). When a nine-amino-acid deletion mutation (of residues 17-25) is made in the amino-terminal region common to ShA and ShB, inactivation is slowed by about threefold for both the fast and slow components of ShB (Isacoff et al. 1990) and for the fast component of ShA (Fig. 2). The prolongation of the macroscopic currents in these mutants is partly due to a prolongation of single-channel burst duration, as shown in the ShB background in Figure 3; i.e., this is due to a slowed rate of transition into the first inactive state. Aldrich and colleagues (this volume) suggest that the amino-terminal region forms a ball that has a net positive charge and produces inactivation by binding to a negatively charged region at the cytoplasmic mouth of the pore and plugging the permeation pathway. In this model, which is similar to one proposed by Armstrong and Bezanilla (1977) for sodium channels (Bezanilla and Armstrong 1977), Shaker products with different amino-terminal regions produce plugs with different on and off rates. The three positively charged residues deleted in ShB(A17-25) and ShA(A17-25) (amino acids 17, 18, and 19) may form part of the plug, but they cannot account for all of the interaction between the plug and the negatively charged region, since a slowed inactivation still takes place in these mutants (Fig. 3). Two other alternative amino-terminal regions contain some positively charged amino acids (Kamb et al. 1988; Schwarz et al. 1988). In contrast, the aminoterminal region specific to ShC consists of entirely hydrophobic residues (Schwarz et al. 1988) but ShC channels nevertheless inactivate as rapidly as ShA (Fig. 2) (Timpe et al. 1988a), suggesting that other portions of the protein also contribute to plug formation.

12 ISACOFF ET AL. ShA m Shg v/////a i pa ShB(Zxl 7-2 5) IH 20 ms +40 mv Figure 3. Single-channel recordings from Shaker products with different amino- and carboxy-terminal regions. In all three variants, depolarization to +40 mv evokes openings early in the step. ShA channels reopen rarely, whereas ShB channels reopen several times, with decreasing frequency, later in the step. This suggests that ShA channels enter a stable inactive state more rapidly than ShB channels. ShB(A17-25) channels reopen frequently, as do ShB channels, but have longer bursts, indicating a slowing of the transition into the first inactive state in the mutant. Steps were given to outside-out patches from a holding potential of -100 mv at 4-sec intervals for ShB and ShB(AI7--25) and from a holding potential of -120 mv at 10-sec intervals for ShA. Beyond these general observations about the kinetic properties peculiar to variant amino- or carboxy-terminal regions, it is also evident that the combination of amino and carboxyl termini is critical in determining how a channel behaves. For example, although ShC and ShA are very similar in inactivation onset, when these two amino-terminal regions are placed in the context of the carboxy-terminal region of ShB--as ShCB and ShB--their kinetics are remarkably different (Fig. 2). Similarly, the inactivation kinetics of ShDA and ShA(A17-25) are very similar, whereas those of ShD and ShB(A17-25) differ greatly (Fig. 2). These observations suggest that the amino- and carboxyterminal regions interact in inactivation gating, a possibility addressed below. In summary, a comparison of the Shaker alternative splicing products indicates that the voltage sensor and pore are likely encoded by the common core of the protein, which includes the $4 and other proposed transmembrane segments (with the exception of H6, which is. nevertheless, almost completely conserved), whereas inactivation is at least partly controlled by the alternative amino- and carboxy-terminal regions (Figs. 2, 3, and 4) (Iverson et al. i988; Timpe et al. I988a,b). The differences in inactivation kinetics of the alternative splicing products may be of physiological significance because these products are differentially distributed in the central nervous system of Drosophila. Whereas a widespread, although nonuniform, distribution is revealed by antibodies against the core region of the protein sequence shared by different Shaker products, antibodies against the amino-terminal region of a subset of the Shaker products show a much more restricted staining pattern (Schwarz et al. 1990). These observations suggest that different Shaker products may, in fact, generate distinct kinetic subtypes of A channels in different neurons. These channels may enhance synaptic transmission by undergoing cumulative inactivation during trains of activity. The type of activity required to produce such an event would be expected

VOLTAGE-GATED POTASSIUM CHANNELS 13 125 ms - ( ill(ill( - r r T - f - t" f f r'""i i, i r i - F- I I I - r... I f///a shcb ShDA II ShA 1 ShA(AI7-25) II I$$$1 I ~'///~ s,8 I;;;] II ~f//~ ShB(A17-25) Figure 4. Recovery from inactivation of variant Shaker products. Recovery is rapid (complete within seconds) for Shaker variants containing the carboxy-terminal region of ShB (with the exception of the chimera ShCB) and very slow (requiring many minutes) for variants containing carboxy-terminal region of ShA. Cells were held at -100 mv, and a pair of 100-msec-long pulses to +4(] mv, separated by varying intervals, were given once every 20-60 sec. to depend on the inactivation kinetics of the variants encoding the relevant channels, with more slowly recovering variants affected at lower frequencies of activity. Multiple Genes Coding for Different Potassium Channel Polypeptides Are Found in Vertebrates and Invertebrates Clearly, alternative splicing of a potassium channel gene accounts for only part of channel diversity in Drosophila. Deletions of most of the Shaker locus from the genome have no effect on other potassium currents, including a neuronal A current that activates at considerably more hyperpolarized potentials than Shaker (Salkoff 1983; Solc et al. 1987). Some of these potassium currents have been shown to be affected by mutations of other genes (Ganetzky and Wu 1986). It appears that potassium channels that differ in voltage dependence, calcium sensitivity, and pharmacology derive from a number of distinct potassium channel genes. Several potassium channel genes have already been isolated from both Drosophila and mammals (cf. Jan and Jan 1990b). They encode potassium channel polypeptides that are structurally related to the Shaker products. Interestingly, for the closest mammalian homologs to Shaker, diversity appears to be generated by the existence of a family of separate genes encoded by single exons, rather than by alternative splicing of a single gene (Chandy et al. 1990). The predicted Shaker potassium channel polypeptides, and their homologs in Drosophila and mammals, resemble each other, as well as one of the four internally homologous domains of sodium and calcium channel subunits, in predicted transmembrane topology, including the presence of one putative transmembrane segment rich in positively charged amino acids called the $4 (Fig. 1). These homologies between voltageactivated channels have led to the suggestion that potassium channels may form into multisubunit channels by assembly of several identical polypeptides and that each subunit of a potassium channel, or pseudosubunit of the sodium and calcium channels, possesses in its $4 segment its own voltage sensor.

14 ISACOFF ET AL Heteromultimeric Potassium Channels Expressed in Xenopus Oocytes Have Distinct Properties Although detailed biochemical and structural analyses of potassium channels have not yet been carried out, electrophysiological studies have been used to test the hypothesis that the channels are composed of several like subunits. When two different species of Shaker mrnas (ShA and ShB, or ShA and the slowly inactivating amino-terminal deletion mutant ShB(A17-25)) are mixed and coinjected into oocytes, they generate currents that cannot be fit by the arithmetic sum of the currents that each mrna induces individually (Fig. 5A,B) (Isacoff et al. 1990); i.e., they cannot be accounted for by the independent expression of the two different populations of channels. Instead, most of the channels that are made in the coinjected oocytes inactivate (Fig. 5A) and recover from inactivation (Fig. 5C) with complex intermediate kinetics. This finding is taken to indicate that polypeptides encoded by the two mrnas coassemble into heteromultimeric channels. Similar conclusions have also been reached by studies in which two species of mrnas coding for different rat brain potassium channel polypeptides were coinjected (Christie et al. 1990; Ruppersberg et al. 1990). The multisubunit character of the channel implies that there may be as many inactivation gates as there are subunits or, alternatively, that one joint gate may exist to which each polypeptide contributes its own amino- and carboxy-terminal regions. It also opens the possibility that the interaction in inactivation gating between the amino- and carboxy-terminal regions, discussed above, may occur between subunits as well as within a subunit. The idea that interaction between subunits plays a role in inactivation gating seems reasonable by analogy with sodium channels in which the junction of the carboxyl terminus of the third and the amino terminus of the fourth internally homologous domains (Fig. 1 ) appears to be critical for inactivation (Vassilev et al. 1988). Related evidence has been obtained for potassium channels by the construction of tandem dimers of Shaker (Isacoff et al. 1990), in which two subunits are encoded by a single mrna with the carboxyl terminus of the first copy tethered to the amino terminus of the second. These tandem constructs produce functional channels with relatively normal inactivation kinetics, both when the channels are homomultimers (Fig. 6A) and when they are heteromultimers (Fig. 6B). The finding that tandem dimers produce functional channels indicates that, like sodium channels, Shaker channels likely have both amino and carboxyl termini on the same side of the membrane and that they are composed of an even number of similar subunits. The apparent absence in coinjection experiments of a current component with rates equal to those of the homomultimers (most obvious for ShB(A17-25; Fig. 5) suggests that either heteromultimer formation is favored over homomultimerization or that assembly is random but that the number of subunits is sufficiently large (/> 4) so that the contribution by homomultimers to the overall current (~< 1/16) is too small to detect, A C 1.0 ShB (A17-25) / ShA B SUM ShA : ShB(,~17 25) 1:3 1:1 3:1 >- [-q > 0 08 0.6 0.4 V z / 2j ~- T ~ ~ CO INJECTION 0.0 ~ IF~i I I I I I 0 10 20 30 40 50 60 70 80 1:1 SLIM ShA 0.5 see TIME (sec) Figure 5. Potassium channels are formed by coassembly of several like subunits. (A) Normalized and superimposed currents from oocytes injected with mrna from ShA and ShB(A17-25) or coinjected with equal amounts of the two show that the coinjected oocytes express channels with kinetics that differ from those expressed in oocytes injected with either mrna alone. (B) Arithmetic sums of average time constants of ShA and ShB(A17-25) currents in ratios of 1:3, 1:1, and 3:1 predict macroscopic currents that would be produced by the expression in coinjected oocytes if the two variant Shaker mrnas produced two independent populations of channels. These predictions clearly do not resemble the actual currents measured in coinjected oocytes as shown in panel A. (C) Recovery from inactivation following a 400-msec depolarization to +40 mv is very fast for ShB(A17-25), very slow for ShA, and intermediate for the coinjected oocytes. The kinetics of recovery in the coinjected oocytes cannot be accounted for by the arithmetic sum of independent populations of ShA and ShB(A17-25) channels as shown for the predicted 1:1 sum of the individual kinetics of ShA and ShB(A17-25). These results indicate that the channels formed in the coinjected oocytes are likely mixed subunit channels formed by coassembly of ShA and ShB(A17-25) polypeptides. (Adapted from Isacoff et al. 1990.)

VOLTAGE-GATED POTASSIUM CHANNELS 15 A m 5hB F//~... Ill 5hB-ShB ~//'2eln [,"//A B ShA I [] 5hB(A17-25) ~//A ShA-ghBQtxl 7-25) Itttl-li V//A Figure 6. Tandem dimers of Shaker cdnas encode functional channels. (Tandem dimers were made by fusing the 3' end of the first copy, via a ten-glutamine linker, to the codon encoding the sixth amino acid of the second copy,) (A) Inactivation of the tandem dimer ShB-ShB resembles that of the wild-type ShB but has a slightly slower and larger second component. (B) As for the production of heteromultimeric channels in oocytes coinjected with two separate Shaker mrna variants, tandem dimers containing two variants produce channels with kinetics that are distinct from those of channels produced by either variant on its own. These results indicate that Shaker potassium channels are likely composed of an even number of subunits and that both the amino and carboxyl termini are likely to be on the same side of the membrane. (Adapted from Isacoff et al. 1990.) Coassembly also occurs between potassium channel polypeptides from the rat (RCK1) and fly (ShB) (Isacoff et al. 1990), indicating that the tertiary structure of channel polypeptides that have diverged evolutionarily can be similar enough to allow for functional interaction, despite the fact that they are only 75% identical in the conserved core at the level of amino acid sequence. The compatibility of divergent channel polypeptides suggests that the capacity for coassembly is as relevant for the functional grouping of potassium channel genes as is sequence homology. It remains to be determined whether heteromultimeric channels form in vivo. If so, the coassembly of different combinations of potassium channel polypeptides provides an additional parameter for the generation of functional diversity. Structural Similarity between Voltage-gated and Second-messenger-gated Channels Although a number of voltage-gated potassium channel sequences have been found to be related, it remains an open question as to whether other potassium chart- nels, e.g., 4-AP-insensitive channels and channels that are gated chemically by substances such as calcium or ATP, also share structural similarity with Shaker. A significant sequence similarity has been found between known voltage-gated cation channels and a cgmpgated cation channel, indicating that the superfamily of voltage-gated cation channels also includes a channel that is gated by a second messenger (Jan and Jan 1990a). This similarity, however, is restricted to a small set of highly conserved residues located in the proposed transmembrane segments. Therefore, although this superfamily may include other channels that are gated by second messengers, and although these channel genes may in several other instances encode a single subunit of a multimeric channel, the overall primary sequence similarity will probably prove to be extremely low, Involvement of the $4 Sequence in Voltage-dependent Activation of the Channel Voltage-gated potassium channels contain a charged intrinsic voltage sensor (the gating charge) that detects

16 ISACOFF ET AL. Table 1. Midpoints of Conductance-Voltage Curves of $4 Mutants Position R362 R365 R368 R371 K374 R377 K380 Basic Substitution + 12 0 0 + 64 0 + 29 a 0 Neutralization +20-12 + 53 a - 16 null null 0 Values (in millivolts) are expressed relative to the midpoint of wild-type ShB (-10mV) so that + and - indicate depolarizing and hyperpolarizing shifts, respectively, and 0 indicates similarity to ShB. Accompanied by a decrease in slope. changes in potential across the membrane, responds to these changes by a movement of charges in the membrane electric field, and presumably triggers the conformational change leading to channel opening. The $4 segment has been proposed to function as the voltage sensor because it contains a basic residue at every third or fourth position, with mainly hydrophobic residues at the intervening positions. These positively charged residues have been proposed to constitute the channel's gating charge and their displacement (toward the extracellular face of the membrane during depolarization and toward the cytoplasmic face during hyperpolarization) to produce the channel's gating current. To test the $4 model, we have substituted each of the seven basic residues in the $4 sequence of ShB individually with the other basic residue (replacing arginine with lysine and vice versa) or with the uncharged residue glutamine (D.M. Papazian et al., in prep.). These mutations do not affect the channel's potassium selectivity, as reflected by the reversal potentials at 1 mm and 40 mm external potassium, or the rate of inactivation. A large fraction of these mutations, however, affected the voltage dependence of channel activation, as determined from normalized conductancevoltage (g-v) curves. The g-v curves were fit to Boltzmann distributions, and the midpoints (Table 1) and slopes were measured. In addition to shifts in midpoints that occurred with little or no change in slope, two mutations greatly reduced the slope of the voltage dependence curve. The specificity of the effects of these $4 mutations on the channel's voltage dependence suggests that the $4 sequence is involved in the voltage-dependent activation of this potassium channel. Similar conclusions have been reached for the sodium channel (Stuhmer et al. 1989). The quantitative effects of individual $4 mutations in Shaker, however, are not predicted by simple considerations of the electrostatic interaction between charged residues and the membrane electric field. Rather, interactions between the $4 sequence and other parts of the channel molecule are likely to be important in determining the ease of transitions between closed and open states, the stability of the various states, and, possibly, the extent of cooperativity between subunits during the transitions. SUMMARY The cloning and characterization of the voltage-activated Shaker potassium channel gene in Drosophila have led to the identification of structural elements involved in potassium channel gating. As found for the voltage-activated sodium channel, the $4 segment, located in the conserved core of the protein, plays a central role in voltage-dependent activation. Potassium channels appear to be formed by the assembly of several polypeptides into multisubunit channels. This is directly analogous to the proposed folding of the four internally homologous pseudosubunits of sodium and calcium channels. The amino- and carboxy-terminal regions of Shaker channels are specialized for, and appear to interact in, inactivation gating. This interaction probably includes interaction between subunits, as may be said for the role in inactivation gating of the junction between the carboxyl terminus of the third domain and amino terminus of the fourth domain of sodium channel (Vassilev et al. 1988). 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Molecular Studies of Voltage-gated Potassium Channels E. Isacoff, D. Papazian, L. Timpe, et al. Cold Spring Harb Symp Quant Biol 1990 55: 9-17 Access the most recent version at doi:10.1101/sqb.1990.055.01.004 References This article cites 35 articles, 13 of which can be accessed free at: http://symposium.cshlp.org/content/55/9.full.html#ref-list-1 Creative Commons License Email Alerting Service Receive free email alerts when new articles cite this article - sign up in the box at the top right corner of the article or click here. To subscribe to Cold Spring Harbor Symposia on Quantitative Biology go to: http://symposium.cshlp.org/subscriptions