Intestinal cell proliferation. I. A comprehensive model of steady-state proliferation in the crypt

Cell replacement in the crypt of the murine small intestine has been studied and modelled mathematically under steady-state conditions. A great deal of information is available for this system, e.g. cell cycle times, S phase durations, the rate of daily cell production, the Paneth cell distribution etc. The purpose of the present work was to consider simultaneously as much of these data as possible and to formulate a model based upon the behaviour of individual cells which adequately accounted for them. A simple mathematical representation of the crypt has been developed. This consists of sixteen stem cells per crypt (TC = 16 hr, TS = 9 hr), and four subsequent transit cell divisions (TC = 11 to 12 hr, TS = 8 hr) before maturation. Experimental data considered to test the modelling were LI and data on the number of vertical runs of similarly labelled cells. All data were obtained from the ileum after 25 microCi [3H]TdR given at 09:00 hours. A number of alternative assumptions have been considered and either accepted or rejected. Two alternative model concepts of cell displacement explain the data equally well. One is dependent upon strong local cell generation age determinance while the other could accommodate any weak local cell displacement process in conjunction with an environmental cut-off determinant at the middle of the crypt. Both models provide new interpretations of the data, e.g. certain rates of lateral cell exchange between neighbouring columns (250 to 350 per crypt per day out of a total of 420 cell divisions per day) can be concluded from run data, while LI data provide information about the mechanisms involved in maintaining a position-related age order in the crypt.