Changes in Both Neuron Intrinsic Properties and Neurotransmission Are Needed to Drive the Increase in GnRH Neuron Firing Rate during Estradiol-Positive Feedback.

Central output of gonadotropin-releasing hormone (GnRH) neurons controls fertility and is sculpted by sex-steroid feedback. A switch of estradiol action from negative to positive feedback initiates a surge of GnRH release, culminating in ovulation. In ovariectomized mice bearing constant-release estradiol implants (OVX+E), GnRH neuron firing is suppressed in the morning (AM) by negative feedback and activated in the afternoon (PM) by positive feedback; no time-of-day-dependent changes occur in OVX mice. In this daily surge model, GnRH neuron intrinsic properties are shifted to favor increased firing during positive feedback. It is unclear whether this shift and the observed concomitant increase in GABAergic transmission, which typically excites GnRH neurons, are independently sufficient for increasing GnRH neuron firing rate during positive feedback or whether both are needed. To test this, we used dynamic clamp to inject selected previously recorded trains of GABAergic postsynaptic conductances (PSgs) collected during the different feedback states of the daily surge model into GnRH neurons from OVX, OVX+E AM, and OVX+E PM mice. PSg trains mimicking positive feedback initiated more action potentials in cells from OVX+E PM mice than negative feedback or OVX (open feedback loop) trains in all three animal models, but the positive-feedback train was most effective when applied to cells during positive feedback. In silico studies of model GnRH neurons in which >1000 PSg trains were tested exhibited the same results. These observations support the hypothesis that GnRH neurons integrate fast-synaptic and intrinsic changes to increase firing rates during positive feedback.SIGNIFICANCE STATEMENT Infertility affects 15%-20% of couples; failure to ovulate is a common cause. Understanding how the brain controls ovulation is critical for new developments in both infertility treatment and contraception. Ovarian estradiol alters both the intrinsic properties of gonadotropin-releasing hormone (GnRH) neurons and synaptic inputs to these cells coincident with production of sustained GnRH release that ultimately triggers ovulation. We demonstrate here using dynamic clamp and mathematical modeling that estradiol-induced shifts in synaptic transmission alone can increase firing output, but that the intrinsic properties of GnRH neurons during positive feedback further poise these cells for increased response to higher frequency synaptic transmission. These data suggest that GnRH neurons integrate fast-synaptic and intrinsic changes to increase firing rates during the preovulatory GnRH surge.

Estradiol Enhances the Depolarizing Response to GABA and AMPA Synaptic Conductances in Arcuate Kisspeptin Neurons by Diminishing Voltage-Gated Potassium Currents.

Synaptic and intrinsic properties interact to sculpt neuronal output. Kisspeptin neurons in the hypothalamic arcuate nucleus help convey homeostatic estradiol feedback to central systems controlling fertility. Estradiol increases membrane depolarization induced by GABAA receptor activation in these neurons. We hypothesized that the mechanisms underlying estradiol-induced alterations in postsynaptic response to GABA, and also AMPA, receptor activation include regulation of voltage-gated potassium currents. Whole-cell recordings of arcuate kisspeptin neurons in brain slices from ovariectomized (OVX) and OVX+estradiol (OVX+E) female mice during estradiol negative feedback revealed that estradiol reduced capacitance, reduced transient and sustained potassium currents, and altered voltage dependence and kinetics of transient currents. Consistent with these observations, estradiol reduced rheobase and action potential latency. To study more directly interactions between synaptic and active intrinsic estradiol feedback targets, dynamic clamp was used to simulate GABA and AMPA conductances. Both GABA and AMPA dynamic clamp-induced postsynaptic potentials (PSPs) were smaller in neurons from OVX than OVX+E mice; blocking transient potassium currents eliminated this difference. To interrogate the role of the estradiol-induced changes in passive intrinsic properties, different Markov model structures based on the properties of the transient potassium current in cells from OVX or OVX+E mice were combined in silico with passive properties reflecting these two endocrine conditions. Some of tested models reproduced the effect on PSPs in silico, revealing that AMPA PSPs were more sensitive to changes in capacitance. These observations support the hypothesis that PSPs in arcuate kisspeptin neurons are regulated by estradiol-sensitive mechanisms including potassium conductances and membrane properties.SIGNIFICANCE STATEMENT Kisspeptin neurons relay estradiol feedback to gonadotropin-releasing hormone neurons, which regulate the reproductive system. The fast synaptic neurotransmitters GABA and glutamate rapidly depolarize arcuate kisspeptin neurons and estradiol increases this depolarization. Estradiol reduced both potassium current in the membrane potential range typically achieved during response to fast synaptic inputs and membrane capacitance. Using simulated GABA and glutamate synaptic inputs, we showed changes in both the passive and active intrinsic properties induced by in vivo estradiol treatment affect the response to synaptic inputs, with capacitance having a greater effect on response to glutamate. The suppression of both passive and active intrinsic properties by estradiol feedback thus renders arcuate kisspeptin neurons more sensitive to fast synaptic inputs.

3D Data Mapping and Real-Time Experiment Control and Visualization in Brain Slices.

Here, we propose two basic concepts that can streamline electrophysiology and imaging experiments in brain slices and enhance data collection and analysis. The first idea is to interface the experiment with a software environment that provides a 3D scene viewer in which the experimental rig, the brain slice, and the recorded data are represented to scale. Within the 3D scene viewer, the user can visualize a live image of the sample and 3D renderings of the recording electrodes with real-time position feedback. Furthermore, the user can control the instruments and visualize their status in real time. The second idea is to integrate multiple types of experimental data into a spatial and temporal map of the brain slice. These data may include low-magnification maps of the entire brain slice, for spatial context, or any other type of high-resolution structural and functional image, together with time-resolved electrical and optical signals. The entire data collection can be visualized within the 3D scene viewer. These concepts can be applied to any other type of experiment in which high-resolution data are recorded within a larger sample at different spatial and temporal coordinates.

Mechanosensitive pore opening of a prokaryotic voltage-gated sodium channel.

Voltage-gated ion channels (VGICs) orchestrate electrical activities that drive mechanical functions in contractile tissues such as the heart and gut. In turn, contractions change membrane tension and impact ion channels. VGICs are mechanosensitive, but the mechanisms of mechanosensitivity remain poorly understood. Here, we leverage the relative simplicity of NaChBac, a prokaryotic voltage-gated sodium channel from Bacillus halodurans, to investigate mechanosensitivity. In whole-cell experiments on heterologously transfected HEK293 cells, shear stress reversibly altered the kinetic properties of NaChBac and increased its maximum current, comparably to the mechanosensitive eukaryotic sodium channel NaV1.5. In single-channel experiments, patch suction reversibly increased the open probability of a NaChBac mutant with inactivation removed. A simple kinetic mechanism featuring a mechanosensitive pore opening transition explained the overall response to force, whereas an alternative model with mechanosensitive voltage sensor activation diverged from the data. Structural analysis of NaChBac identified a large displacement of the hinged intracellular gate, and mutagenesis near the hinge diminished NaChBac mechanosensitivity, further supporting the proposed mechanism. Our results suggest that NaChBac is overall mechanosensitive due to the mechanosensitivity of a voltage-insensitive gating step associated with the pore opening. This mechanism may apply to eukaryotic VGICs, including NaV1.5.

Fast-activating voltage- and calcium-dependent potassium (BK) conductance promotes bursting in pituitary cells: a dynamic clamp study.

The electrical activity pattern of endocrine pituitary cells regulates their basal secretion level. Rat somatotrophs and lactotrophs exhibit spontaneous bursting and have high basal levels of hormone secretion, while gonadotrophs exhibit spontaneous spiking and have low basal hormone secretion. It has been proposed that the difference in electrical activity between bursting somatotrophs and spiking gonadotrophs is due to the presence of large conductance potassium (BK) channels on somatotrophs but not on gonadotrophs. This is one example where the role of an ion channel type may be clearly established. We demonstrate here that BK channels indeed promote bursting activity in pituitary cells. Blocking BK channels in bursting lacto-somatotroph GH4C1 cells changes their firing activity to spiking, while further adding an artificial BK conductance via dynamic clamp restores bursting. Importantly, this burst-promoting effect requires a relatively fast BK activation/deactivation, as predicted by computational models. We also show that adding a fast-activating BK conductance to spiking gonadotrophs converts the activity of these cells to bursting. Together, our results suggest that differences in BK channel expression may underlie the differences in electrical activity and basal hormone secretion levels among pituitary cell types and that the rapid rate of BK channel activation is key to its role in burst promotion.

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.

Kinetic properties and functional dynamics of sodium channels during repetitive spiking in a slow pacemaker neuron.

We examined the kinetic properties of voltage-gated Na(+) channels and their contribution to the repetitive spiking activity of medullary raphé neurons, which exhibit slow pacemaking and strong spiking adaptation. The study is based on a combination of whole-cell patch-clamp, modeling and real-time computation. Na(+) currents were recorded from neurons in brain slices obtained from male and female neonatal rats, using voltage-clamp protocols designed to reduce space-clamp artifacts and to emphasize functionally relevant kinetic features. A detailed kinetic model was formulated to explain the broad range of transient and stationary voltage-dependent properties exhibited by Na(+) currents. The model was tested by injecting via dynamic clamp a model-based current as a substitute for the native TTX-sensitive Na(+) currents, which were pharmacologically blocked. The model-based current reproduced well the native spike shape and spiking frequency. The dynamics of Na(+) channels during repetitive spiking were indirectly examined through this model. By comparing the spiking activities generated with different kinetic models in dynamic-clamp experiments, we determined that state-dependent slow inactivation contributes significantly to spiking adaptation. Through real-time manipulation of the model-based current, we established that suprathreshold Na(+) current mainly controls spike shape, whereas subthreshold Na(+) current modulates spiking frequency and contributes to the pacemaking mechanism. Since the model-based current was injected in the soma, the results also suggest that somatic Na(+) channels are sufficient to establish the essential spiking properties of raphé neurons in vitro.

Isolation of somatic Na+ currents by selective inactivation of axonal channels with a voltage prepulse.

We present a simple and effective method for isolating the somatic Na(+) current recorded under voltage clamp from neurons in brain slices. The principle is to convert the axon from an active compartment capable of generating uncontrolled axonal spikes into a passive structure by selectively inactivating axonal Na(+) channels. Typically, whole-cell currents from intact neurons under somatic voltage clamp contain a mixture of Na(+) current and axial current caused by escaped axonal spikes. We found that a brief prepulse to voltages near spike threshold evokes the axonal spike, which inactivates axonal but not somatic channels. A subsequent voltage step then evokes only somatic Na(+) current from electrotonically proximal sodium channels under good voltage-clamp control. Simulations using a neuron compartmental model support the idea that the prepulse effectively inactivates currents from the axon and isolates well controlled somatic currents. Na(+) currents recorded from cortical pyramidal neurons in slices, using the prepulse, were found to have voltage dependence nearly identical to that of currents recorded from acutely dissociated pyramidal neurons. In addition, studies in dissociated neurons show that the prepulse has no visible effect on the voltage dependence and kinetics of Na(+) currents elicited by the subsequent voltage step, only decreasing the amplitude of the currents by 10-20%. The technique was effective in several neuronal types in brain slices from male and female neonatal rats and mice, including raphé neurons, cortical pyramidal neurons, inferior olivary neurons, and hypoglossal motoneurons.

Dynamic Clamp on a Windows PC.

Dynamic clamp is a powerful tool for interfacing computational models and real cells. We describe here how to set up and carry out dynamic clamp experiments using a patch clamp amplifier, a National Instruments data acquisition card, and the freely available QuB software that operates on a PC running MS Windows.

The mechanism of MICU-dependent gating of the mitochondrial Ca2+uniporter.

Ca2+ entry into mitochondria is through the mitochondrial calcium uniporter complex (MCUcx), a Ca2+-selective channel composed of five subunit types. Two MCUcx subunits (MCU and EMRE) span the inner mitochondrial membrane, while three Ca2+-regulatory subunits (MICU1, MICU2, and MICU3) reside in the intermembrane space. Here, we provide rigorous analysis of Ca2+ and Na+ fluxes via MCUcx in intact isolated mitochondria to understand the function of MICU subunits. We also perform direct patch clamp recordings of macroscopic and single MCUcx currents to gain further mechanistic insights. This comprehensive analysis shows that the MCUcx pore, composed of the EMRE and MCU subunits, is not occluded nor plugged by MICUs during the absence or presence of extramitochondrial Ca2+ as has been widely reported. Instead, MICUs potentiate activity of MCUcx as extramitochondrial Ca2+ is elevated. MICUs achieve this by modifying the gating properties of MCUcx allowing it to spend more time in the open state.

A modeling study of T-type Ca2+ channel gating and modulation by L-cysteine in rat nociceptors.

L-cysteine (L-cys) increases the amplitude of T-type Ca(2+) currents in rat T-rich nociceptor-like dorsal root ganglia neurons. The modulation of T-type Ca(2+) channel gating by L-cys was studied by fitting Markov state models to whole-cell currents recorded from T-rich neurons. The best fitting model tested included three resting states and inactivation from the second resting state and the open state. Inactivation and the final opening step were voltage-independent, whereas transitions between the resting states and deactivation were voltage-dependent. The transition rates between the first two resting states were an order of magnitude faster than those between the second and third resting states, and the voltage-dependency of forward transitions through resting states was two to three times greater than for analogous backward transitions. Analysis with the best fitting model suggested that L-cys increases current amplitude mainly by increasing the transition rate from resting to open and decreasing the transition rate from open to inactivated. An additional model was developed that could account for the bi-exponential time course of recovery from inactivation of the currents and the high frequency of blank sweeps in single channel recordings. This model detected basically the same effects of L-cys on channel gating as the best fitting model.

Raphé neurons stimulate respiratory circuit activity by multiple mechanisms via endogenously released serotonin and substance P.

Brainstem serotonin (5-HT) neurons modulate activity of many neural circuits in the mammalian brain, but in many cases endogenous mechanisms have not been resolved. Here, we analyzed actions of raphé 5-HT neurons on respiratory network activity including at the level of the pre-Bötzinger complex (pre-BötC) in neonatal rat medullary slices in vitro, and in the more intact nervous system of juvenile rats in arterially perfused brainstem-spinal cord preparations in situ. At basal levels of activity, excitation of the respiratory network via simultaneous release of 5-HT and substance P (SP), acting at 5-HT(2A/2C), 5-HT(4), and/or neurokinin-1 receptors, was required to maintain inspiratory motor output in both the neonatal and juvenile systems. The midline raphé obscurus contained spontaneously active 5-HT neurons, some of which projected to the pre-BötC and hypoglossal motoneurons, colocalized 5-HT and SP, and received reciprocal excitatory connections from the pre-BötC. Experimentally augmenting raphé obscurus activity increased motor output by simultaneously exciting pre-BötC and motor neurons. Biophysical analyses in vitro demonstrated that 5-HT and SP modulated background cation conductances in pre-BötC and motor neurons, including a nonselective cation leak current that contributed to the resting potential, which explains the neuronal depolarization that augmented motor output. Furthermore, we found that 5-HT, but not SP, can transform the electrophysiological phenotype of some pre-BötC neurons to intrinsic bursters, providing 5-HT with an additional role in promoting rhythm generation. We conclude that raphé 5-HT neurons excite key circuit components required for generation of respiratory motor output.

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.

Real-time kinetic modeling of voltage-gated ion channels using dynamic clamp.

We propose what to our knowledge is a new technique for modeling the kinetics of voltage-gated ion channels in a functional context, in neurons or other excitable cells. The principle is to pharmacologically block the studied channel type, and to functionally replace it with dynamic clamp, on the basis of a computational model. Then, the parameters of the model are modified in real time (manually or automatically), with the objective of matching the dynamical behavior of the cell (e.g., action potential shape and spiking frequency), but also the transient and steady-state properties of the model (e.g., those derived from voltage-clamp recordings). Through this approach, one may find a model and parameter values that explain both the observed cellular dynamics and the biophysical properties of the channel. We extensively tested the method, focusing on Na(v) models. Complex Markov models (10-12 states or more) could be accurately integrated in real time at >50 kHz using the transition probability matrix, but not the explicit Euler method. The practicality of the technique was tested with experiments in raphe pacemaker neurons. Through automated real-time fitting, a Hodgkin-Huxley model could be found that reproduced well the action potential shape and the spiking frequency. Adding a virtual axonal compartment with a high density of Na(v) channels further improved the action potential shape. The computational procedure was implemented in the free QuB software, running under Microsoft Windows and featuring a friendly graphical user interface.

Kinetic properties of persistent Na+ current orchestrate oscillatory bursting in respiratory neurons.

The rhythmic pattern of breathing depends on the pre-Bötzinger complex (preBötC) in the brainstem, a vital circuit that contains a population of neurons with intrinsic oscillatory bursting behavior. Here, we investigate the specific kinetic properties that enable voltage-gated sodium channels to establish oscillatory bursting in preBötC inspiratory neurons, which exhibit an unusually large persistent Na+ current (INaP). We first characterize the kinetics of INaP in neonatal rat brainstem slices in vitro, using whole-cell patch-clamp and computational modeling, and then test the contribution of INaP to rhythmic bursting in live neurons, using the dynamic clamp technique. We provide evidence that subthreshold activation, persistence at suprathreshold potentials, slow inactivation, and slow recovery from inactivation are kinetic features of INaP that regulate all aspects of intrinsic rhythmic bursting in preBötC neurons. The slow and cumulative inactivation of INaP during the burst active phase controls burst duration and termination, while the slow recovery from inactivation controls the duration of the interburst interval. To demonstrate this mechanism, we develop a Markov state model of INaP that explains a comprehensive set of voltage clamp data. By adding or subtracting a computer-generated INaP from a live neuron via dynamic clamp, we are able to convert nonbursters into intrinsic bursters, and vice versa. As a control, we test a model with inactivation features removed. Adding noninactivating INaP into nonbursters results in a pattern of random transitions between sustained firing and quiescence. The relative amplitude of INaP is the key factor that separates intrinsic bursters from nonbursters and can change the fraction of intrinsic bursters in the preBötC. INaP could thus be an important target for regulating network rhythmogenic properties.

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.