Voltage sensitivity and gating charge in Shaker and Shab family potassium channels

TRPA5 encodes a thermosensitive ankyrin ion channel receptor in a triatomine insect

As ectotherms, insects need heat-sensitive receptors to monitor environmental temperatures and facilitate thermoregulation. We show that TRPA5, a class of ankyrin transient receptor potential (TRP) channels absent in dipteran genomes, may function as insect heat receptors. In the triatomine bug Rhodnius prolixus (order: Hemiptera), a vector of Chagas disease, the channel RpTRPA5B displays a uniquely high thermosensitivity, with biophysical determinants including a large channel activation enthalpy change (72 kcal/mol), a high temperature coefficient (Q10 = 25), and in vitro temperature-induced currents from 53°C to 68°C (T0.5 = 58.6°C), similar to noxious TRPV receptors in mammals. Monomeric and tetrameric ion channel structure predictions show reliable parallels with fruit fly dTRPA1, with structural uniqueness in ankyrin repeat domains, the channel selectivity filter, and potential TRP functional modulator regions. Overall, the finding of a member of TRPA5 as a temperature-activated receptor illustrates the diversity of insect molecular heat detectors.

Loose Coupling between the Voltage Sensor and the Activation Gate in Mammalian HCN Channels Suggests a Gating Mechanism

Voltage-gated potassium (Kv) channels and hyperpolarization-activated cyclic nucleotide-gated (HCN) channels share similar structures but have opposite gating polarity. Kv channels have a strong coupling (>109) between the voltage sensor (S4) and the activation gate: when S4s are activated, the gate is open to >80% but, when S4s are deactivated, the gate is open <10-9 of the time. Using noise analysis, we show that the coupling between S4 and the gate is <200 in HCN channels. In addition, using voltage clamp fluorometry, locking the gate open in a Kv channel drastically altered the energetics of S4 movement. In contrast, locking the gate open or decreasing the coupling between S4 and the gate in HCN channels had only minor effects on the energetics of S4 movement, consistent with a weak coupling between S4 and the gate. We propose that this loose coupling is a prerequisite for the reversed voltage gating in HCN channels.

On molecular steps that activate a voltage sensitive ion channel at critical depolarization

At high transmembrane electric field, a voltage sensitive ion channel is an insulator; when the field is critically reduced, it becomes a conductor of selected ions. The Channel Activation by Electrostatic Repulsion (CAbER) hypothesis proposes that an ordered polarization field of induced dipoles at the high electric field magnitude of the excitable state is overcome by thermal disorder at a critical depolarization. Increased repulsions between positive charges in the S4 segments cause an allosteric transition in which these segments expand and separate in a chiral proteinquake. The increased space allows the P segments to refold and the ion-semiconducting S5 and S6 segments to relax and expand outward in a breathing mode. Stripped permeant ions enter widened hydrogen bonds in the core helices of these segments. Driven by concentration differences and the electric field, the ions hop along transient pathways across the channel, appearing as fractal, stochastic bursts of single-channel currents. To support order amid thermal fluctuations, an object must be of a minimum size. The critical role of an ion channel's size suggests that the evolution of Metazoa became possible only after its DNA had grown enough to code for proteins larger than the correlation length.

Neurotoxin-Derived Optical Probes for Biological and Medical Imaging

The superb specificity and potency of biological toxins targeting various ion channels and receptors are of major interest for the delivery of therapeutics to distinct cell types and subcellular compartments. Fused with reporter proteins or labelled with fluorophores and nanocomposites, animal toxins and their detoxified variants also offer expanding opportunities for visualisation of a range of molecular processes and functions in preclinical models, as well as clinical studies. This article presents state-of-the-art optical probes derived from neurotoxins targeting ion channels, with discussions of their applications in basic and translational biomedical research. It describes the design and production of probes and reviews their applications with advantages and limitations, with prospects for future improvements. Given the advances in imaging tools and expanding research areas benefiting from the use of optical probes, described here resources should assist the discovery process and facilitate high-precision interrogation and therapeutic interventions.

Fifty years of gating currents and channel gating

We celebrate this year the 50th anniversary of the first electrophysiological recordings of the gating currents from voltage-dependent ion channels done in 1973. This retrospective tries to illustrate the context knowledge on channel gating and the impact gating-current recording had then, and how it continued to clarify concepts, elaborate new ideas, and steer the scientific debate in these 50 years. The notion of gating particles and gating currents was first put forward by Hodgkin and Huxley in 1952 as a necessary assumption for interpreting the voltage dependence of the Na and K conductances of the action potential. 20 years later, gating currents were actually recorded, and over the following decades have represented the most direct means of tracing the movement of the gating charges and gaining insights into the mechanisms of channel gating. Most work in the early years was focused on the gating currents from the Na and K channels as found in the squid giant axon. With channel cloning and expression on heterologous systems, other channels as well as voltage-dependent enzymes were investigated. Other approaches were also introduced (cysteine mutagenesis and labeling, site-directed fluorometry, cryo-EM crystallography, and molecular dynamics [MD] modeling) to provide an integrated and coherent view of voltage-dependent gating in biological macromolecules. The layout of this retrospective reflects the past 50 years of investigations on gating currents, first addressing studies done on Na and K channels and then on other voltage-gated channels and non-channel structures. The review closes with a brief overview of how the gating-charge/voltage-sensor movements are translated into pore opening and the pathologies associated with mutations targeting the structures involved with the gating currents.

Gap junctions desynchronize a neural circuit to stabilize insect flight

Insect asynchronous flight is one of the most prevalent forms of animal locomotion used by more than 600,000 species. Despite profound insights into the motor patterns¹, biomechanics^2,3 and aerodynamics underlying asynchronous flight^4,5, the architecture and function of the central-pattern-generating (CPG) neural network remain unclear. Here, on the basis of an experiment-theory approach including electrophysiology, optophysiology, Drosophila genetics and mathematical modelling, we identify a miniaturized circuit solution with unexpected properties. The CPG network consists of motoneurons interconnected by electrical synapses that, in contrast to doctrine, produce network activity splayed out in time instead of synchronized across neurons. Experimental and mathematical evidence support a generic mechanism for network desynchronization that relies on weak electrical synapses and specific excitability dynamics of the coupled neurons. In small networks, electrical synapses can synchronize or desynchronize network activity, depending on the neuron-intrinsic dynamics and ion channel composition. In the asynchronous flight CPG, this mechanism translates unpatterned premotor input into stereotyped neuronal firing with fixed sequences of cell activation that ensure stable wingbeat power and, as we show, is conserved across multiple species. Our findings prove a wider functional versatility of electrical synapses in the dynamic control of neural circuits and highlight the relevance of detecting electrical synapses in connectomics.

Not so optimal: The evolution of mutual information in potassium voltage-gated channels

Potassium voltage-gated (Kv) channels need to detect and respond to rapidly changing ionic concentrations in their environment. With an essential role in regulating electric signaling, they would be expected to be optimal sensors that evolved to predict the ionic concentrations. To explore these assumptions, we use statistical mechanics in conjunction with information theory to model how animal Kv channels respond to changes in potassium concentrations in their environment. By measuring mutual information in representative Kv channel types across a variety of environments, we find two things. First, under weak conditions, there is a gating charge that maximizes mutual information with the environment. Second, as Kv channels evolved, they have moved towards decreasing mutual information with the environment. This either suggests that Kv channels do not need to act as sensors of their environment or that Kv channels have other functionalities that interfere with their role as sensors of their environment.

A gating lever and molecular logic gate that couple voltage and calcium sensor activation to opening in BK potassium channels

BK channels uniquely integrate voltage and calcium signaling in diverse cell types through allosteric activation of their K+-conducting pore by structurally distinct V and Ca2+ sensor domains. Here, we define mechanisms and interaction pathways that link V sensors to the pore by analyzing effects on allosteric coupling of point mutations in the context of Slo1 BK channel structure. A gating lever, mediated by S4/S5 segment interaction within the transmembrane domain, rotates to engage and stabilize the open conformation of the S6 inner pore helix upon V sensor activation. In addition, an indirect pathway, mediated by the carboxyl-terminal cytosolic domain (CTD) and C-linker that connects the CTD to S6, stabilizes the closed conformation when V sensors are at rest. Unexpectedly, this mechanism, which bypasses the covalent connections of C-linker to CTD and pore, also transduces Ca2+-dependent coupling in a manner that is completely nonadditive with voltage, analogous to the function of a digital logic (OR) gate.

Gating intermediates reveal inhibitory role of the voltage sensor in a cyclic nucleotide-modulated ion channel

Understanding how ion channels gate is important for elucidating their physiological roles and targeting them in pathophysiological states. Here, we used SthK, a cyclic nucleotide-modulated channel from Spirochaeta thermophila, to define a ligand-gating trajectory that includes multiple on-pathway intermediates. cAMP is a poor partial agonist for SthK and depolarization increases SthK activity. Tuning the energy landscape by gain-of-function mutations in the voltage sensor domain (VSD) allowed us to capture multiple intermediates along the ligand-activation pathway, highlighting the allosteric linkage between VSD, cyclic nucleotide-binding (CNBD) and pore domains. Small, lateral displacements of the VSD S4 segment were necessary to open the intracellular gate, pointing to an inhibitory VSD at rest. We propose that in wild-type SthK, depolarization leads to such VSD displacements resulting in release of inhibition. In summary, we report conformational transitions along the activation pathway that reveal allosteric couplings between key sites integrating to open the intracellular gate.

To what extent naringenin binding and membrane depolarization shape mitoBK channel gating—A machine learning approach

The large conductance voltage- and Ca2+-activated K+ channels from the inner mitochondrial membrane (mitoBK) are modulated by a number of factors. Among them flavanones, including naringenin (Nar), arise as a promising group of mitoBK channel regulators from a pharmacological point of view. It is well known that in the presence of Nar the open state probability (pop) of mitoBK channels significantly increases. Nevertheless, the molecular mechanism of the mitoBK-Nar interactions remains still unrevealed. It is also not known whether the effects of naringenin administration on conformational dynamics can resemble those which are exerted by the other channel-activating stimuli. In aim to answer this question, we examine whether the dwell-time series of mitoBK channels which were obtained at different voltages and Nar concentrations (yet allowing to reach comparable pops) are discernible by means of artificial intelligence methods, including k-NN and shapelet learning. The obtained results suggest that the structural complexity of the gating dynamics is shaped both by the interaction of channel gate with the voltage sensor (VSD) and the Nar-binding site. For a majority of data one can observe stimulus-specific patterns of channel gating. Shapelet algorithm allows to obtain better prediction accuracy in most cases. Probably, because it takes into account the complexity of local features of a given signal. About 30% of the analyzed time series do not sufficiently differ to unambiguously distinguish them from each other, which can be interpreted in terms of the existence of the common features of mitoBK channel gating regardless of the type of activating stimulus. There exist long-range mutual interactions between VSD and the Nar-coordination site that are responsible for higher levels of Nar-activation (Δpop) at deeply depolarized membranes. These intra-sensor interactions are anticipated to have an allosteric nature.

Mechanism of use-dependent Kv2 channel inhibition by RY785

Understanding the mechanism by which ion channel modulators act is critical for interpretation of their physiological effects and can provide insight into mechanisms of ion channel gating. The small molecule RY785 is a potent and selective inhibitor of Kv2 voltage-gated K+ channels that has a use-dependent onset of inhibition. Here, we investigate the mechanism of RY785 inhibition of rat Kv2.1 (Kcnb1) channels heterologously expressed in CHO-K1 cells. We find that 1 µM RY785 block eliminates Kv2.1 current at all physiologically relevant voltages, inhibiting ≥98% of the Kv2.1 conductance. Both onset of and recovery from RY785 inhibition require voltage sensor activation. Intracellular tetraethylammonium, a classic open-channel blocker, competes with RY785 inhibition. However, channel opening itself does not appear to alter RY785 access. Gating current measurements reveal that RY785 inhibits a component of voltage sensor activation and accelerates voltage sensor deactivation. We propose that voltage sensor activation opens a path into the central cavity of Kv2.1 where RY785 binds and promotes voltage sensor deactivation, trapping itself inside. This gated-access mechanism in conjunction with slow kinetics of unblock supports simple interpretation of RY785 effects: channel activation is required for block by RY785 to equilibrate, after which trapped RY785 will simply decrease the Kv2 conductance density.

The 70-year search for the voltage sensing mechanism of ion channels

This retrospective on the voltage‐sensing mechanisms and gating models of ion channels begins in 1952 with the charged gating particles postulated by Hodgkin and Huxley, viewed as charges moving across the membrane and controlling its permeability to Na⁺ and K⁺ ions. Hodgkin and Huxley postulated that their movement should generate small and fast capacitive currents, which were recorded 20 years later as gating currents. In the early 1980s, several voltage‐dependent channels were cloned and found to share a common architecture: four homologous domains or subunits, each displaying six transmembrane α‐helical segments, with the fourth segment (S4) displaying four to seven positive charges invariably separated by two non‐charged residues. This immediately suggested that this segment was serving as the voltage sensor of the channel (the molecular counterpart of the charged gating particle postulated by Hodgkin and Huxley) and led to the development of the sliding helix model. Twenty years later, the X‐ray crystallographic structures of many voltage‐dependent channels allowed investigation of their gating by molecular dynamics. Further understanding of how channels gate will benefit greatly from the acquisition of high‐resolution structures of each of their relevant functional or structural states. This will allow the application of molecular dynamics and other approaches. It will also be key to investigate the energetics of channel gating, permitting an understanding of the physical and molecular determinants of gating. The use of multiscale hierarchical approaches might finally prove to be a rewarding strategy to overcome the limits of the various single approaches to the study of channel gating.

High spatial density is associated with non-conducting Kv channels from two families

Ion channels are well known for their ability to regulate the cell membrane potential. However, many ion channels also have functions that do not involve ion conductance. Kv2 channels are one family of ion channels whose non-conducting functions are central to mammalian cell physiology. Kv2.1 and Kv2.2 channels form stable contact sites between the endoplasmic reticulum and plasma membrane via an interaction with endoplasmic reticulum resident proteins. To perform this structural role, Kv2 channels are expressed at extremely high densities on the plasma membranes of many cell types, including central pyramidal neurons, α-motoneurons, and smooth muscle cells. Research from our lab and others has shown that the majority of these plasma membrane Kv2.1 channels do not conduct potassium in response to depolarization. The mechanism of this channel silencing is unknown but is thought to be dependent on channel density in the membrane. Furthermore, the prevalence of a non-conducting population of Kv2.2 channels has not been directly tested. In this work we make improved measurements of the numbers of conducting and non-conducting Kv2.1 channels expressed in HEK293 cells and expand the investigation of non-conducting channels to three additional Kv α-subunits: Kv2.2, Kv1.4, and Kv1.5. By comparing the numbers of gating and conducting channels in individual HEK293 cells, we found that on average, only 50% of both Kv2.1 and Kv2.2 channels conducted potassium and, as previously suggested, that fraction decreased with increased channel density in the plasma membrane. At the highest spatial densities tested, which are comparable with those found at Kv2 clusters in situ, only 20% of Kv2.1 and Kv2.2 channels conducted potassium. We also show for the first time that Kv1.4 and Kv1.5 exhibit density-dependent silencing, suggesting that this phenomenon has an underlying mechanism that is shared by Kv channels from multiple families.

The AMIGO1 adhesion protein activates Kv2.1 voltage sensors

Kv2 voltage-gated potassium channels are modulated by amphoterin-induced gene and open reading frame (AMIGO) neuronal adhesion proteins. Here, we identify steps in the conductance activation pathway of Kv2.1 channels that are modulated by AMIGO1 using voltage-clamp recordings and spectroscopy of heterologously expressed Kv2.1 and AMIGO1 in mammalian cell lines. AMIGO1 speeds early voltage-sensor movements and shifts the gating charge-voltage relationship to more negative voltages. The gating charge-voltage relationship indicates that AMIGO1 exerts a larger energetic effect on voltage-sensor movement than is apparent from the midpoint of the conductance-voltage relationship. When voltage sensors are detained at rest by voltage-sensor toxins, AMIGO1 has a greater impact on the conductance-voltage relationship. Fluorescence measurements from voltage-sensor toxins bound to Kv2.1 indicate that with AMIGO1, the voltage sensors enter their earliest resting conformation, yet this conformation is less stable upon voltage stimulation. We conclude that AMIGO1 modulates the Kv2.1 conductance activation pathway by destabilizing the earliest resting state of the voltage sensors.

Conductance stability and Na+ interaction with Shab K+ channels under low K+ conditions

K+ ions exert a structural effect that brings stability to K+ selective pores. Thus, upon bathing Shab channels in 0 K+ solutions the ion conductance, GK, irreversibly collapses. Related to this, studies with isolated KcsA channels have suggested that there is a transition [K+] around which the pore takes one of two conformations, either the low (non-conducting) or high K+ (conducting) crystal structures. We examined this premise by looking at the K+-dependency of GK stability of Shab channels within the cell membrane environment. We found that: K+ effect on GK stability is highly asymmetrical, and that as internal K+ is replaced by Na+ GK drops in a way that suggests a transition internal [K+]. Additionally, we found that external permeant ions inhibit GK drop with a potency that differs from the global selectivity-sequence of K+ pores; the non-permeant TEA inhibited GK drop in a K+-dependent manner. Upon lowering internal [K+] we observed an influx of Na+ at negative potentials. Na+ influx was halted by physiological external [K+], which also restored GK stability. Hyperpolarized potentials afforded GK stability but, as expected, do not restore GK selectivity. For completeness, Na+ interaction with Shab was also assessed at depolarized potentials by looking at Na block followed by permeation (pore unblock) at positive potentials, in solutions approaching the 0 K+ limit. The stabilizing effect of negative potentials along with the non-parallel variation of Na+ permeability and conductance-stability herein reported, show that pore stability and selectivity, although related, are not strictly coupled.

EVAP: A two-photon imaging tool to study conformational changes in endogenous Kv2 channels in live tissues

A primary goal of molecular physiology is to understand how conformational changes of proteins affect the function of cells, tissues, and organisms. Here, we describe an imaging method for measuring the conformational changes of the voltage sensors of endogenous ion channel proteins within live tissue, without genetic modification. We synthesized GxTX-594, a variant of the peptidyl tarantula toxin guangxitoxin-1E, conjugated to a fluorophore optimal for two-photon excitation imaging through light-scattering tissue. We term this tool EVAP (Endogenous Voltage-sensor Activity Probe). GxTX-594 targets the voltage sensors of Kv2 proteins, which form potassium channels and plasma membrane–endoplasmic reticulum junctions. GxTX-594 dynamically labels Kv2 proteins on cell surfaces in response to voltage stimulation. To interpret dynamic changes in fluorescence intensity, we developed a statistical thermodynamic model that relates the conformational changes of Kv2 voltage sensors to degree of labeling. We used two-photon excitation imaging of rat brain slices to image Kv2 proteins in neurons. We found puncta of GxTX-594 on hippocampal CA1 neurons that responded to voltage stimulation and retain a voltage response roughly similar to heterologously expressed Kv2.1 protein. Our findings show that EVAP imaging methods enable the identification of conformational changes of endogenous Kv2 voltage sensors in tissue.

BK Channel Gating Mechanisms: Progresses Toward a Better Understanding of Variants Linked Neurological Diseases

The large conductance Ca2+-activated potassium (BK) channel is activated by both membrane potential depolarization and intracellular Ca2+ with distinct mechanisms. Neural physiology is sensitive to the function of BK channels, which is shown by the discoveries of neurological disorders that are associated with BK channel mutations. This article reviews the molecular mechanisms of BK channel activation in response to voltage and Ca2+ binding, including the recent progress since the publication of the atomistic structure of the whole BK channel protein, and the neurological disorders associated with BK channel mutations. These results demonstrate the unique mechanisms of BK channel activation and that these mechanisms are important factors in linking BK channel mutations to neurological disorders.

Inactivation of Native K Channels

We have experimented with isolated cardiomyocytes of mollusks Helix. During the whole-cell patch-clamp recordings of K⁺ currents a considerable decrease in amplitude was observed upon repeated voltage steps at 0.96 Hz. For these experiments, ventricular cells were depolarized to identical + 20 mV from a holding potential of - 50 mV. The observed spontaneous inhibition of outward currents persisted in the presence of 4-aminopyridine, tetraethylammonium chloride or E-4031, the selective class III antiarrhythmic agent that blocks HERG channels. Similar tendency was retained when components of currents sensitive to either 4-AP or TEA were mathematically subtracted. Waveforms of currents sensitive to 1 and 10 micromolar concentration of E-4031 were distinct comprising prevailingly those activated during up to 200 ms pulses. The outward current activated by a voltage ramp at 60 mV x s^-1 rate revealed an inward rectification around + 20 mV. This feature closely resembles those of the mammalian cardiac delayed rectifier I_Kr.

Mapping Electromechanical Coupling Pathways in Voltage-Gated Ion Channels: Challenges and the Way Forward

Inter- and intra-molecular allosteric interactions underpin regulation of activity in a variety of biological macromolecules. In the voltage-gated ion channel superfamily, the conformational state of the voltage-sensing domain regulates the activity of the pore domain via such long-range allosteric interactions. Although the overall structure of these channels is conserved, allosteric interactions between voltage-sensor and pore varies quite dramatically between the members of this superfamily. Despite the progress in identifying key residues and structural interfaces involved in mediating electromechanical coupling, our understanding of the biophysical mechanisms remains limited. Emerging new structures of voltage-gated ion channels in various conformational states will provide a better three-dimensional view of the process but to conclusively establish a mechanism, we will also need to quantitate the energetic contribution of various structural elements to this process. Using rigorous unbiased metrics, we want to compare the efficiency of electromechanical coupling between various sub-families in order to gain a comprehensive understanding. Furthermore, quantitative understanding of the process will enable us to correctly parameterize computational approaches which will ultimately enable us to predict allosteric activation mechanisms from structures. In this review, we will outline the challenges and limitations of various experimental approaches to measure electromechanical coupling and highlight the best practices in the field.

Fluorescent toxins as ion channel activity sensors

Voltage gated ion channels (VGICs) shape the electrical character of cells by undergoing structural changes in response to membrane depolarization. High-resolution techniques have provided a wealth of data on individual VGIC structures, but the conformational changes of endogenous channels in live cell membranes have remained unexplored. Here, we describe methods for imaging structural changes of voltage-gated K⁺ channels in living cells, using peptidyl toxins labeled with fluorophores that report specific protein conformations. These Endogenous Voltage-sensor Activity Probes (EVAPs) enable study of both VGIC allostery and function in the context of endogenous live-cell membranes under different physiological states. In this chapter, we describe methods for the synthesis, imaging, and analysis of dynamic EVAPs, which can report K⁺ channel activity in complex tissue preparations via 2-photon excitation microscopy, and environment-sensitive EVAPs, which report voltage-dependent conformational changes at the VGIC-toxin interface. The methods here present the utility of current EVAPs and lay the groundwork for the development of other probes that act by similar mechanisms. EVAPs can be correlated with electrophysiology, offering insight into the molecular details of endogenous channel function and allostery in live cells. This enables investigation of conformational changes of channels in their native, functional states, putting structures and models into a context of live-cell membranes. The expansive array of state-dependent ligands and optical probes should enable probes more generally for investigating the molecular motions of endogenous proteins.

High-Resolution Structures of K+ Channels

Potassium channels are present in every living cell and essential to setting up a stable, non-zero transmembrane electrostatic potential which manifests the off-equilibrium livelihood of the cell. They are involved in other cellular activities and regulation, such as the controlled release of hormones, the activation of T-cells for immune response, the firing of action potential in muscle cells and neurons, etc. Pharmacological reagents targeting potassium channels are important for treating various human diseases linked to dysfunction of the channels. High-resolution structures of these channels are very useful tools for delineating the detailed chemical basis underlying channel functions and for structure-based design and optimization of their pharmacological and pharmaceutical agents. Structural studies of potassium channels have revolutionized biophysical understandings of key concepts in the field - ion selectivity, conduction, channel gating, and modulation, making them multi-modality targets of pharmacological regulation. In this chapter, I will select a few high-resolution structures to illustrate key structural insights, proposed allostery behind channel functions, disagreements still open to debate, and channel-lipid interactions and co-evolution. The known structural consensus allows the inference of conserved molecular mechanisms shared among subfamilies of K⁺ channels and makes it possible to develop channel-specific pharmaceutical agents.

An Unorthodox Mechanism Underlying Voltage Sensitivity of TRPV1 Ion Channel

While the capsaicin receptor transient receptor potential vanilloid 1 (TRPV1) channel is a polymodal nociceptor for heat, capsaicin, and protons, the channel's responses to each of these stimuli are profoundly regulated by membrane potential, damping or even prohibiting its response at negative voltages and amplifying its response at positive voltages. Therefore, voltage sensitivity of TRPV1 is anticipated to play an important role in shaping pain responses. How voltage regulates TRPV1 activation remains unknown. Here, it is shown that voltage sensitivity does not originate from the S4 segment like classic voltage-gated ion channels; instead, outer pore acidic residues directly partake in voltage-sensitive activation, with their negative charges collectively constituting the observed gating charges. Outer pore gating-charge movement is titratable by extracellular pH and is allosterically coupled to channel activation, likely by influencing the upper gate in the ion selectivity filter. Elucidating this unorthodox voltage-gating process provides a mechanistic foundation for understanding TRPV1 polymodal gating and opens the door to novel approaches regulating channel activity for pain management.

Deterministic model of Cav3.1 Ca2+ channel and a proposed sequence of its conformations

A family of current-time curves of T-type Ca_v3.1 Ca²⁺ channels available in the literature is simulated by a kinetic model differing from that used for the interpretation of all salient features of Na⁺ and Shaker K⁺ channels by the insertion of a multiplying factor expressing the difference between the working potential ϕ and the reversal potential ϕ_r. This deterministic model is also used to simulate experimental curves taken from the literature for steady-state 'fast inactivation' and for a gradual passage from fast to 'slow inactivation'. A depolarizing pulse induces fast or slow inactivation depending on whether it lasts 100-500 ms or about 1 min, and is believed to cause a collapse of the central pore near the selectivity filter (SF). A number of features of fast and slow inactivation of Ca_v3.1 Ca²⁺ channels are qualitatively interpreted on the basis of a sequence of conformational states. Briefly, the conformation responsible for 'fast inactivation' is assumed to have the activation gate open and the inactivation gate (i.e., the SF) inactive. Immediately after a depolarizing pulse, this conformation is inactive and requires a sufficiently long rest time at a far negative holding potential to recover from inactivation. 'Slow inactivation' is ascribed to a different conformation with the activation gate closed and the SF inactive.

Kv2.1 channels play opposing roles in regulating membrane potential, Ca2+ channel function, and myogenic tone in arterial smooth muscle

The accepted role of the protein Kv2.1 in arterial smooth muscle cells is to form K⁺ channels in the sarcolemma. Opening of Kv2.1 channels causes membrane hyperpolarization, which decreases the activity of L-type Ca_V1.2 channels, lowering intracellular Ca²⁺ ([Ca²⁺]_i) and causing smooth muscle relaxation. A limitation of this model is that it is based exclusively on data from male arterial myocytes. Here, we used a combination of electrophysiology as well as imaging approaches to investigate the role of Kv2.1 channels in male and female arterial myocytes. We confirmed that Kv2.1 plays a canonical conductive role but found it also has a structural role in arterial myocytes to enhance clustering of Ca_V1.2 channels. Less than 1% of Kv2.1 channels are conductive and induce membrane hyperpolarization. Paradoxically, by enhancing the structural clustering and probability of Ca_V1.2-Ca_V1.2 interactions within these clusters, Kv2.1 increases Ca²⁺ influx. These functional impacts of Kv2.1 depend on its level of expression, which varies with sex. In female myocytes, where expression of Kv2.1 protein is higher than in male myocytes, Kv2.1 has conductive and structural roles. Female myocytes have larger Ca_V1.2 clusters, larger [Ca²⁺]_i, and larger myogenic tone than male myocytes. In contrast, in male myocytes, Kv2.1 channels regulate membrane potential but not Ca_V1.2 channel clustering. We propose a model in which Kv2.1 function varies with sex: in males, Kv2.1 channels control membrane potential but, in female myocytes, Kv2.1 plays dual electrical and Ca_V1.2 clustering roles. This contributes to sex-specific regulation of excitability, [Ca²⁺]_i, and myogenic tone in arterial myocytes.

Trans-toxin ion-sensitivity of charybdotoxin-blocked potassium-channels reveals unbinding transitional states

In silico and in vitro studies have made progress in understanding protein–protein complex formation; however, the molecular mechanisms for their dissociation are unclear. Protein–protein complexes, lasting from microseconds to years, often involve induced-fit, challenging computational or kinetic analysis. Charybdotoxin (CTX), a peptide from the Leiurus scorpion venom, blocks voltage-gated K⁺-channels in a unique example of binding/unbinding simplicity. CTX plugs the external mouth of K⁺-channels pore, stopping K⁺-ion conduction, without inducing conformational changes. Conflicting with a tight binding, we show that external permeant ions enhance CTX-dissociation, implying a path connecting the pore, in the toxin-bound channel, with the external solution. This sensitivity is explained if CTX wobbles between several bound conformations, producing transient events that restore the electrical and ionic trans-pore gradients. Wobbling may originate from a network of contacts in the interaction interface that are in dynamic stochastic equilibria. These partially-bound intermediates could lead to distinct, and potentially manipulable, dissociation pathways.

Tale of tail current

The largest biomass of channel proteins is located in unicellular organisms and bacteria that have no organs. However, orchestrated bidirectional ionic currents across the cell membrane via the channels are important for the functioning of organs of organisms, and equally concern both fauna or flora. Several ion channels are activated in the course of action potentials. One of the hallmarks of voltage-dependent channels is a 'tail current' - deactivation as observed after prior and sufficient activation predominantly at more depolarized potentials e.g. for Kv while upon hyperpolarization for HCN α subunits. Tail current also reflects the timing of channel closure that is initiated upon termination of stimuli. Finally, deactivation of currents during repolarization could be a selective estimate for given channel as in case of HERG, if dedicated long and more depolarized 'tail pulse' is used. Since from a holding potential of e.g. -70 mV are often a family of outward K⁺ currents comprising I_A and I_K are simultaneously activated in native cells.

The sources of electrophysiological variability in the retina ofPeriplaneta americana

Variability in the electrophysiological properties of homotypic photoreceptors is widespread and is thought to facilitate functioning under disparate illumination conditions. Compound eyes of insects have three sources of variability: inter-individual, intra-individual, and intra-ommatidial, the latter two overlapping. Here, I explored the causes of variability inPeriplaneta americana, a nocturnal insect characterized by highly variable photoreceptor responses. By recording from photoreceptors in dissociated ommatidia, including consecutive recordings from photoreceptors in the same ommatidium (SO), I studied the variability of six properties: whole-cell membrane capacitance (Cm), phototransduction latency, maximal conductance (Gmax) and the slope factor of the sustained Kv current, absolute sensitivity in dim light, and sustained light-induced current (LIC) amplitude in bright light. Coefficient of variation (CV) metrics were used to compare variances in four experimental groups: SO, same animal (SA), all data combined “full sample” (FS), and full sample of all SO recordings (FSSO). For the normally distributed parametersCm,Gmax, slope factor, and latency, the highest CV values were found in FS and FSSO, intermediate in SA, and the lowest in SO. On average, SO variance accounted for 47% of the full-sample variance in these four parameters. Absolute sensitivity and LIC values were not normally distributed, and the differences in variability between SO and FS/FSSO groups were smaller than for the other four parameters. These results indicate two main sources of variability, intra-ommatidial and inter-individual. Inter-individual variability was investigated by exposing adult cockroaches to constant light or dark for several months. In both groups, the majority of CV measures for the six parameters decreased compared to control, indicating substantial contribution of phenotypic plasticity to inter-individual differences. Analysis of variability of resting potential and elementary voltage responses revealed that resting potential is mainly determined by the sustained Kv conductance, whereas voltage bump amplitude is mainly determined by current bump amplitude andCm.

Unlocking the gating mechanism of Kv2.1 using guangxitoxin

Navarro et al discuss new work using the gating-modifier toxin GxTx to investigate the molecular mechanism of Kv2.1 channel gating.

Cholesterol-Dependent Gating Effects on Ion Channels

Biomembranes separate a live cell from its environment and keep it in an off-equilibrium, steady state. They contain both phospholipids and nonphospholipids, depending on whether there are phosphate groups in the headgroup regions. Cholesterol (CHOL) is one type of nonphospholipids, and one of the most abundant lipid molecules in humans. Its content in plasma membranes and intracellular membranes varies and is tightly regulated. Voltage-gated ion channels are universally present in every cell and are fairly diversified in the eukaryotic domain of life. Our lipid-dependent gating hypothesis postulates that the controlled switch of the voltage-sensor domains (VSDs) in a voltage-gated potassium (Kv) channel between the "down" and the "up" state (gating) is sensitive to the ratio of phospholipids:nonphospholipids in the annular layer around the channel. High CHOL content is found to exert strong inhibitory effects on Kv channels. Such effects have been observed in in vitro membranes, cultured cells, and animal models for cholesterol metabolic defects. Thermodynamic analysis of the CHOL-dependent gating suggests that the inhibitory effects of CHOL result from collective interactions between annular CHOL molecules and the channel, which appear to be a more generic principle behind the CHOL effects on other ion channels and transporters. We will review the recent progress in the CHOL-dependent gating of voltage-gated ion channels, discuss the current technical limitations, and then expand briefly the learned principles to other ion channels that are known to be sensitive to the CHOL-channel interactions.

The tarantula toxin GxTx detains K+ channel gating charges in their resting conformation

Allosteric ligands modulate protein activity by altering the energy landscape of conformational space in ligand-protein complexes. Here we investigate how ligand binding to a K⁺ channel's voltage sensor allosterically modulates opening of its K⁺-conductive pore. The tarantula venom peptide guangxitoxin-1E (GxTx) binds to the voltage sensors of the rat voltage-gated K⁺ (Kv) channel Kv2.1 and acts as a partial inverse agonist. When bound to GxTx, Kv2.1 activates more slowly, deactivates more rapidly, and requires more positive voltage to reach the same K⁺-conductance as the unbound channel. Further, activation kinetics are more sigmoidal, indicating that multiple conformational changes coupled to opening are modulated. Single-channel current amplitudes reveal that each channel opens to full conductance when GxTx is bound. Inhibition of Kv2.1 channels by GxTx results from decreased open probability due to increased occurrence of long-lived closed states; the time constant of the final pore opening step itself is not impacted by GxTx. When intracellular potential is less than 0 mV, GxTx traps the gating charges on Kv2.1's voltage sensors in their most intracellular position. Gating charges translocate at positive voltages, however, indicating that GxTx stabilizes the most intracellular conformation of the voltage sensors (their resting conformation). Kinetic modeling suggests a modulatory mechanism: GxTx reduces the probability of voltage sensors activating, giving the pore opening step less frequent opportunities to occur. This mechanism results in K⁺-conductance activation kinetics that are voltage-dependent, even if pore opening (the rate-limiting step) has no inherent voltage dependence. We conclude that GxTx stabilizes voltage sensors in a resting conformation, and inhibits K⁺ currents by limiting opportunities for the channel pore to open, but has little, if any, direct effect on the microscopic kinetics of pore opening. The impact of GxTx on channel gating suggests that Kv2.1's pore opening step does not involve movement of its voltage sensors.

Linkage analysis reveals allosteric coupling in Kir2.1 channels

Inwardly rectifying potassium (Kir) channels experience strong (blocking) and weak (intrinsic) rectification. Linkage analysis in the form of a conductance Hill plot is a sensitive method of resolving allosteric interactions between the pore and mediators of the Kir gating process.

Potassium-selective inward rectifier (Kir) channels are a class of membrane proteins necessary for maintaining stable resting membrane potentials, controlling excitability, and shaping the final repolarization of action potentials in excitable cells. In addition to the strong inward rectification of the ionic current caused by intracellular blockers, Kir2.1 channels possess “weak” inward rectification observed in inside-out patches after prolonged washout of intracellular blockers. The mechanisms underlying strong inward rectification have been attributed to voltage-dependent block by intracellular Mg²⁺ and polyamines; however, the mechanism responsible for weak rectification remains elusive. Hypotheses include weak voltage-dependent block and intrinsic voltage-dependent gating. Here, we performed a conductance Hill analysis of currents recorded with a double-ramp protocol to evaluate different mechanisms proposed for weak inward rectification of Kir2.1 channels. Linkage analysis in the form of a Hill plot revealed that the ramp currents could be best explained by allosteric coupling between a mildly voltage-dependent pore gate (gating charge ∼0.18 e_o) and a voltage sensor (gating charge ∼1.7 e_o). The proposed voltage sensor stabilized the closing of the pore gate (coupling factor ∼31). We anticipate that the use of linkage analysis will broaden understanding of functional coupling in ion channels and proteins in general.

Insights into the molecular mechanism for hyperpolarization-dependent activation of HCN channels

Hyperpolarization-activated, cyclic nucleotide-gated (HCN) ion channels are both voltage- and ligand-activated membrane proteins that contribute to electrical excitability and pace-making activity in cardiac and neuronal cells. These channels are members of the voltage-gated Kv channel superfamily and cyclic nucleotide-binding domain subfamily of ion channels. HCN channels have a unique feature that distinguishes them from other voltage-gated channels: the HCN channel pore opens in response to hyperpolarizing voltages instead of depolarizing voltages. In the canonical model of electromechanical coupling, based on Kv channels, a change in membrane voltage activates the voltage-sensing domains (VSD) and the activation energy passes to the pore domain (PD) through a covalent linker that connects the VSD to the PD. In this investigation, the covalent linkage between the VSD and PD, the S4-S5 linker, and nearby regions of spHCN channels were mutated to determine the functional role each plays in hyperpolarization-dependent activation. The results show that: (i) the S4-S5 linker is not required for hyperpolarization-dependent activation or ligand-dependent gating; (ii) the S4 C-terminal region (S4_C-term) is not necessary for ligand-dependent gating but is required for hyperpolarization-dependent activation and acts like an autoinhibitory domain on the PD; (iii) the S5_N-term region is involved in VSD-PD coupling and holding the pore closed; and (iv) spHCN channels have two voltage-dependent processes, a hyperpolarization-dependent activation and a depolarization-dependent recovery from inactivation. These results are inconsistent with the canonical model of VSD-PD coupling in Kv channels and elucidate the mechanism for hyperpolarization-dependent activation of HCN channels.

Gating-induced large aqueous volumetric remodeling and aspartate tolerance in the voltage sensor domain of Shaker K+ channels

Neurons encode electrical signals with critically tuned voltage-gated ion channels and enzymes. Dedicated voltage sensor domains (VSDs) in these membrane proteins activate coordinately with an unresolved structural change. Such change conveys the transmembrane translocation of four positively charged arginine side chains, the voltage-sensing residues (VSRs; R1-R4). Countercharges and lipid phosphohead groups likely stabilize these VSRs within the low-dielectric core of the protein. However, the role of hydration, a sign-independent charge stabilizer, remains unclear. We replaced all VSRs and their neighboring residues with negatively charged aspartates in a voltage-gated potassium channel. The ensuing mild functional effects indicate that hydration is also important in VSR stabilization. The voltage dependency of the VSR aspartate variants approached the expected arithmetic summation of charges at VSR positions, as if negative and positive side chains faced similar pathways. In contrast, aspartates introduced between R2 and R3 did not affect voltage dependence as if the side chains moved outside the electric field or together with it, undergoing a large displacement and volumetric remodeling. Accordingly, VSR performed osmotic work at both internal and external aqueous interfaces. Individual VSR contributions to volumetric works approached arithmetical additivity but were largely dissimilar. While R1 and R4 displaced small volumes, R2 and R3 volumetric works were massive and vectorially opposed, favoring large aqueous remodeling during VSD activation. These diverse volumetric works are, at least for R2 and R3, not compatible with VSR translocation across a unique stationary charge transfer center. Instead, VSRs may follow separated pathways across a fluctuating low-dielectric septum.

Modeling squid axon K+ channel by a nucleation and growth kinetic mechanism

A kinetic model accounting for all salient features of the K⁺ channel of the squid giant axon, including the rising phase of the ON gating charge and the Cole-Moore effect, is provided. Upon accounting for a significant feature distinguishing K⁺, Na⁺ and Ca²⁺ channels from channel-forming peptides modeled in our previous 2016 BBA paper, the nucleation-and-growth kinetic model developed therein is extended to simulate ON ionic and gating currents of the K⁺ channel of the squid giant axon at different depolarization potentials by the use of only two free parameters. K⁺ channel opening is considered to proceed by progressive aggregation of single subunits, while they are moving their gating charge outward under depolarizing conditions within their tetrameric structure; K⁺ channel closing proceeds in the opposite direction, by repolarization-induced disaggregation of subunits, accompanied by inward movement of their gating charge.

Neurodevelopmental Disorders Caused by De Novo Variants in KCNB1 Genotypes and Phenotypes

Importance

Knowing the range of symptoms seen in patients with a missense or loss-of-function variant in KCNB1 and how these symptoms correlate with the type of variant will help clinicians with diagnosis and prognosis when treating new patients.

Objectives

To investigate the clinical spectrum associated with KCNB1 variants and the genotype-phenotype correlations.

Design, Setting, and Participants

This study summarized the clinical and genetic information of patients with a presumed pathogenic variant in KCNB1. Patients were identified in research projects or during clinical testing. Information on patients from previously published articles was collected and authors contacted if feasible. All patients were seen at a clinic at one of the participating institutes because of presumed genetic disorder. They were tested in a clinical setting or included in a research project.

Main Outcomes and Measures

The genetic variant and its inheritance and information on the patient's symptoms and characteristics in a predefined format. All variants were identified with massive parallel sequencing and confirmed with Sanger sequencing in the patient. Absence of the variant in the parents could be confirmed with Sanger sequencing in all families except one.

Results

Of 26 patients (10 female, 15 male, 1 unknown; mean age at inclusion, 9.8 years; age range, 2-32 years) with developmental delay, 20 (77%) carried a missense variant in the ion channel domain of KCNB1, with a concentration of variants in region S5 to S6. Three variants that led to premature stops were located in the C-terminal and 3 in the ion channel domain. Twenty-one of 25 patients (84%) had seizures, with 9 patients (36%) starting with epileptic spasms between 3 and 18 months of age. All patients had developmental delay, with 17 (65%) experiencing severe developmental delay; 14 (82%) with severe delay had behavioral problems. The developmental delay was milder in 4 of 6 patients with stop variants and in a patient with a variant in the S2 transmembrane element rather than the S4 to S6 region.

Conclusions and Relevance

De novo KCNB1 missense variants in the ion channel domain and loss-of-function variants in this domain and the C-terminal likely cause neurodevelopmental disorders with or without seizures. Patients with presumed pathogenic variants in KCNB1 have a variable phenotype. However, the type and position of the variants in the protein are (imperfectly) correlated with the severity of the disorder.

Structural Titration of Slo2.2, a Na+-Dependent K+ Channel

The stable structural conformations that occur along the complete reaction coordinate for ion channel opening have never been observed. In this study, we describe the equilibrium ensemble of structures of Slo2.2, a neuronal Na⁺-activated K⁺ channel, as a function of the Na⁺ concentration. We find that Slo2.2 exists in multiple closed conformations whose relative occupancies are independent of Na⁺ concentration. An open conformation emerges from an ensemble of closed conformations in a highly Na⁺-dependent manner, without evidence of Na⁺-dependent intermediates. In other words, channel opening is a highly concerted, switch-like process. The midpoint of the structural titration matches that of the functional titration. A maximum open conformation probability approaching 1.0 and maximum functional open probability approaching 0.7 imply that, within the class of open channels, there is a subclass that is not permeable to ions.

Molecular Determinants of BK Channel Functional Diversity and Functioning

Large-conductance Ca2+- and voltage-activated K+ (BK) channels play many physiological roles ranging from the maintenance of smooth muscle tone to hearing and neurosecretion. BK channels are tetramers in which the pore-forming α subunit is coded by a single gene ( Slowpoke, KCNMA1). In this review, we first highlight the physiological importance of this ubiquitous channel, emphasizing the role that BK channels play in different channelopathies. We next discuss the modular nature of BK channel-forming protein, in which the different modules (the voltage sensor and the Ca2+ binding sites) communicate with the pore gates allosterically. In this regard, we review in detail the allosteric models proposed to explain channel activation and how the models are related to channel structure. Considering their extremely large conductance and unique selectivity to K+, we also offer an account of how these two apparently paradoxical characteristics can be understood consistently in unison, and what we have learned about the conduction system and the activation gates using ions, blockers, and toxins. Attention is paid here to the molecular nature of the voltage sensor and the Ca2+ binding sites that are located in a gating ring of known crystal structure and constituted by four COOH termini. Despite the fact that BK channels are coded by a single gene, diversity is obtained by means of alternative splicing and modulatory β and γ subunits. We finish this review by describing how the association of the α subunit with β or with γ subunits can change the BK channel phenotype and pharmacology.

Pore size matters for potassium channel conductance

Ion channels are membrane proteins that mediate efficient ion transport across the hydrophobic core of cell membranes, an unlikely process in their absence. K⁺ channels discriminate K⁺ over cations with similar radii with extraordinary selectivity and display a wide diversity of ion transport rates, covering differences of two orders of magnitude in unitary conductance. The pore domains of large- and small-conductance K⁺ channels share a general architectural design comprising a conserved narrow selectivity filter, which forms intimate interactions with permeant ions, flanked by two wider vestibules toward the internal and external openings. In large-conductance K⁺ channels, the inner vestibule is wide, whereas in small-conductance channels it is narrow. Here we raise the idea that the physical dimensions of the hydrophobic internal vestibule limit ion transport in K⁺ channels, accounting for their diversity in unitary conductance.

Grafting voltage and pharmacological sensitivity in potassium channels

A classical voltage-gated ion channel consists of four voltage-sensing domains (VSDs). However, the roles of each VSD in the channels remain elusive. We developed a GVTDT (Graft VSD To Dimeric TASK3 channels that lack endogenous VSDs) strategy to produce voltage-gated channels with a reduced number of VSDs. TASK3 channels exhibit a high host tolerance to VSDs of various voltage-gated ion channels without interfering with the intrinsic properties of the TASK3 selectivity filter. The constructed channels, exemplified by the channels grafted with one or two VSDs from Kv7.1 channels, exhibit classical voltage sensitivity, including voltage-dependent opening and closing. Furthermore, the grafted Kv7.1 VSD transfers the potentiation activity of benzbromarone, an activator that acts on the VSDs of the donor channels, to the constructed channels. Our study indicates that one VSD is sufficient to voltage-dependently gate the pore and provides new insight into the roles of VSDs.

Biophysics of BK Channel Gating

BK channels are universal regulators of cell excitability, given their exceptional unitary conductance selective for K(+), joint activation mechanism by membrane depolarization and intracellular [Ca(2+)] elevation, and broad expression pattern. In this chapter, we discuss the structural basis and operational principles of their activation, or gating, by membrane potential and calcium. We also discuss how the two activation mechanisms interact to culminate in channel opening. As members of the voltage-gated potassium channel superfamily, BK channels are discussed in the context of archetypal family members, in terms of similarities that help us understand their function, but also seminal structural and biophysical differences that confer unique functional properties.

Functional diversity of potassium channel voltage-sensing domains

Voltage-gated potassium channels or Kv's are membrane proteins with fundamental physiological roles. They are composed of 2 main functional protein domains, the pore domain, which regulates ion permeation, and the voltage-sensing domain, which is in charge of sensing voltage and undergoing a conformational change that is later transduced into pore opening. The voltage-sensing domain or VSD is a highly conserved structural motif found in all voltage-gated ion channels and can also exist as an independent feature, giving rise to voltage sensitive enzymes and also sustaining proton fluxes in proton-permeable channels. In spite of the structural conservation of VSDs in potassium channels, there are several differences in the details of VSD function found across variants of Kvs. These differences are mainly reflected in variations in the electrostatic energy needed to open different potassium channels. In turn, the differences in detailed VSD functioning among voltage-gated potassium channels might have physiological consequences that have not been explored and which might reflect evolutionary adaptations to the different roles played by Kv channels in cell physiology.

Kv3.1 uses a timely resurgent K(+) current to secure action potential repolarization

High-frequency action potential (AP) transmission is essential for rapid information processing in the central nervous system. Voltage-dependent K_v3 channels play an important role in this process thanks to their high activation threshold and fast closure kinetics, which reduce the neuron's refractory period. However, premature K_v3 channel closure leads to incomplete membrane repolarization, preventing sustainable AP propagation. Here, we demonstrate that K_v3.1b channels solve this problem by producing resurgent K⁺ currents during repolarization, thus ensuring enough repolarizing power to terminate each AP. Unlike previously described resurgent Na⁺ and K⁺ currents, K_v3.1b's resurgent current does not originate from recovery of channel block or inactivation but results from a unique combination of steep voltage-dependent gating kinetics and ultra-fast voltage-sensor relaxation. These distinct properties are readily transferrable onto an orthologue K_v channel by transplanting the voltage-sensor's S3–S4 loop, providing molecular insights into the mechanism by which K_v3 channels contribute to high-frequency AP transmission.

K_v3 potassium channels have an important role in the repolarization of action potentials in fast-spiking neurons. Here, the authors use electrophysiology and modelling to report on an interesting mechanism that might explain their gating behaviour.

Modeling the Influence of Ion Channels on Neuron Dynamics in Drosophila

Voltage gated ion channels play a major role in determining a neuron's firing behavior, resulting in the specific processing of synaptic input patterns. Drosophila and other invertebrates provide valuable model systems for investigating ion channel kinetics and their impact on firing properties. Despite the increasing importance of Drosophila as a model system, few computational models of its ion channel kinetics have been developed. In this study, experimentally observed biophysical properties of voltage gated ion channels from the fruitfly Drosophila melanogaster are used to develop a minimal, conductance based neuron model. We investigate the impact of the densities of these channels on the excitability of the model neuron. Changing the channel densities reproduces different in situ observed firing patterns and induces a switch from integrator to resonator properties. Further, we analyze the preference to input frequency and how it depends on the channel densities and the resulting bifurcation type the system undergoes. An extension to a three dimensional model demonstrates that the inactivation kinetics of the sodium channels play an important role, allowing for firing patterns with a delayed first spike and subsequent high frequency firing as often observed in invertebrates, without altering the kinetics of the delayed rectifier current.

Equilibrium fluctuation relations for voltage coupling in membrane proteins

A general theoretical framework is developed to account for the effects of an external potential on the energetics of membrane proteins. The framework is based on the free energy relation between two (forward/backward) probability densities, which was recently generalized to non-equilibrium processes, culminating in the work-fluctuation theorem. Starting from the probability densities of the conformational states along the "voltage coupling" reaction coordinate, we investigate several interconnected free energy relations between these two conformational states, considering voltage activation of ion channels. The free energy difference between the two conformational states at zero (depolarization) membrane potential (i.e., known as the chemical component of free energy change in ion channels) is shown to be equivalent to the free energy difference between the two "equilibrium" (resting and activated) conformational states along the one-dimensional voltage couplin reaction coordinate. Furthermore, the requirement that the application of linear response approximation to the free energy functionals of voltage coupling should satisfy the general free energy relations, yields a novel closed-form expression for the gating charge in terms of other basic properties of ion channels. This connection is familiar in statistical mechanics, known as the equilibrium fluctuation-response relation. The theory is illustrated by considering the coupling of a unit charge to the external voltage in the two sites near the surface of membrane, representing the activated and resting states. This is done using a coarse-graining (CG) model of membrane proteins, which includes the membrane, the electrolytes and the electrodes. The CG model yields Marcus-type voltage dependent free energy parabolas for the response of the electrostatic environment (electrolytes etc.) to the transition from the initial to the final configuratinal states, leading to equilibrium free energy difference and free energy barrier that follow the trend of the equilibrium fluctuation relation and the Marcus theory of electron transfer. These energetics also allow for a direct estimation of the voltage dependence of channel activation (Q-V curve), offering a quantitative rationale for a correlation between the voltage dependence parabolas and the Q-V curve, upon site-directed mutagenesis or drug binding. Taken together, by introducing the voltage coupling as the energy gap reaction coordinate, our framework brings new perspectives to the thermodynamic models of voltage activation in voltage-sensitive membrane proteins, offering an a framework for a better understating of the structure-function correlations of voltage gating in ion channels as well as electrogenic phenomena in ion pumps and transporters. Significantly, this formulation also provides a powerful bridge between the CG model of voltage coupling and the conventional macroscopic treatments.

Domain and interdomain energetics underlying gating in Shaker-type Kv channels

To understand gating events with a time-base many orders-of-magnitude slower than that of atomic motion in voltage-gated ion channels such as the Shaker-type KV channels, a multiscale physical model is constructed from the experimentally well-characterized voltage-sensor (VS) domains coupled to a hydrophobic gate. The four VS domains are described by a continuum electrostatic model under voltage-clamp conditions, the control of ion flow by the gate domain is described by a vapor-lock mechanism, and the simple coupling principle is informed by known experimental results and trial-and-error. The configurational energy computed for each element is used to produce a total Hamiltonian that is a function of applied voltage, VS positions, and gate radius. We compute statistical-mechanical expectation values of macroscopic laboratory observables. This approach stands in contrast with molecular-dynamic models which are challenged by increasing scale, and kinetic models which assume a probability distribution rather than derive it from the underlying physics. This generic model predicts well the Shaker charge/voltage and conductance/voltage relations; the tight constraints underlying these results allow us to quantitatively assess the underlying physical mechanisms. The total electrical work picked up by the VS domains is an order-of-magnitude larger than the work required to actuate the gate itself, suggesting an energetic basis for the evolutionary flexibility of the voltage-gating mechanism. The cooperative slide-and-interlock behavior of the VS domains described by the VS-gate coupling relation leads to the experimentally observed bistable gating. This engineering approach should prove useful in the investigation of various elements underlying gating characteristics and degraded behavior due to mutation.

Distal spike initiation zone location estimation by morphological simulation of ionic current filtering demonstrated in a novel model of an identified Drosophila motoneuron

Studying ion channel currents generated distally from the recording site is difficult because of artifacts caused by poor space clamp and membrane filtering. A computational model can quantify artifact parameters for correction by simulating the currents only if their exact anatomical location is known. We propose that the same artifacts that confound current recordings can help pinpoint the source of those currents by providing a signature of the neuron’s morphology. This method can improve the recording quality of currents initiated at the spike initiation zone (SIZ) that are often distal to the soma in invertebrate neurons. Drosophila being a valuable tool for characterizing ion currents, we estimated the SIZ location and quantified artifacts in an identified motoneuron, aCC/MN1-Ib, by constructing a novel multicompartmental model. Initial simulation of the measured biophysical channel properties in an isopotential Hodgkin-Huxley type neuron model partially replicated firing characteristics. Adding a second distal compartment, which contained spike-generating Na⁺ and K⁺ currents, was sufficient to simulate aCC’s in vivo activity signature. Matching this signature using a reconstructed morphology predicted that the SIZ is on aCC’s primary axon, 70 μm after the most distal dendritic branching point. From SIZ to soma, we observed and quantified selective morphological filtering of fast activating currents. Non-inactivating K⁺ currents are filtered ∼3 times less and despite their large magnitude at the soma they could be as distal as Na⁺ currents. The peak of transient component (NaT) of the voltage-activated Na⁺ current is also filtered more than the magnitude of slower persistent component (NaP), which can contribute to seizures. The corrected NaP/NaT ratio explains the previously observed discrepancy when the same channel is expressed in different cells. In summary, we used an in vivo signature to estimate ion channel location and recording artifacts, which can be applied to other neurons.

The study of ion channels is essential both for understanding normal brain function and for finding drug targets to treat neurological disease. Traditional experimental techniques remain challenging for recording ion channel currents accurately because of their locations in the neuron. Computer modeling of the three dimensional structure of neurons can provide a correction estimate for the measurement error introduced by neuronal membranes. To achieve this, we developed a modeling approach to localize, and correct for, distant ion channels. We demonstrated this approach by constructing novel computer models of an identified insect motor neuron, which provides a powerful model for studying the central nervous system. Through the study of electrical activity and genetic manipulations, it has been found that the persistent sodium current contributes to seizure. By modeling three dimensional structure, we were able to predict the location of these currents in the neuron, which were more distal than expected. Localizing sodium channels allowed us to predict their properties at origin, which favorably matched isolated recordings of these channels in more compact cells. This result is important in validating the use of heterologous compact cells to study insect sodium channels, and also demonstrates the usefulness of the presented modeling approach for studying channel physiology more generally.