Examples of probability landscapes changing as the location of a cell’s observables on the manifold changes during a cell state transition. The top two rows (i) show the probability landscape changes that are associated with a cell transitioning from state 1 (blue) to state 2 (pink) via the two paths in (A). In this case, the landscapes differ during the transition as the cells take different paths and thus change the probability landscape differently, but the final landscape in state 2 is yet again the same. The probability landscape of cells in state 2 and beyond is the same for all cells that have reached state 2, and there is no memory of the path a cell took to get to this location on the manifold. In the bottom two rows (ii) however, the final state 2 landscapes are not identical and instead are dependent on the paths the cells took to reach state 2. This represents a “memory” of the path cells took during the state transition, which influences their future state trajectories.
