Institut Pasteur, Université Paris Cité, CNRS UMR 3751, Decision and Bayesian Computation, Paris, France.
Université de Paris, UFR de physique, Paris, France.
PLoS Comput Biol. 2023 Feb 2;19(2):e1010088. doi: 10.1371/journal.pcbi.1010088. eCollection 2023 Feb.
Numerous models have been developed to account for the complex properties of the random walks of biomolecules. However, when analysing experimental data, conditions are rarely met to ensure model identification. The dynamics may simultaneously be influenced by spatial and temporal heterogeneities of the environment, out-of-equilibrium fluxes and conformal changes of the tracked molecules. Recorded trajectories are often too short to reliably discern such multi-scale dynamics, which precludes unambiguous assessment of the type of random walk and its parameters. Furthermore, the motion of biomolecules may not be well described by a single, canonical random walk model. Here, we develop a two-step statistical testing scheme for comparing biomolecule dynamics observed in different experimental conditions without having to identify or make strong prior assumptions about the model generating the recorded random walks. We first train a graph neural network to perform simulation-based inference and thus learn a rich summary statistics vector describing individual trajectories. We then compare trajectories obtained in different biological conditions using a non-parametric maximum mean discrepancy (MMD) statistical test on their so-obtained summary statistics. This procedure allows us to characterise sets of random walks regardless of their generating models, without resorting to model-specific physical quantities or estimators. We first validate the relevance of our approach on numerically simulated trajectories. This demonstrates both the statistical power of the MMD test and the descriptive power of the learnt summary statistics compared to estimates of physical quantities. We then illustrate the ability of our framework to detect changes in α-synuclein dynamics at synapses in cultured cortical neurons, in response to membrane depolarisation, and show that detected differences are largely driven by increased protein mobility in the depolarised state, in agreement with previous findings. The method provides a means of interpreting the differences it detects in terms of single trajectory characteristics. Finally, we emphasise the interest of performing various comparisons to probe the heterogeneity of experimentally acquired datasets at different levels of granularity (e.g., biological replicates, fields of view, and organelles).
已经开发了许多模型来解释生物分子随机漫步的复杂性质。然而，在分析实验数据时，很少有条件可以确保模型识别。动力学可能同时受到环境、非平衡通量和跟踪分子构象变化的时空异质性的影响。记录的轨迹通常太短，无法可靠地区分这种多尺度动力学，从而无法明确评估随机漫步的类型及其参数。此外，生物分子的运动可能无法用单个规范的随机漫步模型很好地描述。在这里，我们开发了一种两步统计测试方案，用于比较在不同实验条件下观察到的生物分子动力学，而无需识别或对产生记录的随机漫步的模型做出强烈的先验假设。我们首先训练图神经网络进行基于模拟的推断，从而学习描述单个轨迹的丰富摘要统计向量。然后，我们使用非参数最大均值差异（MMD）统计检验在不同生物条件下获得的轨迹摘要统计信息上进行比较。该过程允许我们无论其生成模型如何，都可以对随机漫步集进行特征描述，而无需诉诸于特定于模型的物理量或估计器。我们首先在数值模拟轨迹上验证了我们方法的相关性。这证明了 MMD 检验的统计功效以及与物理量估计相比所学习的摘要统计信息的描述能力。然后，我们说明了我们的框架在检测培养皮质神经元突触中α-突触核蛋白动力学在膜去极化时的变化的能力，并表明检测到的差异主要是由于去极化状态下蛋白质迁移率增加所致，这与先前的发现一致。该方法提供了一种解释它检测到的差异的方法，即根据单个轨迹特征进行解释。最后，我们强调了在不同粒度（例如，生物学重复、视野和细胞器）下进行各种比较以探测实验获得数据集的异质性的兴趣。
