Does the variability of the cell cycle result from one or many chance events?

Abstract

Smith and Martin^1,2 proposed the transition probability (TP) model to explain the significance of the variability of the cell cycle length of individual cells within a clone or culture. This postulates that the cell cycle length consists of a fixed period of time, which is the same for all members of the population, plus a variable period which is distributed according to a negative exponential function among the individual cell cycles. This variable part is contained entirely within G1, may be controlled hormonally by the organism, and is assumed to result from a single first order random process that terminates the variable part of the cell cycle with constant probability. As originally proposed, the model failed to account for timing of the fastest third of the population³. Minor and Smith⁴ assumed that there is biological variability in the previously presumed constant part of the cycle and that this variability accounts for the failure to see an abrupt discontinuity. They proposed that most of this kind of variation can be cancelled out by comparing sister cells. Thus, they proposed a second plot to test their model, the β-plot. This is a two-cycle semi-logarithmic plot of the percentage of sister-sister cells having a smaller difference in age at division than the time value corresponding to the abscissa of the graph. Their model predicts a straight line starting at 100% at time zero. Any model would require this value at time zero, but theirs requires that the plot be straight and parallel to the terminal slope of the α-plot. Shields and Smith⁵ and Shields⁶ have convincingly shown that for tissue culture cells of both mouse cell lines and Staphylococcus albus, the β-plots are linear for 97–98% of the cell populations and parallel to the α-plots. This has been taken as strong support for the TP model. Recently, in developing computer simulation of a growth controlled (GC) model⁷, I found that certain properties, such as the linearity of β-plots, are very sensitive to the presence of subpopulations of cells with longer doubling times. My major purpose here is to point out three statistical aspects of the cell cycle that are strongly influenced by growth rate heterogeneity for any model of the cell cycle.