Schematics of the linear process and proliferation kinetic curves.

<p>A: We designed a linear process model to describe the essential features of cell movement in a colonic crypt. During each time step, a cell at position <i>i</i> is selected to divide. During mitosis, a mutation may occur with probability <i>u</i>, giving rise to one mutated and one wild type daughter cell, with equal probability of occupying either position <i>i</i> or <i>i</i>+1. Cell division pushes all cells to the right of position <i>i</i> upwards in the crypt by one position. The last cell is shed into the lumen of the colon. B: Cell death may occur after each round of cell division. The number of dying cells follows a Poisson distribution with mean <i>λ</i>; the positions of the dying cells are selected according to a uniform distribution. Dead cells are replaced by replenishing cell divisions. Dying cells at position <i>j</i> can only be replaced by cells of a similar (<i>j</i>+1≤<i>k</i>≤<i>j</i>+δ) or less (<i>k</i><<i>j</i>) differentiated stage. Position <i>k</i> is selected according to the proliferation kinetics curve. If multiple cells die simultaneously, the replenishing cell divisions occur sequentially, in the order of <i>j₍₁₎</i>, <i>j₍₂₎ … j_(m)</i>, where <i>j₍₁₎</i>, <i>j₍₂₎ … j_(m)</i> are ordered death position. The <i>m</i> positions for the replenishing cell divisions are selected according to the reweighted kinetic curve. C: Proliferation kinetic curves as a function of cell positions. The black curve represents the measured labeling index for normal human colon using bromodeoxyuridine (BRDU) <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003082#pcbi.1003082-Potten2" target="_blank">[23]</a>. The colored curves represent the five kinetic curves under investigation. See the <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003082#s2" target="_blank">Methods</a> section for details. Note that curve 1 is in good agreement with the measured labeling index.