Parameter Optimization for Ion Channel Models: Integrating New Data with Known Channel Properties.

Ion channels play a central role in membrane physiology, but to fully understand how they operate, one must have accurate kinetic mechanisms. Estimating kinetics is not trivial when the mechanism is complex, and a large number of parameters must be extracted from data. Furthermore, the information contained in the data is often limited, and the model may not be fully determined. The solution is to reduce the number of parameters and to estimate them in such a way that they not only describe well the new data but also agree with the existing knowledge. In a previous study, we presented a comprehensive formalism for estimating kinetic parameters subject to a variety of explicit and implicit constraints that define quantitative relationships between parameters and describe specific mechanism properties. Here, we introduce the reader to the QuB software, which implements this constraining formalism. QuB features a powerful visual interface and a high-level scripting language that can be used to formulate kinetic models and constraints of arbitrary complexity, and to efficiently estimate the parameters from a variety of experimental data.

Sodium channels implement a molecular leaky integrator that detects action potentials and regulates neuronal firing.

Voltage-gated sodium channels play a critical role in cellular excitability, amplifying small membrane depolarizations into action potentials. Interactions with auxiliary subunits and other factors modify the intrinsic kinetic mechanism to result in new molecular and cellular functionality. We show here that sodium channels can implement a molecular leaky integrator, where the input signal is the membrane potential and the output is the occupancy of a long-term inactivated state. Through this mechanism, sodium channels effectively measure the frequency of action potentials and convert it into Na+ current availability. In turn, the Na+ current can control neuronal firing frequency in a negative feedback loop. Consequently, neurons become less sensitive to changes in excitatory input and maintain a lower firing rate. We present these ideas in the context of rat serotonergic raphe neurons, which fire spontaneously at low frequency and provide critical neuromodulation to many autonomous and cognitive brain functions.

Estimating kinetic mechanisms with prior knowledge II: Behavioral constraints and numerical tests.

Kinetic mechanisms predict how ion channels and other proteins function at the molecular and cellular levels. Ideally, a kinetic model should explain new data but also be consistent with existing knowledge. In this two-part study, we present a mathematical and computational formalism that can be used to enforce prior knowledge into kinetic models using constraints. Here, we focus on constraints that quantify the behavior of the model under certain conditions, and on constraints that enforce arbitrary parameter relationships. The penalty-based optimization mechanism described here can be used to enforce virtually any model property or behavior, including those that cannot be easily expressed through mathematical relationships. Examples include maximum open probability, use-dependent availability, and nonlinear parameter relationships. We use a simple kinetic mechanism to test multiple sets of constraints that implement linear parameter relationships and arbitrary model properties and behaviors, and we provide numerical examples. This work complements and extends the companion article, where we show how to enforce explicit linear parameter relationships. By incorporating more knowledge into the parameter estimation procedure, it is possible to obtain more realistic and robust models with greater predictive power.

Estimating kinetic mechanisms with prior knowledge I: Linear parameter constraints.

To understand how ion channels and other proteins function at the molecular and cellular levels, one must decrypt their kinetic mechanisms. Sophisticated algorithms have been developed that can be used to extract kinetic parameters from a variety of experimental data types. However, formulating models that not only explain new data, but are also consistent with existing knowledge, remains a challenge. Here, we present a two-part study describing a mathematical and computational formalism that can be used to enforce prior knowledge into the model using constraints. In this first part, we focus on constraints that enforce explicit linear relationships involving rate constants or other model parameters. We develop a simple, linear algebra-based transformation that can be applied to enforce many types of model properties and assumptions, such as microscopic reversibility, allosteric gating, and equality and inequality parameter relationships. This transformation converts the set of linearly interdependent model parameters into a reduced set of independent parameters, which can be passed to an automated search engine for model optimization. In the companion article, we introduce a complementary method that can be used to enforce arbitrary parameter relationships and any constraints that quantify the behavior of the model under certain conditions. The procedures described in this study can, in principle, be coupled to any of the existing methods for solving molecular kinetics for ion channels or other proteins. These concepts can be used not only to enforce existing knowledge but also to formulate and test new hypotheses.

The Drosophila Gr28bD product is a non-specific cation channel that can be used as a novel thermogenetic tool.

Extrinsic control of single neurons and neuronal populations is a powerful approach for understanding how neural circuits function. Adding new thermogenetic tools to existing optogenetic and other forms of intervention will increase the complexity of questions that can be addressed. A good candidate for developing new thermogenetic tools is the Drosophila gustatory receptor family, which has been implicated in high-temperature avoidance behavior. We examined the five members of the Gr28b gene cluster for temperature-dependent properties via three approaches: biophysical characterization in Xenopus oocytes, functional calcium imaging in Drosophila motor neurons, and behavioral assays in adult Drosophila. Our results show that Gr28bD expression in Xenopus oocytes produces a non-specific cationic current that is activated by elevated temperatures. This current is non-inactivating and non-voltage dependent. When expressed in Drosophila motor neurons, Gr28bD can be used to change the firing pattern of individual cells in a temperature-dependent fashion. Finally, we show that pan-neuronal or motor neuron expression of Gr28bD can be used to alter fruit fly behavior with elevated temperatures. Together, these results validate the potential of the Gr28bD gene as a founding member of a new class of thermogenetic tools.

Molecular Interactions between Tarantula Toxins and Low-Voltage-Activated Calcium Channels.

Few gating-modifier toxins have been reported to target low-voltage-activated (LVA) calcium channels, and the structural basis of toxin sensitivity remains incompletely understood. Studies of voltage-gated potassium (Kv) channels have identified the S3b-S4 "paddle motif," which moves at the protein-lipid interface to drive channel opening, as the target for these amphipathic neurotoxins. Voltage-gated calcium (Cav) channels contain four homologous voltage sensor domains, suggesting multiple toxin binding sites. We show here that the S3-S4 segments within Cav3.1 can be transplanted into Kv2.1 to examine their individual contributions to voltage sensing and pharmacology. With these results, we now have a more complete picture of the conserved nature of the paddle motif in all three major voltage-gated ion channel types (Kv, Nav, and Cav). When screened with tarantula toxins, the four paddle sequences display distinct toxin binding properties, demonstrating that gating-modifier toxins can bind to Cav channels in a domain specific fashion. Domain III was the most commonly and strongly targeted, and mutagenesis revealed an acidic residue that is important for toxin binding. We also measured the lipid partitioning strength of all toxins tested and observed a positive correlation with their inhibition of Cav3.1, suggesting a key role for membrane partitioning.

Tarantula toxins use common surfaces for interacting with Kv and ASIC ion channels.

Tarantula toxins that bind to voltage-sensing domains of voltage-activated ion channels are thought to partition into the membrane and bind to the channel within the bilayer. While no structures of a voltage-sensor toxin bound to a channel have been solved, a structural homolog, psalmotoxin (PcTx1), was recently crystalized in complex with the extracellular domain of an acid sensing ion channel (ASIC). In the present study we use spectroscopic, biophysical and computational approaches to compare membrane interaction properties and channel binding surfaces of PcTx1 with the voltage-sensor toxin guangxitoxin (GxTx-1E). Our results show that both types of tarantula toxins interact with membranes, but that voltage-sensor toxins partition deeper into the bilayer. In addition, our results suggest that tarantula toxins have evolved a similar concave surface for clamping onto α-helices that is effective in aqueous or lipidic physical environments.

From foe to friend: using animal toxins to investigate ion channel function.

Ion channels are vital contributors to cellular communication in a wide range of organisms, a distinct feature that renders this ubiquitous family of membrane-spanning proteins a prime target for toxins found in animal venom. For many years, the unique properties of these naturally occurring molecules have enabled researchers to probe the structural and functional features of ion channels and to define their physiological roles in normal and diseased tissues. To illustrate their considerable impact on the ion channel field, this review will highlight fundamental insights into toxin-channel interactions and recently developed toxin screening methods and practical applications of engineered toxins.

Structural interactions of a voltage sensor toxin with lipid membranes.

Protein toxins from tarantula venom alter the activity of diverse ion channel proteins, including voltage, stretch, and ligand-activated cation channels. Although tarantula toxins have been shown to partition into membranes, and the membrane is thought to play an important role in their activity, the structural interactions between these toxins and lipid membranes are poorly understood. Here, we use solid-state NMR and neutron diffraction to investigate the interactions between a voltage sensor toxin (VSTx1) and lipid membranes, with the goal of localizing the toxin in the membrane and determining its influence on membrane structure. Our results demonstrate that VSTx1 localizes to the headgroup region of lipid membranes and produces a thinning of the bilayer. The toxin orients such that many basic residues are in the aqueous phase, all three Trp residues adopt interfacial positions, and several hydrophobic residues are within the membrane interior. One remarkable feature of this preferred orientation is that the surface of the toxin that mediates binding to voltage sensors is ideally positioned within the lipid bilayer to favor complex formation between the toxin and the voltage sensor.

Opening the shaker K+ channel with hanatoxin.

Voltage-activated ion channels open and close in response to changes in membrane voltage, a property that is fundamental to the roles of these channels in electrical signaling. Protein toxins from venomous organisms commonly target the S1-S4 voltage-sensing domains in these channels and modify their gating properties. Studies on the interaction of hanatoxin with the Kv2.1 channel show that this tarantula toxin interacts with the S1-S4 domain and inhibits opening by stabilizing a closed state. Here we investigated the interaction of hanatoxin with the Shaker Kv channel, a voltage-activated channel that has been extensively studied with biophysical approaches. In contrast to what is observed in the Kv2.1 channel, we find that hanatoxin shifts the conductance-voltage relation to negative voltages, making it easier to open the channel with membrane depolarization. Although these actions of the toxin are subtle in the wild-type channel, strengthening the toxin-channel interaction with mutations in the S3b helix of the S1-S4 domain enhances toxin affinity and causes large shifts in the conductance-voltage relationship. Using a range of previously characterized mutants of the Shaker Kv channel, we find that hanatoxin stabilizes an activated conformation of the voltage sensors, in addition to promoting opening through an effect on the final opening transition. Chimeras in which S3b-S4 paddle motifs are transferred between Kv2.1 and Shaker Kv channels, as well as experiments with the related tarantula toxin GxTx-1E, lead us to conclude that the actions of tarantula toxins are not simply a product of where they bind to the channel, but that fine structural details of the toxin-channel interface determine whether a toxin is an inhibitor or opener.

Palmitoylation influences the function and pharmacology of sodium channels.

Palmitoylation is a common lipid modification known to regulate the functional properties of various proteins and is a vital step in the biosynthesis of voltage-activated sodium (Nav) channels. We discovered a mutation in an intracellular loop of rNav1.2a (G1079C), which results in a higher apparent affinity for externally applied PaurTx3 and ProTx-II, two voltage sensor toxins isolated from tarantula venom. To explore whether palmitoylation of the introduced cysteine underlies this observation, we compared channel susceptibility to a range of animal toxins in the absence and presence of 2-Br-palmitate, a palmitate analog that prevents palmitate incorporation into proteins, and found that palmitoylation contributes to the increased affinity of PaurTx3 and ProTx-II for G1079C. Further investigations with 2-Br-palmitate revealed that palmitoylation can regulate the gating and pharmacology of wild-type (wt) rNav1.2a. To identify rNav1.2a palmitoylation sites contributing to these phenomena, we substituted three endogenous cysteines predicted to be palmitoylated and found that the gating behavior of this triple cysteine mutant is similar to wt rNav1.2a treated with 2-Br-palmitate. As with chemically depalmitoylated rNav1.2a channels, this mutant also exhibits an increased susceptibility for PaurTx3. Additional mutagenesis experiments showed that palmitoylation of one cysteine in particular (C1182) primarily influences PaurTx3 sensitivity and may enhance the inactivation process of wt rNav1.2a. Overall, our results demonstrate that lipid modifications are capable of altering the gating and pharmacological properties of rNav1.2a.

Structure and orientation of a voltage-sensor toxin in lipid membranes.

Amphipathic protein toxins from tarantula venom inhibit voltage-activated potassium (Kv) channels by binding to a critical helix-turn-helix motif termed the voltage sensor paddle. Although these toxins partition into membranes to bind the paddle motif, their structure and orientation within the membrane are unknown. We investigated the interaction of a tarantula toxin named SGTx with membranes using both fluorescence and NMR spectroscopy. Depth-dependent fluorescence-quenching experiments with brominated lipids suggest that Trp30 in SGTx is positioned approximately 9 A from the center of the bilayer. NMR spectra reveal that the inhibitor cystine knot structure of the toxin does not radically change upon membrane partitioning. Transferred cross-saturation NMR experiments indicate that the toxin's hydrophobic protrusion contacts the hydrophobic core of the membrane, whereas most surrounding polar residues remain at interfacial regions of the bilayer. The inferred orientation of the toxin reveals a twofold symmetry in the arrangement of basic and hydrophobic residues, a feature that is conserved among tarantula toxins. These results have important implications for regions of the toxin involved in recognizing membranes and voltage-sensor paddles, and for the mechanisms by which tarantula toxins alter the activity of different types of ion channels.

Solution structure of GxTX-1E, a high-affinity tarantula toxin interacting with voltage sensors in Kv2.1 potassium channels .

GxTX-1E is a neurotoxin recently isolated from Plesiophrictus guangxiensis venom that inhibits the Kv2.1 channel in pancreatic beta-cells. The sequence of the toxin is related to those of previously studied tarantula toxins that interact with the voltage sensors in Kv channels, and GxTX-1E interacts with the Kv2.1 channel with unusually high affinity, making it particularly useful for structural and mechanistic studies. Here we determined the three-dimensional solution structure of GxTX-1E using NMR spectroscopy and compared it to that of several related tarantula toxins. The molecular structure of GxTX-1E is similar to those of tarantula toxins that target voltage sensors in Kv channels in that it contains an ICK motif, composed of beta-strands, and contains a prominent cluster of solvent-exposed hydrophobic residues surrounded by polar residues. When compared with the structure of SGTx1, a toxin for which mutagenesis data are available, the residue compositions of the two toxins are distinct in regions that are critical for activity, suggesting that their modes of binding to voltage sensors may be different. Interestingly, the structural architecture of GxTX-1E is also similar to that of JZTX-III, a tarantula toxin that interacts with Kv2.1 with low affinity. The most striking structural differences between GxTX-1E and JZTX-III are found in the orientation between the first and second cysteine loops and the C-terminal region of the toxins, suggesting that these regions of GxTX-1E are responsible for its high affinity.

Interactions between lipids and voltage sensor paddles detected with tarantula toxins.

Voltage-activated ion channels open and close in response to changes in voltage, a property that is essential for generating nerve impulses. Studies on voltage-activated potassium (Kv) channels show that voltage-sensor activation is sensitive to the composition of lipids in the surrounding membrane. Here we explore the interaction of lipids with S1-S4 voltage-sensing domains and find that the conversion of the membrane lipid sphingomyelin to ceramide-1-phosphate alters voltage-sensor activation in an S1-S4 voltage-sensing protein lacking an associated pore domain, and that the S3b-S4 paddle motif determines the effects of lipid modification on Kv channels. Using tarantula toxins that bind to paddle motifs within the membrane, we identify mutations in the paddle motif that weaken toxin binding by disrupting lipid-paddle interactions. Our results suggest that lipids bind to voltage-sensing domains and demonstrate that the pharmacological sensitivities of voltage-activated ion channels are influenced by the surrounding lipid membrane.

Tarantula toxins interact with voltage sensors within lipid membranes.

Voltage-activated ion channels are essential for electrical signaling, yet the mechanism of voltage sensing remains under intense investigation. The voltage-sensor paddle is a crucial structural motif in voltage-activated potassium (K(v)) channels that has been proposed to move at the protein-lipid interface in response to changes in membrane voltage. Here we explore whether tarantula toxins like hanatoxin and SGTx1 inhibit K(v) channels by interacting with paddle motifs within the membrane. We find that these toxins can partition into membranes under physiologically relevant conditions, but that the toxin-membrane interaction is not sufficient to inhibit K(v) channels. From mutagenesis studies we identify regions of the toxin involved in binding to the paddle motif, and those important for interacting with membranes. Modification of membranes with sphingomyelinase D dramatically alters the stability of the toxin-channel complex, suggesting that tarantula toxins interact with paddle motifs within the membrane and that they are sensitive detectors of lipid-channel interactions.

Voltage-sensor activation with a tarantula toxin as cargo.

The opening and closing of voltage-activated Na+, Ca2+ and K+ (Kv) channels underlies electrical and chemical signalling throughout biology, yet the structural basis of voltage sensing is unknown. Hanatoxin is a tarantula toxin that inhibits Kv channels by binding to voltage-sensor paddles, crucial helix-turn-helix motifs within the voltage-sensing domains that are composed of S3b and S4 helices. The active surface of the toxin is amphipathic, and related toxins have been shown to partition into membranes, raising the possibility that the toxin is concentrated in the membrane and interacts only weakly and transiently with the voltage sensors. Here we examine the kinetics and state dependence of the toxin-channel interaction and the physical location of the toxin in the membrane. We find that hanatoxin forms a strong and stable complex with the voltage sensors, far outlasting fluctuations of the voltage sensors between resting (closed) conformations at negative voltages and activated (open) conformations at positive voltages. Toxin affinity is reduced by voltage-sensor activation, explaining why the toxin stabilizes the resting conformation. We also find that when hanatoxin partitions into membranes it is localized to an interfacial region, with Trp 30 positioned about 8.5 A from the centre of the bilayer. These results demonstrate that voltage-sensor paddles activate with a toxin as cargo, and suggest that the paddles traverse no more than the outer half of the bilayer during activation.

Solution structure and lipid membrane partitioning of VSTx1, an inhibitor of the KvAP potassium channel.

VSTx1 is a voltage sensor toxin from the spider Grammostola spatulata that inhibits KvAP, an archeabacterial voltage-activated K(+) channel whose X-ray structure has been reported. Although the receptor for VSTx1 and the mechanism of inhibition are unknown, the sequence of the toxin is related to hanatoxin (HaTx) and SGTx, two toxins that inhibit eukaryotic voltage-activated K(+) channels by binding to voltage sensors. VSTx1 has been recently shown to interact equally well with lipid membranes that contain zwitterionic or acidic phospholipids, and it has been proposed that the toxin receptor is located within a region of the channel that is submerged in the membrane. As a first step toward understanding the inhibitory mechanism of VSTx1, we determined the three-dimensional solution structure of the toxin using NMR. Although the structure of VSTx1 is similar to HaTx and SGTx in terms of molecular fold and amphipathic character, the detailed positions of hydrophobic and surrounding charged residues in VSTx1 are very different than what is seen in the other toxins. The amphipathic character of VSTx1, notably the close apposition of basic and hydrophobic residues on one face of the toxin, raises the possibility that the toxin interacts with interfacial regions of the membrane. We reinvestigated the partitioning of VSTx1 into lipid membranes and find that VSTx1 partitioning requires negatively charged phospholipids. Intrinsic tryptophan fluorescence and acrylamide quenching experiments suggest that tryptophan residues on the hydrophobic surface of VSTx1 have a diminished exposure to water when the toxin interacts with membranes. The present results suggest that if membrane partitioning is involved in the mechanism by which VSTx1 inhibits voltage-activated K(+) channels, then binding of the toxin to the channel would likely occur at the interface between the polar headgroups and the hydrophobic phase of the membrane.

Regulation of the tryptophan biosynthetic genes in Bacillus halodurans: common elements but different strategies than those used by Bacillus subtilis.

In Bacillus subtilis, an RNA binding protein called TRAP regulates both transcription and translation of the tryptophan biosynthetic genes. Bacillus halodurans is an alkaliphilic Bacillus species that grows at high pHs. Previous studies of this bacterium have focused on mechanisms of adaptation for growth in alkaline environments. We have characterized the regulation of the tryptophan biosynthetic genes in B. halodurans and compared it to that in B. subtilis. B. halodurans encodes a TRAP protein with 71% sequence identity to the B. subtilis protein. Expression of anthranilate synthetase, the first enzyme in the pathway to tryptophan, is regulated significantly less in B. halodurans than in B. subtilis. Examination of the control of the B. halodurans trpEDCFBA operon both in vivo and in vitro shows that only transcription is regulated, whereas in B. subtilis both transcription of the operon and translation of trpE are controlled. The attenuation mechanism that controls transcription in B. halodurans is similar to that in B. subtilis, but there are some differences in the predicted RNA secondary structures in the B. halodurans trp leader region, including the presence of a potential anti-antiterminator structure. Translation of trpG, which is within the folate operon in both bacilli, is regulated similarly in the two species.