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).

MOTIVATION: Single-molecule localization microscopy allows studying the dynamics of biomolecules in cells and resolving the biophysical properties of the molecules and their environment underlying cellular function. With the continuously growing amount of data produced by individual experiments, the computational cost of quantifying these properties is increasingly becoming the bottleneck of single-molecule analysis. Mining these data requires an integrated and efficient analysis toolbox. RESULTS: We introduce TRamWAy, a modular Python library that features: (i) a conservative tracking procedure for localization data, (ii) a range of sampling techniques for meshing the spatio-temporal support of the data, (iii) computationally efficient solvers for inverse models, with the option of plugging in user-defined functions and (iv) a collection of analysis tools and a simple web-based interface. AVAILABILITY AND IMPLEMENTATION: TRamWAy is a Python library and can be installed with pip and conda. The source code is available at https://github.com/DecBayComp/TRamWAy.