Fig 1.
A workflow showing the study components and approaches.
a) Development of a mathematical model for the Nav1.6-type Na+ current components and its incorporation into a minimal conductance-based model for a bursting neuron. b) Dynamic-clamp validation of model predictions in the brainstem proprioceptive sensory Mes V neurons. c) The observed effects on neural discharge are explained using theoretical stability and uncertainty analyses.
Fig 2.
A Hodgkin-Huxley model for the Nav1.6 Na+ current with the three components.
a) A simulated trace showing total INa; the tree map shows each of the three components: transient INaT, resurgent INaR, and, persistent INaP; These are also highlighted by the color-matched dashed boxes in the top panel. The τdecay shows the order of magnitude of the decay kinetics of the three components. b) Left: A schematic showing a conductance-based minimal model for a bursting neuron with the INa incorporated; other ionic currents in the model include a delayed-rectifier potassium (IK) and a leak current (Ileak). Right: Model simulation demonstrates rhythmic burst discharge and inset highlights the INa current in the model during action potentials, in red. c) Left: Schematic shows the dynamic-clamp experimental approach; Vm is the membrane potential. Right: Membrane potential recorded from a rhythmically bursting sensory neuron; action potentials were blocked using 1μM TTX, and dynamic-clamp model INa was applied to regenerate spikes; double slanted lines indicate break in time; inset highlights the dynamic-clamp INa in red, during action potentials.
Fig 3.
A novel mathematical model for the unusual resurgent component of the Nav1.6-type Na+ current.
a) Left: A schematic showing the voltage-dependent operation of a Na+ channel mediating resurgent current; open-channel block/unblock (green circle); classic inactivation gate (blue ball and chain). Middle: The steady-state voltage-dependencies of open-channel unblocking (1−br∞(V)) and a competing inactivation process hr∞(V) for the novel resurgent component are shown (also see Methods and Results); the magenta shaded region highlights the voltage range over which INaR can be observed during open-channel unblocking. The equation for INaR is shown with novel blocking (br), and inactivation (hr) gating variables. Right: The simulated INaR (in magenta) with peaks occurring during the repolarization phase of action potentials (in black) is shown. b) I. A comparison between simulated INa and experimentally generated INa from voltage-clamp recording is shown; boxed inset shows the experimental protocol typically used to test for voltage-dependent activation of INaR. II. Graphs show the nonlinear current-voltage relationship of peak resurgent current in the model (magenta) and average peak resurgent currents measured from voltage-clamp experiments (black); error bars show standard deviation (n = 5 neurons from 5 animals).
Fig 4.
Physiological consequences of INaR and INaP on burst discharge.
a, c) Simulated membrane voltage demonstrating the effect of gNaR addition (a), and gNaP increase (c) on burst discharge. b, d) Dynamic-clamp experimental traces showing effects of real-time addition of gNaR (b) and gNaP (c) in intrinsically bursting sensory neurons; the red double arrows highlight the opposite effects of increases in gNaR and gNaP on inter-burst intervals in panels (a–d). The boxed inset (left) indicates color coding of traces for panels e–j. The boxed inset (right) highlights burst features quantified in panels (e–j): inter-burst intervals (IBI), burst duration (BD), and inter-spike intervals (ISI. e–j) Box plots showing IBIs (e, h), BDs (f, i), and ISIs (g, j) for application of a series of gNaR or gNaP conductance values (see Results for statistics). Model values of 1x gNaR and gNaP are adjusted to match experimental data for 1x application of the corresponding conductance tested; C is control, values of gNaR used for dynamic-clamp are 2 and 4 nS/pF for 1x and 2x respectively, and, values of gNaP used are 0.25 and 0.375 nS/pF for 1x and 1.5x respectively. Asterisks indicate a p < 0.05 using a Student t-Test for group comparisons.
Fig 5.
Spike timing regularity monitored by INaR.
a, b) Time series graphs showing inter-event intervals (IEIs) under control condition (left panels in both a, b), and dynamic-clamp addition of gNaR (right panel in a), and gNaP (right panel in b). The green and cyan square brackets in each panel highlight the IBI and ISI range respectively. The y-axis shows IEIs on a log scale. Magenta boxes demarcate a representative burst in each case, which is expanded in the graphs in c), corresponding with the bold letters, A, B, C and D. The solid lines in (c) are power regression fit in each case; in all the panels, black open diamonds are control, maroon open diamonds correspond with gNaR application and blue open diamonds correspond with the gNaP application.
Fig 6.
Analysis of a mechanism of action of INaR and INaP.
a-c) The slow INaP inactivation/recovery variable, hP is overlaid (magenta) on membrane voltage traces (grey) under default (a), 1.5x gNaP (b), and 2x gNaR (c) conditions; the dark blue dashed lines in (a-c) indicate the maximum and minimum values of the persistent inactivation variable under default condition; the light green arrow in (b), highlights a reduced peak recovery required for burst onset; the light blue curvy arrows in (b, c) indicate further accumulation of slow inactivation before burst termination. d, e) Bifurcation diagrams showing the steady states and spiking regimes of the membrane voltage (V) and slow INaP inactivation/recovery (hp). The red solid lines represent resting/quiescence states consistent with low values of hp. The meeting points of stable equilibria (red) and unstable equilibria (black solid lines) represents the theoretical threshold for burst onset, the Hopf bifurcation point (see S1 Text). The blue open circles are the unstable periodics that form region of attraction on either side of the stable equilibria for sub-threshold membrane voltage oscillations; the meeting point of the curve of unstable periodics with the stable periodics (green filled circles) represents the theoretical threshold for burst offset/termination, saddle node of periodics (see S1 Text). The dashed boxes in (d) and (e) magnify the burst offset thresholds due to increases in gNaR (d) and gNaP (e); brown dashed arrows in (e) highlight shifts in burst onset thresholds due to gNaP increases; 1X gNaR = 3.3 nS/pF and 1X gNaP = 0.5 nS/pF. f) Schematic showing a negative feedback loop between the unblocking process and the slow inactivation of the Na+ currents. Inset shows membrane potential (top), blocking variable, br (middle) and slow inactivation, hr (bottom), illustrating the negative feedback mechanism.
Fig 7.
Resurgent Na+ current offers burst stability and noise modulation.
a—c) Simulated membrane voltage shows neural activity patterns without any gNaR (a), with additive Gaussian noise input (b), and with subsequent addition of gNaR (c). Expanded regions in (a-c) show membrane voltage sub-threshold oscillations (STO) during an inter-burst interval. Also overlaid is the evolution of the slow sodium inactivation/recovery variable; arrow indicates recovery during IBI, and magenta circle marks an arbitrary time point used to track these trajectories in (d—f). d—f) Bifurcation diagrams with projected trajectories of (h∞,V), shown in magenta to highlight the effect of addition of noise near sub-threshold voltages (e) and then the enlarged region of noise tolerance (highlighted green shaded region) due to addition of gNaR in (f). The magenta circle marks the beginning time points of each trajectory.
Fig 8.
Resurgent Na+ current moderates the entropy of burst discharge.
a) Schematic showing the experimental setup for real-time application of INaR and a stochastic input, INoise (see Methods); the dynamic-clamp current, Idyn is the instantaneous sum of INaR, a step current (Istep) and INoise. b) Simulated time series of two stochastic noise profiles used to disrupt the rhythmic burst discharge in Mes V neurons; Iwhite−noise was generated from a uniformly distributed random number and Iwiener−noise was generated from a normally distributed random number (see Methods). c–d) Raster plots showing patterns of inter-event intervals (IEIs) for the different conditions shown in the model (e), and during dynamic-clamp (f). e–f) Time series of IEI shown on a log scale for the different conditions shown in the model (e), and during dynamic-clamp (f). g–h) Shannon entropy (H) and coefficient of variability (CV) measured for IEIs under the different conditions presented in (c) and (d). Plotted circles for the model represent an average across 10 trials, while individual trials are presented for the data points from two cells. In both (g) and (h), C: control, N: after addition of random noise, 1x and 2x are supplements in gNaR values.
Fig 9.
A consolidated role for persistent and resurgent Na+ currents in information processing.
The schematic shows the broadband input space of a sensory neuron which can produce rhythmic bursting activity. The Nav1.6-type Na+ channels mediating the persistent Na+ current (schematized as a listening ear) enhance neuronal resonance and tune in relevant input frequencies by bandpass filtering (fresonant refers to the resonant frequency of the neuron). Such selected inputs carrying behaviorally relevant stimuli are encoded as bursts but may be prone to uncertainty due to intrinsic or extrinsic stochastic influences. The resurgent Na+ current mediated by the Nav1.6 Na+ channels improve the regularity of spike/burst timing by mitigating the effects of noise by tuning out random spikes between bursts (schematized as a noise cancelling headphone), thus aiding in neural signal processing.