La crescita batterica. I: La legge di crescita della numerosità batterica

Ageno, Mario

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 82 (1988) no. 2, pp. 371-376

Résumé

When a bacterial culture in liquid medium is kept rigorously homogeneous in well defined and constant growth conditions, the growth rate of the optical density and that of the colony number on agar plates are usually different, because the mean bacterial mass is slowly varying. As a consequence, one must take into consideration three different laws of growth: 1) that of the number of cells (colonies on agar plates); 2) that of the biological mass (optical density); and 3) that of the single bacterial cell. In the present paper, the first law of growth is examined. The semilogarithmic plot of the growth curve initially feels the effects of the distribution of the bacterial ages in the inoculum. However, it eventually forgets the initial conditions and takes the wellknown linear trend with constant growth rate. All that demonstrates: 1) That this law of growth and that of the single bacterial cell are independent; and 2) that the doubling time undergoes fluctuations from cell to cell. When the growth rate is independent from the initial conditions, the distribution law of the cell ages must be stationary. Therefore, the question arises as to what kinds of growth curve and cell ages distribution law are compatible with the stationarity of the last. A very simple functional equation gives the answer: the usual exponential growth curve only, and the corresponding stationary distribution law of the cell ages. We surmise that a similar stationarity principle may be valuable also for a large category of other systems.