# A state model of sodium channels

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I am studying by myself Human Physiology. I have encountered the following question:

In the following given model of sodium channel with 3 states open closed blocked (which I assume means inactivated), the rates of going from state to stated are given in the picture below.

a. Write matrix \$Q\$ for the system and find it's eigenvalues. b. What does these values represent?

If anyone has an idea what is the required matrix I will be grateful. Thanks!

There is no standard notation called Q (matrix).

However in this case I think the matrix that they are referring to is the state transition matrix (similar to the adjacency matrix as mentioned by Justas in the comments, but with rates instead of just the connections). Basically you have three states (lets call them A, B and C) and there is a rate for transition from one state to the other. You can also represent these rates in the form of transition probabilities.

You just represent this as a 3×3 matrix. Put zero where there are no such transitions (for example there is no transition from A to A or A to C):

\$\$egin{array}{|l|c|c|c|} hline & A & B & C hline A & 0 & 10 & 0 hline B & 100 & 0 & 50 hline C & 5 & 0 & 0 hline end{array} \$\$

You can then calculate the eigenvalue for this matrix. How to calculate eigenvalues and what is their significance is off-topic in this site. You can easily find out how to calculate eigenvalues. Their significance is something that is not that easy to understand but you can read more about that and can perhaps ask a precise question in Mathematics This Site. Basically, they tell you how the system proceeds in different directions (denoted by eigenvectors).

## A fully coupled transient excited state model for the sodium channel

The behavior under voltage clamp conditions of a coupled kinetic scheme for the sodium channel is examined. The scheme is given diagrammatically by: tano Numerical simulations are presented which show that this model fits the voltage clamp data which are well described by the Hodgkin-Huxley equations, but also gives the sorts of behavior anomalous to the Hodgkin-Huxley model which have been seen experimentally. Further, straightforward changes in parameter values are shown to be capable of mimicking the ways in which some axonal preparations differ from others. Detailed, but admittedly heuristic, arguments are presented for the propositions that: 1) the model is minimal i.e. no simpler kinetic model will fit the array of data simulated, and: 2) the transient excited state is necessary i.e. no model of comparable simplicity with pure voltage dependent kinetics will fit the array of data simulated.

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## Evolution

Sodium channels first appear phylogenetically in the jellyfish, where they enable the organism to transmit electrical signals efficiently throughout a dispersed neural net. Invertebrate Na + channel expression is generally restricted to the nervous system, although in chordates Na + channels are also present in striated muscle. The central selective pressure for Na + channels has remained the same throughout evolution: these molecules are nature's solution to the conundrum of co-ordination and communication within large organisms, particularly when speed is of the essence. Thus, Na + channels are richly concentrated in axons and in muscle, where they are often the most plentiful ion channels. Mammalian heart cells, for example, typically express more than 100 000 Na + channels (Makielski, Sheets, Hanck, January & Fozzard, 1987), but only 20 000 or so L-type Ca 2+ channels (Rose, Balke, Wier & Marban, 1992) and fewer copies of each family of voltage-dependent K + channels.

Na + channels consist of various subunits, but only the principal (α) subunit is required for function. Figure 1A shows that the α subunit has a modular architecture: it consists of four internally homologous domains (labelled I-IV), each of which contains six transmembrane segments and resembles a single α subunit of a voltage-dependent K + channel. The four domains fold together so as to create a central pore whose structural constituents determine the selectivity and conductance properties of the channel. It is noteworthy that Ca 2+ channels have a similar overall architecture, with important differences in various regions (including the pore). Because unicellular organisms express K + and Ca 2+ channels, it is plausible that the simpler K + channels were primordial, with the subsequent evolution of Ca 2+ channels by gene duplication. Na + channels might have arisen in an analogous manner or, more likely, from mutations in a primitive Ca 2+ channel.

A, putative transmembrane folding. The charged S4 segments are shown in yellow, and the pore-lining P segments in green. B, aligned primary amino acid sequences in single-letter code of the P segments in a K + channel (Shaker B), the four domains of the cardiac L-type Ca 2+ channel, and the four domains of the Na + channel. Residues shown in upper case are highly conserved among voltage-dependent Na + channels. The diamonds indicate the external and internal binding sites for tetraethylammonium (TEA) ion in the K + channel and the red boxes outline the putative selectivity filters, although, in the case of the Na + channel, the residues which are most important for selectivity (circled in green) are mostly outside the box.

These evolutionary considerations serve to point out various themes that are general to voltage-dependent ion channels: first, the architecture is modular, consisting either of four homologous subunits (in K + channels) or of four internally homologous domains (in Na + and Ca 2+ channels). Secondly, as depicted in Fig. 1A , the proteins wrap around a central pore. The pore-lining (‘P segment’) regions exhibit exquisite conservation within a given channel family of like selectivity (jellyfish, eel, fruit-fly and human Na + channels have very similar P segments), but not among families with different selectivities ( Fig. 1B ). Third, the general strategy for activation gating is highly conserved: the fourth transmembrane segment (S4), stereotypically studded with positively charged residues, lies within the membrane field and moves in response to depolarization, somehow opening the channel (Stühmer et al. 1989).

## ASIC and ENaC type sodium channels: conformational states and the structures of the ion selectivity filters

The acid-sensing ion channels (ASICs) and epithelial sodium channels (ENaC) are members of a superfamily of channels that play critical roles in mechanosensation, chemosensation, nociception, and regulation of blood volume and pressure. These channels look and function like a tripartite funnel that directs the flow of Na + ions into the cytoplasm via the channel pore in the membrane. The subunits that form these channels share a common structure with two transmembrane segments (TM1 and TM2) and a large extracellular part. In most vertebrates, there are five paralogous genes that code for ASICs (ASIC1-ASIC5), and four for ENaC subunits alpha, beta, gamma, and delta (α, β, γ, and δ). While ASICs can form functional channels as a homo- or heterotrimer, ENaC functions as an obligate heterotrimer composed of α-β-γ or β-γ-δ subunits. The structure of ASIC has been determined in several conformations, including desensitized and open states. This review presents a comparison of the structures of these states using easy-to-understand molecular models of the full complex, the central tunnel that includes an outer vestibule, the channel pore, and ion selectivity filter. The differences in the secondary, tertiary, and quaternary structures of the states are summarized to pinpoint the conformational changes responsible for channel opening. Results of site-directed mutagenesis studies of ENaC subunits are examined in light of ASIC1 models. Based on these comparisons, a molecular model for the selectivity filter of ENaC is built by in silico mutagenesis of an ASIC1 structure. These models suggest that Na + ions pass through the filter in a hydrated state.

Keywords: acid-sensing ion channels conformational changes epithelial sodium channels hydrated ions ion channels protein dynamics protein structure.

## A simple Markov model of sodium channels with a dynamic threshold

Characteristics of action potential generation are important to understanding brain functioning and, thus, must be understood and modeled. It is still an open question what model can describe concurrently the phenomena of sharp spike shape, the spike threshold variability, and the divisive effect of shunting on the gain of frequency-current dependence. We reproduced these three effects experimentally by patch-clamp recordings in cortical slices, but we failed to simulate them by any of 11 known neuron models, including one- and multi-compartment, with Hodgkin-Huxley and Markov equation-based sodium channel approximations, and those taking into account sodium channel subtype heterogeneity. Basing on our voltage-clamp data characterizing the dependence of sodium channel activation threshold on history of depolarization, we propose a 3-state Markov model with a closed-to-open state transition threshold dependent on slow inactivation. This model reproduces the all three phenomena. As a reduction of this model, a leaky integrate-and-fire model with a dynamic threshold also shows the effect of gain reduction by shunt. These results argue for the mechanism of gain reduction through threshold dynamics determined by the slow inactivation of sodium channels.

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## Aldosterone Action and Function

### Mechanisms of the Regulation of Sodium Transport

Aldosterone-mediated transepithelial sodium flux primarily occurs in the cortical collecting ducts and to a lesser extent, in distal convoluted tubules of the nephron and in the distal sigmoid of the colon. In each case, there is a decreasing, distal to proximal, gradient of MR expression. As expected with a nuclear receptor, the temporal pattern of the aldosterone response has a lag period of 30–60 min, followed by an early phase in which preexisting pumps and channels are utilized with a late-phase at 3–6 h. In the late-phase, the number of pumps and channels increases and, with longer exposure, morphological changes are also observed. This time course is consistent with a primarily genomic response, which is to say that ligand-mediated activation of the MR results in the transcriptional regulation of the genes whose encoded proteins either mediate sodium transport per se or modulate components of the transport pathway. Although aldosterone accounts for only a small percentage (

2%) of the sodium reabsorbed in the nephron, the aldosterone-responsive regions in the nephron and indeed bowel are effectively the final arbiter of urinary sodium excretion this critical role is reflected in the number of monogenetic syndromes of hyper- and hypotension in which the etiologic mutation involves a component of the aldosterone-responsive sodium transport pathway.

In the classic model of aldosterone-induced vectorial sodium transport across a polarized epithelium, sodium entry at the apical membrane is through an amiloride-sensitive electrogenic sodium channel with efflux mediated by an energy-dependent sodium pump at the basolateral membrane. These mechanisms are best reflected in the predominant cell type of the collecting duct, the principal cells ( Shibata, 2017 ).

#### Epithelial Sodium Channel

The epithelial sodium channel (ENaC) is central to the aldosterone response ( Soundararajan et al., 2012 ). It consists of three homologous subunits (α, β, and γ) each characterized by two transmembrane domains with intracellular N- and C-termini. All three subunits are required for maximal amiloride-sensitive sodium transport. They form a heterotetromeric complex composed of 2α subunits and one each of the β and γ subunits. The ENaC subunits are members of the DEG/ENaC superfamily of sodium channel genes which are relatively conserved across evolution. The central role of ENaC is reflected both in Liddle syndrome, where activation, secondary to a mutation in the ENaC β or γ subunits results in increased sodium retention and hypertension, or in a subtype of PHA1 where an inactivating mutation in the subunits results in a salt-losing syndrome. Characterization of the mutations in Liddle syndrome identified a motif, proline–proline–proline–X-tyrosine (PY) in the C-terminus of the subunits which is disrupted in all cases. ENaC is a relatively short-lived protein that is ubiquitinated on residues in the N terminus of the α and γ but not β subunits the PY motif interacts with Nedd4-2, a ubiquitin protein-ligase, whose role is to target the channels for proteosomal degradation. Although there is evidence that ENaC subunit gene expression is regulated by aldosterone this is tissue specific with both β- and γENaC subunit mRNA levels being increased in the colon by aldosterone but not in the renal cortex, whereas an increase in αENaC mRNA levels is seen in the inner medulla. Overall, it would seem that aldosterone can increase ENaC synthesis (at least in the late-phase), an effect in the early phase (i.e., a primary effect) is not a feature at least in the distal nephron. Aldosterone does however increase the expression of the serine, threonine kinase, serum and glucocorticoid-regulated kinase-1 (sgk-1), with a time course consistent with an effect on transcription. Sgk-1 directly interacts with Nedd4-2 to block its binding of the ENaC and, as a consequence, slows ENaC degradation. The primary acute effect of aldosterone is thus to increase the number of channels in the apical membrane by reducing their efflux from the plasma membrane. The glucocorticoid-induced leucine zipper protein, which is also aldosterone-induced, acts to repress ERK-signaling, a negative regulator of ENaC, as well as directly interacting with Nedd 4-2. A further aldosterone-induced protein, connector enhancer of kinase repressor of Ras3 (CNK3), serves as a scaffold protein in the assembly of the ENaC-regulatory complex.

Sgk-1 is also involved in the regulation of ENaCα-subunit gene expression through relief of Dotla-Af9-mediated transcriptional repression. Nedd4-2 is regulated by Usp2-45, a deubiquitinylation enzyme which is itself regulated by aldosterone. Sgk-1 requires phosphorylation by the phosphatidylinosital 3-kinase (PI 3-kinase) pathway which may integrate signaling from membrane-associated receptors such as the insulin receptor. PI 3-kinase may be activated by small monomeric G proteins including K-ras 2A which has been identified as an aldosterone-induced gene.

Aldosterone also increases the open probability of the ENaC complexes in the plasma membrane through the action of serine protease such as prostasin and kallikrein which cleave the extracellular loop between the two transmembrane domains of the subunits.

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## Part 2: Calcium-Activated Chloride Channel (CaCC) in the Enigmatic TMEM16 Family

00:00:0723 Hi.
00:00:0823 I am Lily Jan.
00:00:1023 In this second of the two-part series on our studies of ion channels, I will tell you about
00:00:1924 calcium-activated chloride channels.
00:00:2225 This is part of a long-term collaboration I have had with Yuh-Nung Jan.
00:00:2820 Calcium-activated chloride channels have only been molecularly identified in this millennium,
00:00:3620 about a decade ago, even though these channels have been studied ever since the 1980s
00:00:4318 and they have been associated with a number of different functions that are important.
00:00:5317 In this talk, I will first go over the ways we went about identifying the channel molecule,
00:01:0016 and then tell you what we have learned about the function of these channels.
00:01:0706 For a channel of interest, where we know about the function but not the molecules that form these channels,
00:01:1715 one general approach is to identify a rich source for this channel and
00:01:2509 inject pools of RNA into Xenopus oocytes so that the channel activity can be detected
00:01:3402 with recording from the oocytes.
00:01:3705 And we can then subdivide these pools of cDNAs until we end up with a single clone for the channel.
00:01:4613 For this approach to work, however, the Xenopus oocytes used as the expression system
00:01:5503 cannot be expressing the channel of interest.
00:01:5727 So, if we inject water into the Xenopus oocytes, we should see no channel activity.
00:02:0701 This approach of expression cloning was initially pioneered by Julius and Nakanishi.
00:02:1521 And in their early studies using this approach, they cloned a G protein-coupled receptor
00:02:2413 that activates a signaling pathway including the activation of phospholipase C and
00:02:3223 the release of calcium from internal stores.
00:02:3607 And they relied on the calcium-activated chloride channels that are endogenous to the
00:02:4217 Xenopus oocytes to report the activation of this whole signaling pathway.
00:02:5108 And we know that these calcium-activated chloride channels in the Xenopus oocytes
00:02:5703 serve an important function, to prevent polyspermia.
00:03:0124 And these channels actually have been studied in the oocyte ever since the 1980s.
00:03:0806 And for this reason, we know Xenopus oocytes cannot be used as the expression system
00:03:1505 for expression cloning of CaCC.
00:03:1812 And instead, Bjorn Schroeder went to the axolotl oocytes that are physiologically polyspermic.
00:03:2902 And after finding very little endogenous CaCC expression in the axolotl ooctyes, Bjorn used
00:03:3716 these oocytes as the expression system, and Xenopus oocytes as the source of RNA for CaCC
00:03:4708 to clone a calcium-activated chloride channel.
00:03:5125 And that led to the identification of Xenopus TMEM16A as a CaCC.
00:03:5816 And he then tested the mammalian homologues and found that of. in the family with ten members,
00:04:0509 TMEM16A and 16B formed calcium-activated chloride channels.
00:04:1122 And around the same time, Oh's group in Korea and Galietta's group in Italy independently
00:04:2117 came to the conclusion that TMEM16A forms calcium-activated chloride channels,
00:04:2816 but using very different approaches.
00:04:3306 From recent studies, we see that TMEM16A is very broadly expressed in the periphery,
00:04:4125 including epithelial cells and smooth muscle cells.
00:04:4604 And TMEM16B is expressed in multiple brain regions, and also in sensory neurons for
00:04:5420 odorant perception and in photoreceptors.
00:05:0005 In the photoreceptors, the calcium-activated chloride channels formed by TMEM16B reside
00:05:0817 at the ribbon synapse.
00:05:1020 They bind to the PSD95 anchor protein, and they provide negative feedback regulation.
00:05:1910 In the odorant neurons, in the cilia where the odorant will activate G protein-coupled receptors,
00:05:2626 leading to the opening of cyclic nucleotide-gated ion channels that permeate
00:05:3310 both calcium and other positively charged ions like sodium, the calcium will then activate
00:05:4203 calcium-activated chloride channels.
00:05:4426 So, CaCC formed by TMEM16B provides the low-noise high-gain amplification of the odorant signal.
00:05:5720 In the nervous system, we see that TMEM16A is found in sensory neurons in the dorsal root ganglia.
00:06:0720 But TMEM16B is found in different brain regions, in central neurons.
00:06:1406 There's a curious correlation.
00:06:1617 The cells that express 16B tend to express potassium-chloride cotransporters,
00:06:2427 and these cells have low chloride concentration inside.
00:06:3004 And so chloride channels are inhibitory.
00:06:3224 But in the cells like the dorsal root ganglia, and also in immature neurons in the brain,
00:06:4108 the cells use a different transporter, the sodium-potassium-chloride cotransporter.
00:06:4828 And these cells have high chloride concentration, and chloride channels are excitatory.
00:06:5706 And this applies to many different cells in the periphery, and also cells in other organisms,
00:07:0411 including the green algae.
00:07:0601 We know from studies in the 1980s, calcium-activated chloride channels are present in the green algae.
00:07:1517 And actually, these are the channels that are responsible for generating action potentials.
00:07:2115 It's not sodium channels.
00:07:2326 And so we can see the action potentials in this green algae are slower.
00:07:2922 It takes seconds rather than milliseconds, as in the case of action potentials in the
00:07:3514 nerves and muscles.
00:07:3714 And these have been referred to as the calcium. as the chemical action potential because
00:07:4400 it requires the calcium rise to induce the action potential.
00:07:4917 And when the light is switched off, calcium becomes released from chloroplasts.
00:07:5826 And so we can see, then, there is a progressive shortening in the latency for the
00:08:0408 action potential generation.
00:08:0711 And during the action potential, there's further rise in the calcium.
00:08:1113 And that will result in a pause in the cytoplasmic streaming.
00:08:1928 And these are really large cells, as you can see, in the green algae.
00:08:2418 And the cytoplasmic streaming is one way to move, you know, the organelles and materials
00:08:3103 around in the cell.
00:08:3411 Now, back to the animal kingdom.
00:08:3808 In the airway epithelia, we see two different kinds of chloride channels on the apical side,
00:08:4516 the luminal side of the cell.
00:08:4805 One is calcium-activated chloride channel, formed by TMEM16A.
00:08:5314 And the other is CFTR.
00:08:5628 And that's the channel linked to the disease cystic fibrosis.
00:09:0203 And these chloride channels are responsible for controlling, or participate in the control,
00:09:0919 of the thickness of the airway surface liquid, the ASL.
00:09:1520 And that liquid, lining the luminal side of the epithelia, is very important for
00:09:2322 mucociliary clearance of pathogens in the airway.
00:09:3018 In the airway, these calcium-activated chloride channels formed by TMEM16A also facilitate
00:09:3900 the release of mucin into the lumen.
00:09:4222 And from the 1980s, we have learned from studies of different exocrine glands that
00:09:4926 calcium-activated chloride channels are important for controlling the secretion from,
00:09:5616 you know, salivary glands, sweat glands, and so on.
00:10:0005 And these glands express TMEM16A.
00:10:0628 In the smooth muscle, the calcium-activated chloride channels can be activated, for example,
00:10:1502 with the punctal release. a bolus of calcium from internal stores.
00:10:2201 And this would cause the nearby calcium-activated chloride channels on the cell membrane
00:10:2818 to open, leading to what's referred to as STIC: spontaneous transient inward current.
00:10:3700 That will cause depolarization.
00:10:3919 And that will further lead to opening of voltage-gated calcium channels.
00:10:4321 So, it's a positive feedback to sustain the rising calcium and smooth muscle contraction.
00:10:5500 In the gut, you know, the gastrointestinal tract, there are cells referred to as
00:11:0116 interstitial cells of Cajal.
00:11:0416 And likewise, there are calcium-activated chloride channels.
00:11:0823 And when there's a puff of calcium from internal stores, that will generate a STIC,
00:11:1518 marked here, this little rising.
00:11:1821 And this spontaneous transient depolarization will then lead to opening of
00:11:2505 voltage-gated calcium channels, and generate these slow waves.
00:11:3103 The interstitial cells of Cajal are in gap junctions, electrically coupled, with smooth muscles.
00:11:3815 So, in the gut, there's actually a whole network of interstitial cells of Cajal
00:11:4514 electrically coupled to one another and also to smooth muscles.
00:11:5017 And the propagation of these slow waves controls the rhythmic movement of the stomach and the intestines.
00:12:0002 So, we see in the wildtype control the isolated stomach still goes through rhythmic contraction.
00:12:0828 But in the mutant mice, without TMEM16A, the mus. the stomach is not doing that.
00:12:1815 There's no rhythmic movement.
00:12:2125 So, in the interstitial cells of Cajal, TMEM16A is responsible or required for the formation
00:12:3220 of pacemaker activity, these slow waves that control the rhythmic movement of the GI tract.
00:12:4120 In the epithelial cells, at TMEM16A and CFTR, again, are on the luminal side,
00:12:5100 the apical side of the epithelial cells.
00:12:5415 And so having these two different chloride channels on the same side, the luminal side
00:13:0016 of epithelial cells in the intestine, and also in the airway,
00:13:0523 has raised the prospect that perhaps activating calcium-activated chloride channels may be one way to
00:13:1514 reduce or ameliorate some of the symptoms of patients with cystic fibrosis.
00:13:2418 As I mentioned, TMEM16A is very broadly expressed in different epithelial tissues.
00:13:3115 And in these epithelial cells, the channel protein is on the cell membrane and also
00:13:3720 on the surface of cilia, microvilli included.
00:13:4307 And to ask what these channels might be doing, or what functions these channels might have
00:13:4924 in epithelia, Mu He expressed a chloride sensor, a fluorescent protein, in the epithelial cells,
00:13:5724 and found that the fluorescence will change with the external chloride concentration.
00:14:0504 Reducing the chloride concentration will cause a rise in fluorescence.
00:14:0924 And restoring the higher chloride concentration will cause a fall, a drop in the fluorescence intensity.
00:14:1806 And so the fluor. the fluorescence intensity is inversely proportional to
00:14:2411 the chloride concentration in the cytosol.
00:14:2806 And in the mutant cells without 16A, the pink ones, or the control cells treated with
00:14:3814 a blocker of this channel, there's a reduction in the fluorescence intensity.
00:14:4417 So, we see that the channel in these cells controls chloride homeostasis.
00:14:5104 So, without the channel activity, the cytoplasmic chloride concentration is higher.
00:15:0008 And to look at the consequence of varying the chloride concentration,
00:15:0616 one thing Mu He noticed is that recycling endosome trafficking depends on the chloride concentration.
00:15:1515 So, reducing the chloride concentration will increase the appearance of E-cadherin
00:15:2217 in the recycling endosome.
00:15:2524 And the recycling of E-cadherin is a process that happens all the time.
00:15:3126 That allows the cells to rearrange the adherens junctions formed by E-cadherin.
00:15:3927 And this is particularly important when the cells are adjusting their arrangement
00:15:4621 with the neighbors, as in the case of embryogenesis, during development.
00:15:5125 So, in early stages, in these panels, we see that the epithelial cells are still at a stage
00:16:0200 of active proliferation.
00:16:0420 And they pack against each other, mainly as pentagons, with five edges.
00:16:1122 And later in development, then these epithelia stabilized and packed as hexagons, in a honeycomb form.
00:16:2318 And in the mutant mice without TMEM16A, this transition from. to the stable form of epithelia
00:16:3423 is deficient.
00:16:3615 We don't see this transition to hexagons.
00:16:3922 This most likely is the result of the alteration in the recycling of E-cadherin that's required
00:16:4905 for the repacking of epithelial cells.
00:16:5311 And the other effect or control mediated by chloride concentration in the cytoplasm is
00:17:0213 the trafficking of recycling endosomes to the pericentriolar region.
00:17:0828 And the recycling endosomes in this region are actually the membrane supply,
00:17:1511 the source of membrane for ciliogenesis, for the formation of primary cilia.
00:17:2115 And this explains why in the mutants, in multiple tissues, we see much shorter primary cilia.
00:17:3424 And now that we have gone through some of the physiological functions,
00:17:3909 I will switch gears and talk about how these channels work.
00:17:4416 In our recent study in collaboration with my UCSF colleague, Yifan Cheng, we have seen
00:17:5200 the channel. in the structure, with cryo-EM analysis.
00:17:5807 We see that the protein forms a dimer.
00:18:0202 And there are actually very well organized lipids, marked in red, at the interface.
00:18:0927 And we see two calcium ions in each monomer.
00:18:1411 And they are fairly close to where the pore is.
00:18:1802 So, the two calcium ions are coordinated by five acidic residues plus an asparagine.
00:18:2825 And right next to the calcium binding site is the pore.
00:18:3320 That's formed by six of the ten transmembrane segments.
00:18:3927 And three of the six are the transmembrane segments that include the calcium binding sites,
00:18:4606 the acidic residues and asparagine.
00:18:5109 When we mutated residues lining the pore, we found a cluster of residues near
00:19:0024 the constriction of the pore that play a role in gating of the channel, and then, also, pore-lining residues
00:19:0815 all along the pore that are important for anion permeation.
00:19:1320 So, replacement of any one of these pore-lining residues, all ten of them, with alanine,
00:19:2301 one at a time, we see that the permeability to iodide versus the permeability to chloride is altered,
00:19:3020 indicating that these residues along the pore in interact with anions in the pore to control their permeation.
00:19:4305 And the cluster of residues that are near the constriction site appear to influence
00:19:5211 the stability of the protein in the open state versus the closed state of the channel.
00:19:5808 So that alanine mutations of these residues will altered the apparent calcium sensitivity
00:20:0525 of the channel for activation.
00:20:1122 A hallmark feature that has been known ever since the '80s is indicated by the blue triangles
00:20:2126 and the red diamonds in the current-voltage relationship.
00:20:2719 And that is when the calcium concentration in the cytosol is low, the channel shows
00:20:3412 very strong voltage dependence.
00:20:3701 But when the calcium concentration is much higher, there is a linear current-voltage relationship.
00:20:4313 There's very little voltage dependence.
00:20:4526 Our recent study, reported this year in Nature. in Neuron, gives further insight to the way
00:20:5520 the channel works.
00:20:5802 We see that most likely the channel has actually two different open states.
00:21:0408 When the channel, or each monomer, has one calcium bound, it's highly voltage-dependent,
00:21:1313 so the channel is closed unless there is depolarization.
00:21:1928 And so when the membrane is depolarized to a more positive value, we see an instantaneous current.
00:21:2705 That's reflecting this open state.
00:21:3122 And physiologically, the significance of this single. singly-occupied channel is that
00:21:4400 these channels will not really affect the resting membrane potential, but they will
00:21:4925 modulate the excitatory synaptic potential and also the action potential.
00:21:5520 Because, during those synaptic potentials or action potentials, there will be depolarization.
00:22:0311 Now, if we look at the green curve and the blue curve, we see that just having
00:22:1022 different anions going through the pore, the channel activity is different.
00:22:1722 And so the iodide will have a greater effect in potentiating the channel activity compared
00:22:2508 to chloride.
00:22:2713 And so this is one form of positive feedback.
00:22:3104 Once the channel is opened and the anions are going through the pore,
00:22:3517 it will actually potentiate the channel activity.
00:22:4013 And then we see in this voltage clamp experiment with prolonged depolarization,
00:22:4800 there's a gradual rise in the channel activity.
00:22:5119 And that reflects the occupation of the second calcium binding site.
00:22:5703 And when the channel has both calcium binding sites occupied, it transitions into a different
00:23:0414 open conformation that shows no voltage dependence.
00:23:0804 And this increased activity is also physiologically important.
00:23:1402 So, we see in recent studies, in this case recording of neurons from the inferior olive,
00:23:2322 removing the calcium-activated chloride channel formed by TMEM16B will alter the action potential waveform,
00:23:3122 the duration, and also the afterhyperpolarization.
00:23:3620 And in this other example, it's recording from thalamocortical neurons,
00:23:4403 it makes the point that with prolonged depolarization and a whole series of action potentials being generated,
00:23:5314 this prolonged depolarization and calcium entry during the action potential
00:24:0006 will lead to a progressively larger fraction, or a larger number, of the calcium-activated chloride channels
00:24:1104 getting both calcium binding sites occupied and entering into a more active state.
00:24:2126 And that will lead to a progressive decrease in the firing rate.
00:24:2716 And this is the phenomenon known as spike frequency adaptation.
00:24:3621 This makes the point that in mammals the family of TMEM16
00:24:4426 -- TMEM stands for transmembrane protein with unknown function --
00:24:5101 we know that 16A and 16B form calcium-activated chloride channels.
00:24:5608 It was quite surprising to see that the functions of other family members are really very diverse.
00:25:0406 They are not all calcium-activated chloride channels.
00:25:0921 When we just go down the list, we found that TMEM16C behaves as an auxiliary subunit of
00:25:1715 a potassium channel, a sodium-activated potassium channel.
00:25:2205 So, having. the channel has both the alpha subunit and the beta subunit, TMEM16C,
00:25:3019 and will have greater sodium sensitivity and also greater stability.
00:25:3502 So, in the sensory neurons of the dorsal root ganglia, in the wild type there are
00:25:4309 many more of these channels and greater sodium-activated potassium currents then in the TMEM.
00:25:5010 in the animals without TMEM16C.
00:25:5513 And the end result is knocking out TMEM16C will increase the excitability of these sensory neurons
00:26:0419 and also increase the pain sensitivity of the animal.
00:26:1203 And another example is TMEM16F.
00:26:1424 That turns out to be associated, linked, to a human disease that's a bleeding disorder
00:26:2225 known as Scott syndrome.
00:26:2516 And the function of TMEM16F is required for calcium-activated lipid scramblase activity
00:26:3502 in platelet cells and other cell types.
00:26:3904 And the scrambling of lipids in the lipid bilayer allows the lipids marked in red,
00:26:4619 the phosphatidyl serine, to be exposed to the cell surface.
00:26:5112 And that serves as a landing pad for the tissue factors.
00:26:5611 And that eventually leads to the production of thrombin and blood coagulation.
00:27:0515 And for the other members, likely the functions are going to be intriguing but quite different.
00:27:1208 So, those are all still open questions.
00:27:1512 So, for this study of the TMEM16 family, Bjorn Schroeder used those axolotl oocytes for
00:27:2600 expression cloning of the channel.
00:27:2920 And so TMEM16A and B are the calcium-activated chloride channels.
00:27:3515 Fen Huang did the study of TMEM16C that turned out to be an auxiliary subunit of a potassium channel.
00:27:4516 Andrew Kim and Huanghe Yang did the initial study from our lab on TMEM16F that's linked
00:27:5328 to the bleeding disorder.
00:27:5514 Jason Tien, John Gilchrist, Mu He, Shengjie Feng, and Chris Peters have done
00:28:0409 the more recent biophysical and physiological studies, including the cryo EM study in collaboration
00:28:1207 with Yifan Cheng.
00:28:1404 And several other UCSF colleagues, including Dan Minor, Charly Craik, and Michael Grabe.
00:28:2319 The pain study was done together with Allan Basbaum.
00:28:2811 And the bleeding disorder. you know, the blood coagulation study was done in collaboration
00:28:3614 with Shawn Coughlin.
00:28:3821 And all of this is a long-term collaboration with Yuh-Nung Jan.
00:28:4227 And the study was supported by Howard Hughes Medical Institute, NIH,
00:28:4927 and a number of postdoctoral fellowships.
00:28:5300 Thank you.

• Part 1: Introduction to Ion Channels: A Close Look at the Role and Function of Potassium Channels

## Introduction

Voltage-activated sodium channels provide selective and rapidly activating ion pathways required for action potential generation and propagation. The α subunit of these channels contains multiple binding sites for neurotoxins and therapeutically important drugs (Catterall 1992). The molecular nature of many of these binding sites has been identified by systematic site-directed mutagenesis of the α subunit of mammalian sodium channels (Terlau et al. 1991 Ragsdale et al. 1994 Rogers et al. 1996 Cestele et al. 1998 Wang and Wang 1998). Much less is known about the structure–function relationships of insect sodium channels because these proteins have only recently been cloned and the conditions for their functional expression have only recently been identified (Feng et al. 1995 Warmke et al. 1997). This heterologous expression provides new opportunities for structure–function studies because modified ligand binding sites can be identified by selecting for insects with resistance to neurotoxic ligands, especially synthetic chemicals that target insect sodium channels (Bloomquist 1996 Narahashi 1998). Comparative studies between mammalian and insect sodium channels can also provide insight into structure–function relationships because insect sodium channels are particularly sensitive to a number of neurotoxins such as pyrethroids (Narahashi 1996 Vais et al. 1997 Warmke et al. 1997).

Pyrethroids are commonly used as insecticides in crop protection, animal health, and the control of insects that endanger human health. These insecticides combine high insecticidal activity with low mammalian toxicity and constitute >25% of the world insecticide market. The intensive use of pyrethroids over the last 20 yr has led to the development of resistance in many insect species (Sawicki 1985) and this now represents the single most serious threat to their continued, effective use in many pest control programs. An important mechanism of resistance, termed knockdown resistance (or kdr), confers cross resistance to the entire class of pyrethroids and is characterized by a reduced sensitivity of the insect nervous system to these compounds (Bloomquist 1993). This type of resistance has been reported in many important pest species, but is best characterized in the housefly, where several variants of kdr, including the more potent super-kdr factor, have been identified (Farnham et al. 1987). Evidence that resistance results from a modification of the sodium channel initially came from cross-resistance studies with sodium channel neurotoxins and binding studies that indicated a reduced affinity for pyrethroids on the sodium channel of super-kdr houseflies (Pauron et al. 1989). This was further supported by genetic mapping studies that showed close linkage between kdr resistance and the para-type sodium channel gene not only in the housefly (Williamson et al. 1993), but also in the tobacco budworm, Heliothis virescens (Taylor et al. 1993) and the German cockroach, Blattella germanica (Dong and Scott 1994).

Molecular analysis of the full 6.3-kb coding sequence of the housefly para-type sodium channel identified two key amino acid substitutions in pyrethroid-resistant flies, L1014F in domain IIS6 and M918T in the IIS4–S5 linker (Williamson et al. 1996). L1014F is found in both kdr and super-kdr flies, while M918T is present only in super-kdr flies. Remarkably, the L1014F mutation has also been found in a wide range of pyrethroid-resistant strains of a number of other species, including cockroaches (Miyazaki et al. 1996 Dong 1997), the lepidopteran Plutella xylostella (Martinez-Torres et al. 1997), Colorado potato beetles (Lee et al. 1999b), the aphid Myzus persicae (Martinez-Torres et al. 1999b), and the mosquitoes Anopheles gambiae and Culex pipiens (Martinez-Torres et al. 1998, Martinez-Torres et al. 1999a). A different super-kdr mutation was identified in Plutella i.e., a mutation in IIS5 corresponding to the housefly residue T929I (Schuler et al. 1998). To establish the role of these mutations in conferring resistance, we have incorporated the kdr and super-kdr mutations individually and in combination into cloned Drosophila sodium channels. The Drosophila para gene codes for a sodium channel α subunit and we have previously reported the expression of this protein in Xenopus oocytes alone and in combination with tipE, a putative Drosophila sodium channel accessory subunit (Warmke et al. 1997). We found that modification by permethrin, a type I pyrethroid (i.e., one lacking an α-cyano group), is >100-fold more potent for Para than for rat-brain type IIA sodium channels (Warmke et al. 1997 see also Feng et al. 1995). We now report a more extensive characterization of the modification of insect sodium channels by the type II (α-cyano) pyrethroid deltamethrin and show that the kdr and super-kdr mutations alter both the potency and efficacy of this insecticide. The kdr and super-kdr mutations also reduce the potency of cismethrin and cypermethrin to modify housefly sodium channels (Smith et al. 1997 Lee et al. 1999c). Another mutation in IS6 also reduces the affinity for permethrin (Lee et al. 1999a).

Modification of vertebrate Na channels by pyrethroids and other Na channel activators such as the plant alkaloids and halogenated hydrocarbons (DDT) is enhanced by electrical activity. This modification has generally been described with a “foot-in-the-door” model (Hille 1992) i.e., the channels must open before the drug can bind and the drug must dissociate before the channels can close. Although this model can account for most features of the action of the alkaloids veratridine and batrachotoxin (Barnes and Hille 1988 Zong et al. 1992), it has been less successful with the pyrethroids. Depending on the preparation, pyrethroids can increase, decrease, or leave unchanged the amplitude of sodium current, and they sometimes modify channels in the rested state (Chinn and Narahashi 1986 Holloway et al. 1989 Ginsburg and Narahashi 1993). Moreover, pyrethroids have been classified into two major subtypes, I and II, based on their electrophysiological effects (Gammon et al. 1981). For type I pyrethroids, typified by permethrin, there is a good correlation between insecticidal activity and the ability to induce electrical spiking activity in neurons after brief exposure. However, type II pyrethroids, typified by deltamethrin, are disproportionately weak at inducing spiking activity. This has led to the suggestion that some pyrethroids act at sites other than insect Na channels.

We find that deltamethrin effects on Para/TipE sodium channels are far more potent than those previously reported with vertebrate or marine invertebrate channels. This potency allowed us to examine the mechanism of action of deltamethrin at low concentrations of drug (0.1–10 nM). In this concentration range, the voltage dependence of sodium channel modification is simpler to describe and is generally consistent with a modified foot-in-the-door model. The kdr and super-kdr mutations reduce Na channel opening in the absence of drug by reducing the fraction of channels that open in response to depolarization (i.e, the mutations enhance closed-state inactivation). In addition, these mutations reduce the affinity of deltamethrin for Na channels and reduce the time that the channel remains open once drug has bound. Our studies suggest that the super-kdr mutations reduce the number of pyrethroid binding sites per channel from two to one. Thus, the mutations reduce both the potency and efficacy of insecticide action. Finally, we present a means of overcoming pyrethroid resistance.

## Abstract

The crystal structure of NavAb, a bacterial voltage gated Na + channel, exhibits a selectivity filter (SF) wider than that of K + channels. This new structure provides the opportunity to explore the mechanism of conduction and help rationalize its selectivity for sodium. Recent molecular dynamics (MD) simulations of single- and two-ion permeation processes have revealed that a partially hydrated Na + permeates the channel by exploring three SF binding sites while being loosely coupled to other ions and/or water molecules a finding that differs significantly from the behavior of K + selective channels. Herein, we present results derived from a combination of metadynamics and voltage-biased MD simulations that throws more light on the nature of the Na + conduction mechanism. Conduction under 0 mV bias explores several distinct pathways involving the binding of two ions to three possible SF sites. While these pathways are very similar to those observed in the presence of a negative potential (inward conduction), a completely different mechanism operates for outward conduction at positive potentials.

## Sodium ions

A sodium atom that has lost an electron becomes the monatomic charged sodium ion and is denoted by the symbol Na + . Sodium ions have the electronic structure [1] 1s 2 2s 2 2p 6 , as they have become oxidised, having lost the lone electron in its 3s subshell: this is why sodium ions have a +1 charge overall.

### Sodium ions in the human body

Sodium ions are present in the human body playing key roles in several processes, such as in the primary active transport carried out by the Na + /K + -ATPase [2] , during the depolarisation of neuronal cell membranes during an action potential and as an important component in the secondary active transport of glucose which is completed by the Na + -glucose symporter.

When a stimulus causes membrane potential to rise from its resting potential of -70 mV to threshold frequency of -55 mV. It causes the voltage gated sodium channels to open allowing the flow of sodium ions into the cell resulting in depolarisation. Once the neurone reaches peak polarisation the sodium channels close and the potassium channels open allowing the flow of potassium ions out of the cell – this is called repolarization. During repolarisation, too many potassium ions move out of the cell causing the membrane potential to fall too low therefore resulting in hyperpolarisation. When hyperpolarisation occurs, the membrane must restore the potential back to its resting potential by transporting 3 Na + out of the cell and 2K + into the cell via the sodium potassium pump using ATP [3] .

### In compounds

Sodium ions also form ionic compounds with negative ions, a common example being the neutral ionic compound sodium chloride (NaCl), where the sodium ion has a positive +1 charge (Na + ) and the chloride ion has a negative -1 charge (Cl -1 ).