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Bioprocess and Biosystems Engineering

, Volume 34, Issue 1, pp 21–31 | Cite as

Applying dimorphic yeasts as model organisms to study mycelial growth: part 2. Use of mathematical simulations to identify different construction principles in yeast colonies

  • Thomas Walther
  • Holger Reinsch
  • Kai Ostermann
  • Andreas Deutsch
  • Thomas Bley
Original Paper

Abstract

The dimorphic yeasts Candida boidinii and Yarrowia lipolytica were applied as model organisms to study mycelial growth. A mathematical model of hybrid cellular automaton type was developed to analyze the impact of different biological assumptions on the predicted development of filamentous yeast colonies. The one-dimensional model described discrete cells and continuous distribution of nutrients. The simulation algorithm accounted for proliferation of cells, diffusion of nutrient, as well as biomass decay and recycling inside the mycelium. Simulations reproduced the spatio-temporal development of C. boidinii colonies when a diffusion-limited growth algorithm based on the growth of pseudohyphal cells was applied. Development of Y. lipolytica colonies could only be reproduced when proliferation was restricted to the colony boundary, and cell decay and biomass recycling were incorporated into the model. The results suggested that cytoplasm, which served as the secondary nutrient resource, had to be translocated inside the hyphal network.

Keywords

Cellular automaton model Yeast mycelia Nutrient translocation Biomass decay 

List of symbols

A

Growth field area (cm2)

cN

Nutrient concentration (mg mL−1)

D

Diffusion constant (cm2 s−1)

DW

Dry weight fraction of wet biomass

dC

Cell diameter (cm)

h

Height of the growth field (cm)

i

Index of a lattice node

K

Calibration factor for cell density from OD (cm−2)

l

Length of the growth field (cm)

lC

Length of a cell (cm)

mC

Mass of a unit cell (mg)

n

Number of lattice nodes

nC,p

Number of proliferating unit cells

nC,p*

Number of proliferating unit cells placed to lattice node (i + 1)

nC,s

Number of stationary unit cells

OD

Optical density

rN,con

Total nutrient consumption rate (mg mL−1 h−1)

rN,main

Nutrient uptake rate per cell due to maintenance (mg h−1)

rN,prol

Nutrient uptake rate per cell due to proliferation (mg h−1)

rN,rep

Nutrient replenishment rate (mg mL−1 h−1)

R

Specific nutrient uptake rate due to maintenance (mg mg−1 h−1)

s

State of a lattice node

sC

State of a cell

TC

Time constant for cell decay (h)

Δt

Time step for the continuous time scale (h)

Δtp

Replication interval (generation time) (h)

VC

Volume of a cell (mL)

Vi

Volume assigned to one lattice node (mL)

w

Width of the growth field (cm)

Y

Biomass yield on nutrient (mg mg−1)

ρC

Density of wet biomass (mg mL−1)

σ

Fraction of cells

Notes

Acknowledgments

This work was supported by DFG grant 218147.

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Thomas Walther
    • 1
    • 4
  • Holger Reinsch
    • 1
  • Kai Ostermann
    • 2
  • Andreas Deutsch
    • 3
  • Thomas Bley
    • 1
  1. 1.Institute of Food Technology and Bioprocess EngineeringTechnical University DresdenDresdenGermany
  2. 2.Institute of GeneticsTechnical University DresdenDresdenGermany
  3. 3.Center for Information Services and High Performance ComputingTechnical University DresdenDresdenGermany
  4. 4.Laboratoire d’Ingénierie des Systèmes Biologiques et des Procédés, UMR INSA/CNRS 5504, UMR INSA/INRA 792Institut National des Sciences Appliquées (INSA)Toulouse Cedex 04France

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