A data-driven, mathematical model of mammalian cell cycle regulation

Abstract

Few of >150 published cell cycle modeling efforts use significant levels of data for tuning and validation. This reflects the difficultly to generate correlated quantitative data, and it points out a critical uncertainty in modeling efforts. To develop a data-driven model of cell cycle regulation, we used contiguous, dynamic measurements over two time scales (minutes and hours) calculated from static multiparametric cytometry data. The approach provided expression profiles of cyclin A2, cyclin B1, and phospho-S10-histone H3. The model was built by integrating and modifying two previously published models such that the model outputs for cyclins A and B fit cyclin expression measurements and the activation of B cyclin/Cdk1 coincided with phosphorylation of histone H3. The model depends on Cdh1-regulated cyclin degradation during G1, regulation of B cyclin/Cdk1 activity by cyclin A/Cdk via Wee1, and transcriptional control of the mitotic cyclins that reflects some of the current literature. We introduced autocatalytic transcription of E2F, E2F regulated transcription of cyclin B, Cdc20/Cdh1 mediated E2F degradation, enhanced transcription of mitotic cyclins during late S/early G2 phase, and the sustained synthesis of cyclin B during mitosis. These features produced a model with good correlation between state variable output and real measurements. Since the method of data generation is extensible, this model can be continually modified based on new correlated, quantitative data.

Figure 1. Cell cycle expression.

Normalized expression profiles of cyclin A2 (A), cyclin B1 (B), and PHH3 (C), and DNA content (D). A magnified view of the first 25% of the cell cycle is presented in E, and the final 3% of the cell cycle in F. K562 cells were stained, measured by flow cytometry, and sample data were analyzed to produce expression profiles as described in Materials and Methods. Dotted lines demark the G1/S, S/G2, and G2/M boundaries as determined by cell cycle analysis of DNA content and gated enumeration of PHH3 positive mitotic cells.

Figure 2. Model Schematic and comparison of model outputs to expression data I.

A: schematic derived from the Conradie model . Solid lines indicate chemical reactions and dashed lines indicate reaction modification (regulation). B, C, D: normalized comparison of model outputs with K562 data. Simulations were carried out using the published protocols and kinetic rate constants. Since antibodies do not discriminate between active/inactive, free/bound levels, total protein amounts (bound and free, inactive and active) from the model were compared to K562 measurements. As discussed in the text, PHH3 is used as a proxy for the timing of cyclin B/Cdk1 activity onset (identical to total cyclin B/Cdk1 expression in this model).

Figure 3. Model Schematic and comparison of model outputs to expression data II.

A: Schematic derived from the Csikasz-Nagy model . Solid and dashed line representations are as in Figure 2. B, C, D: normalized comparison of model outputs (simulated total protein levels (as in Figure 2) of cyclin A and cyclin B, and cyclin B/Cdk1 activity) to K562 expression data. Simulations were carried out using the published protocols and kinetic rate constants.

Figure 4. Diagram of a new model.

The models presented schematically in Figures 2 and 3 were combined and modifications were introduced to provide better fits to the K562 data. The schematics of the original Csikasz-Nagy model is shown in black, the Conradie model portion is shown in gray, and the new modifications from this study are presented in red. Solid lines indicate chemical reactions and dashed lines regulatory effects. The apparent autocatalytic regulation of cyclin B/Cdk1 synthesis here represents a stabilization of B cyclin synthesis dependent on active cyclin B/Cdk1, whereas the same representation in Figure 2 (Conradie model) represents a Hill equation that is dependent on cyclin B, which is removed here. Thus, the dashed arrow represents a new modification here.

Figure 5. Normalized comparison of the modified model outputs to K562 data.

A, B, D, E, F: total simulated levels (bound and free, inactive and active) of cyclins A and B, and cyclin B/Cdk1 activity (C) are compared to the measured expression profiles of cyclins A2 and B1, and PHH3. D, E: magnified view of early cyclin A and B expression. F: magnified view of the final 3% of the cell cycle. Symbols = data; lines = simulated output. The correlation between PHH3 expression and B cyclin/Cdk1 activity is for mitotic onset only. Since PHH3 is a proxy for B cyclin/Cdk1 activity, there isn’t a rationale for an exact match to the shape on the front side (onset) and we expect the activity to decrease as cyclin B is degraded, whereas it is known that phosphorylation levels of histone H3 (PHH3) decrease after B cyclin degradation (e.g., [59]).

Figure 6. Simulated expression over three successive cell cycles.

Model outputs were normalized to zero and one prior to plotting. cycB = total B cyclin; cycA = total A cyclin, and actCycB = active B cyclin (CycB:Cdk1 in Figure 4).