Fig 1.
MEC stellate cell input-output relationships express a low sensitivity to membrane voltage fluctuations.
(A) Representative examples of stellate cell voltage response to 1 s long current steps with (right panel) and without (left panel) membrane voltage fluctuations. (B) Plot of average f-I relationships under conditions outlined in A. (C) Mean leftward shifts in rheobase (i) and gain (ii) in f-I curves resulting from the introduction of membrane voltage fluctuations. (D) Change in firing rate resulting from membrane voltage fluctuations for low, mid and high spike rate regions of the f-I relationship. For each region, changes in firing rate were calculated using the difference in an individual cell’s firing rate resulting from the introduction of current input fluctuations. (E) Representative examples of stellate cell voltage response to 100 ms long current steps of different amplitudes with and without membrane voltage fluctuations. (F) Average spike-probability curve in the presence of membrane voltage fluctuations. The vertical line indicates average rheobase in the absence of voltage fluctuations for each condition.
Fig 2.
Stellate cells express non-linear membrane properties that shape the voltage trajectory leading up to spike threshold.
(A) Average steady-state input resistance as a function of membrane voltage. Measures were taken in voltage-clamp using a 100 ms duration 5 mV step. (B) Average membrane voltage trajectory (grey lines indicate SEM) associated with approach from rest to first spike. For comparison, the exponential approximation using the membrane time constant measures taken at -75 mV is also shown. (C) Average membrane voltage trajectory (grey lines indicate SEM) associated with the interspike interval. (D) Representative example of an f-V curve from a stellate cell (solid line). Line indicates fit to a power-law function of the form shown in panel inset. Inset also shows box-plot of mean exponent (p) value for the power-law function fit.
Fig 3.
An eLIF model with a large ΔT value accurately captures membrane voltage properties observed in stellate cells.
(A) Plot of I-V curves from eLIF models using different ΔT (2, 5, 15 mV) values, as well as a completely passive model. (B) Plot of input resistance as a function of membrane voltage for models outlined in A. Note, average stellate cell values are best matched by an eLIF using a ΔT value of 15 mV. (C) Voltage trajectories for initial spike approach (i) and interspike interval (ii) for models outlined in A. For comparison, average stellate cell trajectories are also shown. (D) f-V curves for models outlined in A. (F) Plot comparing experimental values for power-law function exponent in stellate cells and eLIF model using a ΔT of 15 mV.
Fig 4.
An eLIF model using a ΔT value of 15 mV generates limited modulation of input-output responses by membrane voltage fluctuations.
(A) Example traces of eLIF models implemented with ΔT = 15 mV (i) and 2 mV (ii). (B) f-I curves in eLIF models with ΔT = 15 mV (i) and 2 mV (ii) with or without membrane voltage fluctuations under baseline (black) or increased membrane conductance (gshunt-grey). (C) Spike-probability curves in eLIF models with ΔT = 15 mV (i) and 2 mV (ii) with or without membrane voltage fluctuations under baseline (black) or increased membrane conductance (gshunt-grey). (D) Changes in firing rate induced by membrane voltage fluctuations for low, mid and high regions of the f-I curves for each model. For comparison, average stellate cell values are also shown. (E) Plots of changes in rheobase (i) and sigmoid slope factor (ii) in spike-probability measures associated with the introduction of membrane voltage fluctuations for each model.
Fig 5.
Reducing ΔT in the eLIF model gradually increases modulation of input-output responses by membrane voltage fluctuations.
(A) eLIF model f-I curve gain is reduced with more a negative Vr value. (B) Comparison of f-I curves for different ΔT values with (solid lines) and without (dash lines) membrane voltage fluctuations. Note, more negative Vr values were used to maintain the same gain with smaller ΔT values. (C) Changes in the initial firing rate of f-I curves induced by membrane voltage fluctuations for the eLIF model using ΔT values. (D) Comparison of spike-probability curves for different ΔT values with (solid lines) and without (dash lines) membrane voltage fluctuations. (E) Plots of changes in rheobase (i) and sigmoid slope factor (ii) on spike-probability measures associated with the introduction of membrane voltage fluctuations for eLIF models using different ΔT values.
Fig 6.
Reduction of persistent Na+ current in an H-H formulism-based conductance model increases modulation of input-output responses by voltage fluctuations.
(A, B) Plot of steady-state membrane input resistance (A) and spike frequency (B) as a function of membrane voltage in the model for 3 different levels of INap (150 nS, 75 nS and 0 nS). (C) f-I relationships in the H-H based model using 150 nS (red), 75 nS (black) and 0 nS (cyan) with (solid line) or without (dashed line) membrane voltage fluctuations. (D) Change in firing rate resulting from membrane voltage fluctuations for low, mid and high spike rate regions of the f-I relationship. (E) Spike probability curves in the H-H based model using 150 nS (red), 75 nS (black) and 0 nS (cyan) with (solid line) or without (dashed line) membrane voltage fluctuations. (F) Plots of changes in rheobase (i) and sigmoid slope factor (ii) on spike-probability measures resulting from the introduction of membrane voltage fluctuations for the H-H based model using different levels of INap.
Fig 7.
The ΔT value determines the sensitivity to membrane voltage fluctuations in the eLIF model by setting the rate of change in membrane voltage and spike discharge probability during the approach to spike threshold.
(A, B) Phase-plane plots for the eLIF model using ΔT values of 15 mV (A) and 2 mV (B). Dotted lines indicate the membrane voltage derivative (dV/dt) value, with sold lines and arrows indicating trajectory and relative rate of change (distance between arrows). A smaller ΔT value results in a faster rate of change in membrane voltage during the approach to voltage threshold (minima of dV/dt line, VT). Insets show membrane voltage trajectory associated with phase-plane plots in A and B. (C) Plot of spike-probability in response to membrane voltage fluctuations during a ~ 4Hz interspike interval for the eLIF model using a ΔT value of 15 mV (red) and 2 mV (blue). (D) Plot of the f-V curves for the eLIF model using a ΔT value of 15 mV (red) and 2 mV (blue) with (solid lines) and without (dashed lines) membrane voltage fluctuations. (E) Plot of voltage trajectory for different levels of applied current for the eLIF model using ΔT values of 15 mV (top) and 2 mV (bottom). Model was solved using an initial condition of -65 mV and stopped once a value of -35 mV was reached. Colored dots indicate mean for each voltage trajectory. (F) Plot of 1/first spike latency as a function of mean membrane voltage (mean of trajectories shown in F).
Fig 8.
Increasing ΔT has a greater impact on the scaling of the f-V relationship than the size of membrane voltage fluctuations.
(A) Plot of the SD of membrane voltage fluctuations as a function of mean voltage using the eLIF model with ΔT = 2 mV and ΔT = 15 mV. The SD of membrane voltage fluctuations is larger with ΔT = 15 mV for voltage values more depolarized than -70 mV due to the increase in membrane resistance. Histogram of membrane voltage fluctuations (Aii) in the eLIF model using a ΔT = 2 mV and ΔT = 15 mV at mean voltages of -71.5 mV and -68 mV. As shown, at -68 mV, the SD of membrane voltage fluctuations is greater (wider distribution) when ΔT is set to -15 mV. (B, C) The shallow f-V relationship with ΔT = 15 mV reduces fluctuation-based modulation of the f-I curve even when membrane voltage fluctuations are substantially larger than those when ΔT = 2 mV. (B) Plot of f-V relationships generated with membrane voltage fluctuations with SD values of 2.3 mV, 3.6 mV and 7.5 mV (measured at -75 mV). Inset shows histogram of membrane voltage fluctuation for the three SD values. To increase the size of voltage fluctuations, the coefficient of current-input fluctuations was increased from 90 to 140 and 280. (C) Increasing the SD of membrane voltage fluctuations to 3.6 mV and 7.5 mV when ΔT = 15 mV generates smaller changes in firing rate relative to ΔT = 2 mV using voltage fluctuations with an SD of 2.6 mV. Inset shows plot of change in firing rate induced by voltage fluctuations for low, mid and high regions (defined as before) of the f-I relationship. Dashed black lines indicate f-V (B) and f-I (C) relationships in the absence of membrane voltage fluctuations.
Fig 9.
Block of voltage-dependent Na+ conductance increases sensitivity to membrane voltage fluctuations in stellate cells.
(A) Steady-state membrane input resistance measures for different holding voltages under control (black squares) and with 10 nM bath applied TTX (grey circles). (B) Example voltage traces from a stellate cell in response to a 100 ms depolarizing current step (i), as well as the average for the first 50 ms (ii) under control (black) and with TTX (grey). Inset (Bi) shows the average fraction of time the voltage trajectory spent above the mid-point for control and under bath applied TTX. (C) Representative examples of stellate cell voltage response to 100 ms long current steps of different amplitudes with and without membrane voltage fluctuations under bath applied TTX. (D) Average spike-probability curves in the presence of membrane voltage fluctuations under control (black) and 10 nM TTX (grey). Vertical lines indicate rheobase in the absence of voltage fluctuations for each condition. (E) Plots of average leftward shift (i) and sigmoid slope factor (ii) for control (black squares) and TTX (grey circles).
Fig 10.
Changes in initial spike and interspike interval voltage trajectory using dynamic clamp.
(A) Average membrane voltage trajectories for initial spike approach in stellate cells under -5 nS (red), control (black) and 15 nS of artificial membrane conductance added with dynamic clamp. Finer lines indicate sem. (B) Plot of average fraction above mid-point for initial spike voltage trajectories using -5 nS, control and 15 nS levels of artificial membrane conductance. (C) Average membrane voltage trajectories in stellate cells using dynamic clamp with -5 nS (red), control (black) and 15 nS (blue) of artificial membrane conductance. (D) Plot of average AHP half duration for the interspike interval voltage trajectories under -5 nS, control and 15 nS of artificial membrane conductance.
Fig 11.
Modulation of stellate cell input-output responses with artificial changes in membrane conductance implemented using dynamic clamp.
(A) Plot of average stellate cell f-I curves using -5 ns (red), control (black) and 15 nS (blue) levels of artificial conductance, as well as in the presence and absence membrane voltage fluctuations. (B) Plot of average gain measured using linear regression using -5 nS, control and 15 nS with (open symbols) and without (closed symbols) membrane voltage fluctuations. (C) Change in rheobase (i) and initial spike rate (ii) in stellate cell f-I curves resulting from the introduction of membrane voltage fluctuations with -5 nS, control and 15 nS levels of added conductance. (D) Plot of average stellate cell spike-probability curves under -5 ns (red), control (black) and 15 nS (blue) with and without membrane voltage fluctuations. (E) Change in rheobase (i) and sigmoid slope factor (ii) in stellate cell spike-probability curves under -5 nS, control and 15 nS resulting from the introduction of membrane voltage fluctuations.