Nonlinear Dynamics of Brewing Yeast Cell Growth in Alginate Micro-Beads


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The nonlinear dynamics of brewing yeast cell growth in porous Ca-alginate matrices is considered experimentally and theoretically. The applications of alginate matrices include the reduction of internal mass transfer resistance, minimized cell leakage and growth restriction due to interactions between matrices and cell membranes comparatively to free cell culture conditions. The effects of micro-bead diameters in the range 0.3-2.0 mm on yeast cell growth were investigated. The stochastic mathematical model from the Langevin class is proposed for the interpretation of cell growth, affected by four micro-processes: micro-environmental quality changes due to nutrient diffusion into the micro-beads, cell leakage, repulsive interactions between boundary layers around the cells themselves, which contribute to the dynamics of cell growth as a negative, nonlinear feedback restriction and random kinetics effects. Such a model is used for the prediction of the optimal diameter of micro-beads, which ensures maximal final cell concentration. The results of cell growth in alginate matrices study have indicated an optimal diameter of 0.5-0.6 mm for micro-beads. Immobilized cells in these beads were not restricted significantly by mass transfer of nutrients and by cell leakage. The highest final cell concentration value indicated the largest feed-back restriction quantified by the constitutive parameter b.



Edited by:

Dragan P. Uskokovic, Slobodan K. Milonjic and Dejan I. Rakovic




I. Pajić-Lijaković et al., "Nonlinear Dynamics of Brewing Yeast Cell Growth in Alginate Micro-Beads ", Materials Science Forum, Vol. 518, pp. 519-524, 2006

Online since:

July 2006




[1] V.A. Nedović, B. Obradović, I. Leskošek-Čukalović, O. Trifunović, R. Pešić and B. Bugarski, Process Biochem. Vol. 37 (2001), p.17.


[2] B. Bugarski, N. Vunjak, G. Jovanović, K. Čuperlović and G. Vunjak-Novaković: J. Serb. Chem. Soc. Vol. 57 [5-6] (1992), p.345.

[3] V.A. Nedović, B. Obradović, I. Leskošek-Čukalović and G. Vunjak-Novaković: Immobilized yeast bioreactor systems for brewing - recent achivements. In: Ph. Thonart, M. Hofman, editors. Focus on Bitechnology Series, Vol. IV: Engineering and Manufacturing for Biotechnology (Dordrecht: Kluwer Academic Publishers 2001).


[4] M.F.A. Goosen: Microencapsulation of Living Cells. In: R.G. Willaert, G.V. Baron and L. Backer, Eds. Immobilized Cell Systems: Modeling and Experimental Methods (Chichester: Willey 1996), 295.

[5] I. Pajić, J. Jelenković-Bulović, M. Mišić-Vuković, D.V. Vuković, G. Jovanović and G. Vunjak-Novaković: J. Serb. Shem. Soc. Vol. 57 [5-6] (1992), p.365.

[6] J.E. Melvik and M. Dornish: Alginate as a carrier for cell immobilisation. In: V. Nedovic and R. Willaert Eds. Fundamentals of cell immobilisation biotechnology (Kluwer Academic Publishers 2004), p.33.


[7] I. Pajić-Lijaković, B. Bugarski and M. Plavšić: Hem. Ind. Vol. 58 [6a] (2004), p.44.

[8] E. Loscar and E.V. Albano: Rep. Prog. Phys. Vol. 66 (2003), p.1343.

[9] M.A. Munoz and T. Hwa: Europhysics Letters Vol. 41.

[2] (1998), p.147.

[10] M.A. Munoz and R. Pastor-Satorras: Phys. Rev. Let. Vol. 90.

[20] (2003), pp.204101-1.

[11] A.B. Cambel: Applied Chaos Theory, A paradigm for complexity (Academic Press, INC., Boston, San Diego, New York 1993), p.91.