Béla Joós

In a variety of neurons, action potentials (APs) initiate at the proximal axon, within a region called the axon initial segment (AIS), which has a high density of voltage-gated sodium channels (Na_Vs) on its membrane. In pyramidal neurons, the proximal AIS has been reported to exhibit a higher proportion of Na_Vs with gating properties that are “right-shifted” to more depolarized voltages, compared to the distal AIS. Further, recent experiments have revealed that as neurons develop, the spatial distribution of Na_V subtypes along the AIS can change substantially, suggesting that neurons tune their excitability by modifying said distribution. When neurons are stimulated axonally, computational modelling has shown that this spatial separation of gating properties in the AIS enhances the backpropagation of APs into the dendrites. In contrast, in the more natural scenario of somatic stimulation, our simulations show that the same distribution can impede backpropagation, suggesting that the choice of orthodromic versus antidromic stimulation can bias or even invert experimental findings regarding the role of Na_V subtypes in the AIS. We implemented a range of hypothetical Na_V distributions in the AIS of three multicompartmental pyramidal cell models and investigated the precise kinetic mechanisms underlying such effects, as the spatial distribution of Na_V subtypes is varied. With axonal stimulation, proximal Na_V availability dominates, such that concentrating right-shifted Na_Vs in the proximal AIS promotes backpropagation. However, with somatic stimulation, the models are insensitive to availability kinetics. Instead, the higher activation threshold of right-shifted Na_Vs in the AIS impedes backpropagation. Therefore, recently observed developmental changes to the spatial separation and relative proportions of Na_V1.2 and Na_V1.6 in the AIS differentially impact activation and availability. The observed effects on backpropagation, and potentially learning via its putative role in synaptic plasticity (e.g. through spike-timing-dependent plasticity), are opposite for orthodromic versus antidromic stimulation, which should inform hypotheses about the impact of the developmentally regulated subcellular localization of these Na_V subtypes.

In a variety of neurons, action potentials (APs) initiate at the proximal axon, within a region called the axon initial segment (AIS), which has a high density of voltage-gated sodium channels (Na _V s) on its membrane. In pyramidal neurons, the proximal AIS has been reported to exhibit a higher proportion of Na _V s with gating properties that are “ right-shift ed” to more depolarized voltages, compared to the distal AIS. Further, recent experiments have revealed that as neurons develop, the spatial distribution of Na _V subtypes along the AIS can change substantially, suggesting that neurons tune their excitability by modifying said distribution. When neurons are stimulated axonally, computational modelling has shown that this spatial separation of gating properties in the AIS enhances the backpropagation of APs into the dendrites. In contrast, in the more natural scenario of somatic stimulation, our simulations show that the same distribution can impede backpropagation. We implemented a range of hypothetical Na _V distributions in the AIS of three multicompartmental pyramidal cell models and investigated the precise kinetic mechanisms underlying such effects, as the spatial distribution of Na _V subtypes is varied. With axonal stimulation, proximal Na _V availability dominates, such that concentrating right-shift ed Na _V s in the proximal AIS promotes backpropagation. However, with somatic stimulation, the models are insensitive to availability . Instead, the higher activation threshold of right-shift ed Na _V s in the AIS impedes backpropagation. Therefore, recently observed developmental changes to the spatial separation and relative proportions of Na _V 1.2 and Na _V 1.6 in the AIS differentially impact activation and availability . The effects on backpropagation, and potentially learning, are opposite for orthodromic versus antidromic stimulation. Author Summary: Neurons use sodium ion currents, controlled by a neuron’s voltage, to trigger signals called action potentials (APs). These APs typically result from synaptic input from other neurons onto the dendrites and soma. An AP is generated at the axon initial segment (AIS) just beyond the soma. From there, it travels down the axon to other cells, but can also propagate “backwards” towards the soma and dendrites. This “backpropagation” allows a comparison at synapses of the timing of outgoing and incoming signals, a feedback process that modifies synaptic connection strengths linked to learning. It is puzzling that in many neurons, sodium ion channels come in two types: high-voltage threshold channels clustered near the soma where the AIS begins, and low-voltage ones further away towards the axon. This separation changes in the early development of the animal, which raises the question of its role in backpropagation. We constructed a detailed mathematical model to explore how separation affects backpropagation. Separation either impedes or enhances learning, depending on whether the AP results from synaptic inputs or, less typically, currents moving backwards from the axon. This is explained by the different effects the separation has on two key kinetic processes that govern sodium currents.

Duchenne muscular dystrophy (DMD) is an X-linked dystrophin-minus muscle-wasting disease. Ion homeostasis in skeletal muscle fibers underperforms as DMD progresses. But though DMD renders these excitable cells intolerant of exertion, sodium overloaded, depolarized, and spontaneously contractile, they can survive for several decades. We show computationally that underpinning this longevity is a strikingly frugal, robust Pump-Leak/Donnan (P-L/D) ion homeostatic process. Unlike neurons, which operate with a costly “Pump-Leak–dominated” ion homeostatic steady state, skeletal muscle fibers operate with a low-cost “Donnan-dominated” ion homeostatic steady state that combines a large chloride permeability with an exceptionally small sodium permeability. Simultaneously, this combination keeps fiber excitability low and minimizes pump expenditures. As mechanically active, long-lived multinucleate cells, skeletal muscle fibers have evolved to handle overexertion, sarcolemmal tears, ischemic bouts, etc.; the frugality of their Donnan dominated steady state lets them maintain the outsized pump reserves that make them resilient during these inevitable transient emergencies. Here, P-L/D model variants challenged with DMD-type insult/injury (low pump-strength, overstimulation, leaky Nav and cation channels) show how chronic “nonosmotic” sodium overload (observed in DMD patients) develops. Profoundly severe DMD ion homeostatic insult/injury causes spontaneous firing (and, consequently, unwanted excitation–contraction coupling) that elicits cytotoxic swelling. Therefore, boosting operational pump-strength and/or diminishing sodium and cation channel leaks should help extend DMD fiber longevity.

The inherited muscle-wasting disease, Duchenne muscular dystrophy (DMD), renders skeletal muscle fibers (SMFs) Na ⁺ -overloaded, ischemic, membrane-damaged, cation-leaky, depolarized, and prone to myogenic firing. DMD fibers nevertheless survive up to 3 decades before succumbing to Ca ²⁺ -necrosis. The Ca ²⁺ -necrosis is explicable, the longevity is not. Modeling here shows that SMFs’ ion homeostasis strategy, a low-cost resilient Pump-Leak/Donnan feedback process we term “Donnan dominated”, underpins that longevity. Together, SMFs’ huge chloride-permeability and tiny sodium-permeability minimize excitability and pump costs, facilitating the outsized SMF pump-reserve that lets DMD fibers withstand deep ischemia and leaky channels. We illustrate how, as these impairments intensify, patients’ chronic Na ⁺ -overload (now non-invasively evident via Na ²³ -MRI) would change. In simulations, prolonged excitation (→physiological Na ⁺ -overloading) and/or intense ischemia (→too little Na ⁺ -pumping) and accumulated bleb-damage (→too much Na ⁺ -leaking) eventually trigger Ca ²⁺ -overloading conditions. Our analysis implies an urgent need to identify SMFs’ pivotal small P _Na , thereby opening new therapeutic remediation routes.

Skeletal muscle fibers (SMFs) and neurons are low and high duty-cycle excitable cells constituting exceptionally large and extraordinarily small fractions of vertebrate bodies. The immense ClC-1-based chloride-permeability (P _Cl ) of SMFs has thwarted understanding of their Pump-Leak/Donnan (P-L/D) ion homeostasis. After formally defining P-L/D set-points and feedbacks, we therefore devise a simple yet demonstrably realistic model for SMFs. Hyper-stimulated, it approximates rodent fibers’ ouabain-sensitive ATP-consumption. Size-matched neuron-model/SMF-model comparisons reveal steady-states occupying two ends of an energetics/resilience P-L/D continuum. Excitable neurons’ costly vulnerable process is Pump-Leak dominated. Electrically-reluctant SMFs’ robust low-cost process is Donnan dominated: collaboratively, Donnan effectors and [big P _Cl ] stabilize V _rest , while SMFs’ exquisitely small P _Na minimizes ATP-consumption, thus maximizing resilience. “Classic” excitable cell homeostasis ([small P _Cl ][big I _Naleak ]), de rigueur for electrically-agile neurons, is untenable for vertebrates’ (including humans’) major tissue. Vertebrate bodies evolved thanks to syncytially-efficient SMFs using a Donnan dominated ([big P _Cl ][small I _Naleak ]) ion homeostatic strategy.

Mild traumatic injury can modify the key sodium (Na⁺) current underlying the excitability of neurons. It causes the activation and inactivation properties of this current to become shifted to more negative trans-membrane voltages. This so-called coupled left shift (CLS) leads to a chronic influx of Na⁺ into the cell that eventually causes spontaneous or “ectopic” firing along the axon, even in the absence of stimuli. The bifurcations underlying this enhanced excitability have been worked out in full ionic models of this effect. Here, we present computational evidence that increased temperature T can exacerbate this pathological state. Conversely, and perhaps of clinical relevance, mild cooling is shown to move the naturally quiescent cell further away from the threshold of ectopic behavior. The origin of this stabilization-by-cooling effect is analyzed by knocking in and knocking out, one at a time, various processes thought to be T-dependent. The T-dependence of the Na⁺ current, quantified by its Q_10‐Na factor, has the biggest impact on the threshold, followed by Q_10‐pump of the sodium-potassium exchanger. Below the ectopic boundary, the steady state for the gating variables and the resting potential are not modified by temperature, since our model separately tallies the Na⁺ and K⁺ ions including their separate leaks through the pump. When only the gating kinetics are considered, cooling is detrimental, but in the full T-dependent model, it is beneficial because the other processes dominate. Cooling decreases the pump’s activity, and since the pump hyperpolarizes, less hyperpolarization should lead to more excitability and ectopic behavior. But actually the opposite happens in the full model because decreased pump activity leads to smaller gradients of Na⁺ and K⁺, which in turn decreases the driving force of the Na⁺ current.

Regulating membrane potential and synaptic function contributes significantly to the energetic costs of brain signaling, but the relative costs of action potentials (APs) and synaptic transmission during high-frequency firing are unknown. The continuous high-frequency (200-600Hz) electric organ discharge (EOD) of Eigenmannia, a weakly electric fish, underlies its electrosensing and communication. EODs reflect APs fired by the muscle-derived electrocytes of the electric organ (EO). Cholinergic synapses at the excitable posterior membranes of the elongated electrocytes control AP frequency. Based on whole-fish O₂ consumption, ATP demand per EOD-linked AP increases exponentially with AP frequency. Continual EOD-AP generation implies first, that ion homeostatic processes reliably counteract any dissipation of posterior membrane E_Na and E_K and second that high frequency synaptic activation is reliably supported. Both of these processes require energy. To facilitate an exploration of the expected energy demands of each, we modify a previous excitability model and include synaptic currents able to drive APs at frequencies as high as 600 Hz. Synaptic stimuli are modeled as pulsatile cation conductance changes, with or without a small (sustained) background conductance. Over the full species range of EOD frequencies (200–600 Hz) we calculate frequency-dependent “Na⁺-entry budgets” for an electrocyte AP as a surrogate for required 3Na⁺/2K⁺-ATPase activity. We find that the cost per AP of maintaining constant-amplitude APs increases nonlinearly with frequency, whereas the cost per AP for synaptic input current is essentially constant. This predicts that Na⁺ channel density should correlate positively with EOD frequency, whereas AChR density should be the same across fish. Importantly, calculated costs (inferred from Na⁺-entry through Nav and ACh channels) for electrocyte APs as frequencies rise are much less than expected from published whole-fish EOD-linked O₂ consumption. For APs at increasingly high frequencies, we suggest that EOD-related costs external to electrocytes (including packaging of synaptic transmitter) substantially exceed the direct cost of electrocyte ion homeostasis.

We examine the effects of the external force, torque, temperature, confinement, and excluded volume interactions (EVIs) on the stability of the helical configuration of an intrinsically straight semiflexible biopolymer inside a cylindrical cell. We find that to stabilize a helix, the confinement from both ends of the cell is more effective than a uniaxial force. We show that under a uniaxial force and in absence of confinement from bottom of the cell, a stable helix is very short. Our results reveal that to maintain a low pitch helix, a torque acting at both ends of the filament is a necessity, and the confinement can reduce the required torque to less than half making it much easier to form a stable helix. Moreover, we find that thermal fluctuations and EVIs have little impact on the stability of a helix. Our results can help understand the existence of the helix and ring configurations of some semiflexible biopolymers, such as MreB homologs, inside a rod-shaped bacteria.

Two features common to diverse sick excitable cells are “leaky” Nav channels and bleb damage-damaged membranes. The bleb damage, we have argued, causes a channel kinetics based “leakiness.” Recombinant (node of Ranvier type) Nav1.6 channels voltage-clamped in mechanically-blebbed cell-attached patches undergo a damage intensity dependent kinetic change. Specifically, they experience a coupled hyperpolarizing (left) shift of the activation and inactivation processes. The biophysical observations on Nav1.6 currents formed the basis of Nav-Coupled Left Shift (Nav-CLS) theory. Node of Ranvier excitability can be modeled with Nav-CLS imposed at varying LS intensities and with varying fractions of total nodal membrane affected. Mild damage from which sick excitable cells might recover is of most interest pathologically. Accordingly, Na⁺/K⁺ ATPase (pump) activity was included in the modeling. As we described more fully in our other recent reviews, Nav-CLS in nodes with pumps proves sufficient to predict many of the pathological excitability phenomena reported for sick excitable cells. This review explains how the model came about and outlines how we have used it. Briefly, we direct the reader to studies in which Nav-CLS is being implemented in larger scale models of damaged excitable tissue. For those who might find it useful for teaching or research purposes, we coded the Nav-CLS/node of Ranvier model (with pumps) in NEURON. We include, here, the resulting “Regimes” plot of classes of excitability dysfunction.