Abstract
Modeling the mycelium morphology of filamentous fungi is valuable in connection with studies of their growth mechanisms, i.e. tip extension and branching, and in this work a general frame for morphological models is presented. The general frame consist of a population balance equation (PBE) for a two-dimensional density function, which describes the properties, i.e. the number of tips and the total hyphal length, of a population of hyphal elements. From the general PBE, balances for the average properties of the population can be derived. After presentation of the general model frame the kinetics for the different processes influencing the mycelium morphology, i.e. spore germination, growth, and hyphal fragmentation, are reviewed. Thereafter follows an overview of different kinetic models presented in the literature. The models are divided into four groups: single hyphal element/branch models; average property models; population models; and morphological structured models. Models within the first three groups are discussed and presented within the general frame. Finally some solutions to the general PBE are presented and aspects on model verification based on experimental data are discussed.
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Abbreviations
- B(α, β):
-
the beta function
- c:
-
steepness/skewness parameter in Eq. (14)
- cv :
-
concentration of vesicles at the hyphal tip
- d:
-
diameter of the hyphae
- ds :
-
diameter of the stirrer
- D:
-
dilution rate
- e:
-
the concentration of hyphal elements
- espore :
-
the inoculum concentrations of spores
- f(lt,n,t):
-
number density function
- f0(lt,n):
-
initial number density function
- f(r):
-
absorption rate of vesicles at the hyphal tip at a radius r from the center axis
- g(z,t):
-
germination frequency
- h(lt,n,z,t):
-
net rate of formation of hyphal elements with the properties (lt,n)
- hf(lt,n,z,t):
-
net rate of formation of hyphal elements with the properties (lt,n) by fragmentation
- hg(lt,n,z,t):
-
net rate of formation of hyphal elements with the properties (lt,n) by germination
- kbran :
-
branching parameter
- ktensile :
-
tensile strength of the hyphal wall
- K:
-
allometric coefficient
- Kbr :
-
saturation parameter
- Kt :
-
saturation parameter
- Kv :
-
saturation parameter in Eq. (25)
- ktip :
-
maximum tip extension rate
- lbranch :
-
the length at which branching starts
- le,av :
-
average effective length
- le,max :
-
maximum effective length at which fragmentation does not occur
- lt :
-
total length of a hyphal element
- lt,av :
-
average total length per hyphal element
- lt,g :
-
length of a newly germinated spore
- ltip :
-
constant in Eq. (19)
- n:
-
number of active growing tips in a hyphal element
- nav :
-
average number of tips per hyphal element
- N:
-
stirrer speed
- p((lt′,n′),(lt,n)):
-
partitioning function
- pl(lt,z,t):
-
probability that a newly germinated spore will have the hyphal length lt
- pn(n,z,t):
-
probability that a newly germinated spore will have n number of tips
- Pg :
-
power input at gassed conditions
- qbran(lt,n,z):
-
branching frequency
- qfrag(lt,n,z):
-
rate of fragmentation
- qtip(lt,n,z):
-
tip extension rate
- r:
-
the radius of the hyphae
- rabs :
-
absorption rate of vesicles at the hyphal tip
- rabs,max :
-
maximum absorption rate of vesicles at the hyphal tip
- F :
-
the normalized germination time
- tc :
-
the circulation time
- tf :
-
the time at which germination stops
- ts :
-
the time at which germination starts
- V:
-
the volume of the culture
- ym :
-
state-vector of the hyphal element
- yviab :
-
the viability of spores
- z:
-
vector of environmental conditions
- α:
-
steepness/skewness parameter in Eq. (13)
- β:
-
steepness/skewness parameter in Eq. (13)
- λ:
-
the time at which half of the viable spores have germinated
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Krabben, P., Nielsen, J. (1998). Modeling the mycelium morphology of Penicillium species in submerged cultures. In: Schügerl, K. (eds) Relation Between Morphology and Process Performances. Advances in Biochemical Engineering/Biotechnology, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0102281
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