Fred J. Sigworth

Data transformations for improved display and fitting of single-channel dwell time histograms

A.L. Blatz and K.L. Magleby (1986a. J. Physiol. [Lond.]. 378:141-174) have demonstrated the usefulness of plotting histograms with a logarithmic time axis to display the distributions of dwell times from recordings of single ionic channels. We derive here the probability density function (pdf) corresponding to logarithmically binned histograms. Plotted on a logarithmic time scale the pdf is a peaked function with an invariant width; this and other properties of the pdf, coupled with a variance-stabilizing (square root) transformation for the ordinate, greatly simplify the interpretation and manual fitting of distributions containing multiple exponential components. We have also examined the statistical errors in estimation, by the maximum-likelihood method, of kinetic parameters from logarithmically binned data. Using binned data greatly accelerates the fitting procedure and introduces significant errors only for bins spaced more widely than 8-16 per decade.

Quantifying the local resolution of cryo-EM density maps

We propose a definition of local resolution for three-dimensional electron cryo-microscopy (cryo-EM) density maps that uses local sinusoidal features. Our algorithm has no free parameters and is applicable to other imaging modalities, including tomography. By evaluating the local resolution of single-particle reconstructions and subtomogram averages for four example data sets, we report variable resolution across a 4- to 40-Å range.

Primary structure and functional expression of a mammalian skeletal muscle sodium channel

We describe the isolation and characterization of a cDNA encoding the alpha subunit of a new voltage-sensitive sodium channel, microI, from rat skeletal muscle. The 1840 amino acid microI peptide is homologous to alpha subunits from rat brain, but, like the protein from eel electroplax, lacks an extended (approximately 200) amino acid segment between homologous domains I and II. Northern blot analysis indicates that the 8.5 kb microI transcript is preferentially expressed in skeletal muscle. Sodium channels expressed in Xenopus oocytes from synthetic RNA encoding microI are blocked by tetrodotoxin and mu-conotoxin at concentrations near 5 nM. The expressed sodium channels have gating kinetics similar to the native channels in rat muscle fibers, except that inactivation occurs more slowly.

Impaired slow inactivation in mutant sodium channels.

Hyperkalemic periodic paralysis (HyperPP) is a disorder in which current through Na+ channels causes a prolonged depolarization of skeletal muscle fibers, resulting in membrane inexcitability and muscle paralysis. Although HyperPP mutations can enhance persistent sodium currents, unaltered slow inactivation would effectively eliminate any sustained currents through the mutant channels. We now report that rat skeletal muscle channels containing the mutation T698M, which corresponds to the human T704M HyperPP mutation, recover very quickly from prolonged depolarizations. Even after holding at -20 mV for 20 min, approximately 25% of the maximal sodium current is available subsequent to a 10-ms hyperpolarization (-100 mV). Under the same conditions, recovery is less than 3% in wild-type channels and in the F1304Q mutant, which has impaired fast inactivation. This effect of the T698M mutation on slow inactivation, in combination with its effects on activation, is expected to result in persistent currents such as that seen in HyperPP muscle.

Structure of the BK potassium channel in a lipid membrane from electron cryomicroscopy

A long-sought goal in structural biology has been the imaging of membrane proteins in their membrane environments. This goal has been achieved through the use of electron crystallography1 in those special cases where a protein forms highly-ordered arrays in lipid bilayers. It has also been achieved by NMR methods1 in proteins up to 50 kDa in size, although milligram quantities of protein and isotopic labeling is required. For structural analysis of large soluble proteins in microgram quantities an increasingly powerful method that does not require crystallization is single-particle reconstruction from electron microscopy of cryogenically-cooled samples (cryo-EM)2. We now report the first singleparticle cryo-EM study of a membrane protein, the human large-conductance calciumand voltageactivated potassium channel3 (BK), in a lipid environment. The new method is called random spherically-constrained (RSC) single-particle reconstruction. BK channels, members of the six-transmembrane-segment (6TM) ion channel family, were reconstituted at low density into lipid vesicles (liposomes), and their function was verified by a potassium flux assay. Vesicles were also frozen in vitreous ice and imaged in an electron microscope. From images of 8,400 individual protein particles a three-dimensional reconstruction of the BK channel and also its membrane environment was obtained at a resolution of 1.7 to 2.0 nm. Not requiring the formation of crystals, the RSC approach promises to be useful in the structural study of many other membrane proteins as well.A long-sought goal in structural biology has been the imaging of membrane proteins in their membrane environments. This goal has been achieved with electron crystallography in those special cases where a protein forms highly ordered arrays in lipid bilayers. It has also been achieved by NMR methods in proteins up to 50 kilodaltons (kDa) in size, although milligram quantities of protein and isotopic labelling are required. For structural analysis of large soluble proteins in microgram quantities, an increasingly powerful method that does not require crystallization is single-particle reconstruction from electron microscopy of cryogenically cooled samples (electron cryomicroscopy (cryo-EM)). Here we report the first single-particle cryo-EM study of a membrane protein, the human large-conductance calcium- and voltage-activated potassium channel (BK), in a lipid environment. The new method is called random spherically constrained (RSC) single-particle reconstruction. BK channels, members of the six-transmembrane-segment (6TM) ion channel family, were reconstituted at low density into lipid vesicles (liposomes), and their function was verified by a potassium flux assay. Vesicles were also frozen in vitreous ice and imaged in an electron microscope. From images of 8,400 individual protein particles, a three-dimensional (3D) reconstruction of the BK channel and its membrane environment was obtained at a resolution of 1.7–2.0 nm. Not requiring the formation of crystals, the RSC approach promises to be useful in the structural study of many other membrane proteins as well.

Functional consequences of a Na+ channel mutation causing hyperkalemic periodic paralysis

Hyperkalemic periodic paralysis (HYPP), one of several inheritable myotonic diseases, results from genetic defects in the human skeletal muscle Na+ channel. In some pedigrees, HYPP is correlated with a single base pair substitution resulting in a Met replacing Thr704 in the fifth transmembrane segment of the second domain. This region is totally conserved between the human and rat channels. We have introduced the human mutation into the corresponding region of the rat muscle Na+ channel cDNA and expressed it in human embryonic kidney 293 cells. Patch-clamp recordings show that this mutation shifts the voltage dependence of activation by 10-15 mV in the negative direction. The shift results in a persistent Na+ current that activates near -70 mV; this phenomenon could underlie the abnormal muscle activity observed in patients with HYPP.

μl Na+ channels expressed transiently in human embryonic kidney cells: Biochemical and biophysical properties

We describe the transient expression of the rat skeletal muscle muI Na+ channel in human embryonic kidney (HEK 293) cells. Functional channels appear at a density of approximately 30 in a 10 microns 2 patch, comparable to those of native excitable cells. Unlike muI currents in oocytes, inactivation gating is predominantly (approximately 97%) fast, although clear evidence is provided for noninactivating gating modes, which have been linked to anomalous behavior in the inherited disorder hyperkalemic periodic paralysis. Sequence-specific antibodies detect a approximately 230 kd glycopeptide. The majority of molecules acquire only neutral oligosaccharides and are retained within the cell. Electrophoretic mobility on SDS gels suggests the molecules may acquire covalently attached lipid. The channel is readily phosphorylated by activation of the protein kinase A and protein kinase C second messenger pathways.

Fragile X mental retardation protein controls gating of the sodium-activated potassium channel Slack

In humans, the absence of Fragile X mental retardation protein (FMRP), an RNA-binding protein, results in Fragile X syndrome, the most common inherited form of intellectual disability. Using biochemical and electrophysiological studies, we found that FMRP binds to the C terminus of the Slack sodium-activated potassium channel to activate the channel in mice. Our findings suggest that Slack activity provides a link between patterns of neuronal firing and changes in protein translation.

Multiple gating modes and the effect of modulating factors on the μI sodium channel

Macroscopic current from the microI skeletal muscle sodium channel expressed in Xenopus oocytes shows inactivation with two exponential components. The major, slower components amplitude decreases with rapid pulsing. When microI cRNA is coinjected with rat skeletal muscle or brain mRNA the faster component becomes predominant. Individual microI channels switch between two principal gating modes, opening either only once per depolarization, or repeatedly in long bursts. These two modes differ in both activation and inactivation kinetics. There is also evidence for additional gating modes. It appears that the equilibrium among gating modes is influenced by a modulating factor encoded in rat skeletal muscle and brain mRNA. The modal gating is similar to that observed in hyperkalemic periodic paralysis.

Three‐dimensional structure of the type 1 inositol 1,4,5‐trisphosphate receptor at 24 Å resolution

We report here the first three‐dimensional structure of the type 1 inositol 1,4,5‐trisphosphate receptor (IP3R). From cryo‐electron microscopic images of purified receptors embedded in vitreous ice, a three‐dimensional structure was determined by use of standard single particle reconstruction techniques. The structure is strikingly different from that of the ryanodine receptor at similar resolution despite molecular similarities between these two calcium release channels. The 24 Å resolution structure of the IP3R takes the shape of an uneven dumbbell, and is ∼170 Å tall. Its larger end is bulky, with four arms protruding laterally by ∼50 Å and, in comparison with the receptor topology, probably corresponds to the cytoplasmic domain of the receptor. The lateral dimension at the height of the protruding arms is ∼155 Å. The smaller end, whose lateral dimension is ∼100 Å, has structural features indicative of the membrane‐spanning domain. A central opening in this domain, which is occluded on the cytoplasmic half, outlines a pathway for calcium flow in the open state of the channel.