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Quantitative Biology

ISSN 2095-4689

ISSN 2095-4697(Online)

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Quant. Biol.    2015, Vol. 3 Issue (2) : 55-68    https://doi.org/10.1007/s40484-015-0043-0
RESEARCH ARTICLE
Mathematical modeling reveals the mechanisms of feedforward regulation in cell fate decisions in budding yeast
Wenlong Li1,Ming Yi2,3,*(),Xiufen Zou1,*()
1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
2. Key Laboratory of Magnetic Resonance in Biological Systems, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
3. Department of Physics, College of Science, Huazhong Agricultural University, Wuhan 430070, China
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Abstract

The determination of cell fate is one of the key questions of developmental biology. Recent experiments showed that feedforward regulation is a novel feature of regulatory networks that controls reversible cellular transitions. However, the underlying mechanism of feedforward regulation-mediated cell fate decision is still unclear. Therefore, using experimental data, we develop a full mathematical model of the molecular network responsible for cell fate selection in budding yeast. To validate our theoretical model, we first investigate the dynamical behaviors of key proteins at the Start transition point and the G1/S transition point; a crucial three-node motif consisting of cyclin (Cln1/2), Substrate/Subunit Inhibitor of cyclin-dependent protein kinase (Sic1) and cyclin B (Clb5/6) is considered at these points. The rapid switches of these important components between high and low levels at two transition check points are demonstrated reasonably by our model. Many experimental observations about cell fate decision and cell size control are also theoretically reproduced. Interestingly, the feedforward regulation provides a reliable separation between different cell fates. Next, our model reveals that the threshold for the amount of WHIskey (Whi5) removed from the nucleus is higher at the Reentry point in pheromone-arrested cells compared with that at the Start point in cycling cells. Furthermore, we analyze the hysteresis in the cell cycle kinetics in response to changes in pheromone concentration, showing that Cln3 is the primary driver of reentry and Cln1/2 is the secondary driver of reentry. In particular, we demonstrate that the inhibition of Cln1/2 due to the accumulation of Factor ARrest (Far1) directly reinforces arrest. Finally, theoretical work verifies that the three-node coherent feedforward motif created by cell FUSion (Fus3), Far1 and STErile (Ste12) ensures the rapid arrest and reversibility of a cellular state. The combination of our theoretical model and the previous experimental data contributes to the understanding of the molecular mechanisms of the cell fate decision at the G1 phase in budding yeast and will stimulate further biological experiments in future.
Keywords cell fate decision      feedforward mechanism      mathematical modeling      hysteresis      reversibility     
Corresponding Author(s): Ming Yi,Xiufen Zou   
Just Accepted Date: 01 April 2015   Online First Date: 28 April 2015    Issue Date: 21 August 2015
 Cite this article:   
Wenlong Li,Ming Yi,Xiufen Zou. Mathematical modeling reveals the mechanisms of feedforward regulation in cell fate decisions in budding yeast[J]. Quant. Biol., 2015, 3(2): 55-68.
 URL:  
https://academic.hep.com.cn/qb/EN/10.1007/s40484-015-0043-0
https://academic.hep.com.cn/qb/EN/Y2015/V3/I2/55
Fig.1  Schematic illustration of two cell network subsystems. All components and reactions considered in our mathematical model are included. All arrows for individual reactions are marked with the corresponding number of this reaction in the model. (A) Cell cycle subsystem of budding yeast in G1 phase. (B) Pheromone-induced MAPK pathway subsystem of budding yeast.
Fig.2  Numerical experiments for cell size control in budding yeast. (A) The definition of the Start point and the G1/S transition point. The Start point occurs when 50% of Whi5 is removed from the nucleus, and the crossing point of the Clb5/6free time course and the Sic1 time course is considered the G1/S transition point. (B) The relationship between the duration of cell cycle and the birth size.
Fig.3  Relationship between the time of pheromone addition and Whi5P activation for pheromone-arrested cells. At the Reentry point, the maximum slope is achieved in this curve of cell fate decision. In pheromone-arrested cells, the Reentry point is defined by the export of approximately 58% of the nuclear Whi5.
Fig.4  Hysteresis in the cell cycle kinetics in response to changes in pheromone concentration. (A) Schematic of the hysteresis experiment. Experimental group cells are exposed to 240 nM α-factor for 30 min (pheromone-arrested cells), and control group cells are not treated with anything (cycling cells). Then, the two groups of cells are exposed to different α-factor concentrations (different conditions). (B) Duration of arrest in pheromone-arrested cells and cycling cells in different conditions. (C) Hysteresis experiment for cells lacking the gene cln1/2. (D) Arrest duration of pheromone-arrested cells lacking the gene cln1/2, pheromone-arrested cells lacking the gene cln3 and pheromone-arrested WT cells in different conditions.
Fig.5  Dynamical analysis for the feedforward motif with slow transcription and fast phosphorylation. (A) Time courses of Fus3PP, synthesized Far1 (i.e., Far1T) and phosphorylated Far1 (i.e., Far1PP) in WT cells pre-exposed to 240 nM pheromone. (B) Phase diagram of the arrest duration and the Far1T abundance at the Reentry point for WT cells, cln1/2Δ cells, and cln3Δ cells for changes in the final pheromone concentration in the hysteresis experiment.
Fig.6  Whi5-threshold and arrest duration are enhanced by increases in the pre-exposed duration. (A) The relationship between the pre-exposed duration and Whi5-threshold. (B) The relationship of the arrest duration and the critical addition time with pre-exposed duration.
Fig.7  . Comparison between the feedforward motif and other structures. (A) Here, we consider four categories of networks that control the level of active Far1. (B) A general response for the networks to a square pulse of the mating pheromone. (C) The steady state relationship between MAPK activity and the mating pheromone. (D). Relationship between the time of pheromone addition and Whi5P activation. (E) Hysteresis experiment for different Far1 regulatory mechanisms. Only the feedforward regulation fulfills all requirements (rapid activation and reentry, ability to continually sense extracellular information, reliable separation of cell fates, and hysteresis effect).
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