A minimal mathematical model combining several regulatory cycles from the budding yeast cell cycle
Jeelean
Lim
Bioengineering Institute, University of Auckland
Model Status
This CellML version of the model has been checked in COR and PCEnv and the model runs to replicate the original published results as depicted in figure 12 of the paper. The units have been checked and are consistent.
Model Structure
ABSTRACT: A novel topology of regulatory networks abstracted from the budding yeast cell cycle is studied by constructing a simple nonlinear model. A ternary positive feedback loop with only positive regulations is constructed with elements that activates the subsequent element in a clockwise fashion. A ternary negative feedback loop with only negative regulations is constructed with the elements that inhibit the subsequent element in an anticlockwise fashion. Positive feedback loop exhibits bistability, whereas the negative feedback loop exhibits limit cycle oscillations. The novelty of the topology is that the corresponding elements in these two homogeneous feedback loops are linked by the binary positive feedback loops with only positive regulations. This results in the emergence of mixed feedback loops in the network that displays complex behaviour like the coexistence of multiple steady states, relaxation oscillations and chaos. Importantly, the arrangement of the feedback loops brings in the notion of checkpoint in the model. The model also exhibits domino-like behaviour, where the limit cycle oscillations take place in a stepwise fashion. As the aforementioned topology is abstracted from the budding yeast cell cycle, the events that govern the cell cycle are considered for the present study. In budding yeast, the sequential activation of the transcription factors, cyclins and their inhibitors form mixed feedback loops. The transcription factors that involve in the positive regulation in a clockwise orientation generates ternary positive feedback loop, while the cyclins and their inhibitors that involve in the negative regulation in an anticlockwise orientation generates ternary negative feedback loop. The mutual regulation between the corresponding elements in the transcription factors and the cyclins and their inhibitors generates binary positive feedback loops. The bifurcation diagram constructed for the whole system can be related to the different events of the cell cycle in terms of dynamical system theory. The checkpoint mechanism that plays an important role in different phases of the cell cycle are accounted for by silencing appropriate feedback loops in the model.
The original paper reference is cited below:
A minimal mathematical model combining several regulatory cycles from the budding yeast cell cycle, K. Sriram, G. Bernot and F. Kepes, 2007, IET systems biology, 1, 326-341.PubMed ID: 18203579
figure 1
Common feedback loops studied in the biological systems
figure 2
Regulatory networks of homogeneous and mixed feedback loops
$\frac{d \mathrm{C\_1}}{d \mathrm{time}}=\frac{\mathrm{v\_12}\mathrm{T\_1}^{n}}{\mathrm{k\_120}^{n}+\mathrm{T\_1}^{n}+\mathrm{C\_2}^{n}}-\mathrm{k\_d4}\mathrm{C\_1}$
$\frac{d \mathrm{C\_2}}{d \mathrm{time}}=\frac{\mathrm{v\_11}\mathrm{T\_2}^{n}}{\mathrm{k\_110}^{n}+\mathrm{T\_2}^{n}+\mathrm{C\_3}^{n}}-\mathrm{k\_d5}\mathrm{C\_2}$
$\frac{d \mathrm{C\_3}}{d \mathrm{time}}=\frac{\mathrm{v\_10}\mathrm{T\_3}^{n}}{\mathrm{k\_100}^{n}+\mathrm{T\_3}^{n}+\mathrm{C\_1}^{n}}-\mathrm{k\_d6}\mathrm{C\_3}$
$\frac{d \mathrm{T\_1}}{d \mathrm{time}}=\mathrm{j\_1}+\frac{\mathrm{v\_d1}\mathrm{T\_3}^{n}}{\mathrm{k\_m1}^{n}+\mathrm{T\_3}^{n}}+\mathrm{k\_c1}\mathrm{C\_1}-\mathrm{k\_d1}\mathrm{T\_1}$
$\frac{d \mathrm{T\_2}}{d \mathrm{time}}=\mathrm{j\_2}+\frac{\mathrm{v\_d2}\mathrm{T\_1}^{n}}{\mathrm{k\_m2}^{n}+\mathrm{T\_1}^{n}}+\mathrm{k\_c2}\mathrm{C\_2}-\mathrm{k\_d2}\mathrm{T\_2}$
$\frac{d \mathrm{T\_3}}{d \mathrm{time}}=\mathrm{j\_3}+\frac{\mathrm{v\_d3}\mathrm{T\_2}^{n}}{\mathrm{k\_m3}^{n}+\mathrm{T\_2}^{n}}+\mathrm{k\_c3}\mathrm{C\_3}-\mathrm{k\_d3}\mathrm{T\_3}$
This is the CellML description of Sriram et al's 2007 mathematical model combining several regulatory cycles from the budding yeast cell cycle This CellML version of the model has been checked in COR and PCEnv and the model runs to replicate the original published results as depicted in figure 12 of the paper. The units have been checked and are consistent.10000500JeeleanLimKrishnamachariSriramJeelean LimIET systems biologycell cyclejlim063@aucklanduni.ac.nzFKepes2009-02-11T00:00:00+00:0018203579keywordA minimal mathematical model combining several regulatory cycles from the budding yeast cell cycle1326341GBernot2007-11-00 00:00Jeelean LimThe University of AucklandAuckland Bioengineering Institute