The Structure of Populations of Budding Yeast in Response to Feedback

Erik Miklos Boczko, Chris C Stowers, Todd R Young


We describe how the hypothesis of communication, consistent with known yeast physiological mechanisms, couples growth and division to produce non-stationary, multimodal population densities, that are collected into an integer number of clusters arrayed along the cell cycle. Theoretical analysis and numerical simulations demonstrate that the cell cycle progression of these clusters produces observable oscillation in environmental variables such as dissolved oxygen. We present experimental data and theoretical simulations that support our model of the periodic population structure that develops during autonomous oscillations.


Autonomous Oscillation, Cell Cycle, Quorum Sensing


.Antoneli F, Dias AP, Golubitsky M, Wang Y, (2005) Patterns of synchrony in lattice dynamical systems. Nonlinearity 18:2193–2209.

.Aston PJ, Bird CM,(1998) Synchronization of coupled systems via parameter perturbations. Phys. Rev. E 57:2787-2794.

.Balmforth, NJ, Sassi R, (2000) A shocking display of synchrony. Bifurcations, patterns and symmetry. Phys. D 143:21-55.

.Ban H, Boczko EM (2008) Age distribution formulas for budding yeast. Vanderbilt University e-archive Technical Report available at

.E.M. Boczko, C. Stowers, T. Gedeon and T.Young (2009) ODE, RDE and SDE models of cell cycle dynamics and clustering in yeast. J. Biological Dynamics 4:328-345. (NIHMS147352)

.T.R. Young, B. Fernandez, R. Buckalew, G. Moses, E.M. Boczko (2012)Clustering in cell cycle dynamics with general response/signaling feedback. J. Theor. Biol. 292:103-115.

.Bose JL, Kim U, Bartowski W, Gunsalus GP, Overlay AM, et al.(2007) Bioluminescence in Vibrio fisheri is controlled by the redox-responsive regulator ArcA. Mol. Microbiol. 65:538-553.

.Boye E, Stokke T, Kleckner N, Skarstad K (1996) Coordinating DNA replication initiation with cell growth: Differential roles for Dna A and Seq A proteins. Proc. Natl. Acad. Sci. 93:12206-12211.

.Buese M, Kopmann A, Diekmann H, Thoma M(1998) Oxygen, pH value, and carbon source induced changes of the mode of oscillation in synchronous continuous culture of Saccharomyces cervisiae. Biotechno. Bioeng. 63:410-417.

.Breeden LL (1997) α-Factor synchronization of budding yeast. Methods in Enzymology 283:332-342.

.Chen H, Fujita M, Feng Q, Clardy J, Fink GR (2004) Tyrosol is a quorum sensing molecule in Candida albicans. Proc. Natl. Acad. Sci. 101:5048-5052.

.Chen Z, Odstrcil EA, Tu BP, McKnight SL(2007) Restriction of DNA replication to the reductive phase of the metabolic cycle protects genome integrity. Science 316:1916-1919.

.Collier J, McAdams HH, Shapiro L (2007) ADNA methylation ratchet governs cell cycle progression through a bacterial cell cycle. Proc. Natl. Acad. Sci. 104:17111-17116.

.Dano S, Sorensen PG, Hynne F (1999) Sustained oscillations in living cells. Nature 402:320-322.

.Dunny GM, Leonard BAB (1997) Cell cell communication in Gram Positive bacteria. Annu. Rev. Microbiol. 51:527-564.

.Edwards JC, Johnson MS, Taylor BL (2006) Differentiation between electron transport and sensing and proton motive force sensing by the Aer and Tsr receptors for aerotaxis. Mol. Microbiol. 62:823-837.

.Ermentrout B, (1991) An adaptive model for synchrony in the firefly Pteroptyxmalaccae. J. Math. Biol. 29: 571-585.

.Finn RK, Wilson RE (1954) Population dynamic behavior of the Chemostat system. Agric. Food Chem. 2:66-69.

.Futcher B (2006) Metabolic cycle, cell cycle and the finishing kick to start. Genome Biology 7:107-111.

.Gage TB, Williams FM, Horton JB, (1984) Division synchrony and the dynamics of microbial populations: a size-specific model. Theoret. Population Biol. 26:296–314.

.Hale JK, (1998)Synchronization by diffusive coupling. Proceedings of Topological Methods in Differential Equations and Dynamical Systems (Krakw-Przegorzay,1996).Univ.Iagel. Acta Math. 36:17-31.

.Heinzle E, Dunn IJ, Furakawa K, Tanner RD(1982) Modeling of sustained oscillations observed in continuous culture of Saccharomyces Cerevisiae. in Modeling and control of biotechnical processes 1st IFAC Workshop:57-65.

.Hense BA, Kuttler C, Muller J, Rothballer M, Hartmann A, Kreft J(2007) Does efficiency sensing unify diffusion and quorum sensing? Nat. Rev. Microbiol. 5:230-239.

.Henson MA (2005) Cell ensemble modeling of metabolic oscillations in continuous yeast cultures. Comput. Chem. Enginer. 29:645-661.

.Hjortsø MA, Nielsen J (1994)A conceptual model of autonomous oscillations in microbial cultures. Chemical Engineering Science, 49:1083-1095.

.Hjortsø MA (1996) Population balance models of autonomous periodic dynamicsin microbial cultures. Their use in process optimization. Can. J. Chem. Engin., 74:612-620.

.Hornby JM, Jensen EC, Lisec AC, Tasto JJ, Jahnke B, et al. (2001)Quorum sensing in the dimorphic fungus Candida albacans is mediated by farnesol. Appl. Environ. Microbiol. 67:2982-2992.

.Jones KD, Kompala DS (1999) Cybernetic model of the growth dynamics of Saccharomyces cervisiae in batch and continuous culture. J. Biotechnol. 71:105-131.

.Jones RP (1989) Biological principles for the effects of ethanol. Enzyme Microb. Technol. 11:130-153.

.[30] Karbowski J, Ermentrout GB, (2002) Synchrony arising from a balanced synapticplasticity in a network of heterogeneous neural oscillators. Phys. Rev. E 65:031902

.Keulers M, Satroutdinov AD, Sazuki T, Kuriyama H (1996) Synchronization affector of autonomous short period sustained oscillation of Saccharomyces cerevisiae. Yeast 12:673 682.

.Klevecz RR (1976) Quantized generation time in mammalian cells as an expression of the cellular clock. Proc. Natl. Acad. Sci. 73:4012-4016.

.Klevecz RR, Kaufman SA, and Shymko RM (1984) Cellular clocks and oscillators. Inter. Rev. Cytol. 86:97-128.

.Klevecz RR, Murray D (2001) Genome wide oscillations in expression. Molecular Biology Reports 28:73-82.

.Koshwanez, J., Holl, M., Marquardt, B., Dragavon, J., Burgess, L., and Meldrum, D. 2004. Identification of budding yeast using a fiber-optic imaging bundle. Rev. Sci. Instr. 75:1363-1365.

.Kuznetsov A, Krn M, Kopell N,(2004/05) Synchrony in a population of hysteresis-based genetic oscillators. SIAM J. Appl. Math. 65:392-425

.Lord PG, Wheals AE (1980) Asymmetricaldivision of Saccharomyces cerevisiae. J. Bacter. 142:808-818.

.Lyon GJ, Novick RP (2004) Peptide signaling in Staphylococcus aureus and other Gram positive bacteria. Peptides 25:1389-1403.

.Lloyd AL, JVAA, (2004) Spatiotemporal dynamics of epidemics: synchrony in meta population models. Topics in biomathematics and related computational problems. Math. Biosci. 188:1-16.

.Mirollo RE, Strogatz SH, (1990) Synchronization of pulse-coupled biological oscillators. SIAM J. Appl. Math. 50:1645-1662.

.Muller D, Exler S, Aguilera-Vazquez L,Guerrero-Martin E, Reuss M (2003) Cyclic AMP mediates the cell cycle dynamics of energy metabolism in Saccharomyces cervisiae. Yeast 20:351-367.

.Munch T, Sonnleitner B, Fiechter A (1992) The decisive role of the Saccharomyces cervisiae cell cycle behavior for dynamic growth characterization. J. Biotechnol. 22:329 352.

.Murray D, Klevecz RR, Lloyd D (2003) Generation and maintenance of synchrony in Saccharomyces cerevisiae continuous culture. Experimental Cell Research 287:10-15.

.Palkova Z, Forstova J (2000) Yeast colonies synchronize their growth and development. J. Cell Science 113:1923-1928.

.Palkova Z, Vachova L (2006) Life within a community: benefits to yeast long term survival. FEMS. Microbiol. Rev. 30:806-824.

.Patnaik PR (2003) Oscillatory metabolism of Saccharomyces cerevisiae: An overview of mechanisms and models. Biotechnology Advances 21:183-192.

.Pikovsky A, Zaks M, Rosenblum M, Osipov G, Kurths J, (1997) Phase synchronization of chaotic oscillations in terms of periodic orbits. Chaos 7:680-687.

.Pringle JR, (1991)Staining of bud scars and other cell wall chitin with calcoflour. Methods In Enzymology 194:732-735.

.Richard P, (2003) The rythm of yeast. FEMS Microbiol. Rev. 27:547-557.

.Rotenberg M, (1977) Selective synchrony of cells ofdifferent cycletimes. J. Theor. Biol. 66:389-398.

.Rulkov NF, Afraimovich VS, (2003) Detectability of nondifferentiable generalized synchrony. Phys. Rev. E 67:066218

.Satroutdinov AD, Kuriyama H, Kobayashi H, (1992) Oscillatory metabolism of Saccharomyces cerevisiae in continuous culture. FEMS Microbiology Lett. 98:261-268.

.Singer RA, Johnston GC (1981) Nature of the G1 phase of the yeast Saccharomyces cerevisiae. Proc. Natl. Acad. Sci 78:3030-3033.

.Stowers C, Boczko EM (2010) Extending cell cycle synchrony and deconvolving population effects in budding yeast through an analysis of volume growth with a structured Leslie model. JBiSE 3:987-1001.

.Stowers C, Robertson JB, Ban H, Tanner RD, Boczko EM (2009) Periodic Fermentor Yield and Enhanced Product Enrichment from Autonomous Oscillations. Applied Biochemistry and Biotechnology 156:59.

.Strogatz SH, Mirollo RE, Matthews PC, (1992) Coupled nonlinear oscillators below the synchronization threshold: relaxation by generalized Landau damping. Phys. Rev. Lett. 68:2730-2733.

.J. Sun, C. Stowers, E.M. Boczko, and D. Li,(2010) Measurement of the Growth Rate of Individual Budding Yeast with Novel MOSFET-Based Microfluidic Coulter Counters. Lab-on-a-chip DOI:10.1039/C005029F.

.Terman D,(2001) Synchrony in networks of neuronal oscillators. Multiple-time-scale dynamical systems (Minneapolis, MN,1997), IMA Vol. Math. Appl. 122:215–232, Springer, New York, 2001.

.Tu BP, Kudlicki A, Rowicka M, McKnight SL (2005) Logic of the yeast metabolic cycle: temporal compartmentation of cellular processes. Science 310:1152-1158.

.Tvegard T, Soltani H, Skjolberg HC, Krohn M, Nilssen EA, et al.(2007) A novel checkpoint mechanism regulating the G1/S transition. Genes and Development 21:649-654.

.Von Meyenburg K (1973) Stable synchronous oscillations in continuous cultures of S. cerevisiae under glucose limitation. In B. Chance (Ed) Biological Biochemical Oscillators Academic Press, NY. 411.

.Walker G (1999) Synchronization of yeast cell populations. Methods in Cell Science 21:87 93.

.Wang J, Liu W, Uno T, Tonozuka H, Mitsui K, Tsurugi K (2000) Cellular stress response oscillate in synchronization with the ultridian oscillation of energy metabolism in the yeast Saccharomyces cervisiae. FEMS Microbiol. Lett. 189:9-13.

.Wolf J, Sohn H-Y, Heinrich R, Kuriyama H (2001) Mathematical analysis of a mechanism for autonomous oscillations in a continuous culture of Saccharomyces cerevisiae. FEBS Lett. 499:230-234.

.Woldringh CL, Huls PG, Vischer NOE (2003) Volume growth of daughter and parent cells during the cell cycle of Saccharomyces cerevisiae a/α as determined by image cytometry. J. Bacteriology 175:3174-3181.

.Xu Z, Tsurugi K (2006) A potential mechanism of energy metabolism oscillation in an aerobic chemostat culture of the yeast Saccharomyces cervisiae. FEBS Journal 273:16961709.

.Zhu G, Zamamiri A, Henson MA, Hjortsø MA (2000) Model predictive control of continuous yeast bioreactors using cell population balance models. Chemical Engineering Science 55:6155-6167.


  • There are currently no refbacks.