Toward a self-similar theory of microbial populations

A fresh quest is made of segregated cell models of microbial populations with a view to determine whether the multivarite distribution of physiological states, during transient growth, can attain self-similar forms (i.e., become time invariant) when each physiological state variable is scaled with respect to its population average. Such self-similar growth situations are believed to be more general than those of balanced growth. The conditions under which self-similarity is possible are investigated. Thus conditions are stipulated on the synthesis rates of different physiological entities, cell division rate, and the partitioning of the parent cell's components among the daughter cells (assuming binary division) in order for self-similar growth to be attained. Subject to the attainment of self-similar growth, it is shown that cytometric data can be analyzed systematically to determine how the rates of syntheses of various biochemical entities and cell division rates vary with the physiological entities that are measured. Inverse problems, represented by algebraic systems, are identified which will potentially allow flow cytometric data to be inverted to yield quantitative information on the absolute rates of cellular growth and reproductory processes as a function of the cell states chosen for measurement. It is suggested that the methods become more effective when cytometry can be used to make direct observations on dividing cells so that the number of unknowns in the inverse problem can be reduced, thus facilitating its more complete solution. Preliminary analysis of cytometric data obtained in the literature show promise of self-similarity and thus the possibility of application of the methods discussed here.