NOBLE -- Neural Operator with Biologically-informed Latent Embeddings to Capture Experimental Variability in Biological Neuron Models

TL;DR

NOBLE addresses the challenge of capturing trial-to-trial variability in bio-realistic neuron dynamics by learning a single neural operator conditioned on a continuous, biologically-informed latent space of neuron features. It maps current injections and latent descriptors to somatic voltage traces, enabling ensemble predictions, interpolation between known HoF models, and rapid generation of novel, biophysically plausible neurons without retraining per model. The approach yields high accuracy on in-distribution and out-of-distribution HoF models, achieves an acceleration of up to 4200× over PDE solvers, and generalizes to human cortical interneurons (PVALB and VIP), offering a pathway toward scalable, multimodal brain-scale simulations. By combining Fourier neural operators with a biologically meaningful embedding, NOBLE provides a versatile framework for linking gene expression, electrophysiology, and morphology in a unified latent space for neuroAI applications.

Abstract

Characterizing the cellular properties of neurons is fundamental to understanding their function in the brain. In this quest, the generation of bio-realistic models is central towards integrating multimodal cellular data sets and establishing causal relationships. However, current modeling approaches remain constrained by the limited availability and intrinsic variability of experimental neuronal data. The deterministic formalism of bio-realistic models currently precludes accounting for the natural variability observed experimentally. While deep learning is becoming increasingly relevant in this space, it fails to capture the full biophysical complexity of neurons, their nonlinear voltage dynamics, and variability. To address these shortcomings, we introduce NOBLE, a neural operator framework that learns a mapping from a continuous frequency-modulated embedding of interpretable neuron features to the somatic voltage response induced by current injection. Trained on synthetic data generated from bio-realistic neuron models, NOBLE predicts distributions of neural dynamics accounting for the intrinsic experimental variability. Unlike conventional bio-realistic neuron models, interpolating within the embedding space offers models whose dynamics are consistent with experimentally observed responses. NOBLE enables the efficient generation of synthetic neurons that closely resemble experimental data and exhibit trial-to-trial variability, offering a $4200\times$ speedup over the numerical solver. NOBLE is the first scaled-up deep learning framework that validates its generalization with real experimental data. To this end, NOBLE captures fundamental neural properties in a unique and emergent manner that opens the door to a better understanding of cellular composition and computations, neuromorphic architectures, large-scale brain circuits, and general neuroAI applications.

Figures (13)

• Figure 1: The Neural Operator with Biologically-informed Latent Embeddings (NOBLE) framework. A) In NOBLE, a current injection and neuron model features are first encoded using the proposed embedding strategy, before passing through a neural operator to produce a prediction for the somatic voltage response. B) NOBLE can be queried in parallel with different model latent representations to produce ensemble predictions. C) The proposed embedding in NOBLE encodes specified neuron features and the input current as a stack of trigonometric time-series, as described in \ref{['sec:embedding']}.
• Figure 2: Creation of Bio-realistic PDE-based Neuron Models. A) Evolutionary optimization process for a neuron of interest, with voltage responses sampled at different generations (top) and the error history with other experimental neurons overlaid in the background (bottom). B) Sample HoF models of various inhibitory cell-types, showing morphology (top), experimental voltage traces (2nd row), simulated voltage traces (3rd row), and spike waveform and frequency-current curves (bottom).
• Figure 3: A) F–I curves from experimental recordings, PDE simulations, and NOBLE predictions on $\{\text{HoF}^{\textit{train}}\}$. For one HoF model, B) compares experimental voltage responses with PDE simulations at a current injection of $0.1\mathrm{nA}$ (top) and $-0.11\mathrm{nA}$ (bottom), and C) compares the corresponding PDE simulation with the NOBLE prediction for the same HoF model.
• Figure 4: A) F–I curves from experimental recordings, PDE simulations, and NOBLE predictions on 50 interpolated HoF models. For one interpolated model, B) compares experimental voltage responses with PDE simulations at a current injection of $0.1\mathrm{nA}$, and C) compares the corresponding PDE simulation with the NOBLE prediction for the same interpolated HoF model.
• Figure 5: A) Distributions of somatic voltage traces across HoF models for current injections of $0.1\mathrm{nA}$ (top) and $-0.11\mathrm{nA}$ (bottom). B) Relative errors of ensemble predictions from PDE simulations and NOBLE models on $\{\text{HoF}^{\textit{train}}\}$ compared to experimental recordings across the four key features.