Dynamic Input Conductances Shape Neuronal Spiking

Any ion channel potentially contributes to each of the representative timescales of the membrane potential activity. Top left, Scheme of an arbitrary high-dimensional conductance-based model. Top center, Variations of the membrane potential V_m and the different voltage-gated conductances g_i over time for a specific set of ion channel densities. Top right, Decomposition of the temporal traces in three different timescales: fast, slow, and ultraslow. Bottom, Reconstruction of the conductance-based model where the contributions of each variable conductance are grouped by timescales, forming the three dynamic input conductances g_f, g_s, and g_u (see Materials and Methods for details about the rigorous construction).

Dynamic input conductances shape neuronal activity. From left to right: fast (g_f), slow (g_s), and ultraslow (g_u) input conductances as a function of the membrane potential V_m. These curves shape the feedback gain of the neuronal circuit in distinct timescales, thereby determining the dynamical activity.

Variations of fast, slow, and ultraslow dynamic input conductances near the threshold potential and peak amplitudes shape spiking activity. a, Fast dynamic input conductance for different values of sodium channel density (left) and associated firing activity in the associated conductance-based model (right). Increased sodium channel density induces an increase in the fast dynamic conductance, which results in an increase in action potential amplitude (up to the saturated value VNa). b, Top, Slow input dynamic conductance for different values of A-type potassium channel density (left) and associated firing activity (right). Changes in A-type potassium channel density affect the value of the slow dynamic conductance at spike threshold, which mainly alters neuron burstiness. Bottom, Slow dynamic input conductance for different values of delayed-rectifier potassium channel density (left) and associated firing activity (right). Changes in delayed-rectifier channel density affects the value of the slow dynamic conductance at up-state, which mainly alters spike repolarization capability. c, Ultraslow dynamic input conductance for different values of calcium-activated potassium channel density (left) and associated firing activity (right). Increased potassium channel density increases the negative peak of the ultraslow dynamic conductance in the subthreshold region, resulting in a decrease in the intraburst frequency.

Sensitivity analysis of model STG neuron spiking activity in the fast (left) and ultraslow (right) timescales. The figure illustrates the six sensitivity curves of the STG model in the fast timescale (a1) and in the ultraslow timescale (b1). The values of the ultraslow sensitivity curves are also plotted at the specific threshold potential, which is a key potential value for excitability properties. a2, Neuronal activity in the absence of sodium and calcium channels (top left), in the presence of sodium channels only (top right), in the presence of T-type calcium channels only (bottom left) and in the presence of slow calcium channels only (bottom right). b2, Neuronal activity (left) and values of the ISIs within each burst (right) of bursters expressing a low (top) and a high (bottom) slow calcium channel density. g_u–, Ultraslow negative feedback; g_u+ ultraslow positive feedback.

Sensitivity analysis of model STG neuron spiking activity in the slow timescale. The figure shows sensitivity curves that extract the effect of conductance variations on the dynamic input conductances (top) and example of predictions that can be made from these sensitivity curves (bottom). a, Sensitivity of the slow dynamic input conductance for each V_m (left), at spike threshold (V_th), and at up-state (V_osc) (center) as well as their localization in V_m (right). b, Model membrane potential variations over time for different value of ḡ_Ca,T, ḡ_Ca,S, and ḡ_K,d. An increase in both slow and T-type calcium channel densities increases neuron burstiness due to their positive effect at spike threshold. However, an increase in T-type calcium channel density quickly results in depolarization block, due to their positive effect in the up state.

Compensation mechanism derived from the sensitivity analysis. a, b, Variation of the slow calcium channel density (top trace) and membrane potential variation over time in the absence and the presence of the compensation mechanism (center traces), and variations of channel densities involved in the compensation mechanism (bottom trace).

Colocalization of sensitivity curves, not activation curves, is crucial for robust compensation. a1, Activation functions (left) and sensitivity functions (right) of A-type potassium channels (blue), T-type calcium channels (red), and slow calcium channels (magenta). a2, Membrane potential variations over time before (left) and after a fivefold increase in slow calcium channel density (top right) and T-type calcium channel density (bottom right) in the presence of the compensation mechanism. b1, b2, Same as a1 and a2, respectively, after a right shift of 4.5 mV in A-type potassium channel activation function.

Comparison of the performances of the compensation mechanism against variations in gcas with and without variations of the applied current I_app.

Comparison of the performances of the compensation mechanism against variations in gcat with and without variations of the applied current I_app in the robust case (half-activation potential of I_k,A shifted as in Fig. 8 of the main manuscript).