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Modeling the Growth of Filamentous Fungi at the Particle Scale in Solid-State Fermentation Systems

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Filaments in Bioprocesses

Part of the book series: Advances in Biochemical Engineering/Biotechnology ((ABE,volume 149))

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Abbreviations

A :

Cross-sectional area of the hypha (µm2)

A L :

Area of contact of the plasma membrane with the extracellular medium (µm2)

c 1 :

Proportionality constant (L3 s−1 g-nutrient−1 g-biomass−1)

c 2 :

Proportionality constant (L g-transporter g-biomass−1)

c 3 :

Proportionality constant (g-nutrient g-transporter-substrate-complex−1 s−1)

\( \left. {C_{{^{{{\text{O}}_{2} }} }}^{{}} } \right|_{j} \) :

O2 concentration around tank j (g-O2 L−1)

\( C_{{^{{{\text{O}}_{2} }} }}^{f} \) :

O2 concentration in the biofilm (g-O2 L−1)

D E :

Effective diffusivity of the enzyme in the solid particle (µm2 s−1)

\( D_{{^{{{\text{O}}_{2} }} }}^{f} \) :

Effective diffusivity of O2 in the biofilm layer (µm2 s−1)

D S :

Diffusivity of maltose inside the hypha (µm2 s−1)

\( D_{S}^{e} \) :

Effective diffusivity of the soluble nutrient or hydrolysis product in the solid particle (µm2 s−1)

E :

Enzyme concentration (g-enzyme L−1)

H(x):

Heaviside function

j :

Number of the tank

\( \left. {J_{E} } \right|_{z = 0} \) :

Flux of enzyme across the surface of the particle (g-enzyme µm−2 s−1)

k c :

Maximum rate of vesicle consumption (g-vesicles s−1)

K C :

Saturation constant for vesicle consumption (g-vesicles L−1)

k cat :

Catalytic constant of the enzyme (g-polymeric-nutrient g-enzyme−1 s−1)

K m :

Saturation constant for the hydrolysis of the polymeric carbon and energy source (g-polymeric-nutrient L−1)

k max :

Maximum specific transport rate of soluble nutrient or hydrolysis product across the plasma membrane (g-nutrient g-transporter−1 s−1)

\( K_{{{\text{O}}_{ 2} }} \) :

Saturation constant for O2 (g-O2 L−1)

k p :

Maximum rate of vesicle production (g-vesicles L−1 s−1)

K P :

Saturation constant for vesicle production (g-nutrient L−1)

K s :

Saturation constant for glucose in growth rate expression (g-nutrient L−1)

K t :

Saturation constant for the absorption of soluble nutrient or hydrolysis product across the membrane (g-nutrient L−1)

L :

Length of the tip-tank (µm)

m :

Maintenance coefficient (g-nutrient g-biomass−1 s−1)

n :

Tank number of the tip-tank

r :

Radial position in the biofilm (µm)

r a :

Rate of absorption across the plasma membrane (g-nutrient s−1)

r E :

Rate of secretion of enzyme (g-enzyme µm−2 s−1)

r EP :

Rate of production of extracellular products (g-extracellular-products s−1)

r IP :

Rate of production of intracellular products (g-intracellular-products s−1)

r LI :

Rate of production of lipids (g-lipids s−1)

r N :

Rate of consumption of alanine (g-alanine s−1)

\( r_{{{\text{O}}_{ 2} }} \) :

Rate of consumption of O2 (g-O2 s−1)

r s :

Rate of consumption of glucose (g-glucose s−1)

r X :

Rate of biomass growth [g-biomass L−1 s−1 for Eq. (12); g-biomass s−1 for Eq. (15)]

S f :

Concentration of soluble nutrient or hydrolysis product in the biofilm (g L−1)

S e :

Concentration of extracellular soluble nutrient or hydrolysis product (g L−1)

S i :

Concentration of intracellular soluble nutrient or hydrolysis product (g L−1)

\( \left. {S_{i} } \right|_{j} \) :

Concentration of maltose in tank j (g-maltose L−1)

S p :

Concentration of polymeric nutrient (g-polymeric-nutrient L−1)

SSF:

Solid-state fermentation

t :

Cultivation time (s)

T :

Transporter concentration per area of the plasma membrane (g-transporter µm−2)

t E :

Time when the secretion of enzyme ceases (s)

v :

Velocity of cytoplasmic flow (µm s−1)

X :

Concentration of biomass (g-biomass L−1)

Y E :

Yield of glucose from starch (g-glucose g-polymeric-nutrient−1)

Y L :

Extension of hyphal length per mass of vesicle consumed (µm g-vesicle−1)

\( Y_{{X/{\text{O}}_{2} }} \) :

Yield of biomass O2 (g-biomass g-O −12 )

\( Y_{\phi } \) :

Yield coefficient for production of vesicles from maltose (g-vesicles g-nutrient−1)

z :

Depth within the solid particle (µm)

η :

Membrane coordinate (µm)

Δz :

Length of a “normal” tank (µm)

θ :

Concentration of the transporter–substrate complex (g-transporter-substrate-complex L−1)

µ max :

Maximum specific growth rate constant (s−1)

ρ X :

Biomass dry weight per volume (g-biomass L−1)

\( \left. \phi \right|_{j} \) :

Concentration of vesicles in tank j (g-vesicles L−1)

ψ :

Velocity of active transport of vesicles (µm s−1)

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Author notes

  1. Wellington Balmant

    Present address: Núcleo de Pesquisa e Desenvolvimento em Energia Autossustentável, Departamento de Engenharia Mecânica, Universidade Federal do Paraná, Centro Politécnico, Cx.P. 19011, Curitiba, 81531-980, Paraná, Brazil

Authors and Affiliations

  1. Departamento de Engenharia Química e Engenharia de Alimentos, Universidade Federal de Santa Catarina, Centro Tecnológico, Cx.P. 476, Florianópolis, 88040-900, Santa Catarina, Brazil

    Maura Harumi Sugai-Guérios & Agenor Furigo Jr

  2. Departamento de Bioquímica e Biologia Molecular, Universidade Federal do Paraná, Centro Politécnico Cx.P. 19046, Curitiba, 81531-980, Paraná, Brazil

    Wellington Balmant & David Alexander Mitchell

  3. Departamento de Química, Universidade Federal do Paraná, Centro Politécnico, Cx.P. 19081, Curitiba, 81531-980, Paraná, Brazil

    Nadia Krieger

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  1. Maura Harumi Sugai-Guérios
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  1. TU Braunschweig, Braunschweig, Germany

    Rainer Krull

  2. TU Dresden, Dresden, Germany

    Thomas Bley

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Sugai-Guérios, M.H., Balmant, W., Furigo, A., Krieger, N., Mitchell, D.A. (2015). Modeling the Growth of Filamentous Fungi at the Particle Scale in Solid-State Fermentation Systems. In: Krull, R., Bley, T. (eds) Filaments in Bioprocesses. Advances in Biochemical Engineering/Biotechnology, vol 149. Springer, Cham. https://doi.org/10.1007/10_2014_299

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