Genetic network controlling cyclins consists of just a few transcription factors—Swi6, Swi4, Mbp1, Mcm1, Fkh1, Fkh2 and Ace2. It was originally derived by Simon et al
) on the basis of genome-wide location analysis (A). The genes of this network control each other and also cyclins that control cell cycle progression and periodicity. They are: B-type cyclins involved in cell cycle progression Clb1,2,4,6 that activate Cdc28 to promote the transition from G2 to M phase or function in formation of mitotic spindles along with Clb3 and Clb4 (Clb6). Another group of genes they control are Cln1,2,3; cyclins involved in regulation of the cell cycle, activating Cdc28 kinase and promoting G1 to S phase transition. Remaining controlled genes are Apc1 that forms largest subunit of the anaphase-promoting complex/cyclosome (APC/C), and kinase inhibitors Sic1 and Far1.
The above-mentioned simulation procedure was used to infer topology and interactions within this network. For this purpose, microarray experiments were used that covered two cell cycles of yeast that had been made in triplicate (2
). Original data were stored as log base 10 values. For further use, the data were exponentiated and individual profiles corresponding to the same gene from the three parallel experiments were averaged and standard deviation for each time point was calculated. Binding interactions among members of this network were identified from ChIP experiments (13
) and have been assembled in . served for the design of necessary simulations, modeling both single regulators and two regulators acting together. The number of necessary simulations is given by the column labeled ‘comb’. In the case of genes for which three regulators were suggested by Simon et al
. (NDD1, SWI5, ACE2, SWI4, CLN3 and CLB2), we also performed a simulation for three regulators. Altogether 125 simulations were made. For each simulation, model parameter estimates were computed (see ‘Materials and Methods’ section), and a statistical test was used to compare average simulated profiles with the average experimentally measured profile. Those simulated profiles passing the statistical test were selected, and the values of the parameters wij
were used to infer the regulators of the given gene and their activity (activator or repressor). The results are summarized in .
Table 1. Regulator binding to the promoters of regulated genes in cyclin/CDK regulators network as identified by ChIP experiments (13)
The results of the inference of regulatory interactions within the cyclin/CDK regulatory network using our simulation procedure
A comparison of and shows the differences between the predictions made solely based on genome-wide location data and data computed using the simulation model. A comparison of the two approaches is given in . shows the following: (i) there was a partial overlap between the genome-wide location data analysis and the results of simulation experiments. (ii) In some cases, the statistical test for the similarity between the simulated and measured target gene expression profiles was satisfied by more than one combination of regulators. (iii) The ‘cc’ column indicates a high correlation between simulated and measured mean expression profiles, a correlation that is always >0.9. The alternative combinations of regulators must be considered equal and cannot be excluded based on differences in the correlation. All are statistically significant, and all are very highly correlated. Interactions suggested by genome-wide location analysis (12
) and those found by the simulations are depicted in . Out of 17 total regulated genes, six of them were found to have the same regulators by genome-wide location analysis and simulations, seven were found to have different regulators and the remaining four genes indicated partial regulator overlap between the two types of analyses. In the following paragraph, individual regulatory interactions and differences between the results of simulation and genome-wide location analysis are discussed.
- FKH1—Suggested control by the Swi4, Mbp1 pair was not confirmed. Control by Fkh2 suggested from ChIP experiments was not able to simulate Fkh1 profile with sufficient accuracy. Although correlation between measured and simulated expression profiles was quite high (0.90), it failed to pass our statistical test in 5 points (approximately at 30h and above 95h, see Supplementary Dataset).
- FKH2—This interaction was not predicted by Simon et al. ChIP data suggested control by Fkh1/Fkh2. Control by Fkh1 or Fkh1/Fkh2 was confirmed by simulation.
- NDD1—Suggested control by Swi6/Swi4/Mbp1 was not confirmed; instead, control only by Swi6 was found.
- SWI5—Suggested control by triplet Fkh2/Ndd1/Mcm1 was confirmed but only for the case in which Ndd1 and Mcm1 acted as repressors. Because in genome-wide location analysis, the type of control was not discussed, so this result can be considered as matching. The same phenomenon was observed for the remaining combinations (Fkh2/Mcm1 or Fkh2/Ndd1 or Fkh1/Ndd1), where Mcm1 and Ndd1 always acted as repressors.
- ACE2—Suggested control by triplet Fkh2/Ndd1/Mcm1 was confirmed with Mcm1 acting as repressor. There was a relatively low influence of Ndd1 (5 times lower than that of Fkh2; see Supplementary Dataset). Other pair-vice combinations for which Fkh2 or Fkh1 acted as activators and the other genes as repressors were identified.
- SWI4—Suggested control by Mcm1/Swi6/Swi4/Mbp1 was confirmed for Mcm1/Swi4/Mbp1. In all known cases, self control of Swi4 was confirmed, accompanied by a second regulator (Mcm1, Cln3 or Mbp1).
- CLN3—No combination of regulators was found to be possible for this gene, including suggested control by Mcm1/Swi5/Ace2.
- CLB4—Suggested control by Fkh1 was confirmed, accompanied by Swi5, which was suggested to act as repressor.
- CLB1—Instead of Mcm1, Clb1 indicated control by Fkh1 or Fkh2, together with Swi5 as repressor.
- CLB2—From the suggested control by Fkh1/Fkh2/Ndd1/Mcm1, only the pair Fkh2/Ndd1 was sufficient to control Clb2, with Ndd1 acting as repressor.
- SIC1, FAR1 and CLN2—No kinetically plausible combination of regulators was found for these genes.
- CLN1—Control by Swi4/Mbp1 was confirmed together with the alternative pair Swi6/Swi4.
- CLB6—Swi4/Mbp1 pair was confirmed together with alternative pair Swi4/Swi6 as well as Swi4/Fkh2.
- GIN4—Suggested control by Mbp1 was confirmed by combination with Swi4 or alternatively Swi6/Swi4 (SBF complex).
- SWE1—Control by Swi4/Mbp1 was confirmed.
The kinetic behavior of transcription of the selected genes was modeled with high accuracy, typically yielding a correlation coefficient between measured and simulated profiles higher than 0.98 (), with statistically significant similarity between measured and simulated expression profiles for 24 out of 25 total measured points.
Comparison of cyclin/CDK control network revealed by genome-wide location analysis and the simulations performed in this article
In several cases, regulation suggested by genome-wide location analysis for two or more regulators proved redundant from the kinetic point of view. For NDD1, genome-wide location analysis suggested three regulators (Swi6/Swi4/Mbp1), whereas for the simulation of Ndd1 kinetics, Swi6 alone was sufficient. Similarly, for SWI4, suggested control is by Mcm1/Swi6/Swi4/Mbp1, whereas for the simulation, the regulators Mcm1/Swi4/Mbp1 were sufficient (). When simulation and experimental variance were used to confirm or reject control by different combinations of regulators for a given target gene, several alternative control patterns for one target gene could be discerned; e.g. for the case of SWI5, control by a triplet Fkh2/Ndd1/Mcm1 was statistically equivalent to control by pairs Fkh2/Mcm1 and Fkh2/Ndd1 (a similar result was obtained for CLB6, SWI4 and CLN1; ). These individual regulator combinations were indistinguishable from each other, and they must be considered equivalent. Such results constitute alternative hypotheses which have to be confirmed independently.
Two complexes SBF (Swi4/Swi6) and MBF (Mbp1/Swi6) are supposed to control cyclins CLN1,2 and CLB5,6 respectively (18
) and NDD1 together with Mbp1 (12
). CLN1,2 was indeed found to be regulated by SBF, alternatively by Swi4/Mbp1 pair. In accordance with the binding experiments SWI4/MBP1 (or alternatively SBF) was found to control also CLB6. Simulation of CLB6 control by MBF suggested by literature showed low correlation with experimental time series (Pearson correlation
0.34). For the control of NDD1, Swi6 only was found to be sufficient although the simulation of the control by MBF showed to be highly correlated with experimental time series as well (Pearson correlation
0.93, see Supplementary Dataset
When the same set of regulators was identified by both experiments (simulation versus genome-wide location analysis), some regulators located by simulation were required to serve as repressors. For example, take ACE2. Both experiments suggest three regulators (Fkh2/Ndd1/Mcm1), but simulation found that Mcm1 must act as repressor, or else the Ace2 expression profile could not be modeled successfully. Similarly for SWI5 (regulators Fkh2/Ndd1/Mcm1), Ndd1 and Mcm1 had to act as repressors to simulate the expression profile of Swi5. Genome-wide location analysis does not address this issue. After searching the literature, we found that for this case, no one has investigated the regulators’ activity as an activator or repressor.
For four particular genes (SIC1, FAR1, CLN2 and CLN3; ), no combination of regulators suggested by ChIP-chip experiments could simulate the kinetics of the target genes with sufficient confidence. Control suggested by genome-wide location analysis was thus not confirmed by simulation. This observation indicates that the control of these genes may follow different pathway than purely transcriptional.
The differences between binding and simulation experiments could be caused principally by two items: measurement inaccuracy and a type of control different than the transcriptional one. Time series of gene expression are usually measured using microarrays, and number of replicates usually does not exceed three. When the measurement covers whole cell cycle or two (as for the data used here), the synchrony of the population decays with time, leading to increase of variance with time. As a result, the average measured expression profile may differ from the real one. As the simulation is designed to fit the experimental data, any error in them distorts final conclusion. Increase of the measurement reproducibility will also increase reliability of the predictions based on the simulations.
The simulation used here, suppose transcriptional control and investigates that this type of control is possible from the kinetic point of view. When other type of control is involved, then the simulation cannot find the correct solution. The same argument holds for interpretation of the binding experiments which say that the regulator binds the promoter, but cannot discover posttranscriptional or other events and cannot even say whether the binding results in transcription. If, e.g. phosphorylation is involved in transcriptional control, the binding experiments’ results, combined with the simulation results, will fail to discover the real control mechanism. The additional information, the phosphorylation, is missing. Control of CLB2 can serve as an example. CLB2 was found to be controlled by Mcm1 together with Fkh2 and co-activator Ndd1. But Clb2-Cdc28 phosphorylates Ndd1, which is important for recruitment to the CLB2 gene promoter, and phosphorylates Fkh2, which enhances the interaction of Fkh2 with Ndd1 (18
). The simulation found that only the pair Fkh2, Ndd1 was sufficient to control CLB2 gene, with Ndd1 acting as repressor. Therefore, the multiple phosphorylations involved in the control were replaced by kinetically acceptable alternative. If the current knowledge indicates that the control of the given gene is transcriptional and the results of kinetic simulation differ from those measured statically (as the binding experiments) it is an indication that the process follows different pathway then suggested, i.e. most probably some information is missing. Therefore, such situations have to be carefully checked and additional experiments have to be designed that would investigate involvement of other possible control mechanisms. As the binding experiments usually indicate several possible combinations of regulators, simulation can choose those combinations which are kinetically possible. Role of the modeling in these cases is in questioning or confirmation of the current knowledge.
Role of the simulation of transcriptional process presented here is in investigation of kinetic plausibility of regulatory interactions suggested by other experiments. The simulation of molecular interactions between transcription factors and promoter of the controlled gene is closest possible approach to the transcriptional process which allows simulating natural variance of the process given by inevitably small number of interacting molecules. When tested against experimentally measured time series, all kinetically plausible regulatory interactions can be revealed. Modeling, in this case, serves as additional confidence level of data interpretation and a means for the design of new experiments leading to discovery of, so far, unknown control mechanisms. Second role of the simulation experiments is in modeling. Once the correct pathway is known, the output caused by changes to the given system can be tested without making expensive experiments. Simulation allows studying the dynamic features of the whole network of regulatory interactions that goes beyond purely experimental observations.