Fig. 2

Spatial model of the crypt with both symmetric and asymmetric divisions. Here, yellow arrows show the direction of cell migration, and black arrows show the divisions. The tail of each black arrow indicates the location of the dividing cell, and the head of the arrow shows the location of the offspring. At each time step, two cells at the top of crypt die, then two cells at position x divide. Cells are chosen for division based on the probability division function p _div (i). Note that only one position i is chosen to undergo division. All the cells at that position undergo division. When a cell divides, it pushes cells above toward the top of the crypt. Here, colors indicate degree of differentiation, with darker colors indicating stem cells. The differentiation level of the cells only affects their probability of undergoing division p _div (i). A symmetric division produces two cells of equal differentiation level as their mother cell. The symmetric pattern couples a differentiation event (daughter cells are placed upstream from the division location) and proliferation event (daughter cells are placed at the same level as the dividing cell). In the asymmetric division pattern, one of daughter cells stays at the same location and the other one is placed upstream