Properties and functional implications of I _h in hippocampal area CA3 interneurons

Abstract

The present study examines the biophysical properties and functional implications of I _h in hippocampal area CA3 interneurons with somata in strata radiatum and lacunosum-moleculare. Characterization studies showed a small maximum h-conductance (2.6 ± 0.3 nS, n = 11), shallow voltage dependence with a hyperpolarized half-maximal activation (V _1/2 = −91 mV), and kinetics characterized by double-exponential functions. The functional consequences of I _h were examined with regard to temporal summation and impedance measurements. For temporal summation experiments, 5-pulse mossy fiber input trains were activated. Blocking I _h with 50 μM ZD7288 resulted in an increase in temporal summation, suggesting that I _h supports sensitivity of response amplitude to relative input timing. Impedance was assessed by applying sinusoidal current commands. From impedance measurements, we found that I _h did not confer theta-band resonance, but flattened the impedance–frequency relations instead. Double immunolabeling for hyperpolarization-activated cyclic nucleotide-gated proteins and glutamate decarboxylase 67 suggests that all four subunits are present in GABAergic interneurons from the strata considered for electrophysiological studies. Finally, a model of I _h was employed in computational analyses to confirm and elaborate upon the contributions of I _h to impedance and temporal summation.

Appendix

I _h was computed as I _h = g _h,max X (V − E _h), where X = X _f F + X _s (1 − F). Parameters X _f and X _s are fast and slow gating variables, F is a voltage-dependent function (see below) describing the fractional contributions of fast activation and deactivation (Fig. 2e), and other terms are as described previously. Because the time constant equations are different for activation and deactivation, the gating variables need to be computed using the appropriate time constant function. In order to decide whether I _h was undergoing activation or deactivation, the normalized h-conductance (X) was compared to the normalized steady-state conductance (X _∞) at each time step and the following logic was applied:

$$ \begin{array}{*{20}{c}} {\text{IF}} \hfill & {X\left( {t - {\text{d}}t} \right) \leqslant {X_{\infty }}(t),\;{\text{THEN}}\;{I_{\text{h}}}\;{\text{is}}\;{\text{activating}}} \hfill \\ {\text{ELSE}} \hfill & {{I_{\text{h}}}\;{\text{is}}\;{\text{deactivating}}} \hfill \\ \end{array} $$

Hence, if I _h was determined to be activating, the gating variables (X _f and X _s) were updated using the activation time constants, and X(t) and I _h(t) were computed using the updated gating variables, otherwise the deactivation time constants were used:

$$ \begin{array}{*{20}{c}} {X \leqslant {X_{\infty }}:} \hfill & {{\tau_{{{\text{A,f}}}}}\frac{{{\text{d}} {X_{\text{f}}}}}{{{\text{d}}t}} = {X_{\infty }} - {X_{\text{f}}}} \hfill \\ \end{array} $$

(7)

$$ {\tau_{{{\text{A,s}}}}}\frac{{{\text{d}} {X_{\text{s}}}}}{{{\text{d}}t}} = {X_{\infty }} - {X_{\text{s}}} $$

(8)

$$ \begin{array}{*{20}{c}} {X > {X_{\infty }}:} \hfill & {{\tau_{{{\text{D,f}}}}}\frac{{{\text{d}} {X_{\text{f}}}}}{{{\text{d}}t}} = {X_{\infty }} - {X_{\text{f}}}} \hfill \\ \end{array} $$

(9)

$$ {\tau_{{{\text{D,s}}}}}\frac{{{\text{d}} {X_{\text{s}}}}}{{d{\text{t}}}} = {X_{\infty }} - {X_{\text{s}}} $$

(10)

All equations were solved via the Euler method, for example, Eq. 6 was solved as follows:

$$ V(t) = V(t - {\text{d}}t) - \frac{{{\text{d}}t}}{{{C_{\text{m}}}}}\;\left( {{I_{\text{h}}}(t) + {g_{\text{L}}} (V(t - {\text{d}}t) - {E_{\text{L}}})} \right) + \frac{{{\text{d}}t}}{{{C_{\text{m}}}}}{I_{\text{ext}}}(t) $$

(11)

The voltage-dependent functions used to describe the kinetic parameters were based on curve fits to the averaged data in Fig. 2 (c, d). The following equation was used for τ _A,s, τ _D,s, and τ _A,f:

$$ \begin{array}{*{20}{c}} {{\tau_{{j,i}}}(V) = \frac{x}{{a\,\exp \,\left( {\frac{V}{{{k_1}}}} \right) + b\,\exp \,\left( {\frac{{ - V}}{{{k_2}}}} \right)}},} \hfill & {i = {\text{ f}},{\text{s}};j = {\text{ A}},{\text{D}}} \hfill \\ \end{array} $$

(12)

The resulting fit parameter sets were {x = 122.1, a = 1.955, b = 0.01528, k ₁ = 22.45, k ₂ = 34.69} for τ _A,s, {x = 30, a = 320.2, b = 0.05197, k ₁ = 7.243, k ₂ = 63.85} for τ _D,s, and {x = 129.5, a = 12.93, b = 0.2166, k ₁ = 22.09, k ₂ = 40.07} for τ _A,f. A linear fit was used for the fast deactivation time constant, τ _D,f(V) = aV + b, with a = 0.3843 and b = 47.34 (see black curves in Fig. 2c, d). The fractional contributions of the fast current components (Fig. 2e) were described by the superimposition of two sigmoid functions:

$$ F(V) = \frac{{{a_1} - B}}{{1 + \exp \,\left( {\frac{{V - V{h_1}}}{{{k_1}}}} \right)}} + \frac{{{a_2} - B}}{{1 + \exp \,\left( { - \frac{{V - V{h_2}}}{{{k_2}}}} \right)}} + B $$

(13)

The resulting parameter sets were {a ₁ = 0.6367, a ₂ = 0.6233, Vh ₁ = −101.1, Vh ₂ = −65, k ₁ = 9.701, k ₂ = 0.3813, B = 0.4499}. The supplementary materials contain additional information regarding the behavior of this model (Figs. S5, S6, and S7). Sample code is available on https://senselab.med.yale.edu/ModelDB (accession number: 140732) [34].