Calibration of stochastic, agent-based neuron growth models with Approximate Bayesian Computation

TL;DR

This paper introduces a Bayesian calibration framework using Approximate Bayesian Computation (ABC) to accurately estimate parameters of stochastic agent-based neuron growth models, validated on synthetic and real data.

Contribution

It presents a novel application of ABC with Sequential Monte Carlo and Wasserstein distance for calibrating complex neuronal growth models.

Findings

ABC with SMC and Wasserstein distance yields accurate posterior distributions.

Calibrated models successfully replicate features of hippocampal pyramidal neurons.

Framework enables robust Bayesian calibration of stochastic agent-based models.

Abstract

Understanding how genetically encoded rules drive and guide complex neuronal growth processes is essential to comprehending the brain's architecture, and agent-based models (ABMs) offer a powerful simulation approach to further develop this understanding. However, accurately calibrating these models remains a challenge. Here, we present a novel application of Approximate Bayesian Computation (ABC) to address this issue. ABMs are based on parametrized stochastic rules that describe the time evolution of small components -- the so-called agents -- discretizing the system, leading to stochastic simulations that require appropriate treatment. Mathematically, the calibration defines a stochastic inverse problem. We propose to address it in a Bayesian setting using ABC. We facilitate the repeated comparison between data and simulations by quantifying the morphological information of single neurons with so-called morphometrics and resort to statistical distances to measure discrepancies between populations thereof. We conduct experiments on synthetic as well as experimental data. We find that ABC utilizing Sequential Monte Carlo sampling and the Wasserstein distance finds accurate posterior parameter distributions for representative ABMs. We further demonstrate that these ABMs capture specific features of pyramidal cells of the hippocampus (CA1). Overall, this work establishes a robust framework for calibrating agent-based neuronal growth models and opens the door for future investigations using Bayesian techniques for model building, verification, and adequacy assessment.