A maximum mean discrepancy approach reveals subtle changes in α-synuclein dynamics
Authors: Verdier Hippolyte , Laurent François , Cassé Alhassan , Vestergaard Christian L. , Specht Christian G. , Masson Jean-Baptiste 
Published: April 2022

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 methodology for comparing biomolecule dynamics observed in different experimental conditions without beforehand identifying the model generating the recorded random walks. We introduce a two-step statistical testing scheme. We first use simulation-based inference to train a graph neural network to learn a fixed-length latent representation of recorded random walks. As a second step, we use a maximum mean discrepancy statistical test on the vectors of learnt features to compare biological conditions. This procedure allows us to characterise sets of random walks regardless of their generating models. We initially tested our approach on numerical trajectories. We then demonstrated its ability to detect changes in α-synuclein dynamics at synapses in cultured cortical neurons in response to membrane depolarisation. Using our methodology, we identify the domains in the latent space where the variations between conditions are the most significant, which provides a way of interpreting the detected differences in terms of single trajectory characteristics. Our data show that changes in α-synuclein dynamics between the chosen conditions are largely driven by increased protein mobility in the depolarised state.

Author summary

The continuous refinement of methods for single molecule tracking in live cells advance our understanding of how biomolecules move inside cells. Analysing the trajectories of single molecules is complicated by their highly erratic and noisy nature and thus requires the use of statistical models of their motion. However, it is often not possible to unambiguously determine a model from a set of short and noisy trajectories. Furthermore, the heterogeneous nature of the cellular environment means that the molecules’ motion is often not properly described by a single model. In this paper we develop a new statistical testing scheme to detect changes in biomolecule dynamics within organelles without needing to identify a model of their motion. We train a graph neural network on large-scale simulations of random walks to learn a latent representation that captures relevant physical properties of a trajectory. We use a kernel-based statistical test within that latent space to compare the properties of two sets of trajectories recorded under different biological conditions. We apply our approach to detect differences in the dynamics of α-synuclein, a presynaptic protein, in axons and boutons during synaptic stimulation. This represents an important step towards automated single-molecule-based read-out of pharmacological action.