Excitability Constraints on Voltage-Gated Sodium Channels

We study how functional constraints bound and shape evolution through an analysis of mammalian voltage-gated sodium channels. The primary function of sodium channels is to allow the propagation of action potentials. Since Hodgkin and Huxley, mathematical models have suggested that sodium channel properties need to be tightly constrained for an action potential to propagate. There are nine mammalian genes encoding voltage-gated sodium channels, many of which are more than ≈90% identical by sequence. This sequence similarity presumably corresponds to similarity of function, consistent with the idea that these properties must be tightly constrained. However, the multiplicity of genes encoding sodium channels raises the question: why are there so many? We demonstrate that the simplest theoretical constraints bounding sodium channel diversity—the requirements of membrane excitability and the uniqueness of the resting potential—act directly on constraining sodium channel properties. We compare the predicted constraints with functional data on mammalian sodium channel properties collected from the literature, including 172 different sets of measurements from 40 publications, wild-type and mutant, under a variety of conditions. The data from all channel types, including mutants, obeys the excitability constraint; on the other hand, channels expressed in muscle tend to obey the constraint of a unique resting potential, while channels expressed in neuronal tissue do not. The excitability properties alone distinguish the nine sodium channels into four different groups that are consistent with phylogenetic analysis. Our calculations suggest interpretations for the functional differences between these groups

Pumilio binds para mRNA and requires nanos and brat to regulate sodium current in drosophila motoneurons

Homeostatic regulation of ionic currents is of paramount importance during periods of synaptic growth or remodeling. Our previous work has identified the translational repressor Pumilio (Pum) as a regulator of sodium current (INa) and excitability in Drosophila motoneurons. In this current study, we show that Pum is able to bind directly the mRNA encoding the Drosophila voltage-gated sodium channel paralytic (para). We identify a putative binding site for Pum in the 3' end of the para open reading frame (ORF). Characterization of the mechanism of action of Pum, using whole-cell patch clamp and real-time reverse transcription-PCR, reveals that the full-length protein is required for translational repression of para mRNA. Additionally, the cofactor Nanos is essential for Pum-dependent para repression, whereas the requirement for Brain Tumor (Brat) is cell type specific. Thus, Pum-dependent regulation of INa in motoneurons requires both Nanos and Brat, whereas regulation in other neuronal types seemingly requires only Nanos but not Brat. We also show that Pum is able to reduce the level of nanos mRNA and as such identify a potential negative-feedback mechanism to protect neurons from overactivity of Pum. Finally, we show coupling between INa (para) and IK (Shal) such that Pum-mediated change in para results in a compensatory change in Shal. The identification of para as a direct target of Pum represents the first ion channel to be translationally regulated by this repressor and the location of the binding motif is the first example in an ORF rather than in the canonical 3'-untranslated region of target transcripts

Bistable dynamics underlying excitability of ion homeostasis in neuron models

When neurons fire action potentials, dissipation of free energy is usually not directly considered, because the change in free energy is often negligible compared to the immense reservoir stored in neural transmembrane ion gradients and the long-term energy requirements are met through chemical energy, i.e., metabolism. However, these gradients can temporarily nearly vanish in neurological diseases, such as migraine and stroke, and in traumatic brain injury from concussions to severe injuries. We study biophysical neuron models based on the Hodgkin-Huxley (HH) formalism extended to include time-dependent ion concentrations inside and outside the cell and metabolic energy-driven pumps. We reveal the basic mechanism of a state of free energy-starvation (FES) with bifurcation analyses showing that ion dynamics is for a large range of pump rates bistable without contact to an ion bath. This is interpreted as a threshold reduction of a new fundamental mechanism of 'ionic excitability' that causes a long-lasting but transient FES as observed in pathological states. We can in particular conclude that a coupling of extracellular ion concentrations to a large glial-vascular bath can take a role as an inhibitory mechanism crucial in ion homeostasis, while the Na$^+$/K$^+$ pumps alone are insufficient to recover from FES. Our results provide the missing link between the HH formalism and activator-inhibitor models that have been successfully used for modeling migraine phenotypes, and therefore will allow us to validate the hypothesis that migraine symptoms are explained by disturbed function in ion channel subunits, Na$^+$/K$^+$ pumps, and other proteins that regulate ion homeostasis.Comment: 14 pages, 8 figures, 4 table

Action potential energy efficiency varies among neuron types in vertebrates and invertebrates.

The initiation and propagation of action potentials (APs) places high demands on the energetic resources of neural tissue. Each AP forces ATP-driven ion pumps to work harder to restore the ionic concentration gradients, thus consuming more energy. Here, we ask whether the ionic currents underlying the AP can be predicted theoretically from the principle of minimum energy consumption. A long-held supposition that APs are energetically wasteful, based on theoretical analysis of the squid giant axon AP, has recently been overturned by studies that measured the currents contributing to the AP in several mammalian neurons. In the single compartment models studied here, AP energy consumption varies greatly among vertebrate and invertebrate neurons, with several mammalian neuron models using close to the capacitive minimum of energy needed. Strikingly, energy consumption can increase by more than ten-fold simply by changing the overlap of the Na+ and K+ currents during the AP without changing the APs shape. As a consequence, the height and width of the AP are poor predictors of energy consumption. In the Hodgkin–Huxley model of the squid axon, optimizing the kinetics or number of Na+ and K+ channels can whittle down the number of ATP molecules needed for each AP by a factor of four. In contrast to the squid AP, the temporal profile of the currents underlying APs of some mammalian neurons are nearly perfectly matched to the optimized properties of ionic conductances so as to minimize the ATP cost

Dual separable feedback systems govern firing rate homeostasis.

Firing rate homeostasis (FRH) stabilizes neural activity. A pervasive and intuitive theory argues that a single variable, calcium, is detected and stabilized through regulatory feedback. A prediction is that ion channel gene mutations with equivalent effects on neuronal excitability should invoke the same homeostatic response. In agreement, we demonstrate robust FRH following either elimination of Kv4/Shal protein or elimination of the Kv4/Shal conductance. However, the underlying homeostatic signaling mechanisms are distinct. Eliminating Shal protein invokes Krüppel-dependent rebalancing of ion channel gene expression including enhanced slo, Shab, and Shaker. By contrast, expression of these genes remains unchanged in animals harboring a CRISPR-engineered, Shal pore-blocking mutation where compensation is achieved by enhanced IKDR. These different homeostatic processes have distinct effects on homeostatic synaptic plasticity and animal behavior. We propose that FRH includes mechanisms of proteostatic feedback that act in parallel with activity-driven feedback, with implications for the pathophysiology of human channelopathies

Recent advances in our understanding of the structure and function of more unusual cation channels.

As their name implies, cation channels allow the regulated flow of cations such as sodium, potassium, calcium, and magnesium across cellular and intracellular membranes. Cation channels have long been known for their fundamental roles in controlling membrane potential and excitability in neurons and muscle. In this review, we provide an update on the recent advances in our understanding of the structure-function relationship and the physiological and pathophysiological role of cation channels. The most exciting developments in the last two years, in our opinion, have been the insights that cryoelectron microscopy has provided into the inner life and the gating of not only voltage-gated channels but also mechanosensitive and calcium- or sodium-activated channels. The mechanosensitive Piezo channels especially have delighted the field not only with a fascinating new type of structure but with important roles in blood pressure regulation and lung function

Episodic neurologic disorders: syndromes, genes, and mechanisms.

Many neurologic diseases cause discrete episodic impairment in contrast with progressive deterioration. The symptoms of these episodic disorders exhibit striking variety. Herein we review what is known of the phenotypes, genetics, and pathophysiology of episodic neurologic disorders. Of these, most are genetically complex, with unknown or polygenic inheritance. In contrast, a fascinating panoply of episodic disorders exhibit Mendelian inheritance. We classify episodic Mendelian disorders according to the primary neuroanatomical location affected: skeletal muscle, cardiac muscle, neuromuscular junction, peripheral nerve, or central nervous system (CNS). Most known Mendelian mutations alter genes that encode membrane-bound ion channels. These mutations cause ion channel dysfunction, which ultimately leads to altered membrane excitability as manifested by episodic disease. Other Mendelian disease genes encode proteins essential for ion channel trafficking or stability. These observations have cemented the channelopathy paradigm, in which episodic disorders are conceptualized as disorders of ion channels. However, we expand on this paradigm to propose that dysfunction at the synaptic and neuronal circuit levels may underlie some episodic neurologic entities

A biophysical model explains the spontaneous bursting behavior in the developing retina

During early development, waves of activity propagate across the retina and play a key role in the proper wiring of the early visual system. During the stage II these waves are triggered by a transient network of neurons, called Starburst Amacrine Cells (SACs), showing a bursting activity which disappears upon further maturation. While several models have attempted to reproduce retinal waves, none of them is able to mimic the rhythmic autonomous bursting of individual SACs and reveal how these cells change their intrinsic properties during development. Here, we introduce a mathematical model, grounded on biophysics, which enables us to reproduce the bursting activity of SACs and to propose a plausible, generic and robust, mechanism that generates it. The core parameters controlling repetitive firing are fast depolarizing $V$-gated calcium channels and hyperpolarizing $V$-gated potassium channels. The quiescent phase of bursting is controlled by a slow after hyperpolarization (sAHP), mediated by calcium-dependent potassium channels. Based on a bifurcation analysis we show how biophysical parameters, regulating calcium and potassium activity, control the spontaneously occurring fast oscillatory activity followed by long refractory periods in individual SACs. We make a testable experimental prediction on the role of voltage-dependent potassium channels on the excitability properties of SACs and on the evolution of this excitability along development. We also propose an explanation on how SACs can exhibit a large variability in their bursting periods, as observed experimentally within a SACs network as well as across different species, yet based on a simple, unique, mechanism. As we discuss, these observations at the cellular level have a deep impact on the retinal waves description.Comment: 25 pages, 13 figures, submitte