We’ll be talking about two fundamental problems and their solution. The title reflects the first problem. Problem 1: As you try to track increasingly fast molecules, you normally increase your frame rate to avoid motion blur and eventually recover a smattering of photons in each frame. At this point, it is impossible to localize molecules in each frame in order to track, let alone link their positions frame to frame to form trajectories. This raises the question: given a smattering of photons in each frame, how do you leverage this information to determine molecular tracks while circumventing the localization and linking paradigm inherent to tracking? Put differently, we propose a new paradigm appropriate for fast molecular tracking. Problem 2: Looking at a bright cell, with fluorescence reporting on the activity of a gene, we ask the question: what fraction of the labeled protein of interest is inherited from the mother cell versus being produced by the current cell? Answering this question immediately presents a mathematical barrier: if inherited, the amount of protein depends on the cell’s division history. Put differently, this seemingly simple inference question becomes mathematically pathological. Here, concretely, we answer this question by proposing a solution through AI-assisted simulation based inference to perform inference on arbitrarily non-Markov processes.
