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.

翻译：理解基因编码规则如何驱动和引导复杂的神经元生长过程对于认识大脑结构至关重要，而基于代理的模型（ABMs）为深化这一理解提供了强大的模拟方法。然而，准确校准这些模型仍然是一个挑战。本文提出了一种应用近似贝叶斯计算（ABC）解决该问题的新方法。ABMs基于参数化的随机规则，这些规则描述了离散化系统的小型组件（即所谓代理）的时间演化，从而产生需要恰当处理的随机模拟。从数学角度看，校准定义了一个随机反问题。我们建议在贝叶斯框架下使用ABC来解决该问题。我们通过所谓的形态计量学量化单个神经元的形态信息，并采用统计距离度量群体间的差异，从而促进数据与模拟之间的重复比较。我们在合成数据及实验数据上进行了验证实验。研究发现，采用序贯蒙特卡罗采样与Wasserstein距离的ABC方法能够为典型ABMs找到准确的后验参数分布。我们进一步证明这些ABMs能够捕捉海马体（CA1区）锥体细胞的特定形态特征。总体而言，本研究建立了一个用于校准基于代理的神经元生长模型的稳健框架，并为未来运用贝叶斯技术进行模型构建、验证与充分性评估的研究开辟了道路。