School on Modeling Infectious Disease Dynamics

The sampling of Markov processes constrained to both initial and final states has been explored theoretically in recent years. In our work, we have devised a novel method to sample such processes, thus translating conceptual results into a practical approach which will find applications in a wide range of disciplines. To illustrate the benefits of our method we sampled trajectories in the Mueller-Brown potential, allowing us to generate transition paths which would otherwise be obtained at a high computational cost with standard Kinetic Monte Carlo methods because commitment to a transition path is essentially a rare event. We then applied our method to a single-cell RNA sequencing dataset of mouse pancreatic cells to investigate the cell differentiation pathways of endocrine-cell precursors. By sampling Markov bridges for a specific differentiation pathway we obtained a time-resolved dynamics that can reveal features such as cell types which behave as bottlenecks. The ensemble of trajectories also gives information about the fluctuations around the most likely path. For example, we quantified the statistical weights of different branches in the differentiation pathway to alpha cells.