I am interested in constructing mathematical models of the kinetics and dynamics of microbial and cellular growth processes. Such models find practical applications in biotechnology and in control and clean-up of environmental pollution. They also contribute to an understanding of biological processes occurring in lakes, rivers, the oceans, and soil.
The processes of interest to my research are carried out by and in populations of microbes or cells. The models recognize that the individual organisms in such a population are not all the same, and that distributions of properties such as cell size, protein content, etc., exist in it. Many years ago my colleagues and I showed that, in general, the dynamics of a microbial or cell population will be described by a so-called population balance equation, or by sets of such equations; a population balance equation is a partial differential-integral equation. After the initial formulation (in 1967) very little progress was made on population balance equation for growth processes because the equations proved to be very difficult to solve even numerically, and because good experimental techniques for gathering data to test such models were not available. Both of these circumstances have now changed. Various techniques, such as flow cytometry, are now available for rapid determination of distributions of properties in populations. And very recently new numerical methods for solving the equations have been developed. It therefore seems time to reexamine population balance equations and their use in modeling microbial and cellular growth processes, and that is what I plan to do in the final phases of my research career.
- Growth Processes in a Cascade of Bioreactors: Mathematical Models (with N.V. Mantzaris, P. Daoutidis, and F. Srienc), AIChE J. 45, 164 (1999).
- Growth Processes in a Cascade of Bioreactors: Comparison of Modeling Approaches (with N.V. Mantzaris, P. Daoutidis, and F. Srienc), AIChE J. 45, 177 (1999).
- Solutions of Population Balance Models Based on a Successive Generations Approach (with j-J. Liou and F. Srienc), Chem. Eng. Sci. 52, 1529 (1997).
- Measurement of Unequal DNA Partitioning in Tetrahymena Pyriformis using Slit-Scanning Flow Cytometry (with P.J. Sweeney and F. Srienc), Biotech. Prog. 10, 19 (1994).
- Determination of Cellular Rate Distributions in Microbial Cell Populations: Feeding Rates in Ciliated Protozoa (with C. Hatzis, P.J. Sweeney, and F. Srienc), Biotech. And Bioeng. 42, 284 (1993).
- Growth Processes in Bioreactors with External Sources of Biomass, AIChE J. 8, 835 (1992).
- Statistics of Particle Uptake by a Population of Filter-Feeding Microorganisms (with F. Srienc, C. Hatzis, and P.J. Sweeney) Cytometry 13, 423 (1992).
- Segregated, Structured, Distributed Models and their Role in Microbial Ecology: A Case Study Based on Work Done on the Filter-Feeding Ciliate Tetrahymena Pyriformis, Microb. Ecol. 22, 139 1991).
- A Discrete Stochastic Model for Microbial Filter Feeding (with C. Hatzis, P. J. Sweeney, and F. Srienc), Mathematical Biosciences 101, 127 (1990).
- Flow Cytometric Measurement of Rates of Particle Uptake from Dilute Suspensions by a Ciliated Protozoan (with D. P. Lavin and F. Srienc), Cytometry 11 , 875 (1990).
- Size Effects on the Uptake of Particles by Populations of Tetrahymena Pyriformis Cells (with D.P. Lavin, C. Hatzis, and F. Srienc), J. of Protozoology 37, 157 (1990).
- Growth of Microbial Populations in Non-Minimal Media: Some Considerations for Modeling (with S. Pavlou), Biotech. And Bioengineering 34, 971 (1989).