What is the bacterial growth law during the division cycle?

For almost 100 years, since Ward (35) studied the growth of bacteria between divisions, there has been discussion, analysis, controversy, and confusion about the "growth law"-the way individual bacteria grow during the division cycle. How do bacteria grow between birth and division? This question is directed to the global aspects of the cell, and much effort has been aimed at understanding the rules governing the increase in mass, weight, length, or area of a growing cell as it proceeds from birth to division. The usual approach to understanding bacterial growth during the division cycle (i.e., the growth of the entire cell rather than of any one of its components) has been to find a simple mathematical formulation that best describes the observations of the growth pattern of the cells. One of the earliest modern studies was that of Bayne-Jones and Adolph (1, 2), who concluded, from the analysis of time lapse films, that Bacillus megatrium and Escherichia coli exhibited exponential growth rates when the length of the cells was used as the criterion of growth. Similarly, a steady, accelerating growth rate for length was observed by Knaysi (19) for Bacillus cereus. The introduction of the static analysis of cell growth by Collins and Richmond (4) marked a new approach to the study of bacterial growth. In concept, the Collins-Richmond mnethod is simple. If one can determine the size distribution of the existing population of bacteria, the size distribution of the cells at division, and the size distribution of the cells at birth, then one can calculate the rate of cell size increase during the division cycle. One may consider the logic of this method as follows. During steady-state growth, the number of cells in any particular size class increases exponentially. This exponential increase in cell number is the result of (i) cells leaving the size class by growth to a larger size class, (ii) cells entering the size class by growth from a smaller size class, (iii) cells leaving the size class by division (primarily from the larger size classes), and (iv) cells entering the size class by birth from the division of larger cells (primarily into the smaller size classes). If the distributions of the newborn and the dividing cells are relatively narrow, then these cells make a negligible contribution to the middle range of the total size distribution. In this case, the distribution of extant cells would accurately reflect the growth rate of cells in the middle of the division cycle. When Collins and Richmond (4) applied their method to B. cereus, they were able to determine that the growth rate was continuously increasing in the middle range of cell sizes. The growth rates at the start and finish of the division cycle, however, were so dependent upon assumptions about the birth and division distributions that no statement could be made about the growth rates at the ends of the size distribution. In contrast to this work, which indicates that there is a continuously increasing rate of synthesis during the division cycle, Kubitschek (22-25) has proposed that growth is linear between divisions. This idea was first suggested by the observation that the uptake of a number of different compounds was constant during the division cycle (22). Measurements of cell density during the division cycle (a constant density was found) and simultaneous measurements of cell size during the division cycle by using a Coulter Counter (a linear increase in size was found) indicated that the mass of the cells increased linearly (25). Kubitschek and Pai (26) have proposed that linear growth is due to variation in the metabolite pool. The pool size compensated precisely for the exponential increase in the macromolecular components of the cell. Therefore, the total mass of the cell-the macromolecular components and the pool-increases linearly. Recently, the problem of cell growth during the division cycle has been approached again by using the CollinsRichmond method. Kirkwood and Burdett (18) prepared electron microscope pictures of steady-state cells of Bacillus subtilis and were able to determine the size and morphological state (mononucleate, binucleate, or septate) of individual cells. They proposed that by applying the CollinsRichmond equation to cells partitioned according to these morphological states, one could obtain a more accurate picture of the growth rate, particularly if the global growth rate of the cell was influenced by the particular morphological changes observed. If at the time that cells changed from monoto binucleate, the growth rate changed, one would be able to derive the growth pattern more accurately. After classifying and measuring over 2,000 cells, Kirkwood and Burdett (18) proposed (i) that the growth rate of mononucleate cells was greater than the growth rate of binucleate cells of the same size, (ii) that the growth rate of binucleate cells was greater than the growth rate of septate cells of the same size, (iii) that there were major transitions in growth coincident with the major transitions in cell morphology (chromosome duplication and the initiation of cross-wall formation), and (iv) that within each class there was a steadily increasing rate of growth that could be termed a linear increase in the growth rate. Regarding the total population, Kirkwood and Burdett (18) concluded that growth corresponded to an exponential rate with a constant additive term. Koppes et al. (21) have applied the Collins-Richmond formula to study the growth rate of E. coli cells. They inverted the method and calculated the cell size distributions expected for various growth laws. Koppes et al. (21) hoped that statistical comparisons of the predicted and experimental data would allow them to choose among different models of cell growth. I believe that their observed distributions may be the best available. They were scrupulous in eliminating bias from the results. For example, they corrected for the probability that the larger cells would be more likely to touch an edge of the photograph and thus not be counted; uncorrected, this would have given an increased frequency of smaller cells.