Simulation-based inference for non-parametric statistical comparison of biomolecule dynamics

Numerous models exist for the random walks of biomolecules, but analyzing real-world data often doesn't align with these models due to a myriad of influencing factors. Existing data may be insufficient or ambiguous, preventing a clear assessment of the biomolecular dynamics. Additionally, a single model might not aptly describe the movement of biomolecules. This study introduces a two-step statistical approach for comparing biomolecular dynamics across varied experiments without needing to pre-define a specific model for the observed random walks. First, a graph neural network is trained to summarise individual trajectories comprehensively. Next, these summaries from different conditions are compared using a non-parametric statistical test called the maximum mean discrepancy (MMD). This approach validates against simulated trajectories, highlighting the MMD test's accuracy and the efficacy of the summary statistics. The method was then applied to study changes in α-synuclein dynamics in neuron cultures, confirming increased protein mobility during membrane depolarization. The technique provides insights into detected differences on a granular level. This promotes a nuanced analysis of varied datasets, considering factors like biological replicates and organelles.