Patterns of Proliferative Activity in the Colonic Crypt Determine Crypt Stability and Rates of Somatic Evolution

Epithelial cells in the colon are arranged in cylindrical structures called crypts in which cellular proliferation and migration are tightly regulated. We hypothesized that the proliferation patterns of cells may determine the stability of crypts as well as the rates of somatic evolution towards colorectal tumorigenesis. Here, we propose a linear process model of colonic epithelial cells that explicitly takes into account the proliferation kinetics of cells as a function of cell position within the crypt. Our results indicate that proliferation kinetics has significant influence on the speed of cell movement, kinetics of mutation propagation, and sensitivity of the system to selective effects of mutated cells. We found that, of all proliferation curves tested, those with mitotic activities concentrated near the stem cell, including the actual proliferation kinetics determined in in vivo labeling experiments, have a greater ability of delaying the rate of mutation accumulation in colonic stem cells compared to hypothetical proliferation curves with mitotic activities focused near the top of the crypt column. Our model can be used to investigate the dynamics of proliferation and mutation accumulation in spatially arranged tissues.Author Summary: Mathematical and computational models have a long and rich history in enhancing our understanding of intestinal epithelial cells. A plethora of models have been proposed to describe different aspects of cellular behavior, including cell proliferation, migration, differentiation, and mutation accumulation. Here, we present a novel approach to examine the effects of proliferation kinetics on the rate of somatic evolution in a spatially arranged model of the colon. Based on our simulation results, we demonstrate that spatially determined proliferation kinetics has the ability to delay the rate of somatic evolution, and changes in proliferation patterns can significantly affect the speed of mutation accumulation. Our work highlights the importance of considering proliferation kinetics as well as the spatial organization of tissues when investigating the dynamics of cancer initiation.