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 & Continuous Dynamical Systems - B, 2014, 19 (4) : 867-881. doi: 10.3934/dcdsb.2014.19.867
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.  doi: 10.1016/S0006-3495(00)76667-7.  Google Scholar

[2]

G. Birol, A. Q. Zamamiri and M. Hjortsø, Frequency analysis of autonomously oscillating yeast cultures,, Process Biochemistry, 35 (2000), 1085.  doi: 10.1016/S0032-9592(00)00144-8.  Google Scholar

[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.  doi: 10.1080/17513750903288003.  Google Scholar

[4]

N. Breitsch, G. Moses, T. Young, E. Boczko, Universality of stable periodic solutions in a cell cycle model,, Revision under review., ().   Google Scholar

[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.   Google Scholar

[6]

R. Corless, G. Gonnet, D. Hare, D. Jeffrey and D. Knuth, On the Lambert W function,, Advances in Computational Mathematics, 5 (1996), 329.  doi: 10.1007/BF02124750.  Google Scholar

[7]

S. Danø, P. G. Sørensen and F. Hynne, Sustained oscillations in living cells,, Letters to Nature, 402 (1999), 320.   Google Scholar

[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.   Google Scholar

[9]

R. K. Finn and R. E. Wilson, Population dynamic behavior of the Chemostat system,, Journal of Agricultural and Food Chemistry, 2 (1954), 66.   Google Scholar

[10]

M. Henson, Modeling the synchronization of yeast respiratory oscillations,, Journal of Theoretical Biology, 231 (2004), 443.  doi: 10.1016/j.jtbi.2004.07.009.  Google Scholar

[11]

A. J. Homburg, T. Young and M. Gharaei, Bifurcations of random differential equations with bounded noise,, in Bounded Stochastic Processes in Physics, (2013), 133.  doi: 10.1007/978-1-4614-7385-5_9.  Google Scholar

[12]

M. A. Hjortsø, A conceptual model of autonomous oscillations in microbial cultures,, Chemical Engineering Science, 49 (1994), 1083.  doi: 10.1016/0009-2509(94)85081-X.  Google Scholar

[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.  doi: 10.1016/0378-1097(96)00277-7.  Google Scholar

[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.  doi: 10.1007/BF00417021.  Google Scholar

[15]

H. K. von Meyenburg, Energetics of the budding cycle of Saccharomyces cerevisiae during glucose limited aerobic growth,, Archives of Microbiology, 66 (1969), 289.   Google Scholar

[16]

P. R. Patnaik, Oscillatory metabolism of Saccharomyces cerevisiae: An overview of mechanisms and models,, Biotechnology Advances, 21 (2003), 183.  doi: 10.1016/S0734-9750(03)00022-3.  Google Scholar

[17]

P. Richard, The rhythm of yeast,, FEMS Microbiology Reviews, 27 (2003), 547.  doi: 10.1016/S0168-6445(03)00065-2.  Google Scholar

[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.  doi: 10.1073/pnas.0809482105.  Google Scholar

[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.  Google Scholar

[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.  doi: 10.1126/science.1120499.  Google Scholar

[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.  doi: 10.1016/j.jtbi.2011.10.002.  Google Scholar

show all references

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.  doi: 10.1016/S0006-3495(00)76667-7.  Google Scholar

[2]

G. Birol, A. Q. Zamamiri and M. Hjortsø, Frequency analysis of autonomously oscillating yeast cultures,, Process Biochemistry, 35 (2000), 1085.  doi: 10.1016/S0032-9592(00)00144-8.  Google Scholar

[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.  doi: 10.1080/17513750903288003.  Google Scholar

[4]

N. Breitsch, G. Moses, T. Young, E. Boczko, Universality of stable periodic solutions in a cell cycle model,, Revision under review., ().   Google Scholar

[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.   Google Scholar

[6]

R. Corless, G. Gonnet, D. Hare, D. Jeffrey and D. Knuth, On the Lambert W function,, Advances in Computational Mathematics, 5 (1996), 329.  doi: 10.1007/BF02124750.  Google Scholar

[7]

S. Danø, P. G. Sørensen and F. Hynne, Sustained oscillations in living cells,, Letters to Nature, 402 (1999), 320.   Google Scholar

[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.   Google Scholar

[9]

R. K. Finn and R. E. Wilson, Population dynamic behavior of the Chemostat system,, Journal of Agricultural and Food Chemistry, 2 (1954), 66.   Google Scholar

[10]

M. Henson, Modeling the synchronization of yeast respiratory oscillations,, Journal of Theoretical Biology, 231 (2004), 443.  doi: 10.1016/j.jtbi.2004.07.009.  Google Scholar

[11]

A. J. Homburg, T. Young and M. Gharaei, Bifurcations of random differential equations with bounded noise,, in Bounded Stochastic Processes in Physics, (2013), 133.  doi: 10.1007/978-1-4614-7385-5_9.  Google Scholar

[12]

M. A. Hjortsø, A conceptual model of autonomous oscillations in microbial cultures,, Chemical Engineering Science, 49 (1994), 1083.  doi: 10.1016/0009-2509(94)85081-X.  Google Scholar

[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.  doi: 10.1016/0378-1097(96)00277-7.  Google Scholar

[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.  doi: 10.1007/BF00417021.  Google Scholar

[15]

H. K. von Meyenburg, Energetics of the budding cycle of Saccharomyces cerevisiae during glucose limited aerobic growth,, Archives of Microbiology, 66 (1969), 289.   Google Scholar

[16]

P. R. Patnaik, Oscillatory metabolism of Saccharomyces cerevisiae: An overview of mechanisms and models,, Biotechnology Advances, 21 (2003), 183.  doi: 10.1016/S0734-9750(03)00022-3.  Google Scholar

[17]

P. Richard, The rhythm of yeast,, FEMS Microbiology Reviews, 27 (2003), 547.  doi: 10.1016/S0168-6445(03)00065-2.  Google Scholar

[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.  doi: 10.1073/pnas.0809482105.  Google Scholar

[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.  Google Scholar

[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.  doi: 10.1126/science.1120499.  Google Scholar

[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.  doi: 10.1016/j.jtbi.2011.10.002.  Google Scholar

[1]

Pengyu Chen. Non-autonomous stochastic evolution equations with nonlinear noise and nonlocal conditions governed by noncompact evolution families. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020383

[2]

Maoding Zhen, Binlin Zhang, Vicenţiu D. Rădulescu. Normalized solutions for nonlinear coupled fractional systems: Low and high perturbations in the attractive case. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020379

[3]

Min Chen, Olivier Goubet, Shenghao Li. Mathematical analysis of bump to bucket problem. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5567-5580. doi: 10.3934/cpaa.2020251

[4]

Bahaaeldin Abdalla, Thabet Abdeljawad. Oscillation criteria for kernel function dependent fractional dynamic equations. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020443

[5]

Vieri Benci, Sunra Mosconi, Marco Squassina. Preface: Applications of mathematical analysis to problems in theoretical physics. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020446

[6]

Ilyasse Lamrani, Imad El Harraki, Ali Boutoulout, Fatima-Zahrae El Alaoui. Feedback stabilization of bilinear coupled hyperbolic systems. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020434

[7]

Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056

[8]

Yining Cao, Chuck Jia, Roger Temam, Joseph Tribbia. Mathematical analysis of a cloud resolving model including the ice microphysics. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 131-167. doi: 10.3934/dcds.2020219

[9]

Yangrong Li, Shuang Yang, Qiangheng Zhang. Odd random attractors for stochastic non-autonomous Kuramoto-Sivashinsky equations without dissipation. Electronic Research Archive, 2020, 28 (4) : 1529-1544. doi: 10.3934/era.2020080

[10]

Lin Shi, Xuemin Wang, Dingshi Li. Limiting behavior of non-autonomous stochastic reaction-diffusion equations with colored noise on unbounded thin domains. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5367-5386. doi: 10.3934/cpaa.2020242

[11]

Yichen Zhang, Meiqiang Feng. A coupled $ p $-Laplacian elliptic system: Existence, uniqueness and asymptotic behavior. Electronic Research Archive, 2020, 28 (4) : 1419-1438. doi: 10.3934/era.2020075

[12]

Xavier Carvajal, Liliana Esquivel, Raphael Santos. On local well-posedness and ill-posedness results for a coupled system of mkdv type equations. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020382

[13]

Gunther Uhlmann, Jian Zhai. Inverse problems for nonlinear hyperbolic equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 455-469. doi: 10.3934/dcds.2020380

[14]

Predrag S. Stanimirović, Branislav Ivanov, Haifeng Ma, Dijana Mosić. A survey of gradient methods for solving nonlinear optimization. Electronic Research Archive, 2020, 28 (4) : 1573-1624. doi: 10.3934/era.2020115

[15]

Thomas Bartsch, Tian Xu. Strongly localized semiclassical states for nonlinear Dirac equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 29-60. doi: 10.3934/dcds.2020297

[16]

Hua Chen, Yawei Wei. Multiple solutions for nonlinear cone degenerate elliptic equations. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020272

[17]

Abdelghafour Atlas, Mostafa Bendahmane, Fahd Karami, Driss Meskine, Omar Oubbih. A nonlinear fractional reaction-diffusion system applied to image denoising and decomposition. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020321

[18]

Xuefei He, Kun Wang, Liwei Xu. Efficient finite difference methods for the nonlinear Helmholtz equation in Kerr medium. Electronic Research Archive, 2020, 28 (4) : 1503-1528. doi: 10.3934/era.2020079

[19]

Thierry Cazenave, Ivan Naumkin. Local smooth solutions of the nonlinear Klein-gordon equation. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020448

[20]

Zhiyan Ding, Qin Li, Jianfeng Lu. Ensemble Kalman Inversion for nonlinear problems: Weights, consistency, and variance bounds. Foundations of Data Science, 2020  doi: 10.3934/fods.2020018

2019 Impact Factor: 1.27

Metrics

  • PDF downloads (41)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]