Kinetic modeling of Nav1.7 provides insight into erythromelalgia-associated F1449V mutation

A Novel Antigen Design Strategy to Isolate Single-Domain Antibodies that Target Human Nav1.7 and Reduce Pain in Animal Models

Genetic studies have identified the voltage-gated sodium channel 1.7 (Nav1.7) as pain target. Due to the ineffectiveness of small molecules and monoclonal antibodies as therapeutics for pain, single-domain antibodies (VHHs) are developed against the human Nav1.7 (hNav1.7) using a novel antigen presentation strategy. A 70 amino-acid peptide from the hNav1.7 protein is identified as a target antigen. A recombinant version of this peptide is grafted into the complementarity determining region 3 (CDR3) loop of an inert VHH in order to maintain the native 3D conformation of the peptide. This antigen is used to isolate one VHH able to i) bind hNav1.7, ii) slow the deactivation of hNav1.7, iii) reduce the ability of eliciting action potentials in nociceptors, and iv) reverse hyperalgesia in in vivo rat and mouse models. This VHH exhibits the potential to be developed as a therapeutic capable of suppressing pain. This novel antigen presentation strategy can be applied to develop biologics against other difficult targets such as ion channels, transporters and GPCRs.

The Hodgkin-Huxley-Katz Prize Lecture: A Markov model with permeation-dependent gating that accounts for resurgent current of voltage-gated Na channels

Many neurons that fire high-frequency action potentials express specialized voltage-gated Na channel complexes that not only conduct transient current upon depolarization, but also pass resurgent current upon repolarization. The resurgent current is associated with recovery of transient current, even at moderately negative potentials where fast inactivation is usually absorbing. The combined results of many experimental studies have led to the hypothesis that resurgent current flows upon repolarization when an endogenous blocking protein that occludes open channels at depolarized potentials is expelled by inwardly permeating Na ions. Additional observations have suggested that the position of the voltage sensor of domain IV regulates the affinity of the channel for the putative blocker. To test the effectiveness of a kinetic scheme incorporating these features, here we develop and justify a Markov model with states grounded in known Na channel conformations. Simulations were designed to investigate whether including a permeation-dependent unblocking rate constant and two open-blocked states, superimposed on conformations and voltage-sensitive movements present in all voltage-gated Na channels, is sufficient to account for the unusual gating of channels with a resurgent component. Optimizing rate constant parameters against a wide range of experimental data from cerebellar Purkinje cells demonstrates that a kinetic scheme for Na channels incorporating the novel aspects of a permeation-dependent unblock, as well as distinct high- and low-affinity blocked states, reproduces all the attributes of experimentally recorded Na currents in a physiologically plausible manner.

Kinetic and thermodynamic modeling of a voltage-gated sodium channel

Like all biological and chemical reactions, ion channel kinetics are highly sensitive to changes in temperature. Therefore, it is prudent to investigate channel dynamics at physiological temperatures. However, most ion channel investigations are performed at room temperature due to practical considerations, such as recording stability and technical limitations. This problem is especially severe for the fast voltage-gated sodium channel, whose activation kinetics are faster than the time constant of the standard patch-clamp amplifier at physiological temperatures. Thus, biologically detailed simulations of the action potential generation evenly scale the kinetic models of voltage-gated channels acquired at room temperature. To quantitatively study voltage-gated sodium channels' temperature sensitivity, we recorded sodium currents from nucleated patches extracted from the rat's layer five neocortical pyramidal neurons at several temperatures from 13.5 to 30 °C. We use these recordings to model the kinetics of the voltage-gated sodium channel as a function of temperature. We show that the temperature dependence of activation differs from that of inactivation. Furthermore, the data indicate that the sustained current has a different temperature dependence than the fast current. Our kinetic and thermodynamic analysis of the current provided a numerical model spanning the entire temperature range. This model reproduced vital features of channel activation and inactivation. Furthermore, the model also reproduced action potential dependence on temperature. Thus, we provide an essential building block for the generation of biologically detailed models of cortical neurons.

The Macro- and Micro-Mechanics of the Colon and Rectum II: Theoretical and Computational Methods

Abnormal colorectal biomechanics and mechanotransduction associate with an array of gastrointestinal diseases, including inflammatory bowel disease, irritable bowel syndrome, diverticula disease, anorectal disorders, ileus, and chronic constipation. Visceral pain, principally evoked from mechanical distension, has a unique biomechanical component that plays a critical role in mechanotransduction, the process of encoding mechanical stimuli to the colorectum by sensory afferents. To fully understand the underlying mechanisms of visceral mechanical neural encoding demands focused attention on the macro- and micro-mechanics of colon tissue. Motivated by biomechanical experiments on the colon and rectum, increasing efforts focus on developing constitutive frameworks to interpret and predict the anisotropic and nonlinear biomechanical behaviors of the multilayered colorectum. We will review the current literature on computational modeling of the colon and rectum as well as the mechanical neural encoding by stretch sensitive afferent endings, and then highlight our recent advances in these areas. Current models provide insight into organ- and tissue-level biomechanics as well as the stretch-sensitive afferent endings of colorectal tissues yet an important challenge in modeling theory remains. The research community has not connected the biomechanical models to those of mechanosensitive nerve endings to create a cohesive multiscale framework for predicting mechanotransduction from organ-level biomechanics.

Computational analysis of a 9D model for a small DRG neuron

Small dorsal root ganglion (DRG) neurons are primary nociceptors which are responsible for sensing pain. Elucidation of their dynamics is essential for understanding and controlling pain. To this end, we present a numerical bifurcation analysis of a small DRG neuron model in this paper. The model is of Hodgkin-Huxley type and has 9 state variables. It consists of a Na_v1.7 and a Na_v1.8 sodium channel, a leak channel, a delayed rectifier potassium, and an A-type transient potassium channel. The dynamics of this model strongly depend on the maximal conductances of the voltage-gated ion channels and the external current, which can be adjusted experimentally. We show that the neuron dynamics are most sensitive to the Na_v1.8 channel maximal conductance ([Formula: see text]). Numerical bifurcation analysis shows that depending on [Formula: see text] and the external current, different parameter regions can be identified with stable steady states, periodic firing of action potentials, mixed-mode oscillations (MMOs), and bistability between stable steady states and stable periodic firing of action potentials. We illustrate and discuss the transitions between these different regimes. We further analyze the behavior of MMOs. As the external current is decreased, we find that MMOs appear after a cyclic limit point. Within this region, bifurcation analysis shows a sequence of isolated periodic solution branches with one large action potential and a number of small amplitude peaks per period. For decreasing external current, the number of small amplitude peaks is increasing and the distance between the large amplitude action potentials is growing, finally tending to infinity and thereby leading to a stable steady state. A closer inspection reveals more complex concatenated MMOs in between these periodic MMO branches, forming Farey sequences. Lastly, we also find small solution windows with aperiodic oscillations which seem to be chaotic. The dynamical patterns found here-as consequences of bifurcation points regulated by different parameters-have potential translational significance as repetitive firing of action potentials imply pain of some form and intensity; manipulating these patterns by regulating the different parameters could aid in investigating pain dynamics.

Estimating neuronal conductance model parameters using dynamic action potential clamp

BACKGROUND

Parameterization of neuronal membrane conductance models relies on data acquired from current clamp (CC) or voltage clamp (VC) recordings. Although the CC approach provides key information on a neuron's firing properties, it is often difficult to disentangle the influence of multiple conductances that contribute to the excitation properties of a real neuron. Isolation of a single conductance using pharmacological agents or heterologous expression simplifies analysis but requires extensive VC evaluation to explore the complete state behavior of the channel of interest.

NEW METHOD

We present an improved parameterization approach that uses data derived from dynamic action potential clamp (DAPC) recordings to extract conductance equation parameters. We demonstrate the utility of the approach by applying it to the standard Hodgkin-Huxley conductance model although other conductance models could be easily incorporated as well.

RESULTS

Using a fully simulated setup we show that, with as few as five action potentials previously recorded in DAPC mode, sodium conductance equation parameters can be determined with average parameter errors of less than 4% while action potential firing accuracy approaches 100%. In real DAPC experiments, we show that by "training" our model with five or fewer action potentials, subsequent firing lasting for several seconds could be predicted with ˜96% mean firing rate accuracy and 94% temporal overlap accuracy.

COMPARISON WITH EXISTING METHODS

Our DAPC-based approach surpasses the accuracy of VC-based approaches for extracting conductance equation parameters with a significantly reduced temporal overhead.

CONCLUSION

DAPC-based approach will facilitate the rapid and systematic characterization of neuronal channelopathies.

Depolarization of the conductance-voltage relationship in the NaV1.5 mutant, E1784K, is due to altered fast inactivation

E1784K is the most common mixed long QT syndrome/Brugada syndrome mutant in the cardiac voltage-gated sodium channel NaV1.5. E1784K shifts the midpoint of the channel conductance-voltage relationship to more depolarized membrane potentials and accelerates the rate of channel fast inactivation. The depolarizing shift in the midpoint of the conductance curve in E1784K is exacerbated by low extracellular pH. We tested whether the E1784K mutant shifts the channel conductance curve to more depolarized membrane potentials by affecting the channel voltage-sensors. We measured ionic currents and gating currents at pH 7.4 and pH 6.0 in Xenopus laevis oocytes. Contrary to our expectation, the movement of gating charges is shifted to more hyperpolarized membrane potentials by E1784K. Voltage-clamp fluorimetry experiments show that this gating charge shift is due to the movement of the DIVS4 voltage-sensor being shifted to more hyperpolarized membrane potentials. Using a model and experiments on fast inactivation-deficient channels, we show that changes to the rate and voltage-dependence of fast inactivation are sufficient to shift the conductance curve in E1784K. Our results localize the effects of E1784K to DIVS4, and provide novel insight into the role of the DIV-VSD in regulating the voltage-dependencies of activation and fast inactivation.

Is realistic neuronal modeling realistic?

Scientific models are abstractions that aim to explain natural phenomena. A successful model shows how a complex phenomenon arises from relatively simple principles while preserving major physical or biological rules and predicting novel experiments. A model should not be a facsimile of reality; it is an aid for understanding it. Contrary to this basic premise, with the 21st century has come a surge in computational efforts to model biological processes in great detail. Here we discuss the oxymoronic, realistic modeling of single neurons. This rapidly advancing field is driven by the discovery that some neurons don't merely sum their inputs and fire if the sum exceeds some threshold. Thus researchers have asked what are the computational abilities of single neurons and attempted to give answers using realistic models. We briefly review the state of the art of compartmental modeling highlighting recent progress and intrinsic flaws. We then attempt to address two fundamental questions. Practically, can we realistically model single neurons? Philosophically, should we realistically model single neurons? We use layer 5 neocortical pyramidal neurons as a test case to examine these issues. We subject three publically available models of layer 5 pyramidal neurons to three simple computational challenges. Based on their performance and a partial survey of published models, we conclude that current compartmental models are ad hoc, unrealistic models functioning poorly once they are stretched beyond the specific problems for which they were designed. We then attempt to plot possible paths for generating realistic single neuron models.

Aromatase inhibitors augment nociceptive behaviors in rats and enhance the excitability of sensory neurons

Although aromatase inhibitors (AIs) are commonly used therapies for breast cancer, their use is limited because they produce arthralgia in a large number of patients. To determine whether AIs produce hypersensitivity in animal models of pain, we examined the effects of the AI, letrozole, on mechanical, thermal, and chemical sensitivity in rats. In ovariectomized (OVX) rats, administering a single dose of 1 or 5mg/kg letrozole significantly reduced mechanical paw withdrawal thresholds, without altering thermal sensitivity. Repeated injection of 5mg/kg letrozole in male rats produced mechanical, but not thermal, hypersensitivity that extinguished when drug dosing was stopped. A single dose of 5mg/kg letrozole or daily dosing of letrozole or exemestane in male rats also augmented flinching behavior induced by intraplantar injection of 1000nmol of adenosine 5'-triphosphate (ATP). To determine whether sensitization of sensory neurons contributed to AI-induced hypersensitivity, we evaluated the excitability of neurons isolated from dorsal root ganglia of male rats chronically treated with letrozole. Both small and medium-diameter sensory neurons isolated from letrozole-treated rats were more excitable, as reflected by increased action potential firing in response to a ramp of depolarizing current, a lower resting membrane potential, and a lower rheobase. However, systemic letrozole treatment did not augment the stimulus-evoked release of the neuropeptide calcitonin gene-related peptide (CGRP) from spinal cord slices, suggesting that the enhanced nociceptive responses were not secondary to an increase in peptide release from sensory endings in the spinal cord. These results provide the first evidence that AIs modulate the excitability of sensory neurons, which may be a primary mechanism for the effect of these drugs to augment pain behaviors in rats.

Modulation of human Nav1.7 channel gating by synthetic α-scorpion toxin OD1 and its analogs

Nine different voltage-gated sodium channel isoforms are responsible for inducing and propagating action potentials in the mammalian nervous system. The Nav1.7 channel isoform plays an important role in conducting nociceptive signals. Specific mutations of this isoform may impair gating behavior of the channel resulting in several pain syndromes. In addition to channel mutations, similar or opposite changes in gating may be produced by spider and scorpion toxins binding to different parts of the voltage-gated sodium channel. In the present study, we analyzed the effects of the α-scorpion toxin OD1 and 2 synthetic toxin analogs on the gating properties of the Nav1.7 sodium channel. All toxins potently inhibited channel inactivation, however, both toxin analogs showed substantially increased potency by more than one order of magnitude when compared with that of wild-type OD1. The decay phase of the whole-cell Na(+) current was substantially slower in the presence of toxins than in their absence. Single-channel recordings in the presence of the toxins revealed that Na(+) current inactivation slowed due to prolonged flickering of the channel between open and closed states. Our findings support the voltage-sensor trapping model of α-scorpion toxin action, in which the toxin prevents a conformational change in the domain IV voltage sensor that normally leads to fast channel inactivation.

Bridging scales through multiscale modeling: a case study on protein kinase A

The goal of multiscale modeling in biology is to use structurally based physico-chemical models to integrate across temporal and spatial scales of biology and thereby improve mechanistic understanding of, for example, how a single mutation can alter organism-scale phenotypes. This approach may also inform therapeutic strategies or identify candidate drug targets that might otherwise have been overlooked. However, in many cases, it remains unclear how best to synthesize information obtained from various scales and analysis approaches, such as atomistic molecular models, Markov state models (MSM), subcellular network models, and whole cell models. In this paper, we use protein kinase A (PKA) activation as a case study to explore how computational methods that model different physical scales can complement each other and integrate into an improved multiscale representation of the biological mechanisms. Using measured crystal structures, we show how molecular dynamics (MD) simulations coupled with atomic-scale MSMs can provide conformations for Brownian dynamics (BD) simulations to feed transitional states and kinetic parameters into protein-scale MSMs. We discuss how milestoning can give reaction probabilities and forward-rate constants of cAMP association events by seamlessly integrating MD and BD simulation scales. These rate constants coupled with MSMs provide a robust representation of the free energy landscape, enabling access to kinetic, and thermodynamic parameters unavailable from current experimental data. These approaches have helped to illuminate the cooperative nature of PKA activation in response to distinct cAMP binding events. Collectively, this approach exemplifies a general strategy for multiscale model development that is applicable to a wide range of biological problems.

Experimental and computational evidence for an essential role of NaV1.6 in spike initiation at stretch-sensitive colorectal afferent endings

Stretch-sensitive afferents comprise ∼33% of the pelvic nerve innervation of mouse colorectum, which are activated by colorectal distension and encode visceral nociception. Stretch-sensitive colorectal afferent endings respond tonically to stepped or ramped colorectal stretch, whereas dissociated colorectal dorsal root ganglion neurons generally fail to spike repetitively upon stepped current stimulation. The present study investigated this difference in the neural encoding characteristics between the soma and afferent ending using pharmacological approaches in an in vitro mouse colon-nerve preparation and complementary computational simulations. Immunohistological staining and Western blots revealed the presence of voltage-gated sodium channel (NaV) 1.6 and NaV1.7 at sensory neuronal endings in mouse colorectal tissue. Responses of stretch-sensitive colorectal afferent endings were significantly reduced by targeting NaV1.6 using selective antagonists (μ-conotoxin GIIIa and μ-conotoxin PIIIa) or tetrodotoxin. In contrast, neither selective NaV1.8 (A803467) nor NaV1.7 (ProTX-II) antagonists attenuated afferent responses to stretch. Computational simulation of a colorectal afferent ending that incorporated independent Markov models for NaV1.6 and NaV1.7, respectively, recapitulated the experimental findings, suggesting a necessary role for NaV1.6 in encoding tonic spiking by stretch-sensitive afferents. In addition, computational simulation of a dorsal root ganglion soma showed that, by adding a NaV1.6 conductance, a single-spiking neuron was converted into a tonic spiking one. These results suggest a mechanism/channel to explain the difference in neural encoding characteristics between afferent somata and sensory endings, likely caused by differential expression of ion channels (e.g., NaV1.6) at different parts of the neuron.

Dynamic-clamp analysis of wild-type human Nav1.7 and erythromelalgia mutant channel L858H

The link between sodium channel Nav1.7 and pain has been strengthened by identification of gain-of-function mutations in patients with inherited erythromelalgia (IEM), a genetic model of neuropathic pain in humans. A firm mechanistic link to nociceptor dysfunction has been precluded because assessments of the effect of the mutations on nociceptor function have thus far depended on electrophysiological recordings from dorsal root ganglia (DRG) neurons transfected with wild-type (WT) or mutant Nav1.7 channels, which do not permit accurate calibration of the level of Nav1.7 channel expression. Here, we report an analysis of the function of WT Nav1.7 and IEM L858H mutation within small DRG neurons using dynamic-clamp. We describe the functional relationship between current threshold for action potential generation and the level of WT Nav1.7 conductance in primary nociceptive neurons and demonstrate the basis for hyperexcitability at physiologically relevant levels of L858H channel conductance. We demonstrate that the L858H mutation, when modeled using dynamic-clamp at physiological levels within DRG neurons, produces a dramatically enhanced persistent current, resulting in 27-fold amplification of net sodium influx during subthreshold depolarizations and even greater amplification during interspike intervals, which provide a mechanistic basis for reduced current threshold and enhanced action potential firing probability. These results show, for the first time, a linear correlation between the level of Nav1.7 conductance and current threshold in DRG neurons. Our observations demonstrate changes in sodium influx that provide a mechanistic link between the altered biophysical properties of a mutant Nav1.7 channel and nociceptor hyperexcitability underlying the pain phenotype in IEM.

Optimizing ion channel models using a parallel genetic algorithm on graphical processors

We have recently shown that we can semi-automatically constrain models of voltage-gated ion channels by combining a stochastic search algorithm with ionic currents measured using multiple voltage-clamp protocols. Although numerically successful, this approach is highly demanding computationally, with optimization on a high performance Linux cluster typically lasting several days. To solve this computational bottleneck we converted our optimization algorithm for work on a graphical processing unit (GPU) using NVIDIA's CUDA. Parallelizing the process on a Fermi graphic computing engine from NVIDIA increased the speed ∼180 times over an application running on an 80 node Linux cluster, considerably reducing simulation times. This application allows users to optimize models for ion channel kinetics on a single, inexpensive, desktop "super computer," greatly reducing the time and cost of building models relevant to neuronal physiology. We also demonstrate that the point of algorithm parallelization is crucial to its performance. We substantially reduced computing time by solving the ODEs (Ordinary Differential Equations) so as to massively reduce memory transfers to and from the GPU. This approach may be applied to speed up other data intensive applications requiring iterative solutions of ODEs.