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1.  Stimulation-induced ectopicity and propagation windows in model damaged axons 
Neural tissue injuries render voltage-gated Na+ channels (Nav) leaky, thereby altering excitability, disrupting propagation and causing neuropathic pain related ectopic activity. In both recombinant systems and native excitable membranes, membrane damage causes the kinetically-coupled activation and inactivation processes of Nav channels to undergo hyperpolarizing shifts. This damage-intensity dependent change, called coupled left-shift (CLS), yields a persistent or “subthreshold” Nav window conductance. Nodes of Ranvier simulations involving various degrees of mild CLS showed that, as the system’s channel/pump fluxes attempt to re-establish ion homeostasis, the CLS elicits hyperexcitability, subthreshold oscillations and neuropathic type action potential (AP) bursts. CLS-induced intermittent propagation failure was studied in simulations of stimulated axons, but pump contributions were ignored, leaving open an important question: does mild-injury (small CLS values, pumps functioning well) render propagation-competent but still quiescent axons vulnerable to further impairments as the system attempts to cope with its normal excitatory inputs? We probe this incipient diffuse axonal injury scenario using a 10-node myelinated axon model. Fully restabilized nodes with mild damage can, we show, become ectopic signal generators (“ectopic nodes”) because incoming APs stress Na+/K+ gradients, thereby altering spike thresholds. Comparable changes could contribute to acquired sodium channelopathies as diverse as epileptic phenomena and to the neuropathic amplification of normally benign sensory inputs. Input spike patterns, we found, propagate with good fidelity through an ectopically firing site only when their frequencies exceed the ectopic frequency. This “propagation window” is a robust phenomenon, occurring despite Gaussian noise, large jitter and the presence of several consecutive ectopic nodes.
Electronic supplementary material
The online version of this article (doi:10.1007/s10827-014-0521-9) contains supplementary material, which is available to authorized users.
doi:10.1007/s10827-014-0521-9
PMCID: PMC4224747  PMID: 25110188
Ectopicity onset; Phase locking; Neuropathic pain; Coupled left-shift (CLS); Nav1.6 acquired channelopathies
3.  Spontaneous Excitation Patterns Computed for Axons with Injury-like Impairments of Sodium Channels and Na/K Pumps 
PLoS Computational Biology  2012;8(9):e1002664.
In injured neurons, “leaky” voltage-gated sodium channels (Nav) underlie dysfunctional excitability that ranges from spontaneous subthreshold oscillations (STO), to ectopic (sometimes paroxysmal) excitation, to depolarizing block. In recombinant systems, mechanical injury to Nav1.6-rich membranes causes cytoplasmic Na+-loading and “Nav-CLS”, i.e., coupled left-(hyperpolarizing)-shift of Nav activation and availability. Metabolic injury of hippocampal neurons (epileptic discharge) results in comparable impairment: left-shifted activation and availability and hence left-shifted INa-window. A recent computation study revealed that CLS-based INa-window left-shift dissipates ion gradients and impairs excitability. Here, via dynamical analyses, we focus on sustained excitability patterns in mildly damaged nodes, in particular with more realistic Gaussian-distributed Nav-CLS to mimic “smeared” injury intensity. Since our interest is axons that might survive injury, pumps (sine qua non for live axons) are included. In some simulations, pump efficacy and system volumes are varied. Impacts of current noise inputs are also characterized. The diverse modes of spontaneous rhythmic activity evident in these scenarios are studied using bifurcation analysis. For “mild CLS injury”, a prominent feature is slow pump/leak-mediated EIon oscillations. These slow oscillations yield dynamic firing thresholds that underlie complex voltage STO and bursting behaviors. Thus, Nav-CLS, a biophysically justified mode of injury, in parallel with functioning pumps, robustly engenders an emergent slow process that triggers a plethora of pathological excitability patterns. This minimalist “device” could have physiological analogs. At first nodes of Ranvier and at nociceptors, e.g., localized lipid-tuning that modulated Nav midpoints could produce Nav-CLS, as could co-expression of appropriately differing Nav isoforms.
Author Summary
Nerve cells damaged by trauma, stroke, epilepsy, inflammatory conditions etc, have chronically leaky sodium channels that eventually kill. The usual job of sodium channels is to make brief voltage signals –action potentials– for long distance propagation. After sodium channels open to generate action potentials, sodium pumps work harder to re-establish the intracellular/extracellular sodium imbalance that is, literally, the neuron's battery for firing action potentials. Wherever tissue damage renders membranes overly fluid, we hypothesize, sodium channels become chronically leaky. Our experimental findings justify this. In fluidized membranes, sodium channel voltage sensors respond too easily, letting channels spend too much time open. Channels leak, pumps respond. By mathematical modeling, we show that in damaged channel-rich membranes the continual pump/leak counterplay would trigger the kinds of bizarre intermittent action potential bursts typical of injured neurons. Arising ectopically from injury regions, such neuropathic firing is unrelated to events in the external world. Drugs that can silence these deleterious electrical barrages without blocking healthy action potentials are needed. If fluidized membranes house the problematic leaky sodium channels, then drug side effects could be diminished by using drugs that accumulate most avidly into fluidized membranes, and that bind their targets with highest affinity there.
doi:10.1371/journal.pcbi.1002664
PMCID: PMC3441427  PMID: 23028273
4.  Left-Shifted Nav Channels in Injured Bilayer: Primary Targets for Neuroprotective Nav Antagonists? 
Mechanical, ischemic, and inflammatory injuries to voltage-gated sodium channel (Nav)-rich membranes of axon initial segments and nodes of Ranvier render Nav channels dangerously leaky. By what means? The behavior of recombinant Nav1.6 (Wang et al., 2009) leads us to postulate that, in neuropathologic conditions, structural degradation of axolemmal bilayer fosters chronically left-shifted Nav channel operation, resulting in ENa rundown. This “sick excitable cell Nav-leak” would encompass left-shifted fast- and slow-mode based persistent INa (i.e., Iwindow and slow-inactivating INa). Bilayer-damage-induced electrophysiological dysfunctions of native-Nav channels, and effects on inhibitors on those channels, should, we suggest, be studied in myelinated axons, exploiting INa(V,t) hysteresis data from sawtooth ramp clamp. We hypothesize that (like dihydropyridines for Ca channels), protective lipophilic Nav antagonists would partition more avidly into disorderly bilayers than into the well-packed bilayers characteristic of undamaged, healthy plasma membrane. Whereas inhibitors using aqueous routes would access all Navs equally, differential partitioning into “sick bilayer” would co-localize lipophilic antagonists with “sick-Nav channels,” allowing for more specific targeting of impaired cells. Molecular fine-tuning of Nav antagonists to favor more avid partitioning into damaged than into intact bilayers could reduce side effects. In potentially salvageable neurons of traumatic and/or ischemic penumbras, in inflammatory neuropathies, in muscular dystrophy, in myocytes of cardiac infarct borders, Nav-leak driven excitotoxicity overwhelms cellular repair mechanisms. Precision-tuning of a lipophilic Nav antagonist for greatest efficacy in mildly damaged membranes could render it suitable for the prolonged continuous administration needed to allow for the remodeling of the excitable membranes, and thus functional recovery.
doi:10.3389/fphar.2012.00019
PMCID: PMC3284691  PMID: 22375118
traumatic brain injury; spinal; riluzole; ranolazine; simulation; modeling

Results 1-4 (4)