# American Institute of Mathematical Sciences

June  2014, 19(4): 867-881. doi: 10.3934/dcdsb.2014.19.867

## Cell cycle clustering and quorum sensing in a response / signaling mediated feedback model

 1 Morton Hall 321, Ohio University, Athens, OH, 45701, United States

Received  January 2013 Revised  September 2013 Published  April 2014

RS feedback models have been successful in explaining the observed phenomenon of clustering in autonomous oscillation in yeast, but current models do not include the biological reality of dynamical delay and do not have the related property of quorum sensing. Here an RS type ODE model for cell cycle feedback, including an explicit term modeling a chemical feedback mediating agent, is analyzed. New dynamics include population dependent effects: subcritical pitchfork bifurcations, and quorum sensing occur. The model suggests new experimental directions in autonomous oscillation in yeast.
Citation: Richard L Buckalew. Cell cycle clustering and quorum sensing in a response / signaling mediated feedback model. Discrete and Continuous Dynamical Systems - B, 2014, 19 (4) : 867-881. doi: 10.3934/dcdsb.2014.19.867
##### References:
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##### References:
 [1] M. Bier, B. M. Bakker and H. V. Westerhoff, How yeast cells synchronize their glycolytic oscillations: A perturbation analytic treatment, Biophysical Journal, 78 (2000), 1087-1093. doi: 10.1016/S0006-3495(00)76667-7. [2] G. Birol, A. Q. Zamamiri and M. Hjortsø, Frequency analysis of autonomously oscillating yeast cultures, Process Biochemistry, 35 (2000), 1085-1091. doi: 10.1016/S0032-9592(00)00144-8. [3] E. Boczko, T. Gedeon, C. Stowers and T. Young, ODE, RDE and SDE models of cell cycle dynamics and clustering in yeast, Journal of Biological Dynamics, 4 (2010), 328-345. doi: 10.1080/17513750903288003. [4] N. Breitsch, G. Moses, T. Young, E. Boczko, Universality of stable periodic solutions in a cell cycle model,, Revision under review., (). [5] C. Chen and K. McDonald, Oscillatory behavior of Saccharomyces cerevisiae in continuous culture: II. Analysis of cell synchronization and metabolism, Biotechnology and Bioengineering, 36 (1990), 28-38. [6] R. Corless, G. Gonnet, D. Hare, D. Jeffrey and D. Knuth, On the Lambert W function, Advances in Computational Mathematics, 5 (1996), 329-359. doi: 10.1007/BF02124750. [7] S. Danø, P. G. Sørensen and F. Hynne, Sustained oscillations in living cells, Letters to Nature, 402 (1999), 320-322. [8] S. De Monte, F. d'Ovidio, S. Danø and P. G. Sørensen, Dynamical quorum sensing: Population density encoded in cellular dynamics, PNAS, 104 (2007), 18377-18381 [9] R. K. Finn and R. E. Wilson, Population dynamic behavior of the Chemostat system, Journal of Agricultural and Food Chemistry, 2 (1954), 66-69. [10] M. Henson, Modeling the synchronization of yeast respiratory oscillations, Journal of Theoretical Biology, 231 (2004), 443-458. doi: 10.1016/j.jtbi.2004.07.009. [11] A. J. Homburg, T. Young and M. Gharaei, Bifurcations of random differential equations with bounded noise, in Bounded Stochastic Processes in Physics, Biology and Engineering (ed. A. D'Onofrio), Birkhäuser-Springer, 2013, 133-149. doi: 10.1007/978-1-4614-7385-5_9. [12] M. A. Hjortsø, A conceptual model of autonomous oscillations in microbial cultures, Chemical Engineering Science, 49 (1994), 1083-1095. doi: 10.1016/0009-2509(94)85081-X. [13] M. Keulers, T. Suzuki, A. D. Satroutdinov and H. Kuriuama, Autonomous metabolic oscillation in continuous culture of Saccharomyces cerevisiae grown on ethanol, FEMS Microbiology Letters, 142 (1996), 253-258. doi: 10.1016/0378-1097(96)00277-7. [14] M. T. Kuenzi and A. Fiechter, Changes in carbohydrate composition and trehalose-activity during the budding cycle of Saccharomyces cerevisiae, Archives of Microbiology, 64 (1969), 396-407. doi: 10.1007/BF00417021. [15] H. K. von Meyenburg, Energetics of the budding cycle of Saccharomyces cerevisiae during glucose limited aerobic growth, Archives of Microbiology, 66 (1969), 289-303. [16] P. R. Patnaik, Oscillatory metabolism of Saccharomyces cerevisiae: An overview of mechanisms and models, Biotechnology Advances, 21 (2003), 183-192. doi: 10.1016/S0734-9750(03)00022-3. [17] P. Richard, The rhythm of yeast, FEMS Microbiology Reviews, 27 (2003), 547-557. doi: 10.1016/S0168-6445(03)00065-2. [18] J. B. Robertson, C. C. Stowers, E. M. Boczko and C. H. Johnson, Real-time luminescence monitoring of cell-cycle and respiratory oscillations in yeast, PNAS, 105 (2008), 17988-17993. doi: 10.1073/pnas.0809482105. [19] M. R. Tinsley, A. F. Taylor, Z. Huang and K. Showalter, Emergence of collective behavior in groups of excitable catalyst-loaded particles, spatiotemporal dynamical quorum sensing, Physical Review Letters, 102 (2009). doi: 10.1103/PhysRevLett.102.158301. [20] B. P. Tu, A. Kudlicki, M. Rowicka and S. L. McKnight, Logic of the yeast metabolic cycle: Temporal compartmentalization of cellular processes, Science, 310 (2005), 1152-1158. doi: 10.1126/science.1120499. [21] T. Young, B. Fernandez, R. Buckalew, G. Moses and E. Boczko, Clustering in cell cycle dynamics with general response/signaling feedback, Journal of Theoretical Biology, 292 (2012), 103-115. doi: 10.1016/j.jtbi.2011.10.002.
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