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.

Restoration of high-sensitivity and adapting vision with a cone opsin.

Inherited and age-related retinal degenerative diseases cause progressive loss of rod and cone photoreceptors, leading to blindness, but spare downstream retinal neurons, which can be targeted for optogenetic therapy. However, optogenetic approaches have been limited by either low light sensitivity or slow kinetics, and lack adaptation to changes in ambient light, and not been shown to restore object vision. We find that the vertebrate medium wavelength cone opsin (MW-opsin) overcomes these limitations and supports vision in dim light. MW-opsin enables an otherwise blind retinitis pigmenotosa mouse to discriminate temporal and spatial light patterns displayed on a standard LCD computer tablet, displays adaption to changes in ambient light, and restores open-field novel object exploration under incidental room light. By contrast, rhodopsin, which is similar in sensitivity but slower in light response and has greater rundown, fails these tests. Thus, MW-opsin provides the speed, sensitivity and adaptation needed to restore patterned vision.

A biphasic locomotor response to acute unsignaled high temperature exposure in Drosophila.

Unsignaled stress can have profound effects on animal behavior. While most investigation of stress-effects on behavior follows chronic exposures, less is understood about acute exposures and potential after-effects. We examined walking activity in Drosophila following acute exposure to high temperature or electric shock. Compared to initial walking activity, flies first increase walking with exposure to high temperatures then have a strong reduction in activity. These effects are related to the intensity of the high temperature and number of exposures. The reduction in walking activity following high temperature and electric shock exposures survives context changes and lasts at least five hours. Reduction in the function of the biogenic amines octopamine / tyramine and serotonin both strongly blunt the increase in locomotor activity with high temperature exposure. However, neither set of biogenic amines alter the long lasting depression in walking activity after exposure.

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.