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1.  Determination of parameter identifiability in nonlinear biophysical models: A Bayesian approach 
The Journal of General Physiology  2014;143(3):401-416.
A Bayesian approach can be used to determine the reliability of estimated parameters in biophysical models.
A major goal of biophysics is to understand the physical mechanisms of biological molecules and systems. Mechanistic models are evaluated based on their ability to explain carefully controlled experiments. By fitting models to data, biophysical parameters that cannot be measured directly can be estimated from experimentation. However, it might be the case that many different combinations of model parameters can explain the observations equally well. In these cases, the model parameters are not identifiable: the experimentation has not provided sufficient constraining power to enable unique estimation of their true values. We demonstrate that this pitfall is present even in simple biophysical models. We investigate the underlying causes of parameter non-identifiability and discuss straightforward methods for determining when parameters of simple models can be inferred accurately. However, for models of even modest complexity, more general tools are required to diagnose parameter non-identifiability. We present a method based in Bayesian inference that can be used to establish the reliability of parameter estimates, as well as yield accurate quantification of parameter confidence.
PMCID: PMC3933937  PMID: 24516188
2.  Calcium-dependent stoichiometries of the KCa2.2 (SK) intracellular domain/calmodulin complex in solution 
The Journal of General Physiology  2014;143(2):231-252.
Biophysical analyses indicate that the Ca2+-activated K+ channel SK2 binds calmodulin with multiple stoichiometries, distinct from the two SK2-two calmodulin stoichiometry identified by crystallography.
Ca2+ activates SK Ca2+-activated K+ channels through the protein Ca2+ sensor, calmodulin (CaM). To understand how SK channels operate, it is necessary to determine how Ca2+ regulates CaM binding to its target on SK. Tagless, recombinant SK peptide (SKp), was purified for binding studies with CaM at low and high Ca2+ concentrations. Composition gradient multi-angle light scattering accurately measures the molar mass, stoichiometry, and affinity of protein complexes. In 2 mM Ca2+, SKp and CaM bind with three different stoichiometries that depend on the molar ratio of SKp:CaM in solution. These complexes include 28 kD 1SKp/1CaM, 39 kD 2SKp/1CaM, and 44 kD 1SKp/2CaM. A 2SKp/2CaM complex, observed in prior crystallographic studies, is absent. At <5 nM Ca2+, 1SKp/1CaM and 2SKp/1CaM were observed; however, 1SKp/2CaM was absent. Analytical ultracentrifugation was used to characterize the physical properties of the three SKp/CaM stoichiometries. In high Ca2+, the sedimentation coefficient is smaller for a 1SKp:1CaM solution than it is for either 2SKp:1CaM or 1SKp:2CaM. At low Ca2+ and at >100 µM protein concentrations, a molar excess of SKp over CaM causes aggregation. Aggregation is not observed in Ca2+ or with CaM in molar excess. In low Ca2+ both 1SKp:1CaM and 1SKp:2CaM solutions have similar sedimentation coefficients, which is consistent with the absence of a 1SKp/2CaM complex in low Ca2+. These results suggest that complexes with stoichiometries other than 2SKp/2CaM are important in gating.
PMCID: PMC4001768  PMID: 24420768
3.  Charge substitution for a deep-pore residue reveals structural dynamics during BK channel gating 
The Journal of General Physiology  2011;138(2):137-154.
The pore-lining amino acids of ion channel proteins reside on the interface between a polar (the pore) and a nonpolar environment (the rest of the protein). The structural dynamics of this region, which physically controls ionic flow, are essential components of channel gating. Using large-conductance, Ca2+-dependent K+ (BK) channels, we devised a systematic charge–substitution method to probe conformational changes in the pore region during channel gating. We identified a deep-pore residue (314 in hSlo1) as a marker of structural dynamics. We manipulated the charge states of this residue by substituting amino acids with different valence and pKa, and by adjusting intracellular pH. We found that the charged states of the 314 residues stabilized an open state of the BK channel. With models based on known structures of related channels, we postulate a dynamic rearrangement of the deep-pore region during BK channel opening/closing, which involves a change of the degree of pore exposure for 314.
PMCID: PMC3149437  PMID: 21746846
4.  EF hands at the N-lobe of calmodulin are required for both SK channel gating and stable SK–calmodulin interaction 
The Journal of General Physiology  2009;134(4):281-293.
Small conductance calcium-activated potassium (SK) channels respond to intracellular Ca2+ via constitutively associated calmodulin (CaM). Previous studies have proposed a modular design for the interaction between CaM and SK channels. The C-lobe and the linker of CaM are thought to regulate the constitutive binding, whereas the N-lobe binds Ca2+ and gates SK channels. However, we found that coexpression of mutant CaM (E/Q) where the N-lobe has only one functional EF hand leads to rapid rundown of SK channel activity, which can be recovered with exogenously applied wild-type (WT), but not mutant, CaM. Our results suggest that the mutation at the N-lobe EF hand disrupts the stable interaction between CaM and SK channel subunits, such that mutant CaM dissociates from the channel complex when the inside of the membrane is exposed to CaM-free solution. The disruption of the stable interaction does not directly result from the loss of Ca2+-binding capacity because SK channels and WT CaM can stably interact in the absence of Ca2+. These findings question a previous conclusion that CaM where the N-lobe has only one functional EF hand can stably support the gating of SK channels. They cannot be explained by the current model of modular interaction between CaM and SK channels, and they imply a role for N-lobe EF hand residues in binding to the channel subunits. Additionally, we found that a potent enhancer for SK channels, 3-oxime-6,7-dichloro-1H-indole-2,3-dione (NS309), enables the recovery of channel activity with CaM (E/Q), suggesting that NS309 stabilizes the interaction between CaM and SK channels. CaM (E/Q) can regulate Ca2+-dependent gating of SK channels in the presence of NS309, but with a lower apparent Ca2+ affinity than WT CaM.
PMCID: PMC2757765  PMID: 19752189
5.  State-dependent Block of BK Channels by Synthesized Shaker Ball Peptides 
The Journal of General Physiology  2006;128(4):423-441.
Crystal structures of potassium channels have strongly corroborated an earlier hypothetical picture based on functional studies, in which the channel gate was located on the cytoplasmic side of the pore. However, accessibility studies on several types of ligand-sensitive K+ channels have suggested that their activation gates may be located near or within the selectivity filter instead. It remains to be determined to what extent the physical location of the gate is conserved across the large K+ channel family. Direct evidence about the location of the gate in large conductance calcium-activated K+ (BK) channels, which are gated by both voltage and ligand (calcium), has been scarce. Our earlier kinetic measurements of the block of BK channels by internal quaternary ammonium ions have raised the possibility that they may lack a cytoplasmic gate. We show in this study that a synthesized Shaker ball peptide (ShBP) homologue acts as a state-dependent blocker for BK channels when applied internally, suggesting a widening at the intracellular end of the channel pore upon gating. This is consistent with a gating-related conformational change at the cytoplasmic end of the pore-lining helices, as suggested by previous functional and structural studies on other K+ channels. Furthermore, our results from two BK channel mutations demonstrate that similar types of interactions between ball peptides and channels are shared by BK and other K+ channel types.
PMCID: PMC2151574  PMID: 16966472
6.  State-independent Block of BK Channels by an Intracellular Quaternary Ammonium 
The Journal of General Physiology  2006;128(3):347-364.
Intracellular blockade by quaternary ammonium (QA) molecules of many potassium channels is state dependent, where the requirement for channel opening is evidenced by a time-dependent component of block in the macroscopic record. Whether this is the case for Ca2+- and voltage-activated potassium (BK) channels, however, remains unclear. Previous work (Li, W., and R.W. Aldrich. 2004. J. Gen. Physiol. 124:43–57) tentatively proposed a state-dependent, trapping model, but left open the possibility of state-independent block. Here, we found BK channel blockade by a novel QA derivative, bbTBA, was time dependent, raising the possibility of state-dependent, open channel block. Alternatively, the observed voltage dependence of block could be sufficient to explain time-dependent block. We have used steady-state and kinetic measurements of bbTBA blockade in order to discriminate between these two possibilities. bbTBA did not significantly slow deactivation kinetics at potentials between −200 and −100 mV, suggesting that channels can close unhindered by bound bbTBA. We further find no evidence that bbTBA is trapped inside BK channels after closing. Measurements of steady state fractional block at +40 mV revealed a 1.3-fold change in apparent affinity for a 33-fold change in Po, in striking contrast to the 31-fold change predicted by state-dependent block. Finally, the appearance of a third kinetic component of bbTBA blockade at high concentrations is incompatible with state-dependent block. Our results suggest that access of intracellular bbTBA to the BK channel cavity is not strictly gated by channel opening and closing, and imply that the permeation gate for BK channels may not be intracellular.
PMCID: PMC2151567  PMID: 16940557
7.  Binding of a Gating Modifier Toxin Induces Intersubunit Cooperativity Early in the Shaker K Channel's Activation Pathway 
The Journal of General Physiology  2006;128(1):119-132.
Potassium currents from voltage-gated Shaker K channels activate with a sigmoid rise. The degree of sigmoidicity in channel opening kinetics confirms that each subunit of the homotetrameric Shaker channel undergoes more than one conformational change before the channel opens. We have examined effects of two externally applied gating modifiers that reduce the sigmoidicity of channel opening. A toxin from gastropod mucus, 6-bromo-2-mercaptotryptamine (BrMT), and divalent zinc are both found to slow the same conformational changes early in Shaker's activation pathway. Sigmoidicity measurements suggest that zinc slows a conformational change independently in each channel subunit. Analysis of activation in BrMT reveals cooperativity among subunits during these same early steps. A lack of competition with either agitoxin or tetraethylammonium indicates that BrMT binds channel subunits outside of the external pore region in an allosterically cooperative fashion. Simulations including negatively cooperative BrMT binding account for its ability to induce gating cooperativity during activation. We conclude that cooperativity among K channel subunits can be greatly altered by experimental conditions.
PMCID: PMC2151558  PMID: 16801385
8.  Relationship between Pore Occupancy and Gating in BK Potassium Channels 
The Journal of General Physiology  2006;127(5):557-576.
Permeant ions can have significant effects on ion channel conformational changes. To further understand the relationship between ion occupancy and gating conformational changes, we have studied macroscopic and single-channel gating of BK potassium channels with different permeant monovalent cations. While the slopes of the conductance–voltage curve were reduced with respect to potassium for all permeant ions, BK channels required stronger depolarization to open only when thallium was the permeant ion. Thallium also slowed the activation and deactivation kinetics. Both the change in kinetics and the shift in the GV curve were dependent on the thallium passing through the permeation pathway, as well as on the concentration of thallium. There was a decrease in the mean open time and an increase in the number of short flicker closing events with thallium as the permeating ion. Mean closed durations were unaffected. Application of previously established allosteric gating models indicated that thallium specifically alters the opening and closing transition of the channel and does not alter the calcium activation or voltage activation pathways. Addition of a closed flicker state into the allosteric model can account for the effect of thallium on gating. Consideration of the thallium concentration dependence of the gating effects suggests that the flicker state may correspond to the collapsed selectivity filter seen in crystal structures of the KcsA potassium channel under the condition of low permeant ion concentration.
PMCID: PMC2151521  PMID: 16636204
9.  Unique Inner Pore Properties of BK Channels Revealed by Quaternary Ammonium Block 
Potassium channels have a very wide distribution of single-channel conductance, with BK type Ca2+-activated K+ channels having by far the largest. Even though crystallographic views of K+ channel pores have become available, the structural basis underlying BK channels' large conductance has not been completely understood. In this study we use intracellularly applied quaternary ammonium compounds to probe the pore of BK channels. We show that molecules as large as decyltriethylammonium (C10) and tetrabutylammonium (TBA) have much faster block and unblock rates in BK channels when compared with any other tested K+ channel types. Additionally, our results suggest that at repolarization large QA molecules may be trapped inside blocked BK channels without slowing the overall process of deactivation. Based on these findings we propose that BK channels may differ from other K+ channels in its geometrical design at the inner mouth, with an enlarged cavity and inner pore providing less spatially restricted access to the cytoplasmic solution. These features could potentially contribute to the large conductance of BK channels.
PMCID: PMC2229608  PMID: 15197222
potassium channel; conductance; patch clamp
10.  Mutations in the S4 Region Isolate the Final Voltage-dependent Cooperative Step in Potassium Channel Activation  
The Journal of General Physiology  1999;113(3):389-414.
Charged residues in the S4 transmembrane segment play a key role in determining the sensitivity of voltage-gated ion channels to changes in voltage across the cell membrane. However, cooperative interactions between subunits also affect the voltage dependence of channel opening, and these interactions can be altered by making substitutions at uncharged residues in the S4 region. We have studied the activation of two mutant Shaker channels that have different S4 amino acid sequences, ILT (V369I, I372L, and S376T) and Shaw S4 (the S4 of Drosophila Shaw substituted into Shaker), and yet have very similar ionic current properties. Both mutations affect cooperativity, making a cooperative transition in the activation pathway rate limiting and shifting it to very positive voltages, but analysis of gating and ionic current recordings reveals that the ILT and Shaw S4 mutant channels have different activation pathways. Analysis of gating currents suggests that the dominant effect of the ILT mutation is to make the final cooperative transition to the open state of the channel rate limiting in an activation pathway that otherwise resembles that of Shaker. The charge movement associated with the final gating transition in ILT activation can be measured as an isolated component of charge movement in the voltage range of channel opening and accounts for 13% (∼1.8 e0) of the total charge moved in the ILT activation pathway. The remainder of the ILT gating charge (87%) moves at negative voltages, where channels do not open, and confirms the presence of Shaker-like conformational changes between closed states in the activation pathway. In contrast to ILT, the activation pathway of Shaw S4 seems to involve a single cooperative charge-moving step between a closed and an open state. We cannot detect any voltage-dependent transitions between closed states for Shaw S4. Restoring basic residues that are missing in Shaw S4 (R1, R2, and K7) rescues charge movement between closed states in the activation pathway, but does not alter the voltage dependence of the rate-limiting transition in activation.
PMCID: PMC2222902  PMID: 10051516
gating; ion channel; patch clamp; Shaker
11.  Functional Consequences of a Decreased Potassium Affinity in a Potassium Channel Pore  
The Journal of General Physiology  1999;113(2):347-358.
Ions bound near the external mouth of the potassium channel pore impede the C-type inactivation conformational change (Lopez-Barneo, J., T. Hoshi, S. Heinemann, and R. Aldrich. 1993. Receptors Channels. 1:61– 71; Baukrowitz, T., and G. Yellen. 1995. Neuron. 15:951–960). In this study, we present evidence that the occupancy of the C-type inactivation modulatory site by permeant ions is not solely dependent on its intrinsic affinity, but is also a function of the relative affinities of the neighboring sites in the potassium channel pore. The A463C mutation in the S6 region of Shaker decreases the affinity of an internal ion binding site in the pore (Ogielska, E.M., and R.W. Aldrich, 1998). However, we have found that this mutation also decreases the C-type inactivation rate of the channel. Our studies indicate that the C-type inactivation effects observed with substitutions at position A463 most likely result from changes in the pore occupancy of the channel, rather than a change in the C-type inactivation conformational change. We have found that a decrease in the potassium affinity of the internal ion binding site in the pore results in lowered (electrostatic) interactions among ions in the pore and as a result prolongs the time an ion remains bound at the external C-type inactivation site. We also present evidence that the C-type inactivation constriction is quite local and does not involve a general collapse of the selectivity filter. Our data indicate that in A463C potassium can bind within the selectivity filter without interfering with the process of C-type inactivation.
PMCID: PMC2223370  PMID: 9925829
C-type inactivation; ion interactions; potassium affinity; Shaker
12.  Voltage-dependent Gating of Single Wild-Type and S4 Mutant KAT1 Inward Rectifier Potassium Channels  
The Journal of General Physiology  1998;112(6):679-713.
The voltage-dependent gating mechanism of KAT1 inward rectifier potassium channels was studied using single channel current recordings from Xenopus oocytes injected with KAT1 mRNA. The inward rectification properties of KAT1 result from an intrinsic gating mechanism in the KAT1 channel protein, not from pore block by an extrinsic cation species. KAT1 channels activate with hyperpolarizing potentials from −110 through −190 mV with a slow voltage-dependent time course. Transitions before first opening are voltage dependent and account for much of the voltage dependence of activation, while transitions after first opening are only slightly voltage dependent. Using burst analysis, transitions near the open state were analyzed in detail. A kinetic model with multiple closed states before first opening, a single open state, a single closed state after first opening, and a closed-state inactivation pathway accurately describes the single channel and macroscopic data. Two mutations neutralizing charged residues in the S4 region (R177Q and R176L) were introduced, and their effects on single channel gating properties were examined. Both mutations resulted in depolarizing shifts in the steady state conductance–voltage relationship, shortened first latencies to opening, decreased probability of terminating bursts, and increased burst durations. These effects on gating were well described by changes in the rate constants in the kinetic model describing KAT1 channel gating. All transitions before the open state were affected by the mutations, while the transitions after the open state were unaffected, implying that the S4 region contributes to the early steps in gating for KAT1 channels.
PMCID: PMC2229449  PMID: 9834140
single channel analysis; S4 region; Arabidopsis thaliana; site-directed mutagenesis; activation
13.  A Mutation in S6 of Shaker Potassium Channels Decreases the K+ Affinity of an Ion Binding Site Revealing Ion–Ion Interactions in the Pore  
The Journal of General Physiology  1998;112(2):243-257.
Under physiological conditions, potassium channels are extraordinarily selective for potassium over other ions. However, in the absence of potassium, certain potassium channels can conduct sodium. Sodium flux is blocked by the addition of low concentrations of potassium. Potassium affinity, and therefore the ability to block sodium current, varies among potassium channel subtypes (Korn, S.J., and S.R. Ikeda. 1995. Science. 269:410–412; Starkus, J.G., L. Kuschel, M.D. Rayner, and S.H. Heinemann. 1997. J. Gen. Physiol. 110:539–550). The Shaker potassium channel conducts sodium poorly in the presence of very low (micromolar) potassium due to its high potassium affinity (Starkus, J.G., L. Kuschel, M.D. Rayner, and S.H. Heinemann. 1997. J. Gen. Physiol. 110:539–550; Ogielska, E.M., and R.W. Aldrich. 1997. Biophys. J. 72:A233 [Abstr.]). We show that changing a single residue in S6, A463C, decreases the apparent internal potassium affinity of the Shaker channel pore from the micromolar to the millimolar range, as determined from the ability of potassium to block the sodium currents. Independent evidence that A463C decreases the apparent affinity of a binding site in the pore comes from a study of barium block of potassium currents. The A463C mutation decreases the internal barium affinity of the channel, as expected if barium blocks current by binding to a potassium site in the pore. The decrease in the apparent potassium affinity in A463C channels allows further study of possible ion interactions in the pore. Our results indicate that sodium and potassium can occupy the pore simultaneously and that multiple occupancy results in interactions between ions in the channel pore.
PMCID: PMC2525752  PMID: 9689030
Shaker; Na+ permeation; ion selectivity; S6; K+ affinity
14.  Uncharged S4 Residues and Cooperativity in Voltage-dependent Potassium Channel Activation  
The Journal of General Physiology  1998;111(3):421-439.
Substitution of the S4 of Shaw into Shaker alters cooperativity in channel activation by slowing a cooperative transition late in the activation pathway. To determine the amino acids responsible for the functional changes in Shaw S4, we created several mutants by substituting amino acids from Shaw S4 into Shaker. The S4 amino acid sequences of Shaker and Shaw S4 differ at 11 positions. Simultaneous substitution of just three noncharged residues from Shaw S4 into Shaker (V369I, I372L, S376T; ILT) reproduces the kinetic and voltage-dependent properties of Shaw S4 channel activation. These substitutions cause very small changes in the structural and chemical properties of the amino acid side chains. In contrast, substituting the positively charged basic residues in the S4 of Shaker with neutral or negative residues from the S4 of Shaw S4 does not reproduce the shallow voltage dependence or other properties of Shaw S4 opening. Macroscopic ionic currents for ILT could be fit by modifying a single set of transitions in a model for Shaker channel gating (Zagotta, W.N., T. Hoshi, and R.W. Aldrich. 1994. J. Gen. Physiol. 103:321–362). Changing the rate and voltage dependence of a final cooperative step in activation successfully reproduces the kinetic, steady state, and voltage-dependent properties of ILT ionic currents. Consistent with the model, ILT gating currents activate at negative voltages where the channel does not open and, at more positive voltages, they precede the ionic currents, confirming the existence of voltage-dependent transitions between closed states in the activation pathway. Of the three substitutions in ILT, the I372L substitution is primarily responsible for the changes in cooperativity and voltage dependence. These results suggest that noncharged residues in the S4 play a crucial role in Shaker potassium channel gating and that small steric changes in these residues can lead to large changes in cooperativity within the channel protein.
PMCID: PMC2217114  PMID: 9482709
Shaker; gating; ion channel; patch clamp
15.  Role of the S4 in Cooperativity of Voltage-dependent Potassium Channel Activation 
The Journal of General Physiology  1998;111(3):399-420.
Charged residues in the S4 transmembrane segment of voltage-gated cation channels play a key role in opening channels in response to changes in voltage across the cell membrane. However, the molecular mechanism of channel activation is not well understood. To learn more about the role of the S4 in channel gating, we constructed chimeras in which S4 segments from several divergent potassium channels, Shab, Shal, Shaw, and Kv3.2, were inserted into a Shaker potassium channel background. These S4 donor channels have distinctly different voltage-dependent gating properties and S4 amino acid sequences. None of the S4 chimeras have the gating behavior of their respective S4 donor channels. The conductance–voltage relations of all S4 chimeras are shifted to more positive voltages and the slopes are decreased. There is no consistent correlation between the nominal charge content of the S4 and the slope of the conductance–voltage relation, suggesting that the mutations introduced by the S4 chimeras may alter cooperative interactions in the gating process. We compared the gating behavior of the Shaw S4 chimera with its parent channels, Shaker and Shaw, in detail. The Shaw S4 substitution alters activation gating profoundly without introducing obvious changes in other channel functions. Analysis of the voltage-dependent gating kinetics suggests that the dominant effect of the Shaw S4 substitution is to alter a single cooperative transition late in the activation pathway, making it rate limiting. This interpretation is supported further by studies of channels assembled from tandem heterodimer constructs with both Shaker and Shaw S4 subunits. Activation gating in the heterodimer channels can be predicted from the properties of the homotetrameric channels only if it is assumed that the mutations alter a cooperative transition in the activation pathway rather than independent transitions.
PMCID: PMC2217113  PMID: 9482708
Shaker; voltage-dependent gating; patch clamp
16.  BK calcium-activated potassium channels regulate circadian behavioral rhythms and pacemaker output 
Nature neuroscience  2006;9(8):1041-1049.
Spontaneous action potentials in the suprachiasmatic nucleus (SCN) are necessary for normal circadian timing of behavior in mammals. The SCN exhibits a daily oscillation in spontaneous firing rate (SFR), but the ionic conductances controlling SFR and the relationship of SFR to subsequent circadian behavioral rhythms are not understood. We show that daily expression of the large conductance Ca2+-activated K+ channel (BK) in the SCN is controlled by the intrinsic circadian clock. BK channel–null mice (Kcnma1−/−) have increased SFRs in SCN neurons selectively at night and weak circadian amplitudes in multiple behaviors timed by the SCN. Kcnma1−/− mice show normal expression of clock genes such as Arntl1 (Bmal1), indicating a role for BK channels in SCN pacemaker output, rather than in intrinsic time-keeping. Our findings implicate BK channels as important regulators of the SFR and suggest that the SCN pacemaker governs the expression of circadian behavioral rhythms through SFR modulation.
PMCID: PMC2909323  PMID: 16845385
17.  Immunolocalization of the Ca2+-Activated K+ Channel Slo1 in Axons and Nerve Terminals of Mammalian Brain and Cultured Neurons 
Ca2+-activated voltage-dependent K+ channels (Slo1, KCa1.1, Maxi-K, or BK channel) play a crucial role in controlling neuronal signaling by coupling channel activity to both membrane depolarization and intracellular Ca2+ signaling. In mammalian brain, immunolabeling experiments have shown staining for Slo1 channels predominantly localized to axons and presynaptic terminals of neurons. We have developed anti-Slo1 mouse monoclonal antibodies that have been extensively characterized for specificity of staining against recombinant Slo1 in heterologous cells, and native Slo1 in mammalian brain, and definitively by the lack of detectable immunoreactivity against brain samples from Slo1 knockout mice. Here we provide precise immunolocalization of Slo1 in rat brain with one of these monoclonal antibodies and show that Slo1 is accumulated in axons and synaptic terminal zones associated with glutamatergic synapses in hippocampus and GABAergic synapses in cerebellum. By using cultured hippocampal pyramidal neurons as a model system, we show that heterologously expressed Slo1 is initially targeted to the axonal surface membrane, and with further development in culture, become localized in presynaptic terminals. These studies provide new insights into the polarized localization of Slo1 channels in mammalian central neurons and provide further evidence for a key role in regulating neurotransmitter release in glutamatergic and GABAergic terminals.
PMCID: PMC2605666  PMID: 16566008
BK channel; ion channel; localization; protein trafficking; mAb
18.  Statistical Limits to the Identification of Ion Channel Domains by Sequence Similarity 
The Journal of General Physiology  2006;127(6):755-766.
The study of ion channel function is constrained by the availability of structures for only a small number of channels. A commonly used bioinformatics technique is to assert, based on sequence similarity, that a domain within a channel of interest has the same structure as a reference domain for which the structure is known. This technique, while useful, is often employed when there is only a slight similarity between the channel of interest and the domain of known structure. In this study, we exploit recent advances in structural genomics to calculate the sequence-based probability of the presence of putative domains in a number of ion channels. We find strong support for the presence of many domains that have been proposed in the literature. For example, eukaryotic and prokaryotic CLC proteins almost certainly share a common structure. A number of proposed domains, however, are not as well supported. In particular, for the COOH terminus of the BK channel we find a number of literature proposed domains for which the assertion of common structure based on common sequence has a nontrivial probability of error.
PMCID: PMC2151544  PMID: 16735758
19.  A Gastropod Toxin Selectively Slows Early Transitions in the Shaker K Channel's Activation Pathway 
The Journal of General Physiology  2004;123(6):685-696.
A toxin from a marine gastropod's defensive mucus, a disulfide-linked dimer of 6-bromo-2-mercaptotryptamine (BrMT), was found to inhibit voltage-gated potassium channels by a novel mechanism. Voltage-clamp experiments with Shaker K channels reveal that externally applied BrMT slows channel opening but not closing. BrMT slows K channel activation in a graded fashion: channels activate progressively slower as the concentration of BrMT is increased. Analysis of single-channel activity indicates that once a channel opens, the unitary conductance and bursting behavior are essentially normal in BrMT. Paralleling its effects against channel opening, BrMT greatly slows the kinetics of ON, but not OFF, gating currents. BrMT was found to slow early activation transitions but not the final opening transition of the Shaker ILT mutant, and can be used to pharmacologically distinguish early from late gating steps. This novel toxin thus inhibits activation of Shaker K channels by specifically slowing early movement of their voltage sensors, thereby hindering channel opening. A model of BrMT action is developed that suggests BrMT rapidly binds to and stabilizes resting channel conformations.
PMCID: PMC2234574  PMID: 15148327
Shaker; Kv; gating; potassium channel; neurotoxin
20.  Coupling between Voltage Sensor Activation, Ca2+ Binding and Channel Opening in Large Conductance (BK) Potassium Channels 
The Journal of General Physiology  2002;120(3):267-305.
To determine how intracellular Ca2+ and membrane voltage regulate the gating of large conductance Ca2+-activated K+ (BK) channels, we examined the steady-state and kinetic properties of mSlo1 ionic and gating currents in the presence and absence of Ca2+ over a wide range of voltage. The activation of unliganded mSlo1 channels can be accounted for by allosteric coupling between voltage sensor activation and the closed (C) to open (O) conformational change (Horrigan, F.T., and R.W. Aldrich. 1999. J. Gen. Physiol. 114:305–336; Horrigan, F.T., J. Cui, and R.W. Aldrich. 1999. J. Gen. Physiol. 114:277–304). In 0 Ca2+, the steady-state gating charge-voltage (QSS-V) relationship is shallower and shifted to more negative voltages than the conductance-voltage (GK-V) relationship. Calcium alters the relationship between Q-V and G-V, shifting both to more negative voltages such that they almost superimpose in 70 μM Ca2+. This change reflects a differential effect of Ca2+ on voltage sensor activation and channel opening. Ca2+ has only a small effect on the fast component of ON gating current, indicating that Ca2+ binding has little effect on voltage sensor activation when channels are closed. In contrast, open probability measured at very negative voltages (less than −80 mV) increases more than 1,000-fold in 70 μM Ca2+, demonstrating that Ca2+ increases the C-O equilibrium constant under conditions where voltage sensors are not activated. Thus, Ca2+ binding and voltage sensor activation act almost independently, to enhance channel opening. This dual-allosteric mechanism can reproduce the steady-state behavior of mSlo1 over a wide range of conditions, with the assumption that activation of individual Ca2+ sensors or voltage sensors additively affect the energy of the C-O transition and that a weak interaction between Ca2+ sensors and voltage sensors occurs independent of channel opening. By contrast, macroscopic IK kinetics indicate that Ca2+ and voltage dependencies of C-O transition rates are complex, leading us to propose that the C-O conformational change may be described by a complex energy landscape.
PMCID: PMC2229516  PMID: 12198087
calcium; potassium channel; BK channel; gating current; ion channel gating
21.  Modification of Cyclic Nucleotide–Gated Ion Channels by Ultraviolet Light 
The Journal of General Physiology  2000;116(2):227-252.
We irradiated cyclic nucleotide–gated ion channels in situ with ultraviolet light to probe the role of aromatic residues in ion channel function. UV light reduced the current through excised membrane patches from Xenopus oocytes expressing the α subunit of bovine retinal cyclic nucleotide–gated channels irreversibly, a result consistent with permanent covalent modification of channel amino acids by UV light. The magnitude of the current reduction depended only on the total photon dose delivered to the patches, and not on the intensity of the exciting light, indicating that the functionally important photochemical modification(s) occurred from an excited state reached by a one-photon absorption process. The wavelength dependence of the channels' UV light sensitivity (the action spectrum) was quantitatively consistent with the absorption spectrum of tryptophan, with a small component at long wavelengths, possibly due to cystine absorption. This spectral analysis suggests that UV light reduced the currents at most wavelengths studied by modifying one or more “target” tryptophans in the channels. Comparison of the channels' action spectrum to the absorption spectrum of tryptophan in various solvents suggests that the UV light targets are in a water-like chemical environment. Experiments on mutant channels indicated that the UV light sensitivity of wild-type channels was not conferred exclusively by any one of the 10 tryptophan residues in a subunit. The similarity in the dose dependences of channel current reduction and tryptophan photolysis in solution suggests that photochemical modification of a small number of tryptophan targets in the channels is sufficient to decrease the currents.
PMCID: PMC2229495  PMID: 10919869
cyclic guanine monophosphate; electrophysiology; ligand-gated; ion channel gating; ultraviolet light
22.  Effects of Ultraviolet Modification on the Gating Energetics of Cyclic Nucleotide–Gated Channels 
The Journal of General Physiology  2000;116(2):253-282.
Middendorf et al. (Middendorf, T.R., R.W. Aldrich, and D.A. Baylor. 2000. J. Gen. Physiol. 116:227–252) showed that ultraviolet light decreases the current through cloned cyclic nucleotide–gated channels from bovine retina activated by high concentrations of cGMP. Here we probe the mechanism of the current reduction. The channels' open probability before irradiation, Po(0), determined the sign of the change in current amplitude that occurred upon irradiation. UV always decreased the current through channels with high initial open probabilities [Po(0) > 0.3]. Manipulations that promoted channel opening antagonized the current reduction by UV. In contrast, UV always increased the current through channels with low initial open probabilities [Po(0) ≤ 0.02], and the magnitude of the current increase varied inversely with Po(0). The dual effects of UV on channel currents and the correlation of both effects with Po(0) suggest that the channels contain two distinct classes of UV target residues whose photochemical modification exerts opposing effects on channel gating. We present a simple model based on this idea that accounts quantitatively for the UV effects on the currents and provides estimates for the photochemical quantum yields and free energy costs of modifying the UV targets. Simulations indicate that UV modification may be used to produce and quantify large changes in channel gating energetics in regimes where the associated changes in open probability are not measurable by existing techniques.
PMCID: PMC2229492  PMID: 10919870
cyclic guanine monophosphate; electrophysiology; ligand-gated channel; ion channel gating; ultraviolet light
23.  Determinants of Voltage-Dependent Gating and Open-State Stability in the S5 Segment of Shaker Potassium Channels 
The Journal of General Physiology  1999;114(2):215-242.
The best-known Shaker allele of Drosophila with a novel gating phenotype, Sh5, differs from the wild-type potassium channel by a point mutation in the fifth membrane-spanning segment (S5) (Gautam, M., and M.A. Tanouye. 1990. Neuron. 5:67–73; Lichtinghagen, R., M. Stocker, R. Wittka, G. Boheim, W. Stühmer, A. Ferrus, and O. Pongs. 1990. EMBO [Eur. Mol. Biol. Organ.] J. 9:4399–4407) and causes a decrease in the apparent voltage dependence of opening. A kinetic study of Sh5 revealed that changes in the deactivation rate could account for the altered gating behavior (Zagotta, W.N., and R.W. Aldrich. 1990. J. Neurosci. 10:1799–1810), but the presence of intact fast inactivation precluded observation of the closing kinetics and steady state activation. We studied the Sh5 mutation (F401I) in ShB channels in which fast N-type inactivation was removed, directly confirming this conclusion. Replacement of other phenylalanines in S5 did not result in substantial alterations in voltage-dependent gating. At position 401, valine and alanine substitutions, like F401I, produce currents with decreased apparent voltage dependence of the open probability and of the deactivation rates, as well as accelerated kinetics of opening and closing. A leucine residue is the exception among aliphatic mutants, with the F401L channels having a steep voltage dependence of opening and slow closing kinetics. The analysis of sigmoidal delay in channel opening, and of gating current kinetics, indicates that wild-type and F401L mutant channels possess a form of cooperativity in the gating mechanism that the F401A channels lack. The wild-type and F401L channels' entering the open state gives rise to slow decay of the OFF gating current. In F401A, rapid gating charge return persists after channels open, confirming that this mutation disrupts stabilization of the open state. We present a kinetic model that can account for these properties by postulating that the four subunits independently undergo two sequential voltage-sensitive transitions each, followed by a final concerted opening step. These channels differ primarily in the final concerted transition, which is biased in favor of the open state in F401L and the wild type, and in the opposite direction in F401A. These results are consistent with an activation scheme whereby bulky aromatic or aliphatic side chains at position 401 in S5 cooperatively stabilize the open state, possibly by interacting with residues in other helices.
PMCID: PMC2230647  PMID: 10435999
gating current; ion channel; site-directed mutagenesis; activation; cooperativity
24.  Allosteric Voltage Gating of Potassium Channels II 
The Journal of General Physiology  1999;114(2):305-336.
Large-conductance Ca2+-activated K+ channels can be activated by membrane voltage in the absence of Ca2+ binding, indicating that these channels contain an intrinsic voltage sensor. The properties of this voltage sensor and its relationship to channel activation were examined by studying gating charge movement from mSlo Ca2+-activated K+ channels in the virtual absence of Ca2+ (<1 nM). Charge movement was measured in response to voltage steps or sinusoidal voltage commands. The charge–voltage relationship (Q–V) is shallower and shifted to more negative voltages than the voltage-dependent open probability (G–V). Both ON and OFF gating currents evoked by brief (0.5-ms) voltage pulses appear to decay rapidly (τON = 60 μs at +200 mV, τOFF = 16 μs at −80 mV). However, QOFF increases slowly with pulse duration, indicating that a large fraction of ON charge develops with a time course comparable to that of IK activation. The slow onset of this gating charge prevents its detection as a component of IgON, although it represents ∼40% of the total charge moved at +140 mV. The decay of IgOFF is slowed after depolarizations that open mSlo channels. Yet, the majority of open channel charge relaxation is too rapid to be limited by channel closing. These results can be understood in terms of the allosteric voltage-gating scheme developed in the preceding paper (Horrigan, F.T., J. Cui, and R.W. Aldrich. 1999. J. Gen. Physiol. 114:277–304). The model contains five open (O) and five closed (C) states arranged in parallel, and the kinetic and steady-state properties of mSlo gating currents exhibit multiple components associated with C–C, O–O, and C–O transitions.
PMCID: PMC2230644  PMID: 10436004
calcium; potassium channel; BK channel; ion channel gating; gating current
25.  Allosteric Voltage Gating of Potassium Channels I 
The Journal of General Physiology  1999;114(2):277-304.
Activation of large conductance Ca2+-activated K+ channels is controlled by both cytoplasmic Ca2+ and membrane potential. To study the mechanism of voltage-dependent gating, we examined mSlo Ca2+-activated K+ currents in excised macropatches from Xenopus oocytes in the virtual absence of Ca2+ (<1 nM). In response to a voltage step, IK activates with an exponential time course, following a brief delay. The delay suggests that rapid transitions precede channel opening. The later exponential time course suggests that activation also involves a slower rate-limiting step. However, the time constant of IK relaxation [τ(IK)] exhibits a complex voltage dependence that is inconsistent with models that contain a single rate limiting step. τ(IK) increases weakly with voltage from −500 to −20 mV, with an equivalent charge (z) of only 0.14 e, and displays a stronger voltage dependence from +30 to +140 mV (z = 0.49 e), which then decreases from +180 to +240 mV (z = −0.29 e). Similarly, the steady state GK–V relationship exhibits a maximum voltage dependence (z = 2 e) from 0 to +100 mV, and is weakly voltage dependent (z ≅ 0.4 e) at more negative voltages, where Po = 10−5–10−6. These results can be understood in terms of a gating scheme where a central transition between a closed and an open conformation is allosterically regulated by the state of four independent and identical voltage sensors. In the absence of Ca2+, this allosteric mechanism results in a gating scheme with five closed (C) and five open (O) states, where the majority of the channel's voltage dependence results from rapid C–C and O–O transitions, whereas the C–O transitions are rate limiting and weakly voltage dependent. These conclusions not only provide a framework for interpreting studies of large conductance Ca2+-activated K+ channel voltage gating, but also have important implications for understanding the mechanism of Ca2+ sensitivity.
PMCID: PMC2230643  PMID: 10436003
calcium; KCa channel; large conductance Ca2+-activated K+ channel; ion channel gating

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