A MATHEMATICAL MODEL FOR THE GROWTH OF A SINGLE BACTERIAL CELL *

Changes in bacterial cell size and shape due to changes in the abiotic environment have been observed for decades.’ The changing surface-to-volume ratio has the potential of profoundly affecting cell Yet very few of the multitude of mathematical models suggested for the description of bacterial growth6’ allow for the possible inclusion of the effects of changes in cell geometry; most are models of how a whole culture will grow. The purpose of this paper is to describe a mathematical model for the growth of an individual cell. Other advantages of an individual cell model are the ease with which temporal and spatial events in the cell division cycle can be included. It is impossible to include such information in nonsegregated mathematical models and often computationally difficult to include such events in segregated models. Cell structure and the interactions of major metabolic pathways can readily and accurately be included in a single-cell model. Although similar information can be incorporated in whole culture models, such efforts have often been marred by subtle errors in model formulation’ which would have been readily avoided in formulating an individual cell model. Single-cell models do have limitations. They are accurate representations of the growth of a bacterial culture only if the moments of distribution of cellular properties higher than the first-order are not important. The single-cell model should accurately represent the growth of a synchronous culture and perhaps growth in a steady-state continuous culture. However, such an assumption would obviously fail in a culture where only 50% of the cells were viable. Such a limitation could conceivably be removed by dividing the culture into different subpopulations based on, for example, cell size and composition, and assigning one or more individual cells to that fraction. Several models for the growth of an individual cell have been po~tulated.~*~-” These models all contain one or more arbitrary constraints on the computer “growth” of the cell. Examples of such constraints are mode of growth (exponential), timing of cell division, culture conditions (balanced growth only), no explicit accounting of the abiotic environment (e.g. nutrient uptake), and cell shape. In this paper we present for the first time a single-cell model unconstrained in any way by the investigator. All that needs to be specified is the initial nutrient composition in the medium and temperature and pH. Cell growth, DNA initiation, crosswall formation, changes in cell size and