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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.  Action potential initiation in damaged axon initial segment 
BMC Neuroscience  2014;15(Suppl 1):P135.
doi:10.1186/1471-2202-15-S1-P135
PMCID: PMC4125031
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
5.  Voltage-Gated Channel Mechanosensitivity: Fact or Friction? 
The heart is a continually active pulsatile fluid pump. It generates appropriate forces by precisely timed and spaced engagement of its contractile machinery. Largely, it makes its own control signals, the most crucial of which are precisely timed and spaced fluxes of ions across the sarcolemma, achieved by the timely opening and closing of diverse voltage-gated channels (VGC). VGCs have four voltage sensors around a central ion-selective pore that opens and closes under the influence of membrane voltage. Operation of any VGC is secondarily tuned by the mechanical state (i.e., structure) of the bilayer in which it is embedded. Rates of opening and closing, in other words, vary with bilayer structure. Thus, in the intensely mechanical environment of the myocardium and its vasculature, VGCs kinetics might be routinely modulated by reversible and irreversible nano-scale changes in bilayer structure. If subtle bilayer deformations are routine in the pumping heart, VGCs could be subtly transducing bilayer mechanical signals, thereby tuning cardiac rhythmicity, collectively contributing to mechano-electric feedback. Reversible bilayer deformations would be expected with changing shear flows and tissue distension, while irreversible bilayer restructuring occurs with ischemia, inflammation, membrane remodeling, etc. I suggest that tools now available could be deployed to help probe whether/how the inherent mechanosensitivity of VGCs – an attribute substantially reflecting the dependence of voltage sensor stability on bilayer structure – contributes to cardiac rhythmicity. Chief among these tools are voltage sensor toxins (whose inhibitory efficacy varies with the mechanical state of bilayer) and arrhythmia-inducing VGC mutants with distinctive mechano-phenotypes.
doi:10.3389/fphys.2011.00025
PMCID: PMC3107450  PMID: 21660289
stretch; mechano-electric feedback; arrhythmias; ectopic excitation; LQT3; pacemaker; sodium channel; bleb
6.  Force Spectroscopy Measurements Show That Cortical Neurons Exposed to Excitotoxic Agonists Stiffen before Showing Evidence of Bleb Damage 
PLoS ONE  2013;8(8):e73499.
In ischemic and traumatic brain injury, hyperactivated glutamate (N-methyl-D-aspartic acid, NMDA) and sodium (Nav) channels trigger excitotoxic neuron death. Na+, Ca++ and H2O influx into affected neurons elicits swelling (increased cell volume) and pathological blebbing (disassociation of the plasma membrane’s bilayer from its spectrin-actomyosin matrix). Though usually conflated in injured tissue, cell swelling and blebbing are distinct processes. Around an injury core, salvageable neurons could be mildly swollen without yet having suffered the bleb-type membrane damage that, by rendering channels leaky and pumps dysfunctional, exacerbates the excitotoxic positive feedback spiral. Recognizing when neuronal inflation signifies non-lethal osmotic swelling versus blebbing should further efforts to salvage injury-penumbra neurons. To assess whether the mechanical properties of osmotically-swollen versus excitotoxically-blebbing neurons might be cytomechanically distinguishable, we measured cortical neuron elasticity (gauged via atomic force microscopy (AFM)-based force spectroscopy) upon brief exposure to hypotonicity or to excitotoxic agonists (glutamate and Nav channel activators, NMDA and veratridine). Though unperturbed by solution exchange per se, elasticity increased abruptly with hypotonicity, with NMDA and with veratridine. Neurons then invariably softened towards or below the pre-treatment level, sometimes starting before the washout. The initial channel-mediated stiffening bespeaks an abrupt elevation of hydrostatic pressure linked to NMDA or Nav channel-mediated ion/H2O fluxes, together with increased [Ca++]int-mediated submembrane actomyosin contractility. The subsequent softening to below-control levels is consistent with the onset of a lethal level of bleb damage. These findings indicate that dissection/identification of molecular events during the excitotoxic transition from stiff/swollen to soft/blebbing is warranted and should be feasible.
doi:10.1371/journal.pone.0073499
PMCID: PMC3758302  PMID: 24023686
7.  Membrane Stretch Slows the Concerted Step prior to Opening in a Kv Channel 
The Journal of General Physiology  2006;127(6):687-701.
In the simplest model of channel mechanosensitivity, expanded states are favored by stretch. We showed previously that stretch accelerates voltage-dependent activation and slow inactivation in a Kv channel, but whether these transitions involve expansions is unknown. Thus, while voltage-gated channels are mechanosensitive, it is not clear whether the simplest model applies. For Kv pore opening steps, however, there is excellent evidence for concerted expansion motions. To ask how these motions respond to stretch, therefore, we have used a Kv1 mutant, Shaker ILT, in which the step immediately prior to opening is rate limiting for voltage-dependent current.
Macroscopic currents were measured in oocyte patches before, during, and after stretch. Invariably, and directly counter to prediction for expansion-derived free energy, ILT current activation (which is limited by the concerted step prior to pore opening) slowed with stretch and the g(V) curve reversibly right shifted. In WTIR (wild type, inactivation removed), the g(V) (which reflects independent voltage sensor motions) is left shifted. Stretch-induced slowing of ILT activation was fully accounted for by a decreased basic forward rate, with no change of gating charge. We suggest that for the highly cooperative motions of ILT activation, stretch-induced disordering of the lipid channel interface may yield an entropy increase that dominates over any stretch facilitation of expanded states. Since tail current τ(V) reports on the opposite (closing) motions, ILT and WTIR τ(V)tail were determined, but the stretch responses were too complex to shed much light.
Shaw is the Kv3 whose voltage sensor, introduced into Shaker, forms the chimera that ILT mimics. Since Shaw2 F335A activation was reportedly a first-order concerted transition, we thought its activation might, like ILT's, slow with stretch. However, Shaw2 F335A activation proved to be sigmoid shaped, so its rate-limiting transition was not a concerted pore-opening transition. Moreover, stretch, via an unidentified non–rate-limiting transition, augmented steady-state current in Shaw2 F335A.
Since putative area expansion and compaction during ILT pore opening and closing were not the energetically consequential determinants of stretch modulation, models incorporating fine details of bilayer structural forces will probably be needed to explain how, for Kv channels, bilayer stretch slows some transitions while accelerating others.
doi:10.1085/jgp.200509394
PMCID: PMC2151533  PMID: 16735754
8.  Membrane Tension Accelerates Rate-limiting Voltage-dependent Activation and Slow Inactivation Steps in a Shaker Channel 
The Journal of General Physiology  2004;123(2):135-154.
A classical voltage-sensitive channel is tension sensitive—the kinetics of Shaker and S3–S4 linker deletion mutants change with membrane stretch (Tabarean, I.V., and C.E. Morris. 2002. Biophys. J. 82:2982–2994.). Does stretch distort the channel protein, producing novel channel states, or, more interestingly, are existing transitions inherently tension sensitive? We examined stretch and voltage dependence of mutant 5aa, whose ultra-simple activation (Gonzalez, C., E. Rosenman, F. Bezanilla, O. Alvarez, and R. Latorre. 2000. J. Gen. Physiol. 115:193–208.) and temporally matched activation and slow inactivation were ideal for these studies. We focused on macroscopic patch current parameters related to elementary channel transitions: maximum slope and delay of current rise, and time constant of current decline. Stretch altered the magnitude of these parameters, but not, or minimally, their voltage dependence. Maximum slope and delay versus voltage with and without stretch as well as current rising phases were well described by expressions derived for an irreversible four-step activation model, indicating there is no separate stretch-activated opening pathway. This model, with slow inactivation added, explains most of our data. From this we infer that the voltage-dependent activation path is inherently stretch sensitive. Simulated currents for schemes with additional activation steps were compared against datasets; this showed that generally, additional complexity was not called for. Because the voltage sensitivities of activation and inactivation differ, it was not possible to substitute depolarization for stretch so as to produce the same overall PO time course. What we found, however, was that at a given voltage, stretch-accelerated current rise and decline almost identically—normalized current traces with and without stretch could be matched by a rescaling of time. Rate-limitation of the current falling phase by activation was ruled out. We hypothesize, therefore, that stretch-induced bilayer decompression facilitates an in-plane expansion of the protein in both activation and inactivation. Dynamic structural models of this class of channels will need to take into account the inherent mechanosensitivity of voltage-dependent gating.
doi:10.1085/jgp.200308965
PMCID: PMC2217428  PMID: 14744987
mechanosensitive; 5aa linker mutant; voltage-gated; stretch; S3–S4
9.  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

Results 1-9 (9)