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Mathematical model for Trametes versicolor growth in submerged cultivation

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Trametes versicolor is a white-rot fungus known as a producer of extracellular enzymes such as laccase, manganese-peroxidase, and lignin-peroxidase. The production of these enzymes requires detailed knowledge of the growth characteristics and physiology of the fungus. Submerged cultivations of T. versicolor on glucose, fructose, and sucrose as sole carbon sources were performed in shake flasks. Sucrose hydrolysis catalyzed by the whole cells of T. versicolor was considered as one-step enzymatic reaction described with Michaelis–Menten kinetics. Kinetic parameters of invertase-catalyzed sucrose hydrolysis were estimated (Km = 7.99 g dm−3 and Vm = 0.304 h−1). Monod model was used for description of kinetics of T.versicolor growth on glucose and fructose as sole carbon sources. Growth associated model parameters were estimated from the experimental results obtained by independent experiments \( \left( {\mu_{\max }^{\text{G}} = 0. 1 4 {\text{ h}}^{ - 1} ,\;K_{\text{S}}^{\text{G}} = 8.0 6 {\text{ g dm}}^{ - 3} ,\;\mu_{\max }^{\text{F}} = 0. 3 7 {\text{ h}}^{ - 1} {\text{ and }}K_{\text{S}}^{\text{F}} = 5 4. 8 {\text{ g dm}}^{ - 3} } \right). \) Developed mathematical model is in good agreement with the experimental results.

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D s :

Diffusion coefficient (cm2 s−1)

K m :

Michaelis–Menten constant (g dm−3)

K S :

Monod constant (g dm−3)

r :

Radius (mm)

r :

Rate of enzymatic hydrolysis (g dm−3 h−1)

T :

Temperature (°C)

t :

Time (h)

V m :

Maximal reaction rate (h−1)

Y :

Yield coefficient biomass–substrate (g g−1)

γ :

Concentration (g dm−3)


Biomass growth rate (h−1)

μmax :

Maximal biomass growth rate (h−1)

Φ :

Thiele module (–)


Initial conditions










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This study was supported by the Croatian Ministry of Science, Education and Sports (Contract Grant Number 125-1252086-2793), and by The National Foundation for Science, Higher Education and Technological Development of the Republic of Croatia (Program NZZ Installation Grant).

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Correspondence to Bruno Zelić.

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Tišma, M., Sudar, M., Vasić-Rački, Đ. et al. Mathematical model for Trametes versicolor growth in submerged cultivation. Bioprocess Biosyst Eng 33, 749–758 (2010). https://doi.org/10.1007/s00449-009-0398-6

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  • Trametes versicolor
  • Invertase kinetics
  • Biomass growth
  • Mathematical model