Theoretical analysis of a method for determining the pattern of macromolecular synthesis during the cell cycle

The dual-labelling centrifugal-elutriation method has been extensively used to study patterns of macromolecular synthesis and accumulation in the yeast cell cycle. Cells are long-term labelled with a radioactive precursor for about 1.5 cycles (a measure of macromolecular mass), then pulse-labelled with a precursor containing a different radioactive isotope for the final 0.1 cycle (a measure of rate of synthesis). Harvested cells are fractionated into cell cycle stages by centrifugal elutriation, and changes in pulse : long-term labelling during the cycle determined. This pattern of change is compared with theoretical changes in rate : mass calculated for various patterns of synthesis. Using this method, it has been suggested that rates of synthesis and accumulation of several types of RNA and protein all increase exponentially through the cycle. In contrast, experiments using synchronous cultures or zonal centrifugation for cell cycle analysis have suggested other synthetic patterns, including periodic doubling in rate in each cycle. In this paper we analyse whether the dual-labelling, centrifugal-elutriation method is capable of discriminating between exponential and periodic rate-doubling patterns. Three possible sources of imprecision in the method and its application are examined. (1) Theoretical rate : mass curves have been simulated for macromolecules with a wider range of properties than previously considered. It is shown that for some important classes, such as messenger RNAs, with turnover rates in the range measured experimentally, and proteins, differences between rate : mass curves for exponential and periodic rate-doubling models are considerably smaller than previously suggested. (2) Long-term labelling is shown to be an accurate measure of macromolecular mass, but pulse-labelling can be inadequate as a measure of rate of synthesis. The error is greater with RNAs with faster turnover, and again reduces the ability of the method to discriminate exponential and periodic rate-doubling models of synthesis. The error is greater with RNAs with faster turnover, and again reduces the ability of the method to discriminate exponential and periodic rate-doubling models of synthesis. (3) Imperfections in cell cycle fractionation by centrifugal elutriation are examined, and by computer simulation it is shown that these also reduce the ability of the method to distinguish between the two models of synthesis. The three sources of imprecision are cumulative. It is concluded from simulation analyses that the differences between exponential and periodic rate-doubling patterns analysed by the method would be so small as to be almost impossible to establish against the background of error in experimental measurement. We therefore suggest that in practice, the dual-labelling centrifugal-elutriation method is unable to discriminate between the exponentially increasing and periodic rate-doubling models. The mathematical treatment developed in this paper should be applicable to analysis of other methods and cell cycle events.