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Fig. 2 | BMC Systems Biology

Fig. 2

From: Inference of spatiotemporal effects on cellular state transitions from time-lapse microscopy

Fig. 2

Spatiotemporal simulation and analysis of cell state transitions. a In our model, a cell in state I (black) can divide or transition into state II (cyan). The transition is governed by the transition rate λ, which can depend on features like time, position, cell cycle, or the local cell density. This unidirectional transition model is inspired by cellular differentiation where a undifferentiated progenitor cell irreversibly transitions into a more differentiated cell type. b Visualization of a cellular genealogy in space and time with cells in state I (black to gray) and state II (cyan to blue). c Tree view of the genealogy depicted in b (coloring as in a). d Local cell density is modeled via a set of annular basis functions ϕ k with inner radii k Δ r and constant thickness Δ r (green circles). Cells are indicated as crosses. e Linear combinations of the ϕ k can approximate any density dependence (e.g. a tophat kernel, upper panel, or a Gaussian kernel, lower panel). f The tree structured data is transformed into a data matrix by discretizing time (t 0,…,t 4 in this example) and creating one sample (i.e. one column) for each cell at each time interval, simulating a measurement process. For each cell i and each timepoint t, we record different features (i.e. rows), e.g. cell coordinates x i(t) and y i(t), the spatial features \({\phi ^{i}_{0}}(t), {\phi ^{i}_{1}}(t),\ldots \) (illustrated in d) and state transition events Y within the time interval

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