We have introduced two methods for the synchronization of empirical cell cycle data (consisting of a time series of average output and information on the distribution of cells over the cell cycle) which differ in the assumptions about the source of variation within the cell. Both methods resulted in similar enhancements of the experimental data of Stuart & Wittenberg (1995) on CLN2 transcription in partially synchronized cultures of budding yeast. In one case, the original data could not support the conclusion that there is an enhancement of CLN2 transcription in a strain lacking functional CLN1 and CLN3 (compared to a control lacking all functional CLN's, which does not execute Start). But when the data is ''synchronized'' according to our methods the enhanced expression of CLN2 at start is evident (fig. 1). This judgement reinforces another experiment of Stuart & Wittenberg (fig. 2) which also show the periodic expression of CLN2 in the strain which lacks functional CLN1 and CLN3. Application of the transformation methods to this particular experiment indicates the strength of mathematical synchronization. However, with the knowledge we have about the budding yeast cell cycle we could not judge which method is the right one to apply. Luckily the results from using either method were quite similar but unfortunately not identical. We consider our synchronization methods more as tools to increase the precision of qualitative comparisons rather than as tools to obtain quantitative answers. Certainly it is advisable to analyze data with both methods if one cannot beforehand judge the validity of either method.
Once it is decided that a particular system is represented by one of the two methods, quantification is in reach if one can reliably estimate the underlying distributions of individuals. Only then is it important to focus on the quality of parameter estimation. Since in many cases a qualitative answer is sufficient, we currently did not put much effort into determining the errors made in parameter estimation. The Mathematica@ functions used here do not provide error estimates for the parameters directly, and the Mathematica@ package is certainly not the most suitable for attacking this problem in general. Our next goal therefore is to develop a specific software package suitable for experimentalists at the workbench.
In the experiments described above, information about the probability distributions was obtained from the fraction of budded cells. We think that adding a time series for the total number of cells to this set of data would provide insight in the validity of the assumption that cells do traverse the cell cycle from budding to division more or less deterministically.
Creanor & Mitchison (1982, 1994) have put forward two synchronization methods. Their 1982 method, developed in collaboration with D.A. Williams is most similar to the one used here. In that method the distribution of cells over the cell cycle was multivariate. Besides differences in age, also variability in cell cycle length and time of birth was included. Both of these methods assume that cells progress through the cell cycle deterministically, an assumption made here as well. In our models variability in the moment of birth and cell cycle duration are integrated in the age distributions we fit to the experimental data. Both methods of Creanor & Mitchison presume some functional form of the individual output function. Our methods are mere translators, i.e. under the assumptions that one can precisely determine the distribution of the cells over the cell cycle and that cells move through the cell cycle deterministically, the individual output function is determined uniquely by the time series of average output of the cells and this distribution.
Although introduced here for cell cycle experiments this method is helpful for any study in which information about individual behavior can only be obtained from the partially synchronized output of many individuals.