The physiological variability of channel density in hippocampal CA1 pyramidal cells and interneurons explored using a unified data-driven modeling workflow

Abstract

Every neuron is part of a network, exerting its function by transforming multiple spatiotemporal synaptic input patterns into a single spiking output. This function is specified by the particular shape and passive electrical properties of the neuronal membrane, and the composition and spatial distribution of ion channels across its processes. For a variety of physiological or pathological reasons, the intrinsic input/output function may change during a neuron's lifetime. This process results in high variability in the peak specific conductance of ion channels in individual neurons. The mechanisms responsible for this variability are not well understood, although there are clear indications from experiments and modeling that degeneracy and correlation among multiple channels may be involved. Here, we studied this issue in biophysical models of hippocampal CA1 pyramidal neurons and interneurons. Using a unified data-driven simulation workflow and starting from a set of experimental recordings and morphological reconstructions obtained from rats, we built and analyzed several ensembles of morphologically and biophysically accurate single cell models with intrinsic electrophysiological properties consistent with experimental findings. The results suggest that the set of conductances expressed in any given hippocampal neuron may be considered as belonging to two groups: one subset is responsible for the major characteristics of the firing behavior in each population and the other is responsible for a robust degeneracy. Analysis of the model neurons suggests several experimentally testable predictions related to the combination and relative proportion of the different conductances that should be expressed on the membrane of different types of neurons for them to fulfill their role in the hippocampus circuitry.

Fig 1. The 3D reconstructions of CA1 cells in rat hippocampus used in this study.

(Top) Pyramidal cells; dendrites are shown in black, axons in red; cell identifier, from left: 990803, oh140807_A0_idJ, oh140807_A0_idH, oh140807_A0_idG, oh140807_A0_idF, 050921AM2, oh140807_A0_idC, oh140807_A0_idB, oh140807_A0_idA; (Bottom) Interneurons, from left to right: basket cell (dendrites in black, axon in pink [Cell number 990111HP2]); bistratified cell (dendrites in black, axon in blue [Cell number 980513B]); axo-axonic cell (dendrites in black, axon in purple [Cell number 970911C]); OLM cell (dendrites in black, axon in dark blue [Cell number 011017HP2]); Ivy cell (dendrites in black; axon in light pink [Cell number 010710HP2]); perforant path associated cell (dendrites in black, axon in red [Cell number 011127HP1]); Schaffer collateral-associated cell (dendrites in black, axon in green [Cell number 990827IN5HP3]). Reconstructions by Joanne Falck and Sigrun Lange. SO Stratum Oriens, SP Stratum Pyramidale, SR Stratum Radiatum, SLM Stratum Lacunosum-Moleculare. 3D reconstructions of the PPA, OLM, axo-axonic cells and of other examples of different types of cells are available in S1 Fig of Mercer and Thomson [17].

Fig 2. Experimental voltage traces used for the optimization pipeline.

(Top) Typical somatic traces obtained during a step current stimulation protocol (-0.4, 0.4 and 0.8 nA for 400 ms) from intracellular recordings performed using sharp electrodes on CA1 pyramidal cells (left) and interneurons (right) classified as continuous accommodating cells (cAC); (bottom) typical traces from interneurons classified as bursting accommodating, bAC, (left) and continuous non-accommodating, cNAC, (right) cells [18].

Fig 3. Model optimization.

Typical optimization results for cAC pyramidal cells (top) and interneurons (bottom). The top left graph of each panel shows a few examples of model traces from three individuals during a current injection of -0.4, 0.4, and 0.8 nA (black, red, and blue traces, respectively). The right graph of each panel reports the objective scores for the best individual. The bottom left graph in each panel shows a typical evolution of the total score during an optimization run.

Fig 4. Optimization results.

(A) Comparison between typical experimental and model traces for each e-types under different somatic current injection. (B) Peak amplitude of an AP backpropagating in the main apical dendritic trunk of different pyramidal cell models, as a function of the distance from the soma. Each trace refers to a different morphology, as indicated. Abbreviations: cAC, continuous accommodating cells; cAC, bursting accommodating cells; cNAC, continuous non-accommodating cells.

Fig 5. Input/Output properties.

Number of spikes as a function of the input current from experiments (blue traces) and models (red traces) for the various e-types. The insets show the corresponding average values. Abbreviations as in Fig 4.

Fig 6. Degeneracy in CA1 pyramidal neurons.

Optimized values for all parameters, obtained for the 10 best individuals from each optimization. The X-axis represents the individual optimizations (each composed by 10 individuals), the Y-axis is the parameter’s name. The pixel colors represent the value of the parameter, normalized to the maximum value obtained from all optimizations of a given e-type. The color scale is shown on the right. Abbreviations as in Fig 4. In all cases the total error was in the range of 29–42 sd.

Fig 7. Degeneracy from different morphologies.

(A) (Black symbols): the total error calculated from the best individual obtained for each morphology; the dotted line identifies the maximum total error. (Open symbols): total error calculated from all morphologies equipped with the set of conductances obtained for oh140521_B0_Rat_idA. (B) Soma area, total cell volume, and number of sections of all morphologies.

Fig 8. Degeneracy in CA1 pyramidal neurons.

(A) Distribution of the normalized values obtained for the somatic K_M, dendritic Na, I_h and Ra. (B) Radar plot with the values obtained for a subset of conductances. Parameters’ values were sorted for those obtained for Cagk (black line); Traces on the left are model traces from individuals #30, 46, 50 and 102 under a 0.4 nA somatic current injection. (C) Number of spikes elicited by a 0.4 nA current injection in each individual. Abbreviations as in Fig 4.

Fig 9. Degeneracy in CA1 interneurons.

Radar plots with the values obtained for a subset of conductances. Parameters were sorted for the somatic Na values (black line); the bar graph on the right of each radar plot represents the corresponding spike count from each individual.

Fig 10. Differences among CA1 neuron populations.

(A) Pie charts showing for the different e-types the proportion of each conductance with respect to the total average peak conductance calculated across all individuals. (B) Schematic representation of a Pairwise Multiple Comparison Procedure (Dunn’s Method), between each pair of e-types. The colored boxes indicate cases for which p<0.050. Dark blue or cyan indicates that the average value of the first component is significantly lower or higher, respectively, than the second one. An empty box indicates no statistically significant difference.