A universal workflow for creation, validation, and generalization of detailed neuronal models

Abstract

Detailed single-neuron modeling is widely used to study neuronal functions. While cellular and functional diversity across the mammalian cortex is vast, most of the available computational tools focus on a limited set of specific features characteristic of a single neuron. Here, we present a generalized automated workflow for the creation of robust electrical models and illustrate its performance by building cell models for the rat somatosensory cortex. Each model is based on a 3D morphological reconstruction and a set of ionic mechanisms. We use an evolutionary algorithm to optimize neuronal parameters to match the electrophysiological features extracted from experimental data. Then we validate the optimized models against additional stimuli and assess their generalizability on a population of similar morphologies. Compared to the state-of-the-art canonical models, our models show 5-fold improved generalizability. This versatile approach can be used to build robust models of any neuronal type.

Figure 1

E-model-building workflow Schematic illustration of the steps involved in creating neuronal models. See “single-cell model-building workflow” section for a description of the pipeline.

Figure 2

E-features of the SSCx neuronal e-types (A) Exemplar patch-clamp voltage recordings of 11 e-types. Each subplot consists of exemplar traces for three stimuli: long depolarizing current (2 s), hyperpolarizing current (1 s), and a short depolarizing current (50 ms). (B) Exemplar subset of extracted features from experimental recordings for each e-type. The e-features presented here are firing frequency (for injected current corresponding to 300% from the rheobase), number of bursts (current of 150% from the rheobase), logarithm of the slope of ISIs (log(ISI slope); i.e., current of 150% from the rheobase), AP amplitude (current of 150% from the rheobase), AP full width at half maximum (AP FWHM; i.e., current of 150% from the rheobase) and input resistance (current of −40 pA). All features are plotted as mean value $\pm$ the standard deviation.

Figure 3

E-feature scores for all e-models optimized E-feature descriptions can be found in Table S6. Blue represents low- and yellow high-cost function values, respectively.

Figure 4

Model construction and optimization results (A) Layer 5 thick-tufted pyramidal cell (L5PC) morphology showing the mechanisms inserted in different morphological sections: the apical dendrites (green), soma (red), basal dendrites (blue), axon initial segment, AIS (thin yellow cylinder), and myelinated axon (thick orange cylinder). (B) Scores and exemplar traces of the optimized L5PC model for e-features of single action potentials (APWaveform), firing properties (Step/IDrest), input resistance and hyperpolarization features (IV), back-propagating action potential and peak intracellular calcium concentration recorded in the apical dendrites, soma and AIS, (bAP, for pyramidal neurons only), and spike recovery (SpikeRec). The resting membrane potential (RMP), holding current, and threshold current are also optimized as e-features. (C) In silico voltage recordings obtained from e-models (one for each e-type) for three protocols: IDrest (150%/140% from the rheobase), IV (−100% from the rheobase), and APWaveform (320%/350% from the rheobase). These e-models are in close agreement with various experimental e-types, as shown in Figure 2A.

Figure 5

Synaptic and somatic validations of L5TPC electrical model (A) Schematic representation of the experimental setup. (B) Predicted bAP amplitude measured at different locations on apical (green dots) or basal (blue dots) dendrites and experimental results from literature (red dots). The data were fitted with an exponential for the in silico (black dashed lines) and experimental (red dashed lines) results. The color bar indicates the diameter of apical and basal dendrites at different distances from soma. (C) Predicted dendritic to somatic attenuation ratios for in silico EPSP amplitudes measured at different locations on apical (green dots) and basal (blue dots) dendrites. Color code is similar to (B). (D) Somatic validation. For each injected somatic stimulus (the left-most column, black) an exemplar voltage trace is plotted from the recorded data (middle column, green) and from the e-model’s response (the right-most column, blue). (E) Feature scores calculated based on the model responses and experimental recordings in (D).

Figure 6

Sensitivity analysis and degeneracy (A) Analysis of the sensitivity of e-features to changes in the parameter values. The matrix represents slopes of e-features values. The sensitivity is presented for e-features extracted based on three protocols (bAP, step $150\%$ and IV $-100\%$). Colors reflect the value of the slope, with slopes greater than 1 represented in yellow. (B) Currentscape plots of two L5PC e-models, with two different sets of maximal intrinsic conductances. Top: model responses to the same current stimuli (step 150$\%$). Bottom: black-filled plots represent total positive (top) and negative (bottom) currents in the cell during the stimuli. The middle panel represents the contribution of ionic inward and outward currents during the stimuli, and each color curve reveals the contribution of one particular ionic current as the percentage of the total current during the simulation.

Figure 7

Generalization of electrical models (A) Examples of the traces for L5PC me-combination, in response to the depolarizing step of 150%. Traces of me-combinations that pass (left, orange and red traces) and (right, blue and red traces) the generalization procedure. Red traces correspond to the optimized canonical e-model. (B) Example of e-feature scores for me-combos that pass (orange) and fail (blue) generalization. E-features were extracted for three depolarization protocols (steps 150%, 200%, 280%). (C) Example of the morphological properties of L5PC me-combinations that passed and failed generalization. Plot illustrates the relation between the total surface area of the AIS (axon up to $40\mu m$) and the total surface area of the proximal dendritic compartments (up to $500\mu m$ in path length) for 1,000 randomly sampled L5PC morphologies. Red dots represent failed morphologies, black dots represent passed morphologies. Size of dots represents size of the soma. (D) Parameter sensitivity analysis for the firing frequency e-feature in response to the depolarizing stimuli (150%). Dependency of e-feature score is plotted versus normalized value of the parameters. The blue line represents axonal sodium, orange represents somatic sodium, black lines represent all other parameters. Maximum score is clipped at 10. (E and F) Sensitivity analysis with the exemplar morphology (similar to Figure 6) of the sodium conductance parameter in the axon (F) and soma (E) on the cost (red) and all features (gray). Red represents the value of these parameters for this cADpyr e-model (0.33 for axon and 0.29 for soma). (G) For each combination of m-type and e-type, we display the fraction of accepted cells, with total fraction for each e-type on the left.

Figure 8

A visual representation of the code base Orange circles indicate the interactive Python notebooks, while blue circles represent the Python modules. Pink circles correspond to the files that contain parameters for all cell types in the SSCx. Although the full demonstration primarily focuses on the L5PC example, we still provide the configuration for all other cell types as a resource for the community.