A mathematical model for the growth of mycelial pellet populations

In liquid culture, filamentous organisms often grow in the form of pellets. Growth result in an increase in radius, whereas shear forces result in release of hyphal fragments which act as centers for further pellet growth and development. A previously published model for pellet growth of filamentous microorganisms has been examined and is found to be unstable for certain parameter values. This instability has been identified as being due to inaccuracies in estimating the numbers of fragments which seed the pellet population. A revised model has been formulated, based on similar premises, but adopting a finite element approach. This considers the population of pellets to be distributed in a range of size classes. Growth results in movement to classes of increasing pellet size, while fragments enter the smallest size class, from which they grow to form further pellets. The revised model is stable and predicts changes in the distribution of pellet sizes within a population growing in liquid batch culture. It considers pellet growth and death, with fragmentation providing new centers of growth within the pellet population, and predicts the effects of shear forces on pellet growth and size distribution. Predictions of pellet size distributions are tested using previously published data on the growth of fungal pellets and further predictions are generated which are suitable for experimental testing using cultures of filamentous fungi or actinomycetes.