A schematic diagram of a two-stage cell lineage model. (A) A cartoon of one colonic crypt and the relative location of cells at different lineage stage adapted from [7, 24]. (B) A diagram of an un-branched cell lineage that starts with progenitor cells, regarded as a combination of stem cells and transient amplifying cells, leading to terminally differentiated (TD) cells that may undergo death. Replication of progenitor cells may be enhanced by Wnt signaling and be inhibited by BMP signaling. Wnt and BMP are produced by progenitor cells and TD cells, respectively. Wnt has an autoregulation feedback and produces Wnt inhibitor which in turn represses Wnt.