BPS2026 – Learning jump distance distributions with normalizing flows

An important step toward characterizing dynamics of biomolecules in living systems is to obtain the jump distance distribution (JDD), representing a particle’s transition probability over space between adjacent frames. Here, our focus is to obtain JDD’s in biologically relevant regimes which include higher particle densities and lower SNRs, while avoiding bias from mislinking between frames. To address these complex scenarios, we introduce a deep learning approach using normalizing flows to deconvolute the JDD from inter-frame distance distributions mixing true jumps and background distances between different particles. This approach rigorously obtains the JDD by maximizing the likelihood of the full mixture distribution, circumventing histogram subtraction methods which leverage heuristic thresholds and bin sizes. In doing so, we provide a flexible and continuous approximation of JDDs with the potential to treat dynamics complicated by transport, confinement, cellular geometry, and other cellular features. We demonstrate our method on two experimental data sets with distinct dynamics: (1) aerolysin, a monomeric pore-forming toxin, diffusing on membranes, and (2) nanofluidics in hexagonal boron nitride (hBN), a 2D material, where fluorescent emissions from neighboring surface defects form apparent trajectories.