A new framework is developed by extending the existing population balance framework for modeling the growth of microbial populations. The new class of multistaged corpuscular models allows further structuring of the microbial life cycle into separate phases or stages and thus facilitates the incorporation of cell cycle phenomena to population models. These multistaged models consist of systems of population balance equations coupled by appropriate boundary conditions. The specific form of the equations depend on the assumed forms for the transition rate functions, the growth rate functions, and the partitioning function, which determines how the biological material is distributed at division. A growth model for ciliated protozoa is formulated to demonstrate the proposed framework. To obtain a solution to the system of the partial integro differential equations that results from such formulation, we adopted a Monte Carlo simulation technique which is very stable, versatile, and insensitive to the complexity of the model. The theory and implementation of the Monte Carlo simulation algorithm is analyzed and results from the simulation of the ciliate growth model are presented. The proposed approach seems to be promising for integrating single-cell mechanisms into population models.
Bibliographical noteFunding Information:
This research was supported by the National Science Foundation, Grant No. NSF/BCS-9001095 and by a grant from the University of Minnesota Supercomputer Institute providing computer time on the CRAY X-MP EAl464 at the Minnesota Supercomputer Center.
- Cell cycle
- Ciliate growth
- Population balance
- Segregated model