Research article

Time scale and dimension analysis of a budding yeast cell cycle model

Anna Lovrics¹ , Attila Csikász-Nagy² , István Gy Zsély¹ , Judit Zádor¹ , Tamás Turányi¹ and Béla Novák²

¹Laboratory for Chemical Kinetics, Institute of Chemistry, Eötvös University (ELTE), Pázmány P. sétány 1/A, H-1117 Budapest, Hungary

²Molecular Network Dynamics Research Group of the Hungarian Academy of Sciences and Budapest University of Technology and Economics, Gellért tér 4, H-1521 Budapest, Hungary

author email corresponding author email

BMC Bioinformatics 2006, 7:494doi:10.1186/1471-2105-7-494

Published:	9 November 2006

Abstract

Background

The progress through the eukaryotic cell division cycle is driven by an underlying molecular regulatory network. Cell cycle progression can be considered as a series of irreversible transitions from one steady state to another in the correct order. Although this view has been put forward some time ago, it has not been quantitatively proven yet. Bifurcation analysis of a model for the budding yeast cell cycle has identified only two different steady states (one for G1 and one for mitosis) using cell mass as a bifurcation parameter. By analyzing the same model, using different methods of dynamical systems theory, we provide evidence for transitions among several different steady states during the budding yeast cell cycle.

Results

By calculating the eigenvalues of the Jacobian of kinetic differential equations we have determined the stability of the cell cycle trajectories of the Chen model. Based on the sign of the real part of the eigenvalues, the cell cycle can be divided into excitation and relaxation periods. During an excitation period, the cell cycle control system leaves a formerly stable steady state and, accordingly, excitation periods can be associated with irreversible cell cycle transitions like START, entry into mitosis and exit from mitosis. During relaxation periods, the control system asymptotically approaches the new steady state. We also show that the dynamical dimension of the Chen's model fluctuates by increasing during excitation periods followed by decrease during relaxation periods. In each relaxation period the dynamical dimension of the model drops to one, indicating a period where kinetic processes are in steady state and all concentration changes are driven by the increase of cytoplasmic growth.

Conclusion

We apply two numerical methods, which have not been used to analyze biological control systems. These methods are more sensitive than the bifurcation analysis used before because they identify those transitions between steady states that are not controlled by a bifurcation parameter (e.g. cell mass). Therefore by applying these tools for a cell cycle control model, we provide a deeper understanding of the dynamical transitions in the underlying molecular network.