Ion-channel regulation of response decorrelation in a heterogeneous multi-scale model of the dentate gyrus

Abstract

Heterogeneities in biological neural circuits manifest in afferent connectivity as well as in local-circuit components such as neuronal excitability, neural structure and local synaptic strengths. The expression of adult neurogenesis in the dentate gyrus (DG) amplifies local-circuit heterogeneities and guides heterogeneities in afferent connectivity. How do neurons and their networks endowed with these distinct forms of heterogeneities respond to perturbations to individual ion channels, which are known to change under several physiological and pathophysiological conditions? We sequentially traversed the ion channels-neurons-network scales and assessed the impact of eliminating individual ion channels on conductance-based neuronal and network models endowed with disparate local-circuit and afferent heterogeneities. We found that many ion channels differentially contributed to specific neuronal or network measurements, and the elimination of any given ion channel altered several functional measurements. We then quantified the impact of ion-channel elimination on response decorrelation, a well-established metric to assess the ability of neurons in a network to convey complementary information, in DG networks endowed with different forms of heterogeneities. Notably, we found that networks constructed with structurally immature neurons exhibited functional robustness, manifesting as minimal changes in response decorrelation in the face of ion-channel elimination. Importantly, the average change in output correlation was dependent on the eliminated ion channel but invariant to input correlation. Our analyses suggest that neurogenesis-driven structural heterogeneities could assist the DG network in providing functional resilience to molecular perturbations.

Keywords: Adult neurogenesis; Channel decorrelation; Computational model; Heterogeneities hippocampus; Intrinsic plasticity; Ion channels; Multiscale analysis.

Graphical abstract

Fig. 1

Multi-scale modeling framework for assessing the impact of ion channel knockouts on cellular and network physiology of the dentate gyrus during virtual arena traversal.A–B, Conductance-based models for granule cells (GC) and basket cells (BC) were built using several experimentally derived ion channel conductances for these neurons. Symbols employed: g_L: Leak conductance; g_NaF: Fast sodium conductance; g_KDR: Delayed rectifier potassium conductance; g_BK: Big-conductance calcium-activated potassium conductance; g_SK: Small-conductance calcium-activated potassium conductance; g_BK: A-type transient potassium conductance; g_HCN: Hyperpolarization-activated cyclic-nucleotide-gated (HCN) nonspecific cation conductance; i_CaT: T-type calcium current; i_CaL: L-type calcium current; i_CaN: N-type calcium current; i_GABAA: GABA_A receptor current; i_AMPA: AMPA receptor current; i_MEC: current from medial entorhinal cortical cells; i_LEC: current from lateral entorhinal cortical cells. Note that all sodium, potassium and nonspecific cation channels were modeled using a Nernstian framework are represented as parallel conductances; all calcium currents and receptor currents were modeled using the Goldman-Hodgkin-Katz (GHK) formulation, and therefore are represented as dependent currents; the inputs from entorhinal cortex were modeled as currents that were dependent on animal traversal and are represented as current sources. C, A virtual animal was allowed to run in an arena of 1 ​m ​× ​1 ​m (left panel) for a period of 1000 ​s to allow complete traversal of the entire arena. The animal’s location in this arena was fed into a dentate gyrus network made of interconnected granule and basket cells (middle panel). The voltage outputs of granule cells were recorded to obtain firing rate profiles and spatial rate maps (last panel) by overlaying neuronal firing rate over the temporally aligned spatial location of the virtual animal. D, The network employed here was not a homogeneous network, but employed several biological heterogeneities expressed in the dentate gyrus. Intrinsic heterogeneities represented variability in ion channel densities and neuronal intrinsic properties, and was accounted for by employing a multi-parametric multi-objective stochastic search (MPMOSS) paradigm (Mishra and Narayanan, 2019). Synaptic heterogeneities represented the strength of the local BC $\to$ GC and GC $\to$ BC connections, and were modeled by altering the AMPAR and GABA_A receptor permeability. These receptor permeabilities were varied within a range where the excitation-inhibition balance was maintained and the overall firing rates of GCs and BCs were within experimentally observed ranges. Structural heterogeneities were introduced to model surface area changes in granule cells consequent to adult neurogenesis, and were incorporated by adjusting the geometry of the GC models. Afferent heterogeneities were representative of the uniquely sparse connectivity from the entorhinal cortices to the DG, and were modeled by feeding each GC and BC neuron with different afferent inputs. This scenario was compared with a case where all GCs and BCs were given identical afferent inputs.

Fig. 2

Virtual knockout of individual channels resulted in heterogeneous and differential impact on different sub- and supra-threshold electrophysiological measurements in a valid population of dentate granule cells.A, Left: Voltage responses to current pulses of −50 to +50 ​pA, in steps of 10 ​pA, for 500 ​ms employed for input resistance (R_in) calculation. Right: Voltage traces showing firing rate (f₁₅₀) and spike pattern in response to a 150 ​pA current injection for 950 ​ms for the same granule cell model. B–D, Same as (A) but for different valid models of granule cell. Valid models 36 (A) and 50 (B), respectively represent the minimum and maximum percentage change in input resistance (Fig. 3G) after virtual knockout of HCN ion channels. Valid models 100 (C) and 41 (D), respectively represent the minimum and maximum percentage change in f₁₅₀ (Fig. 3F) after virtual knockout of L-type calcium ion channels. Across panels, black traces represent the valid base model and traces of other colors depict those after virtual knockout of nine different ion channels in the chosen model.

Fig. 3

The mapping between individual ion channels and different electrophysiological measurements was many-to-many, with virtual knockout of individual ion channels yielding differential and variable effects on different measurements.A–H, Plots of percentage changes in different electrophysiological measurements obtained after virtual knockout of individual ion channels from valid models of granule (N_valid ​= ​126 for GC, black) and basket (N_valid ​= ​54 for GC, red) cell population obtained using MPMOSS. Percentage changes were calculated by comparing the measurement after virtual knockout of the specific ion channel with the measurement in the corresponding base model. Individual panels represent the following intrinsic measurements: A, action potential amplitude, V_AP; B, action potential half-width, T_APHW; C, action potential threshold, V_th; D, fast after hyperpolarization potential, V_AHP; E, ISI ratio; F, firing rate in response to 150 ​pA current injection, f₁₅₀; G, input resistance, R_in; and G, sag ratio. p values were obtained using Wilcoxon signed rank test, where the percentage change in measurements were tested for significance from a “no change” scenario. ∗: p ​< ​0.01, ∗∗: p ​< ​0.001.

Fig. 4

Granule cell firing profiles and spatial maps depicting the heterogenous impact of virtually knocking out individual ion channels from granule cells in a network receiving identical afferent inputs.A, Left: Spike patterns (gray) overlaid with firing rates (red) for a 100 ​s period for valid GC model 50, residing in a GC-BC network endowed with intrinsic and synaptic heterogeneities and receiving identical afferent inputs. Center: Instantaneous firing rates of GC model 50 for the entire 1000 ​s of animal traversal across the arena. Right: Color-coded spatial rate maps showing firing rate of GC model 50 superimposed on the trajectory of the virtual animal. The top-most panels represents these measurements for the base model (where all ion channels are intact), and the other panels depict these measurements obtained after virtual knockout of individual ion channels from the granule cell population of the network. B, Same as (A) for GC model 44 residing in the same network. Models 50 and 44 respectively showed maximum and minimum changes in firing rate after virtual knockout of BK ion channel (see Fig. 5A). The network employed in this illustrative example was endowed with intrinsic and synaptic heterogeneities, but did not express structural heterogeneities.

Fig. 5

Virtual knockout of individual ion channels from granule cells resulted in differential and variable impact on channel decorrelation in networks endowed with distinct heterogeneities and receiving identical afferent inputs.A, Difference in firing rates (Eq. (12)) for all granule cells in the network, represented as quartiles. Firing rate of each cell was computed from the spike count of the cell for the entire 1000 ​s traversal of the virtual animal. p values were obtained using Wilcoxon signed rank test, where the change in firing rate was tested for significance from a “no change” scenario. ∗∗∗: p ​< ​0.001. B, Cumulative distribution of inter-neuronal pairwise firing rate correlation coefficients for networks built with either the base models, or with models after virtual knockout of individual ion channels. Shown are plots for the base model network and for the networks built with GC neurons where one of the 7 ion channels was virtually knocked out. C, Distribution of percentage changes in correlation coefficients for neuronal responses from the VKM network, compared to the respective base model coefficients. Shown are plots corresponding to percentage changes in networks built with GC neurons where one of the 7 ion channels was virtually knocked out. For (A–C), plots are shown for simulations performed with three distinct networks and associated virtual knockouts: network with a fully mature GC population (left), network with a GC population of heterogeneous age (center) and network with a fully immature GC population (right). Note that all three networks are endowed with intrinsic and synaptic heterogeneities. All neurons in the network received identical afferent inputs.

Fig. 6

Virtual knockout of individual ion channels from granule cells resulted in differential and variable impact on channel decorrelation in networks endowed with distinct heterogeneities and receiving heterogeneous afferent inputs.A, Difference in firing rates (Eq. (12)) for all granule cells in the network, represented as quartiles. Firing rate of each cell was computed from the spike count of the cell for the entire 1000 ​s traversal of the virtual animal. p values were obtained using Wilcoxon signed rank test, where the change in firing rate was tested for significance from a “no change” scenario. ∗∗∗: p ​< ​0.001. B, Cumulative distribution of inter-neuronal pairwise firing rate correlation coefficients for networks built with either the base models, or with models after virtual knockout of individual ion channels. Shown are plots for the base model network and for the networks built with GC neurons where one of the 7 ion channels was virtually knocked out. In comparing the graphs in panel B to those in Fig. 5B, note that the X axes of graphs in this panel span –0.5 to 0.5, and not –1 to 1 as in Fig. 5B. C, Distribution of percentage changes in correlation coefficients for neuronal responses from the VKM network, compared to the respective base model coefficients. Shown are plots corresponding to percentage changes in networks built with GC neurons where one of the 7 ion channels was virtually knocked out. For (A–C), plots are shown for simulations performed with three distinct networks and associated virtual knockouts: network with a fully mature GC population (left), network with a GC population of heterogeneous age (center) and network with a fully immature GC population (right). Note that all three networks are endowed with intrinsic and synaptic heterogeneities. Neurons in the network received heterogeneous afferent inputs.

Fig. 7

The impact of virtual knockout of individual ion channels on the degree of channel decorrelation depends on the specific ion channel being knocked out, and reduced in the presence of immature neurons. A, Pairwise response (output) correlation plotted as a function of the corresponding pairwise input correlation, for the base model network and for networks built with GC neurons where one of the 7 ion channels was virtually knocked out. B, Percentage change in response (output) decorrelation in VKM networks with reference to the corresponding channel decorrelation in the base model, plotted as functions of input correlation. For (A–B), plots are shown for simulations performed with three distinct networks and associated virtual knockouts: network with a fully mature GC population (left), network with a GC population of heterogeneous age (center) and network with a fully immature GC population (right). Note that all three networks are endowed with intrinsic and synaptic heterogeneities. In all cases, network outcomes are represented as solid or open circles, when the network received identical or heterogeneous afferent input, respectively. Note that the input correlation is unity for networks receiving identical inputs, whereas input correlation is dependent on specific pairs of inputs when the network receives heterogeneous inputs.

Fig. 8

Functional resilience to ion-channel elimination introduced by the incorporation of immature neurons was prevalent in a larger network.A, Pairwise response (output) correlation plotted as a function of the corresponding pairwise input correlation, for the base model network and for networks built with GC neurons where 3 of the 7 ion channels was virtually knocked out. B, Percentage change in response (output) decorrelation in VKM networks with reference to the corresponding channel decorrelation in the base model, plotted as functions of input correlation. For (A–B), plots are shown for simulations performed with three distinct networks and associated virtual knockouts: network with a fully mature GC population (left), network with GC population of heterogeneous age (middle) and network with a fully immature GC population (right). Note that all the networks are endowed with intrinsic and synaptic heterogeneities.