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Journal of Applied Nonlinear Dynamics 5(3) (2016) 243--267 | DOI:10.5890/JAND.2016.09.001

Gregory Moses; Denise Scalfano

Department of Mathematics, Ohio University, Athens, OH45701-3074, USA

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Abstract

We continue our study of the dynamics of the yeast cell division cycle, in particular a feedback model where cells in one fixed part of the cycle, the Signaling region, affect the growth of cells in another part of the cycle, the Responsive region. This causes cells to cluster together as they pass through their cell division cycles, a known biological phenomenon that had been previously unexplained. In previous work, these regions were assumed to have disjoint interiors. We consider the dynamics when oscillators are coupled directly to themselves by allowing the responsive and signaling regions to overlap. We see that although the dynamics in an important subspace are largely preserved, the dynamics of the system in the full phase space exhibit less clearly quantifiable behavior. While in previously studied models, stability in the clustered subspace implies stability in the full phase space, here this is not the case, and the clustered subspace only unreliably predicts the behavior in the full phase space.

References

1. [1]	Boczko, E., Stowers, C., Gedeon, T., and Young, T. (2010), ODE, RDE and SDE Models of Cell Cycle Dynamics and Clustering in Yeast, J. Biolog. Dynamics, 4, 328-345. ArXiv: math.young.16113.

2. [2]	Robertson, J.B., Stowers, C.C., Boczko, E.M., and Johnson, C.H. (2008), Real-time luminescence monitoring of cell-cycle and respiratory oscillations in yeast, Proc Natl Acad Sci U S A, 105(46), 17988-93. PMCID:2584751.

3. [3]	Klevecz, R.R. and Murray, D. (2001), Genome wide oscillations in expression, Molecular Biology Reports, 28, 73-82.

4. [4]	Kuenzi, M.T. and Fiechter, A. (1969), Changes in carbohydrate composition and trehalose activity during the budding cycle of Saccharomyces cerevisiae, Arch. Microbiol., 64 (1969), pp. 396-407.

5. [5]	von Meyenburg, H.K. (1969), Energetics of the budding cycle of Saccharomyces cerevisiae during glucose limited aerobic growth, Arch. Microbiol., 66, 289-303.

6. [6]	Stowers, C., Young, T. and Boczko, E., (2011), The structure of populations of budding yeast in response to feedback, Hypoth. Life Sci., 1, 71 - 84.

7. [7]	Young, T., Fernandez, B., Buckalew, R., Moses, G., and Boczko, E. (2012), Clustering in cell cycle dynamics with general response/signaling feedback, Journal of Theoretical Biology, 292, 103-115.

8. [8]	Buckalew, R.(2014), Cell cycle clustering in a nonlinear mediated feedback model, DCDS B, 19(4), 867-881.

9. [9]	Gong, X., Buckalew, R., Young, T., and Boczko, E. (2014), Cell cycle dynamics in a response/signaling feedback system with a gap, Journal of Biological Dynamics, 8:1, 79-98.

10. [10]	Buckalew, R., Tanda, S., Finley, K., and Young, T, Statistical evidence for internuclear feedback in early Drosophila embryogenesis. Submitted.

11. [11]	Gong, X., Moses, G., Neiman, A., and Young, T. (2014), Noise-induced dispersion and breakup of clusters in cell cycle dynamics, J. Theor. Biology, 355, 160-169.

12. [12]	Breitsch, N., Moses, G., Boczko, E., and Young, T. (2014), Cell cycle dynamics: clustering is universal in negative feedback systems, Journal of Mathematical Biology, to appear.

13. [13]	Moses, G., Instability of positive feedback in a signaling/response model. In preparation.