A RANDOM WALK MODEL FOR THE ANALYSIS OF THE ISOPRENALINE-STIMULATED PROLIFERATIVE RESPONSE OF THE RAT SUBMAXILLARY GLAND

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Abstract
In a series of papers, Hodgson, Radley and Koschel have studied the proliferative response of the rat submaxillary gland to the drug isoprenaline. They found that whereas the mitotic activity of the gland is normally very low, a single injection of isoprenaline will stimulate a wave of DNA synthesis and repeated administration at daily intervals, or longer, results in further waves of DNA synthesis. An explanation of these observations was proposed by Radley, Hodgson & Koschel (1976) who introduced the concept that administration of isoprenaline resulted in a period of enhanced ‘biochemical activity’ of the cells. In this paper we present a stochastic model, based on a random walk model introduced by Hopper & Brockwell (1978), to represent quantitatively the concept of ‘biochemical activity'. It is shown that the parameters of this model can be adjusted to fit the observed data. It is noted that the simpler Smith & Martin model (1973), which is a special case of our random walk model, can also be fitted to the data. However, there is experimental evidence that contradicts an assumption of the Smith & Martin model, but agrees with the predictions of our model. The random walk model also reveals that the different responses of the cell population to different injection schedules cannot be fully explained by changes in the cell population's biochemical activity distribution.