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This paper develops a model of the cell cycle from the assumption that the rate of progression from one mitosis to the next is limited by the time taken to complete a defined sequence of rate-limiting chemical reactions. The model is shown to be related to earlier models which represent limiting forms of this more rigorous description. Earlier models were classified as stochastic or deterministic, but in this case, while the overall structure is deterministic, the individual steps are stochastically variable. Thus, this description demonstrates that both views were partially correct but were incomplete in detail. By applying the model to several experimental cell cycle curves, sets of coefficients corresponding to reaction rate constants could be obtained. A striking feature of these results is that only a small number (1-3) of slow steps dominated the rate of cell division. A discussion of some recent experimental results suggests possible candidates for the few slow rate-limiting steps, and outlines a rigorous method of testing the model.
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Cell proliferation in adenocarcinomas induced in the rat's colon by parenteral injection of 1,2-dimethylhydrazine was compared with that in normal colonic epithelium by means of autoradiographs. The distinct zone of proliferation, typical of the intestines, was not observed in the tumours, and cells replicated nearly in all segments of neoplasms. Tumour enterocytes were found to have a longer short mitotic cycle (16 instead of 11 hrs), due, chiefly, to an extension of G1-period duration. They were also characterized by a more pronounced heterogeneity as far as the values of ts and tG2 are concerned, and, probably, by the formation of an R2-population. Both the index of S-phase (29%) and labelled cell fraction (87%) after 6 injections of 3H-thymidine spaced at six-hour intervals, were lower in adenocarcinomas than in the zone of maximum proliferation in the descending colon (45 and 100%, respectively) and yet higher than the same parameters calculated for the whole population of the intestinal epithelium (17 and 60%, respectively). As far as proliferation parameters go, adenocarcinoma cells highly resemble those of the crypt bottom population in control animals, which was found to consist of several subpopulations with a varying mean duration of the mitotic cycle, and where stem enterocytes are likely to occur. When enterocytes become malignant, disturbances in their differentiation decrease cell shedding into the intestinal lumen and, thus, cause tumours to arise and develop.
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A stage-by-stage study of disturbances in enterocyte proliferation in the ileum and descending colon in the course of tumour induction by treatment with 1,2-dimethylhydrazine was performed. Even at early stages, an expansion of the zone of epithelial cell proliferation in the crypts and migration of dividing cells as far as to the crypt mouth, which is a manifestation of enterocyte differentiation disturbances, were observed. Enterocytes of the crypts chiefly proliferated through a short cycle, the mean duration of which was slightly greater than in normal intestinal tissue. The reduced cell loss in the epithelium and resultant disturbances of its steady state led to the accumulation of great numbers of atypical cells in the superficial layers of the crypts and formation of carcinomas in situ in the descending colon. The microscopically unaltered sections of the mucosa, prior to development of overt neoplastic changes carcinomas in situ, superficial cancers and small-size adenocarcinomas revealed a simplified structure of enterocyte population, as compared with normal epithelium. As tumours progressed, the heterogeneity of its component cell subpopulations increased, and several subpopulations, differing in mean duration of the mitotic cycle, were formed. Pathologic mitoses made up a greater portion (50-60 per cent) of the dividing cells of the descending colon, as compared with ordinary 4 per cent at all stages of experimental tumour induction.
Benzene and toluene are metabolized by microsomal preparations in a closed metabolism flask. The Km values for benzene and toluene were 8.0 and 10.3 microM; the Vmax values were 17.2 and 20.8 nmol/g liver/min, respectively. By the use of a toxicokinetic model which acknowledges the potential for perfusion limitations on in vivo metabolism, the in vivo Km values (in terms of atmospheric concentration) for benzene and toluene were calculated based on the constants determined in vitro. The predicted in vivo constants were 0.20 and 0.21 mg/L, respectively. In vivo Km values experimentally determined by gas uptake techniques in the same strain of animal were 0.13 and 0.59 mg/L for benzene and toluene, respectively. For benzene predicted values and observed values for Km gave good correlation. The values for toluene did not correlate quite as well. The Vmax values predicted by direct conversion of the values obtained in vitro were 3.3 and 4.7 mg/kg/hr for benzene and toluene, respectively, and agreed well with the respective values observed in vivo of 2.2 and 4.6 mg/kg/hr. The model appeared capable of accurately predicting in vivo Km values from in vitro constants. Vmax values were predicted directly from in vitro constants.